Abstract
In this paper, we investigate the progression of Ascending Thoracic Aortic Aneurysms (ATAA) using a computational model of Growth and Remodeling (G&R) taking into account the composite (elastin, four collagen fiber families and Smooth Muscle Cells—SMCs) and multi-layered (media and adventitia) nature of the aorta. The G&R model, which is based on the homogenized Constrained Mixture theory, is implemented as a UMAT in the Abaqus finite-element package. Each component of the mixture is assigned a strain energy density function: nearly-incompressible neo-Hookean for elastin and Fung-type for collagen and SMCs. Active SMCs tension is additionally considered, through a length-tension relationship having a classic inverted parabola shape, in order to investigate its effects on the progression of ATAA in a patient-specific model. A sensitivity analysis is performed to evaluate the potential impact of variations in the parameters of the length-tension relationships. These variations reflect in variations of SMCs normal tone during ATAA progression, with active stress contributions ranging between 30% (best case scenario) and 0% (worst case scenario) of the total wall circumferential stress. Low SMCs active stress in the worst case scenarios, in fact, affect the rates of collagen deposition by which the elastin loss is gradually compensated by collagen deposition in the simulated ATAA progression, resulting eventually in larger aneurysm diameters. The types of length-tension relationships leading to a drop of SMCs active stress in our simulations reveal a critical condition which could also result in SMCs apoptosis.
Highlights
Nowadays, the paramount importance of mechanobiology is widely acknowledged in morphogenesis and pathogenesis (Humphrey, 2008)
In order to quantify the contribution of Smooth Muscle Cells (SMCs) active tone in the stress distribution field, two ratios were considered, namely (1) the ratio of the SMCs active stress with respect to the SMCs stresses (Rm); and (2) the ratio between the SMCs active stress and the total stress field (Rt)
These ratios are shown in percentage depending on the maximum SMCs active stretches for different rates of collagen deposition (Figure 2) and damage times (Figure 3) due to elastin degradation
Summary
The paramount importance of mechanobiology is widely acknowledged in morphogenesis and pathogenesis (Humphrey, 2008). Valentín et al (2013) established a non-linear model using the Finite Element Method (FEM) on the basis of the Constrained Mixture Theory (CMT) aimed at facilitating numerical analyses of arterial adaptation and maladaptation. They could predict changes in fiber orientations and quantities, degradation of elastin and loss of Smooth Muscle Cells (SMCs), including disease progression and evolving geometries. Lin et al (2017) combined homogenization and the CMT to simulate the dilatation of abdominal aortic aneurysms Their methodology could capture important aspects, such as mass turnover in arterial walls with a low computational cost. Latorre and Humphrey (2018a) introduced a new rate-based CMM formulation suitable for studying mechanobiological equilibrium and stability of soft tissues exposed to transient or sustained changes, permitting direct resolution of G&R problems with a quasi-static approach
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