Ellen Kuhl

All Publications

• On automated model discovery and a universal material subroutine for hyperelastic materials COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Peirlinck, M., Linka, K., Hurtado, J. A., Kuhl, E. 2024; 418

  View details for DOI 10.1016/j.cma.2023.116534

  View details for Web of Science ID 001096624500001

• Discovering the mechanics of artificial and real meat COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING St Pierre, S. R., Rajasekharan, D., Darwin, E. C., Linka, K., Levenston, M. E., Kuhl, E. 2023; 415

  View details for DOI 10.1016/j.cma.2023.116236

  View details for Web of Science ID 001047757200001

• Automated model discovery for skin: Discovering the best model, data, and experiment COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Linka, K., Tepole, A., Holzapfel, G. A., Kuhl, E. 2023; 410

  View details for DOI 10.1016/j.cma.2023.116007

  View details for Web of Science ID 000970580000001

• Automated model discovery for human brain using Constitutive Artificial Neural Networks. Acta biomaterialia Linka, K., Pierre, S. R., Kuhl, E. 2023

  Abstract

  The brain is our softest and most vulnerable organ, and understanding its physics is a challenging but significant task. Throughout the past decade, numerous competing models have emerged to characterize its response to mechanical loading. However, selecting the best constitutive model remains a heuristic process that strongly depends on user experience and personal preference. Here we challenge the conventional wisdom to first select a constitutive model and then fit its parameters to data. Instead, we propose a new strategy that simultaneously discovers both model and parameters. We integrate more than a century of knowledge in thermodynamics and state-of-the-art machine learning to build a Constitutive Artificial Neural Network that enables automated model discovery. Our design paradigm is to reverse engineer the network from a set of functional building blocks that are, by design, a generalization of popular constitutive models, including the neo Hookean, Blatz Ko, Mooney Rivlin, Demiray, Gent, and Holzapfel models. By constraining input, output, activation functions, and architecture, our network a priori satisfies thermodynamic consistency, objectivity, symmetry, and polyconvexity. We demonstrate that-out of more than 4000 models-our network autonomously discovers the model and parameters that best characterize the behavior of human gray and white matter under tension, compression, and shear. Importantly, our network weights translate naturally into physically meaningful parameters, such as shear moduli of 1.82kPa, 0.88kPa, 0.94kPa, and 0.54kPa for the cortex, basal ganglia, corona radiata, and corpus callosum. Our results suggest that Constitutive Artificial Neural Networks have the potential to induce a paradigm shift in soft tissue modeling, from user-defined model selection to automated model discovery. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN. STATEMENT OF SIGNIFICANCE: Human brain is ultrasoft, difficult to test, and challenging to model. Numerous competing constitutive models exist, but selecting the best model remains a matter of personal preference. Here we automate the process of model selection. We formulate the problem of autonomous model discovery as a neural network and capitalize on the powerful optimizers in deep learning. However, rather than using a conventional neural network, we reverse engineer our own Constitutive Artificial Neural Network from a set of modular building blocks, which we rationalize from common constitutive models. When trained with tension, compression, and shear experiments of gray and white matter, our network simultaneously discovers both model and parameters that describes the data better than any existing invariant-based model. Our network could induce a paradigm shift from user-defined model selection to automated model discovery.

  View details for DOI 10.1016/j.actbio.2023.01.055

  View details for PubMedID 36736643

• A new family of Constitutive Artificial Neural Networks towards automated model discovery COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Linka, K., Kuhl, E. 2023; 403

  View details for DOI 10.1016/j.cma.2022.115731

  View details for Web of Science ID 000906896000011

• Bayesian Physics Informed Neural Networks for real-world nonlinear dynamical systems COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Linka, K., Schafer, A., Meng, X., Zou, Z., Karniadakis, G., Kuhl, E. 2022; 402

  View details for DOI 10.1016/j.cma.2022.115346

  View details for Web of Science ID 000922067100005

• Bayesian Physics-Based Modeling of Tau Propagation in Alzheimer's Disease. Frontiers in physiology Schafer, A., Peirlinck, M., Linka, K., Kuhl, E., Alzheimer's Disease Neuroimaging Initiative (ADNI) 2021; 12: 702975

  Abstract

  Amyloid-beta and hyperphosphorylated tau protein are known drivers of neuropathology in Alzheimer's disease. Tau in particular spreads in the brains of patients following a spatiotemporal pattern that is highly sterotypical and correlated with subsequent neurodegeneration. Novel medical imaging techniques can now visualize the distribution of tau in the brain in vivo, allowing for new insights to the dynamics of this biomarker. Here we personalize a network diffusion model with global spreading and local production terms to longitudinal tau positron emission tomography data of 76 subjects from the Alzheimer's Disease Neuroimaging Initiative. We use Bayesian inference with a hierarchical prior structure to infer means and credible intervals for our model parameters on group and subject levels. Our results show that the group average protein production rate for amyloid positive subjects is significantly higher with 0.019±0.27/yr, than that for amyloid negative subjects with -0.143±0.21/yr (p = 0.0075). These results support the hypothesis that amyloid pathology drives tau pathology. The calibrated model could serve as a valuable clinical tool to identify optimal time points for follow-up scans and predict the timeline of disease progression.

  View details for DOI 10.3389/fphys.2021.702975

  View details for PubMedID 34335308

• The reproduction number of COVID-19 and its correlation with public health interventions. Computational mechanics Linka, K., Peirlinck, M., Kuhl, E. 2020: 1-16

  Abstract

  Throughout the past six months, no number has dominated the public media more persistently than the reproduction number of COVID-19. This powerful but simple concept is widely used by the public media, scientists, and political decision makers to explain and justify political strategies to control the COVID-19 pandemic. Here we explore the effectiveness of political interventions using the reproduction number of COVID-19 across Europe. We propose a dynamic SEIR epidemiology model with a time-varying reproduction number, which we identify using machine learning. During the early outbreak, the basic reproduction number was 4.22 ± 1.69, with maximum values of 6.33 and 5.88 in Germany and the Netherlands. By May 10, 2020, it dropped to 0.67 ± 0.18, with minimum values of 0.37 and 0.28 in Hungary and Slovakia. We found a strong correlation between passenger air travel, driving, walking, and transit mobility and the effective reproduction number with a time delay of 17.24 ± 2.00 days. Our new dynamic SEIR model provides the flexibility to simulate various outbreak control and exit strategies to inform political decision making and identify safe solutions in the benefit of global health.

  View details for DOI 10.1007/s00466-020-01880-8

  View details for PubMedID 32836597

  View details for PubMedCentralID PMC7385940

• Outbreak dynamics of COVID-19 in Europe and the effect of travel restrictions Comp Meth Biomech Biomed Eng Linka, K., Peirlinck, M., Sahli Costabal, F., Kuhl, E. 2020; 23: 710-717

  View details for DOI 10.1080/10255842.2020.1759560

• Network Diffusion Modeling Explains Longitudinal Tau PET Data. Frontiers in neuroscience Schafer, A., Mormino, E. C., Kuhl, E. 2020; 14: 566876

  Abstract

  Alzheimer's disease is associated with the cerebral accumulation of neurofibrillary tangles of hyperphosphorylated tau protein. The progressive occurrence of tau aggregates in different brain regions is closely related to neurodegeneration and cognitive impairment. However, our current understanding of tau propagation relies almost exclusively on postmortem histopathology, and the precise propagation dynamics of misfolded tau in the living brain remain poorly understood. Here we combine longitudinal positron emission tomography and dynamic network modeling to test the hypothesis that misfolded tau propagates preferably along neuronal connections. We follow 46 subjects for three or four annual positron emission tomography scans and compare their pathological tau profiles against brain network models of intracellular and extracellular spreading. For each subject, we identify a personalized set of model parameters that characterizes the individual progression of pathological tau. Across all subjects, the mean protein production rate was 0.21 ± 0.15 and the intracellular diffusion coefficient was 0.34 ± 0.43. Our network diffusion model can serve as a tool to detect non-clinical symptoms at an earlier stage and make informed predictions about the timeline of neurodegeneration on an individual personalized basis.

  View details for DOI 10.3389/fnins.2020.566876

  View details for PubMedID 33424532

• Integrating machine learning and multiscale modeling-perspectives, challenges, and opportunities in the biological, biomedical, and behavioral sciences. NPJ digital medicine Alber, M. n., Buganza Tepole, A. n., Cannon, W. R., De, S. n., Dura-Bernal, S. n., Garikipati, K. n., Karniadakis, G. n., Lytton, W. W., Perdikaris, P. n., Petzold, L. n., Kuhl, E. n. 2019; 2: 115

  Abstract

  Fueled by breakthrough technology developments, the biological, biomedical, and behavioral sciences are now collecting more data than ever before. There is a critical need for time- and cost-efficient strategies to analyze and interpret these data to advance human health. The recent rise of machine learning as a powerful technique to integrate multimodality, multifidelity data, and reveal correlations between intertwined phenomena presents a special opportunity in this regard. However, machine learning alone ignores the fundamental laws of physics and can result in ill-posed problems or non-physical solutions. Multiscale modeling is a successful strategy to integrate multiscale, multiphysics data and uncover mechanisms that explain the emergence of function. However, multiscale modeling alone often fails to efficiently combine large datasets from different sources and different levels of resolution. Here we demonstrate that machine learning and multiscale modeling can naturally complement each other to create robust predictive models that integrate the underlying physics to manage ill-posed problems and explore massive design spaces. We review the current literature, highlight applications and opportunities, address open questions, and discuss potential challenges and limitations in four overarching topical areas: ordinary differential equations, partial differential equations, data-driven approaches, and theory-driven approaches. Towards these goals, we leverage expertise in applied mathematics, computer science, computational biology, biophysics, biomechanics, engineering mechanics, experimentation, and medicine. Our multidisciplinary perspective suggests that integrating machine learning and multiscale modeling can provide new insights into disease mechanisms, help identify new targets and treatment strategies, and inform decision making for the benefit of human health.

  View details for DOI 10.1038/s41746-019-0193-y

  View details for PubMedID 31799423

  View details for PubMedCentralID PMC6877584

• Connectomics of neurodegeneration. Nature neuroscience Kuhl, E. n. 2019; 22 (8): 1200–1202

  View details for DOI 10.1038/s41593-019-0459-3

  View details for PubMedID 31346294

• Data-driven hyperelasticity, Part II: A canonical framework for anisotropic soft biological tissues JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Tikenogullari, O., Acan, A., Kuhl, E., Dal, H. 2023; 181

  View details for DOI 10.1016/j.jmps.2023.105453

  View details for Web of Science ID 001152926200001

• Discovering a reaction-diffusion model for Alzheimer's disease by combining PINNs with symbolic regression COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Zhang, Z., Zou, Z., Kuhl, E., Karniadakis, G. 2024; 419

  View details for DOI 10.1016/j.cma.2023.116647

  View details for Web of Science ID 001126494800001

• Automated model discovery for muscle using constitutive recurrent neural networks. Journal of the mechanical behavior of biomedical materials Wang, L. M., Linka, K., Kuhl, E. 2023; 145: 106021

  Abstract

  The stiffness of soft biological tissues not only depends on the applied deformation, but also on the deformation rate. To model this type of behavior, traditional approaches select a specific time-dependent constitutive model and fit its parameters to experimental data. Instead, a new trend now suggests a machine-learning based approach that simultaneously discovers both the best model and best parameters to explain given data. Recent studies have shown that feed-forward constitutive neural networks can robustly discover constitutive models and parameters for hyperelastic materials. However, feed-forward architectures fail to capture the history dependence of viscoelastic soft tissues. Here we combine a feed-forward constitutive neural network for the hyperelastic response and a recurrent neural network for the viscous response inspired by the theory of quasi-linear viscoelasticity. Our novel rheologically-informed network architecture discovers the time-independent initial stress using the feed-forward network and the time-dependent relaxation using the recurrent network. We train and test our combined network using unconfined compression relaxation experiments of passive skeletal muscle and compare our discovered model to a neo Hookean standard linear solid, to an advanced mechanics-based model, and to a vanilla recurrent neural network with no mechanics knowledge. We demonstrate that, for limited experimental data, our new constitutive recurrent neural network discovers models and parameters that satisfy basic physical principles and generalize well to unseen data. We discover a Mooney-Rivlin type two-term initial stored energy function that is linear in the first invariant I1 and quadratic in the second invariant I2 with stiffness parameters of 0.60 kPa and 0.55 kPa. We also discover a Prony-series type relaxation function with time constants of 0.362s, 2.54s, and 52.0s with coefficients of 0.89, 0.05, and 0.03. Our newly discovered model outperforms both the neo Hookean standard linear solid and the vanilla recurrent neural network in terms of prediction accuracy on unseen data. Our results suggest that constitutive recurrent neural networks can autonomously discover both model and parameters that best explain experimental data of soft viscoelastic tissues. Our source code, data, and examples are available at https://github.com/LivingMatterLab.

  View details for DOI 10.1016/j.jmbbm.2023.106021

  View details for PubMedID 37473576

• Benchmarking physics-informed frameworks for data-driven hyperelasticity COMPUTATIONAL MECHANICS Tac, V., Linka, K., Sahli-Costabal, F., Kuhl, E., Tepole, A. 2023

  View details for DOI 10.1007/s00466-023-02355-2

  View details for Web of Science ID 000998752700001

• Validating MRI-Derived Myocardial Stiffness Estimates Using In Vitro Synthetic Heart Models. Annals of biomedical engineering Kolawole, F. O., Peirlinck, M., Cork, T. E., Levenston, M., Kuhl, E., Ennis, D. B. 2023

  Abstract

  Impaired cardiac filling in response to increased passive myocardial stiffness contributes to the pathophysiology of heart failure. By leveraging cardiac MRI data and ventricular pressure measurements, we can estimate in vivo passive myocardial stiffness using personalized inverse finite element models. While it is well-known that this approach is subject to uncertainties, only few studies quantify the accuracy of these stiffness estimates. This lack of validation is, at least in part, due to the absence of ground truth in vivo passive myocardial stiffness values. Here, using 3D printing, we created soft, homogenous, isotropic, hyperelastic heart phantoms of varying geometry and stiffness and simulate diastolic filling by incorporating the phantoms into an MRI-compatible left ventricular inflation system. We estimate phantom stiffness from MRI and pressure data using inverse finite element analyses based on a Neo-Hookean model. We demonstrate that our identified softest and stiffest values of 215.7 and 512.3kPa agree well with the ground truth of 226.2 and 526.4kPa. Overall, our estimated stiffnesses revealed a good agreement with the ground truth ([Formula: see text] error) across all models. Our results suggest that MRI-driven computational constitutive modeling can accurately estimate synthetic heart material stiffnesses in the range of 200-500kPa.

  View details for DOI 10.1007/s10439-023-03164-7

  View details for PubMedID 36914919

• Bayesian design optimization of biomimetic soft actuators COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kaczmarski, B., Moulton, D. E., Goriely, A., Kuhl, E. 2023; 408

  View details for DOI 10.1016/j.cma.2023.115939

  View details for Web of Science ID 000948556600001

• A Simulation Tool for Physics-Informed Control of Biomimetic Soft Robotic Arms IEEE ROBOTICS AND AUTOMATION LETTERS Kaczmarski, B., Goriely, A., Kuhl, E., Moulton, D. E. 2023; 8 (2): 936-943

  View details for DOI 10.1109/LRA.2023.3234819

  View details for Web of Science ID 000915826000005

• Image-based axon model highlights heterogeneity in initiation of damage. Biophysical journal Wang, L. M., Goodman, M. B., Kuhl, E. 2022

  Abstract

  Head injury simulations predict the occurrence of traumatic brain injury by placing a threshold on the calculated strains for axon tracts within the brain. However, a current roadblock to accurate injury prediction is the selection of an appropriate axon damage threshold. While several computational studies have used models of the axon cytoskeleton to investigate damage initiation, these models all employ an idealized, homogeneous axonal geometry. This homogeneous geometry with regularly spaced microtubules, evenly distributed throughout the model, overestimates axon strength because in reality, the axon cytoskeleton is heterogeneous. In the heterogeneous cytoskeleton, the weakest cross section determines the initiation of failure, but these weak spots are not present in a homogeneous model. Addressing one source of heterogeneity in the axon cytoskeleton, we present a new semi-automated image analysis pipeline for using serial section transmission electron micrographs (ssTEM) to reconstruct the microtubule geometry of an axon. The image analysis procedure locates microtubules within the images, traces them throughout the image stack, and reconstructs the microtubule structure as a finite element mesh. We demonstrate the image analysis approach using a C. elegans touch receptor neuron due to the availability of high-quality ssTEM datasets. The results of the analysis highlight the heterogeneity of the microtubule structure in the spatial variation of both microtubule number and length. Simulations comparing this image-based geometry to homogeneous geometries show that structural heterogeneity in the image-based model creates significant spatial variation in deformation. The homogeneous geometries, on the other hand, deform more uniformly. Since no single homogeneous model can replicate the mechanical behavior of the image-based model, our results argue that heterogeneity in axon microtubule geometry should be considered in determining accurate axon failure thresholds.

  View details for DOI 10.1016/j.bpj.2022.11.2946

  View details for PubMedID 36461640

• How viscous is the beating heart?: Insights from a computational study. Computational mechanics Tikenoğulları, O. Z., Costabal, F. S., Yao, J., Marsden, A., Kuhl, E. 2022; 70 (3): 565-579

  Abstract

  Understanding tissue rheology is critical to accurately model the human heart. While the elastic properties of cardiac tissue have been extensively studied, its viscous properties remain an issue of ongoing debate. Here we adopt a viscoelastic version of the classical Holzapfel Ogden model to study the viscous timescales of human cardiac tissue. We perform a series of simulations and explore stress-relaxation curves, pressure-volume loops, strain profiles, and ventricular wall strains for varying viscosity parameters. We show that the time window for model calibration strongly influences the parameter identification. Using a four-chamber human heart model, we observe that, during the physiologically relevant time scales of the cardiac cycle, viscous relaxation has a negligible effect on the overall behavior of the heart. While viscosity could have important consequences in pathological conditions with compromised contraction or relaxation properties, we conclude that, for simulations within the physiological range of a human heart beat, we can reasonably approximate the human heart as hyperelastic.

  View details for DOI 10.1007/s00466-022-02180-z

  View details for PubMedID 37274842

  View details for PubMedCentralID PMC10237084

• Correlating the microstructural architecture and macrostructural behaviour of the brain. Acta biomaterialia Hoppstädter, M., Püllmann, D., Seydewitz, R., Kuhl, E., Böl, M. 2022

  Abstract

  The computational simulation of pathological conditions and surgical procedures, for example the removal of cancerous tissue, can contribute crucially to the future of medicine. Especially for brain surgery, these methods can be important, as the ultra-soft tissue controls vital functions of the body. However, the microstructural interactions and their effects on macroscopic material properties remain incompletely understood. Therefore, we investigated the mechanical behaviour of brain tissue under three different deformation modes, axial tension, compression, and semi-confined compression, in different anatomical regions, and for varying axon orientation. In addition, we characterised the underlying microstructure in terms of myelin, cells, glial cells and neuron area fraction, and density. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction (Spearman's correlation coefficient of rs=0.40 and rs=0.33), whereas the compressive shear modulus decreases with increasing glial cell area (rs=-0.33). Our study finds that tissue non-linearity significantly depends on the myelin area fraction (rs=0.47), cell density (rs=0.41) and glial cell area (rs=0.49). Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain. STATEMENT OF SIGNIFICANCE: Within this article, we investigate the mechanical behaviour of brain tissue under three different deformation modes, in different anatomical regions, and for varying axon orientation. Further, we characterise the underlying microstructure in terms of various constituents. The correlation of these quantities with the material parameters of the anisotropic Ogden model reveals a decrease in shear modulus with increasing myelin area fraction. Strikingly, the tensile shear modulus correlates positively with cell and neuronal area fraction, whereas the compressive shear modulus decreases with increasing glial cell area. Our study finds that tissue non-linearity significantly depends on the myelin area fraction, cell density, and glial cell area. Our results provide an important step towards understanding the micromechanical load transfer that leads to the non-linear macromechanical behaviour of the brain.

  View details for DOI 10.1016/j.actbio.2022.08.034

  View details for PubMedID 36002124

• Rheology of growing axons PHYSICAL REVIEW RESEARCH Oliveri, H., de Rooij, R., Kuhl, E., Goriely, A. 2022; 4 (3)

  View details for DOI 10.1103/PhysRevResearch.4.033125

  View details for Web of Science ID 000860436200001

• Active filaments I: Curvature and torsion generation JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Kaczmarski, B., Moulton, D. E., Kuhl, E., Goriely, A. 2022; 164

  View details for DOI 10.1016/j.jmps.2022.104918

  View details for Web of Science ID 000807382900003

• Correlating tau pathology to brain atrophy using a physics-based Bayesian model ENGINEERING WITH COMPUTERS Schafer, A., Chaggar, P., Goriely, A., Kuhl, E. 2022

  View details for DOI 10.1007/s00366-022-01660-3

  View details for Web of Science ID 000807327600001

• How viscous is the beating heart? Insights from a computational study COMPUTATIONAL MECHANICS Tikenogullari, O., Costabal, F., Yao, J., Marsden, A., Kuhl, E. 2022

  View details for DOI 10.1007/s00466-022-02180-z

  View details for Web of Science ID 000799405900001

• Mechanics of axon growth and damage: A systematic review of computational models. Seminars in cell & developmental biology Wang, L. M., Kuhl, E. 2022

  Abstract

  Normal axon development depends on the action of mechanical forces both generated within the cytoskeleton and outside the cell, but forces of large magnitude or rate cause damage instead. Computational models aid scientists in studying the role of mechanical forces in axon growth and damage. These studies use simulations to evaluate how different sources of force generation within the cytoskeleton interact with each other to regulate axon elongation and retraction. Furthermore, mathematical models can help optimize externally applied tension to promote axon growth without causing damage. Finally, scientists also use simulations of axon damage to investigate how forces are distributed among different components of the axon and how the tissue surrounding an axon influences its susceptibility to injury. In this review, we discuss how computational studies complement experimental studies in the areas of axon growth, regeneration, and damage.

  View details for DOI 10.1016/j.semcdb.2022.04.019

  View details for PubMedID 35474150

• How drugs modulate the performance of the human heart COMPUTATIONAL MECHANICS Peirlinck, M., Yao, J., Sahli Costabal, F., Kuhl, E. 2022

  View details for DOI 10.1007/s00466-022-02146-1

  View details for Web of Science ID 000765688100001

• Sex Matters: A Comprehensive Comparison of Female and Male Hearts. Frontiers in physiology St Pierre, S. R., Peirlinck, M., Kuhl, E. 2022; 13: 831179

  Abstract

  Cardiovascular disease in women remains under-diagnosed and under-treated. Recent studies suggest that this is caused, at least in part, by the lack of sex-specific diagnostic criteria. While it is widely recognized that the female heart is smaller than the male heart, it has long been ignored that it also has a different microstructural architecture. This has severe implications on a multitude of cardiac parameters. Here, we systematically review and compare geometric, functional, and structural parameters of female and male hearts, both in the healthy population and in athletes. Our study finds that, compared to the male heart, the female heart has a larger ejection fraction and beats at a faster rate but generates a smaller cardiac output. It has a lower blood pressure but produces universally larger contractile strains. Critically, allometric scaling, e.g., by lean body mass, reduces but does not completely eliminate the sex differences between female and male hearts. Our results suggest that the sex differences in cardiac form and function are too complex to be ignored: the female heart is not just a small version of the male heart. When using similar diagnostic criteria for female and male hearts, cardiac disease in women is frequently overlooked by routine exams, and it is diagnosed later and with more severe symptoms than in men. Clearly, there is an urgent need to better understand the female heart and design sex-specific diagnostic criteria that will allow us to diagnose cardiac disease in women equally as early, robustly, and reliably as in men.Systematic Review Registration: https://livingmatter.stanford.edu/.

  View details for DOI 10.3389/fphys.2022.831179

  View details for PubMedID 35392369

• Growth and remodeling in the pulmonary autograft: computational evaluation using kinematic growth models and constrained mixture theory. International journal for numerical methods in biomedical engineering Vastmans, J., Maes, L., Peirlinck, M., Vanderveken, E., Rega, F., Kuhl, E., Famaey, N. 2021: e3549

  Abstract

  Computational investigations of how soft tissues grow and remodel are gaining more and more interest and several growth and remodeling theories have been developed. Roughly, two main groups of theories for soft tissues can be distinguished: kinematic-based growth theory and theories based on constrained mixture theory. Our goal was to apply these two theories on the same experimental data. Within the experiment, a pulmonary artery was exposed to systemic conditions. The change in diameter was followed-up over time. A mechanical and microstructural analysis of native pulmonary artery and pulmonary autograft was conducted. Whereas the kinematic-based growth theory is able to accurately capture the growth of the tissue, it does not account for the mechanobiological processes causing this growth. The constrained mixture theory takes into account the mechanobiological processes including removal, deposition and adaptation of all structural constituents, allowing us to simulate a changing microstructure and mechanical behavior. This article is protected by copyright. All rights reserved.

  View details for DOI 10.1002/cnm.3545

  View details for PubMedID 34724357

• Effects of B.1.1.7 and B.1.351 on COVID-19 Dynamics: A Campus Reopening Study. Archives of computational methods in engineering : state of the art reviews Linka, K., Peirlinck, M., Schäfer, A., Tikenogullari, O. Z., Goriely, A., Kuhl, E. 2021: 1-12

  Abstract

  The timing and sequence of safe campus reopening has remained the most controversial topic in higher education since the outbreak of the COVID-19 pandemic. By the end of March 2020, almost all colleges and universities in the United States had transitioned to an all online education and many institutions have not yet fully reopened to date. For a residential campus like Stanford University, the major challenge of reopening is to estimate the number of incoming infectious students at the first day of class. Here we learn the number of incoming infectious students using Bayesian inference and perform a series of retrospective and projective simulations to quantify the risk of campus reopening. We create a physics-based probabilistic model to infer the local reproduction dynamics for each state and adopt a network SEIR model to simulate the return of all undergraduates, broken down by their year of enrollment and state of origin. From these returning student populations, we predict the outbreak dynamics throughout the spring, summer, fall, and winter quarters using the inferred reproduction dynamics of Santa Clara County. We compare three different scenarios: the true outbreak dynamics under the wild-type SARS-CoV-2, and the hypothetical outbreak dynamics under the new COVID-19 variants B.1.1.7 and B.1.351 with 56% and 50% increased transmissibility. Our study reveals that even small changes in transmissibility can have an enormous impact on the overall case numbers. With no additional countermeasures, during the most affected quarter, the fall of 2020, there would have been 203 cases under baseline reproduction, compared to 4727 and 4256 cases for the B.1.1.7 and B.1.351 variants. Our results suggest that population mixing presents an increased risk for local outbreaks, especially with new and more infectious variants emerging across the globe. Tight outbreak control through mandatory quarantine and test-trace-isolate strategies will be critical in successfully managing these local outbreak dynamics.

  View details for DOI 10.1007/s11831-021-09638-y

  View details for PubMedID 34456557

  View details for PubMedCentralID PMC8381867

• Effects of B.1.1.7 and B.1.351 on COVID-19 Dynamics: A Campus Reopening Study ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING Linka, K., Peirlinck, M., Schaefer, A., Tikenogullari, O., Goriely, A., Kuhl, E. 2021

  View details for DOI 10.1007/s11831-021-09638-y

  View details for Web of Science ID 000687524400001

• COVID-19 dynamics across the US: A deep learning study of human mobility and social behavior COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Bhouri, M., Costabal, F., Wang, H., Linka, K., Peirlinck, M., Kuhl, E., Perdikaris, P. 2021; 382

  View details for DOI 10.1016/j.cma.2021.113891

  View details for Web of Science ID 000654331500001

• Multiscale modeling meets machine learning: What can we learn? Archives of computational methods in engineering : state of the art reviews Peng, G. C., Alber, M., Tepole, A. B., Cannon, W. R., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W. W., Perdikaris, P., Petzold, L., Kuhl, E. 2021; 28 (3): 1017-1037

  Abstract

  Machine learning is increasingly recognized as a promising technology in the biological, biomedical, and behavioral sciences. There can be no argument that this technique is incredibly successful in image recognition with immediate applications in diagnostics including electrophysiology, radiology, or pathology, where we have access to massive amounts of annotated data. However, machine learning often performs poorly in prognosis, especially when dealing with sparse data. This is a field where classical physics-based simulation seems to remain irreplaceable. In this review, we identify areas in the biomedical sciences where machine learning and multiscale modeling can mutually benefit from one another: Machine learning can integrate physics-based knowledge in the form of governing equations, boundary conditions, or constraints to manage ill-posted problems and robustly handle sparse and noisy data; multiscale modeling can integrate machine learning to create surrogate models, identify system dynamics and parameters, analyze sensitivities, and quantify uncertainty to bridge the scales and understand the emergence of function. With a view towards applications in the life sciences, we discuss the state of the art of combining machine learning and multiscale modeling, identify applications and opportunities, raise open questions, and address potential challenges and limitations. We anticipate that it will stimulate discussion within the community of computational mechanics and reach out to other disciplines including mathematics, statistics, computer science, artificial intelligence, biomedicine, systems biology, and precision medicine to join forces towards creating robust and efficient models for biological systems.

  View details for DOI 10.1007/s11831-020-09405-5

  View details for PubMedID 34093005

  View details for PubMedCentralID PMC8172124

• Are college campuses superspreaders? A data-driven modeling study. Computer methods in biomechanics and biomedical engineering Lu, H., Weintz, C., Pace, J., Indana, D., Linka, K., Kuhl, E. 2021: 1–11

  Abstract

  The COVID-19 pandemic continues to present enormous challenges for colleges and universities and strategies for save reopening remain a topic of ongoing debate. Many institutions that reopened cautiously in the fall experienced a massive wave of infections and colleges were soon declared as the new hotspots of the pandemic. However, the precise effects of college outbreaks on their immediate neighborhood remain largely unknown. Here we show that the first two weeks of instruction present a high-risk period for campus outbreaks and that these outbreaks tend to spread into the neighboring communities. By integrating a classical mathematical epidemiology model and Bayesian learning, we learned the dynamic reproduction number for 30 colleges from their daily case reports. Of these 30 institutions, 14 displayed a spike of infections within the first two weeks of class, with peak seven-day incidences well above 1,000 per 100,000, an order of magnitude larger than the nation-wide peaks of 70 and 150 during the first and second waves of the pandemic. While most colleges were able to rapidly reduce the number of new infections, many failed to control the spread of the virus beyond their own campus: Within only two weeks, 17 campus outbreaks translated directly into peaks of infection within their home counties. These findings suggests that college campuses are at risk to develop an extreme incidence of COVID-19 and become superspreaders for neighboring communities. We anticipate that tight test-trace-quarantine strategies, flexible transition to online instruction, and-most importantly-compliance with local regulations will be critical to ensure a safe campus reopening after the winter break.

  View details for DOI 10.1080/10255842.2020.1869221

  View details for PubMedID 33439055

• Global and local mobility as a barometer for COVID-19 dynamics. Biomechanics and modeling in mechanobiology Linka, K. n., Goriely, A. n., Kuhl, E. n. 2021

  Abstract

  The spreading of infectious diseases including COVID-19 depends on human interactions. In an environment where behavioral patterns and physical contacts are constantly evolving according to new governmental regulations, measuring these interactions is a major challenge. Mobility has emerged as an indicator for human activity and, implicitly, for human interactions. Here, we study the coupling between mobility and COVID-19 dynamics and show that variations in global air traffic and local driving mobility can be used to stratify different disease phases. For ten European countries, our study shows a maximal correlation between driving mobility and disease dynamics with a time lag of [Formula: see text] days. Our findings suggest that trends in local mobility allow us to forecast the outbreak dynamics of COVID-19 for a window of two weeks and adjust local control strategies in real time.

  View details for DOI 10.1007/s10237-020-01408-2

  View details for PubMedID 33449276

  View details for PubMedCentralID PMC7809648

• Sex Differences in Drug-Induced Arrhythmogenesis. Frontiers in physiology Peirlinck, M., Sahli Costabal, F., Kuhl, E. 2021; 12: 708435

  Abstract

  The electrical activity in the heart varies significantly between men and women and results in a sex-specific response to drugs. Recent evidence suggests that women are more than twice as likely as men to develop drug-induced arrhythmia with potentially fatal consequences. Yet, the sex-specific differences in drug-induced arrhythmogenesis remain poorly understood. Here we integrate multiscale modeling and machine learning to gain mechanistic insight into the sex-specific origin of drug-induced cardiac arrhythmia at differing drug concentrations. To quantify critical drug concentrations in male and female hearts, we identify the most important ion channels that trigger male and female arrhythmogenesis, and create and train a sex-specific multi-fidelity arrhythmogenic risk classifier. Our study reveals that sex differences in ion channel activity, tissue conductivity, and heart dimensions trigger longer QT-intervals in women than in men. We quantify the critical drug concentration for dofetilide, a high risk drug, to be seven times lower for women than for men. Our results emphasize the importance of including sex as an independent biological variable in risk assessment during drug development. Acknowledging and understanding sex differences in drug safety evaluation is critical when developing novel therapeutic treatments on a personalized basis. The general trends of this study have significant implications on the development of safe and efficacious new drugs and the prescription of existing drugs in combination with other drugs.

