Vahidullah Tac

All Publications

• Tissue expansion mitigates radiation-induced skin fibrosis in a porcine model. Acta biomaterialia Nunez-Alvarez, L., Ledwon, J. K., Applebaum, S., Progri, B., Han, T., Laudo, J., Tac, V., Gosain, A. K., Tepole, A. B. 2024

  Abstract

  Tissue expansion (TE) is the primary method for breast reconstruction after mastectomy. In many cases, mastectomy patients undergo radiation treatment (XR). Radiation is known to induce skin fibrosis and is one of the main causes for complications during post-mastectomy breast reconstruction. TE, on the other hand, induces a pro-regenerative response that culminates in growth of new skin. However, the combined effect of XR and TE on skin mechanics is unknown. Here we used the porcine model of TE to study the effect of radiation on skin fibrosis through biaxial testing, histological analysis, and kinematic analysis of skin deformation over time. We found that XR leads to stiffening of skin compared to control based on a shift in the transition stretch (transition between a low stiffness and an exponential stress-strain region characteristic of collagenous tissue). The change in transition stretch can be explained by thicker, more aligned collagen fiber bundles measured in histology images. Skin subjected to both XR+TE showed similar micostructure to controls as well as similar biaxial response, suggesting that physiological remodeling of collagen induced by TE partially counteracts pro-fibrotic XR effects. Skin growth was indirectly assessed with a kinematic approach that quantified increase in permanent area changes without reduction in thickness, suggesting production of new tissue driven by TE even in the presence of radiation treatment. Future work will focus on the detailed biological mechanisms by which TE counteracts radiation induced fibrosis. STATEMENT OF SIGNIFICANCE: Breast cancer is the most prevalent in women and its treatment often results in total breast removal (mastectomy), followed by reconstruction using tissue expanders. Radiation, which is used in about a third of breast reconstruction cases, can lead to significant complications. The timing of radiation treatment remains controversial. Radiation is known to cause immediate skin damage and long-term fibrosis. Tissue expansion leads to a pro-regenerative response involving collagen remodeling. Here we show that tissue expansion immediately prior to radiation can reduce the level of radiation-induced fibrosis. Thus, we anticipate that this new evidence will open up new avenues of investigation into how the collagen remodeling and pro-regenerative effects of tissue expansion can be leverage to prevent radiation-induced fibrosis.

  View details for DOI 10.1016/j.actbio.2024.09.035

  View details for PubMedID 39326692

• Data-driven continuum damage mechanics with built-in physics. Extreme Mechanics Letters Tac, V., Kuhl, E., Tepole, A. B. 2024; 71

  Abstract

  Soft materials such as rubbers and soft tissues often undergo large deformations and experience damage degradation that impairs their function. This energy dissipation mechanism can be described in a thermodynamically consistent framework known as continuum damage mechanics. Recently, data-driven methods have been developed to capture complex material behaviors with unmatched accuracy due to the high flexibility of deep learning architectures. Initial efforts focused on hyperelastic materials, and recent advances now offer the ability to satisfy physics constraints such as polyconvexity of the strain energy density function by default. However, modeling inelastic behavior with deep learning architectures and built-in physics has remained challenging. Here we show that neural ordinary differential equations (NODEs), which we used previously to model arbitrary hyperelastic materials with automatic polyconvexity, can be extended to model energy dissipation in a thermodynamically consistent way by introducing an inelastic potential: a monotonic yield function. We demonstrate the inherent flexibility of our network architecture in terms of different damage models proposed in the literature. Our results suggest that our NODEs re-discover the true damage function from synthetic stress-deformation history data. In addition, they can accurately characterize experimental skin and subcutaneous tissue data.

  View details for DOI 10.1016/j.eml.2024.102220

  View details for PubMedID 39372561

  View details for PubMedCentralID PMC11449040

• Generative hyperelasticity with physics-informed probabilistic diffusion fields ENGINEERING WITH COMPUTERS Tac, V., Rausch, M. K., Bilionis, I., Sahli Costabal, F., Tepole, A. 2024

  View details for DOI 10.1007/s00366-024-01984-2

  View details for Web of Science ID 001226809000001

• Benchmarking physics-informed frameworks for data-driven hyperelasticity. Computational mechanics Taç, V., Linka, K., Sahli-Costabal, F., Kuhl, E., Tepole, A. B. 2024; 73 (1): 49-65

  Abstract

  Data-driven methods have changed the way we understand and model materials. However, while providing unmatched flexibility, these methods have limitations such as reduced capacity to extrapolate, overfitting, and violation of physics constraints. Recently, frameworks that automatically satisfy these requirements have been proposed. Here we review, extend, and compare three promising data-driven methods: Constitutive Artificial Neural Networks (CANN), Input Convex Neural Networks (ICNN), and Neural Ordinary Differential Equations (NODE). Our formulation expands the strain energy potentials in terms of sums of convex non-decreasing functions of invariants and linear combinations of these. The expansion of the energy is shared across all three methods and guarantees the automatic satisfaction of objectivity, material symmetries, and polyconvexity, essential within the context of hyperelasticity. To benchmark the methods, we train them against rubber and skin stress-strain data. All three approaches capture the data almost perfectly, without overfitting, and have some capacity to extrapolate. This is in contrast to unconstrained neural networks which fail to make physically meaningful predictions outside the training range. Interestingly, the methods find different energy functions even though the prediction on the stress data is nearly identical. The most notable differences are observed in the second derivatives, which could impact performance of numerical solvers. On the rich data used in these benchmarks, the models show the anticipated trade-off between number of parameters and accuracy. Overall, CANN, ICNN and NODE retain the flexibility and accuracy of other data-driven methods without compromising on the physics. These methods are ideal options to model arbitrary hyperelastic material behavior.

