A Novel Approach to Account for Non-Affine Fiber Kinematics in Structural Continuum Models for Heart Valves Leaflets

In the ongoing development of continuum models for soft tissues and related biological materials, structural approaches continue to have much appeal, and have the focus of our laboratory’s work (1). Structural constitutive models integrate information on tissue composition and structure, avoiding ambiguities in material characterization. However, critical structural information (such as fiber orientation) must be modeled using assumed statistical distributions, with the distribution parameters estimated from fits to the mechanical test data. Thus, full realization of structural approaches continues to be limited without direct quantitative structural information for direct implementation or to validate model predictions. While we have addressed these issues (2), non-affine fiber kinematics have been known to occur in heart valve leaflet tissues, especially under more extreme deformations (3, 4). However, current structural model theories continue to rely on the assumption of affine fiber kinematics. In present work we present a theoretical framework that accounts for non-affine deformations that still allows for the basic framework of the current structural models to be utilized.