  View details for DOI 10.3389/fphys.2021.708435

  View details for PubMedID 34489728

• Visualizing the invisible: The effect of asymptomatic transmission on the outbreak dynamics of COVID-19. Computer methods in applied mechanics and engineering Peirlinck, M., Linka, K., Sahli Costabal, F., Bhattacharya, J., Bendavid, E., Ioannidis, J. P., Kuhl, E. 2020; 372: 113410

  Abstract

  Understanding the outbreak dynamics of the COVID-19 pandemic has important implications for successful containment and mitigation strategies. Recent studies suggest that the population prevalence of SARS-CoV-2 antibodies, a proxy for the number of asymptomatic cases, could be an order of magnitude larger than expected from the number of reported symptomatic cases. Knowing the precise prevalence and contagiousness of asymptomatic transmission is critical to estimate the overall dimension and pandemic potential of COVID-19. However, at this stage, the effect of the asymptomatic population, its size, and its outbreak dynamics remain largely unknown. Here we use reported symptomatic case data in conjunction with antibody seroprevalence studies, a mathematical epidemiology model, and a Bayesian framework to infer the epidemiological characteristics of COVID-19. Our model computes, in real time, the time-varying contact rate of the outbreak, and projects the temporal evolution and credible intervals of the effective reproduction number and the symptomatic, asymptomatic, and recovered populations. Our study quantifies the sensitivity of the outbreak dynamics of COVID-19 to three parameters: the effective reproduction number, the ratio between the symptomatic and asymptomatic populations, and the infectious periods of both groups. For nine distinct locations, our model estimates the fraction of the population that has been infected and recovered by Jun 15, 2020 to 24.15% (95% CI: 20.48%-28.14%) for Heinsberg (NRW, Germany), 2.40% (95% CI: 2.09%-2.76%) for Ada County (ID, USA), 46.19% (95% CI: 45.81%-46.60%) for New York City (NY, USA), 11.26% (95% CI: 7.21%-16.03%) for Santa Clara County (CA, USA), 3.09% (95% CI: 2.27%-4.03%) for Denmark, 12.35% (95% CI: 10.03%-15.18%) for Geneva Canton (Switzerland), 5.24% (95% CI: 4.84%-5.70%) for the Netherlands, 1.53% (95% CI: 0.76%-2.62%) for Rio Grande do Sul (Brazil), and 5.32% (95% CI: 4.77%-5.93%) for Belgium. Our method traces the initial outbreak date in Santa Clara County back to January 20, 2020 (95% CI: December 29, 2019-February 13, 2020). Our results could significantly change our understanding and management of the COVID-19 pandemic: A large asymptomatic population will make isolation, containment, and tracing of individual cases challenging. Instead, managing community transmission through increasing population awareness, promoting physical distancing, and encouraging behavioral changes could become more relevant.

  View details for DOI 10.1016/j.cma.2020.113410

  View details for PubMedID 33518823

  View details for PubMedCentralID PMC7831913

• Folding drives cortical thickness variations EUROPEAN PHYSICAL JOURNAL-SPECIAL TOPICS Holland, M. A., Budday, S., Li, G., Shen, D., Goriely, A., Kuhl, E. 2020; 229 (17-18): 2757–78

  View details for DOI 10.1140/epjst/e2020-000001-6

  View details for Web of Science ID 000590141900003

• Folding drives cortical thickness variations. The European physical journal. Special topics Holland, M. A., Budday, S., Li, G., Shen, D., Goriely, A., Kuhl, E. 2020; 229 (17-18): 2757-2778

  Abstract

  The cortical thickness is a characteristic biomarker for a wide variety of neurological disorders. While the structural organization of the cerebral cortex is tightly regulated and evolutionarily preserved, its thickness varies widely between 1.5 and 4.5 mm across the healthy adult human brain. It remains unclear whether these thickness variations are a cause or consequence of cortical development. Recent studies suggest that cortical thickness variations are primarily a result of genetic effects. Previous studies showed that a simple homogeneous bilayered system with a growing layer on an elastic substrate undergoes a unique symmetry breaking into a spatially heterogeneous system with discrete gyri and sulci. Here, we expand on that work to explore the evolution of cortical thickness variations over time to support our finding that cortical pattern formation and thickness variations can be explained - at least in part - by the physical forces that emerge during cortical folding. Strikingly, as growth progresses, the developing gyri universally thicken and the sulci thin, even in the complete absence of regional information. Using magnetic resonance images, we demonstrate that these naturally emerging thickness variations agree with the cortical folding pattern in n = 9 healthy adult human brains, in n = 564 healthy human brains ages 7-64, and in n = 73 infant brains scanned at birth, and at ages one and two. Additionally, we show that cortical organoids develop similar patterns throughout their growth. Our results suggest that genetic, geometric, and physical events during brain development are closely interrelated. Understanding regional and temporal variations in cortical thickness can provide insight into the evolution and causative factors of neurological disorders, inform the diagnosis of neurological conditions, and assess the efficacy of treatment options.

  View details for DOI 10.1140/epjst/e2020-000001-6

  View details for PubMedID 37275766

  View details for PubMedCentralID PMC10237175

• Protein-protein interactions in neurodegenerative diseases: A conspiracy theory. PLoS computational biology Thompson, T. B., Chaggar, P., Kuhl, E., Goriely, A., Alzheimers Disease Neuroimaging Initiative 2020; 16 (10): e1008267

  Abstract

  Neurodegenerative diseases such as Alzheimer's or Parkinson's are associated with the prion-like propagation and aggregation of toxic proteins. A long standing hypothesis that amyloid-beta drives Alzheimer's disease has proven the subject of contemporary controversy; leading to new research in both the role of tau protein and its interaction with amyloid-beta. Conversely, recent work in mathematical modeling has demonstrated the relevance of nonlinear reaction-diffusion type equations to capture essential features of the disease. Such approaches have been further simplified, to network-based models, and offer researchers a powerful set of computationally tractable tools with which to investigate neurodegenerative disease dynamics. Here, we propose a novel, coupled network-based model for a two-protein system that includes an enzymatic interaction term alongside a simple model of aggregate transneuronal damage. We apply this theoretical model to test the possible interactions between tau proteins and amyloid-beta and study the resulting coupled behavior between toxic protein clearance and proteopathic phenomenology. Our analysis reveals ways in which amyloid-beta and tau proteins may conspire with each other to enhance the nucleation and propagation of different diseases, thus shedding new light on the importance of protein clearance and protein interaction mechanisms in prion-like models of neurodegenerative disease.

  View details for DOI 10.1371/journal.pcbi.1008267

  View details for PubMedID 33048932

• Neuronal Oscillations on Evolving Networks: Dynamics, Damage, Degradation, Decline, Dementia, and Death. Physical review letters Goriely, A., Kuhl, E., Bick, C. 2020; 125 (12): 128102

  Abstract

  Neurodegenerative diseases, such as Alzheimer's or Parkinson's disease, show characteristic degradation of structural brain networks. This degradation eventually leads to changes in the network dynamics and degradation of cognitive functions. Here, we model the progression in terms of coupled physical processes: The accumulation of toxic proteins, given by a nonlinear reaction-diffusion transport process, yields an evolving brain connectome characterized by weighted edges on which a neuronal-mass model evolves. The progression of the brain functions can be tested by simulating the resting-state activity on the evolving brain network. We show that while the evolution of edge weights plays a minor role in the overall progression of the disease, dynamic biomarkers predict a transition over a period of 10 years associated with strong cognitive decline.

  View details for DOI 10.1103/PhysRevLett.125.128102

  View details for PubMedID 33016724

• Fifty Shades of Brain: A Review on the Mechanical Testing and Modeling of Brain Tissue ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING Budday, S., Ovaert, T. C., Holzapfel, G. A., Steinmann, P., Kuhl, E. 2020; 27 (4): 1187–1230

  View details for DOI 10.1007/s11831-019-09352-w

  View details for Web of Science ID 000565732400010

• Editorial overview: Biomechanics and mechanobiology of tissue growth and remodeling: Current opinions CURRENT OPINION IN BIOMEDICAL ENGINEERING Kuhl, E., Humphrey, J. D. 2020; 15: A1-A2

  View details for DOI 10.1016/j.cobme.2020.06.001

  View details for Web of Science ID 000655324800001

• Is it safe to lift COVID-19 travel bans? The Newfoundland story COMPUTATIONAL MECHANICS Linka, K., Rahman, P., Goriely, A., Kuhl, E. 2020

  View details for DOI 10.1007/s00466-020-01899-x

  View details for Web of Science ID 000563727500002

• Special Issue on Uncertainty Quantification, Machine Learning, and Data-Driven Modeling of Biological Systems COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Tepole, A., Nordsletten, D., Garikipati, K., Kuhl, E. 2020; 362

  View details for DOI 10.1016/j.cma.2020.112832

  View details for Web of Science ID 000515542500033

• Towards microstructure-informed material models for human brain tissue ACTA BIOMATERIALIA Budday, S., Sarem, M., Starck, L., Sommer, G., Pfefferle, J., Phunchago, N., Kuhl, E., Paulsen, F., Steinmann, P., Shastri, V. P., Holzapfel, G. A. 2020; 104: 53–65

  Abstract

  Emerging evidence suggests that the mechanical behavior of the brain plays a critical role in development, disease, and aging. Recent studies have begun to characterize the mechanical behavior of gray and white matter tissue and to identify sets of material models that best reproduce the stress-strain behavior of different brain regions. Yet, these models are mainly phenomenological in nature, their parameters often lack clear physical interpretation, and they fail to correlate the mechanical behavior to the underlying microstructural composition. Here we make a first attempt towards identifying general relations between microstructure and mechanics with the ultimate goal to develop microstructurally motivated constitutive equations for human brain tissue. Using histological staining, we analyze the microstructure of brain specimens from different anatomical regions, the cortex, basal ganglia, corona radiata, and corpus callosum, and identify the regional stiffness and viscosity under multiple loading conditions, simple shear, compression, and tension. Strikingly, our study reveals a negative correlation between cell count and stiffness, a positive correlation between myelin content and stiffness, and a negative correlation between proteoglycan content and stiffness. Additionally, our analysis shows a positive correlation between lipid and proteoglycan content and viscosity. We demonstrate how understanding the microstructural origin of the macroscopic behavior of the brain can help us design microstructure-informed material models for human brain tissue that inherently capture regional heterogeneities. This study represents an important step towards using brain tissue stiffness and viscosity as early diagnostic markers for clinical conditions including chronic traumatic encephalopathy, Alzheimer's and Parkinson's disease, or multiple sclerosis. STATEMENT OF SIGNIFICANCE: The complex and heterogeneous mechanical properties of brain tissue play a critical role for brain function. To understand and predict how brain tissue properties vary in space and time, it will be key to link the mechanical behavior to the underlying microstructural composition. Here we use histological staining to quantify area fractions of microstructural components of mechanically tested specimens and evaluate their individual contributions to the nonlinear macroscopic mechanical response. We further propose a microstructure-informed material model for human brain tissue that inherently captures regional heterogeneities. The current work provides unprecedented insights into the biomechanics of human brain tissue, which are highly relevant to develop refined computational models for brain tissue behavior or to advance neural tissue engineering.

  View details for DOI 10.1016/j.actbio.2019.12.030

  View details for Web of Science ID 000517348400005

  View details for PubMedID 31887455

• Physics-Informed Neural Networks for Cardiac Activation Mapping FRONTIERS IN PHYSICS Costabal, F., Yang, Y., Perdikaris, P., Hurtado, D. E., Kuhl, E. 2020; 8

  View details for DOI 10.3389/fphy.2020.00042

  View details for Web of Science ID 000525287400001

• Multiscale Modeling Meets Machine Learning: What Can We Learn? ARCHIVES OF COMPUTATIONAL METHODS IN ENGINEERING Peng, G. Y., Alber, M., Tepole, A., Cannon, W., De, S., Dura-Bernal, S., Garikipati, K., Karniadakis, G., Lytton, W. W., Perdikaris, P., Petzold, L., Kuhl, E. 2020

  View details for DOI 10.1007/s11831-020-09405-5

  View details for Web of Science ID 000520045900001

• Classifying Drugs by their Arrhythmogenic Risk Using Machine Learning. Biophysical journal Sahli-Costabal, F., Seo, K., Ashley, E., Kuhl, E. 2020

  Abstract

  All medications have adverse effects. Among the most serious of these are cardiac arrhythmias. Current paradigms for drug safety evaluation are costly, lengthy, conservative, and impede efficient drug development. Here, we combine multiscale experiment and simulation, high-performance computing, and machine learning to create a risk estimator to stratify new and existing drugs according to their proarrhythmic potential. We capitalize on recent developments in machine learning and integrate information across 10 orders of magnitude in space and time to provide a holistic picture of the effects of drugs, either individually or in combination with other drugs. We show, both experimentally and computationally, that drug-induced arrhythmias are dominated by the interplay between two currents with opposing effects: the rapid delayed rectifier potassium current and the L-type calcium current. Using Gaussian process classification, we create a classifier that stratifies drugs into safe and arrhythmic domains for any combinations of these two currents. We demonstrate that our classifier correctly identifies the risk categories of 22 common drugs exclusively on the basis of their concentrations at 50% current block. Our new risk assessment tool explains under which conditions blocking the L-type calcium current can delay or even entirely suppress arrhythmogenic events. Using machine learning in drug safety evaluation can provide a more accurate and comprehensive mechanistic assessment of the proarrhythmic potential of new drugs. Our study paves the way toward establishing science-based criteria to accelerate drug development, design safer drugs, and reduce heart rhythm disorders.

  View details for DOI 10.1016/j.bpj.2020.01.012

  View details for PubMedID 32023435

• Nervous Tissue Stiffens Postinjury. Biophysical journal Kuhl, E. 2020; 118 (2): 276–78

  View details for DOI 10.1016/j.bpj.2019.09.050

  View details for PubMedID 31968236

• Data-driven modeling of COVID-19-Lessons learned. Extreme Mechanics Letters Kuhl, E. n. 2020: 100921

  Abstract

  Understanding the outbreak dynamics of COVID-19 through the lens of mathematical models is an elusive but significant goal. Within only half a year, the COVID-19 pandemic has resulted in more than 19 million reported cases across 188 countries with more than 700,000 deaths worldwide. Unlike any other disease in history, COVID-19 has generated an unprecedented volume of data, well documented, continuously updated, and broadly available to the general public. Yet, the precise role of mathematical modeling in providing quantitative insight into the COVID-19 pandemic remains a topic of ongoing debate. Here we discuss the lessons learned from six month of modeling COVID-19. We highlight the early success of classical models for infectious diseases and show why these models fail to predict the current outbreak dynamics of COVID-19. We illustrate how data-driven modeling can integrate classical epidemiology modeling and machine learning to infer critical disease parameters-in real time-from reported case data to make informed predictions and guide political decision making. We critically discuss questions that these models can and cannot answer and showcase controversial decisions around the early outbreak dynamics, outbreak control, and exit strategies. We anticipate that this summary will stimulate discussion within the modeling community and help provide guidelines for robust mathematical models to understand and manage the COVID-19 pandemic. EML webinar speakers, videos, and overviews are updated at https://imechanica.org/node/24098.

  View details for DOI 10.1016/j.eml.2020.100921

  View details for PubMedID 32837980

  View details for PubMedCentralID PMC7427559

• Modeling the life cycle of the human brain Current Opinion in Biomedical Engineering Budday, S., Kuhl, E. 2020; 15: 16-25

  View details for DOI 10.1016/j.cobme.2019.12.009

• Outbreak dynamics of COVID-19 in China and the United States. Biomechanics and modeling in mechanobiology Peirlinck, M. n., Linka, K. n., Sahli Costabal, F. n., Kuhl, E. n. 2020

  Abstract

  On March 11, 2020, the World Health Organization declared the coronavirus disease 2019, COVID-19, a global pandemic. In an unprecedented collective effort, massive amounts of data are now being collected worldwide to estimate the immediate and long-term impact of this pandemic on the health system and the global economy. However, the precise timeline of the disease, its transmissibility, and the effect of mitigation strategies remain incompletely understood. Here we integrate a global network model with a local epidemic SEIR model to quantify the outbreak dynamics of COVID-19 in China and the United States. For the outbreak in China, in [Formula: see text] provinces, we found a latent period of 2.56 ± 0.72 days, a contact period of 1.47 ± 0.32 days, and an infectious period of 17.82 ± 2.95 days. We postulate that the latent and infectious periods are disease-specific, whereas the contact period is behavior-specific and can vary between different provinces, states, or countries. For the early stages of the outbreak in the United States, in [Formula: see text] states, we adopted the disease-specific values from China and found a contact period of 3.38 ± 0.69 days. Our network model predicts that-without the massive political mitigation strategies that are in place today-the United States would have faced a basic reproduction number of 5.30 ± 0.95 and a nationwide peak of the outbreak on May 10, 2020 with 3 million infections. Our results demonstrate how mathematical modeling can help estimate outbreak dynamics and provide decision guidelines for successful outbreak control. We anticipate that our model will become a valuable tool to estimate the potential of vaccination and quantify the effect of relaxing political measures including total lockdown, shelter in place, and travel restrictions for low-risk subgroups of the population or for the population as a whole.

  View details for DOI 10.1007/s10237-020-01332-5

  View details for PubMedID 32342242

• Modeling and simulation of infectious diseases. Computational mechanics Zohdi, T. I., Kuhl, E. n. 2020: 1

  View details for DOI 10.1007/s00466-020-01901-6

  View details for PubMedID 32836603

  View details for PubMedCentralID PMC7435220

• Multi-fidelity classification using Gaussian processes: Accelerating the prediction of large-scale computational models COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Costabal, F., Perdikaris, P., Kuhl, E., Hurtado, D. E. 2019; 357

  View details for DOI 10.1016/j.cma.2019.112602

  View details for Web of Science ID 000490427600030

• Viscoelasticity of the axon limits stretch-mediated growth COMPUTATIONAL MECHANICS Wang, L. M., Kuhl, E. 2019

  View details for DOI 10.1007/s00466-019-01784-2

  View details for Web of Science ID 000492917700001

• Do annuloplasty rings designed to treat ischemic/functional mitral regurgitation alter left-ventricular dimensions in the acutely ischemic ovine heart? JOURNAL OF THORACIC AND CARDIOVASCULAR SURGERY Bothe, W., Kvitting, J., Rausch, M. K., Timek, T. A., Swanson, J. C., Liang, D. H., Walther, M., Kuhl, E., Ingels, N. B., Miller, D. 2019; 158 (4): 1058–68

  View details for DOI 10.1016/j.jtcvs.2018.12.077

  View details for Web of Science ID 000486317100031

• On the implementation of finite deformation gradient-enhanced damage models COMPUTATIONAL MECHANICS Ostwald, R., Kuhl, E., Menzel, A. 2019; 64 (3): 847–77

  View details for DOI 10.1007/s00466-019-01684-5

  View details for Web of Science ID 000479049200014

• The Shrinking Brain: Cerebral Atrophy Following Traumatic Brain Injury ANNALS OF BIOMEDICAL ENGINEERING Harris, T. C., de Rooij, R., Kuhl, E. 2019; 47 (9): 1941–59

  View details for DOI 10.1007/s10439-018-02148-2

  View details for Web of Science ID 000489738300008

• Growth and remodelling of living tissues: perspectives, challenges and opportunities. Journal of the Royal Society, Interface Ambrosi, D., Ben Amar, M., Cyron, C. J., DeSimone, A., Goriely, A., Humphrey, J. D., Kuhl, E. 2019; 16 (157): 20190233

  Abstract

  One of the most remarkable differences between classical engineering materials and living matter is the ability of the latter to grow and remodel in response to diverse stimuli. The mechanical behaviour of living matter is governed not only by an elastic or viscoelastic response to loading on short time scales up to several minutes, but also by often crucial growth and remodelling responses on time scales from hours to months. Phenomena of growth and remodelling play important roles, for example during morphogenesis in early life as well as in homeostasis and pathogenesis in adult tissues, which often adapt to changes in their chemo-mechanical environment as a result of ageing, diseases, injury or surgical intervention. Mechano-regulated growth and remodelling are observed in various soft tissues, ranging from tendons and arteries to the eye and brain, but also in bone, lower organisms and plants. Understanding and predicting growth and remodelling of living systems is one of the most important challenges in biomechanics and mechanobiology. This article reviews the current state of growth and remodelling as it applies primarily to soft tissues, and provides a perspective on critical challenges and future directions.

  View details for DOI 10.1098/rsif.2019.0233

  View details for PubMedID 31431183

• Predicting critical drug concentrations and torsadogenic risk using a multiscale exposure-response simulator PROGRESS IN BIOPHYSICS & MOLECULAR BIOLOGY Costabal, F., Yao, J., Sher, A., Kuhl, E. 2019; 144: 61–76

  View details for DOI 10.1016/j.pbiomolbio.2018.10.003

  View details for Web of Science ID 000472812100007

• Revisiting the wrinkling of elastic bilayers I: linear analysis PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Alawiye, H., Kuhl, E., Goriely, A. 2019; 377 (2144)

  View details for DOI 10.1098/rsta.2018.0076

  View details for Web of Science ID 000465498500009

• Revisiting the wrinkling of elastic bilayersI: linear analysis. Philosophical transactions. Series A, Mathematical, physical, and engineering sciences Alawiye, H., Kuhl, E., Goriely, A. 2019; 377 (2144): 20180076

  Abstract

  Wrinkling is a universal instability occurring in a wide variety of engineering and biological materials. It has been studied extensively for many different systems but a full description is still lacking. Here, we provide a systematic analysis of the wrinkling of a thin hyperelastic film over a substrate in plane strain using stream functions. For comparison, we assume that wrinkling is generated either by the isotropic growth of the film or by the lateral compression of the entire system. We perform an exhaustive linear analysis of the wrinkling problem for all stiffness ratios and under a variety of additional boundary and material effects. Namely, we consider the effect of added pressure, surface tension, an upper substrate and fibres. We obtain analytical estimates of the instability in the two asymptotic regimes of long and short wavelengths. This article is part of the theme issue 'Rivlin's legacy in continuum mechanics and appliedmathematics'.

  View details for PubMedID 30879422

• Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Costabal, F., Matsuno, K., Yao, J., Perdikaris, P., Kuhl, E. 2019; 348: 313–33

  View details for DOI 10.1016/j.cma.2019.01.033

  View details for Web of Science ID 000462472400012

• Machine learning in drug development: Characterizing the effect of 30 drugs on the QT interval using Gaussian process regression, sensitivity analysis, and uncertainty quantification. Computer methods in applied mechanics and engineering Costabal, F. S., Matsuno, K., Yao, J., Perdikaris, P., Kuhl, E. 2019; 348: 313-333

  Abstract

  Prolonged QT intervals are a major risk factor for ventricular arrhythmias and a leading cause of sudden cardiac death. Various drugs are known to trigger QT interval prolongation and increase the proarrhythmic potential. Yet, how precisely the action of drugs on the cellular level translates into QT interval prolongation on the whole organ level remains insufficiently understood. Here we use machine learning techniques to systematically characterize the effect of 30 common drugs on the QT interval. We combine information from high fidelity three-dimensional human heart simulations with low fidelity one-dimensional cable simulations to build a surrogate model for the QT interval using multi-fidelity Gaussian process regression. Once trained and cross-validated, we apply our surrogate model to perform sensitivity analysis and uncertainty quantification. Our sensitivity analysis suggests that compounds that block the rapid delayed rectifier potassium current IKr have the greatest prolonging effect of the QT interval, and that blocking the L-type calcium current ICaL and late sodium current INaL shortens the QT interval. Our uncertainty quantification allows us to propagate the experimental variability from individual block-concentration measurements into the QT interval and reveals that QT interval uncertainty is mainly driven by the variability in IKr block. In a final validation study, we demonstrate an excellent agreement between our predicted QT interval changes and the changes observed in a randomized clinical trial for the drugs dofetilide, quinidine, ranolazine, and verapamil. We anticipate that both the machine learning methods and the results of this study will have great potential in the efficient development of safer drugs.

  View details for DOI 10.1016/j.cma.2019.01.033

  View details for PubMedID 32863454

  View details for PubMedCentralID PMC7454226

• A physics-based model explains the prion-like features of neurodegeneration in Alzheimer's disease, Parkinson's disease, and amyotrophic lateral sclerosis JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Weickenmeier, J., Jucker, M., Goriely, A., Kuhl, E. 2019; 124: 264–81

  View details for DOI 10.1016/j.jmps.2018.10.013

  View details for Web of Science ID 000459368300015

• Understanding the mechanical link between oriented cell division and cerebellar morphogenesis. Soft matter Lejeune, E., Dortdivanlioglu, B., Kuhl, E., Linder, C. 2019

  Abstract

  The cerebellum is a tightly folded structure located at the back of the head. Unlike the folds of the cerebrum, the folds of the cerebellum are aligned such that the external surface appears to be covered in parallel grooves. Experiments have shown that anchoring center initiation drives cerebellar foliation. However, the mechanism guiding the location of these anchoring centers, and subsequently cerebellar morphology, remains poorly understood. In particular, there is no definitive mechanistic explanation for the preferential emergence of parallel folds instead of an irregular folding pattern like in the cerebral cortex. Here we use mechanical modeling on the cellular and tissue scales to show that the oriented granule cell division observed in the experimental setting leads to the characteristic parallel folding pattern of the cerebellum. Specifically, we propose an agent-based model of cell clones, a strategy for propagating information from our in silico cell clones to the tissue scale, and an analytical solution backed by numerical results to understand how differential growth between the cerebellar layers drives geometric instability in three dimensional space on the tissue scale. This proposed mechanical model provides further insight into the process of anchoring center initiation and establishes a framework for future multiscale mechanical analysis of developing organs.

  View details for PubMedID 30758032

• Do annuloplasty rings designed to treat ischemic/functional mitral regurgitation alter left-ventricular dimensions in the acutely ischemic ovine heart? The Journal of thoracic and cardiovascular surgery Bothe, W., Escobar Kvitting, J., Rausch, M. K., Timek, T. A., Swanson, J. C., Liang, D. H., Walther, M., Kuhl, E., Ingels, N. B., Miller, D. C. 2019

  Abstract

  OBJECTIVE: To quantify the effects of annuloplasty rings designed to treat ischemic/functional mitral regurgitation on left ventricular septal-lateral (S-L) and commissure-commissure (C-C) dimensions.METHODS: Radiopaque markers were placed as opposing pairs on the S-L and C-C aspects of the mitral annulus and the basal, equatorial, and apical level of the left ventricle (LV) in 30 sheep. Ten true-sized Carpentier-Edwards Physio (PHY), Edwards IMR ETlogix (ETL), and GeoForm (GEO; all from Edwards Lifesciences, Irvine, Calif) annuloplasty rings were inserted in a releasable fashion. After 90seconds of left circumflex artery occlusion with the ring implanted (RING), 4-dimensional marker coordinates were obtained using biplane videofluoroscopy. After ring release, another data set was acquired after another 90seconds of left circumflex artery occlusion (NO RING). S-L and C-C diameters were computed as the distances between the respective marker pairs at end-diastole. Percent change in diameters was calculated between RING versus NO RING as 100*(diameter in centimeters [RING]-diameter in centimeters [NO RING])/diameter in centimeters [NO RING]).RESULTS: Compared with NO RING, all ring types (PHY, ETL, and GEO) reduced mitral annular S-L dimensions by -20.7±5.6%, -26.8±3.9%, and -34.5±3.8%, respectively. GEO reduced the S-L dimensions of the LV at the basal level only by -2.3±2.4%, whereas all other S-L dimensions of the LV remained unchanged with all 3 rings implanted. PHY, ETL, and GEO reduced mitral annular C-C dimensions by -17.5±4.8%, -19.6±2.5, and -8.3±4.9%, respectively, but none of the rings altered the C-C dimensions of the LV.CONCLUSIONS: Despite radical reduction of mitral annular size, disease-specific ischemic/functional mitral regurgitation annuloplasty rings do not induce relevantchanges of left ventricular dimensions in the acutely ischemic ovine heart.

  View details for PubMedID 30803776

• Prion-like spreading of Alzheimer's disease within the brain's connectome. Journal of the Royal Society, Interface Fornari, S. n., Schäfer, A. n., Jucker, M. n., Goriely, A. n., Kuhl, E. n. 2019; 16 (159): 20190356

  Abstract

  The prion hypothesis states that misfolded proteins can act as infectious agents that template the misfolding and aggregation of healthy proteins to transmit a disease. Increasing evidence suggests that pathological proteins in neurodegenerative diseases adopt prion-like mechanisms and spread across the brain along anatomically connected networks. Local kinetic models of protein misfolding and global network models of protein spreading provide valuable insight into several aspects of prion-like diseases. Yet, to date, these models have not been combined to simulate how pathological proteins multiply and spread across the human brain. Here, we create an efficient and robust tool to simulate the spreading of misfolded protein using three classes of kinetic models, the Fisher-Kolmogorov model, the Heterodimer model and the Smoluchowski model. We discretize their governing equations using a human brain network model, which we represent as a weighted Laplacian graph generated from 418 brains from the Human Connectome Project. Its nodes represent the anatomic regions of interest and its edges are weighted by the mean fibre number divided by the mean fibre length between any two regions. We demonstrate that our brain network model can predict the histopathological patterns of Alzheimer's disease and capture the key characteristic features of finite-element brain models at a fraction of their computational cost: simulating the spatio-temporal evolution of aggregate size distributions across the human brain throughout a period of 40 years takes less than 7 s on a standard laptop computer. Our model has the potential to predict biomarker curves, aggregate size distributions, infection times, and the effects of therapeutic strategies including reduced production and increased clearance of misfolded protein.

  View details for DOI 10.1098/rsif.2019.0356

  View details for PubMedID 31615329

• Spatially-extended nucleation-aggregation-fragmentation models for the dynamics of prion-like neurodegenerative protein-spreading in the brain and its connectome. Journal of theoretical biology Fornari, S. n., Schäfer, A. n., Kuhl, E. n., Goriely, A. n. 2019: 110102

  Abstract

  The prion-like hypothesis of neurodegenerative diseases states that the accumulation of misfolded proteins in the form of aggregates is responsible for tissue death and its associated neurodegenerative pathology and cognitive decline. Some disease-specific misfolded proteins can interact with healthy proteins to form long chains that are transported through the brain along axonal pathways. Since aggregates of different sizes have different transport properties and toxicity, it is important to follow independently their evolution in space and time. Here, we model the spreading and propagation of aggregates of misfolded proteins in the brain using the general Smoluchowski theory of nucleation, aggregation, and fragmentation. The transport processes considered here are either anisotropic diffusion along axonal bundles or discrete Laplacian transport along a network. In particular, we model the spreading and aggregation of both amyloid-β and τ molecules in the brain connectome. We show that these two models lead to different size distributions and different propagation along the network. A detailed analysis of these two models reveals the existence of four different stages with different dynamics and invasive properties.

  View details for DOI 10.1016/j.jtbi.2019.110102

  View details for PubMedID 31809717

• Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci. Physical review letters Holland, M., Budday, S., Goriely, A., Kuhl, E. 2018; 121 (22): 228002

  Abstract

  Wrinkling instabilities appear in soft materials when a flat elastic layer on an elastic substrate is sufficiently stressed that it buckles with a wavy pattern to minimize the energy of the system. This instability is known to play an important role in engineering, but it also appears in many biological systems. In these systems, the stresses responsible for the wrinkling instability are often created through differential growth of the two layers. Beyond the instability, the upper and lower sides of the elastic layer are subject to different forces. This difference in forces leads to an interesting symmetry breaking whereby the thickness becomes larger at ridges than at valleys. Here we carry out an extensive analysis of this phenomenon by combining analytical, computational, and simple polymer experiments to show that symmetry breaking is a generic property of such systems. We apply our idea to the cortical folding of the brain for which it has been known for over a century that there is a thickness difference between gyri and sulci. An extensive analysis of hundreds of human brains reveals a systematic region-dependent thickness variation. Our results suggest that the evolving thickness patterns during brain development, similar to our polymer experiments, follow simple physics-based laws: Gyri are universally thicker than sulci.

  View details for DOI 10.1103/PhysRevLett.121.228002

  View details for PubMedID 30547630

• Symmetry Breaking in Wrinkling Patterns: Gyri Are Universally Thicker than Sulci PHYSICAL REVIEW LETTERS Holland, M., Budday, S., Goriely, A., Kuhl, E. 2018; 121 (22)

  View details for DOI 10.1103/PhysRevLett.121.228002

  View details for Web of Science ID 000451581600020

• Modeling the Axon as an Active Partner with the Growth Cone in Axonal Elongation BIOPHYSICAL JOURNAL de Rooij, R., Kuhl, E., Miller, K. E. 2018; 115 (9): 1783–95

  View details for DOI 10.1016/j.bpj.2018.08.047

  View details for Web of Science ID 000449422100019

• Predicting critical drug concentrations and torsadogenic risk using a multiscale exposure-response simulator. Progress in biophysics and molecular biology Sahli Costabal, F., Yao, J., Sher, A., Kuhl, E. 2018

  Abstract

  Torsades de pointes is a serious side effect of many drugs that can trigger sudden cardiac death, even in patients with structurally normal hearts. Torsadogenic risk has traditionally been correlated with the blockage of a specific potassium channel and a prolonged recovery period in the electrocardiogram. However, the precise mechanisms by which single channel block translates into heart rhythm disorders remain incompletely understood. Here we establish a multiscale exposure-response simulator that converts block-concentration characteristics from single cell recordings into three-dimensional excitation profiles and electrocardiograms to rapidly assess torsadogenic risk. For the drug dofetilide, we characterize the QT interval and heart rate at different drug concentrations and identify the critical concentration at the onset of torsades de pointes: For dofetilide concentrations of 2x, 3x, and 4x, as multiples of the free plasma concentration Cmax=2.1nM, the QT interval increased by+62.0%,+71.2%, and+82.3% compared to baseline, and the heart rate changed by-21.7%,-23.3%, and+88.3%. The last number indicates that, at the critical concentration of 4x, the heart spontaneously developed an episode of a torsades-like arrhythmia. Strikingly, this critical drug concentration is higher than the concentration estimated from early afterdepolarizations in single cells and lower than in one-dimensional cable models. Our results highlight the importance of whole heart modeling and explain, at least in part, why current regulatory paradigms often fail to accurately quantify the pro-arrhythmic potential of a drug. Our exposure-response simulator could provide a more mechanistic assessment of pro-arrhythmic risk and help establish science-based guidelines to reduce rhythm disorders, design safer drugs, and accelerate drug development.

