Adrián Buganza Tepole

Calibrating thermomechanical material models from experiments is challenging because deformation, temperature, and force responses are strongly coupled, while measurements are usually restricted to specimen surfaces. We present a full-field calibration framework for coupled finite-strain thermomechanical material models using boundary displacement, reaction-force data, and temperature. The forward model is formulated as a near-incompressible thermo-hyperelastic problem with thermomechanical coupling derived from a Helmholtz free energy, and the inverse problem is posed as a PDE-constrained optimization problem with weighted observation terms for the available data streams. Reduced gradients are computed with adjoint sensitivities that are obtained by automatic differentiation, enabling gradient-based calibration of nonlinear transient thermomechanical systems. The formulation is first verified on synthetic examples involving uniform thermal preconditioning and localized transient rod contact, where the ground-truth parameters are recovered from full-field measurements and force observations. The same workflow is then applied to experimental thermomechanical data by first calibrating a hyperelastic mechanical baseline from cyclic equibiaxial loading and subsequently identifying thermal expansion and directional shrinkage parameters from surface-temperature and boundary-force histories. The results demonstrate that coupled thermomechanical parameters can be inferred from experimentally accessible surface data without requiring volumetric observations.

Calibrating thermomechanical material models from experiments is challenging because deformation, temperature, and force responses are strongly coupled, while measurements are usually restricted to specimen surfaces. We present a full-field calibration framework for coupled finite-strain thermomechanical material models using boundary displacement, reaction-force data, and temperature. The forward model is formulated as a near-incompressible thermo-hyperelastic problem with thermomechanical coupling derived from a Helmholtz free energy, and the inverse problem is posed as a PDE-constrained optimization problem with weighted observation terms for the available data streams. Reduced gradients are computed with adjoint sensitivities that are obtained by automatic differentiation, enabling gradient-based calibration of nonlinear transient thermomechanical systems. The formulation is first verified on synthetic examples involving uniform thermal preconditioning and localized transient rod contact, where the ground-truth parameters are recovered from full-field measurements and force observations. The same workflow is then applied to experimental thermomechanical data by first calibrating a hyperelastic mechanical baseline from cyclic equibiaxial loading and subsequently identifying thermal expansion and directional shrinkage parameters from surface-temperature and boundary-force histories. The results demonstrate that coupled thermomechanical parameters can be inferred from experimentally accessible surface data without requiring volumetric observations.

Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain largely unexplored. Here, we present a Neural Ordinary Differential Equation (NODE) ROM framework that learns latent dynamics of coupled mechanical deformation and tissue growth, demonstrated in the context of skin growth during tissue expansion (TE). TE is a challenging problem involving nonlinear contact, history-dependent material behavior, and mechanobiology driven growth. The displacement field is compressed via Proper Orthogonal Decomposition (POD) into a low-dimensional latent space, and a NODE learns the resulting dynamics conditioned on patient-specific parameters. To address long-horizon error accumulation, a key challenge in autoregressive latent dynamical models, we propose a closed-loop architecture in which encoded features of the evolving growth field are fed back into the dynamics at each step. We compare feedback representations of increasing expressiveness: scalar, linear POD-based, and nonlinear CNN-based. The CNN-based growth feature feedback substantially stabilizes long-horizon rollouts. The best model captures 90.3% of validation cases within clinical tolerance based on the final skin area gain, compared to 43.7% for the open-loop baseline. Moreover, the NODE ROM achieves over 20000x the speed of full finite element simulations. More broadly, these results suggest that selectively retaining inexpensive physics of the state evolution and feeding features from these fields back into the latent dynamical system is a promising strategy for stable and accurate ROMs of G&R in biological tissues.

Reduced-order models (ROMs) are essential for rapid simulation of complex biomechanical systems and for bridging the gap between high fidelity models and clinical application. However, ROMs for tissue growth and remodeling (G&R) remain largely unexplored. Here, we present a Neural Ordinary Differential Equation (NODE) ROM framework that learns latent dynamics of coupled mechanical deformation and tissue growth, demonstrated in the context of skin growth during tissue expansion (TE). TE is a challenging problem involving nonlinear contact, history-dependent material behavior, and mechanobiology driven growth. The displacement field is compressed via Proper Orthogonal Decomposition (POD) into a low-dimensional latent space, and a NODE learns the resulting dynamics conditioned on patient-specific parameters. To address long-horizon error accumulation, a key challenge in autoregressive latent dynamical models, we propose a closed-loop architecture in which encoded features of the evolving growth field are fed back into the dynamics at each step. We compare feedback representations of increasing expressiveness: scalar, linear POD-based, and nonlinear CNN-based. The CNN-based growth feature feedback substantially stabilizes long-horizon rollouts. The best model captures 90.3% of validation cases within clinical tolerance based on the final skin area gain, compared to 43.7% for the open-loop baseline. Moreover, the NODE ROM achieves over 20000x the speed of full finite element simulations. More broadly, these results suggest that selectively retaining inexpensive physics of the state evolution and feeding features from these fields back into the latent dynamical system is a promising strategy for stable and accurate ROMs of G&R in biological tissues.

