Biology subjects

Holzapfel, G. A.

Publications and source records attributed to Holzapfel, G. A..

10 recordsLinked to original sources

bioRxiv2026

Feasibility study of fluid-structure-growth modelling in the context of endogenous tissue restoration

In situ tissue engineering exploits natural inflammatory responses to turn a synthetic vascular graft into a regenerated, functioning, and living vessel through endogenous tissue restoration. Despite promising preclinical results, challenges remain, especially in high-pressure regimes. To better understand the underlying biological processes and predict long-term outcomes of graft implantation, we propose an in silico approach. We account for the solid mechanics of conduit grafts in high and low pressure regimes, the wall shear stresses, and long-term growth and remodeling through two reduced-order fluid-structure-growth models. The first employs an artificial neural network surrogate model to compute the time-averaged wall shear stress at every growth step, whereas the second evaluates a fully-coupled fluid-structure interaction model every 60 time steps. We thoroughly verify both models and confirm acceptable model-form errors, then calibrate them against data from animal experiments. A validation study comparing in silico predictions with unseen animal data of carotid and pulmonary conduit grafts confirms that the model remains reliable up to at least one month of prediction time, hence in the future enabling in silico optimization of short-term endogenous tissue restoration in tissue engineering vascular grafts.

bioengineering↗

bioRxiv2026

Mechanical fidelity of brain tissue phantoms: A comparative experimental characterization of equilibrium and dissipative behavior

Despite lacking a dedicated structural function, brain tissue is exposed to severe mechanical loading during accidents and trauma, with potentially permanent or lethal consequences. Therefore, characterizing its mechanical behavior assumes particular importance for designing protective equipment, planning surgeries, and training neurosurgeons, tasks that often rely on physical brain replicas made from phantom materials. Although the mechanics of brain tissue has been extensively studied, the selection of suitable phantom materials still relies on simplified metrics that fail to capture the highly nonlinear and rate-dependent behavior of the brain. In this work, we characterize the mechanical response at low-to-medium strain rates of common synthetic brain phantom materials, including Sylgard 527, Ecoflex Gel, and a composite hydrogel, and establish rigorous comparisons with porcine brain tissue as a benchmark. To this end, we employ a multi-step stress relaxation protocol under both uniaxial extension and compression across two different strain rates, introduce thermodynamic metrics, and perform comparisons based on rigorous statistical analysis. In particular, we isolate the thermodynamic equilibrium stress-strain curves, representing the baseline material's response, from rate-dependent dissipative inelastic effects, relatable to viscoelastic and poroelastic mechanisms. Our results provide a thorough comparison, revealing critical limitations in existing simulant materials and highlighting significant space for developing improved brain surrogates. The comprehensive dataset collected can also support the calibration of constitutive models, enhancing the predictive accuracy of numerical simulations involving brain tissue and its surrogates. More broadly, this study highlights the need to move beyond simplistic, scalar-metric-based comparisons of mechanical responses across materials.

biophysics↗

bioRxiv2026

Effective porosity and fluid flow in macroporous ultrasoft hydrogels: An experimental characterization

Hydrogels are the preferred materials for applications mimicking soft tissues due to their high water content and tunable mechanical properties. The state of the water in these hydrated networks governs their response to mechanical loading through coupled interstitial flow and large deformations of the solid network. Reliable experimental methods for quantifying the fraction of mobile fluid during mechanical deformation remain limited. Within the theoretical framework of mixture theory, we describe hydrogels as hydrated biphasic media consisting of a deformable incompressible solid matrix and a mobile fluid phase. We developed a mechanical testing protocol that enables the experimental separation of solid and fluid contributions under loading. The method is demonstrated using biocompatible and highly versatile hydrogel phantoms of varying compositions. Controlled, incremental drained confined compression of the hydrogel samples results in free-water fractions of approximately 40%, 60%, and 77%, reflecting the systematic influence of the polymer content on the porosity and fluid mobility. Comparison with cryo-SEM-derived surface porosity reveals statistically significant differences and highlights the scale-dependent sensitivity of surface measurements compared to bulk measurements. This study introduces a new mechanical method for quantifying the free-water fraction in macroporous, ultrasoft, highly hydrated biomaterials. Furthermore, the multi-step protocols enable the separation of dissipative, fluid-related relaxation from the equilibrium response of the solid skeleton, allowing direct calibration of constitutive models for macroporous soft solids. The proposed method provides a reliable basis for the development and optimization of hydrogels for applications where fluid transport is critical, such as neural interfaces, bioelectronic platforms, and tissue-engineered constructs.

bioengineering↗

bioRxiv2025

Community Challenge towards Consensus on Characterization of Biological Tissue: C4Bios First Findings

