A material modeling approach for the effective response of planar soft tissues for efficient computational simulations.

One of the most crucial aspects of biomechanical simulations of physiological systems that seek to predict the outcomes of disease, injury, and surgical interventions is the underlying soft tissue constitutive model. Soft tissue constitutive modeling approaches have become increasingly complex, often utilizing meso- and multi-scale methods for greater predictive capability and linking to the underlying biological mechanisms. However, such modeling approaches are associated with substantial computational costs. One solution is to use effective constitutive models in place of meso- and multi-scale models in numerical simulations but derive their responses by homogenizing the responses of the underlying meso- or multi-scale models. A robust effective constitutive model can thus drastically increase the speed of simulations for a wide range of meso- and multi-scale models. However, there is no consensus on how to develop a single effective constitutive model and optimal methods for parameter estimation for a wide range of soft tissue responses. In the present study, we developed an effective constitutive model which can fully reproduce the response of a wide range of planar soft tissues, along with a method for robust and fast-convergent parameter estimation. We then evaluated our approach and demonstrated its ability to handle materials of widely varying degrees of stiffness and anisotropy. Furthermore, we demonstrated the robutst performance of the meso-structural to effective constitutive model framework in finite element simulations of tri-leaflet heart valves. We conclude that the effective constitutive modeling approach has significant potential for improving the computational efficiency and numerical robustness of multi-scale and meso-scale models, facilitating efficient soft tissue simulations in such demanding applications as inverse modeling and growth.