Soft materials such as rubbers, hydrogels, and biological tissues undergo damage in the form of stiffness degradation without apparent changes in their stress-free geometry. Accurate simulation of this behavior is critical in applications ranging from soft robotics to the design of medical devices, yet two persistent challenges are the difficulty of constructing flexible, thermodynamically consistent constitutive models, and the mesh dependence of finite element solutions caused by strain softening. Here we address both challenges simultaneously by combining physics-augmented neural network constitutive models with a gradient-enhanced damage formulation implemented within the differentiable finite element framework JAX-FEM. The elastic strain energy and the damage yield function are each parameterized by input-convex neural networks (ICNNs), which enforce polyconvexity and satisfaction of the Clausius--Duhem inequality by design. The gradient-enhanced formulation introduces a non-local damage field governed by an additional partial differential equation, regularizing the spatial distribution of damage and eliminating mesh dependence. The implementation is validated through local stress-strain fits, single-element parametric studies, a mesh and solution strategy study for a uniform deformation case, and a notched plate simulation. The results demonstrate that the proposed framework enables flexible, data-driven, mesh-independent damage simulation for a broad class of soft materials. We anticipate that the open-source implementation will lower the barrier to adopting physics-augmented neural network constitutive models.

Soft materials such as rubbers, hydrogels, and biological tissues undergo damage in the form of stiffness degradation without apparent changes in their stress-free geometry. Accurate simulation of this behavior is critical in applications ranging from soft robotics to the design of medical devices, yet two persistent challenges are the difficulty of constructing flexible, thermodynamically consistent constitutive models, and the mesh dependence of finite element solutions caused by strain softening. Here we address both challenges simultaneously by combining physics-augmented neural network constitutive models with a gradient-enhanced damage formulation implemented within the differentiable finite element framework JAX-FEM. The elastic strain energy and the damage yield function are each parameterized by input-convex neural networks (ICNNs), which enforce polyconvexity and satisfaction of the Clausius--Duhem inequality by design. The gradient-enhanced formulation introduces a non-local damage field governed by an additional partial differential equation, regularizing the spatial distribution of damage and eliminating mesh dependence. The implementation is validated through local stress-strain fits, single-element parametric studies, a mesh and solution strategy study for a uniform deformation case, and a notched plate simulation. The results demonstrate that the proposed framework enables flexible, data-driven, mesh-independent damage simulation for a broad class of soft materials. We anticipate that the open-source implementation will lower the barrier to adopting physics-augmented neural network constitutive models.

Classical phase-field theories of brittle fracture capture toughness-controlled crack growth but do not account for the material's strength surface, which governs fracture nucleation in the absence of cracks. The phase-field formulation of Kumar et al. (2020) proposed a blueprint for incorporating the strength surface while preserving toughness-controlled propagation by introducing a nucleation driving force and presented results for the Drucker-Prager surface. Following this blueprint, Chockalingam (2025) recently derived a general driving-force expression that incorporates arbitrary strength surfaces. The present work implements this driving force within a finite-element framework and incorporates representative strength surfaces that span diverse mathematical and physical characteristics-the Mohr-Coulomb, 3D Hoek-Brown, and Mogi-Coulomb surfaces. Through simulations of canonical fracture problems, the formulation is comprehensively validated across fracture regimes, capturing (i) nucleation under uniform stress, (ii) crack growth from large pre-existing flaws, and (iii) fracture governed jointly by strength and toughness. While the strength surfaces examined here already encompass a broad range of brittle materials, the results demonstrate the generality and robustness of the proposed driving-force construction for materials governed by arbitrary strength surfaces.

Accurately identifying the mechanical behavior of heterogeneous materials is a central challenge in materials science, with implications for the design of composites, metamaterials, and engineered biological tissue. Conventional inverse methods require closed-form constitutive models and are often restricted to simplified geometries or homogeneous properties, limiting their ability to capture complex, spatially varying material responses. Here, we introduce a fully data-driven framework for inverse characterization that recovers the complete constitutive behavior of heterogeneous solids directly from full-field displacement data, without prescribing a specific material law. Our approach combines neural ordinary differential equation (NODE) constitutive models, which inherently satisfy key thermodynamic and mathematical constraints, with a hyper-network that maps each material point to its local NODE, enabling continuous representation of arbitrary spatial variation in material properties. The loss function at the center of the method includes the strong form of equilibrium and traction boundary conditions. We demonstrate the method’s robustness on synthetic datasets, including heterogeneous isotropic and anisotropic materials, noise-contaminated measurements, and complex geometries, and validate it with digital image correlation experiments on 3D-printed elastomers. This framework provides a general, physically consistent route to inferring heterogeneous constitutive behavior from experimental data, offering new opportunities for accurate mechanical characterization across a broad range of material systems.

