Geometric Interpretability of Hyperelastic Models Fitted to Tissue Biomechanical Data

Abstract

This work reveals the geometric interpretability of hyperelastic constitutive models fitted to mechanics data of biological tissue, addressing the long-overlooked prediction reliability issue arising from dual constraints of model limitations (structural complexity and physical idealization) and data challenges (finiteness and uncertainty). We evaluate three representative models—the eight-chain model, the Ogden model, and the neural network-derived gray matter model—under Bayesian model calibration, which naturally extends from the inherent uncertainties in biological tissue mechanical response data. By combining diverse mechanics datasets and priors with varying levels of informativeness, we analyze how data and prior constraints influence sloppiness. Posterior samples of model parameters are used to derive the sensitivity matrix of the cost function, uncovering the local geometric features of the cost landscape. Our results demonstrate the pervasive sloppiness in multi-parameter hyperelastic constitutive models, which can only be mitigated by high-quality data and informative priors. Beyond defining robust sloppiness metrics, this work provides actionable insights, such as guiding model selection and offering geometric constraints in machine learning-based automated model discovery.