Topology-aware Constitutive Models for Extracellular Fiber Network Mechanics
Please login to view abstract download link
Relying on intuitive understanding, data availability, and fixed physical assumptions, traditional constitutive models often fall short in accurately predicting the non-affine behaviors of materials with fibrous microstructures, such as the extracellular space surrounding cells in soft tissues [1]. Instead of using histology-derived strain energy functions, FE2 homogenization computes the macroscopic stress by volume-averaging the mesoscale stress obtained by solving the mechanical equilibrium on discrete microstructures reconstructed from high-resolution images [2]. This approach offers greater fidelity but at a high computational cost [3]. Data-driven modeling is promising, yet standard neural networks (NNs) overlook material theory and require large datasets. Physics-informed and constitutive artificial NNs embed physical laws via the loss function and the architecture, respectively [4, 3]. However, most remain histology-inspired with limited access to microstructural features. HyperCANs advance this direction by devising a methodology to account for microstructural variability within lattice-based metamaterials [5]. In this work, we explore what HyperCANs [5] bring to the table to model the non-affine mechanics of extracellular fiber networks. Using meta-learning, we develop a microstructure-informed constitutive model for biological tissue, trained on the responses of our topology-based representative volume elements [1]. The hypernetwork receives as input the structural descriptors and dynamically generates the parameters of a thermodynamically consistent target network that maps strain to stress. By conditioning the tissue response on the microstructure, the proposed model offers a promising framework for advancing the field of tissue biomechanics and mechanobiology. [1] Cardona S., Peirlinck M., Fereidoonnezhad B., J. Mech. Phys. Solids 205 (2025). [2] Stylianopoulos T., Barocas V.H., Comput. Methods Appl. Mech. Eng. 196:2981–2990 (2007). [3] Linka K., Hillgärtner M., Abdolazizi K.P., Aydin R.C., Itskov M., Cyron C.J., J. Comput. Phys. 429:110010 (2021). [4] Liu M., Liang L., Sun W., Comput. Methods Appl. Mech. Eng. 372:113402 (2020). [5] Zheng L., Kochmann D.M., Kumar S., Extreme Mech. Lett. 72:102243 (2024).