Accurate in vivo characterization of skin mechanical properties is essential for diagnostics and treatment planning across dermatological and surgical applications. Existing noninvasive techniques are limited in capturing the nonlinear and anisotropic behavior of skin. In this work, we propose a Bayesian inference framework that leverages active membranes to induce desired deformations and infer patient-specific skin properties from a measured strain field. A finite element model of skin-membrane interaction, parameterized using the Holzapfel-Gasser-Ogden model, is used to generate strain field data under various membrane actuation conditions. To overcome the computational cost of repeated simulations required for Bayesian sampling, we construct a data-driven surrogate using principal component analysis for dimensionality reduction and Gaussian process regression for rapid evaluation. Our approach enables probabilistic inference of key skin parameters, including shear modulus, fiber stiffness, dispersion, and orientation. An advantage of the proposed method is that inference of skin biomechanics does not require direct force measurements; rather, the method relies on known properties of active membranes (which can be tested ahead of time). The method does require strain field measurements. Through synthetic studies, we demonstrate that our method accurately recovers most model parameters even under moderate levels of spatially correlated noise, and that multiframe or multimembrane observations significantly enhance identifiability. These results establish the potential of active membranes as a viable platform for noninvasive, in vivo skin biomechanics assessment.

PURPOSE: Breast-conserving surgery (BCS) is the standard of care for early-stage breast cancer, offering recurrence and survival rates comparable to mastectomy while preserving healthy breast tissue. However, surgical cavity healing post-BCS often leads to highly variable tissue remodeling, including scar tissue formation and contracture, leading to visible breast deformation or asymmetry. These outcomes significantly impact patient quality of life but are difficult to predict due to the complex interplay between biologic healing processes and individual patient variability. To address this challenge, we extended our calibrated computational mechanobiological model of post-BCS healing by incorporating diagnostic imaging data to evaluate how patient-specific breast and tumor characteristics influence healing trajectories and deformation. METHODS: The model captured multi-scale biologic and biomechanical processes, including fibroblast activity, collagen remodeling, and nonlinear tissue mechanics, to simulate time-dependent tissue remodeling. Patient-specific breast and tumor geometries from preoperative magnetic resonance imaging (MRI) were integrated into finite element simulations of cavity healing, whose outputs trained Gaussian process surrogate models for rapid prediction of healing dynamics and breast surface deformation across diverse patient profiles. RESULTS: These models revealed how factors including breast density, cavity volume, breast volume, and cavity depth influence post-surgical cavity contraction and measures of breast surface deformation. CONCLUSION: This framework has the potential to provide a personalized, predictive tool for surgical planning and decision-making, enabling clinicians and patients to anticipate healing trajectories and cosmetic outcomes, with the goal of optimizing surgical results and enhancing patient quality of life.

Abstract Accurate in vivo characterization of skin mechanical properties is essential for diagnostics and treatment planning across dermatological and surgical applications. Existing noninvasive techniques are limited in capturing the nonlinear and anisotropic behavior of skin. In this work, we propose a Bayesian inference framework that leverages active membranes to induce desired deformations and infer patient-specific skin properties from a measured strain field. A finite element model of skin-membrane interaction, parameterized using the Holzapfel-Gasser-Ogden model, is used to generate strain field data under various membrane actuation conditions. To overcome the computational cost of repeated simulations required for Bayesian sampling, we construct a data-driven surrogate using principal component analysis for dimensionality reduction and Gaussian process regression for rapid evaluation. Our approach enables probabilistic inference of key skin parameters, including shear modulus, fiber stiffness, dispersion, and orientation. An advatange of the proposed method is that inference of skin biomechanics does not require direct force measurements. Rather, the method relies on known properties of active membranes (which can be tested ahead of time). The method does require strain field measurements. Through synthetic studies, we demonstrate that our method accurately recovers most model parameters even under moderate levels of spatially correlated noise, and that multi-frame or multi-membrane observations significantly enhance identifiability. These results establish the potential of active membranes as a viable platform for noninvasive, in vivo skin biomechanics assessment.

Classical phase-field theories of brittle fracture capture toughness-controlled crack growth but do not account for the material's strength surface, which governs fracture nucleation in the absence of cracks. The phase-field formulation of Kumar et al. (2020) proposed a blueprint for incorporating the strength surface while preserving toughness-controlled propagation by introducing a nucleation driving force and presented results for the Drucker-Prager surface. Following this blueprint, Chockalingam (2025) recently derived a general driving-force expression that incorporates arbitrary strength surfaces. The present work implements this driving force within a finite-element framework and incorporates representative strength surfaces that span diverse mathematical and physical characteristics-the Mohr-Coulomb, 3D Hoek-Brown, and Mogi-Coulomb surfaces. Through simulations of canonical fracture problems, the formulation is comprehensively validated across fracture regimes, capturing (i) nucleation under uniform stress, (ii) crack growth from large pre-existing flaws, and (iii) fracture governed jointly by strength and toughness. While the strength surfaces examined here already encompass a broad range of brittle materials, the results demonstrate the generality and robustness of the proposed driving-force construction for materials governed by arbitrary strength surfaces.

