Reconstructing vascular homeostasis by growth-based prestretch and optimal fiber deposition

Abstract

Computational modeling of cardiovascular biomechanics should generally start from a homeostatic state. This is particularly relevant for image-based modeling, where the reference configuration is the loaded in vivo state obtained from imaging. This state includes residual stress of the vascular constituents, as well as anisotropy from the spatially varying orientation of collagen and smooth muscle fibers. Estimation of the residual stress and fiber orientation fields is a formidable challenge in realistic applications. To help address this challenge, we herein develop a growth based Algorithm to recover a residual stress distribution in vascular domains such that the stress state in the loaded configuration is equal to a prescribed homeostatic stress distribution at physiologic pressure. A stress-driven fiber deposition process is included in the framework, which defines the distribution of the fiber alignments in the vascular homeostatic state based on a minimization procedure. Numerical simulations are conducted to test this two-stage homeostasis generation algorithm in both idealized and non-idealized geometries, yielding results that agree favorably with prior numerical and experimental data.

Keywords: Constrained mixture; Image-based modeling; Residual stress; Vascular tissue mechanics.