  View details for PubMedID 30482568

• The Shrinking Brain: Cerebral Atrophy Following Traumatic Brain Injury. Annals of biomedical engineering Harris, T. C., de Rooij, R., Kuhl, E. 2018

  Abstract

  Cerebral atrophy in response to traumatic brain injury is a well-documented phenomenon in both primary investigations and review articles. Recent atrophy studies focus on exploring the region-specific patterns of cerebral atrophy; yet, there is no study that analyzes and synthesizes the emerging atrophy patterns in a single comprehensive review. Here we attempt to fill this gap in our current knowledge by integrating the current literature into a cohesive theory of preferential brain tissue loss and by identifying common risk factors for accelerated atrophy progression. Our review reveals that observations for mild traumatic brain injury remain inconclusive, whereas observations for moderate-to-severe traumatic brain injury converge towards robust patterns: brain tissue loss is on the order of 5% per year, and occurs in the form of generalized atrophy, across the entire brain, or focal atrophy, in specific brain regions. The most common regions of focal atrophy are the thalamus, hippocampus, and cerebellum in gray matter and the corpus callosum, corona radiata, and brainstem in white matter. We illustrate the differences of generalized and focal gray and white matter atrophy on emerging deformation and stress profiles across the whole brain using computational simulation. The characteristic features of our atrophy simulations-a widening of the cortical sulci, a gradual enlargement of the ventricles, and a pronounced cortical thinning-agree well with clinical observations. Understanding region-specific atrophy patterns in response to traumatic brain injury has significant implications in modeling, simulating, and predicting injury outcomes. Computational modeling of brain atrophy could open new strategies for physicians to make informed decisions for whom, how, and when to administer pharmaceutical treatment to manage the chronic loss of brain structure and function.

  View details for PubMedID 30341741

• Multiphysics of Prionlike Diseases: Progression and Atrophy. Physical review letters Weickenmeier, J., Kuhl, E., Goriely, A. 2018; 121 (15): 158101

  Abstract

  Many neurodegenerative diseases are related to the propagation and accumulation of toxic proteins throughout the brain. The lesions created by aggregates of these toxic proteins further lead to cell death and accelerated tissue atrophy. A striking feature of some of these diseases is their characteristic pattern and evolution, leading to well-codified disease stages visible to neuropathology and associated with various cognitive deficits and pathologies. Here, we simulate the anisotropic propagation and accumulation of toxic proteins in full brain geometry. We show that the same model with different initial seeding zones reproduces the characteristic evolution of different prionlike diseases. We also recover the expected evolution of the total toxic protein load. Finally, we couple our transport model to a mechanical atrophy model to obtain the typical degeneration patterns found in neurodegenerative diseases.

  View details for PubMedID 30362787

• Modeling the Axon as an Active Partner with the Growth Cone in Axonal Elongation. Biophysical journal de Rooij, R., Kuhl, E., Miller, K. E. 2018

  Abstract

  Forces generated by the growth cone are vital for the proper development of the axon and thus brain function. Although recent experiments show that forces are generated along the axon, it is unknown whether the axon plays a direct role in controlling growth cone advance. Here, we use analytic and finite element modeling of microtubule dynamics and the activity of the molecular motors myosin and dynein to investigate mechanical force balance along the length of the axon and its effects on axonal outgrowth. Our modeling indicates that the paradoxical effects of stabilizing microtubules and the consequences of microtubule disassembly on axonal outgrowth can be explained by changes in the passive and active mechanical properties of axons. Our findings suggest that a full understanding of growth cone motility requires a consideration of the mechanical contributions of the axon. Our study not only has potential applications during neurodevelopment but might also help identify strategies to manipulate and promote axonal regrowth to treat neurodegeneration.

  View details for PubMedID 30309611

• Mechanical Cues in Spinal Cord Injury. Biophysical journal Kuhl, E. 2018

  View details for PubMedID 30119835

• Physical Biology of Axonal Damage FRONTIERS IN CELLULAR NEUROSCIENCE de Rooij, R., Kuhl, E. 2018; 12: 144

  Abstract

  Excessive physical impacts to the head have direct implications on the structural integrity at the axonal level. Increasing evidence suggests that tau, an intrinsically disordered protein that stabilizes axonal microtubules, plays a critical role in the physical biology of axonal injury. However, the precise mechanisms of axonal damage remain incompletely understood. Here we propose a biophysical model of the axon to correlate the dynamic behavior of individual tau proteins under external physical forces to the evolution of axonal damage. To propagate damage across the scales, we adopt a consistent three-step strategy: First, we characterize the axonal response to external stretches and stretch rates for varying tau crosslink bond strengths using a discrete axonal damage model. Then, for each combination of stretch rates and bond strengths, we average the axonal force-stretch response of n = 10 discrete simulations, from which we derive and calibrate a homogenized constitutive model. Finally, we embed this homogenized model into a continuum axonal damage model of [1-d]-type in which d is a scalar damage parameter that is driven by the axonal stretch and stretch rate. We demonstrate that axonal damage emerges naturally from the interplay of physical forces and biological crosslinking. Our study reveals an emergent feature of the crosslink dynamics: With increasing loading rate, the axonal failure stretch increases, but axonal damage evolves earlier in time. For a wide range of physical stretch rates, from 0.1 to 10 /s, and biological bond strengths, from 1 to 100 pN, our model predicts a relatively narrow window of critical damage stretch thresholds, from 1.01 to 1.30, which agrees well with experimental observations. Our biophysical damage model can help explain the development and progression of axonal damage across the scales and will provide useful guidelines to identify critical damage level thresholds in response to excessive physical forces.

  View details for PubMedID 29928193

• Improving tissue expansion protocols through computational modeling JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Lee, T., Vaca, E. E., Ledwon, J. K., Bae, H., Topczewska, J. M., Turin, S. Y., Kuhl, E., Gosain, A. K., Tepole, A. 2018; 82: 224–34

  Abstract

  Tissue expansion is a common technique in reconstructive surgery used to grow skin in vivo for correction of large defects. Despite its popularity, there is a lack of quantitative understanding of how stretch leads to growth of new skin. This has resulted in several arbitrary expansion protocols that rely on the surgeon's personal training and experience rather than on accurate predictive models. For example, choosing between slow or rapid expansion, or small or large inflation volumes remains controversial. Here we explore four tissue expansion protocols by systematically varying the inflation volume and the protocol duration in a porcine model. The quantitative analysis combines three-dimensional photography, isogeometric kinematics, and finite growth theory. Strikingly, all four protocols generate similar peak stretches, but different growth patterns: Smaller filling volumes of 30 ml per inflation did not result in notable expander-induced growth neither for the short nor for the long protocol; larger filling volumes of 60 ml per inflation trigger skin adaptation, with larger expander-induced growth in regions of larger stretch, and more expander-induced growth for the 14-day compared to the 10-day expansion protocol. Our results suggest that expander-induced growth is not triggered by the local stretch alone. While stretch is clearly a driver for growth, the local stretch at a given point is not enough to predict the expander-induced growth at that location. From a clinical perspective, our study suggests that longer expansion protocols are needed to ensure sufficient growth of sizable skin patches.

  View details for PubMedID 29627733

• Predicting drug-induced arrhythmias by multiscale modeling INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Costabal, F., Yao, J., Kuhl, E. 2018; 34 (5): e2964

  Abstract

  Drugs often have undesired side effects. In the heart, they can induce lethal arrhythmias such as torsades de pointes. The risk evaluation of a new compound is costly and can take a long time, which often hinders the development of new drugs. Here, we establish a high-resolution, multiscale computational model to quickly assess the cardiac toxicity of new and existing drugs. The input of the model is the drug-specific current block from single cell electrophysiology; the output is the spatio-temporal activation profile and the associated electrocardiogram. We demonstrate the potential of our model for a low-risk drug, ranolazine, and a high-risk drug, quinidine: For ranolazine, our model predicts a prolonged QT interval of 19.4% compared with baseline and a regular sinus rhythm at 60.15 beats per minute. For quinidine, our model predicts a prolonged QT interval of 78.4% and a spontaneous development of torsades de pointes both in the activation profile and in the electrocardiogram. Our model reveals the mechanisms by which electrophysiological abnormalities propagate across the spatio-temporal scales, from specific channel blockage, via altered single cell action potentials and prolonged QT intervals, to the spontaneous emergence of ventricular tachycardia in the form of torsades de pointes. Our model could have important implications for researchers, regulatory agencies, and pharmaceutical companies on rationalizing safe drug development and reducing the time-to-market of new drugs.

  View details for PubMedID 29424967

• A physical multifield model predicts the development of volume and structure in the human brain JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS de Rooij, R., Kuhl, E. 2018; 112: 563–76

  View details for DOI 10.1016/j.jmps.2017.12.011

  View details for Web of Science ID 000426536400031

• Interpreting Activation Mapping of Atrial Fibrillation: A Hybrid Computational/Physiological Study ANNALS OF BIOMEDICAL ENGINEERING Costabal, F., Zaman, J. B., Kuhl, E., Narayan, S. M. 2018; 46 (2): 257–69

  Abstract

  Atrial fibrillation is the most common rhythm disorder of the heart associated with a rapid and irregular beating of the upper chambers. Activation mapping remains the gold standard to diagnose and interpret atrial fibrillation. However, fibrillatory activation maps are highly sensitive to far-field effects, and often disagree with other optical mapping modalities. Here we show that computational modeling can identify spurious non-local components of atrial fibrillation electrograms and improve activation mapping. We motivate our approach with a cohort of patients with potential drivers of persistent atrial fibrillation. In a computational study using a monodomain Maleckar model, we demonstrate that in organized rhythms, electrograms successfully track local activation, whereas in atrial fibrillation, electrograms are sensitive to spiral wave distance and number, spiral tip trajectories, and effects of fibrosis. In a clinical study, we analyzed n = 15 patients with persistent atrial fibrillation that was terminated by limited ablation. In five cases, traditional activation maps revealed a spiral wave at sites of termination; in ten cases, electrogram timings were ambiguous and activation maps showed incomplete reentry. By adjusting electrogram timing through computational modeling, we found rotational activation, which was undetectable with conventional methods. Our results demonstrate that computational modeling can identify non-local deflections to improve activation mapping and explain how and where ablation can terminate persistent atrial fibrillation. Our hybrid computational/physiological approach has the potential to optimize map-guided ablation and improve ablation therapy in atrial fibrillation.

  View details for PubMedID 29214421

  View details for PubMedCentralID PMC5880222

• Growth and remodeling play opposing roles during postnatal human heart valve development SCIENTIFIC REPORTS Oomen, P. A., Holland, M. A., Bouten, C. C., Kuhl, E., Loerakker, S. 2018; 8: 1235

  Abstract

  Tissue growth and remodeling are known to govern mechanical homeostasis in biological tissue, but their relative contributions to homeostasis remain unclear. Here, we use mechanical models, fueled by experimental findings, to demonstrate that growth and remodeling have different effects on heart valve stretch homeostasis during physiological postnatal development. Two developmental stages were considered: early-stage (from infant to adolescent) and late-stage (from adolescent to adult) development. Our models indicated that growth and remodeling play opposing roles in preserving tissue stretch and with time. During early-stage development, excessive tissue stretch was decreased by tissue growth and increased by remodeling. In contrast, during late-stage development tissue stretch was decreased by remodeling and increased by growth. Our findings contribute to an improved understanding of native heart valve adaptation throughout life, and are highly relevant for the development of tissue-engineered heart valves.

  View details for PubMedID 29352179

• Microtubule Polymerization and Cross-Link Dynamics Explain Axonal Stiffness and Damage BIOPHYSICAL JOURNAL de Rooij, R., Kuhl, E. 2018; 114 (1): 201–12

  Abstract

  Axonal damage is a critical indicator for traumatic effects of physical impact to the brain. However, the precise mechanisms of axonal damage are still unclear. Here, we establish a mechanistic and highly dynamic model of the axon to explore the evolution of damage in response to physical forces. Our axon model consists of a bundle of dynamically polymerizing and depolymerizing microtubules connected by dynamically detaching and reattaching cross-links. Although the probability of cross-link attachment depends exclusively on thermal fluctuations, the probability of detachment increases in the presence of physical forces. We systematically probe the landscape of axonal stretch and stretch rate and characterize the overall axonal force, stiffness, and damage as a direct result of the interplay between microtubule and cross-link dynamics. Our simulations reveal that slow loading is dominated by cross-link dynamics, a net reduction of cross-links, and a gradual accumulation of damage, whereas fast loading is dominated by cross-link deformations, a rapid increase in stretch, and an immediate risk of rupture. Microtubule polymerization and depolymerization decrease the overall axonal stiffness, but do not affect the evolution of damage at timescales relevant to axonal failure. Our study explains different failure mechanisms in the axon as emergent properties of microtubule polymerization, cross-link dynamics, and physical forces. We anticipate that our model will provide insight into causal relations by which molecular mechanisms determine the timeline and severity of axon damage after a physical impact to the brain.

  View details for PubMedID 29320687

  View details for PubMedCentralID PMC5773766

• Magnetic resonance elastography of the brain: A comparison between pigs and humans JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Weickenmeier, J., Kurt, M., Ozkaya, E., Wintermark, M., Pauly, K., Kuhl, E. 2018; 77: 702–10

  Abstract

  Magnetic resonance elastography holds promise as a non-invasive, easy-to-use, in vivo biomarker for neurodegenerative diseases. Throughout the past decade, pigs have gained increased popularity as large animal models for human neurodegeneration. However, the volume of a pig brain is an order of magnitude smaller than the human brain, its skull is 40% thicker, and its head is about twice as big. This raises the question to which extent established vibration devices, actuation frequencies, and analysis tools for humans translate to large animal studies in pigs. Here we explored the feasibility of using human brain magnetic resonance elastography to characterize the dynamic properties of the porcine brain. In contrast to humans, where vibration devices induce an anterior-posterior displacement recorded in transverse sections, the porcine anatomy requires a dorsal-ventral displacement recorded in coronal sections. Within these settings, we applied a wide range of actuation frequencies, from 40Hz to 90Hz, and recorded the storage and loss moduli for human and porcine brains. Strikingly, we found that optimal actuation frequencies for humans translate one-to-one to pigs and reliably generate shear waves for elastographic post-processing. In a direct comparison, human and porcine storage and loss moduli followed similar trends and increased with increasing frequency. When translating these frequency-dependent storage and loss moduli into the frequency-independent stiffnesses and viscosities of a standard linear solid model, we found human values of μ1=1.3kPa, μ2=2.1kPa, and η=0.025kPas and porcine values of μ1=2.0kPa, μ2=4.9kPa, and η=0.046kPas. These results suggest that living human brain is softer and less viscous than dead porcine brain. Our study compares, for the first time, magnetic resonance elastography in human and porcine brains, and paves the way towards systematic interspecies comparison studies and ex vivo validation of magnetic resonance elastography as a whole.

  View details for PubMedID 28919161

• Predicting the cardiac toxicity of drugs using a novel multiscale exposure-response simulator COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Costabal, F., Yao, J., Kuhl, E. 2018; 21 (3): 232–46

  Abstract

  A common but serious side effect of many drugs is torsades de pointes, a rhythm disorder that can have fatal consequences. Torsadogenic risk has traditionally been associated with blockage of a specific potassium channel and an increased recovery period in the electrocardiogram. However, the mechanisms that trigger torsades de pointes remain incompletely understood. Here we establish a computational model to explore how drug-induced effects propagate from the single channel, via the single cell, to the whole heart level. Our mechanistic exposure-response simulator translates block-concentration characteristics for arbitrary drugs into three-dimensional excitation profiles and electrocardiogram recordings to rapidly assess torsadogenic risk. For the drug of dofetilide, we show that this risk is highly dose-dependent: at a concentration of 1x, QT prolongation is 55% but the heart maintains its regular sinus rhythm; at 5.7x, QT prolongation is 102% and the heart spontaneously transitions into torsades de points; at 30x, QT prolongation is 132% and the heart adapts a quasi-depolarized state with numerous rapidly flickering local excitations. Our simulations suggest that neither potassium channel blockage nor QT interval prolongation alone trigger torsades de pointes. The underlying mechanism predicted by our model is early afterdepolarization, which translates into pronounced U waves in the electrocardiogram, a signature that is correctly predicted by our model. Beyond the risk assessment of existing drugs, our exposure-response simulator can become a powerful tool to optimize the co-administration of drugs and, ultimately, guide the design of new drugs toward reducing life threatening drug-induced rhythm disorders in the heart.

  View details for PubMedID 29493299

• Determining the Differential Effects of Stretch and Growth in Tissue-Expanded Skin: Combining Isogeometric Analysis and Continuum Mechanics in a Porcine Model DERMATOLOGIC SURGERY Purnell, C. A., Gart, M. S., Buganza-Tepole, A., Tomaszewski, J. P., Topczewska, J. M., Kuhl, E., Gosain, A. K. 2018; 44 (1): 48–52

  Abstract

  The relative effects of skin growth and stretch during tissue expansion have not been studied. The authors use novel analytic techniques that allow calculation of these factors at any point of a skin patch.The authors sought to determine how stretch and growth change with different expansion rates and to correlate these values with histologic and cellular changes in skin.Two minipigs were implanted with a total of 5 tissue expanders under tattooed skin grids. One pig was expanded over 35 days and the second over 15 days. Isogeometric analysis allowed calculation of growth and stretch. Expanders with similar total deformation were compared between protocols. Regression analysis determined predictive effects of stretch and growth on histologic data from the second animal.Deformation was more attributable to stretch in rapid than in slow expansion (1.40 vs1.12, p < .001). Growth was higher in slow expansion than in rapid (1.52 vs 1.07, p < .001). Both growth and stretch predicted epidermal thickness, dermal thinning, and keratinocyte proliferation. Growth predicted vascularity.Isogeometric analysis allows determination of precise surface area changes for correlation to microscopic-level data. Using the model, the authors identified that skin deformation in rapid expansion is more attributable to stretch.

  View details for PubMedID 28692604

• Pilot Findings of Brain Displacements and Deformations during Roller Coaster Rides JOURNAL OF NEUROTRAUMA Kuo, C., Wu, L. C., Ye, P. P., Laksari, K., Camarillo, D. B., Kuhl, E. 2017; 34 (22): 3198–3205

  Abstract

  With 300,000,000 riders annually, roller coasters are a popular recreational activity. Although the number of roller coaster injuries is relatively low, the precise effect of roller coaster rides on our brains remains unknown. Here we present the quantitative characterization of brain displacements and deformations during roller coaster rides. For two healthy adult male subjects, we recorded head accelerations during three representative rides, and, for comparison, during running and soccer headers. From the recordings, we simulated brain displacements and deformations using rigid body dynamics and finite element analyses. Our findings show that despite having lower linear accelerations than sports head impacts, roller coasters may lead to brain displacements and strains comparable to mild soccer headers. The peak change in angular velocity on the rides was 9.9 rad/sec, which was higher than the 5.6 rad/sec in soccer headers with ball velocities reaching 7 m/sec. Maximum brain surface displacements of 4.0 mm and maximum principal strains of 7.6% were higher than in running and similar to soccer headers, but below the reported average concussion strain. Brain strain rates during roller coaster rides were similar to those in running, and lower than those in soccer headers. Strikingly, on the same ride and at a similar position, the two subjects experienced significantly different head kinematics and brain deformation. These results indicate that head motion and brain deformation during roller coaster rides are highly sensitive to individual subjects. Although our study suggests that roller coaster rides do not present an immediate risk of acute brain injury, their long-term effects require further longitudinal study.

  View details for PubMedID 28683585

• Dimensional, Geometrical, and Physical Constraints in Skull Growth. Physical review letters Weickenmeier, J., Fischer, C., Carter, D., Kuhl, E., Goriely, A. 2017; 118 (24): 248101

  Abstract

  After birth, the skull grows and remodels in close synchrony with the brain to allow for an increase in intracranial volume. Increase in skull area is provided primarily by bone accretion at the sutures. Additional remodeling, to allow for a change in curvatures, occurs by resorption on the inner surface of the bone plates and accretion on their outer surfaces. When a suture fuses too early, normal skull growth is disrupted, leading to a deformed final skull shape. The leading theory assumes that the main stimulus for skull growth is provided by mechanical stresses. Based on these ideas, we first discuss the dimensional, geometrical, and kinematic synchrony between brain, skull, and suture growth. Second, we present two mechanical models for skull growth that account for growth at the sutures and explain the various observed dysmorphologies. These models demonstrate the particular role of physical and geometrical constraints taking place in skull growth.

  View details for DOI 10.1103/PhysRevLett.118.248101

  View details for PubMedID 28665667

• The importance of mechano-electrical feedback and inertia in cardiac electromechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Costabal, F., Concha, F. A., Hurtado, D. E., Kuhl, E. 2017; 320: 352–68

  Abstract

  In the past years, a number cardiac electromechanics models have been developed to better understand the excitation-contraction behavior of the heart. However, there is no agreement on whether inertial forces play a role in this system. In this study, we assess the influence of mass in electromechanical simulations, using a fully coupled finite element model. We include the effect of mechano-electrical feedback via stretch activated currents. We compare five different models: electrophysiology, electromechanics, electromechanics with mechano-electrical feedback, electromechanics with mass, and electromechanics with mass and mechano-electrical feedback. We simulate normal conduction to study conduction velocity and spiral waves to study fibrillation. During normal conduction, mass in conjunction with mechano-electrical feedback increased the conduction velocity by 8.12% in comparison to the plain electrophysiology case. During the generation of a spiral wave, mass and mechano-electrical feedback generated secondary wavefronts, which were not present in any other model. These secondary wavefronts were initiated in tensile stretch regions that induced electrical currents. We expect that this study will help the research community to better understand the importance of mechanoelectrical feedback and inertia in cardiac electromechanics.

  View details for PubMedID 29056782

  View details for PubMedCentralID PMC5646712

• Wrinkling instabilities in soft bilayered systems PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Budday, S., Andres, S., Walter, B., Steinmann, P., Kuhl, E. 2017; 375 (2093)

  Abstract

  Wrinkling phenomena control the surface morphology of many technical and biological systems. While primary wrinkling has been extensively studied, experimentally, analytically and computationally, higher-order instabilities remain insufficiently understood, especially in systems with stiffness contrasts well below 100. Here, we use the model system of an elastomeric bilayer to experimentally characterize primary and secondary wrinkling at moderate stiffness contrasts. We systematically vary the film thickness and substrate prestretch to explore which parameters modulate the emergence of secondary instabilities, including period-doubling, period-tripling and wrinkle-to-fold transitions. Our experiments suggest that period-doubling is the favourable secondary instability mode and that period-tripling can emerge under disturbed boundary conditions. High substrate prestretch can suppress period-doubling and primary wrinkles immediately transform into folds. We combine analytical models with computational simulations to predict the onset of primary wrinkling, the post-buckling behaviour, secondary bifurcations and the wrinkle-to-fold transition. Understanding the mechanisms of pattern selection and identifying the critical control parameters of wrinkling will allow us to fabricate smart surfaces with tunable properties and to control undesired surface patterns like in the asthmatic airway.This article is part of the themed issue 'Patterning through instabilities in complex media: theory and applications.'

  View details for DOI 10.1098/rsta.2016.0163

  View details for Web of Science ID 000398215500009

  View details for PubMedID 28373385

• The mechanical importance of myelination in the central nervous system. Journal of the mechanical behavior of biomedical materials Weickenmeier, J., de Rooij, R., Budday, S., Ovaert, T. C., Kuhl, E. 2017

  Abstract

  Neurons in the central nervous system are surrounded and cross-linked by myelin, a fatty white substance that wraps around axons to create an electrically insulating layer. The electrical function of myelin is widely recognized; yet, its mechanical importance remains underestimated. Here we combined nanoindentation testing and histological staining to correlate brain stiffness to the degree of myelination in immature, pre-natal brains and mature, post-natal brains. We found that both gray and white matter tissue stiffened significantly (p≪0.001) upon maturation: the gray matter stiffness doubled from 0.31±0.20kPa pre-natally to 0.68±0.20kPa post-natally; the white matter stiffness tripled from 0.45±0.18kPa pre-natally to 1.33±0.64kPa post-natally. At the same time, the white matter myelin content increased significantly (p≪0.001) from 58±2% to 74±9%. White matter stiffness and myelin content were correlated with a Pearson correlation coefficient of ρ=0.92 (p≪0.001). Our study suggests that myelin is not only important to ensure smooth electrical signal propagation in neurons, but also to protect neurons against physical forces and provide a strong microstructural network that stiffens the white matter tissue as a whole. Our results suggest that brain tissue stiffness could serve as a biomarker for multiple sclerosis and other forms of demyelinating disorders. Understanding how tissue maturation translates into changes in mechanical properties and knowing the precise brain stiffness at different stages of life has important medical implications in development, aging, and neurodegeneration.

  View details for DOI 10.1016/j.jmbbm.2017.04.017

  View details for PubMedID 28462864

• Quantification of Strain in a Porcine Model of Skin Expansion Using Multi-View Stereo and Isogeometric Kinematics JOVE-JOURNAL OF VISUALIZED EXPERIMENTS Tepole, A. B., Vaca, E. E., Purnell, C. A., Gart, M., McGrath, J., Kuhl, E., Gosain, A. K. 2017

  Abstract

  Tissue expansion is a popular technique in plastic and reconstructive surgery that grows skin in vivo for correction of large defects such as burns and giant congenital nevi. Despite its widespread use, planning and executing an expansion protocol is challenging due to the difficulty in measuring the deformation imposed at each inflation step and over the length of the procedure. Quantifying the deformation fields is crucial, as the distribution of stretch over time determines the rate and amount of skin grown at the end of the treatment. In this manuscript, we present a method to study tissue expansion in order to gain quantitative knowledge of the deformations induced during an expansion process. This experimental protocol incorporates multi-view stereo and isogeometric kinematic analysis in a porcine model of tissue expansion. Multi-view stereo allows three-dimensional geometric reconstruction from uncalibrated sequences of images. The isogeometric kinematic analysis uses splines to describe the regional deformations between smooth surfaces with few mesh points. Our protocol has the potential to bridge the gap between basic scientific inquiry regarding the mechanics of skin expansion and the clinical setting. Eventually, we expect that the knowledge gained with our methodology will enable treatment planning using computational simulations of skin deformation in a personalized manner.

  View details for DOI 10.3791/55052

  View details for Web of Science ID 000401077600013

  View details for PubMedID 28448015

• Modeling molecular mechanisms in the axon COMPUTATIONAL MECHANICS de Rooij, R., Miller, K. E., Kuhl, E. 2017; 59 (3): 523-537

  View details for DOI 10.1007/s00466-016-1359-y

  View details for Web of Science ID 000394999900009

• The mechanics of decompressive craniectomy: Personalized simulations COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Weickenmeier, J., Butler, C. A., Young, P. G., Goriely, A., Kuhl, E. 2017; 314: 180-195

  View details for DOI 10.1016/j.cma.2016.08.011

  View details for Web of Science ID 000392782900011

• The Pursuit of Engineering the Ideal Heart Valve Replacement or Repair: A Special Issue of the Annals of Biomedical Engineering. Annals of biomedical engineering Dasi, L. P., Grande-Allen, J., Kunzelman, K., Kuhl, E. 2017; 45 (2): 307-309

  View details for DOI 10.1007/s10439-017-1801-0

  View details for PubMedID 28150054

• A virtual sizing tool for mitral valve annuloplasty. International journal for numerical methods in biomedical engineering Rausch, M. K., Zöllner, A. M., Genet, M., Baillargeon, B., Bothe, W., Kuhl, E. 2017; 33 (2)

  Abstract

  Functional mitral regurgitation, a backward leakage of the mitral valve, is a result of left ventricular growth and mitral annular dilatation. Its gold standard treatment is mitral annuloplasty, the surgical reduction in mitral annular area through the implantation of annuloplasty rings. Recurrent regurgitation rates may, however, be as high as 30% and more. While the degree of annular downsizing has been linked to improved long-term outcomes, too aggressive downsizing increases the risk of ring dehiscences and significantly impairs repair durability. Here, we prototype a virtual sizing tool to quantify changes in annular dimensions, surgically induced tissue strains, mitral annular stretches, and suture forces in response to mitral annuloplasty. We create a computational model of dilated cardiomyopathy onto which we virtually implant annuloplasty rings of different sizes. Our simulations confirm the common intuition that smaller rings are more invasive to the surrounding tissue, induce higher strains, and require larger suture forces than larger rings: The total suture force was 2.2 N for a 24-mm ring, 1.9 N for a 28-mm ring, and 0.8 N for a 32-mm ring. Our model predicts the highest risk of dehiscence in the septal and postero-lateral annulus where suture forces are maximal. These regions co-localize with regional peaks in myocardial strain and annular stretch. Our study illustrates the potential of realistic predictive simulations in cardiac surgery to identify areas at risk for dehiscence, guide the selection of ring size and shape, rationalize the design of smart annuloplasty rings and, ultimately, improve long-term outcomes after surgical mitral annuloplasty. Copyright © 2016 John Wiley & Sons, Ltd.

  View details for DOI 10.1002/cnm.2788

  View details for PubMedID 27028496

• Mechanical characterization of human brain tissue ACTA BIOMATERIALIA Budday, S., Sommer, G., Birkl, C., Langkammer, C., Haybaeck, J., Kohnert, J., Bauer, M., Paulsen, F., Steinmann, P., Kuhl, E., Holzapfel, G. A. 2017; 48: 319-340

  Abstract

  Mechanics are increasingly recognized to play an important role in modulating brain form and function. Computational simulations are a powerful tool to predict the mechanical behavior of the human brain in health and disease. The success of these simulations depends critically on the underlying constitutive model and on the reliable identification of its material parameters. Thus, there is an urgent need to thoroughly characterize the mechanical behavior of brain tissue and to identify mathematical models that capture the tissue response under arbitrary loading conditions. However, most constitutive models have only been calibrated for a single loading mode. Here, we perform a sequence of multiple loading modes on the same human brain specimen - simple shear in two orthogonal directions, compression, and tension - and characterize the loading-mode specific regional and directional behavior. We complement these three individual tests by combined multiaxial compression/tension-shear tests and discuss effects of conditioning and hysteresis. To explore to which extent the macrostructural response is a result of the underlying microstructural architecture, we supplement our biomechanical tests with diffusion tensor imaging and histology. We show that the heterogeneous microstructure leads to a regional but not directional dependence of the mechanical properties. Our experiments confirm that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry. Using our measurements, we compare the performance of five common constitutive models, neo-Hookean, Mooney-Rivlin, Demiray, Gent, and Ogden, and show that only the isotropic modified one-term Ogden model is capable of representing the hyperelastic behavior under combined shear, compression, and tension loadings: with a shear modulus of 0.4-1.4kPa and a negative nonlinearity parameter it captures the compression-tension asymmetry and the increase in shear stress under superimposed compression but not tension. Our results demonstrate that material parameters identified for a single loading mode fail to predict the response under arbitrary loading conditions. Our systematic characterization of human brain tissue will lead to more accurate computational simulations, which will allow us to determine criteria for injury, to develop smart protection systems, and to predict brain development and disease progression.There is a pressing need to characterize the mechanical behavior of human brain tissue under multiple loading conditions, and to identify constitutive models that are able to capture the tissue response under these conditions. We perform a sequence of experimental tests on the same brain specimen to characterize the regional and directional behavior, and we supplement our tests with DTI and histology to explore to which extent the macrostructural response is a result of the underlying microstructure. Results demonstrate that human brain tissue is nonlinear and viscoelastic, with a pronounced compression-tension asymmetry, and we show that the multiaxial data can best be captured by a modified version of the one-term Ogden model.

  View details for DOI 10.1016/j.actbio.2016.10.036

  View details for Web of Science ID 000393247000027

  View details for PubMedID 27989920

• Instabilities of soft films on compliant substrates JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Holland, M. A., Li, B., Feng, X. Q., Kuhl, E. 2017; 98: 350-365

  View details for DOI 10.1016/j.jmps.2016.09.012

  View details for Web of Science ID 000390972900019

• Passive Stretch Induces Structural and Functional Maturation of Engineered Heart Muscle as Predicted by Computational Modeling. Stem cells (Dayton, Ohio) Abilez, O. J., Tzatzalos, E. n., Yang, H. n., Zhao, M. T., Jung, G. n., Zöllner, A. M., Tiburcy, M. n., Riegler, J. n., Matsa, E. n., Shukla, P. n., Zhuge, Y. n., Chour, T. n., Chen, V. C., Burridge, P. W., Karakikes, I. n., Kuhl, E. n., Bernstein, D. n., Couture, L. A., Gold, J. D., Zimmermann, W. H., Wu, J. C. 2017

  Abstract

  The ability to differentiate human pluripotent stem cells (hPSCs) into cardiomyocytes (CMs) makes them an attractive source for repairing injured myocardium, disease modeling, and drug testing. Although current differentiation protocols yield hPSC-CMs to >90% efficiency, hPSC-CMs exhibit immature characteristics. With the goal of overcoming this limitation, we tested the effects of varying passive stretch on engineered heart muscle (EHM) structural and functional maturation, guided by computational modeling.Human embryonic stem cells (hESCs, H7 line) or human induced pluripotent stem cells (hiPSCs, IMR-90 line) were differentiated to human pluripotent stem cell-derived cardiomyocytes (hPSC-CMs) in vitro using a small molecule based protocol. hPSC-CMs were characterized by troponin(+) flow cytometry as well as electrophysiological measurements. Afterwards, 1.2 x 10(6) hPSC-CMs were mixed with 0.4 x 10(6) human fibroblasts (IMR-90 line) (3:1 ratio) and Type-I collagen. The blend was cast into custom-made 12-mm long polydimethylsiloxane (PDMS) reservoirs to vary nominal passive stretch of EHMs to 5, 7, or 9 mm. EHM characteristics were monitored for up to 50 days, with EHMs having a passive stretch of 7 mm giving the most consistent formation. Based on our initial macroscopic observations of EHM formation, we created a computational model that predicts the stress distribution throughout EHMs, which is a function of cellular composition, cellular ratio, and geometry. Based on this predictive modeling, we show cell alignment by immunohistochemistry and coordinated calcium waves by calcium imaging. Furthermore, coordinated calcium waves and mechanical contractions were apparent throughout entire EHMs. The stiffness and active forces of hPSC-derived EHMs are comparable to rat neonatal cardiomyocyte-derived EHMs. Three-dimensional EHMs display increased expression of mature cardiomyocyte genes including sarcomeric protein troponin-T, calcium and potassium ion channels, β-adrenergic receptors, and t-tubule protein caveolin-3.Passive stretch affects the structural and functional maturation of EHMs. Based on our predictive computational modeling, we show how to optimize cell alignment and calcium dynamics within EHMs. These findings provide a basis for the rational design of EHMs, which enables future scale-up productions for clinical use in cardiovascular tissue engineering. This article is protected by copyright. All rights reserved.