Reactive oxygen species (ROS) are second messengers that drive wound closure. However, the mechanism by which ROS regulate wound contraction to facilitate wound healing remains unclear. Here, we report that ROS counteract wound contraction by inhibiting the phosphorylation of myosin regulatory light chain. Acute ROS inhibition, through pharmacological perturbations, disturbs wound relaxation, delays wound closure, and impairs regrowth after amputation. Moreover, actomyosin inhibition relaxes tailfin contraction without impairing wound closure or regrowth. Overcontraction, on the other hand, impedes wound closure. Meanwhile, chronic depletion of epithelial ROS during embryonic development, achieved through morpholino-mediated knockdown of the duox gene, alters tissue stiffness, as measured using atomic force microscopy-based nanoindentation. Despite a reduced contraction force, the wound also appears to be overcontracted, with delayed healing and regrowth. An in silico linear elasticity simulation to calculate the second principal stress based on node-wise prescribed displacement recapitulated the contraction dynamics during acute and chronic ROS inhibition. Together, our results provide a novel understanding of how ROS facilitate wound closure, a process instrumental in restoring tissue integrity and maintaining homeostasis.

Abstract Purpose Breast-conserving surgery (BCS) is the standard of care for early-stage breast cancer, offering recurrence and survival rates comparable to mastectomy while preserving healthy breast tissue. However, surgical cavity healing post-BCS often leads to highly variable tissue remodeling, including scar tissue formation and contracture, leading to visible breast deformation or asymmetry. These outcomes significantly impact patient quality of life but are difficult to predict due to the complex interplay between biological healing processes and individual patient variability. To address this challenge, we extended our previously calibrated computational mechanobiological model of post-BCS healing by incorporating diagnostic imaging data to evaluate how patient-specific breast and tumor characteristics shape healing trajectories and breast deformation. Methods The model captured multiscale biological and biomechanical processes, including fibroblast activity, collagen remodeling, and nonlinear tissue mechanics, to simulate time-dependent tissue remodeling. Preoperative magnetic resonance imaging (MRI) scans provided patient-specific breast and tumor geometries and characteristics, which were integrated into finite element simulations of cavity healing. Simulation outputs were used to train Gaussian process surrogate models, enabling rapid, accurate prediction of healing dynamics and breast surface deformation across diverse patient profiles. Results These models revealed how factors including breast density, cavity volume, breast volume, and cavity depth influence post-surgical cavity contraction and measures of breast surface deformation. Conclusion This framework has the potential to provide a personalized, predictive tool for surgical planning and decision-making, enabling clinicians and patients to anticipate healing trajectories and cosmetic outcomes, with the goal of optimizing surgical results and enhancing patient quality of life.

Cerebrospinal flow dynamics (CSF) plays a critical role in structural disorders of the central nervous system (CNS) and in the design of effective procedures for intrathecal drug delivery. Medical imaging techniques have only partially characterized CSF dynamics. Computational models have the potential to offer a high-resolution description of CSF flow and advance our mechanistic understanding. However, anatomically-accurate computational models of CSF dynamics in the spinal canal have largely ignored the compliance of the spinal tissues, which is critical to understand the pulse wave velocity and the craniocaudal decay of CSF pulsations. Here, we propose a mixed-dimensional fluid-structure interaction method that enables high-fidelity simulations of CSF dynamics on anatomically-accurate models of the spinal canal, considering the tissue compliance effects emerging from the dura mater and epidural fat. Our mixed-dimensional approach bypasses a critical computational bottleneck that emerges from the multiscale geometry of spinal tissues. Our results show that accurate modeling of tissue compliance is critical to capture key elements of CSF dynamics. This work opens new possibilities to control and optimize intrathecal drug delivery and to understand structural abnormalities of the CNS.

We propose a data-driven constitutive framework for anisotropic damage mechanics based on the second-order damage tensor approach for both compressible and incompressible materials. The formulation is thermodynamically consistent and satisfies the Clausius-Duhem inequality. The strain energy density potentials are expressed as isotropic functions of the right Cauchy-Green deformation tensor, along with structural tensors that encode anisotropy either present in the virgin material or resulting from damage. To guarantee the polyconvexity condition, non-decreasing convex neural networks with inputs that ensure polyconvexity are used to parameterize the strain energy density potentials. The model vanishes in the undeformed state, fulfilling the normality condition. In contrast to classical [1-d] damage models, the expressiveness of the new data-driven model is enhanced by employing a family of nonlinear, convex, decreasing functions to capture the effect of damage. Damage evolution is governed through a damage potential, where the corresponding threshold is defined in terms of the damage conjugate forces. As a special case of the general formulation, a new anisotropic generic format is introduced to predict constitutive responses under damage-induced anisotropy in initially isotropic materials. To reduce the computational burden during training, a decoupled training scheme is introduced, and its accuracy is demonstrated in all numerical examples. These include benchmarks for incompressible isotropic, transversely isotropic, and compressible orthotropic materials. The framework is also validated against experimental data capturing anisotropic Mullins-type damage.

