A phenomenological model for atherosclerotic plaque growth and rupture

The objective of this communication is to develop a computer-based framework for the overall coupled phenomena leading to growth and rupture of atherosclerotic plaques. The modeling is purposely simplified to expose the dominant phenomenological controlling mechanisms, and their coupled interaction. The main ingredients of the present simplified modeling approach, describing the events that occur due to the presence and oxidation of excess low-density lipoprotein (LDL) in the intima, are: (i) adhesion of monocytes to the endothelial surface, which is controlled by the intensity of the blood flow and the adhesion molecules stimulated by the excess LDL, (ii) penetration of the monocytes into the intima and subsequent inflammation of the tissue, and (iii) rupture of the plaque accompanied with some degree of thrombus formation or even subsequent occlusive thrombosis. The set of resulting coupled equations, each modeling entirely different physical events, is solved using an iterative staggering scheme, which allows the equations to be solved in a computationally convenient decoupled fashion. Theoretical convergence properties of the scheme are given as a function of physical parameters involved. A numerical example is given to illustrate the modeling approach and an a priori prediction for time to rupture as a function of arterial geometry, diameter of the monocyte, adhesion stress, bulk modulus of the ruptured wall material, blood viscosity, flow rate and mass density of the monocytes.