Martin R. Pfaller is an Instructor in the Department of Pediatrics (Cardiology) in the group of Alison L. Marsden. He received his B.Sc., M.Sc., and Ph.D. in Mechanical Engineering from the Technical University of Munich, working with Wolfgang A. Wall. During his Ph.D., he validated an efficient yet physiologically accurate boundary condition to account for the mechanical support of the heart within its surroundings, which has been adopted by various research groups worldwide. He further demonstrated how projection-based model order reduction could speed up model personalization from patient data, such as magnetic resonance imaging or blood pressure measurements. His current work focuses on cardiovascular fluid dynamics. He developed reduced-physics models to make blood flow simulations faster and more reliable. Further, he developed a fluid-solid-growth interaction model in blood vessels. His future research will predict the heart’s long-term function in heart diseases, supported by an NIH Pathway to Independence Award (K99/R00) and Stanford MCHRI Instructor K Award Support. He will quantify the risk of heart failure after a heart attack with a stability analysis validated with imaging data in swine and humans. This research will improve our understanding of biomechanical mechanisms leading to heart failure and help to identify patients at risk, enable personalized therapies, and facilitate the optimal design of medical devices. As an Assistant Professor, Martin will start his research group at Yale University in the Department of Biomedical Engineering in July 2024.
Honors & Awards
NIH Pathway to Independence Award (K99/R00), National Heart, Lung, and Blood Institute (2022-2027)
Instructor K Award Support, Stanford Maternal and Child Health Research Institute (2022-2024)
Travel Award, Additional Ventures (2022)
Travel Award, Stanford Cardiovascular Institute (2022)
Dissertation Award, Association of German Engineers (VDI) (2019)
Winner Science Slam, Technical University of Munich (2017)
Departmental Teaching Award, Technical University of Munich (2017)
Departmental Teaching Award, Technical University of Munich (2016)
Exchange Scholarship, German Academic Exchange Service (DAAD) (2013)
Exchange Scholarship, Prof. Dr.-Ing. Erich Müller-Stiftung (2013)
Postdoc, Stanford University, Pediatrics - Cardiology (2022)
Ph.D., Technical University of Munich, Mechanical Engineering (2019)
M.Sc., Technical University of Munich, Mechanical Engineering (2013)
B.Sc., Technical University of Munich, Mechanical Engineering (2012)
Computational Stability Analysis to Predict Heart Failure after Myocardial Infarction, Stanford University (September 1, 2022)
Automated generation of 0D and 1D reduced-order models of patient-specific blood flow.
International journal for numerical methods in biomedical engineering
Three-dimensional (3D) cardiovascular fluid dynamics simulations typically require hours to days of computing time on a high-performance computing cluster. One-dimensional (1D) and lumped-parameter zero-dimensional (0D) models show great promise for accurately predicting blood bulk flow and pressure waveforms with only a fraction of the cost. They can also accelerate uncertainty quantification, optimization, and design parameterization studies. Despite several prior studies generating 1D and 0D models and comparing them to 3D solutions, these were typically limited to either 1D or 0D and a singular category of vascular anatomies. This work proposes a fully automated and openly available framework to generate and simulate 1D and 0D models from 3D patient-specific geometries, automatically detecting vessel junctions and stenosis segments. Our only input is the 3D geometry; we do not use any prior knowledge from 3D simulations. All computational tools presented in this work are implemented in the open-source software platform SimVascular. We demonstrate the reduced-order approximation quality against rigid-wall 3D solutions in a comprehensive comparison with N=72 publicly available models from various anatomies, vessel types, and disease conditions. Relative average approximation errors of flows and pressures typically ranged from 1% to 10% for both 1D and 0D models, measured at the outlets of terminal vessel branches. In general, 0D model errors were only slightly higher than 1D model errors despite requiring only a third of the 1D runtime. Automatically generated ROMs can significantly speed up model development and shift the computational load from high-performance machines to personal computers. This article is protected by copyright. All rights reserved.
View details for DOI 10.1002/cnm.3639
View details for PubMedID 35875875
On the Periodicity of Cardiovascular Fluid Dynamics Simulations.
