Development of an MRI/FEA Framework for Analysis of Subject-Specific Aortic Compliance: Part II- Constitutive Law Development and Prediction of Heterogeneous vessel Composition and Deformation

Abstract

This paper, the second of two parts, presents a novel subject-specific in-silico framework in which we uncover the relationship between the spatially varying constituents of the aorta and the non-linear compliance of the vessel during the cardiac cycle uncovered in Part I. In Part II a novel microstructurally motivated constitutive model is developed, and simulations reveal that internal vessel contractility, due to pre-stretched elastin and actively generated smooth muscle stress, must be incorporated, along with collagen strain stiffening, in order to accurately predict the non-linear pressure-area relationship observed in-vivo. Modelling of elastin and smooth muscle contractility allows for the identification of the reference vessel configuration at zero-lumen pressure, in addition to accurately predicting high- and low-compliance regimes under a physiological range of pressures. This modelling approach is also shown to capture the key features of elastin and SMC knockout experiments. The volume fractions of the constituent components of the aortic material model were computed so that the in-silico pressure-area curves accurately predict the corresponding MRI data at each location. Simulations reveal that collagen and smooth muscle volume fractions increase distally, while elastin volume fraction decreases distally, consistent with reported histological data. Furthermore, the strain at which collagen transitions from low to high stiffness is lower in the abdominal aorta, again supporting the histological finding that collagen waviness is lower in this distally. The analyses presented in this paper provides new insights into the heterogeneous structure-function relationship that underlies aortic biomechanics. This novel subject-specific MRI/FEA methodology provides a foundation for personalised in-silico clinical analysis and tailored aortic device development.