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The LDL-HDL profile determines the risk of atherosclerosis: a mathematical model
1Mathematical Biosciences Institute, The Ohio State University, Columbus, Ohio, United States of America.
Insights
This study models atherosclerosis plaque formation, linking blood cholesterol levels to risk. Mathematical simulations reveal how LDL and HDL concentrations dictate plaque growth or regression, creating a risk map.
Area of Science:
- Cardiovascular Biology
- Biomedical Engineering
- Mathematical Modeling
Background:
- Atherosclerosis, a leading cause of death, involves arterial plaque buildup.
- Plaque growth increases blood flow shear force, potentially causing rupture and heart attack.
- Cholesterol levels, specifically LDL and HDL, are known risk factors for plaque formation.
Purpose of the Study:
- To develop a mathematical model simulating atherosclerosis plaque formation.
- To investigate the influence of key biological variables on plaque development.
- To create a predictive risk map based on LDL and HDL concentrations.
Main Methods:
- Developed a system of partial differential equations to model plaque evolution.
- Incorporated variables including LDL, HDL, free radicals, oxidized LDL, MMP, TIMP, cytokines (MCP-1, IFN-γ, IL-12, PDGF), and cells (macrophages, foam cells, T cells, smooth muscle cells).
- Simulated the model to analyze plaque dynamics under varying conditions.
Main Results:
- Simulations demonstrate that the interplay between LDL and HDL concentrations determines plaque fate (growth or disappearance).
- A comprehensive risk map was generated, illustrating plaque development risk for various (LDL, HDL) pairs.
- The model successfully integrates multiple biological factors influencing atherosclerosis.
Conclusions:
- Blood cholesterol levels (LDL and HDL) are critical determinants of atherosclerosis progression.
- The developed mathematical model provides a valuable tool for understanding and predicting plaque development.
- This research offers insights into personalized risk assessment for cardiovascular disease.
Abstract:
Atherosclerosis, the leading death in the United State, is a disease in which a plaque builds up inside the arteries. As the plaque continues to grow, the shear force of the blood flow through the decreasing cross section of the lumen increases. This force may eventually cause rupture of the plaque, resulting in the formation of thrombus, and possibly heart attack. It has long been recognized that the formation of a plaque relates to the cholesterol concentration in the blood. For example, individuals with LDL above 190 mg/dL and HDL below 40 mg/dL are at high risk, while individuals with LDL below 100 mg/dL and HDL above 50 mg/dL are at no risk. In this paper, we developed a mathematical model of the formation of a plaque, which includes the following key variables: LDL and HDL, free radicals and oxidized LDL, MMP and TIMP, cytockines: MCP-1, IFN-γ, IL-12 and PDGF, and cells: macrophages, foam cells, T cells and smooth muscle cells. The model is given by a system of partial differential equations with in evolving plaque. Simulations of the model show how the combination of the concentrations of LDL and HDL in the blood determine whether a plaque will grow or disappear. More precisely, we create a map, showing the risk of plaque development for any pair of values (LDL,HDL).
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