Annals of biomedical engineering
Three-dimensional cardiovascular fluid dynamics simulations typically require computation of several cardiac cycles before they reach a periodic solution, rendering them computationally expensive. Furthermore, there is currently no standardized method to determine whether a simulation has yet reached that periodic state. In this work, we propose the use of an asymptotic error measurement to quantify the difference between simulation results and their ideal periodic state using open-loop lumped-parameter modeling. We further show that initial conditions are crucial in reducing computational time and develop an automated framework to generate appropriate initial conditions from a one-dimensional model of blood flow. We demonstrate the performance of our initialization method using six patient-specific models from the Vascular Model Repository. In our examples, our initialization protocol achieves periodic convergence within one or two cardiac cycles, leading to a significant reduction in computational cost compared to standard methods. All computational tools used in this work are implemented in the open-source software platform SimVascular. Automatically generated initial conditions have the potential to significantly reduce computation time in cardiovascular fluid dynamics simulations.
View details for DOI 10.1007/s10439-021-02796-x
View details for PubMedID 34169398
Using parametric model order reduction for inverse analysis of large nonlinear cardiac simulations
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
Predictive high-fidelity finite element simulations of human cardiac mechanics commonly require a large number of structural degrees of freedom. Additionally, these models are often coupled with lumped-parameter models of hemodynamics. High computational demands, however, slow down model calibration and therefore limit the use of cardiac simulations in clinical practice. As cardiac models rely on several patient-specific parameters, just one solution corresponding to one specific parameter set does not at all meet clinical demands. Moreover, while solving the nonlinear problem, 90% of the computation time is spent solving linear systems of equations. We propose to reduce the structural dimension of a monolithically coupled structure-Windkessel system by projection onto a lower-dimensional subspace. We obtain a good approximation of the displacement field as well as of key scalar cardiac outputs even with very few reduced degrees of freedom, while achieving considerable speedups. For subspace generation, we use proper orthogonal decomposition of displacement snapshots. Following a brief comparison of subspace interpolation methods, we demonstrate how projection-based model order reduction can be easily integrated into a gradient-based optimization. We demonstrate the performance of our method in a real-world multivariate inverse analysis scenario. Using the presented projection-based model order reduction approach can significantly speed up model personalization and could be used for many-query tasks in a clinical setting.
View details for DOI 10.1002/cnm.3320
View details for Web of Science ID 000515254400001
View details for PubMedID 32022424
The importance of the pericardium for cardiac biomechanics: from physiology to computational modeling
BIOMECHANICS AND MODELING IN MECHANOBIOLOGY
2019; 18 (2): 503–29
The human heart is enclosed in the pericardial cavity. The pericardium consists of a layered thin sac and is separated from the myocardium by a thin film of fluid. It provides a fixture in space and frictionless sliding of the myocardium. The influence of the pericardium is essential for predictive mechanical simulations of the heart. However, there is no consensus on physiologically correct and computationally tractable pericardial boundary conditions. Here, we propose to model the pericardial influence as a parallel spring and dashpot acting in normal direction to the epicardium. Using a four-chamber geometry, we compare a model with pericardial boundary conditions to a model with fixated apex. The influence of pericardial stiffness is demonstrated in a parametric study. Comparing simulation results to measurements from cine magnetic resonance imaging reveals that adding pericardial boundary conditions yields a better approximation with respect to atrioventricular plane displacement, atrial filling, and overall spatial approximation error. We demonstrate that this simple model of pericardial-myocardial interaction can correctly predict the pumping mechanisms of the heart as previously assessed in clinical studies. Utilizing a pericardial model not only can provide much more realistic cardiac mechanics simulations but also allows new insights into pericardial-myocardial interaction which cannot be assessed in clinical measurements yet.
View details for DOI 10.1007/s10237-018-1098-4
View details for Web of Science ID 000461323600018
View details for PubMedID 30535650
Non-invasive Estimation of Pressure Drop Across Aortic Coarctations: Validation of 0D and 3D Computational Models with In Vivo Measurements.
Annals of biomedical engineering
Blood pressure gradient ([Formula: see text]) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of [Formula: see text] estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations. Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N = 17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. [Formula: see text] across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation. The 0D simulations were extremely efficient ([Formula: see text] 15 s computation time) compared to 3D simulations ([Formula: see text] 30 h computation time on a cluster). However, the 0D [Formula: see text] estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as [Formula: see text] [Formula: see text] 20 mmHg) with 76% accuracy and 3D simulations improved this to 88%. Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.
View details for DOI 10.1007/s10439-024-03457-5
View details for PubMedID 38341399
A Fluid-Solid-Growth Solver for Cardiovascular Modeling.
