A free boundary mathematical model of atherosclerosis

Abstract

This paper is devoted to the study of a mathematical model of atherosclerosis in one-dimensional geometry with a free boundary. The motion of the boundary is attributable to the concentration of cells in the intima and their interaction in the subendothelial space in addition to their influx through the boundary. A mathematical model that describes the main inflammatory processes in atherosclerosis is proposed, then, by considering some simplifications, a reduced model is obtained. Using a change of variables, the reduced model is converted to a fixed boundary model with space- and time-dependent coefficients and nonlinear terms. We study the existence of solution for the fixed boundary model starting with a model with linear terms then by applying the fixed point theorem. The wave solution is as well investigated along with numerical simulations. Then, we return to the reduced model, prove the existence of solution and present numerical results. Finally, we generalize the results to the complete model initially proposed.

Keywords:

• Atherosclerosis
• mathematical modeling
• reaction–diffusion equations
• free boundary problem

Maths:

• 35K57
• 35R35
• 35Q92

Disclosure statement

No potential conflict of interest was reported by the author(s).