An Inverse Optimization Approach Toward Testing Different Hypotheses of Vascular Homeostasis Using Image-based Models

Abstract

Vascular mechanical homeostasis is a fundamental assumption in modeling vascular growth and remodeling. Meanwhile, it is a matter of debate, which mechanical quantity is responsible for governing the vascular growth and remodeling process. Recently, an optimization method has been proposed to estimate the optimal distributions of arterial wall thickness and anisotropy, such that a homeostatic condition is satisfied. In this study, the same optimization technique is utilized to investigate variations in the distribution of wall thickness and anisotropy due to different homeostatic assumptions, while two geometric models, one from a healthy aorta and one from a healthy internal iliac artery, are independently used. Prior to optimization, material constitutive parameters are estimated by fitting biaxial mechanical test data from human aorta and prescribed into the optimization process. Objective functions are set to restore both the original arterial geometry and the homeostatic state based on either intramural stress or cyclic circumferential stretch. Different homeostatic assumptions lead to distinct results for the optimal distributions of wall thickness and anisotropy. Namely, the cyclic stretch homeostatic assumption yields lower levels of the wall thickness as well as a less longitudinal variation of anisotropy. However, the arterial wall is consistently found to be thicker on the concave regions rather than on the convex regions. With further improvements in the application of the boundary conditions, the presented computational method seems promising to enhance our understanding of the vascular mechanical homeostasis and shall serve as a basis for conducting validation experiments.