Computer methods in applied mechanics and engineering
2023; 417 (Pt B)
We implement full, three-dimensional constrained mixture theory for vascular growth and remodeling into a finite element fluid-structure interaction (FSI) solver. The resulting "fluid-solid-growth" (FSG) solver allows long term, patient-specific predictions of changing hemodynamics, vessel wall morphology, tissue composition, and material properties. This extension from short term (FSI) to long term (FSG) simulations increases clinical relevance by enabling mechanobioloigcally-dependent studies of disease progression in complex domains.
View details for DOI 10.1016/j.cma.2023.116312
View details for PubMedID 38044957
Learning reduced-order models for cardiovascular simulations with graph neural networks.
Computers in biology and medicine
2023; 168: 107676
Reduced-order models based on physics are a popular choice in cardiovascular modeling due to their efficiency, but they may experience loss in accuracy when working with anatomies that contain numerous junctions or pathological conditions. We develop one-dimensional reduced-order models that simulate blood flow dynamics using a graph neural network trained on three-dimensional hemodynamic simulation data. Given the initial condition of the system, the network iteratively predicts the pressure and flow rate at the vessel centerline nodes. Our numerical results demonstrate the accuracy and generalizability of our method in physiological geometries comprising a variety of anatomies and boundary conditions. Our findings demonstrate that our approach can achieve errors below 3% for pressure and flow rate, provided there is adequate training data. As a result, our method exhibits superior performance compared to physics-based one-dimensional models while maintaining high efficiency at inference time.
View details for DOI 10.1016/j.compbiomed.2023.107676
View details for PubMedID 38039892
Non-invasive estimation of pressure drop across aortic coarctations: validation of 0D and 3D computational models with in vivo measurements.
medRxiv : the preprint server for health sciences
Blood pressure gradient (ΔP) across an aortic coarctation (CoA) is an important measurement to diagnose CoA severity and gauge treatment efficacy. Invasive cardiac catheterization is currently the gold-standard method for measuring blood pressure. The objective of this study was to evaluate the accuracy of ΔP estimates derived non-invasively using patient-specific 0D and 3D deformable wall simulations.Medical imaging and routine clinical measurements were used to create patient-specific models of patients with CoA (N=17). 0D simulations were performed first and used to tune boundary conditions and initialize 3D simulations. ΔP across the CoA estimated using both 0D and 3D simulations were compared to invasive catheter-based pressure measurements for validation.The 0D simulations were extremely efficient (~15 secs computation time) compared to 3D simulations (~30 hrs computation time on a cluster). However, the 0D ΔP estimates, unsurprisingly, had larger mean errors when compared to catheterization than 3D estimates (12.1 ± 9.9 mmHg vs 5.3 ± 5.4 mmHg). In particular, the 0D model performance degraded in cases where the CoA was adjacent to a bifurcation. The 0D model classified patients with severe CoA requiring intervention (defined as ΔP≥20 mmHg) with 76% accuracy and 3D simulations improved this to 88%.Overall, a combined approach, using 0D models to efficiently tune and launch 3D models, offers the best combination of speed and accuracy for non-invasive classification of CoA severity.
View details for DOI 10.1101/2023.09.05.23295066
View details for PubMedID 37732242
View details for PubMedCentralID PMC10508787
A homogenized constrained mixture model of cardiac growth and remodeling: analyzing mechanobiological stability and reversal.
Biomechanics and modeling in mechanobiology
Cardiac growth and remodeling (G&R) patterns change ventricular size, shape, and function both globally and locally. Biomechanical, neurohormonal, and genetic stimuli drive these patterns through changes in myocyte dimension and fibrosis. We propose a novel microstructure-motivated model that predicts organ-scale G&R in the heart based on the homogenized constrained mixture theory. Previous models, based on the kinematic growth theory, reproduced consequences of G&R in bulk myocardial tissue by prescribing the direction and extent of growth but neglected underlying cellular mechanisms. In our model, the direction and extent of G&R emerge naturally from intra- and extracellular turnover processes in myocardial tissue constituents and their preferred homeostatic stretch state. We additionally propose a method to obtain a mechanobiologically equilibrated reference configuration. We test our model on an idealized 3D left ventricular geometry and demonstrate that our model aims to maintain tensional homeostasis in hypertension conditions. In a stability map, we identify regions of stable and unstable G&R from an identical parameter set with varying systolic pressures and growth factors. Furthermore, we show the extent of G&R reversal after returning the systolic pressure to baseline following stage 1 and 2 hypertension. A realistic model of organ-scale cardiac G&R has the potential to identify patients at risk of heart failure, enable personalized cardiac therapies, and facilitate the optimal design of medical devices.
