Microstructure-Based Constitutive Models for Coronary Artery Adventitia

Abstract

A structure-based constitutive model can accurately predict mechanical behaviors of blood vessels and enables a better understanding vascular patho-physiology. Most microstructural models assume affine deformation, i.e., fiber constituent deforms as the same as the tissue, and employ idealized microstructure due to the limited morphological data on vessel constituents. The goal of this chapter is to (1) introduce a new microstructural mechanical model that removes the affine deformation assumption and (2) to obtain quantitative microstructural data of coronary arteries. We develop a micromechanics-based constitutive model of fibrous tissue to take into consideration non-affine deformation that intrinsically induced by heterogeneous interactions between the constituents. Elastin fibers, cells, and ground substance are collectively considered as a solid-like matrix while collagen fibers is a reinforced phase. The model accounts for the waviness, orientation and spatial distributions of collagen fibers and provides a good prediction of macroscopic responses of the tissue which agree well with the finite element simulation results as a golden standard. We then use multiphoton microscopy to quantify the geometrical features of elastin and collagen fibers under mechanical loads. Simultaneous loading-imaging of the coronary adventitia allows measurements of the morphometry and in situ deformation of individual fibers. The population of fibers geometrical parameters including orientation angle, waviness, width and area fraction were measured at no-load state and the mechanical loading--deformation relation of fiber geometrical parameter were obtained as well. The present model and experimental studies are seminal for structural models and will lead to a better understanding of vascular biomechanics.