Long time evolution of atherosclerotic plaques

Area of Science:

• Cardiovascular science
• Mathematical modeling
• Biophysics

Background:

• Atherosclerosis plaque evolution is complex and not fully understood.
• Wall shear stress (WSS) plays a critical role in atherosclerotic plaque progression.
• Existing models often simplify the interplay between plaque growth and blood flow dynamics.

Purpose of the Study:

• To develop a qualitative mathematical model of atherosclerosis plaque growth.
• To investigate the influence of wall shear stress on plaque evolution.
• To analyze the impact of LDL cholesterol levels on plaque progression and lumen diameter.

Main Methods:

• Formulated a qualitative mathematical model using ordinary differential equations.
• Simulated plaque constituents' concentrations under varying conditions.
• Compared two models: Model A (WSS as a parameter) and Model B (WSS coupled to blood flow).

Main Results:

• Both models demonstrated marginally stable equilibria where plaques grow transiently.
• Model A exhibited bi-stability: transient growth or unlimited growth above an LDL cholesterol threshold.
• Model B eliminated bi-stability but showed critical LDL levels causing drastic lumen reduction, sensitive to WSS.

Conclusions:

• Mathematical modeling provides insights into atherosclerosis dynamics.
• Wall shear stress is a crucial factor modulating plaque growth and lumen patency.
• High LDL cholesterol intake poses a significant risk for rapid lumen narrowing in atherosclerosis.