We propose a new framework for identifying mechanical properties of heterogeneous materials without a closed-form constitutive equation. Given a full-field measurement of the displacement field, for instance as obtained from digital image correlation (DIC), a continuous approximation of the strain field is obtained by training a neural network that incorporates Fourier features to effectively capture sharp gradients in the data. A physics-based data-driven method built upon ordinary neural differential equations (NODEs) is employed to discover constitutive equations. The NODE framework can represent arbitrary materials while satisfying constraints in the theory of constitutive equations by default. To account for heterogeneity, a hyper-network is defined, where the input is the material coordinate system, and the output is the NODE-based constitutive equation. The parameters of the hyper-network are optimized by minimizing a multi-objective loss function that includes penalty terms for violations of the strong form of the equilibrium equations of elasticity and the associated Neumann boundary conditions. We showcase the framework with several numerical examples, including heterogeneity arising from variations in material parameters, spatial transitions from isotropy to anisotropy, material identification in the presence of noise, and, ultimately, application to experimental data. As the numerical results suggest, the proposed approach is robust and general in identifying the mechanical properties of heterogeneous materials with very few assumptions, making it a suitable alternative to classical inverse methods.

An unsupervised machine learning method is introduced to align medical images in the context of the large deformation elasticity coupled with growth and remodeling biophysics. The technique, which stems from the principle of minimum potential energy in solid mechanics, consists of two steps: Firstly, in the predictor step, the geometric registration is achieved by minimizing a loss function composed of a dissimilarity measure and a regularizing term. Secondly, the physics of the problem, including the equilibrium equations along with growth mechanics, are enforced in a corrector step by minimizing the potential energy corresponding to a Dirichlet problem, where the predictor solution defines the boundary condition and is maintained by distance functions. The features of the new solution procedure, as well as the nature of the registration problem, are highlighted by considering several examples. In particular, registration problems containing large non-uniform deformations caused by extension, shearing, and bending of multiply-connected regions are used as benchmarks. In addition, we analyzed a benchmark biological example (registration for brain data) to showcase that the new deep learning method competes with available methods in the literature. We then applied the method to various datasets. First, we analyze the regrowth of the zebrafish embryonic fin from confocal imaging data. Next, we evaluate the quality of the solution procedure for two examples related to the brain. For one, we apply the new method for 3D image registration of longitudinal magnetic resonance images of the brain to assess cerebral atrophy, where a first-order ODE describes the volume loss mechanism. For the other, we explore cortical expansion during early fetal brain development by coupling the elastic deformation with morphogenetic growth dynamics. The method and examples show the ability of our framework to attain high-quality registration and, concurrently, solve large deformation elasticity balance equations and growth and remodeling dynamics.

Abstract Fluctuations and propagation of cytosolic calcium levels at both the cellular and tissue levels show complex patterns, referred to as calcium signatures, that regulate growth, organ development, damage responses, and survival. The quantitative analysis of calcium signatures at the cellular level is essential for identifying unique patterns that coordinate biological processes. However, a versatile framework applicable to multiple tissue types, allowing researchers to compare, measure, and validate diverse responses and recognize conserved patterns across model organisms, is missing. Here, we present a post-processing tool, CalciumInsights, which leverages the R packages Shiny and Golem. This tool has a graphical user interface and does not require software programming experience to perform calcium signal analysis. The open-source software has a modular framework with standardized functionalities that can be tailored for various research approaches. CalciumInsights provides descriptive statistical analysis through various metrics extracted from dynamic calcium transients and oscillations, such as peak amplitude, area under the curve, frequency, among others. The tool was evaluated with fluorescence imaging data from three model organisms: Danio rerio , Arabidopsis thaliana , and Drosophila melanogaster , demonstrating its ability to analyze diverse biological responses and models. Finally, the open-source nature of CalciumInsights enables community-driven improvements and developments for enabling new applications. Author Summary This manuscript introduces CalciumInsights, an open-source tool for calcium signature analysis. Designed to be a versatile tool that works with various tissue types and biological systems, CalciumInsights has an easy-to-use graphical user interface. Our program simplifies metrics extraction while maintaining the quality of the analysis by integrating several algorithms. CalciumInsights stands out for its user-friendliness, ease of use, and robust data exploration features, such as tunable filters for improved accuracy. These features promote inclusivity and lower barriers to scientific research by making calcium signature analysis accessible to users of all programming skill levels.

