Incorporation of regional mechanical heterogeneity into finite-element simulations of soft biological tissues

This study is focused on a critical blind spot in the soft tissue biomechanics field-spatial mechanical heterogeneity. Despite abundant experimental evidence indicating that soft biological tissues exhibit regional heterogeneity, particularly in their mechanical properties, incorporation of this heterogeneity into material descriptions of finite-element models has been limited. In this work, gradual spatial variation of mechanical properties is modeled by adopting principles of the theory of functionally graded materials. Using regional biaxial data and the Holzapfel-Gasser-Ogden constitutive model, this paper demonstrates a method to average the mechanical response from tested regions to estimate the response of untested intermediate tissue regions and the use of Fourier functions to capture continuous spatial variations of material parameters. This spatial material parameter dependency was then implemented in a finite-element model's material description using the USDFLD subroutine in Abaqus (2022). This model is referred to as the continuous heterogeneous model and was compared with two other approaches that are used to account for spatial mechanical heterogeneity in soft biological tissues: 1) the homogeneous model that utilizes the averaged mechanical response from all tested specimens, and 2) the segmental heterogeneous model that employs distinct material descriptions for geometrically divided segments of the tissue model. All three approaches to modeling were demonstrated using two biomechanically relevant idealized geometries and boundary conditions: the human ascending aortic aneurysm simulated by a thin-walled cylinder and the back skin simulated by a planar strip. Results demonstrate that implementing spatial heterogeneity markedly affects the stress/displacement fields compared to the homogeneous model. Moreover, between the segmental and continuous heterogeneous approaches, the latter offers advantages such as mitigating stress discontinuities due to abrupt property changes. These findings highlight the impact of accounting for spatial mechanical heterogeneity in finite-element modeling of soft biological tissues and provide a foundation for future research exploring the improved material description in computational models and simulations of soft tissue biomechanics.