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

  View details for PubMedID 38741577

  View details for PubMedCentralID PMC11090478

• Data-driven anisotropic finite viscoelasticity using neural ordinary differential equations. Computer methods in applied mechanics and engineering Taç, V., Rausch, M., Costabal, F. S., Tepole, A. B. 2023; 411

  Abstract

  We develop a fully data-driven model of anisotropic finite viscoelasticity using neural ordinary differential equations as building blocks. We replace the Helmholtz free energy function and the dissipation potential with data-driven functions that a priori satisfy physics-based constraints such as objectivity and the second law of thermodynamics. Our approach enables modeling viscoelastic behavior of materials under arbitrary loads in three-dimensions even with large deformations and large deviations from the thermodynamic equilibrium. The data-driven nature of the governing potentials endows the model with much needed flexibility in modeling the viscoelastic behavior of a wide class of materials. We train the model using stress-strain data from biological and synthetic materials including humain brain tissue, blood clots, natural rubber and human myocardium and show that the data-driven method outperforms traditional, closed-form models of viscoelasticity.

  View details for DOI 10.1016/j.cma.2023.116046

  View details for PubMedID 37426992

  View details for PubMedCentralID PMC10327622

• Data-driven Modeling of the Mechanical Behavior of Anisotropic Soft Biological Tissue. Engineering with computers Tac, V., Sree, V. D., Rausch, M. K., Tepole, A. B. 2022; 38 (5): 4167-4182

  Abstract

  Closed-form constitutive models are the standard to describe soft tissue mechanical behavior. However, inherent pitfalls of an explicit functional form include poor fits to the data, non-uniqueness of fit, and sensitivity to parameters. Here we design deep neural networks (DNN) that satisfy desirable physics constraints in order to replace expert models of tissue mechanics. To guarantee stress-objectivity, the DNN takes strain (pseudo)-invariants as inputs, and outputs the strain energy and its derivatives. Polyconvexity of strain energy is enforced through the loss function. Direct prediction of both energy and derivative functions enables the computation of the elasticity tensor needed for a finite element implementation. We showcase the DNN ability to learn the anisotropic mechanical behavior of porcine and murine skin from biaxial test data. A multi-fidelity scheme that combines high fidelity experimental data with a low fidelity analytical approximation yields the best performance. Finite element simulations of tissue expansion with the DNN model illustrate the potential of this method to impact medical device design for skin therapeutics. We expect that the open data and software from this work will broaden the use of data-driven constitutive models of tissue mechanics.

  View details for DOI 10.1007/s00366-022-01733-3

  View details for PubMedID 38031587

  View details for PubMedCentralID PMC10686525

• Data-driven Tissue Mechanics with Polyconvex Neural Ordinary Differential Equations. Computer methods in applied mechanics and engineering Tac, V., Sahli Costabal, F., Tepole, A. B. 2022; 398

  Abstract

  Data-driven methods are becoming an essential part of computational mechanics due to their advantages over traditional material modeling. Deep neural networks are able to learn complex material response without the constraints of closed-form models. However, data-driven approaches do not a priori satisfy physics-based mathematical requirements such as polyconvexity, a condition needed for the existence of minimizers for boundary value problems in elasticity. In this study, we use a recent class of neural networks, neural ordinary differential equations (N-ODEs), to develop data-driven material models that automatically satisfy polyconvexity of the strain energy. We take advantage of the properties of ordinary differential equations to create monotonic functions that approximate the derivatives of the strain energy with respect to deformation invariants. The monotonicity of the derivatives guarantees the convexity of the energy. The N-ODE material model is able to capture synthetic data generated from closed-form material models, and it outperforms conventional models when tested against experimental data on skin, a highly nonlinear and anisotropic material. We also showcase the use of the N-ODE material model in finite element simulations of reconstructive surgery. The framework is general and can be used to model a large class of materials, especially biological soft tissues. We therefore expect our methodology to further enable data-driven methods in computational mechanics.

  View details for DOI 10.1016/j.cma.2022.115248

  View details for PubMedID 38045634

  View details for PubMedCentralID PMC10691864

• Predicting the mechanical properties of biopolymer gels using neural networks trained on discrete fiber network data COMPUTER METHODS IN APPLIED MECHANICS AND ENGINEERING Leng, Y., Tac, V., Calve, S., Tepole, A. B. 2021; 387

  View details for DOI 10.1016/j.cma.2021.114160

  View details for Web of Science ID 000708703300009

• Micromechanical modelling of carbon nanotube reinforced composite materials with a functionally graded interphase JOURNAL OF COMPOSITE MATERIALS Tac, V., Gurses, E. 2019; 53 (28-30): 4337-4348

  View details for DOI 10.1177/0021998319857126

  View details for Web of Science ID 000487078400032

• Dynamic Frictional Sliding Modes between Two Homogenous Interfaces Taj, W., Coker, D., Karamis, M. B., Nair, F., Savas, S., Gocer, A., Hamamci, M. IOP PUBLISHING LTD. 2018

  View details for DOI 10.1088/1757-899X/295/1/012001

  View details for Web of Science ID 000448617300001