Mathematical modeling of intraplaque neovascularization and hemorrhage in a carotid atherosclerotic plaque

Abstract

Background: Growing experimental evidence has identified neovascularization from the adventitial vasa vasorum and induced intraplaque hemorrhage (IPH) as critical indicators during the development of vulnerable atherosclerotic plaques. In this study, we propose a mathematical model incorporating intraplaque angiogenesis and hemodynamic calculation of the microcirculation, to obtain the quantitative evaluation of the influences of intraplaque neovascularization and hemorrhage on vulnerable plaque development. A two-dimensional nine-point model of angiogenic microvasculature is generated based on the histology of a patient’s carotid plaque. The intraplaque angiogenesis model includes three key cells (endothelial cells, smooth muscle cells, and macrophages) and three key chemical factors (vascular endothelial growth factors, extracellular matrix, and matrix metalloproteinase), which densities and concentrations are described by a series of reaction–diffusion equations. The hemodynamic calculation by coupling the intravascular blood flow, the extravascular plasma flow, and the transvascular transport is carried out on the generated angiogenic microvessel network. We then define the IPH area by using the plasma concentration in the interstitial tissue, as well as the extravascular transport across the capillary wall. Results: The simulational results reproduce a series of pathophysiological phenomena during the atherosclerotic plaque progression. It is found that the high microvessel density region at the shoulder areas and the extravascular flow across the leaky wall of the neovasculature contribute to the IPH observed widely in vulnerable plaques. The simulational results are validated by both the in vivo MR imaging data and in vitro experimental observations and show significant consistency in quantity ground. Moreover, the sensitivity analysis of model parameters reveals that the IPH area and extent can be reduced significantly by decreasing the MVD and the wall permeability of the neovasculature. Conclusions: The current quantitative model could help us to better understand the roles of microvascular and intraplaque hemorrhage during the carotid plaque progression.