Mathematical models for vulnerable plaques

Abstract

A plaque is an accumulation and swelling in the artery walls and typically consists of cells, cell debris, lipids, calcium deposits and fibrous connective tissue. A person is likely to have many plaques inside his/her body even if they are healthy. However plaques may become "vulnerable", "high-risk" or "thrombosis-prone" if the person engages in a high-fat diet and does not exercise regularly.

In this study group, we proposed two mathematical models to describe plaque growth and rupture.
The first model is a mechanical one that approximately treats the plaque as an inflating elastic balloon. In this model, the pressure inside the core increases and then decreases suggesting that plaque stabilization and prevention of rupture is possible.
The second model is a biochemical one that focuses on the role of MMPs in degrading the fibrous plaque cap. The cap stress, MMP concentration, plaque volume and cap thickness are coupled together in a system of phenomenological equations. The equations always predict an eventual rupture since the volume, stresses and MMP concentrations generally grow without bound. The main weakness of the model is that many of the important parameters that control the behavior of the plaque are unknown.

The two simple models suggested by this group could serve as a springboard for more realistic theoretical studies. But most importantly, we hope they will motivate more experimental work to quantify some of the important mechanical and biochemical properties of vulnerable plaques.