A bio-lattice deep learning framework for modeling discrete biological materials

Biological tissues dynamically adapt their mechanical properties at the microscale in response to stimuli, often governed by discrete interacting mechanisms that dictate the material's behavior at the macroscopic scale. An approach to model the discrete nature of these elemental units is the Lattice Spring Modeling (LSM). However, the interactions in biological matter can present a high degree of complexity and heterogeneity at the macroscale, posing a computational challenge in multiscale modeling. In this work, we propose a novel machine learning-based multiscale framework that integrates deep neural networks (DNNs), the finite element method (FEM), and a LSM-inspired microstructure description to investigate the behavior of discrete, spatially heterogeneous materials. We develop a versatile, assumption-free lattice framework for interacting discrete units, and derive a consistent multiscale connection with our FEM implementation. A single DNN is trained to learn the constitutive equations of various particle configurations and boundary conditions, enabling rapid response predictions of heterogeneous biological tissues. We demonstrate the effectiveness of our approach with extensive testing, starting with benchmark cases and progressively increasing the complexity of the microstructures. We explored materials ranging from soft to hard inclusions, then combined them to form a macroscopically homogeneous material, a gradient-varying polycrystalline solid, and fully randomized configurations. Our results show that the model accurately captures the material response across these spatially varying structures.