  View details for PubMedID 29086457

• The mechanics of decompressive craniectomy: Bulging in idealized geometries JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Weickenmeier, J., Kuhl, E., Goriely, A. 2016; 96: 572-590

  View details for DOI 10.1016/j.jmps.2016.08.009

  View details for Web of Science ID 000386744600032

• Terminating atrial fibrillation by cooling the heart. Heart rhythm Narayan, S. M., Baykaner, T., Sahli Costabal, F., Kuhl, E. 2016; 13 (11): 2259-2260

  View details for DOI 10.1016/j.hrthm.2016.07.017

  View details for PubMedID 27435588

• Stress Singularities in Swelling Soft Solids PHYSICAL REVIEW LETTERS Goriely, A., Weickenmeier, J., Kuhl, E. 2016; 117 (13)

  Abstract

  When a swelling soft solid is rigidly constrained on all sides except for a circular opening, it will bulge out to expand as observed during decompressive craniectomy, a surgical procedure used to reduce stresses in swollen brains. While the elastic energy of the solid decreases throughout this process, large stresses develop close to the opening. At the point of contact, the stresses exhibit a singularity similar to the ones found in the classic punch indentation problem. Here, we study the stresses generated by swelling and the evolution of the bulging shape associated with this process. We also consider the possibility of damage triggered by zones of either high shear stresses or high fiber stretches.

  View details for DOI 10.1103/PhysRevLett.117.138001

  View details for Web of Science ID 000383851000021

  View details for PubMedID 27715096

• Brain stiffness increases with myelin content. Acta biomaterialia Weickenmeier, J., de Rooij, R., Budday, S., Steinmann, P., Ovaert, T. C., Kuhl, E. 2016; 42: 265-272

  Abstract

  Brain stiffness plays an important role in neuronal development and disease, but reported stiffness values vary significantly for different species, for different brains, and even for different regions within the same brain. Despite extensive research throughout the past decade, the mechanistic origin of these stiffness variations remains elusive. Here we show that brain tissue stiffness is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. In 116 indentation tests of six freshly harvested bovine brains, we found that the cerebral stiffnesses of 1.33±0.63kPa in white matter and 0.68±0.20kPa in gray matter were significantly different (p<0.01). Strikingly, while the inter-specimen variation was rather moderate, the minimum and maximum cerebral white matter stiffnesses of 0.59±0.19 kPa and 2.36±0.64kPa in each brain varied by a factor of four on average. To provide a mechanistic interpretation for this variation, we performed a histological characterization of the tested brain regions. We stained the samples with hematoxylin and eosin and luxol fast blue and quantified the local myelin content using image analysis. Interestingly, we found that the cerebral white matter stiffness increased with increasing myelin content, from 0.72kPa at a myelin content of 64-2.45kPa at a myelin content of 89%, with a Pearson correlation coefficient of ρ=0.91 (p<0.01). This direct correlation could have significant neurological implications. During development, our results could help explain why immature, incompletely myelinated brains are softer than mature, myelinated brains and more vulnerable to mechanical insult as evident, for example, in shaken baby syndrome. During demyelinating disease, our findings suggest to use stiffness alterations as clinical markers for demyelination to quantify the onset of disease progression, for example, in multiple sclerosis. Taken together, our study indicates that myelin might play a more important function than previously thought: It not only insulates signal propagation and improves electrical function of single axons, it also provides structural support and mechanical stiffness to the brain as a whole.Increasing evidence suggests that the mechanical environment of the brain plays an important role in neuronal development and disease. Reported stiffness values vary significantly, but the origin of these variations remains unknown. Here we show that stiffness of our brain is correlated to the underlying tissue microstructure and directly proportional to the local myelin content. Myelin has been discovered in 1854 as an insulating layer around nerve cells to improve electric signal propagation. Our study now shows that it also plays an important mechanical role: Using a combined mechanical characterization and histological characterization, we found that the white matter stiffness increases linearly with increasing myelin content, from 0.5kPa at a myelin content of 63-2.5kPa at 92%.

  View details for DOI 10.1016/j.actbio.2016.07.040

  View details for PubMedID 27475531

• Elastosis during airway wall remodeling explains multiple co-existing instability patterns JOURNAL OF THEORETICAL BIOLOGY Eskandari, M., Javili, A., Kuhl, E. 2016; 403: 209-218

  Abstract

  Living structures can undergo morphological changes in response to growth and alterations in microstructural properties in response to remodeling. From a biological perspective, airway wall inflammation and airway elastosis are classical hallmarks of growth and remodeling during chronic lung disease. From a mechanical point of view, growth and remodeling trigger mechanical instabilities that result in inward folding and airway obstruction. While previous analytical and computational studies have focused on identifying the critical parameters at the onset of folding, few have considered the post-buckling behavior. All prior studies assume constant microstructural properties during the folding process; yet, clinical studies now reveal progressive airway elastosis, the degeneration of elastic fibers associated with a gradual stiffening of the inner layer. Here, we explore the influence of temporally evolving material properties on the post-bifurcation behavior of the airway wall. We show that a growing and stiffening inner layer triggers an additional subsequent bifurcation after the first instability occurs. Evolving material stiffnesses provoke failure modes with multiple co-existing wavelengths, associated with the superposition of larger folds evolving on top of the initial smaller folds. This phenomenon is exclusive to material stiffening and conceptually different from the phenomenon of period doubling observed in constant-stiffness growth. Our study suggests that the clinically observed multiple wavelengths in diseased airways are a result of gradual airway wall stiffening. While our evolving material properties are inspired by the clinical phenomenon of airway elastosis, the underlying concept is broadly applicable to other types of remodeling including aneurysm formation or brain folding.

  View details for DOI 10.1016/j.jtbi.2016.05.022

  View details for Web of Science ID 000378987100019

  View details for PubMedID 27211101

• Generating Purkinje networks in the human heart. Journal of biomechanics Sahli Costabal, F., Hurtado, D. E., Kuhl, E. 2016; 49 (12): 2455-2465

  Abstract

  The Purkinje network is an integral part of the excitation system in the human heart. Yet, to date, there is no in vivo imaging technique to accurately reconstruct its geometry and structure. Computational modeling of the Purkinje network is increasingly recognized as an alternative strategy to visualize, simulate, and understand the role of the Purkinje system. However, most computational models either have to be generated manually, or fail to smoothly cover the irregular surfaces inside the left and right ventricles. Here we present a new algorithm to reliably create robust Purkinje networks within the human heart. We made the source code of this algorithm freely available online. Using Monte Carlo simulations, we demonstrate that the fractal tree algorithm with our new projection method generates denser and more compact Purkinje networks than previous approaches on irregular surfaces. Under similar conditions, our algorithm generates a network with 1219±61 branches, three times more than a conventional algorithm with 419±107 branches. With a coverage of 11±3mm, the surface density of our new Purkije network is twice as dense as the conventional network with 22±7mm. To demonstrate the importance of a dense Purkinje network in cardiac electrophysiology, we simulated three cases of excitation: with our new Purkinje network, with left-sided Purkinje network, and without Purkinje network. Simulations with our new Purkinje network predicted more realistic activation sequences and activation times than simulations without. Six-lead electrocardiograms of the three case studies agreed with the clinical electrocardiograms under physiological conditions, under pathological conditions of right bundle branch block, and under pathological conditions of trifascicular block. Taken together, our results underpin the importance of the Purkinje network in realistic human heart simulations. Human heart modeling has the potential to support the design of personalized strategies for single- or bi-ventricular pacing, radiofrequency ablation, and cardiac defibrillation with the common goal to restore a normal heart rhythm.

  View details for DOI 10.1016/j.jbiomech.2015.12.025

  View details for PubMedID 26748729

  View details for PubMedCentralID PMC4917481

• Partial LVAD restores ventricular outputs and normalizes LV but not RV stress distributions in the acutely failing heart in silico INTERNATIONAL JOURNAL OF ARTIFICIAL ORGANS Sack, K. L., Baillargeon, B., Acevedo-Bolton, G., Genet, M., Rebelo, N., Kuhl, E., Klein, L., Weiselthaler, G. M., Burkhoff, D., Franz, T., Guccione, J. M. 2016; 39 (8): 421-430

  Abstract

  Heart failure is a worldwide epidemic that is unlikely to change as the population ages and life expectancy increases. We sought to detail significant recent improvements to the Dassault Systèmes Living Heart Model (LHM) and use the LHM to compute left ventricular (LV) and right ventricular (RV) myofiber stress distributions under the following 4 conditions: (1) normal cardiac function; (2) acute left heart failure (ALHF); (3) ALHF treated using an LV assist device (LVAD) flow rate of 2 L/min; and (4) ALHF treated using an LVAD flow rate of 4.5 L/min.Incorporating improved systolic myocardial material properties in the LHM resulted in its ability to simulate the Frank-Starling law of the heart. We decreased myocardial contractility in the LV myocardium so that LV ejection fraction decreased from 56% to 28%. This caused mean LV end diastolic (ED) stress to increase to 508% of normal, mean LV end systolic (ES) stress to increase to 113% of normal, mean RV ED stress to decrease to 94% of normal and RV ES to increase to 570% of normal. When ALHF in the model was treated with an LVAD flow rate of 4.5 L/min, most stress results normalized. Mean LV ED stress became 85% of normal, mean LV ES stress became 109% of normal and mean RV ED stress became 95% of normal. However, mean RV ES stress improved less dramatically (to 342% of normal values).These simulations strongly suggest that an LVAD is effective in normalizing LV stresses but not RV stresses that become elevated as a result of ALHF.

  View details for DOI 10.5301/ijao.5000520

  View details for Web of Science ID 000388286900004

  View details for PubMedID 27646633

  View details for PubMedCentralID PMC5067236

• Computational modeling of acute myocardial infarction COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Saez, P., Kuhl, E. 2016; 19 (10): 1107-1115

  Abstract

  Myocardial infarction, commonly known as heart attack, is caused by reduced blood supply and damages the heart muscle because of a lack of oxygen. Myocardial infarction initiates a cascade of biochemical and mechanical events. In the early stages, cardiomyocytes death, wall thinning, collagen degradation, and ventricular dilation are the immediate consequences of myocardial infarction. In the later stages, collagenous scar formation in the infarcted zone and hypertrophy of the non-infarcted zone are auto-regulatory mechanisms to partly correct for these events. Here we propose a computational model for the short-term adaptation after myocardial infarction using the continuum theory of multiplicative growth. Our model captures the effects of cell death initiating wall thinning, and collagen degradation initiating ventricular dilation. Our simulations agree well with clinical observations in early myocardial infarction. They represent a first step toward simulating the progression of myocardial infarction with the ultimate goal to predict the propensity toward heart failure as a function of infarct intensity, location, and size.

  View details for DOI 10.1080/10255842.2015.1105965

  View details for Web of Science ID 000373937700009

  View details for PubMedID 26583449

• Using 3D Printing to Create Personalized Brain Models for Neurosurgical Training and Preoperative Planning. World neurosurgery Ploch, C. C., Mansi, C. S., Jayamohan, J., Kuhl, E. 2016; 90: 668-674

  Abstract

  Three-dimensional (3D) printing holds promise for a wide variety of biomedical applications, from surgical planning, practicing, and teaching to creating implantable devices. The growth of this cheap and easy additive manufacturing technology in orthopedic, plastic, and vascular surgery has been explosive; however, its potential in the field of neurosurgery remains underexplored. A major limitation is that current technologies are unable to directly print ultrasoft materials like human brain tissue.In this technical note, the authors present a new technology to create deformable, personalized models of the human brain.The method combines 3D printing, molding, and casting to create a physiologically, anatomically, and tactilely realistic model based on magnetic resonance images. Created from soft gelatin, the model is easy to produce, cost-efficient, durable, and orders of magnitude softer than conventionally printed 3D models. The personalized brain model cost $50, and its fabrication took 24 hours.In mechanical tests, the model stiffness (E = 25.29 ± 2.68 kPa) was 5 orders of magnitude softer than common 3D printed materials, and less than an order of magnitude stiffer than mammalian brain tissue (E = 2.64 ± 0.40 kPa). In a multicenter surgical survey, model size (100.00%), visual appearance (83.33%), and surgical anatomy (81.25%) were perceived as very realistic. The model was perceived as very useful for patient illustration (85.00%), teaching (94.44%), learning (100.00%), surgical training (95.00%), and preoperative planning (95.00%).With minor refinements, personalized, deformable brain models created via 3D printing will improve surgical training and preoperative planning with the ultimate goal to provide accurate, customized, high-precision treatment.

  View details for DOI 10.1016/j.wneu.2016.02.081

  View details for PubMedID 26924117

• The Incompatibility of Living Systems: Characterizing Growth-Induced Incompatibilities in Expanded Skin ANNALS OF BIOMEDICAL ENGINEERING Tepole, A. B., Gart, M., Purnell, C. A., Gosain, A. K., Kuhl, E. 2016; 44 (5): 1734-1752

  Abstract

  Skin expansion is a common surgical technique to correct large cutaneous defects. Selecting a successful expansion protocol is solely based on the experience and personal preference of the operating surgeon. Skin expansion could be improved by predictive computational simulations. Towards this goal, we model skin expansion using the continuum framework of finite growth. This approach crucially relies on the concept of incompatible configurations. However, aside from the classical opening angle experiment, our current understanding of growth-induced incompatibilities remains rather vague. Here we visualize and characterize incompatibilities in living systems using skin expansion in a porcine model: We implanted and inflated two expanders, crescent, and spherical, and filled them to 225 cc throughout a period of 21 days. To quantify the residual strains developed during this period, we excised the expanded skin patches and subdivided them into smaller pieces. Skin growth averaged 1.17 times the original area for the spherical and 1.10 for the crescent expander, and displayed significant regional variations. When subdivided into smaller pieces, the grown skin patches retracted heterogeneously and confirmed the existence of incompatibilities. Understanding skin growth through mechanical stretch will allow surgeons to improve-and ultimately personalize-preoperative treatment planning in plastic and reconstructive surgery.

  View details for DOI 10.1007/s10439-015-1467-4

  View details for Web of Science ID 000374665900032

  View details for PubMedID 26416721

  View details for PubMedCentralID PMC4809792

• Multiphysics and multiscale modelling, data - model fusion and integration of organ physiology in the clinic: ventricular cardiac mechanics INTERFACE FOCUS Chabiniok, R., Wang, V. Y., Hadjicharalambous, M., Asner, L., Lee, J., Sermesant, M., Kuhl, E., Young, A. A., Moireau, P., Nash, M. P., Chapelle, D., Nordsletten, D. A. 2016; 6 (2): 20150083

  Abstract

  With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.

  View details for PubMedID 27051509

  View details for PubMedCentralID PMC4759748

• Response to Letters Regarding Article, "Segmental Aortic Stiffening Contributes to Experimental Abdominal Aortic Aneurysm Development" CIRCULATION Raaz, U., Zoellner, A. M., Schellinger, I. N., Toh, R., Nakagami, F., Brandt, M., Emrich, F. C., Kayama, Y., Eken, S., Adam, M., Maegdefessel, L., Hertel, T., Deng, A., Jagger, A., Buerke, M., Dalman, R. L., Spin, J. M., Kuhl, E., Tsao, P. S. 2016; 133 (1): E11–E12

  View details for PubMedID 26719393

  View details for PubMedCentralID PMC4704124

• Biophysics: Unfolding the brain Nature Physics Kuhl, E. 2016

  View details for DOI 10.1038/nphys3641

• Modeling Pathologies of Diastolic and Systolic Heart Failure ANNALS OF BIOMEDICAL ENGINEERING Genet, M., Lee, L. C., BAILLARGEON, B., Guccione, J. M., Kuhl, E. 2016; 44 (1): 112-127

  Abstract

  Chronic heart failure is a medical condition that involves structural and functional changes of the heart and a progressive reduction in cardiac output. Heart failure is classified into two categories: diastolic heart failure, a thickening of the ventricular wall associated with impaired filling; and systolic heart failure, a dilation of the ventricles associated with reduced pump function. In theory, the pathophysiology of heart failure is well understood. In practice, however, heart failure is highly sensitive to cardiac microstructure, geometry, and loading. This makes it virtually impossible to predict the time line of heart failure for a diseased individual. Here we show that computational modeling allows us to integrate knowledge from different scales to create an individualized model for cardiac growth and remodeling during chronic heart failure. Our model naturally connects molecular events of parallel and serial sarcomere deposition with cellular phenomena of myofibrillogenesis and sarcomerogenesis to whole organ function. Our simulations predict chronic alterations in wall thickness, chamber size, and cardiac geometry, which agree favorably with the clinical observations in patients with diastolic and systolic heart failure. In contrast to existing single- or bi-ventricular models, our new four-chamber model can also predict characteristic secondary effects including papillary muscle dislocation, annular dilation, regurgitant flow, and outflow obstruction. Our prototype study suggests that computational modeling provides a patient-specific window into the progression of heart failure with a view towards personalized treatment planning.

  View details for DOI 10.1007/s10439-015-1351-2

  View details for Web of Science ID 000367330800010

  View details for PubMedCentralID PMC4670609

• Constitutive Modeling of Brain Tissue: Current Perspectives APPLIED MECHANICS REVIEWS de Rooij, R., Kuhl, E. 2016; 68 (1)

  View details for DOI 10.1115/1.4032436

  View details for Web of Science ID 000388740800001

• Computational modeling of chemo-bio-mechanical coupling: a systems-biology approach toward wound healing. Computer methods in biomechanics and biomedical engineering Buganza Tepole, A., Kuhl, E. 2016; 19 (1): 13-30

  Abstract

  Wound healing is a synchronized cascade of chemical, biological, and mechanical phenomena, which act in concert to restore the damaged tissue. An imbalance between these events can induce painful scarring. Despite intense efforts to decipher the mechanisms of wound healing, the role of mechanics remains poorly understood. Here, we establish a computational systems biology model to identify the chemical, biological, and mechanical mechanisms of scar formation. First, we introduce the generic problem of coupled chemo-bio-mechanics. Then, we introduce the model problem of wound healing in terms of a particular chemical signal, inflammation, a particular biological cell type, fibroblasts, and a particular mechanical model, isotropic hyperelasticity. We explore the cross-talk between chemical, biological, and mechanical signals and show that all three fields have a significant impact on scar formation. Our model is the first step toward rigorous multiscale, multifield modeling in wound healing. Our formulation has the potential to improve effective wound management and optimize treatment on an individualized patient-specific basis.

  View details for DOI 10.1080/10255842.2014.980821

  View details for PubMedID 25421487

• Tri-layer wrinkling as a mechanism for anchoring center initiation in the developing cerebellum SOFT MATTER Lejeune, E., Javili, A., Weickenmeier, J., Kuhl, E., Linder, C. 2016; 12 (25): 5613-5620

  Abstract

  During cerebellar development, anchoring centers form at the base of each fissure and remain fixed in place while the rest of the cerebellum grows outward. Cerebellar foliation has been extensively studied; yet, the mechanisms that control anchoring center initiation and position remain insufficiently understood. Here we show that a tri-layer model can predict surface wrinkling as a potential mechanism to explain anchoring center initiation and position. Motivated by the cerebellar microstructure, we model the developing cerebellum as a tri-layer system with an external molecular layer and an internal granular layer of similar stiffness and a significantly softer intermediate Purkinje cell layer. Including a weak intermediate layer proves key to predicting surface morphogenesis, even at low stiffness contrasts between the top and bottom layers. The proposed tri-layer model provides insight into the hierarchical formation of anchoring centers and establishes an essential missing link between gene expression and evolution of shape.

  View details for DOI 10.1039/c6sm00526h

  View details for Web of Science ID 000378935000013

  View details for PubMedID 27252048

• Tau-ism: The Yin and Yang of Microtubule Sliding, Detachment, and Rupture BIOPHYSICAL JOURNAL van den Bedem, H., Kuhl, E. 2015; 109 (11): 2215-2217

  View details for DOI 10.1016/j.bpj.2015.10.020

  View details for Web of Science ID 000365929500001

  View details for PubMedCentralID PMC4675861

• Systems biology and mechanics of growth WILEY INTERDISCIPLINARY REVIEWS-SYSTEMS BIOLOGY AND MEDICINE Eskandari, M., Kuhl, E. 2015; 7 (6): 401-412

  View details for DOI 10.1002/wsbm.1312

  View details for PubMedID 26352286

• Secondary instabilities modulate cortical complexity in the mammalian brain PHILOSOPHICAL MAGAZINE Budday, S., Steinmann, P., Kuhl, E. 2015; 95 (28-30): 3244-3256

  View details for DOI 10.1080/14786435.2015.1024184

  View details for Web of Science ID 000364157500011

• Period-doubling and period-tripling in growing bilayered systems PHILOSOPHICAL MAGAZINE Budday, S., Kuhl, E., Hutchinson, J. W. 2015; 95 (28-30): 3208-3224

  View details for DOI 10.1080/14786435.2015.1014443

  View details for Web of Science ID 000364157500009

• Multi-view stereo analysis reveals anisotropy of prestrain, deformation, and growth in living skin. Biomechanics and modeling in mechanobiology Buganza Tepole, A., Gart, M., Purnell, C. A., Gosain, A. K., Kuhl, E. 2015; 14 (5): 1007-1019

  Abstract

  Skin expansion delivers newly grown skin that maintains histological and mechanical features of the original tissue. Although it is the gold standard for cutaneous defect correction today, the underlying mechanisms remain poorly understood. Here we present a novel technique to quantify anisotropic prestrain, deformation, and growth in a porcine skin expansion model. Building on our recently proposed method, we combine two novel technologies, multi-view stereo and isogeometric analysis, to characterize skin kinematics: Upon explantation, a unit square retracts ex vivo to a square of average dimensions of [Formula: see text]. Upon expansion, the unit square deforms in vivo into a rectangle of average dimensions of [Formula: see text]. Deformations are larger parallel than perpendicular to the dorsal midline suggesting that skin responds anisotropically with smaller deformations along the skin tension lines. Upon expansion, the patch grows in vivo by [Formula: see text] with respect to the explanted, unexpanded state. Growth is larger parallel than perpendicular to the midline, suggesting that elevated stretch activates mechanotransduction pathways to stimulate tissue growth. The proposed method provides a powerful tool to characterize the kinematics of living skin. Our results shed light on the mechanobiology of skin and help us to better understand and optimize clinically relevant procedures in plastic and reconstructive surgery.

  View details for DOI 10.1007/s10237-015-0650-8

  View details for PubMedID 25634600

  View details for PubMedCentralID PMC4520804

• Mechanics of the brain: perspectives, challenges, and opportunities BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Goriely, A., Geers, M. G., Holzapfel, G. A., Jayamohan, J., Jerusalem, A., Sivaloganathan, S., Squier, W., Van Dommelen, J. A., Waters, S., Kuhl, E. 2015; 14 (5): 931-965

  Abstract

  The human brain is the continuous subject of extensive investigation aimed at understanding its behavior and function. Despite a clear evidence that mechanical factors play an important role in regulating brain activity, current research efforts focus mainly on the biochemical or electrophysiological activity of the brain. Here, we show that classical mechanical concepts including deformations, stretch, strain, strain rate, pressure, and stress play a crucial role in modulating both brain form and brain function. This opinion piece synthesizes expertise in applied mathematics, solid and fluid mechanics, biomechanics, experimentation, material sciences, neuropathology, and neurosurgery to address today's open questions at the forefront of neuromechanics. We critically review the current literature and discuss challenges related to neurodevelopment, cerebral edema, lissencephaly, polymicrogyria, hydrocephaly, craniectomy, spinal cord injury, tumor growth, traumatic brain injury, and shaken baby syndrome. The multi-disciplinary analysis of these various phenomena and pathologies presents new opportunities and suggests that mechanical modeling is a central tool to bridge the scales by synthesizing information from the molecular via the cellular and tissue all the way to the organ level.

  View details for DOI 10.1007/s10237-015-0662-4

  View details for Web of Science ID 000360862600001

  View details for PubMedID 25716305

  View details for PubMedCentralID PMC4562999

• Patient-Specific Airway Wall Remodeling in Chronic Lung Disease. Annals of biomedical engineering Eskandari, M., Kuschner, W. G., Kuhl, E. 2015; 43 (10): 2538-2551

  Abstract

  Chronic lung disease affects more than a quarter of the adult population; yet, the mechanics of the airways are poorly understood. The pathophysiology of chronic lung disease is commonly characterized by mucosal growth and smooth muscle contraction of the airways, which initiate an inward folding of the mucosal layer and progressive airflow obstruction. Since the degree of obstruction is closely correlated with the number of folds, mucosal folding has been extensively studied in idealized circular cross sections. However, airflow obstruction has never been studied in real airway geometries; the behavior of imperfect, non-cylindrical, continuously branching airways remains unknown. Here we model the effects of chronic lung disease using the nonlinear field theories of mechanics supplemented by the theory of finite growth. We perform finite element analysis of patient-specific Y-branch segments created from magnetic resonance images. We demonstrate that the mucosal folding pattern is insensitive to the specific airway geometry, but that it critically depends on the mucosal and submucosal stiffness, thickness, and loading mechanism. Our results suggests that patient-specific airway models with inherent geometric imperfections are more sensitive to obstruction than idealized circular models. Our models help to explain the pathophysiology of airway obstruction in chronic lung disease and hold promise to improve the diagnostics and treatment of asthma, bronchitis, chronic obstructive pulmonary disease, and respiratory failure.

  View details for DOI 10.1007/s10439-015-1306-7

  View details for PubMedID 25821112

• Computational aspects of growth-induced instabilities through eigenvalue analysis COMPUTATIONAL MECHANICS Javili, A., Dortdivanlioglu, B., Kuhl, E., Linder, C. 2015; 56 (3): 405-420

  View details for DOI 10.1007/s00466-015-1178-6

  View details for Web of Science ID 000359381500002

• Isogeometric Kirchhoff-Love shell formulations for biological membranes COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Tepole, A. B., Kabaria, H., Bletzinger, K., Kuhl, E. 2015; 293: 328-347

  View details for DOI 10.1016/j.cma.2015.05.006

  View details for Web of Science ID 000361475900016

• Isogeometric Kirchhoff-Love shell formulations for biological membranes. Computer methods in applied mechanics and engineering Tepole, A. B., Kabaria, H., Bletzinger, K. U., Kuhl, E. 2015; 293: 328-347

  Abstract

  Computational modeling of thin biological membranes can aid the design of better medical devices. Remarkable biological membranes include skin, alveoli, blood vessels, and heart valves. Isogeometric analysis is ideally suited for biological membranes since it inherently satisfies the C1-requirement for Kirchhoff-Love kinematics. Yet, current isogeometric shell formulations are mainly focused on linear isotropic materials, while biological tissues are characterized by a nonlinear anisotropic stress-strain response. Here we present a thin shell formulation for thin biological membranes. We derive the equilibrium equations using curvilinear convective coordinates on NURBS tensor product surface patches. We linearize the weak form of the generic linear momentum balance without a particular choice of a constitutive law. We then incorporate the constitutive equations that have been designed specifically for collagenous tissues. We explore three common anisotropic material models: Mooney-Rivlin, May Newmann-Yin, and Gasser-Ogden-Holzapfel. Our work will allow scientists in biomechanics and mechanobiology to adopt the constitutive equations that have been developed for solid three-dimensional soft tissues within the framework of isogeometric thin shell analysis.

  View details for DOI 10.1016/j.cma.2015.05.006

  View details for PubMedID 26251556

  View details for PubMedCentralID PMC4522709

• Heterogeneous growth-induced prestrain in the heart JOURNAL OF BIOMECHANICS Genet, M., Rausch, M. K., Lee, L. C., Choy, S., Zhao, X., Kassab, G. S., Kozerke, S., Guccione, J. M., Kuhl, E. 2015; 48 (10): 2080-2089

  Abstract

  Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

  View details for DOI 10.1016/j.jbiomech.2015.03.012

  View details for Web of Science ID 000358459800055

  View details for PubMedCentralID PMC4492830

• Physical biology of human brain development FRONTIERS IN CELLULAR NEUROSCIENCE Budday, S., Steinmann, P., Kuhl, E. 2015; 9

  Abstract

  Neurodevelopment is a complex, dynamic process that involves a precisely orchestrated sequence of genetic, environmental, biochemical, and physical events. Developmental biology and genetics have shaped our understanding of the molecular and cellular mechanisms during neurodevelopment. Recent studies suggest that physical forces play a central role in translating these cellular mechanisms into the complex surface morphology of the human brain. However, the precise impact of neuronal differentiation, migration, and connection on the physical forces during cortical folding remains unknown. Here we review the cellular mechanisms of neurodevelopment with a view toward surface morphogenesis, pattern selection, and evolution of shape. We revisit cortical folding as the instability problem of constrained differential growth in a multi-layered system. To identify the contributing factors of differential growth, we map out the timeline of neurodevelopment in humans and highlight the cellular events associated with extreme radial and tangential expansion. We demonstrate how computational modeling of differential growth can bridge the scales-from phenomena on the cellular level toward form and function on the organ level-to make quantitative, personalized predictions. Physics-based models can quantify cortical stresses, identify critical folding conditions, rationalize pattern selection, and predict gyral wavelengths and gyrification indices. We illustrate that physical forces can explain cortical malformations as emergent properties of developmental disorders. Combining biology and physics holds promise to advance our understanding of human brain development and enable early diagnostics of cortical malformations with the ultimate goal to improve treatment of neurodevelopmental disorders including epilepsy, autism spectrum disorders, and schizophrenia.

  View details for DOI 10.3389/fncel.2015.00257

  View details for Web of Science ID 000357831600001

  View details for PubMedID 26217183

  View details for PubMedCentralID PMC4495345

• Emerging Brain Morphologies from Axonal Elongation ANNALS OF BIOMEDICAL ENGINEERING Holland, M. A., Miller, K. E., Kuhl, E. 2015; 43 (7): 1640-1653

  Abstract

  Understanding the characteristic morphology of our brain remains a challenging, yet important task in human evolution, developmental biology, and neurosciences. Mathematical modeling shapes our understanding of cortical folding and provides functional relations between cortical wavelength, thickness, and stiffness. Yet, current mathematical models are phenomenologically isotropic and typically predict non-physiological, periodic folding patterns. Here we establish a mechanistic model for cortical folding, in which macroscopic changes in white matter volume are a natural consequence of microscopic axonal growth. To calibrate our model, we consult axon elongation experiments in chick sensory neurons. We demonstrate that a single parameter, the axonal growth rate, explains a wide variety of in vitro conditions including immediate axonal thinning and gradual thickness restoration. We embed our axonal growth model into a continuum model for brain development using axonal orientation distributions motivated by diffusion spectrum imaging. Our simulations suggest that white matter anisotropy-as an emergent property from directional axonal growth-intrinsically induces symmetry breaking, and predicts more physiological, less regular morphologies with regionally varying gyral wavelengths and sulcal depths. Mechanistic modeling of brain development could establish valuable relationships between brain connectivity, brain anatomy, and brain function.

  View details for DOI 10.1007/s10439-015-1312-9

  View details for Web of Science ID 000358258200014

  View details for PubMedCentralID PMC4497873

• A new sparse matrix vector multiplication graphics processing unit algorithm designed for finite element problems INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Wong, J., Kuhl, E., Darve, E. 2015; 102 (12): 1784-1814

  View details for DOI 10.1002/nme.4865

  View details for Web of Science ID 000354625300002

• Mechanical properties of gray and white matter brain tissue by indentation. Journal of the mechanical behavior of biomedical materials Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., Kuhl, E. 2015; 46: 318-330

  Abstract

  The mammalian brain is composed of an outer layer of gray matter, consisting of cell bodies, dendrites, and unmyelinated axons, and an inner core of white matter, consisting primarily of myelinated axons. Recent evidence suggests that microstructural differences between gray and white matter play an important role during neurodevelopment. While brain tissue as a whole is rheologically well characterized, the individual features of gray and white matter remain poorly understood. Here we quantify the mechanical properties of gray and white matter using a robust, reliable, and repeatable method, flat-punch indentation. To systematically characterize gray and white matter moduli for varying indenter diameters, loading rates, holding times, post-mortem times, and locations we performed a series of n=192 indentation tests. We found that indenting thick, intact coronal slices eliminates the common challenges associated with small specimens: it naturally minimizes boundary effects, dehydration, swelling, and structural degradation. When kept intact and hydrated, brain slices maintained their mechanical characteristics with standard deviations as low as 5% throughout the entire testing period of five days post mortem. White matter, with an average modulus of 1.895kPa±0.592kPa, was on average 39% stiffer than gray matter, p<0.01, with an average modulus of 1.389kPa±0.289kPa, and displayed larger regional variations. It was also more viscous than gray matter and responded less rapidly to mechanical loading. Understanding the rheological differences between gray and white matter may have direct implications on diagnosing and understanding the mechanical environment in neurodevelopment and neurological disorders.

