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Published on: December 7, 2013
A Lipid-Structured Model of Atherosclerosis with Macrophage Proliferation
Keith L Chambers1,2, Michael G Watson1,3, Mary R Myerscough4
1School of Mathematics and Statistics, The University of Sydney, Sydney, NSW, 2006, Australia.
Insights
Macrophage proliferation in atherosclerotic plaques, modeled mathematically, helps reduce lipid content and redistributes fat among cells. This process differs from cell recruitment, impacting plaque development and stability.
Area of Science:
- Cardiovascular Biology
- Mathematical Biology
- Immunology
Background:
- Atherosclerotic plaques, characterized by fatty deposits, are a primary cause of heart attacks and strokes.
- Macrophages are key immune cells within plaques, influencing plaque growth and regression.
- Macrophage proliferation is crucial in mid-stage plaque development, yet is underrepresented in mathematical models.
Purpose of the Study:
- To mathematically model macrophage proliferation within atherosclerotic plaques.
- To reframe the Ford et al. lipid-structured model to incorporate proliferation dynamics.
- To analyze the impact of proliferation on plaque lipid content and macrophage lipid distribution.
Main Methods:
- Reframing a lipid-structured mathematical model to include macrophage proliferation.
- Modeling proliferation as a non-local decrease in the lipid structural variable.
- Performing steady-state analysis to evaluate model predictions.
Main Results:
- Macrophage proliferation aids in lowering the eventual lipid content of necrotic cores.
- Proliferation distributes the lipid load more evenly among plaque macrophages.
- Proliferative plaques show different lipid distribution patterns compared to recruitment-dominant plaques, with less skewing and a peak near endogenous lipid content.
Conclusions:
- Macrophage proliferation is a significant factor in atherosclerotic plaque development, influencing lipid accumulation and distribution.
- Mathematical modeling provides insights into the distinct roles of proliferation versus recruitment in macrophage dynamics within plaques.
- Understanding these dynamics can inform strategies for managing atherosclerosis and its complications.
Abstract:
Atherosclerotic plaques are fatty deposits that form in the walls of major arteries and are one of the major causes of heart attacks and strokes. Macrophages are the main immune cells in plaques and macrophage dynamics influence whether plaques grow or regress. Macrophage proliferation is a key process in atherosclerosis, particularly in the development of mid-stage plaques, but very few mathematical models include proliferation. In this paper we reframe the lipid-structured model of Ford et al. (J Theor Biol 479:48-63, 2019. https://doi.org/10.1016/j.jtbi.2019.07.003 ) to account for macrophage proliferation. Proliferation is modelled as a non-local decrease in the lipid structural variable. Steady state analysis indicates that proliferation assists in reducing eventual necrotic core lipid content and spreads the lipid load of the macrophage population amongst the cells. The contribution of plaque macrophages from proliferation relative to recruitment from the bloodstream is also examined. The model suggests that a more proliferative plaque differs from an equivalent (defined as having the same lipid content and cell numbers) recruitment-dominant plaque in the way lipid is distributed amongst the macrophages. The macrophage lipid distribution of an equivalent proliferation-dominant plaque is less skewed and exhibits a local maximum near the endogenous lipid content.
