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.

旨在预测疾病，损伤和手术干预结果的生理系统生物力学模拟的最关键方面之一是基本的软组织本构模型。软组织本构模型方法变得越来越复杂，通常使用中尺度和多尺度方法来提高预测能力并将其链接到潜在的生物学机制。然而，这样的建模方法与大量的计算成本相关联。一种解决方案是在数值模拟中使用有效的本构模型代替中尺度和多尺度模型，但通过均化基础的中尺度或多尺度模型的响应来得出它们的响应。因此，健壮的有效本构模型可以极大地提高各种中尺度和多尺度模型的仿真速度。但是，关于如何为各种软组织反应开发单一有效的本构模型和参数估计的最佳方法尚无共识。在本研究中，我们开发了一种有效的本构模型，可以充分再现各种平面软组织的响应，并提供了一种健壮且快速收敛的参数估计方法。然后，我们评估了我们的方法，并证明了其处理刚度和各向异性程度各异的材料的能力。此外，我们在三叶式心脏瓣膜的有限元模拟中证明了从细观结构到有效本构模型框架的最鲁棒的性能。