This study investigates methodological variability across various expert laboratories worldwide, with regards to characterizing the mechanical properties of biological tissues. Two testing rounds were conducted on the specific use case of uniaxial tensile testing of porcine aorta. In the first round, 24 labs were invited to apply their established methods to assess inter-laboratory variability. This revealed significant methodological diversity and associated variability in the stress-stretch results, underscoring the necessity for a standardized approach. In the second round, a consensus protocol was collaboratively developed and adopted by 19 labs in an attempt to minimize variability. This involved standardized sample preparation and uniformity in testing protocol, including the use of a common cutting and thickness measurement tool. Despite protocol harmonization, significant variability persisted across labs, which could not be solely attributed to inherent biological differences in tissue samples. These results illustrate the challenges in unifying testing methods across different research settings, underlining the necessity for further refinement of testing practices. Enhancing consistency in biomechanical experiments is pivotal when comparing results across studies, as well as when using the resulting material properties for in silico simulations in medical research.

bioengineering↗

bioRxiv2025

Discovering dispersion: How robust is automated model discovery for human myocardial tissue?

Computational modeling has become an integral tool for understanding the interaction between structural organization and functional behavior in a wide range of biological tissues, including the human myocardium. Traditional constitutive models, and recent models generated by automated model discovery, are often based on the simplifying assumption of perfectly aligned fiber families. However, experimental evidence suggests that many fibrous tissues exhibit local dispersion, which can significantly influence their mechanical behavior. Here, we integrate the generalized structure tensor (GST) approach into automated material model discovery to represent fibers that are distributed with rotational symmetry around three mean orthogonal directions--fiber, sheet, and normal--by using probabilistic descriptions of the orientation. Using biaxial extension and triaxial shear data from human myocardium, we systematically vary the degree of directional dispersion and stress measurement noise to explore the robustness of the discovered models. Our findings reveal that small dispersion in the fiber direction and arbitrary dispersion in the sheet and normal directions improve the goodness of fit and enable recovery of a previously proposed four-term model in terms of the isotropic second invariant, two dispersed anisotropic invariants and one coupling invariant. Our approach demonstrates strong robustness and consistently identifies similar model terms, even in the presence of up to 7% random noise in the stress data. In summary, our study suggests that automated model discovery based on the powerful generalized structure tensors is robust to noise and captures microstructural uncertainty and heterogeneity in a physiologically meaningful way.

bioengineering↗

bioRxiv2024

Discovering uncertainty: Bayesian constitutive artificial neural networks

Understanding uncertainty is critical, especially when data are sparse and variations are large. Bayesian neural networks offer a powerful strategy to build predictable models from sparse data, and inherently quantify both, aleatoric uncertainties of the data and epistemic uncertainties of the model. Yet, classical Bayesian neural networks ignore the fundamental laws of physics, they are non-interpretable, and their parameters have no physical meaning. Here we integrate concepts of Bayesian learning and constitutive neural networks to discover interpretable models, parameters, and uncertainties that best explain soft matter systems. Instead of training an individual constitutive neural network and learning point values of the network weights, we train an ensemble of networks and learn probability distributions of the weights, along with their means, standard deviations, and credible intervals. We use variational Bayesian inference and adopt an efficient backpropagation-compatible algorithm that approximates the true probability distributions by simpler distributions and minimizes their divergence through variational learning. When trained on synthetic data, our Bayesian constitutive neural network successfully rediscovers the initial model, even in the presence of noise, and robustly discovers uncertainties, even from incomplete data. When trained on real data from healthy and aneurysmal human arteries, our network discovers a model with more stretch stiffening, more anisotropy, and more uncertainty for diseased than for healthy arteries. Our results demonstrate that Bayesian constitutive neural networks can successfully discriminate between healthy and diseased arteries, robustly discover interpretable models and parameters for both, and efficiently quantify uncertainties in model discovery. We anticipate our approach to generalize to other soft biomedical systems for which real-world data are rare and inter-personal variations are large. Ultimately, our calculated uncertainties will help enhance model robustness, promote personalized predictions, enable informed decision-making, and build confidence in automated model discovery and simulation. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

bioengineering↗

bioRxiv2024

Automated model discovery for human cardiac tissue: Discovering the best model and parameters

For more than half a century, scientists have developed mathematical models to understand the behavior of the human heart. Today, we have dozens of heart tissue models to choose from, but selecting the best model is limited to expert professionals, prone to user bias, and vulnerable to human error. Here we take the human out of the loop and automate the process of model discovery. Towards this goal, we establish a novel incompressible orthotropic constitutive neural network to simultaneously discover both, model and parameters, that best explain human cardiac tissue. Notably, our network features 32 individual terms, 8 isotropic and 24 anisotropic, and fully autonomously selects the best model, out of more than 4 billion possible combinations of terms. We demonstrate that we can successfully train the network with triaxial shear and biaxial extension tests and systematically sparsify the parameter vector with L1-regularization. Strikingly, we robustly discover a four-term model that features a quadratic term in the second invariant I2, and exponential quadratic terms in the fourth and eighth invariants I4f, I4n, and I8fs. Importantly, our discovered model is interpretable by design and has parameters with well-defined physical units. We show that it outperforms popular existing myocardium models and generalizes well, from homogeneous laboratory tests to heterogeneous whole heart simulations. This is made possible by a new universal material subroutine that directly takes the discovered network weights as input. Automating the process of model discovery has the potential to democratize cardiac modeling, broaden participation in scientific discovery, and accelerate the development of innovative treatments for cardiovascular disease. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

bioengineering↗

bioRxiv2023

Democratizing biomedical simulation through automated model discovery and a universal material subroutine