Tissue expansion is an integral component of reconstructive surgery used to promote native skin growth. This process is driven by the gradual inflation of the tissue expander placed subcutaneously on the patient's body. Despite its widespread use, the lack of in vivo evidence on the biological processes underlying skin growth has limited technological advancements. Here, we explore the gene and protein expression changes that control mechanically induced skin growth during tissue expansion. Using a porcine tissue expansion model, we revealed that skin expansion disrupts key components responsible for epithelial integrity, as evidenced by the loss of E-cadherin and alpha-catenin expression in expanded skin compared to the unexpanded control. This disruption correlates with the translocation of the transcriptional factor YAP1 from the membrane to the nucleus, activating keratinocyte proliferation and possibly regulating other critical processes involved in skin adaptation to mechanical stretch. Our data show that in vivo cell proliferation is mediated by force-induced changes in the composition of molecular complexes formed by E-cadherin, alpha-catenin, and YAP1.

Breast reconstruction using tissue expanders is the primary treatment option following mastectomy. Although skin growth in response to chronic supra-physiological stretch is well-established, individual patient factors such as breast shape, volume, skin prestrain, and mechanical properties, create unique deformation and growth patterns. The inability to predict skin growth and deformation prior to treatment often leads to complications and suboptimal esthetic outcomes. Personalized predictive simulations offer a promising solution to these challenges. We present a pipeline for predictive computational models of skin growth in tissue expansion. At the start of treatment, we collect three-dimensional (3D) photos and create an initial finite element model. Our framework accounts for uncertainties in treatment protocols, mechanical properties, and biological parameters. These uncertainties are informed by surgeon input, existing literature on mechanical properties, and prior research on porcine models for biological parameters. By collecting 3D photos longitudinally during treatment, and integrating the data through a Bayesian framework, we can systematically reduce uncertainty in the predictions. Calibrated personalized models are sampled using Monte Carlo methods, which require thousands of model evaluations. To overcome the computational limitations of directly evaluating the finite element model, we use Gaussian process surrogate models. We anticipate that this pipeline can be used to guide patient treatment in the near future.

ABSTRACT Reactive oxygen species (ROS) are second messengers that drive wound closure. However, the mechanism by which ROS regulate wound contraction to facilitate wound healing remains unclear. Here, we report that ROS counteract wound contraction by inhibiting the phosphorylation of myosin regulatory light chain. Acute ROS inhibition, through pharmacological perturbations, disturbs wound relaxation, delays wound closure, and impairs regrowth following amputation. Moreover, actomyosin inhibition relaxes tailfin contraction without impairing wound closure or regrowth. Over-contraction, on the other hand, impedes wound closure. Meanwhile, chronic depletion of epithelial ROS during embryonic development, achieved through morpholino-mediated knockdown of the duox gene, alters tissue stiffness, as measured using atomic force microscopy-based nanoindentation. Despite a reduced contraction force, the wound also appears to be over-contracted, with delayed healing and regrowth. An in silico linear elasticity simulation to calculate the second principal stress based on node-wise prescribed displacement recapitulated the contraction dynamics during acute and chronic ROS inhibition. Together, our results provide a novel understanding of how reactive oxygen species (ROS) facilitate wound closure, a process instrumental in restoring tissue integrity and maintaining homeostasis.

Tissue expansion (TE), an essential technique in reconstructive surgery, leverages the growth of skin in response to stretch. However, human skin growth dynamics have not been evaluated in vivo. Previously, we quantified this process in a porcine model and developed a calibrated computational framework. Here, we create patient-specific finite element (FE) models of skin growth in TE using longitudinal 3D photos collected during TE treatment. These geometries enable Bayesian model calibration, accounting for uncertainties in boundary conditions, mechanical properties, and biological parameters. The framework incorporates prior knowledge from the porcine model as well as literature information on human skin mechanics. The likelihood function assesses alignment between predicted and observed geometries, and predicted and observed skin growth. To efficiently sample the posterior distribution, we use Markov Chain Monte Carlo (MCMC) with Gaussian process surrogates, reducing computational cost. This pipeline is demonstrated in five TE cases. Post-calibration, FE models closely match 3D photos, with errors below 2 mm on average. Notably, Bayesian calibration collapses the critical stretch parameter posterior distribution. This study presents the first in vivo measurement of human skin growth, confirming that FE models accurately capture TE in the clinical setting, and that porcine-derived parameters provide a strong prior for Bayesian calibration in the clinical case. These findings support the development of personalized digital twins for TE, enhancing surgical planning and outcomes.