  View details for DOI 10.1016/j.jmbbm.2015.02.024

  View details for PubMedID 25819199

  View details for PubMedCentralID PMC4395547

• Mechanical properties of gray and white matter brain tissue by indentation. Journal of the mechanical behavior of biomedical materials Budday, S., Nay, R., de Rooij, R., Steinmann, P., Wyrobek, T., Ovaert, T. C., Kuhl, E. 2015; 46: 318-330

  View details for DOI 10.1016/j.jmbbm.2015.02.024

  View details for PubMedID 25819199

• Segmental Aortic Stiffening Contributes to Experimental Abdominal Aortic Aneurysm Development CIRCULATION Raaz, U., Zoellner, A. M., Schellinger, I. N., Toh, R., Nakagami, F., Brandt, M., Emrich, F. C., Kayama, Y., Eken, S., Adam, M., Maegdefessel, L., Hertel, T., Deng, A., Jagger, A., Buerke, M., Dalman, R. L., Spin, J. M., Kuhl, E., Tsao, P. S. 2015; 131 (20): 1783-1795

  Abstract

  Stiffening of the aortic wall is a phenomenon consistently observed in age and in abdominal aortic aneurysm (AAA). However, its role in AAA pathophysiology is largely undefined.Using an established murine elastase-induced AAA model, we demonstrate that segmental aortic stiffening precedes aneurysm growth. Finite-element analysis reveals that early stiffening of the aneurysm-prone aortic segment leads to axial (longitudinal) wall stress generated by cyclic (systolic) tethering of adjacent, more compliant wall segments. Interventional stiffening of AAA-adjacent aortic segments (via external application of surgical adhesive) significantly reduces aneurysm growth. These changes correlate with the reduced segmental stiffness of the AAA-prone aorta (attributable to equalized stiffness in adjacent segments), reduced axial wall stress, decreased production of reactive oxygen species, attenuated elastin breakdown, and decreased expression of inflammatory cytokines and macrophage infiltration, and attenuated apoptosis within the aortic wall, as well. Cyclic pressurization of segmentally stiffened aortic segments ex vivo increases the expression of genes related to inflammation and extracellular matrix remodeling. Finally, human ultrasound studies reveal that aging, a significant AAA risk factor, is accompanied by segmental infrarenal aortic stiffening.The present study introduces the novel concept of segmental aortic stiffening as an early pathomechanism generating aortic wall stress and triggering aneurysmal growth, thereby delineating potential underlying molecular mechanisms and therapeutic targets. In addition, monitoring segmental aortic stiffening may aid the identification of patients at risk for AAA.

  View details for DOI 10.1161/CIRCULATIONAHA.114.012377

  View details for PubMedID 25904646

• Morphoelastic control of gastro-intestinal organogenesis: Theoretical predictions and numerical insights JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Balbi, V., Kuhl, E., Ciarletta, P. 2015; 78: 493-510

  View details for DOI 10.1016/j.jmps.2015.02.016

  View details for Web of Science ID 000356733700026

• Use it or lose it: multiscale skeletal muscle adaptation to mechanical stimuli. Biomechanics and modeling in mechanobiology Wisdom, K. M., Delp, S. L., Kuhl, E. 2015; 14 (2): 195-215

  Abstract

  Skeletal muscle undergoes continuous turnover to adapt to changes in its mechanical environment. Overload increases muscle mass, whereas underload decreases muscle mass. These changes are correlated with, and enabled by, structural alterations across the molecular, subcellular, cellular, tissue, and organ scales. Despite extensive research on muscle adaptation at the individual scales, the interaction of the underlying mechanisms across the scales remains poorly understood. Here, we present a thorough review and a broad classification of multiscale muscle adaptation in response to a variety of mechanical stimuli. From this classification, we suggest that a mathematical model for skeletal muscle adaptation should include the four major stimuli, overstretch, understretch, overload, and underload, and the five key players in skeletal muscle adaptation, myosin heavy chain isoform, serial sarcomere number, parallel sarcomere number, pennation angle, and extracellular matrix composition. Including this information in multiscale computational models of muscle will shape our understanding of the interacting mechanisms of skeletal muscle adaptation across the scales. Ultimately, this will allow us to rationalize the design of exercise and rehabilitation programs, and improve the long-term success of interventional treatment in musculoskeletal disease.

  View details for DOI 10.1007/s10237-014-0607-3

  View details for PubMedID 25199941

  View details for PubMedCentralID PMC4352121

• A computational model that predicts reverse growth in response to mechanical unloading BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Lee, L. C., Genet, M., Acevedo-Bolton, G., Ordovas, K., Guccione, J. M., Kuhl, E. 2015; 14 (2): 217-229

  Abstract

  Ventricular growth is widely considered to be an important feature in the adverse progression of heart diseases, whereas reverse ventricular growth (or reverse remodeling) is often considered to be a favorable response to clinical intervention. In recent years, a number of theoretical models have been proposed to model the process of ventricular growth while little has been done to model its reverse. Based on the framework of volumetric strain-driven finite growth with a homeostatic equilibrium range for the elastic myofiber stretch, we propose here a reversible growth model capable of describing both ventricular growth and its reversal. We used this model to construct a semi-analytical solution based on an idealized cylindrical tube model, as well as numerical solutions based on a truncated ellipsoidal model and a human left ventricular model that was reconstructed from magnetic resonance images. We show that our model is able to predict key features in the end-diastolic pressure-volume relationship that were observed experimentally and clinically during ventricular growth and reverse growth. We also show that the residual stress fields generated as a result of differential growth in the cylindrical tube model are similar to those in other nonidentical models utilizing the same geometry.

  View details for DOI 10.1007/s10237-014-0598-0

  View details for Web of Science ID 000350871000002

  View details for PubMedID 24888270

  View details for PubMedCentralID PMC4254895

• Secondary instabilities modulate cortical complexity in the mammalian brain. Philosophical magazine (Abingdon, England) Budday, S., Steinmann, P., Kuhl, E. 2015; 95 (28-30): 3244-3256

  Abstract

  Disclosing the origin of convolutions in the mammalian brain remains a scientific challenge. Primary folds form before we are born: they are static, well defined, and highly preserved across individuals. Secondary folds occur and disappear throughout our entire life time: they are dynamic, irregular, and highly variable among individuals. While extensive research has improved our understanding of primary folding in the mammalian brain, secondary folding remains understudied and poorly understood. Here, we show that secondary instabilities can explain the increasing complexity of our brain surface as we age. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we explore the critical conditions for secondary instabilities. We show that with continuing growth, our brain surface continues to bifurcate into increasingly complex morphologies. Our results suggest that even small geometric variations can have a significant impact on surface morphogenesis. Secondary bifurcations, and with them morphological changes during childhood and adolescence, are closely associated with the formation and loss of neuronal connections. Understanding the correlation between neuronal connectivity, cortical thickness, surface morphology, and ultimately behavior, could have important implications on the diagnostics, classification, and treatment of neurological disorders.

  View details for DOI 10.1080/14786435.2015.1024184

  View details for PubMedID 26523123

  View details for PubMedCentralID PMC4627640

• Period-doubling and period-tripling in growing bilayered systems. Philosophical magazine (Abingdon, England) Budday, S., Kuhl, E., Hutchinson, J. W. 2015; 95 (28-30): 3208-3224

  Abstract

  Growing layers on elastic substrates are capable of creating a wide variety of surface morphologies. Moderate growth generates a regular pattern of sinusoidal wrinkles with a homogeneous energy distribution. While the critical conditions for periodic wrinkling have been extensively studied, the rich pattern formation beyond this first instability point remains poorly understood. Here we show that upon continuing growth, the energy progressively localizes and new complex morphologies emerge. Previous studies have often overlooked these secondary bifurcations; they have focused on large stiffness ratios between layer and substrate, where primary instabilities occur early, long before secondary instabilities emerge. We demonstrate that secondary bifurcations are particularly critical in the low stiffness ratio regime, where the critical conditions for primary and secondary instabilities move closer together. Amongst all possible secondary bifurcations, the mode of period-doubling plays a central role - it is energetically favorable over all other modes. Yet, we can numerically suppress period-doubling, by choosing boundary conditions, which favor alternative higher order modes. Our results suggest that in the low stiffness regime, pattern formation is highly sensitive to small imperfections: surface morphologies emerge rapidly, change spontaneously, and quickly become immensely complex. This is a common paradigm in developmental biology. Our results have significantly applications in the morphogenesis of living systems where growth is progressive and stiffness ratios are low.

  View details for DOI 10.1080/14786435.2015.1014443

  View details for PubMedID 26752977

  View details for PubMedCentralID PMC4704805

• On high heels and short muscles: a multiscale model for sarcomere loss in the gastrocnemius muscle. Journal of theoretical biology Zöllner, A. M., Pok, J. M., McWalter, E. J., Gold, G. E., Kuhl, E. 2015; 365: 301-310

  Abstract

  High heels are a major source of chronic lower limb pain. Yet, more than one third of all women compromise health for looks and wear high heels on a daily basis. Changing from flat footwear to high heels induces chronic muscle shortening associated with discomfort, fatigue, reduced shock absorption, and increased injury risk. However, the long-term effects of high-heeled footwear on the musculoskeletal kinematics of the lower extremities remain poorly understood. Here we create a multiscale computational model for chronic muscle adaptation to characterize the acute and chronic effects of global muscle shortening on local sarcomere lengths. We perform a case study of a healthy female subject and show that raising the heel by 13cm shortens the gastrocnemius muscle by 5% while the Achilles tendon remains virtually unaffected. Our computational simulation indicates that muscle shortening displays significant regional variations with extreme values of 22% in the central gastrocnemius. Our model suggests that the muscle gradually adjusts to its new functional length by a chronic loss of sarcomeres in series. Sarcomere loss varies significantly across the muscle with an average loss of 9%, virtually no loss at the proximal and distal ends, and a maximum loss of 39% in the central region. These changes reposition the remaining sarcomeres back into their optimal operating regime. Computational modeling of chronic muscle shortening provides a valuable tool to shape our understanding of the underlying mechanisms of muscle adaptation. Our study could open new avenues in orthopedic surgery and enhance treatment for patients with muscle contracture caused by other conditions than high heel wear such as paralysis, muscular atrophy, and muscular dystrophy.

  View details for DOI 10.1016/j.jtbi.2014.10.036

  View details for PubMedID 25451524

  View details for PubMedCentralID PMC4262722

• The emergence of extracellular matrix mechanics and cell traction forces as important regulators of cellular self-organization BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Checa, S., Rausch, M. K., Petersen, A., Kuhl, E., Duda, G. N. 2015; 14 (1): 1-13

  Abstract

  Physical cues play a fundamental role in a wide range of biological processes, such as embryogenesis, wound healing, tumour invasion and connective tissue morphogenesis. Although it is well known that during these processes, cells continuously interact with the local extracellular matrix (ECM) through cell traction forces, the role of these mechanical interactions on large scale cellular and matrix organization remains largely unknown. In this study, we use a simple theoretical model to investigate cellular and matrix organization as a result of mechanical feedback signals between cells and the surrounding ECM. The model includes bi-directional coupling through cellular traction forces to deform the ECM and through matrix deformation to trigger cellular migration. In addition, we incorporate the mechanical contribution of matrix fibres and their reorganization by the cells. We show that a group of contractile cells will self-polarize at a large scale, even in homogeneous environments. In addition, our simulations mimic the experimentally observed alignment of cells in the direction of maximum stiffness and the building up of tension as a consequence of cell and fibre reorganization. Moreover, we demonstrate that cellular organization is tightly linked to the mechanical feedback loop between cells and matrix. Cells with a preference for stiff environments have a tendency to form chains, while cells with a tendency for soft environments tend to form clusters. The model presented here illustrates the potential of simple physical cues and their impact on cellular self-organization. It can be used in applications where cell-matrix interactions play a key role, such as in the design of tissue engineering scaffolds and to gain a basic understanding of pattern formation in organogenesis or tissue regeneration.

  View details for DOI 10.1007/s10237-014-0581-9

  View details for Web of Science ID 000347250500001

  View details for PubMedID 24718853

• Neuromechanics: From Neurons to Brain ADVANCES IN APPLIED MECHANICS, VOL 48 Goriely, A., Budday, S., Kuhl, E. 2015; 48: 79-139

  View details for DOI 10.1016/bs.aams.2015.10.002

  View details for Web of Science ID 000370509200003

• Human Cardiac Function Simulator for the Optimal Design of a Novel Annuloplasty Ring with a Sub-valvular Element for Correction of Ischemic Mitral Regurgitation. Cardiovascular engineering and technology Baillargeon, B., Costa, I., Leach, J. R., Lee, L. C., Genet, M., Toutain, A., Wenk, J. F., Rausch, M. K., Rebelo, N., Acevedo-Bolton, G., Kuhl, E., Navia, J. L., Guccione, J. M. 2015; 6 (2): 105-116

  Abstract

  Ischemic mitral regurgitation is associated with substantial risk of death. We sought to: (1) detail significant recent improvements to the Dassault Systèmes human cardiac function simulator (HCFS); (2) use the HCFS to simulate normal cardiac function as well as pathologic function in the setting of posterior left ventricular (LV) papillary muscle infarction; and (3) debut our novel device for correction of ischemic mitral regurgitation. We synthesized two recent studies of human myocardial mechanics. The first study presented the robust and integrative finite element HCFS. Its primary limitation was its poor diastolic performance with an LV ejection fraction below 20% caused by overly stiff ex vivo porcine tissue parameters. The second study derived improved diastolic myocardial material parameters using in vivo MRI data from five normal human subjects. We combined these models to simulate ischemic mitral regurgitation by computationally infarcting an LV region including the posterior papillary muscle. Contact between our novel device and the mitral valve apparatus was simulated using Dassault Systèmes SIMULIA software. Incorporating improved cardiac geometry and diastolic myocardial material properties in the HCFS resulted in a realistic LV ejection fraction of 55%. Simulating infarction of posterior papillary muscle caused regurgitant mitral valve mechanics. Implementation of our novel device corrected valve dysfunction. Improvements in the current study to the HCFS permit increasingly accurate study of myocardial mechanics. The first application of this simulator to abnormal human cardiac function suggests that our novel annuloplasty ring with a sub-valvular element will correct ischemic mitral regurgitation.

  View details for DOI 10.1007/s13239-015-0216-z

  View details for PubMedID 25984248

  View details for PubMedCentralID PMC4427655

• Pattern Selection in Growing Tubular Tissues PHYSICAL REVIEW LETTERS Ciarletta, P., Balbi, V., Kuhl, E. 2014; 113 (24)

  Abstract

  Tubular organs display a wide variety of surface morphologies including circumferential and longitudinal folds, square and hexagonal undulations, and finger-type protrusions. Surface morphology is closely correlated to tissue function and serves as a clinical indicator for physiological and pathological conditions, but the regulators of surface morphology remain poorly understood. Here, we explore the role of geometry and elasticity on the formation of surface patterns. We establish morphological phase diagrams for patterns selection and show that increasing the thickness or stiffness ratio between the outer and inner tubular layers induces a gradual transition from circumferential to longitudinal folding. Our results suggest that physical forces act as regulators during organogenesis and give rise to the characteristic circular folds in the esophagus, the longitudinal folds in the valves of Kerckring, the surface networks in villi, and the crypts in the large intestine.

  View details for DOI 10.1103/PhysRevLett.113.248101

  View details for Web of Science ID 000346387700022

  View details for PubMedID 25541805

• The role of mechanics during brain development JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Budday, S., Steinmann, P., Kuhl, E. 2014; 72: 75-92

  View details for DOI 10.1016/j.jmps.2014.07.010

  View details for Web of Science ID 000343841900005

• The Generalized Hill Model: A Kinematic Approach Towards Active Muscle Contraction. Journal of the mechanics and physics of solids Göktepe, S., Menzel, A., Kuhl, E. 2014; 72: 20-39

  Abstract

  Excitation-contraction coupling is the physiological process of converting an electrical stimulus into a mechanical response. In muscle, the electrical stimulus is an action potential and the mechanical response is active contraction. The classical Hill model characterizes muscle contraction though one contractile element, activated by electrical excitation, and two non-linear springs, one in series and one in parallel. This rheology translates into an additive decomposition of the total stress into a passive and an active part. Here we supplement this additive decomposition of the stress by a multiplicative decomposition of the deformation gradient into a passive and an active part. We generalize the one-dimensional Hill model to the three-dimensional setting and constitutively define the passive stress as a function of the total deformation gradient and the active stress as a function of both the total deformation gradient and its active part. We show that this novel approach combines the features of both the classical stress-based Hill model and the recent active-strain models. While the notion of active stress is rather phenomenological in nature, active strain is micro-structurally motivated, physically measurable, and straightforward to calibrate. We demonstrate that our model is capable of simulating excitation-contraction coupling in cardiac muscle with its characteristic features of wall thickening, apical lift, and ventricular torsion.

  View details for DOI 10.1016/j.jmps.2014.07.015

  View details for PubMedID 25221354

  View details for PubMedCentralID PMC4159623

• The role of mechanics during brain development. Journal of the mechanics and physics of solids Budday, S., Steinmann, P., Kuhl, E. 2014; 72: 75-92

  Abstract

  Convolutions are a classical hallmark of most mammalian brains. Brain surface morphology is often associated with intelligence and closely correlated to neurological dysfunction. Yet, we know surprisingly little about the underlying mechanisms of cortical folding. Here we identify the role of the key anatomic players during the folding process: cortical thickness, stiffness, and growth. To establish estimates for the critical time, pressure, and the wavelength at the onset of folding, we derive an analytical model using the Föppl-von-Kármán theory. Analytical modeling provides a quick first insight into the critical conditions at the onset of folding, yet it fails to predict the evolution of complex instability patterns in the post-critical regime. To predict realistic surface morphologies, we establish a computational model using the continuum theory of finite growth. Computational modeling not only confirms our analytical estimates, but is also capable of predicting the formation of complex surface morphologies with asymmetric patterns and secondary folds. Taken together, our analytical and computational models explain why larger mammalian brains tend to be more convoluted than smaller brains. Both models provide mechanistic interpretations of the classical malformations of lissencephaly and polymicrogyria. Understanding the process of cortical folding in the mammalian brain has direct implications on the diagnostics of neurological disorders including severe retardation, epilepsy, schizophrenia, and autism.

  View details for DOI 10.1016/j.jmps.2014.07.010

  View details for PubMedID 25202162

  View details for PubMedCentralID PMC4156279

• The generalized Hill model: A kinematic approach towards active muscle contraction JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Menzel, A., Kuhl, E. 2014; 72: 20-39

  View details for DOI 10.1016/j.jmps.2014.07.015

  View details for Web of Science ID 000343841900002

• Modeling and simulation of viscous electro-active polymers EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Vogel, F., Goktepe, S., Steinmann, P., Kuhl, E. 2014; 48: 112-128

  View details for DOI 10.1016/j.euromechsol.2014.02.001

  View details for Web of Science ID 000342879100011

• The Living Heart Project: A robust and integrative simulator for human heart function. European journal of mechanics. A, Solids Baillargeon, B., Rebelo, N., Fox, D. D., Taylor, R. L., Kuhl, E. 2014; 48: 38-47

  Abstract

  The heart is not only our most vital, but also our most complex organ: Precisely controlled by the interplay of electrical and mechanical fields, it consists of four chambers and four valves, which act in concert to regulate its filling, ejection, and overall pump function. While numerous computational models exist to study either the electrical or the mechanical response of its individual chambers, the integrative electro-mechanical response of the whole heart remains poorly understood. Here we present a proof-of-concept simulator for a four-chamber human heart model created from computer topography and magnetic resonance images. We illustrate the governing equations of excitation-contraction coupling and discretize them using a single, unified finite element environment. To illustrate the basic features of our model, we visualize the electrical potential and the mechanical deformation across the human heart throughout its cardiac cycle. To compare our simulation against common metrics of cardiac function, we extract the pressure-volume relationship and show that it agrees well with clinical observations. Our prototype model allows us to explore and understand the key features, physics, and technologies to create an integrative, predictive model of the living human heart. Ultimately, our simulator will open opportunities to probe landscapes of clinical parameters, and guide device design and treatment planning in cardiac diseases such as stenosis, regurgitation, or prolapse of the aortic, pulmonary, tricuspid, or mitral valve.

  View details for DOI 10.1016/j.euromechsol.2014.04.001

  View details for PubMedID 25267880

  View details for PubMedCentralID PMC4175454

• Modeling and Simulation of Viscous Electro-Active Polymers. European journal of mechanics. A, Solids Vogel, F., Göktepe, S., Steinmann, P., Kuhl, E. 2014; 48: 112-128

  Abstract

  Electro-active materials are capable of undergoing large deformation when stimulated by an electric field. They can be divided into electronic and ionic electro-active polymers (EAPs) depending on their actuation mechanism based on their composition. We consider electronic EAPs, for which attractive Coulomb forces or local re-orientation of polar groups cause a bulk deformation. Many of these materials exhibit pronounced visco-elastic behavior. Here we show the development and implementation of a constitutive model, which captures the influence of the electric field on the visco-elastic response within a geometrically non-linear finite element framework. The electric field affects not only the equilibrium part of the strain energy function, but also the viscous part. To adopt the familiar additive split of the strain from the small strain setting, we formulate the governing equations in the logarithmic strain space and additively decompose the logarithmic strain into elastic and viscous parts. We show that the incorporation of the electric field in the viscous response significantly alters the relaxation and hysteresis behavior of the model. Our parametric study demonstrates that the model is sensitive to the choice of the electro-viscous coupling parameters. We simulate several actuator structures to illustrate the performance of the method in typical relaxation and creep scenarios. Our model could serve as a design tool for micro-electro-mechanical systems, microfluidic devices, and stimuli-responsive gels such as artificial skin, tactile displays, or artificial muscle.

  View details for DOI 10.1016/j.euromechsol.2014.02.001

  View details for PubMedID 25267881

  View details for PubMedCentralID PMC4175517

• The Living Heart Project: A robust and integrative simulator for human heart function EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Baillargeon, B., Rebelo, N., Fox, D. D., Taylor, R. L., Kuhl, E. 2014; 48: 38-47

  View details for DOI 10.1016/j.euromechsol.2014.04.001

  View details for Web of Science ID 000342879100005

• Characterization of living skin using multi-view stereo and isogeometric analysis. Acta biomaterialia Buganza Tepole, A., Gart, M., Gosain, A. K., Kuhl, E. 2014; 10 (11): 4822-4831

  Abstract

  Skin is our interface with the outside world. In its natural environment, it displays unique mechanical characteristics, such as prestretch and growth. While there is a general agreement on the physiological importance of these features, they remain poorly characterized, mainly because they are difficult to access with standard laboratory techniques. Here we present a new, inexpensive technique to characterize living skin using multi-view stereo and isogeometric analysis. Based on easy-to-create hand-held camera images, we quantify prestretch, deformation and growth in a controlled porcine model of chronic skin expansion. Over a period of 5 weeks, we gradually inflate an implanted tissue expander, take weekly photographs of the experimental scene, reconstruct the geometry from a tattooed surface grid and create parametric representations of the skin surface. After 5 weeks of expansion, our method reveals an average area prestretch of 1.44, an average area stretch of 1.87 and an average area growth of 2.25. Area prestretch is maximal in the ventral region with a value of 2.37, whereas area stretch and area growth are maximal above the center of the expander, with values of 4.05 and 4.81, respectively. Our study has immediate impact on understanding living skin to optimize treatment planning and decision making in plastic and reconstructive surgery. Beyond these direct implications, our experimental design has broad applications in clinical research and basic sciences: it serves as a simple, robust, low cost, easy-to-use tool to reconstruct living membranes, which are difficult to characterize in a conventional laboratory setup.

  View details for DOI 10.1016/j.actbio.2014.06.037

  View details for PubMedID 25016279

  View details for PubMedCentralID PMC4186913

• Application of finite element modeling to optimize flap design with tissue expansion. Plastic and reconstructive surgery Buganza-Tepole, A., Steinberg, J. P., Kuhl, E., Gosain, A. K. 2014; 134 (4): 785-792

  Abstract

  Tissue expansion is a widely used technique to create skin flaps for the correction of sizable defects in reconstructive plastic surgery. Major complications following the inset of expanded flaps include breakdown and uncontrolled scarring secondary to excessive tissue tension. Although it is recognized that mechanical forces may significantly impact the success of defect repair with tissue expansion, a mechanical analysis of tissue stresses has not previously been attempted. Such analyses have the potential to optimize flap design preoperatively.The authors establish computer-aided design as a tool with which to explore stress profiles for two commonly used flap designs, the direct advancement flap and the double back-cut flap. The authors advanced both flaps parallel and perpendicular to the relaxed skin tension lines to quantify the impact of tissue anisotropy on stress distribution profiles.Stress profiles were highly sensitive to flap design and orientation of relaxed skin tension lines, with stress minimized when flaps were advanced perpendicular to relaxed skin tension lines. Maximum stresses in advancement flaps occurred at the distal end of the flap, followed by the base. The double back-cut design increased stress at the lateral edges of the flap.The authors conclude that finite element modeling may be used to effectively predict areas of increased flap tension. Performed preoperatively, such modeling can allow for the optimization of flap design and a potential reduction in complications such as flap dehiscence and hypertrophic scarring.

  View details for DOI 10.1097/PRS.0000000000000553

  View details for PubMedID 24945952

  View details for PubMedCentralID PMC4216239

• Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery COMPUTERS & STRUCTURES Tepole, A. B., Gosain, A. K., Kuhl, E. 2014; 143: 32-39

  View details for DOI 10.1016/j.compstruc.2014.07.004

  View details for Web of Science ID 000341481500004

• Computational modeling of skin: Using stress profiles as predictor for tissue necrosis in reconstructive surgery. Computers & structures Tepole, A. B., Gosain, A. K., Kuhl, E. 2014; 143: 32-39

  Abstract

  Local skin flaps have revolutionized reconstructive surgery. Mechanical loading is critical for flap survival: Excessive tissue tension reduces blood supply and induces tissue necrosis. However, skin flaps have never been analyzed mechanically. Here we explore the stress profiles of two common flap designs, direct advancement flaps and double back-cut flaps. Our simulations predict a direct correlation between regions of maximum stress and tissue necrosis. This suggests that elevated stress could serve as predictor for flap failure. Our model is a promising step towards computer-guided reconstructive surgery with the goal to minimize stress, accelerate healing, minimize scarring, and optimize tissue use.

  View details for DOI 10.1016/j.compstruc.2014.07.004

  View details for PubMedID 25225454

  View details for PubMedCentralID PMC4162094

• Generating fibre orientation maps in human heart models using Poisson interpolation COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Wong, J., Kuhl, E. 2014; 17 (11): 1217-1226

  Abstract

  Smoothly varying muscle fibre orientations in the heart are critical to its electrical and mechanical function. From detailed histological studies and diffusion tensor imaging, we now know that fibre orientations in humans vary gradually from approximately - 70° in the outer wall to +80° in the inner wall. However, the creation of fibre orientation maps for computational analyses remains one of the most challenging problems in cardiac electrophysiology and cardiac mechanics. Here, we show that Poisson interpolation generates smoothly varying vector fields that satisfy a set of user-defined constraints in arbitrary domains. Specifically, we enforce the Poisson interpolation in the weak sense using a standard linear finite element algorithm for scalar-valued second-order boundary value problems and introduce the feature to be interpolated as a global unknown. User-defined constraints are then simply enforced in the strong sense as Dirichlet boundary conditions. We demonstrate that the proposed concept is capable of generating smoothly varying fibre orientations, quickly, efficiently and robustly, both in a generic bi-ventricular model and in a patient-specific human heart. Sensitivity analyses demonstrate that the underlying algorithm is conceptually able to handle both arbitrarily and uniformly distributed user-defined constraints; however, the quality of the interpolation is best for uniformly distributed constraints. We anticipate our algorithm to be immediately transformative to experimental and clinical settings, in which it will allow us to quickly and reliably create smooth interpolations of arbitrary fields from data-sets, which are sparse but uniformly distributed.

  View details for DOI 10.1080/10255842.2012.739167

  View details for Web of Science ID 000334018600006

  View details for PubMedID 23210529

  View details for PubMedCentralID PMC3656979

• A mechanical model predicts morphological abnormalities in the developing human brain SCIENTIFIC REPORTS Budday, S., Raybaud, C., Kuhl, E. 2014; 4

  Abstract

  The developing human brain remains one of the few unsolved mysteries of science. Advancements in developmental biology, neuroscience, and medical imaging have brought us closer than ever to understand brain development in health and disease. However, the precise role of mechanics throughout this process remains underestimated and poorly understood. Here we show that mechanical stretch plays a crucial role in brain development. Using the nonlinear field theories of mechanics supplemented by the theory of finite growth, we model the human brain as a living system with a morphogenetically growing outer surface and a stretch-driven growing inner core. This approach seamlessly integrates the two popular but competing hypotheses for cortical folding: axonal tension and differential growth. We calibrate our model using magnetic resonance images from very preterm neonates. Our model predicts that deviations in cortical growth and thickness induce morphological abnormalities. Using the gyrification index, the ratio between the total and exposed surface area, we demonstrate that these abnormalities agree with the classical pathologies of lissencephaly and polymicrogyria. Understanding the mechanisms of cortical folding in the developing human brain has direct implications in the diagnostics and treatment of neurological disorders, including epilepsy, schizophrenia, and autism.

  View details for DOI 10.1038/srep05644

  View details for Web of Science ID 000338763700006

  View details for PubMedID 25008163

  View details for PubMedCentralID PMC4090617

• Computational modelling of electrocardiograms: repolarisation and T-wave polarity in the human heart COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Hurtado, D. E., Kuhl, E. 2014; 17 (9): 986-996

  Abstract

  For more than a century, electrophysiologists, cardiologists and engineers have studied the electrical activity of the human heart to better understand rhythm disorders and possible treatment options. Although the depolarisation sequence of the heart is relatively well characterised, the repolarisation sequence remains a subject of great controversy. Here, we study regional and temporal variations in both depolarisation and repolarisation using a finite element approach. We discretise the governing equations in time using an unconditionally stable implicit Euler backward scheme and in space using a consistently linearised Newton-Raphson-based finite element solver. Through systematic parameter-sensitivity studies, we establish a direct relation between a normal positive T-wave and the non-uniform distribution of the controlling parameter, which we have termed refractoriness. To establish a healthy baseline model, we calibrate the refractoriness using clinically measured action potential durations at different locations in the human heart. We demonstrate the potential of our model by comparing the computationally predicted and clinically measured depolarisation and repolarisation profiles across the left ventricle. The proposed framework allows us to explore how local action potential durations on the microscopic scale translate into global repolarisation sequences on the macroscopic scale. We anticipate that our calibrated human heart model can be widely used to explore cardiac excitation in health and disease. For example, our model can serve to identify optimal pacing sites in patients with heart failure and to localise optimal ablation sites in patients with cardiac fibrillation.

  View details for DOI 10.1080/10255842.2012.729582

  View details for Web of Science ID 000333954600006

  View details for PubMedID 23113842

• Computational modeling of hypertensive growth in the human carotid artery COMPUTATIONAL MECHANICS Saez, P., Pena, E., Martinez, M. A., Kuhl, E. 2014; 53 (6): 1183-1196

  View details for DOI 10.1007/s00466-013-0959-z

  View details for Web of Science ID 000335669100006

• Computational modeling of hypertensive growth in the human carotid artery. Computational mechanics Sáez, P., Peña, E., Martínez, M. A., Kuhl, E. 2014; 53 (6): 1183-1196

  Abstract

  Arterial hypertension is a chronic medical condition associated with an elevated blood pressure. Chronic arterial hypertension initiates a series of events, which are known to collectively initiate arterial wall thickening. However, the correlation between macrostructural mechanical loading, microstructural cellular changes, and macrostructural adaptation remains unclear. Here, we present a microstructurally motivated computational model for chronic arterial hypertension through smooth muscle cell growth. To model growth, we adopt a classical concept based on the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. Motivated by clinical observations, we assume that the driving force for growth is the stretch sensed by the smooth muscle cells. We embed our model into a finite element framework, where growth is stored locally as an internal variable. First, to demonstrate the features of our model, we investigate the effects of hypertensive growth in a real human carotid artery. Our results agree nicely with experimental data reported in the literature both qualitatively and quantitatively.

  View details for DOI 10.1007/s00466-013-0959-z

  View details for PubMedID 25342868

  View details for PubMedCentralID PMC4203466

• On the mechanics of growing thin biological membranes. Journal of the mechanics and physics of solids Rausch, M. K., Kuhl, E. 2014; 63: 128-140

  Abstract

  Despite their seemingly delicate appearance, thin biological membranes fulfill various crucial roles in the human body and can sustain substantial mechanical loads. Unlike engineering structures, biological membranes are able to grow and adapt to changes in their mechanical environment. Finite element modeling of biological growth holds the potential to better understand the interplay of membrane form and function and to reliably predict the effects of disease or medical intervention. However, standard continuum elements typically fail to represent thin biological membranes efficiently, accurately, and robustly. Moreover, continuum models are typically cumbersome to generate from surface-based medical imaging data. Here we propose a computational model for finite membrane growth using a classical midsurface representation compatible with standard shell elements. By assuming elastic incompressibility and membrane-only growth, the model a priori satisfies the zero-normal stress condition. To demonstrate its modular nature, we implement the membrane growth model into the general-purpose non-linear finite element package Abaqus/Standard using the concept of user subroutines. To probe efficiently and robustness, we simulate selected benchmark examples of growing biological membranes under different loading conditions. To demonstrate the clinical potential, we simulate the functional adaptation of a heart valve leaflet in ischemic cardiomyopathy. We believe that our novel approach will be widely applicable to simulate the adaptive chronic growth of thin biological structures including skin membranes, mucous membranes, fetal membranes, tympanic membranes, corneoscleral membranes, and heart valve membranes. Ultimately, our model can be used to identify diseased states, predict disease evolution, and guide the design of interventional or pharmaceutic therapies to arrest or revert disease progression.

