Comparison of Analytical and Finite Element Implementation of Exponential Constitutive Models for Valve Tissue Under Micropipette Aspiration

Abstract

Micropipette aspiration (MA) has been widely used to measure the biomechanical properties of cells and biomaterials [1]. Typically a linear elastic half-space model is used to fit the experimental load-deformation data [1]. However, load-deformation relationships for most biological tissues are highly nonlinear, suggesting alternative constitutive models are necessary. In the case of aortic heart valve tissue, exponential-type constitutive models have been found to fit the biaxial stress-strain behavior well [2]. Based on these studies, Butcher et al. used an exponential constitutive model to characterize the response of chicken embryonic valve (atrioventricular cushion) under MA [3]. To do so, they implemented an analytical exponential constitutive model [2] and directly related the stress and strain to the experimentally measured pressure and aspiration length. This allowed the authors to fit the tissue MA data without accounting for the complexities of the boundary conditions and multicomponent strain field inherent in MA. However, it is unclear whether the material parameters estimated using this approach are different from those estimated by solving the more complex boundary value problem, which presumably more faithfully simulates the physical process of tissue aspiration.