A data‐driven constitutive model for soft biological tissues

Abstract

AbstractConstitutive modeling of soft biological tissues is crucial for biomedical simulations and a deep understanding of tissue mechanics. Classical constitutive models have a fixed mathematical expression, however, the microstructure and the corresponding macro‐mechanical response of different tissue types can vary significantly. A model that works for one tissue may not work for another kind of tissue, and choosing the right model may become challenging. To solve this issue, this study introduces a new data‐driven approach to creating a unified model for predicting the mechanical response of various tissue classes. The proposed model is based on B‐Spline approximations and assumes the strain energy function can be divided into volumetric, isotropic, and anisotropic components. The B‐Spline ansatz replaces partial derivatives of free energy energy function with respect to invariants with control points and polynomial degree, and allows the use of existing dispersion models. The model adapts its control point values to reduce the error between data and prediction until a threshold is reached, and is thermodynamically consistent through the use of optimization constraints. The model is demonstrated on various biological tissues, showing excellent fitting capabilities with a minimal number of control points. The outcome is a generic framework that can model any tissue given the data from experiments and imaging techniques.