View details for DOI 10.1007/s10237-023-01747-w
View details for PubMedID 37482576
Beyond CFD: Emerging methodologies for predictive simulation in cardiovascular health and disease.
2023; 4 (1): 011301
Physics-based computational models of the cardiovascular system are increasingly used to simulate hemodynamics, tissue mechanics, and physiology in evolving healthy and diseased states. While predictive models using computational fluid dynamics (CFD) originated primarily for use in surgical planning, their application now extends well beyond this purpose. In this review, we describe an increasingly wide range of modeling applications aimed at uncovering fundamental mechanisms of disease progression and development, performing model-guided design, and generating testable hypotheses to drive targeted experiments. Increasingly, models are incorporating multiple physical processes spanning a wide range of time and length scales in the heart and vasculature. With these expanded capabilities, clinical adoption of patient-specific modeling in congenital and acquired cardiovascular disease is also increasing, impacting clinical care and treatment decisions in complex congenital heart disease, coronary artery disease, vascular surgery, pulmonary artery disease, and medical device design. In support of these efforts, we discuss recent advances in modeling methodology, which are most impactful when driven by clinical needs. We describe pivotal recent developments in image processing, fluid-structure interaction, modeling under uncertainty, and reduced order modeling to enable simulations in clinically relevant timeframes. In all these areas, we argue that traditional CFD alone is insufficient to tackle increasingly complex clinical and biological problems across scales and systems. Rather, CFD should be coupled with appropriate multiscale biological, physical, and physiological models needed to produce comprehensive, impactful models of mechanobiological systems and complex clinical scenarios. With this perspective, we finally outline open problems and future challenges in the field.
View details for DOI 10.1063/5.0109400
View details for PubMedID 36686891
svMorph: Interactive Geometry-Editing Tools for Virtual Patient-Specific Vascular Anatomies.
Journal of biomechanical engineering
We propose svMorph, a framework for interactive virtual sculpting of patient-specific vascular anatomic models. Our framework includes three tools for the creation of tortuosity, aneurysms, and stenoses in tubular vascular geometries. These shape edits are performed via geometric operations on the surface mesh and vessel centerline curves of the input model. The tortuosity tool also uses the physics-based Oriented Particles method, coupled with linear blend skinning, to achieve smooth, elastic-like deformations. Our tools can be applied separately or in combination to produce simulation-suitable morphed models. They are also compatible with popular vascular modeling software, such as SimVascular. To illustrate our tools, we morph several image-based, patient-specific models to create a range of shape changes and simulate the resulting hemodynamics via three-dimensional, computational fluid dynamics. We also demonstrate the ability to quickly estimate the hemodynamic effects of the shape changes via automated generation of associated zero-dimensional lumped-parameter models.
View details for DOI 10.1115/1.4056055
View details for PubMedID 36282508
Blood flow modeling reveals improved collateral artery performance during the regenerative period in mammalian hearts.
Nature cardiovascular research
2022; 1 (8): 775-790
Collateral arteries bridge opposing artery branches, forming a natural bypass that can deliver blood flow downstream of an occlusion. Inducing coronary collateral arteries could treat cardiac ischemia, but more knowledge on their developmental mechanisms and functional capabilities is required. Here we used whole-organ imaging and three-dimensional computational fluid dynamics modeling to define spatial architecture and predict blood flow through collaterals in neonate and adult mouse hearts. Neonate collaterals were more numerous, larger in diameter and more effective at restoring blood flow. Decreased blood flow restoration in adults arose because during postnatal growth coronary arteries expanded by adding branches rather than increasing diameters, altering pressure distributions. In humans, adult hearts with total coronary occlusions averaged 2 large collaterals, with predicted moderate function, while normal fetal hearts showed over 40 collaterals, likely too small to be functionally relevant. Thus, we quantify the functional impact of collateral arteries during heart regeneration and repair-a critical step toward realizing their therapeutic potential.
View details for DOI 10.1038/s44161-022-00114-9
View details for PubMedID 37305211
View details for PubMedCentralID PMC10256232
Model order reduction of flow based on a modular geometrical approximation of blood vessels.