  View details for DOI 10.1016/j.jmps.2013.09.015

  View details for PubMedID 24563551

  View details for PubMedCentralID PMC3927878

• A novel strategy to identify the critical conditions for growth-induced instabilities JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Javili, A., Steinmann, P., Kuhl, E. 2014; 29: 20-32

  Abstract

  Geometric instabilities in living structures can be critical for healthy biological function, and abnormal buckling, folding, or wrinkling patterns are often important indicators of disease. Mathematical models typically attribute these instabilities to differential growth, and characterize them using the concept of fictitious configurations. This kinematic approach toward growth-induced instabilities is based on the multiplicative decomposition of the total deformation gradient into a reversible elastic part and an irreversible growth part. While this generic concept is generally accepted and well established today, the critical conditions for the formation of growth-induced instabilities remain elusive and poorly understood. Here we propose a novel strategy for the stability analysis of growing structures motivated by the idea of replacing growth by prestress. Conceptually speaking, we kinematically map the stress-free grown configuration onto a prestressed initial configuration. This allows us to adopt a classical infinitesimal stability analysis to identify critical material parameter ranges beyond which growth-induced instabilities may occur. We illustrate the proposed concept by a series of numerical examples using the finite element method. Understanding the critical conditions for growth-induced instabilities may have immediate applications in plastic and reconstructive surgery, asthma, obstructive sleep apnoea, and brain development.

  View details for DOI 10.1016/j.jmbbm.2013.08.017

  View details for Web of Science ID 000330085700003

  View details for PubMedID 24041754

• Growing matter: a review of growth in living systems. Journal of the mechanical behavior of biomedical materials Kuhl, E. 2014; 29: 529-43

  Abstract

  Living systems can grow, develop, adapt, and evolve. These phenomena are non-intuitive to traditional engineers and often difficult to understand. Yet, classical engineering tools can provide valuable insight into the mechanisms of growth in health and disease. Within the past decade, the concept of incompatible configurations has evolved as a powerful tool to model growing systems within the framework of nonlinear continuum mechanics. However, there is still a substantial disconnect between the individual disciplines, which explore the phenomenon of growth from different angles. Here we show that the nonlinear field theories of mechanics provide a unified concept to model finite growth by means of a single tensorial internal variable, the second order growth tensor. We review the literature and categorize existing growth models by means of two criteria: the microstructural appearance of growth, either isotropic or anisotropic; and the microenvironmental cues that drive the growth process, either chemical or mechanical. We demonstrate that this generic concept is applicable to a broad range of phenomena such as growing arteries, growing tumors, growing skin, growing airway walls, growing heart valve leaflets, growing skeletal muscle, growing plant stems, growing heart valve annuli, and growing cardiac muscle. The proposed approach has important biological and clinical applications in atherosclerosis, in-stent restenosis, tumor invasion, tissue expansion, chronic bronchitis, mitral regurgitation, limb lengthening, tendon tear, plant physiology, dilated and hypertrophic cardiomyopathy, and heart failure. Understanding the mechanisms of growth in these chronic conditions may open new avenues in medical device design and personalized medicine to surgically or pharmacologically manipulate development and alter, control, or revert disease progression.

  View details for DOI 10.1016/j.jmbbm.2013.10.009

  View details for PubMedID 24239171

• Human pluripotent stem cell tools for cardiac optogenetics. Conference proceedings : ... Annual International Conference of the IEEE Engineering in Medicine and Biology Society. IEEE Engineering in Medicine and Biology Society. Annual Conference Zhuge, Y., Patlolla, B., Ramakrishnan, C., Beygui, R. E., Zarins, C. K., Deisseroth, K., Kuhl, E., Abilez, O. J. 2014; 2014: 6171-6174

  Abstract

  It is likely that arrhythmias should be avoided for therapies based on human pluripotent stem cell (hPSC)-derived cardiomyocytes (CM) to be effective. Towards achieving this goal, we introduced light-activated channelrhodopsin-2 (ChR2), a cation channel activated with 480 nm light, into human embryonic stem cells (hESC). By using in vitro approaches, hESC-CM are able to be activated with light. ChR2 is stably transduced into undifferentiated hESC via a lentiviral vector. Via directed differentiation, hESC(ChR2)-CM are produced and subjected to optical stimulation. hESC(ChR2)-CM respond to traditional electrical stimulation and produce similar contractility features as their wild-type counterparts but only hESC(ChR2)-CM can be activated by optical stimulation. Here it is shown that a light sensitive protein can enable in vitro optical control of hESC-CM and that this activation occurs optimally above specific light stimulation intensity and pulse width thresholds. For future therapy, in vivo optical stimulation along with optical inhibition could allow for acute synchronization of implanted hPSC-CM with patient cardiac rhythms.

  View details for DOI 10.1109/EMBC.2014.6945038

  View details for PubMedID 25571406

• On the Role of Mechanics in Chronic Lung Disease. Materials (Basel, Switzerland) Eskandari, M., Pfaller, M. R., Kuhl, E. 2013; 6 (12): 5639-5658

  Abstract

  Progressive airflow obstruction is a classical hallmark of chronic lung disease, affecting more than one fourth of the adult population. As the disease progresses, the inner layer of the airway wall grows, folds inwards, and narrows the lumen. The critical failure conditions for airway folding have been studied intensely for idealized circular cross-sections. However, the role of airway branching during this process is unknown. Here, we show that the geometry of the bronchial tree plays a crucial role in chronic airway obstruction and that critical failure conditions vary significantly along a branching airway segment. We perform systematic parametric studies for varying airway cross-sections using a computational model for mucosal thickening based on the theory of finite growth. Our simulations indicate that smaller airways are at a higher risk of narrowing than larger airways and that regions away from a branch narrow more drastically than regions close to a branch. These results agree with clinical observations and could help explain the underlying mechanisms of progressive airway obstruction. Understanding growth-induced instabilities in constrained geometries has immediate biomedical applications beyond asthma and chronic bronchitis in the diagnostics and treatment of chronic gastritis, obstructive sleep apnea and breast cancer.

  View details for DOI 10.3390/ma6125639

  View details for PubMedID 28788414

  View details for PubMedCentralID PMC5452755

• Mathematical modeling of collagen turnover in biological tissue JOURNAL OF MATHEMATICAL BIOLOGY Saez, P., Pena, E., Angel Martinez, M., Kuhl, E. 2013; 67 (6-7): 1765-1793

  Abstract

  We present a theoretical and computational model for collagen turnover in soft biological tissues. Driven by alterations in the mechanical environment, collagen fiber bundles may undergo important chronic changes, characterized primarily by alterations in collagen synthesis and degradation rates. In particular, hypertension triggers an increase in tropocollagen synthesis and a decrease in collagen degradation, which lead to the well-documented overall increase in collagen content. These changes are the result of a cascade of events, initiated mainly by the endothelial and smooth muscle cells. Here, we represent these events collectively in terms of two internal variables, the concentration of growth factor TGF-[Formula: see text] and tissue inhibitors of metalloproteinases TIMP. The upregulation of TGF-[Formula: see text] increases the collagen density. The upregulation of TIMP also increases the collagen density through decreasing matrix metalloproteinase MMP. We establish a mathematical theory for mechanically-induced collagen turnover and introduce a computational algorithm for its robust and efficient solution. We demonstrate that our model can accurately predict the experimentally observed collagen increase in response to hypertension reported in literature. Ultimately, the model can serve as a valuable tool to predict the chronic adaptation of collagen content to restore the homeostatic equilibrium state in vessels with arbitrary micro-structure and geometry.

  View details for DOI 10.1007/s00285-012-0613-y

  View details for Web of Science ID 000326898300016

  View details for PubMedID 23129392

• On the Role of Mechanics in Chronic Lung Disease MATERIALS Eskandari, M., Pfaller, M. R., Kuhl, E. 2013; 6 (12): 5639-5658

  Abstract

  Progressive airflow obstruction is a classical hallmark of chronic lung disease, affecting more than one fourth of the adult population. As the disease progresses, the inner layer of the airway wall grows, folds inwards, and narrows the lumen. The critical failure conditions for airway folding have been studied intensely for idealized circular cross-sections. However, the role of airway branching during this process is unknown. Here, we show that the geometry of the bronchial tree plays a crucial role in chronic airway obstruction and that critical failure conditions vary significantly along a branching airway segment. We perform systematic parametric studies for varying airway cross-sections using a computational model for mucosal thickening based on the theory of finite growth. Our simulations indicate that smaller airways are at a higher risk of narrowing than larger airways and that regions away from a branch narrow more drastically than regions close to a branch. These results agree with clinical observations and could help explain the underlying mechanisms of progressive airway obstruction. Understanding growth-induced instabilities in constrained geometries has immediate biomedical applications beyond asthma and chronic bronchitis in the diagnostics and treatment of chronic gastritis, obstructive sleep apnea and breast cancer.

  View details for DOI 10.3390/ma6125639

  View details for Web of Science ID 000330297600014

  View details for PubMedCentralID PMC5452755

• Growth on demand: Reviewing the mechanobiology of stretched skin JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Zoellner, A. M., Holland, M. A., Honda, K. S., Gosain, A. K., Kuhl, E. 2013; 28: 495-509

  View details for DOI 10.1016/j.jmbbm.2013.03.018

  View details for Web of Science ID 000328234500044

• Computational modeling of chemo-electro-mechanical coupling: A novel implicit monolithic finite element approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Wong, J., Goektepe, S., Kuhl, E. 2013; 29 (10): 1104-1133

  Abstract

  Computational modeling of the human heart allows us to predict how chemical, electrical, and mechanical fields interact throughout a cardiac cycle. Pharmacological treatment of cardiac disease has advanced significantly over the past decades, yet it remains unclear how the local biochemistry of an individual heart cell translates into global cardiac function. Here, we propose a novel, unified strategy to simulate excitable biological systems across three biological scales. To discretize the governing chemical, electrical, and mechanical equations in space, we propose a monolithic finite element scheme. We apply a highly efficient and inherently modular global-local split, in which the deformation and the transmembrane potential are introduced globally as nodal degrees of freedom, whereas the chemical state variables are treated locally as internal variables. To ensure unconditional algorithmic stability, we apply an implicit backward Euler finite difference scheme to discretize the resulting system in time. To increase algorithmic robustness and guarantee optimal quadratic convergence, we suggest an incremental iterative Newton-Raphson scheme. The proposed algorithm allows us to simulate the interaction of chemical, electrical, and mechanical fields during a representative cardiac cycle on a patient-specific geometry, robust and stable, with calculation times on the order of 4 days on a standard desktop computer.Copyright © 2013 John Wiley & Sons, Ltd.

  View details for DOI 10.1002/cnm.2565

  View details for Web of Science ID 000325500200006

  View details for PubMedID 23798328

• Mechanics of the Mitral Annulus in Chronic Ischemic Cardiomyopathy ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Tibayan, F. A., Ingels, N. B., Miller, D. C., Kuhl, E. 2013; 41 (10): 2171-2180

  Abstract

  Approximately one third of all patients undergoing open-heart surgery for repair of ischemic mitral regurgitation present with residual and recurrent mitral valve leakage upon follow up. A fundamental quantitative understanding of mitral valve remodeling following myocardial infarction may hold the key to improved medical devices and better treatment outcomes. Here we quantify mitral annular strains and curvature in nine sheep 5 ± 1 weeks after controlled inferior myocardial infarction of the left ventricle. We complement our marker-based mechanical analysis of the remodeling mitral valve by common clinical measures of annular geometry before and after the infarct. After 5 ± 1 weeks, the mitral annulus dilated in septal-lateral direction by 15.2% (p = 0.003) and in commissure-commissure direction by 14.2% (p < 0.001). The septal annulus dilated by 10.4% (p = 0.013) and the lateral annulus dilated by 18.4% (p < 0.001). Remarkably, in animals with large degree of mitral regurgitation and annular remodeling, the annulus dilated asymmetrically with larger distortions toward the lateral-posterior segment. Strain analysis revealed average tensile strains of 25% over most of the annulus with exception for the lateral-posterior segment, where tensile strains were 50% and higher. Annular dilation and peak strains were closely correlated to the degree of mitral regurgitation. A complementary relative curvature analysis revealed a homogenous curvature decrease associated with significant annular circularization. All curvature profiles displayed distinct points of peak curvature disturbing the overall homogenous pattern. These hinge points may be the mechanistic origin for the asymmetric annular deformation following inferior myocardial infarction. In the future, this new insight into the mechanism of asymmetric annular dilation may support improved device designs and possibly aid surgeons in reconstructing healthy annular geometry during mitral valve repair.

  View details for DOI 10.1007/s10439-013-0813-7

  View details for PubMedID 23636575

• Mechanics of the mitral valve: a critical review, an in vivo parameter identification, and the effect of prestrain. Biomechanics and modeling in mechanobiology Rausch, M. K., Famaey, N., Shultz, T. O., Bothe, W., Miller, D. C., Kuhl, E. 2013; 12 (5): 1053-1071

  Abstract

  Alterations in mitral valve mechanics are classical indicators of valvular heart disease, such as mitral valve prolapse, mitral regurgitation, and mitral stenosis. Computational modeling is a powerful technique to quantify these alterations, to explore mitral valve physiology and pathology, and to classify the impact of novel treatment strategies. The selection of the appropriate constitutive model and the choice of its material parameters are paramount to the success of these models. However, the in vivo parameters values for these models are unknown. Here, we identify the in vivo material parameters for three common hyperelastic models for mitral valve tissue, an isotropic one and two anisotropic ones, using an inverse finite element approach. We demonstrate that the two anisotropic models provide an excellent fit to the in vivo data, with local displacement errors in the sub-millimeter range. In a complementary sensitivity analysis, we show that the identified parameter values are highly sensitive to prestrain, with some parameters varying up to four orders of magnitude. For the coupled anisotropic model, the stiffness varied from 119,021 kPa at 0 % prestrain via 36 kPa at 30 % prestrain to 9 kPa at 60 % prestrain. These results may, at least in part, explain the discrepancy between previously reported ex vivo and in vivo measurements of mitral leaflet stiffness. We believe that our study provides valuable guidelines for modeling mitral valve mechanics, selecting appropriate constitutive models, and choosing physiologically meaningful parameter values. Future studies will be necessary to experimentally and computationally investigate prestrain, to verify its existence, to quantify its magnitude, and to clarify its role in mitral valve mechanics.

  View details for DOI 10.1007/s10237-012-0462-z

  View details for PubMedID 23263365

  View details for PubMedCentralID PMC3634889

• On the effect of prestrain and residual stress in thin biological membranes JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Rausch, M. K., Kuhl, E. 2013; 61 (9): 1955-1969

  View details for DOI 10.1016/j.jmps.2013.04.005

  View details for Web of Science ID 000322296900005

• On the mechanics of thin films and growing surfaces MATHEMATICS AND MECHANICS OF SOLIDS Holland, M. A., Kosmata, T., Goriely, A., Kuhl, E. 2013; 18 (6): 561-575

  Abstract

  Many living structures are coated by thin films, which have distinct mechanical properties from the bulk. In particular, these thin layers may grow faster or slower than the inner core. Differential growth creates a balanced interplay between tension and compression and plays a critical role in enhancing structural rigidity. Typical examples with a compressive outer surface and a tensile inner core are the petioles of celery, caladium, or rhubarb. While plant physiologists have studied the impact of tissue tension on plant rigidity for more than a century, the fundamental theory of growing surfaces remains poorly understood. Here, we establish a theoretical and computational framework for continua with growing surfaces and demonstrate its application to classical phenomena in plant growth. To allow the surface to grow independently of the bulk, we equip it with its own potential energy and its own surface stress. We derive the governing equations for growing surfaces of zero thickness and obtain their spatial discretization using the finite-element method. To illustrate the features of our new surface growth model we simulate the effects of growth-induced longitudinal tissue tension in a stalk of rhubarb. Our results demonstrate that different growth rates create a mechanical environment of axial tissue tension and residual stress, which can be released by peeling off the outer layer. Our novel framework for continua with growing surfaces has immediate biomedical applications beyond these classical model problems in botany: it can be easily extended to model and predict surface growth in asthma, gastritis, obstructive sleep apnoea, brain development, and tumor invasion. Beyond biology and medicine, surface growth models are valuable tools for material scientists when designing functionalized surfaces with distinct user-defined properties.

  View details for DOI 10.1177/1081286513485776

  View details for Web of Science ID 000323118900002

  View details for PubMedCentralID PMC9718492

• On the mechanics of thin films and growing surfaces. Mathematics and mechanics of solids : MMS Holland, M. A., Kosmata, T., Goriely, A., Kuhl, E. 2013; 18 (6): 561-575

  Abstract

  Many living structures are coated by thin films, which have distinct mechanical properties from the bulk. In particular, these thin layers may grow faster or slower than the inner core. Differential growth creates a balanced interplay between tension and compression and plays a critical role in enhancing structural rigidity. Typical examples with a compressive outer surface and a tensile inner core are the petioles of celery, caladium, or rhubarb. While plant physiologists have studied the impact of tissue tension on plant rigidity for more than a century, the fundamental theory of growing surfaces remains poorly understood. Here, we establish a theoretical and computational framework for continua with growing surfaces and demonstrate its application to classical phenomena in plant growth. To allow the surface to grow independently of the bulk, we equip it with its own potential energy and its own surface stress. We derive the governing equations for growing surfaces of zero thickness and obtain their spatial discretization using the finite-element method. To illustrate the features of our new surface growth model we simulate the effects of growth-induced longitudinal tissue tension in a stalk of rhubarb. Our results demonstrate that different growth rates create a mechanical environment of axial tissue tension and residual stress, which can be released by peeling off the outer layer. Our novel framework for continua with growing surfaces has immediate biomedical applications beyond these classical model problems in botany: it can be easily extended to model and predict surface growth in asthma, gastritis, obstructive sleep apnoea, brain development, and tumor invasion. Beyond biology and medicine, surface growth models are valuable tools for material scientists when designing functionalized surfaces with distinct user-defined properties.

  View details for DOI 10.1177/1081286513485776

  View details for PubMedID 36466793

  View details for PubMedCentralID PMC9718492

• On the mechanics of continua with boundary energies and growing surfaces JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Papastavrou, A., Steinmann, P., Kuhl, E. 2013; 61 (6): 1446-1463

  View details for DOI 10.1016/j.jmps.2013.01.007

  View details for Web of Science ID 000318579500012

• Systems-based approaches toward wound healing PEDIATRIC RESEARCH Tepole, A. B., Kuhl, E. 2013; 73 (4): 553-563

  Abstract

  Wound healing in the pediatric patient is of utmost clinical and social importance because hypertrophic scarring can have aesthetic and psychological sequelae, from early childhood to late adolescence. Wound healing is a well-orchestrated reparative response affecting the damaged tissue at the cellular, tissue, organ, and system scales. Although tremendous progress has been made toward understanding wound healing at the individual temporal and spatial scales, its effects across the scales remain severely understudied and poorly understood. Here, we discuss the critical need for systems-based computational modeling of wound healing across the scales, from short-term to long-term and from small to large. We illustrate the state of the art in systems modeling by means of three key signaling mechanisms: oxygen tension-regulating angiogenesis and revascularization; transforming growth factor-β (TGF-β) kinetics controlling collagen deposition; and mechanical stretch stimulating cellular mitosis and extracellular matrix (ECM) remodeling. The complex network of biochemical and biomechanical signaling mechanisms and the multiscale character of the healing process make systems modeling an integral tool in exploring personalized strategies for wound repair. A better mechanistic understanding of wound healing in the pediatric patient could open new avenues in treating children with skin disorders such as birth defects, skin cancer, wounds, and burn injuries.

  View details for DOI 10.1038/pr.2013.3

  View details for Web of Science ID 000317554900008

  View details for PubMedID 23314298

  View details for PubMedCentralID PMC3615085

• Characterisation of electrophysiological conduction in cardiomyocyte co-cultures using co-occurrence analysis COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Chen, M. Q., Wong, J., Kuhl, E., Giovangrandi, L., Kovacs, G. T. 2013; 16 (2): 185-197

  Abstract

  Cardiac arrhythmias are disturbances of the electrical conduction pattern in the heart with severe clinical implications. The damage of existing cells or the transplantation of foreign cells may disturb functional conduction pathways and may increase the risk of arrhythmias. Although these conduction disturbances are easily accessible with the human eye, there is no algorithmic method to extract quantitative features that quickly portray the conduction pattern. Here, we show that co-occurrence analysis, a well-established method for feature recognition in texture analysis, provides insightful quantitative information about the uniformity and the homogeneity of an excitation wave. As a first proof-of-principle, we illustrate the potential of co-occurrence analysis by means of conduction patterns of cardiomyocyte-fibroblast co-cultures, generated both in vitro and in silico. To characterise signal propagation in vitro, we perform a conduction analysis of co-cultured murine HL-1 cardiomyocytes and murine 3T3 fibroblasts using microelectrode arrays. To characterise signal propagation in silico, we establish a conduction analysis of co-cultured electrically active, conductive cardiomyocytes and non-conductive fibroblasts using the finite element method. Our results demonstrate that co-occurrence analysis is a powerful tool to create purity-conduction relationships and to quickly quantify conduction patterns in terms of co-occurrence energy and contrast. We anticipate this first preliminary study to be a starting point for more sophisticated analyses of different co-culture systems. In particular, in view of stem cell therapies, we expect co-occurrence analysis to provide valuable quantitative insight into the integration of foreign cells into a functional host system.

  View details for DOI 10.1080/10255842.2011.615310

  View details for PubMedID 21970595

• A three-constituent damage model for arterial clamping in computer-assisted surgery BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Famaey, N., Vander Sloten, J., Kuhl, E. 2013; 12 (1): 123-136

  Abstract

  Robotic surgery is an attractive, minimally invasive and high precision alternative to conventional surgical procedures. However, it lacks the natural touch and force feedback that allows the surgeon to control safe tissue manipulation. This is an important problem in standard surgical procedures such as clamping, which might induce severe tissue damage. In complex, heterogeneous, large deformation scenarios, the limits of the safe loading regime beyond which tissue damage occurs are unknown. Here, we show that a continuum damage model for arteries, implemented in a finite element setting, can help to predict arterial stiffness degradation and to identify critical loading regimes. The model consists of the main mechanical constituents of arterial tissue: extracellular matrix, collagen fibres and smooth muscle cells. All constituents are allowed to degrade independently in response to mechanical overload. To demonstrate the modularity and portability of the proposed model, we implement it in a commercial finite element programme, which allows to keep track of damage progression via internal variables. The loading history during arterial clamping is simulated through four successive steps, incorporating residual strains. The results of our first prototype simulation demonstrate significant regional variations in smooth muscle cell damage. In three additional steps, this damage is evaluated by simulating an isometric contraction experiment. The entire finite element simulation is finally compared with actual in vivo experiments. In the short term, our computational simulation tool can be useful to optimise surgical tools with the goal to minimise tissue damage. In the long term, it can potentially be used to inform computer-assisted surgery and identify safe loading regimes, in real time, to minimise tissue damage during robotic tissue manipulation.

  View details for DOI 10.1007/s10237-012-0386-7

  View details for Web of Science ID 000313480100011

  View details for PubMedID 22446834

• A fully implicit finite element method for bidomain models of cardiac electromechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Dal, H., Goektepe, S., Kaliske, M., Kuhl, E. 2013; 253: 323-336

  View details for DOI 10.1016/j.cma.2012.07.004

  View details for Web of Science ID 000313134600021

• Evidence of adaptive mitral leaflet growth JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. 2012; 15: 208-217

  Abstract

  Ischemic mitral regurgitation is mitral insufficiency caused by myocardial infarction. Recent studies suggest that mitral leaflets have the potential to grow and reduce the degree of regurgitation. Leaflet growth has been associated with papillary muscle displacement, but role of annular dilation in leaflet growth is unclear. We tested the hypothesis that chronic leaflet stretch, induced by papillary muscle tethering and annular dilation, triggers chronic leaflet growth. To decipher the mechanisms that drive the growth process, we further quantified regional and directional variations of growth. Five adult sheep underwent coronary snare and marker placement on the left ventricle, papillary muscles, mitral annulus, and mitral leaflet. After eight days, we tightened the snares to create inferior myocardial infarction. We recorded marker coordinates at baseline, acutely (immediately post-infarction), and chronically (five weeks post-infarction). From these coordinates, we calculated acute and chronic changes in ventricular, papillary muscle, and annular geometry along with acute and chronic leaflet strains. Chronic left ventricular dilation of 17.15% (p<0.001) induced chronic posterior papillary muscle displacement of 13.49 mm (p=0.07). Chronic mitral annular area, commissural and septal-lateral distances increased by 32.50% (p=0.010), 14.11% (p=0.007), and 10.84% (p=0.010). Chronic area, circumferential, and radial growth were 15.57%, 5.91%, and 3.58%, with non-significant regional variations (p=0.868). Our study demonstrates that mechanical stretch, induced by annular dilation and papillary muscle tethering, triggers mitral leaflet growth. Understanding the mechanisms of leaflet adaptation may open new avenues to pharmacologically or surgically manipulate mechanotransduction pathways to augment mitral leaflet area and reduce the degree of regurgitation.

  View details for DOI 10.1016/j.jmbbm.2012.07.001

  View details for Web of Science ID 000313598800020

  View details for PubMedID 23159489

  View details for PubMedCentralID PMC3508091

• Stretching Skeletal Muscle: Chronic Muscle Lengthening through Sarcomerogenesis PLOS ONE Zoellner, A. M., Abilez, O. J., Boel, M., Kuhl, E. 2012; 7 (10)

  Abstract

  Skeletal muscle responds to passive overstretch through sarcomerogenesis, the creation and serial deposition of new sarcomere units. Sarcomerogenesis is critical to muscle function: It gradually re-positions the muscle back into its optimal operating regime. Animal models of immobilization, limb lengthening, and tendon transfer have provided significant insight into muscle adaptation in vivo. Yet, to date, there is no mathematical model that allows us to predict how skeletal muscle adapts to mechanical stretch in silico. Here we propose a novel mechanistic model for chronic longitudinal muscle growth in response to passive mechanical stretch. We characterize growth through a single scalar-valued internal variable, the serial sarcomere number. Sarcomerogenesis, the evolution of this variable, is driven by the elastic mechanical stretch. To analyze realistic three-dimensional muscle geometries, we embed our model into a nonlinear finite element framework. In a chronic limb lengthening study with a muscle stretch of 1.14, the model predicts an acute sarcomere lengthening from 3.09[Formula: see text]m to 3.51[Formula: see text]m, and a chronic gradual return to the initial sarcomere length within two weeks. Compared to the experiment, the acute model error was 0.00% by design of the model; the chronic model error was 2.13%, which lies within the rage of the experimental standard deviation. Our model explains, from a mechanistic point of view, why gradual multi-step muscle lengthening is less invasive than single-step lengthening. It also explains regional variations in sarcomere length, shorter close to and longer away from the muscle-tendon interface. Once calibrated with a richer data set, our model may help surgeons to prevent muscle overstretch and make informed decisions about optimal stretch increments, stretch timing, and stretch amplitudes. We anticipate our study to open new avenues in orthopedic and reconstructive surgery and enhance treatment for patients with ill proportioned limbs, tendon lengthening, tendon transfer, tendon tear, and chronically retracted muscles.

  View details for DOI 10.1371/journal.pone.0045661

  View details for Web of Science ID 000309388500010

  View details for PubMedID 23049683

  View details for PubMedCentralID PMC3462200

• Stretching skin: The physiological limit and beyond. International journal of non-linear mechanics Tepole, A. B., Gosain, A. K., Kuhl, E. 2012; 47 (8): 938-949

  Abstract

  The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

  View details for DOI 10.1016/j.ijnonlinmec.2011.07.006

  View details for PubMedID 23459410

  View details for PubMedCentralID PMC3583021

• Stretching skin: The physiological limit and beyond INTERNATIONAL JOURNAL OF NON-LINEAR MECHANICS Tepole, A. B., Gosain, A. K., Kuhl, E. 2012; 47 (8): 938-949

  Abstract

  The goal of this manuscript is to establish a novel computational model for skin to characterize its constitutive behavior when stretched within and beyond its physiological limits. Within the physiological regime, skin displays a reversible, highly nonlinear, stretch locking, and anisotropic behavior. We model these characteristics using a transversely isotropic chain network model composed of eight wormlike chains. Beyond the physiological limit, skin undergoes an irreversible area growth triggered through mechanical stretch. We model skin growth as a transversely isotropic process characterized through a single internal variable, the scalar-valued growth multiplier. To discretize the evolution of growth in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To illustrate the characteristic features of skin growth, we first compare the two simple model problems of displacement- and force-driven growth. Then, we model the process of stretch-induced skin growth during tissue expansion. In particular, we compare the spatio-temporal evolution of stress, strain, and area gain for four commonly available tissue expander geometries. We believe that the proposed model has the potential to open new avenues in reconstructive surgery and rationalize critical process parameters in tissue expansion, such as expander geometry, expander size, expander placement, and inflation timing.

  View details for DOI 10.1016/j.ijnonlinmec.2011.07.006

  View details for Web of Science ID 000307613200010

  View details for PubMedCentralID PMC3583021

• How Do Annuloplasty Rings Affect Mitral Annular Strains in the Normal Beating Ovine Heart? Meeting of the American-Heart-Association Bothe, W., Rausch, M. K., Kvitting, J. E., Echtner, D. K., Walther, M., Ingels, N. B., Kuhl, E., Miller, D. C. LIPPINCOTT WILLIAMS & WILKINS. 2012: S231–S238

  Abstract

  We hypothesized that annuloplasty ring implantation alters mitral annular strains in a normal beating ovine heart preparation.Sheep had 16 radiopaque markers sewn equally spaced around the mitral annulus. Edwards Cosgrove partial flexible band (COS; n=12), St Jude complete rigid saddle-shaped annuloplasty ring (RSA; n=10), Carpentier-Edwards Physio (PHY; n=11), Edwards IMR ETlogix (ETL; n=11), and GeoForm (GEO; n=12) annuloplasty rings were implanted in a releasable fashion. Four-dimensional marker coordinates were obtained using biplane videofluoroscopy with the ring inserted (ring) and after ring release (control). From marker coordinates, a functional spatio-temporal representation of each annulus was generated through a best fit using 16 piecewise cubic Hermitian splines. Absolute total mitral annular ring strains were calculated from the relative change in length of the tangent vector to the annular curve as strains occurring from control to ring state at end-systole. In addition, average Green-Lagrange strains occurring from control to ring state at end-systole along the annulus were calculated. Absolute total mitral annular ring strains were smallest for COS and greatest for ETL. Strains for RSA, PHY, and GEO were similar. Except for COS in the septal mitral annular segment, all rings induced compressive strains along the entire annulus, with greatest values occurring at the lateral mitral annular segment.In healthy, beating ovine hearts, annuloplasty rings (COS, RSA, PHY, ETL, and GEO) induce compressive strains that are predominate in the lateral annular region, smallest for flexible partial bands (COS) and greatest for an asymmetrical rigid ring type with intrinsic septal-lateral downsizing (ETL). However, the ring type with the most drastic intrinsic septal-lateral downsizing (GEO) introduced strains similar to physiologically shaped rings (RSA and PHY), indicating that ring effects on annular strain profiles cannot be estimated from the degree of septal-lateral downsizing.

  View details for DOI 10.1161/CIRCULATIONAHA.111.084046

  View details for PubMedID 22965988

• Growing skin: tissue expansion in pediatric forehead reconstruction. Biomechanics and modeling in mechanobiology Zöllner, A. M., Buganza Tepole, A., Gosain, A. K., Kuhl, E. 2012; 11 (6): 855-867

  Abstract

  Tissue expansion is a common surgical procedure to grow extra skin through controlled mechanical over-stretch. It creates skin that matches the color, texture, and thickness of the surrounding tissue, while minimizing scars and risk of rejection. Despite intense research in tissue expansion and skin growth, there is a clear knowledge gap between heuristic observation and mechanistic understanding of the key phenomena that drive the growth process. Here, we show that a continuum mechanics approach, embedded in a custom-designed finite element model, informed by medical imaging, provides valuable insight into the biomechanics of skin growth. In particular, we model skin growth using the concept of an incompatible growth configuration. We characterize its evolution in time using a second-order growth tensor parameterized in terms of a scalar-valued internal variable, the in-plane area growth. When stretched beyond the physiological level, new skin is created, and the in-plane area growth increases. For the first time, we simulate tissue expansion on a patient-specific geometric model, and predict stress, strain, and area gain at three expanded locations in a pediatric skull: in the scalp, in the forehead, and in the cheek. Our results may help the surgeon to prevent tissue over-stretch and make informed decisions about expander geometry, size, placement, and inflation. We anticipate our study to open new avenues in reconstructive surgery and enhance treatment for patients with birth defects, burn injuries, or breast tumor removal.

  View details for DOI 10.1007/s10237-011-0357-4

  View details for PubMedID 22052000

  View details for PubMedCentralID PMC3425448

• Anisotropic density growth of bone-A computational micro-sphere approach INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Waffenschmidt, T., Menzel, A., Kuhl, E. 2012; 49 (14): 1928-1946

  View details for DOI 10.1016/j.ijsolstr.2012.03.035

  View details for Web of Science ID 000305441600002

• Growth and remodeling of the left ventricle: A case study of myocardial infarction and surgical ventricular restoration MECHANICS RESEARCH COMMUNICATIONS Klepach, D., Lee, L. C., Wenk, J. F., Ratcliffe, M. B., Zohdi, T. I., Navia, J. L., Kassab, G. S., Kuhl, E., Guccione, J. M. 2012; 42: 134-141

  Abstract

  Cardiac growth and remodeling in the form of chamber dilation and wall thinning are typical hallmarks of infarct-induced heart failure. Over time, the infarct region stiffens, the remaining muscle takes over function, and the chamber weakens and dilates. Current therapies seek to attenuate these effects by removing the infarct region or by providing structural support to the ventricular wall. However, the underlying mechanisms of these therapies are unclear, and the results remain suboptimal. Here we show that myocardial infarction induces pronounced regional and transmural variations in cardiac form. We introduce a mechanistic growth model capable of predicting structural alterations in response to mechanical overload. Under a uniform loading, this model predicts non-uniform growth. Using this model, we simulate growth in a patient-specific left ventricle. We compare two cases, growth in an infarcted heart, pre-operative, and growth in the same heart, after the infarct was surgically excluded, post-operative. Our results suggest that removing the infarct and creating a left ventricle with homogeneous mechanical properties does not necessarily reduce the driving forces for growth and remodeling. These preliminary findings agree conceptually with clinical observations.

