Bifurcation for a free-boundary problem modeling small plaques with reverse cholesterol transport

Abstract

In this paper, we rigorously analyze a free boundary model of plaque growth under the influence of reverse cholesterol transport (RCT). We will analyze a model with a highly nonlinear and mutually coupled PDE system of plaque growth dynamics, including LDL and HDL cholesterol, M1 inflammatory and M2 anti-inflammatory macrophages, and foam cells. This free boundary problem is associated with two different types of surfaces: a vascular surface with the boundary set to r=1 and the interface Γ(t) between the plaque and blood flow. For this model, the explicit stationary solutions are nonexistent due to the highly nonlinear nature of the problem. We shall first prove the existence and uniqueness of the radially symmetric stationary solution. Then, we shall combine parameters into a single bifurcation parameter μ, and establish the existence of a sequence μn, such that for each μn(n≥2), the symmetry-breaking stationary solutions bifurcate from the radially symmetric stationary solutions for sufficiently small plaques.