Accurate constitutive models of soft materials are crucial for understanding their mechanical behavior and ensuring reliable predictions in the design process. To this end, scientific machine learning research has produced flexible and general material model architectures that can capture the behavior of a wide range of materials, reducing the need for expert-constructed closed-form models. The focus has gradually shifted towards embedding physical constraints in the network architecture to regularize these over-parameterized models. Two popular approaches are input convex neural networks (ICNN) and neural ordinary differential equations (NODE). A related alternative has been the generalization of closed-form models, such as sparse regression from a large library. Remarkably, all prior work using ICNN or NODE uses the invariants of the Cauchy-Green tensor and none uses the principal stretches. In this work, we construct general polyconvex functions of the principal stretches in a physics-aware deep-learning framework and offer insights and comparisons to invariant-based formulations. The framework is based on recent developments to characterize polyconvex functions in terms of convex functions of the right stretch tensor $\mathbf{U}$, its cofactor $\text{cof}\mathbf{U}$, and its determinant $J$. Any convex function of a symmetric second-order tensor can be described with a convex and symmetric function of its eigenvalues. Thus, we first describe convex functions of $\mathbf{U}$ and $\text{cof}\mathbf{U}$ in terms of their respective eigenvalues using deep Holder sets composed with ICNN functions. A third ICNN takes as input $J$ and the two convex functions of $\mathbf{U}$ and $\text{cof}\mathbf{U}$, and returns the strain energy as output. The ability of the model to capture arbitrary materials is demonstrated using synthetic and experimental data.

The skin is a multilayered organ with microstructural and antomical heterogeneities that contribute to its unique mechanophysiology. Between the epidermis layer at the top and the dermis layer below, the basal keratinocytes form an interface with sinusoidal-like geometry termed rete ridges. In previous computational work we showed that the rete ridges contribute to lower delamination risk by increasing surface area and reducing the stress jump across the interface. Experimentally, we and others have shown that upon repeated tissue expansion and growth, physiological rete ridge frequency is preserved. Here we implement a 2D multilayered skin model where each layer is able to grow in response to applied loading toward recovering the layer-specific homeostatic stretch. Our simulations support the hypothesis that mechanics of growing tissue can explain secondary buckling and new rete ridge formation in tissue expansion. The process is robust with respect to parameters such as homeostatic stretch, layer thicknesses, and shear moduli of the different layers. Thicker epidermis suppresses higher frequency features, and so does a stiffer epidermis with respect to the basal layer. Interestingly, new rete ridge valleys are formed at locations that were originally peaks of the sine wave, whereas original valleys remain valleys. This pattern might have a connection to the localization of stem cell and transient amplifying cells in the epidermis. This study does not discard the role of cell-cell signaling dynamics, but rather emphasizes the possibility of achieving robust geometric patterns with simple rules of growing tissue, even in the absence of complex regulatory networks.

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) and an increase in the high modulus (modulus computed with stress-stretch data past the transition point). 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 microstructure 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.

Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today's finite element analysis packages come with a set of pre-programmed material models, which may exhibit restricted validity in capturing the intricate mechanical behavior of these materials. Regrettably, incorporating a modified or novel material model in a finite element analysis package requires non-trivial in-depth knowledge of tensor algebra, continuum mechanics, and computer programming, making it a complex task that is prone to human error. Here we design a universal material subroutine, which automates the integration of novel constitutive models of varying complexity in non-linear finite element packages, with no additional analytical derivations and algorithmic implementations. We demonstrate the versatility of our approach to seamlessly integrate innovative constitutive models from the material point to the structural level through a variety of soft matter case studies: a frontal impact to the brain; reconstructive surgery of the scalp; diastolic loading of arteries and the human heart; and the dynamic closing of the tricuspid valve. Our universal material subroutine empowers all users, not solely experts, to conduct reliable engineering analysis of soft matter systems. We envision that this framework will become an indispensable instrument for continued innovation and discovery within the soft matter community at large.

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.

Abstract Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. $$R^2 = 0.9353$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9353</mml:mn> </mml:mrow> </mml:math> ) as well as the subject-specific shear modulus ( $$R^2 = 0.9801$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9801</mml:mn> </mml:mrow> </mml:math> ), growth rate ( $$R^2 = 0.8649$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.8649</mml:mn> </mml:mrow> </mml:math> ), and natural pre-stretch ( $$R^2 = 0.9783$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:msup> <mml:mi>R</mml:mi> <mml:mn>2</mml:mn> </mml:msup> <mml:mo>=</mml:mo> <mml:mn>0.9783</mml:mn> </mml:mrow> </mml:math> ) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols.