Personalized computational simulations have emerged as a vital tool to understand the biomechanical factors of a disease, predict disease progression, and design personalized intervention. Material modeling is critical for realistic biomedical simulations, and poor model selection can have life-threatening consequences for the patient. However, selecting the best model requires a profound domain knowledge and is limited to a few highly specialized experts in the field. Here we explore the feasibility of eliminating user involvement and automate the process of material modeling in finite element analyses. We leverage recent developments in constitutive neural networks, machine learning, and artificial intelligence to discover the best constitutive model from thousands of possible combinations of a few functional building blocks. We integrate all discoverable models into the finite element workflow by creating a universal material subroutine that contains more than 60,000 models, made up of 16 individual terms. We prototype this workflow using biaxial extension tests from healthy human arteries as input and stress and stretch profiles across the human aortic arch as output. Our results suggest that constitutive neural networks can robustly discover various flavors of arterial models from data, feed these models directly into a finite element simulation, and predict stress and strain profiles that compare favorably to the classical Holzapfel model. Replacing dozens of individual material subroutines by a single universal material subroutine-populated directly via automated model discovery-will make finite element simulations more user-friendly, more robust, and less vulnerable to human error. Democratizing finite element simulation by automating model selection could induce a paradigm shift in physics-based modeling, broaden access to simulation technologies, and empower individuals with varying levels of expertise and diverse backgrounds to actively participate in scientific discovery and push the boundaries of biomedical simulation.

bioengineering↗

bioRxiv2022

Automated model discovery for skin:Discovering the best model, data, and experiment

Choosing the best constitutive model and the right set of model parameters is at the heart of continuum mechanics. For decades, the gold standard in constitutive modeling has been to first select a model and then fit its parameters to data. However, the success of this approach is highly dependent on user experience and personal preference. Here we propose a new method that simultaneously and fully autonomously discovers the best model and parameters to explain experimental data. Mathematically, the model finding is translated into a complex non-convex optimization problem. We solve this problem by formulating it as a neural network, and leveraging the success, robustness, and stability of the optimization tools developed in classical neural network modeling. Instead of using a classical off-the-shelf neural network, we design a new family of Constitutive Artificial Neural Networks with activation functions that feature popular constitutive models and parameters that have a clear physical interpretation. Our new network inherently satisfies general kinematic, thermodynamic, and physical constraints and trains robustly, even with sparse data. We illustrate its potential for biaxial extension experiments on skin and demonstrate that the majority of network weights train to zero, while the small subset of non-zero weights defines the discovered model. Unlike classical network weights, these weights are physically interpretable and translate naturally into engineering parameters and microstructural features such as stiffness and fiber orientation. Our results suggest that Constitutive Artificial Neural Networks enable automated model, parameter, and experiment discovery and could initiate a paradigm shift in constitutive modeling, from user-defined to automated model selection and parameterization. Our source code, data, and examples are available at https://github.com/LivingMatterLab/CANN.

bioengineering↗

bioRxiv2019

Numerical simulation of the viral entry into a cell driven by the receptor diffusion

This study focuses on the receptor driven endocytosis typical of viral entry into a cell. A locally increased density of receptors at the time of contact between the cell and the virus is necessary in this case. The virus is considered as a substrate with fixed receptors on its surface, while the receptors of the host cell are free to move over its membrane, allowing a local change in their concentration. In the contact zone the membrane inflects and forms an envelope around the virus. The created vesicle imports its cargo into the cell. The described process is simulated by the diffusion equation accompanied by two boundary conditions. The first boundary condition states that the conservation of binders expressed as the local rate of change of density has to be equal to the negative of the local flux divergence. The second boundary condition represents the energy balance condition with contributions due to the binding of receptors, the free energy of the membrane, its curvature and the kinetic energy due to the motion of the front. The described moving boundary problem in terms of the binder density and the velocity of the adhesion front is well posed and relies on biomechanically motivated assumptions. The problem is numerically solved by using the finite difference method, and the illustrative examples have been chosen to show the influence of the mobility of the receptors and of their initial densities on the velocity of the process.\n\nSIGNIFICANCEThe receptor driven endocytosis represents one of the most important mechanisms for the viral entry into a cell. However, the high velocities and small characteristic length scale cause many difficulties during the experimental investigation of such a process. This calls upon the application of virtual computer simulations investigating the process parameters and identifying factors inhibiting or completely ceasing the viral entry into cells. The development of methods for the optimization of the cell immunity system is aimed to as the final goal.

cell biology↗