  View details for DOI 10.1016/j.mechrescom.2012.03.005

  View details for Web of Science ID 000304847400015

  View details for PubMedCentralID PMC3390946

• Computational Optogenetics: A Novel Continuum Framework for the Photoelectrochemistry of Living Systems. Journal of the mechanics and physics of solids Wong, J., Abilez, O. J., Kuhl, E. 2012; 60 (6): 1158-1178

  Abstract

  Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to virtually probe landscapes of process parameters, and to identify optimal photostimulation sequences with the goal to pace human hearts with light and, ultimately, to restore mechanical function.

  View details for DOI 10.1016/j.jmps.2012.02.004

  View details for PubMedID 22773861

  View details for PubMedCentralID PMC3388516

• Computational optogenetics: A novel continuum framework for the photoelectrochemistry of living systems JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Wong, J., Abilez, O. J., Kuhl, E. 2012; 60 (6): 1158-1178

  Abstract

  Electrical stimulation is currently the gold standard treatment for heart rhythm disorders. However, electrical pacing is associated with technical limitations and unavoidable potential complications. Recent developments now enable the stimulation of mammalian cells with light using a novel technology known as optogenetics. The optical stimulation of genetically engineered cells has significantly changed our understanding of electrically excitable tissues, paving the way towards controlling heart rhythm disorders by means of photostimulation. Controlling these disorders, in turn, restores coordinated force generation to avoid sudden cardiac death. Here, we report a novel continuum framework for the photoelectrochemistry of living systems that allows us to decipher the mechanisms by which this technology regulates the electrical and mechanical function of the heart. Using a modular multiscale approach, we introduce a non-selective cation channel, channelrhodopsin-2, into a conventional cardiac muscle cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, this channel opens and allows sodium ions to enter the cell, inducing electrical activation. In side-by-side comparisons with conventional heart muscle cells, we show that photostimulation directly increases the sodium concentration, which indirectly decreases the potassium concentration in the cell, while all other characteristics of the cell remain virtually unchanged. We integrate our model cells into a continuum model for excitable tissue using a nonlinear parabolic second order partial differential equation, which we discretize in time using finite differences and in space using finite elements. To illustrate the potential of this computational model, we virtually inject our photosensitive cells into different locations of a human heart, and explore its activation sequences upon photostimulation. Our computational optogenetics tool box allows us to virtually probe landscapes of process parameters, and to identify optimal photostimulation sequences with the goal to pace human hearts with light and, ultimately, to restore mechanical function.

  View details for DOI 10.1016/j.jmps.2012.02.004

  View details for Web of Science ID 000303285600007

  View details for PubMedCentralID PMC3388516

• Frontiers in growth and remodeling MECHANICS RESEARCH COMMUNICATIONS Menzel, A., Kuhl, E. 2012; 42: 1-14

  View details for DOI 10.1016/j.mechrescom.2012.02.007

  View details for Web of Science ID 000304847400001

• Kinematics of cardiac growth: In vivo characterization of growth tensors and strains JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Tsamis, A., Cheng, A., Nguyen, T. C., Langer, F., Miller, D. C., Kuhl, E. 2012; 8: 165-177

  Abstract

  Progressive growth and remodeling of the left ventricle are part of the natural history of chronic heart failure and strong clinical indicators for survival. Accompanied by changes in cardiac form and function, they manifest themselves in alterations of cardiac strains, fiber stretches, and muscle volume. Recent attempts to shed light on the mechanistic origin of heart failure utilize continuum theories of growth to predict the maladaptation of the heart in response to pressure or volume overload. However, despite a general consensus on the representation of growth through a second order tensor, the precise format of this growth tensor remains unknown. Here we show that infarct-induced cardiac dilation is associated with a chronic longitudinal growth, accompanied by a chronic thinning of the ventricular wall. In controlled in vivo experiments throughout a period of seven weeks, we found that the lateral left ventricular wall adjacent to the infarct grows longitudinally by more than 10%, thins by more than 25%, lengthens in fiber direction by more than 5%, and decreases its volume by more than 15%. Our results illustrate how a local loss of blood supply induces chronic alterations in structure and function in adjacent regions of the ventricular wall. We anticipate our findings to be the starting point for a series of in vivo studies to calibrate and validate constitutive models for cardiac growth. Ultimately, these models could be useful to guide the design of novel therapies, which allow us to control the progression of heart failure.

  View details for DOI 10.1016/j.jmbbm.2011.12.006

  View details for Web of Science ID 000302586300015

  View details for PubMedID 22402163

  View details for PubMedCentralID PMC3298662

• On the biomechanics and mechanobiology of growing skin JOURNAL OF THEORETICAL BIOLOGY Zoellner, A. M., Tepole, A. B., Kuhl, E. 2012; 297: 166-175

  Abstract

  Skin displays an impressive functional plasticity, which allows it to adapt gradually to environmental changes. Tissue expansion takes advantage of this adaptation, and induces a controlled in situ skin growth for defect correction in plastic and reconstructive surgery. Stretches beyond the skin's physiological limit invoke several mechanotransduction pathways, which increase mitotic activity and collagen synthesis, ultimately resulting in a net gain in skin surface area. However, the interplay between mechanics and biology during tissue expansion remains unquantified. Here, we present a continuum model for skin growth that summarizes the underlying mechanotransduction pathways collectively in a single phenomenological variable, the strain-driven area growth. We illustrate the governing equations for growing biological membranes, and demonstrate their computational solution within a nonlinear finite element setting. In displacement-controlled equi-biaxial extension tests, the model accurately predicts the experimentally observed histological, mechanical, and structural features of growing skin, both qualitatively and quantitatively. Acute and chronic elastic uniaxial stretches are 25% and 10%, compared to 36% and 10% reported in the literature. Acute and chronic thickness changes are -28% and -12%, compared to -22% and -7% reported in the literature. Chronic fractional weight gain is 3.3, compared to 2.7 for wet weight and 3.3 for dry weight reported in the literature. In two clinical cases of skin expansion in pediatric forehead reconstruction, the model captures the clinically observed mechanical and structural responses, both acutely and chronically. Our results demonstrate that the field theories of continuum mechanics can reliably predict the mechanical manipulation of thin biological membranes by controlling their mechanotransduction pathways through mechanical overstretch. We anticipate that the proposed skin growth model can be generalized to arbitrary biological membranes, and that it can serve as a valuable tool to virtually manipulate living tissues, simply by means of changes in the mechanical environment.

  View details for DOI 10.1016/j.jtbi.2011.12.022

  View details for Web of Science ID 000300652000016

  View details for PubMedID 22227432

  View details for PubMedCentralID PMC3278515

• Computational modeling of bone density profiles in response to gait: a subject-specific approach BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Pang, H., Shiwalkar, A. P., Madormo, C. M., Taylor, R. E., Andriacchi, T. P., Kuhl, E. 2012; 11 (3-4): 379-390

  Abstract

  The goal of this study is to explore the potential of computational growth models to predict bone density profiles in the proximal tibia in response to gait-induced loading. From a modeling point of view, we design a finite element-based computational algorithm using the theory of open system thermodynamics. In this algorithm, the biological problem, the balance of mass, is solved locally on the integration point level, while the mechanical problem, the balance of linear momentum, is solved globally on the node point level. Specifically, the local bone mineral density is treated as an internal variable, which is allowed to change in response to mechanical loading. From an experimental point of view, we perform a subject-specific gait analysis to identify the relevant forces during walking using an inverse dynamics approach. These forces are directly applied as loads in the finite element simulation. To validate the model, we take a Dual-Energy X-ray Absorptiometry scan of the subject's right knee from which we create a geometric model of the proximal tibia. For qualitative validation, we compare the computationally predicted density profiles to the bone mineral density extracted from this scan. For quantitative validation, we adopt the region of interest method and determine the density values at fourteen discrete locations using standard and custom-designed image analysis tools. Qualitatively, our two- and three-dimensional density predictions are in excellent agreement with the experimental measurements. Quantitatively, errors are less than 3% for the two-dimensional analysis and less than 10% for the three-dimensional analysis. The proposed approach has the potential to ultimately improve the long-term success of possible treatment options for chronic diseases such as osteoarthritis on a patient-specific basis by accurately addressing the complex interactions between ambulatory loads and tissue changes.

  View details for DOI 10.1007/s10237-011-0318-y

  View details for Web of Science ID 000300518000008

  View details for PubMedID 21604146

• Mitral Valve Annuloplasty A Quantitative Clinical and Mechanical Comparison of Different Annuloplasty Devices ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Bothe, W., Kvitting, J. E., Swanson, J. C., Miller, D. C., Kuhl, E. 2012; 40 (3): 750-761

  Abstract

  Mitral valve annuloplasty is a common surgical technique used in the repair of a leaking valve by implanting an annuloplasty device. To enhance repair durability, these devices are designed to increase leaflet coaptation, while preserving the native annular shape and motion; however, the precise impact of device implantation on annular deformation, strain, and curvature is unknown. In this article, we quantify how three frequently used devices significantly impair native annular dynamics. In controlled in vivo experiments, we surgically implanted 11 flexible-incomplete, 11 semi-rigid-complete, and 12 rigid-complete devices around the mitral annuli of 34 sheep, each tagged with 16 equally spaced tantalum markers. We recorded four-dimensional marker coordinates using biplane videofluoroscopy, first with device and then without, which were used to create mathematical models using piecewise cubic splines. Clinical metrics (characteristic anatomical distances) revealed significant global reduction in annular dynamics upon device implantation. Mechanical metrics (strain and curvature fields) explained this reduction via a local loss of anterior dilation and posterior contraction. Overall, all three devices unfavorably caused reduction in annular dynamics. The flexible-incomplete device, however, preserved native annular dynamics to a larger extent than the complete devices. Heterogeneous strain and curvature profiles suggest the need for heterogeneous support, which may spawn more rational design of annuloplasty devices using design concepts of functionally graded materials.

  View details for DOI 10.1007/s10439-011-0442-y

  View details for PubMedID 22037916

• SPECIAL ISSUE ACTIVE TISSUE MODELING: FROM SINGLE MUSCLE CELLS TO MUSCULAR CONTRACTION INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Kuhl, E. 2012; 10 (2): VII-VIII

  View details for Web of Science ID 000302835000001

• COMPUTATIONAL MODELLING OF OPTOGENETICS IN CARDIAC CELLS ASME Summer Bioengineering Conference (SBC) Wong, J., Abilez, O., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 355–356

  View details for Web of Science ID 000325036600177

• CHRONIC MITRAL VALVE LEAFLET GROWTH FOLLOWING MYOCARDIAL INFARCTION ASME Summer Bioengineering Conference (SBC) Rausch, M. K., Tibayan, F. A., Miller, D. C., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 1015–1016

  View details for Web of Science ID 000325036600507

• FINITE ELEMENT MODELING OF FLAP DESIGN AFTER SKIN EXPANSION ASME Summer Bioengineering Conference (SBC) Tepole, A. B., Zollner, A. M., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 1017–1018

  View details for Web of Science ID 000325036600508

• MODELING GROWTH IN TISSUE EXPANSION ASME Summer Bioengineering Conference (SBC) Zoellner, A. M., Tepole, A. B., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2012: 213–214

  View details for Web of Science ID 000325036600106

• Computational modeling of electrocardiograms: Repolarization and T-wave polarity in the human heart Comp Meth Biomech Biomed Eng, accepted for publication. Hurtado D, Kuhl E 2012
• Consistent formulation of the growth process at the kinematic and constitutive level for soft tissues composed of multiple constituents COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Schmid, H., PAULI, L., Paulus, A., Kuhl, E., Itskov, M. 2012; 15 (5): 547-561

  Abstract

  Previous studies have investigated the possibilities of modelling the change in volume and change in density of biomaterials. This can be modelled at the constitutive or the kinematic level. This work introduces a consistent formulation at the kinematic and constitutive level for growth processes. Most biomaterials consist of many constituents and can be approximated as being incompressible. These two conditions (many constituents and incompressibility) suggest a straightforward implementation in the context of the finite element (FE) method which could now be validated more easily against histological measurements. Its key characteristic variable is the normalised partial mass change. Using the concept of homeostatic equilibrium, we suggest two complementary growth laws in which the evolution of the normalised partial mass change is governed by an ordinary differential equation in terms of either the Piola-Kirchhoff stress or the Green-Lagrange strain. We combine this approach with the classical incompatibility condition and illustrate its algorithmic implementation within a fully nonlinear FE approach. This approach is first illustrated for a simple uniaxial tension and extension test for pure volume change and pure density change and is validated against previous numerical results. Finally, a physiologically based example of a two-phase model is presented which is a combination of volume and density changes. It can be concluded that the effect of hyper-restoration may be due to the systemic effect of degradation and adaptation of given constituents.

  View details for DOI 10.1080/10255842.2010.548325

  View details for Web of Science ID 000303561200010

  View details for PubMedID 21347909

• A fully implicit finite element method for bidomain models of cardiac electrophysiology COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Dal, H., Goktepe, S., Kaliske, M., Kuhl, E. 2012; 15 (6): 645-656

  Abstract

  This work introduces a novel, unconditionally stable and fully coupled finite element method for the bidomain system of equations of cardiac electrophysiology. The transmembrane potential Φ(i)-Φ(e) and the extracellular potential Φ(e) are treated as independent variables. To this end, the respective reaction-diffusion equations are recast into weak forms via a conventional isoparametric Galerkin approach. The resultant nonlinear set of residual equations is consistently linearised. The method results in a symmetric set of equations, which reduces the computational time significantly compared to the conventional solution algorithms. The proposed method is inherently modular and can be combined with phenomenological or ionic models across the cell membrane. The efficiency of the method and the comparison of its computational cost with respect to the simplified monodomain models are demonstrated through representative numerical examples.

  View details for DOI 10.1080/10255842.2011.554410

  View details for Web of Science ID 000303560100008

  View details for PubMedID 21491253

• IN VITRO/IN SILICO CHARACTERIZATION OF ACTIVE AND PASSIVE STRESSES IN CARDIAC MUSCLE INTERNATIONAL JOURNAL FOR MULTISCALE COMPUTATIONAL ENGINEERING Boel, M., Abilez, O. J., Assar, A. N., Zarins, C. K., Kuhl, E. 2012; 10 (2): 171-188

  View details for Web of Science ID 000302835000006

• Computational modeling of growth: systemic and pulmonary hypertension in the heart BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Rausch, M. K., Dam, A., Goktepe, S., Abilez, O. J., Kuhl, E. 2011; 10 (6): 799-811

  Abstract

  We introduce a novel constitutive model for growing soft biological tissue and study its performance in two characteristic cases of mechanically induced wall thickening of the heart. We adopt the concept of an incompatible growth configuration introducing the multiplicative decomposition of the deformation gradient into an elastic and a growth part. The key feature of the model is the definition of the evolution equation for the growth tensor which we motivate by pressure-overload-induced sarcomerogenesis. In response to the deposition of sarcomere units on the molecular level, the individual heart muscle cells increase in diameter, and the wall of the heart becomes progressively thicker. We present the underlying constitutive equations and their algorithmic implementation within an implicit nonlinear finite element framework. To demonstrate the features of the proposed approach, we study two classical growth phenomena in the heart: left and right ventricular wall thickening in response to systemic and pulmonary hypertension.

  View details for DOI 10.1007/s10237-010-0275-x

  View details for Web of Science ID 000296634000001

  View details for PubMedID 21188611

  View details for PubMedCentralID PMC3235798

• Growing skin: A computational model for skin expansion in reconstructive surgery JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Tepole, A. B., Ploch, C. J., Wong, J., Gosain, A. K., Kuhl, E. 2011; 59 (10): 2177-2190

  Abstract

  The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

  View details for DOI 10.1016/j.jmps.2011.05.004

  View details for Web of Science ID 000295549500013

  View details for PubMedCentralID PMC3212404

• Growing skin: A computational model for skin expansion in reconstructive surgery. Journal of the mechanics and physics of solids Tepole, A. B., Ploch, C. J., Wong, J., Gosain, A. K., Kuhl, E. 2011; 59 (10): 2177-2190

  Abstract

  The goal of this manuscript is to establish a novel computational model for stretch-induced skin growth during tissue expansion. Tissue expansion is a common surgical procedure to grow extra skin for reconstructing birth defects, burn injuries, or cancerous breasts. To model skin growth within the framework of nonlinear continuum mechanics, we adopt the multiplicative decomposition of the deformation gradient into an elastic and a growth part. Within this concept, we characterize growth as an irreversible, stretch-driven, transversely isotropic process parameterized in terms of a single scalar-valued growth multiplier, the in-plane area growth. To discretize its evolution in time, we apply an unconditionally stable, implicit Euler backward scheme. To discretize it in space, we utilize the finite element method. For maximum algorithmic efficiency and optimal convergence, we suggest an inner Newton iteration to locally update the growth multiplier at each integration point. This iteration is embedded within an outer Newton iteration to globally update the deformation at each finite element node. To demonstrate the characteristic features of skin growth, we simulate the process of gradual tissue expander inflation. To visualize growth-induced residual stresses, we simulate a subsequent tissue expander deflation. In particular, we compare the spatio-temporal evolution of area growth, elastic strains, and residual stresses for four commonly available tissue expander geometries. We believe that predictive computational modeling can open new avenues in reconstructive surgery to rationalize and standardize clinical process parameters such as expander geometry, expander size, expander placement, and inflation timing.

  View details for DOI 10.1016/j.jmps.2011.05.004

  View details for PubMedID 22081726

  View details for PubMedCentralID PMC3212404

• Active contraction of cardiac muscle: In vivo characterization of mechanical activation sequences in the beating heart JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Tsamis, A., Bothe, W., Kvitting, J. E., Swanson, J. C., Miller, D. C., Kuhl, E. 2011; 4 (7): 1167-1176

  Abstract

  Progressive alterations in cardiac wall strains are a classic hallmark of chronic heart failure. Accordingly, the objectives of this study are to establish a baseline characterization of cardiac strains throughout the cardiac cycle, to quantify temporal, regional, and transmural variations of active fiber contraction, and to identify pathways of mechanical activation in the healthy beating heart. To this end, we insert two sets of twelve radiopaque beads into the heart muscle of nine sheep; one in the anterior-basal and one in the lateral-equatorial left ventricular wall. During three consecutive heartbeats, we record the bead coordinates via biplane videofluoroscopy. From the resulting four-dimensional data sets, we calculate the temporally and transmurally varying Green-Lagrange strains in the anterior and lateral wall. To quantify active contraction, we project the strains onto the local muscle fiber directions. We observe that mechanical activation is initiated at the endocardium slightly after end diastole and progresses transmurally outward, reaching the epicardium slightly before end systole. Accordingly, fibers near the outer wall are in contraction for approximately half of the cardiac cycle while fibers near the inner wall are in contraction almost throughout the entire cardiac cycle. In summary, cardiac wall strains display significant temporal, regional, and transmural variations. Quantifying wall strain profiles might be of particular clinical significance when characterizing stages of left ventricular remodeling, but also of engineering relevance when designing new biomaterials of similar structure and function.

  View details for DOI 10.1016/j.jmbbm.2011.03.027

  View details for Web of Science ID 000294187500025

  View details for PubMedID 21783125

  View details for PubMedCentralID PMC3143370

• Multiscale Computational Models for Optogenetic Control of Cardiac Function BIOPHYSICAL JOURNAL Abilez, O. J., Wong, J., Prakash, R., Deisseroth, K., Zarins, C. K., Kuhl, E. 2011; 101 (6): 1326-1334

  Abstract

  The ability to stimulate mammalian cells with light has significantly changed our understanding of electrically excitable tissues in health and disease, paving the way toward various novel therapeutic applications. Here, we demonstrate the potential of optogenetic control in cardiac cells using a hybrid experimental/computational technique. Experimentally, we introduced channelrhodopsin-2 into undifferentiated human embryonic stem cells via a lentiviral vector, and sorted and expanded the genetically engineered cells. Via directed differentiation, we created channelrhodopsin-expressing cardiomyocytes, which we subjected to optical stimulation. To quantify the impact of photostimulation, we assessed electrical, biochemical, and mechanical signals using patch-clamping, multielectrode array recordings, and video microscopy. Computationally, we introduced channelrhodopsin-2 into a classic autorhythmic cardiac cell model via an additional photocurrent governed by a light-sensitive gating variable. Upon optical stimulation, the channel opens and allows sodium ions to enter the cell, inducing a fast upstroke of the transmembrane potential. We calibrated the channelrhodopsin-expressing cell model using single action potential readings for different photostimulation amplitudes, pulse widths, and frequencies. To illustrate the potential of the proposed approach, we virtually injected channelrhodopsin-expressing cells into different locations of a human heart, and explored its activation sequences upon optical stimulation. Our experimentally calibrated computational toolbox allows us to virtually probe landscapes of process parameters, and identify optimal photostimulation sequences toward pacing hearts with light.

  View details for DOI 10.1016/j.bpj.2011.08.004

  View details for Web of Science ID 000295197300006

  View details for PubMedID 21943413

  View details for PubMedCentralID PMC3177076

• Rigid, Complete Annuloplasty Rings Increase Anterior Mitral Leaflet Strains in the Normal Beating Ovine Heart Annual Meeting of the American-Heart-Association Bothe, W., Kuhl, E., Kvitting, J. E., Rausch, M. K., Goektepe, S., Swanson, J. C., Farahmandnia, S., Ingels, N. B., Miller, D. C. LIPPINCOTT WILLIAMS & WILKINS. 2011: S81–S96

  Abstract

  Annuloplasty ring or band implantation during surgical mitral valve repair perturbs mitral annular dimensions, dynamics, and shape, which have been associated with changes in anterior mitral leaflet (AML) strain patterns and suboptimal long-term repair durability. We hypothesized that rigid rings with nonphysiological three-dimensional shapes, but not saddle-shaped rigid rings or flexible bands, increase AML strains.Sheep had 23 radiopaque markers inserted: 7 along the anterior mitral annulus and 16 equally spaced on the AML. True-sized Cosgrove-Edwards flexible, partial band (n=12), rigid, complete St Jude Medical rigid saddle-shaped (n=12), Carpentier-Edwards Physio (n=12), Edwards IMR ETlogix (n=11), and Edwards GeoForm (n=12) annuloplasty rings were implanted in a releasable fashion. Under acute open-chest conditions, 4-dimensional marker coordinates were obtained using biplane videofluoroscopy along with hemodynamic parameters with the ring inserted and after release. Marker coordinates were triangulated, and the largest maximum principal AML strains were determined during isovolumetric relaxation. No relevant changes in hemodynamics occurred. Compared with the respective control state, strains increased significantly with rigid saddle-shaped annuloplasty ring, Carpentier-Edwards Physio, Edwards IMR ETlogix, and Edwards GeoForm (0.14 ± 0.05 versus 0.16 ± 0.05, P=0.024, 0.15 ± 0.03 versus 0.18 ± 0.04, P=0.020, 0.11 ± 0.05 versus 0.14 ± 0.05, P=0.042, and 0.13 ± 0.05 versus 0.16 ± 0.05, P=0.009), but not with Cosgrove-Edwards band (0.15 ± 0.05 versus 0.15 ± 0.04, P=0.973).Regardless of three-dimensional shape, rigid, complete annuloplasty rings, but not a flexible, partial band, increased AML strains in the normal beating ovine heart. Clinical studies are needed to determine whether annuloplasty rings affect AML strains in patients, and, if so, whether ring-induced perturbations in leaflet strain states are linked to repair failure.

  View details for DOI 10.1161/CIRCULATIONAHA.110.011163

  View details for PubMedID 21911823

• A novel method for quantifying the in-vivo mechanical effect of material injected into a myocardial infarction. Annals of thoracic surgery Wenk, J. F., Eslami, P., Zhang, Z., Xu, C., Kuhl, E., Gorman, J. H., Robb, J. D., Ratcliffe, M. B., Gorman, R. C., Guccione, J. M. 2011; 92 (3): 935-941

  Abstract

  Infarcted regions of myocardium exhibit functional impairment ranging in severity from hypokinesis to dyskinesis. We sought to quantify the effects of injecting a calcium hydroxyapatite-based tissue filler on the passive material response of infarcted left ventricles.Three-dimensional finite element models of the left ventricle were developed using three-dimensional echocardiography data from sheep with a treated and untreated anteroapical infarct, to estimate the material properties (stiffness) in the infarct and remote regions. This was accomplished by matching experimentally determined left ventricular volumes, and minimizing radial strain in the treated infarct, which is indicative of akinesia. The nonlinear stress-strain relationship for the diastolic myocardium was anisotropic with respect to the local muscle fiber direction, and an elastance model for active fiber stress was incorporated.It was found that the passive stiffness parameter, C, in the treated infarct region is increased by nearly 345 times the healthy remote value. Additionally, the average myofiber stress in the treated left ventricle was significantly reduced in both the remote and infarct regions.Overall, injection of tissue filler into the infarct was found to render it akinetic and reduce stress in the left ventricle, which could limit the adverse remodeling that leads to heart failure.

  View details for DOI 10.1016/j.athoracsur.2011.04.089

  View details for PubMedID 21871280

• Characterization of Mitral Valve Annular Dynamics in the Beating Heart ANNALS OF BIOMEDICAL ENGINEERING Rausch, M. K., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2011; 39 (6): 1690-1702

  Abstract

  The objective of this study is to establish a mathematical characterization of the mitral valve annulus that allows a precise qualitative and quantitative assessment of annular dynamics in the beating heart. We define annular geometry through 16 miniature markers sewn onto the annuli of 55 sheep. Using biplane videofluoroscopy, we record marker coordinates in vivo. By approximating these 16 marker coordinates through piecewise cubic splines, we generate a smooth mathematical representation of the 55 mitral annuli. We time-align these 55 annulus representations with respect to characteristic hemodynamic time points to generate an averaged baseline annulus representation. To characterize annular physiology, we extract classical clinical metrics of annular form and function throughout the cardiac cycle. To characterize annular dynamics, we calculate displacements, strains, and curvature from the discrete mathematical representations. To illustrate potential future applications of this approach, we create rapid prototypes of the averaged mitral annulus at characteristic hemodynamic time points. In summary, this study introduces a novel mathematical model that allows us to identify temporal, regional, and inter-subject variations of clinical and mechanical metrics that characterize mitral annular form and function. Ultimately, this model can serve as a valuable tool to optimize both surgical and interventional approaches that aim at restoring mitral valve competence.

  View details for DOI 10.1007/s10439-011-0272-y

  View details for PubMedID 21336803

• In vivo dynamic strains of the ovine anterior mitral valve leaflet JOURNAL OF BIOMECHANICS Rausch, M. K., Bothe, W., Kvitting, J. E., Goektepe, S., Miller, D. C., Kuhl, E. 2011; 44 (6): 1149-1157

  Abstract

  Understanding the mechanics of the mitral valve is crucial in terms of designing and evaluating medical devices and techniques for mitral valve repair. In the current study we characterize the in vivo strains of the anterior mitral valve leaflet. On cardiopulmonary bypass, we sew miniature markers onto the leaflets of 57 sheep. During the cardiac cycle, the coordinates of these markers are recorded via biplane fluoroscopy. From the resulting four-dimensional data sets, we calculate areal, maximum principal, circumferential, and radial leaflet strains and display their profiles on the averaged leaflet geometry. Average peak areal strains are 13.8±6.3%, maximum principal strains are 13.0±4.7%, circumferential strains are 5.0±2.7%, and radial strains are 7.8±4.3%. Maximum principal strains are largest in the belly region, where they are aligned with the circumferential direction during diastole switching into the radial direction during systole. Circumferential strains are concentrated at the distal portion of the belly region close to the free edge of the leaflet, while radial strains are highest in the center of the leaflet, stretching from the posterior to the anterior commissure. In summary, leaflet strains display significant temporal, regional, and directional variations with largest values inside the belly region and toward the free edge. Characterizing strain distribution profiles might be of particular clinical significance when optimizing mitral valve repair techniques in terms of forces on suture lines and on medical devices.

  View details for DOI 10.1016/j.jbiomech.2011.01.020

  View details for PubMedID 21306716

• Perspectives on biological growth and remodeling JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Ambrosi, D., Ateshian, G. A., Arruda, E. M., Cowin, S. C., Dumais, J., Goriely, A., Holzapfel, G. A., Humphrey, J. D., Kemkemer, R., Kuhl, E., Olberding, J. E., Taber, L. A., Garikipati, K. 2011; 59 (4): 863-883

  Abstract

  The continuum mechanical treatment of biological growth and remodeling has attracted considerable attention over the past fifteen years. Many aspects of these problems are now well-understood, yet there remain areas in need of significant development from the standpoint of experiments, theory, and computation. In this perspective paper we review the state of the field and highlight open questions, challenges, and avenues for further development.

  View details for DOI 10.1016/j.jmps.2010.12.011

  View details for Web of Science ID 000289136300008

• Computational modeling of electrochemical coupling: A novel finite element approach towards ionic models for cardiac electrophysiology COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Wong, J., Goktepe, S., Kuhl, E. 2011; 200 (45-46): 3139-3158

  View details for DOI 10.1016/j.cma.2011.07.003

  View details for Web of Science ID 000295753800016

• Computational modeling of passive myocardium INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Goektepe, S., Acharya, S. N., Wong, J., Kuhl, E. 2011; 27 (1): 1-12

  View details for DOI 10.1002/cnm.1402

  View details for Web of Science ID 000287141000001

• Anterior Mitral Leaflet Curvature During the Cardiac Cycle in the Normal Ovine Heart CIRCULATION Kvitting, J. E., Bothe, W., Goektepe, S., Rausch, M. K., Swanson, J. C., Kuhl, E., Ingels, N. B., Miller, D. C. 2010; 122 (17): 1683-1689

  Abstract

  The dynamic changes of anterior mitral leaflet (AML) curvature are of primary importance for optimal left ventricular filling and emptying but are incompletely characterized.Sixteen radiopaque markers were sutured to the AML in 11 sheep, and 4-dimensional marker coordinates were acquired with biplane videofluoroscopy. A surface subdivision algorithm was applied to compute the curvature across the AML at midsystole and at maximal valve opening. Septal-lateral (SL) and commissure-commissure (CC) curvature profiles were calculated along the SL AML meridian (M(SL))and CC AML meridian (M(CC)), respectively, with positive curvature being concave toward the left atrium. At midsystole, the M(SL) was concave near the mitral annulus, turned from concave to convex across the belly, and was convex along the free edge. At maximal valve opening, the M(SL) was flat near the annulus, turned from slightly concave to convex across the belly, and flattened toward the free edge. In contrast, the M(CC) was concave near both commissures and convex at the belly at midsystole but convex near both commissures and concave at the belly at maximal valve opening.While the SL curvature of the AML along the M(SL) is similar across the belly region at midsystole and early diastole, the CC curvature of the AML along the M(CC) flips, with the belly being convex to the left atrium at midsystole and concave at maximal valve opening. These curvature orientations suggest optimal left ventricular inflow and outflow shapes of the AML and should be preserved during catheter or surgical interventions.

  View details for DOI 10.1161/CIRCULATIONAHA.110.961243

  View details for PubMedID 20937973

• A generic approach towards finite growth with examples of athlete's heart, cardiac dilation, and cardiac wall thickening JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Goktepe, S., Abilez, O. J., Kuhl, E. 2010; 58 (10): 1661-1680

  View details for DOI 10.1016/j.jmps.2010.07.003

  View details for Web of Science ID 000282856200014

• A multiscale model for eccentric and concentric cardiac growth through sarcomerogenesis JOURNAL OF THEORETICAL BIOLOGY Goktepe, S., Abilez, O. J., Parker, K. K., Kuhl, E. 2010; 265 (3): 433-442

  Abstract

  We present a novel computational model for maladaptive cardiac growth in which kinematic changes of the cardiac chambers are attributed to alterations in cytoskeletal architecture and in cellular morphology. We adopt the concept of finite volume growth characterized through the multiplicative decomposition of the deformation gradient into an elastic part and a growth part. The functional form of its growth tensor is correlated to sarcomerogenesis, the creation and deposition of new sarcomere units. In response to chronic volume-overload, an increased diastolic wall strain leads to the addition of sarcomeres in series, resulting in a relative increase in cardiomyocyte length, associated with eccentric hypertrophy and ventricular dilation. In response to chronic pressure-overload, an increased systolic wall stress leads to the addition of sacromeres in parallel, resulting in a relative increase in myocyte cross sectional area, associated with concentric hypertrophy and ventricular wall thickening. The continuum equations for both forms of maladaptive growth are discretized in space using a nonlinear finite element approach, and discretized in time using the implicit Euler backward scheme. We explore a generic bi-ventricular heart model in response to volume- and pressure-overload to demonstrate how local changes in cellular morphology translate into global alterations in cardiac form and function.

