Stability of periodic solution for a free boundary problem modeling small plaques

Area of Science:

• Cardiovascular disease modeling
• Mathematical biology
• Biomedical engineering

Background:

• Existing plaque growth models often assume constant nutrient supply, which is unrealistic.
• Arterial plaque formation involves complex interactions between low-density lipoprotein (LDL) and high-density lipoprotein (HDL).
• Previous models primarily used 2D cross-sections, with recent extensions to 3D plaque dynamics.

Purpose of the Study:

• To perform linear stability analysis on a previously identified periodic solution for arterial plaque growth.
• To investigate the impact of periodic nutrient supply (LDL and HDL) on plaque dynamics.
• To validate analytical findings with simulation results.

Main Methods:

• Linear stability analysis of a periodic solution derived from a mathematical model of arterial plaque.
• Numerical simulations to confirm the stability and behavior of the periodic solution under varying conditions.
• Modeling plaque growth using 2D cross-section approximations of blood vessels.

Main Results:

• The periodic solution, representing oscillating plaque growth and shrinkage, was found to be stable under specific conditions of periodic nutrient supply.
• Simulations demonstrated that fluctuations in LDL and HDL concentrations, when periodic, can indeed lead to sustained, non-constant plaque behavior.
• The stability analysis provides crucial insights into the conditions under which plaque size may fluctuate rather than continuously grow or shrink.

Conclusions:

• Periodic variations in cholesterol supply can result in stable, oscillating plaque growth, a significant departure from constant-supply models.
• This research enhances our understanding of arterial plaque dynamics by incorporating realistic, periodic nutrient fluctuations.
• The findings have implications for developing more accurate predictive models of atherosclerosis and potential therapeutic strategies.