Understanding the Parameter Influence on Lesion Growth for a Mechanobiology Model of Atherosclerosis

Abstract

In this work, we analyse the influence of the parameters of a mathematical model, previously proposed by the authors, for reproducing atheroma plaque in arteries. The model uses Navier–Stokes equations to calculate the blood flow along the lumen in a transient mode. It also uses Darcy’s law, Kedem–Katchalsky equations, and the three-pore model to simulate plasma and substance flows across the endothelium. The behaviours of all substances in the arterial wall are modelled with convection–diffusion–reaction equations, and finally, plaque growth is calculated. We consider a 2D geometry of a carotid artery, but the model can be extrapolated to other geometries or arteries, such as the coronaries or the aorta. A mono-variant sensitivity analysis of the model parameters was performed, with values of ±25% and ±10%, with respect to the values of the previous model. The results were analysed with respect to the volume in the plaque of foam cells (FC), synthetic smooth muscle cells (SSMC), and collagen fibre. It was observed that the volume in the plaque of the different substances (FC, SSMC, and collagen) has a strong influence on the results, so it could be used to analyse the vulnerability of plaque. The stenosis ratio of the plaque was also analysed, showing a strong influence on the results as well. Parameters that influence all the results considered when ranged ±10% are the rate of LDL degradation and the diffusion coefficients of LDL and monocytes in the arterial wall. Furthermore, it was observed that the change in the volume of foam cells in the plaque has a greater influence on the stenosis ratio than the change of synthetic smooth muscle cells or collagen fibre.

Integrating Computational and Biological Hemodynamic Approaches to Improve Modeling of Atherosclerotic Arteries

“…[89] Different processes within the atherogenesis inflammatory response can be modeled, such as LDL oxidation, [123] monocyte chemoattractant protein-1 secretion, [124] monocyte recruitment, [125] monocyte to macrophage differentiation, [126] foam cell formation and accumulation, [127] T-cell recruitment and the role of interferon-𝛾, [127] the proliferation of SMCs, [125] and collagen formation. [128] Ordinary differential equations or partial differential equations of these processes are typically used to simulate plaque growth and can be used to predict plaque rupture events using 2D [129] or 3D geometry. [130] To demonstrate this, a study utilized one-way FSI to model atherosclerotic growth, which incorporated vessel wall thickening, lipoprotein transport through the arterial wall, and inflammation modeling via ordinary differential equations and diffusion and convection equations to evaluate endothelial shear stress throughout the geometry.…”