Computer methods in applied mechanics and engineering
We are interested in a reduced order method for the efficient simulation of blood flow in arteries. The blood dynamics is modeled by means of the incompressible Navier-Stokes equations. Our algorithm is based on an approximated domain-decomposition of the target geometry into a number of subdomains obtained from the parametrized deformation of geometrical building blocks (e.g., straight tubes and model bifurcations). On each of these building blocks, we build a set of spectral functions by Proper Orthogonal Decomposition of a large number of snapshots of finite element solutions (offline phase). The global solution of the Navier-Stokes equations on a target geometry is then found by coupling linear combinations of these local basis functions by means of spectral Lagrange multipliers (online phase). Being that the number of reduced degrees of freedom is considerably smaller than their finite element counterpart, this approach allows us to significantly decrease the size of the linear system to be solved in each iteration of the Newton-Raphson algorithm. We achieve large speedups with respect to the full order simulation (in our numerical experiments, the gain is at least of one order of magnitude and grows inversely with respect to the reduced basis size), whilst still retaining satisfactory accuracy for most cardiovascular simulations.
View details for DOI 10.1016/j.cma.2021.113762
View details for PubMedID 34176992
Automatic mapping of atrial fiber orientations for patient-specific modeling of cardiac electromechanics using image registration
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
2019; 35 (6): e3190
Knowledge of appropriate local fiber architecture is necessary to simulate patient-specific electromechanics in the human heart. However, it is not yet possible to reliably measure in vivo fiber directions especially in human atria. Thus, we present a method that defines the fiber architecture in arbitrarily shaped atria using image registration and reorientation methods based on atlas atria with fibers predefined from detailed histological observations. Thereby, it is possible to generate detailed fiber families in every new patient-specific geometry in an automated, time-efficient process. We demonstrate the good performance of the image registration and fiber definition on 10 differently shaped human atria. Additionally, we show that characteristics of the electrophysiological activation pattern that appear in the atlas atria also appear in the patients' atria. We arrive to analogous conclusions for coupled electro-mechano-hemodynamical computations.
View details for DOI 10.1002/cnm.3190
View details for Web of Science ID 000471315800008
View details for PubMedID 30829001
View details for PubMedCentralID PMC6619047
An adaptive hybridizable discontinuous Galerkin approach for cardiac electrophysiology
INTERNATIONAL JOURNAL FOR NUMERICAL METHODS IN BIOMEDICAL ENGINEERING
2018; 34 (5): e2959
Cardiac electrophysiology simulations are numerically challenging because of the propagation of a steep electrochemical wave front and thus require discretizations with small mesh sizes to obtain accurate results. In this work, we present an approach based on the hybridizable discontinuous Galerkin method (HDG), which allows an efficient implementation of high-order discretizations into a computational framework. In particular, using the advantage of the discontinuous function space, we present an efficient p-adaptive strategy for accurately tracking the wave front. The HDG allows to reduce the overall degrees of freedom in the final linear system to those only on the element interfaces. Additionally, we propose a rule for a suitable integration accuracy for the ionic current term depending on the polynomial order and the cell model to handle high-order polynomials. Our results show that for the same number of degrees of freedom, coarse high-order elements provide more accurate results than fine low-order elements. Introducing p-adaptivity further reduces computational costs while maintaining accuracy by restricting the use of high-order elements to resolve the wave front. For a patient-specific simulation of a cardiac cycle, p-adaptivity reduces the average number of degrees of freedom by 95% compared to the nonadaptive model. In addition to reducing computational costs, using coarse meshes with our p-adaptive high-order HDG method also simplifies practical aspects of mesh generation and postprocessing.
View details for DOI 10.1002/cnm.2959
View details for Web of Science ID 000431995600005
View details for PubMedID 29316340
Multiphysics Modeling of the Atrial Systole under Standard Ablation Strategies
CARDIOVASCULAR ENGINEERING AND TECHNOLOGY
2017; 8 (2): 205–18
The aim of this study was to develop a computational framework to compare the impact of standard ablation concepts on the mechanical performance of the atria, since different line combinations cannot be applied in practice to the same patient. For this purpuse, we coupled electro-mechano-hemodynamic mathematical models based on biophysical principles and simulate the contractile performance of the atria. We computed systolic pressures and volumes in two patient-specific atrial geometries (one of normal size and one hypertrophied) with various ablation concepts. We found that our computational model is able to detect the differences in the left atrial contractility and ejection fraction for various electrical activation sequences resulting from different ablation line combinations. We show that multiphysics modeling has the potential to quantify the hemodynamic performance of left atria for different ablation lines, which could be used as additional pre-operative clinical information for the choice of the ablation concept in the future.
View details for DOI 10.1007/s13239-017-0308-z
View details for Web of Science ID 000402142300008
View details for PubMedID 28512679
On the Role of Mechanics in Chronic Lung Disease
2013; 6 (12): 5639-5658
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