Cells intricately sense mechanical forces from their surroundings, driving biophysical and biochemical activities. This mechanosensing phenomenon occurs at the cell-matrix interface, where mechanical forces resulting from cellular motion, such as migration or matrix stretching, are exchanged through surface receptors, primarily integrins, and their corresponding matrix ligands. A pivotal player in this interaction is the α 5 β 1 integrin and fibronectin (FN) bond, known for its role in establishing cell adhesion sites for migration. However, upregulation of the α 5 β 1 -FN bond is associated with uncontrolled cell metastasis. This bond operates through catch bond dynamics, wherein the bond lifetime paradoxically increases with greater force. The mechanism sustaining the characteristic catch bond dynamics of α 5 β 1 -FN remains unclear. Leveraging molecular dynamics simulations, our approach unveils a pivot-clip mechanism. Two key binding sites on FN, namely the synergy site and the RGD (Arg-Gly-Asp) motif, act as active points for structural changes in α 5 β 1 integrin. Conformational adaptations at these sites are induced by a series of hydrogen bond formations and breaks at the synergy site. We disrupt these adaptations through a double mutation on FN, known to reduce cell adhesion. A whole-cell finite-element model is employed to elucidate how the synergy site may promote dynamic α 5 β 1 -FN binding, resisting cell contraction. In summary, our study integrates molecular- and cellular-level modeling to propose that FN's synergy site reinforces cell adhesion through enhanced binding dynamics and a mechanosensitive pivot-clip mechanism. This work sheds light on the interplay between mechanical forces and cell-matrix interactions, contributing to our understanding of cellular behaviors in physiological and pathological contexts.

Many natural materials exhibit highly complex, nonlinear, anisotropic, and heterogeneous mechanical properties. Recently, it has been demonstrated that data-driven strain energy functions possess the flexibility to capture the behavior of these complex materials with high accuracy while satisfying physics-based constraints. However, most of these approaches disregard the uncertainty in the estimates and the spatial heterogeneity of these materials. In this work, we leverage recent advances in generative models to address these issues. We use as building block neural ordinary equations (NODE) that—by construction—create polyconvex strain energy functions, a key property of realistic hyperelastic material models. We combine this approach with probabilistic diffusion models to generate new samples of strain energy functions. This technique allows us to sample a vector of Gaussian white noise and translate it to NODE parameters thereby representing plausible strain energy functions. We extend our approach to spatially correlated diffusion resulting in heterogeneous material properties for arbitrary geometries. We extensively test our method with synthetic and experimental data on biological tissues and run finite element simulations with various degrees of spatial heterogeneity. We believe this approach is a major step forward including uncertainty in predictive, data-driven models of hyperelasticity.

Soft materials play an integral part in many aspects of modern life including autonomy, sustainability, and human health, and their accurate modeling is critical to understand their unique properties and functions. Today's finite element analysis packages come with a set of pre-programmed material models, which may exhibit restricted validity in capturing the intricate mechanical behavior of these materials. Regrettably, incorporating a modified or novel material model in a finite element analysis package requires non-trivial in-depth knowledge of tensor algebra, continuum mechanics, and computer programming, making it a complex task that is prone to human error. Here we design a universal material subroutine, which automates the integration of novel constitutive models of varying complexity in non-linear finite element packages, with no additional analytical derivations and algorithmic implementations. We demonstrate the versatility of our approach to seamlessly integrate innovative constituent models from the material point to the structural level through a variety of soft matter case studies: a frontal impact to the brain; reconstructive surgery of the scalp; diastolic loading of arteries and the human heart; and the dynamic closing of the tricuspid valve. Our universal material subroutine empowers all users, not solely experts, to conduct reliable engineering analysis of soft matter systems. We envision that this framework will become an indispensable instrument for continued innovation and discovery within the soft matter community at large.

Since their invention, tissue expanders, which are designed to trigger additional skin growth, have revolutionised many reconstructive surgeries. Currently, however, the sole quantitative method to assess skin growth requires skin excision. Thus, in the context of patient outcomes, a machine learning method which uses non-invasive measurements to predict in vivo skin growth and other skin properties, holds significant value. In this study, the finite element method was used to simulate a typical skin expansion protocol and to perform various simulated wave propagation experiments during the first few days of expansion on 1,000 individual virtual subjects. An artificial neural network trained on this dataset was shown to be capable of predicting the future skin growth at 7 days (avg. R2 = 0.9353) as well as the subject-specific shear modulus (R2 = 0.9801), growth rate (R2 = 0.8649), and natural pre-stretch (R2 = 0.9783) with a very high degree of accuracy. The method presented here has implications for the real-time prediction of patient-specific skin expansion outcomes and could facilitate the development of patient-specific protocols.

Soft actuators, distinguished by their complex nonlinear behavior, are difficult to model analytically and cumbersome to prototype. Finite element (FE) models allow for more efficient behavioral prediction, but often require onerous setup, especially for large systems. We present a physics-informed neural network model formed by combining a low fidelity analytical model and input-convex neural networks to learn an underlying energy potential for the actuator from experimental and finite element simulation data. In doing this, the neural network can provide sufficiently accurate predictions about systems made up of multiple units, essentially scaling the model from a single unit to an assembly of many. To test this concept, we compare predictions of the deformation of a 5-actuator system from an FE model and from the physics-informed neural network. The neural network, which provides a prediction similar in accuracy to the FE equivalent, can more easily be adjusted to execute systems of greater quantities of units without drastic increases in computational consumption. In this way, we can scale our predictive understanding with adequate accuracy without compounding resources.