  View details for DOI 10.1016/j.jtbi.2010.04.023

  View details for Web of Science ID 000280374100023

  View details for PubMedID 20447409

• Natural element analysis of the Cahn-Hilliard phase-field model COMPUTATIONAL MECHANICS Rajagopal, A., Fischer, P., Kuhl, E., Steinmann, P. 2010; 46 (3): 471-493

  View details for DOI 10.1007/s00466-010-0490-4

  View details for Web of Science ID 000277937300008

• Anterior mitral leaflet curvature in the beating ovine heart: a case study using videofluoroscopic markers and subdivision surfaces BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Goektepe, S., Bothe, W., Kvitting, J. E., Swanson, J. C., Ingels, N. B., Miller, D. C., Kuhl, E. 2010; 9 (3): 281-293

  Abstract

  The implantation of annuloplasty rings is a common surgical treatment targeted to re-establish mitral valve competence in patients with mitral regurgitation. It is hypothesized that annuloplasty ring implantation influences leaflet curvature, which in turn may considerably impair repair durability. This research is driven by the vision to design repair devices that optimize leaflet curvature to reduce valvular stress. In pursuit of this goal, the objective of this manuscript is to quantify leaflet curvature in ovine models with and without annuloplasty ring using in vivo animal data from videofluoroscopic marker analysis. We represent the surface of the anterior mitral leaflet based on 23 radiopaque markers using subdivision surfaces techniques. Quartic box-spline functions are applied to determine leaflet curvature on overlapping subdivision patches. We illustrate the virtual reconstruction of the leaflet surface for both interpolating and approximating algorithms. Different scalar-valued metrics are introduced to quantify leaflet curvature in the beating heart using the approximating subdivision scheme. To explore the impact of annuloplasty ring implantation, we analyze ring-induced curvature changes at characteristic instances throughout the cardiac cycle. The presented results demonstrate that the fully automated subdivision surface procedure can successfully reconstruct a smooth representation of the anterior mitral valve from a limited number of markers at a high temporal resolution of approximately 60 frames per minute.

  View details for DOI 10.1007/s10237-009-0176-z

  View details for Web of Science ID 000277711400003

• Computational modeling of electrocardiograms: A finite element approach toward cardiac excitation INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING Kotikanyadanam, M., Goktepe, S., Kuhl, E. 2010; 26 (5): 524-533

  View details for DOI 10.1002/cnm.1273

  View details for Web of Science ID 000277552200003

• Stress concentrations in fractured compact bone simulated with a special class of anisotropic gradient elasticity INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Gitman, I. M., Askes, H., Kuhl, E., Aifantis, E. C. 2010; 47 (9): 1099-1107

  View details for DOI 10.1016/j.ijsolstr.2009.11.020

  View details for Web of Science ID 000276127200001

• Atrial and ventricular fibrillation: computational simulation of spiral waves in cardiac tissue ARCHIVE OF APPLIED MECHANICS Goktepe, S., Wong, J., Kuhl, E. 2010; 80 (5): 569-580

  View details for DOI 10.1007/s00419-009-0384-0

  View details for Web of Science ID 000275787600011

• Characterization of indentation response and stiffness reduction of bone using a continuum damage model JOURNAL OF THE MECHANICAL BEHAVIOR OF BIOMEDICAL MATERIALS Zhang, J., Michalenko, M. M., Kuhl, E., Ovaert, T. C. 2010; 3 (2): 189-202

  Abstract

  Indentation tests can be used to characterize the mechanical properties of bone at small load/length scales offering the possibility of utilizing very small test specimens, which can be excised using minimally-invasive procedures. In addition, the need for mechanical property data from bone may be a requirement for fundamental multi-scale experiments, changes in nano- and micro-mechanical properties (e.g., as affected by changes in bone mineral density) due to drug therapies, and/or the development of computational models. Load vs. indentation depth data, however, is more complex than those obtained from typical macro-scale experiments, primarily due to the mixed state of stress, and thus interpretation of the data and extraction of mechanical properties is more challenging. Previous studies have shown that cortical bone exhibits a visco-elastic response combined with permanent deformation during indentation tests, and that the load vs. indentation depth response can be simulated using a visco-elastic/plastic material model. The model successfully captures the loading and creep displacement behavior, however, it does not adequately reproduce the unloading response near the end of the unloading cycle, where a pronounced decrease in contact stiffness is observed. It is proposed that the stiffness reduction observed in bone results from an increase in damage; therefore, a plastic-damage model was investigated and shown capable of simulating a typical bone indentation response through an axisymmetric finite element simulation. The plastic-damage model was able to reproduce the full indentation response, especially the reduced stiffness behavior exhibited during the latter stages of unloading. The results suggest that the plastic-damage model is suitable for describing the complex indentation response of bone and may provide further insight into the relationship between model parameters and mechanical/physical properties.

  View details for DOI 10.1016/j.jmbbm.2009.08.001

  View details for Web of Science ID 000274987000007

  View details for PubMedID 20129418

  View details for PubMedCentralID PMC2818081

• Electromechanics of the heart: a unified approach to the strongly coupled excitation-contraction problem COMPUTATIONAL MECHANICS Goektepe, S., Kuhl, E. 2010; 45 (2-3): 227-243

  View details for DOI 10.1007/s00466-009-0434-z

  View details for Web of Science ID 000272118100009

• Computational Homogenization of Confined Frictional Granular Matter IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials Meier, H. A., Steinmann, P., Kuhl, E. SPRINGER. 2010: 157–169

  View details for DOI 10.1007/978-90-481-9195-6_12

  View details for Web of Science ID 000290694500012

• Dilation and Hypertrophy: A Cell-Based Continuum Mechanics Approach Towards Ventricular Growth and Remodeling International-Union-of-Theoretical-and-Applied-Mechanics Symposium on Cellular, Molecular and Tissue Mechanics Ulerich, J., Goektepe, S., Kuhl, E. SPRINGER. 2010: 237–244

  View details for DOI 10.1007/978-90-481-3348-2_20

  View details for Web of Science ID 000276397800020

• IN VITRO ASSESSMENT OF RAT HEART FORCE GENERATION: A QUANTITATIVE APPROACH FOR PREDICTING OUTCOMES FROM PLURIPOTENT STEM CELL-DERIVED THERAPY FOR MYOCARDIAL INFARCTION 12th ASME Summer Bioengineering Conference Guillou, L., Abilez, O. J., Baugh, J., Billakanti, G., Zarins, C. K., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2010: 717–718

  View details for Web of Science ID 000290705300359

• Regional stiffening of the mitral valve anterior leaflet in the beating ovine heart JOURNAL OF BIOMECHANICS Krishnamurthy, G., Itoh, A., Swanson, J. C., Bothe, W., Karlsson, M., Kuhl, E., Miller, D. C., Ingels, N. B. 2009; 42 (16): 2697-2701

  Abstract

  Left atrial muscle extends into the proximal third of the mitral valve (MV) anterior leaflet and transient tensing of this muscle has been proposed as a mechanism aiding valve closure. If such tensing occurs, regional stiffness in the proximal anterior mitral leaflet will be greater during isovolumic contraction (IVC) than isovolumic relaxation (IVR) and this regional stiffness difference will be selectively abolished by beta-receptor blockade. We tested this hypothesis in the beating ovine heart. Radiopaque markers were sewn around the MV annulus and on the anterior MV leaflet in 10 sheep hearts. Four-dimensional marker coordinates were obtained from biplane videofluoroscopy before (CRTL) and after administration of esmolol (ESML). Heterogeneous finite element models of each anterior leaflet were developed using marker coordinates over matched pressures during IVC and IVR for CRTL and ESML. Leaflet displacements were simulated using measured left ventricular and atrial pressures and a response function was computed as the difference between simulated and measured displacements. Circumferential and radial elastic moduli for ANNULAR, BELLY and EDGE leaflet regions were iteratively varied until the response function reached a minimum. The stiffness values at this minimum were interpreted as the in vivo regional material properties of the anterior leaflet. For all regions and all CTRL beats IVC stiffness was 40-58% greater than IVR stiffness. ESML reduced ANNULAR IVC stiffness to ANNULAR IVR stiffness values. These results strongly implicate transient tensing of leaflet atrial muscle during IVC as the basis of the ANNULAR IVC-IVR stiffness difference.

  View details for DOI 10.1016/j.jbiomech.2009.08.028

  View details for PubMedID 19766222

• Towards the treatment of boundary conditions for global crack path tracking in three-dimensional brittle fracture COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2009; 45 (1): 91-107

  View details for DOI 10.1007/s00466-009-0417-0

  View details for Web of Science ID 000270428100007

• Mechanics in biology: cells and tissues PREFACE PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Ambrosi, D., Garikipati, K., Kuhl, E. 2009; 367 (1902): 3335-3337

  View details for DOI 10.1098/rsta.2009.0122

  View details for Web of Science ID 000268735700001

  View details for PubMedID 19657002

• Stress-strain behavior of mitral valve leaflets in the beating ovine heart JOURNAL OF BIOMECHANICS Krishnamurthy, G., Itoh, A., Bothe, W., Swanson, J. C., Kuhl, E., Karlsson, M., Miller, D. C., Ingels, N. B. 2009; 42 (12): 1909-1916

  Abstract

  Excised anterior mitral leaflets exhibit anisotropic, non-linear material behavior with pre-transitional stiffness ranging from 0.06 to 0.09 N/mm(2) and post-transitional stiffness from 2 to 9 N/mm(2). We used inverse finite element (FE) analysis to test, for the first time, whether the anterior mitral leaflet (AML), in vivo, exhibits similar non-linear behavior during isovolumic relaxation (IVR). Miniature radiopaque markers were sewn to the mitral annulus, AML, and papillary muscles in 8 sheep. Four-dimensional marker coordinates were obtained using biplane videofluoroscopic imaging during three consecutive cardiac cycles. A FE model of the AML was developed using marker coordinates at the end of isovolumic relaxation (when pressure difference across the valve is approximately zero), as the reference state. AML displacements were simulated during IVR using measured left ventricular and atrial pressures. AML elastic moduli in the radial and circumferential directions were obtained for each heartbeat by inverse FEA, minimizing the difference between simulated and measured displacements. Stress-strain curves for each beat were obtained from the FE model at incrementally increasing transmitral pressure intervals during IVR. Linear regression of 24 individual stress-strain curves (8 hearts, 3 beats each) yielded a mean (+/-SD) linear correlation coefficient (r(2)) of 0.994+/-0.003 for the circumferential direction and 0.995+/-0.003 for the radial direction. Thus, unlike isolated leaflets, the AML, in vivo, operates linearly over a physiologic range of pressures in the closed mitral valve.

  View details for DOI 10.1016/j.jbiomech.2009.05.018

  View details for PubMedID 19535081

• Computational modeling of cardiac electrophysiology: A novel finite element approach INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Goektepe, S., Kuhl, E. 2009; 79 (2): 156-178

  View details for DOI 10.1002/nme.2571

  View details for Web of Science ID 000267788300002

• Active stiffening of mitral valve leaflets in the beating heart AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Itoh, A., Krishnamurthy, G., Swanson, J. C., Ennis, D. B., Bothe, W., Kuhl, E., Karlsson, M., Davis, L. R., Miller, D. C., Ingels, N. B. 2009; 296 (6): H1766-H1773

  Abstract

  The anterior leaflet of the mitral valve (MV), viewed traditionally as a passive membrane, is shown to be a highly active structure in the beating heart. Two types of leaflet contractile activity are demonstrated: 1) a brief twitch at the beginning of each beat (reflecting contraction of myocytes in the leaflet in communication with and excited by left atrial muscle) that is relaxed by midsystole and whose contractile activity is eliminated with beta-receptor blockade and 2) sustained tone during isovolumic relaxation, insensitive to beta-blockade, but doubled by stimulation of the neurally rich region of aortic-mitral continuity. These findings raise the possibility that these leaflets are neurally controlled tissues, with potentially adaptive capabilities to meet the changing physiological demands on the heart. They also provide a basis for a permanent paradigm shift from one viewing the leaflets as passive flaps to one viewing them as active tissues whose complex function and dysfunction must be taken into account when considering not only therapeutic approaches to MV disease, but even the definitions of MV disease itself.

  View details for DOI 10.1152/ajpheart.00120.2009

  View details for PubMedID 19363135

• Computational modeling of muscular thin films for cardiac repair COMPUTATIONAL MECHANICS Boel, M., Reese, S., Parker, K. K., Kuhl, E. 2009; 43 (4): 535-544

  View details for DOI 10.1007/s00466-008-0328-5

  View details for Web of Science ID 000263059500008

• CRITICAL LOADING DURING SERVE: MODELING STRESS-INDUCED BONE GROWTH IN PERFORMANCE TENNIS PLAYERS ASME Summer Bioengineering Conference Taylor, R. E., Zheng, C., Jackson, R. P., Doll, J. C., Chen, J., Holzbaur, K. R., Besier, T., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 201–202

  View details for Web of Science ID 000263364700101

• EXPLORING CELLULAR TENSEGRITY: PHYSICAL MODELING AND COMPUTATIONAL SIMULATION ASME Summer Bioengineering Conference Zheng, C. H., Doll, J., Gu, E., Hager-Barnard, E., Huang, Z., Kia, A., Ortiz, M., Petzold, B., Usul, T., Kwon, R., Jacobs, C., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 283–284

  View details for Web of Science ID 000263364700142

• FIRST ATTEMPTS TOWARDS THE COMPUTATIONAL SIMULATION OF NOVEL STEM-CELL BASED POST INFARCT THERAPIES ASME Summer Bioengineering Conference Ulerich, J. P., Goktepe, S., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 417–418

  View details for Web of Science ID 000263364700209

• COMPUTATIONAL SIMULATION OF TRAVELING ARRHYTHMIC WAVES IN MYOCARDIAL TISSUE ASME Summer Bioengineering Conference Wong, J., Goektepe, S., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 829–830

  View details for Web of Science ID 000280089000415

• HOW TO TREAT THE LOSS OF BEAT: MODELING AND SIMULATION OF VENTRICULAR GROWTH AND REMODELING AND NOVEL POST-INFARCTION THERAPIES ASME Summer Bioengineering Conference Goktepe, S., Ulerich, J. P., Kuhl, E. AMER SOC MECHANICAL ENGINEERS. 2009: 971–972

  View details for Web of Science ID 000263364700486

• QUANTIFICATION OF IN VIVO STRESSES IN THE OVINE ANTERIOR MITRAL VALVE LEAFLET ASME Summer Bioengineering Conference Krishnamurthy, G., Ltoh, A., Bothe, W., Ennis, D. B., Swanson, J. C., Kuhl, E., Miller, D. C., Ingels, N. B. AMER SOC MECHANICAL ENGINEERS. 2009: 131–132

  View details for Web of Science ID 000263364700066

• On the Multiscale Computation of Con"ned Granular Media ECCOMAS Multidisciplinary Jubilee Symposium on Computational Challenges in Materials, Structures and Fluids Meier, H. A., Steinmann, P., Kuhl, E. SPRINGER-VERLAG BERLIN. 2009: 121–133

  View details for Web of Science ID 000267056200009

• The phenomenon of twisted growth: humeral torsion in dominant arms of high performance tennis players COMPUTER METHODS IN BIOMECHANICS AND BIOMEDICAL ENGINEERING Taylor, R. E., Zheng, C., Jackson, R. P., Doll, J. C., Chen, J. C., Holzbaur, K. R., Besier, T., Kuhl, E. 2009; 12 (1): 83-93

  Abstract

  This manuscript is driven by the need to understand the fundamental mechanisms that cause twisted bone growth and shoulder pain in high performance tennis players. Our ultimate goal is to predict bone mass density in the humerus through computational analysis. The underlying study spans a unique four level complete analysis consisting of a high-speed video analysis, a musculoskeletal analysis, a finite element based density growth analysis and an X-ray based bone mass density analysis. For high performance tennis players, critical loads are postulated to occur during the serve. From high-speed video analyses, the serve phases of maximum external shoulder rotation and ball impact are identified as most critical loading situations for the humerus. The corresponding posts from the video analysis are reproduced with a musculoskeletal analysis tool to determine muscle attachment points, muscle force vectors and overall forces of relevant muscle groups. Collective representative muscle forces of the deltoid, latissimus dorsi, pectoralis major and triceps are then applied as external loads in a fully 3D finite element analysis. A problem specific nonlinear finite element based density analysis tool is developed to predict functional adaptation over time. The density profiles in response to the identified critical muscle forces during serve are qualitatively compared to X-ray based bone mass density analyses.

  View details for DOI 10.1080/10255840802178046

  View details for PubMedID 18654877

• Acceleration insensitive encapsulated silicon microresonator APPLIED PHYSICS LETTERS Jha, C. M., Salvia, J., Chandorkar, S. A., Melamud, R., Kuhl, E., Kenny, T. W. 2008; 93 (23)

  View details for DOI 10.1063/1.3036536

  View details for Web of Science ID 000261699700087

• Modeling three-dimensional crack propagation-A comparison of crack path tracking strategies INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Jaeger, R., Steinmann, R., Kuhl, E. 2008; 76 (9): 1328-1352

  View details for DOI 10.1002/nme.2353

  View details for Web of Science ID 000261111400002

• Visualization of particle interactions in granular media IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS Meier, H. A., Schlemmer, M., Wagner, C., Kerren, A., Hagen, H., Kuhl, E., Steinmann, P. 2008; 14 (5): 1110-1125

  Abstract

  Interaction between particles in so-called granular media, such as soil and sand, plays an important role in the context of geomechanical phenomena and numerous industrial applications. A two scale homogenization approach based on a micro and a macro scale level is briefly introduced in this paper. Computation of granular material in such a way gives a deeper insight into the context of discontinuous materials and at the same time reduces the computational costs. However, the description and the understanding of the phenomena in granular materials are not yet satisfactory. A sophisticated problem-specific visualization technique would significantly help to illustrate failure phenomena on the microscopic level. As main contribution, we present a novel 2D approach for the visualization of simulation data, based on the above outlined homogenization technique. Our visualization tool supports visualization on micro scale level as well as on macro scale level. The tool shows both aspects closely arranged in form of multiple coordinated views to give users the possibility to analyze the particle behavior effectively. A novel type of interactive rose diagrams was developed to represent the dynamic contact networks on the micro scale level in a condensed and efficient way.

  View details for DOI 10.1109/TVCG.2008.65

  View details for Web of Science ID 000257371400011

  View details for PubMedID 18599921

• Material properties of the ovine mitral valve anterior leaflet in vivo from inverse finite element analysis AMERICAN JOURNAL OF PHYSIOLOGY-HEART AND CIRCULATORY PHYSIOLOGY Krishnamurthy, G., Ennis, D. B., Itoh, A., Bothe, W., Swanson, J. C., Karlsson, M., Kuhl, E., Miller, D. C., Ingels, N. B. 2008; 295 (3): H1141-H1149

  Abstract

  We measured leaflet displacements and used inverse finite-element analysis to define, for the first time, the material properties of mitral valve (MV) leaflets in vivo. Sixteen miniature radiopaque markers were sewn to the MV annulus, 16 to the anterior MV leaflet, and 1 on each papillary muscle tip in 17 sheep. Four-dimensional coordinates were obtained from biplane videofluoroscopic marker images (60 frames/s) during three complete cardiac cycles. A finite-element model of the anterior MV leaflet was developed using marker coordinates at the end of isovolumic relaxation (IVR; when the pressure difference across the valve is approximately 0), as the minimum stress reference state. Leaflet displacements were simulated during IVR using measured left ventricular and atrial pressures. The leaflet shear modulus (G(circ-rad)) and elastic moduli in both the commisure-commisure (E(circ)) and radial (E(rad)) directions were obtained using the method of feasible directions to minimize the difference between simulated and measured displacements. Group mean (+/-SD) values (17 animals, 3 heartbeats each, i.e., 51 cardiac cycles) were as follows: G(circ-rad) = 121 +/- 22 N/mm2, E(circ) = 43 +/- 18 N/mm2, and E(rad) = 11 +/- 3 N/mm2 (E(circ) > E(rad), P < 0.01). These values, much greater than those previously reported from in vitro studies, may result from activated neurally controlled contractile tissue within the leaflet that is inactive in excised tissues. This could have important implications, not only to our understanding of mitral valve physiology in the beating heart but for providing additional information to aid the development of more durable tissue-engineered bioprosthetic valves.

  View details for DOI 10.1152/ajpheart.00284.2008

  View details for PubMedID 18621858

• On local tracking algorithms for the simulation of three-dimensional discontinuities COMPUTATIONAL MECHANICS Jaeger, P., Steinmann, P., Kuhl, E. 2008; 42 (3): 395-406

  View details for DOI 10.1007/s00466-008-0249-3

  View details for Web of Science ID 000256254000005

• A note on the generation of periodic granular microstructures based on grain size distributions INTERNATIONAL JOURNAL FOR NUMERICAL AND ANALYTICAL METHODS IN GEOMECHANICS MEIER, H. A., Kuhl, E., Steinmann, P. 2008; 32 (5): 509-522

  View details for DOI 10.1002/nag.635

  View details for Web of Science ID 000255319200004

• Time-dependent fibre reorientation of transversely isotropic continua - Finite element formulation and consistent linearization INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Himpel, G., Menzel, A., Kuhl, E., Steinmann, P. 2008; 73 (10): 1413-1433

  View details for DOI 10.1002/nme.2124

  View details for Web of Science ID 000253694300004

• Brittle fracture during folding of rocks: A finite element study PHILOSOPHICAL MAGAZINE Jager, P., Schmalholz, S. M., Schmid, D. W., Kuhl, E. 2008; 88 (28-29): 3245-3263

  View details for DOI 10.1080/14786430802320101

  View details for Web of Science ID 000261803800004

• Computational modelling of thermal impact welded PEEK/steel single lap tensile specimens COMPUTATIONAL MATERIALS SCIENCE Utzinger, J., Bos, M., Floeck, M., Menzel, A., Kuhl, E., Renz, R., Friedrich, K., Schlarb, A. K., Steinmann, P. 2008; 41 (3): 287-296

  View details for DOI 10.1016/j.commatsci.2007.04.015

  View details for Web of Science ID 000254338500004

• Towards mulitscale computation of confined granular media - Contact forces, stresses and tangent operators Techn Mech Meier HA, Steinmann P, Kuhl E 2008; 28: 32-42
• A continuum model for remodeling in living structures JOURNAL OF MATERIALS SCIENCE Kuhl, E., Holzapfel, G. A. 2007; 42 (21): 8811-8823

  View details for DOI 10.1007/s10853-007-1917-y

  View details for Web of Science ID 000249213300006

• Diamond elements: A finite element/discrete-mechanics approximation scheme with guaranteed optimal convergence in incompressible elasticity INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Hauret, P., Kuhl, E., Ortiz, M. 2007; 72 (3): 253-294

  View details for DOI 10.1002/nme.1992

  View details for Web of Science ID 000250277400001

• Computational modeling of arterial wall growth - Attempts towards patient-specific simulations based on computer tomography Workshop on Mathematical Methods and Models of Continuum Biomechanics Kuhl, E., Maas, R., Himpel, G., Menzel, A. SPRINGER HEIDELBERG. 2007: 321–31

  Abstract

  The present manuscript documents our first experiences with a computational model for stress-induced arterial wall growth and in-stent restenosis related to atherosclerosis. The underlying theoretical framework is provided by the kinematics of finite growth combined with open system thermodynamics. The computational simulation is embedded in a finite element approach in which growth is essentially captured by a single scalar-valued growth factor introduced as internal variable on the integration point level. The conceptual simplicity of the model enables its straightforward implementation into standard commercial finite element codes. Qualitative studies of stress-induced changes of the arterial wall thickness in response to balloon angioplasty or stenting are presented to illustrate the features of the suggested growth model. First attempts towards a patient-specific simulation based on realistic artery morphologies generated from computer tomography data are discussed.

  View details for DOI 10.1007/s10237-006-0062-x

  View details for Web of Science ID 000249307500005

  View details for PubMedID 17119902

• Computational modeling of mineral unmixing and growth - An application of the Cahn-Hilliard equation COMPUTATIONAL MECHANICS Kuhl, E., Schmid, D. W. 2007; 39 (4): 439-451

  View details for DOI 10.1007/s00466-006-0041-1

  View details for Web of Science ID 000243968400008

• Towards the algorithmic treatment of 3D strong discontinuities COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2007; 23 (2): 97-108

  View details for DOI 10.1002/cnm.885

  View details for Web of Science ID 000244089800002

• On the application of Hansbo's method for interface problems IUTAM Symposium on Discretization Methods for Evolving Discontinuities Kuhl, E., Jaeger, P., Mergheim, J., Steinmann, P. SPRINGER. 2007: 255–265

  View details for Web of Science ID 000251312200015

• On deformational and configurational mechanics of micromorphic hyperelasticity - Theory and computation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Hirschberger, C. B., Kuhl, E., Steinmann, P. 2007; 196 (41-44): 4027-4044

  View details for DOI 10.1016/j.cma.2007.02.015

  View details for Web of Science ID 000249301500002

• A discontinuous Galerkin method for the Cahn-Hilliard equation JOURNAL OF COMPUTATIONAL PHYSICS Wells, G. N., Kuhl, E., Garikipati, K. 2006; 218 (2): 860-877

  View details for DOI 10.1016/j.jcp.2006.03.010

  View details for Web of Science ID 000242461200021

• On the convexity of transversely isotropic chain network models Symposium on Instabilities Across the Scales Kuhl, E., Menzel, A., Garikipati, K. TAYLOR & FRANCIS LTD. 2006: 3241–58

  View details for DOI 10.1080/14786430500080296

  View details for Web of Science ID 000237931000007

• An illustration of the equivalence of the loss of ellipticity conditions in spatial and material settings of hyperelasticity EUROPEAN JOURNAL OF MECHANICS A-SOLIDS Kuhl, E., Askes, H., Steinmann, P. 2006; 25 (2): 199-214

  View details for DOI 10.1016/j.euromechsol.2005.07.008

  View details for Web of Science ID 000236610600001

• Modeling and simulation of remodeling in soft biological tissues IUTAM Symposium on Mechanics of Biological Tissue Kuhl, E., Menzel, A., Garikipati, K., Arruda, E. M., Grosh, K. SPRINGER-VERLAG BERLIN. 2006: 77–89

  View details for Web of Science ID 000237286900006

• Structural optimization by simultaneous equilibration of spatial and material forces COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Askes, H., Bargmann, S., Kuhl, E., Steinmann, P. 2005; 21 (8): 433-442

  View details for DOI 10.1002/cnm.758

  View details for Web of Science ID 000231331400004

• Remodeling of biological tissue: Mechanically induced reorientation of a transversely isotropic chain network JOURNAL OF THE MECHANICS AND PHYSICS OF SOLIDS Kuhl, E., Garikipati, K., Arruda, E. M., Grosh, K. 2005; 53 (7): 1552-1573

  View details for DOI 10.1016/j.jmps.2005.03.002

  View details for Web of Science ID 000230058500005

• A finite element method for the computational modelling of cohesive cracks INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2005; 63 (2): 276-289

  View details for Web of Science ID 000228913400007

• Computational modelling of isotropic multiplicative growth CMES-COMPUTER MODELING IN ENGINEERING & SCIENCES Himpel, G., Kuhl, E., Menzel, A., Steinmann, P. 2005; 8 (2): 119-134

  View details for Web of Science ID 000230077000003

• A hyperelastodynamic ALE formulation based on referential, spatial and material settings of continuum mechanics ACTA MECHANICA Kuhl, E., Steinmann, P. 2005; 174 (3-4): 201-222

  View details for DOI 10.1007/s00707-004-0200-4

  View details for Web of Science ID 000227999700005

• Computational modeling of hip replacement surgery - Total hip replacement vs. hip resurfacing Techn Mech Kuhl E, Balle F 2005; 25: 107-114
• Material force method. Continuum damage & thermo-hyperelasticity EUROMECH Colloquium 445 Denzer, R., Liebe, T., Kuhl, E., Barth, F. J., Steinmann, P. SPRINGER. 2005: 95–104

  View details for Web of Science ID 000233193400010

• Computational spatial and material settings of continuum mechanics. An Arbitrary Lagrangian Eulerian formulation EUROMECH Colloquium 445 Kuhl, E., Askes, H., Steinmann, P. SPRINGER. 2005: 115–125

  View details for Web of Science ID 000233193400012

• A hybrid discontinuous Galerkin/interface method for the computational modelling of failure COMMUNICATIONS IN NUMERICAL METHODS IN ENGINEERING Mergheim, J., Kuhl, E., Steinmann, P. 2004; 20 (7): 511-519

  View details for DOI 10.1002/cnm.689

  View details for Web of Science ID 000222538700002

• Computational modeling of healing: an application of the material force method BIOMECHANICS AND MODELING IN MECHANOBIOLOGY Kuhl, E., Steinmann, P. 2004; 2 (4): 187-203

  Abstract

  The basic aim of the present contribution is the qualitative simulation of healing phenomena typically encountered in hard and soft tissue mechanics. The mechanical framework is provided by the theory of open system thermodynamics, which will be formulated in the spatial as well as in the material motion context. While the former typically aims at deriving the density and the spatial motion deformation field in response to given spatial forces, the latter will be applied to determine the material forces in response to a given density and material deformation field. We derive a general computational framework within the finite element context that will serve to evaluate both the spatial and the material motion problem. However, once the spatial motion problem has been solved, the solution of the material motion problem represents a mere post-processing step and is thus extremely cheap from a computational point of view. The underlying algorithm will be elaborated systematically by means of two prototype geometries subjected to three different representative loading scenarios, tension, torsion, and bending. Particular focus will be dedicated to the discussion of the additional information provided by the material force method. Since the discrete material node point forces typically point in the direction of potential material deposition, they can be interpreted as a driving force for the healing mechanism.

  View details for DOI 10.1007/s10237-003-0034-3

  View details for Web of Science ID 000208283300001

  View details for PubMedID 14872320

• On the impact of configurational mechanics on computational mechanics Symposium on Configurational Mechanics held at the 5th Euromech Solid Mechanics Conference Kuhl, E., Steinmann, P. A A BALKEMA PUBLISHERS. 2004: 15–29

  View details for Web of Science ID 000189444500002

• Material forces in open system mechanics COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Steinmann, P. 2004; 193 (23-26): 2357-2381

  View details for DOI 10.1016/j.cma.2004.01.022

  View details for Web of Science ID 000221274800013

• Application of the material force method to thermo-hyperelasticity COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Denzer, R., Barth, F. J., Steinmann, P. 2004; 193 (30-32): 3303-3325

  View details for DOI 10.1016/j.cma.2003.09.021

  View details for Web of Science ID 000222540900008

• An ALE formulation based on spatial and material settings of continuum mechanics. Part 1: Generic hyperelastic formulation COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Kuhl, E., Askes, H., Steinmann, P. 2004; 193 (39-41): 4207-4222

  View details for DOI 10.1016/j.cma.2003.09.030

  View details for Web of Science ID 000224018200008

• An ALE formulation based on spatial and material settings of continuum mechanics. Part 2: Classification and applications COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Askes, H., Kuhl, E., Steinmann, P. 2004; 193 (39-41): 4223-4245

  View details for DOI 10.1016/j.cma.2003.09.031

  View details for Web of Science ID 000224018200009

• Theory and numerics of geometrically non-linear open system mechanics INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN ENGINEERING Kuhl, E., Steinmann, P. 2003; 58 (11): 1593-1615

  View details for DOI 10.1002/nme.827

  View details for Web of Science ID 000186438000001

• Mass- and volume-specific views on thermodynamics for open systems PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES Kuhl, E., Steinmann, P. 2003; 459 (2038): 2547-2568

  View details for DOI 10.1098/rspa.2003.1119

  View details for Web of Science ID 000185739200009

• Computational modeling of growth - A critical review, a classification of concepts and two new consistent approaches COMPUTATIONAL MECHANICS Kuhl, E., Menzel, A., Steinmann, P. 2003; 32 (1-2): 71-88

  View details for DOI 10.1007/S00466-003-0463-Y

  View details for Web of Science ID 000185915200008

• An arbitrary Lagrangian Eulerian finite-element approach for fluid-structure interaction phenomena Int J Num Meth Eng Kuhl E, Hulshoff S, de Borst R 2003; 57: 117-142
• On spatial and material settings of thermo-hyperelastodynamics for open systems ACTA MECHANICA Kuhl, E., Steinmann, P. 2003; 160 (3-4): 179-217

  View details for DOI 10.1007/s00707-002-0974-1

  View details for Web of Science ID 000181493700004

• Thermodynamics of open systems with application to chemomechanical problems EURO-C 2003 Conference Kuhl, E., Steinmann, P. A A BALKEMA PUBLISHERS. 2003: 463–472

  View details for Web of Science ID 000182406800050

• A thermodynamically consistent approach to microplane theory. Part II. Dissipation and inelastic constitutive modeling INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Kuhl, E., Steinmann, P., Carol, I. 2001; 38 (17): 2933-2952

  View details for Web of Science ID 000167747700003

• New thermodynamic approach to microplane model. Part II: Dissipation and inelastic constitutive modelling Int J Solids Structures Kuhl E, Carol I, Steinmann P 2001; 38: 2933-2952
• A comparison of discrete granular material models with continuous microplane formulations Granular Matter Kuhl E, D'Addetta GA, Herrmann HJ, Ramm E 2000; 2: 123-135
• Failure analysis for elasto-plastic material models on different levels of observation Int J Solids Structures Kuhl E, Ramm E, Willam KJ 2000; 37: 7259-7280
• Microplane modelling of cohesive frictional materials Eur J Mech/A:Solids Kuhl E, Ramm E 2000; 19: S121-S143
• An anisotropic gradient damage model for quasi-brittle materials Comp Meth Appl Mech Eng Kuhl E, Ramm E, de Borst R 2000; 183: 87-103
• Parameter identification of gradient enhanced damage models with the finite element method Eur J Mech/A: Solids Mahnken R, Kuhl E 1999; 18: 819-835
• Simulation of strain localization with gradient enhanced damage models Comp Mat Sci Kuhl E, Ramm E 1999; 16: 176-185
• Aspects of non-associated single crystal plasticity: Influence of non-Schmid effects and localization analysis INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES Steinmann, P., Kuhl, E., Stein, E. 1998; 35 (33): 4437-4456

  View details for Web of Science ID 000075278600007

• On the linearization of the microplane model Mech Coh Fric Mat Kuhl E, Ramm E 1998; 2: 343-364
• Modelling and computations of instability phenomena in multisurface plasticity Comp Mech Sawischlewski E, Steinmann P, Stein E 1996; 18: 245-258