Computational and Mathematical Methods in Medicine
Volume 9 (2008), Issue 2, Pages 121-142
doi:10.1080/17486700701865554
Original Article
Stability Analysis of a Model of Atherogenesis: An Energy Estimate Approach
1Department of Mathematics, Texas Tech University, Lubbock, TX, USA
2Division of Cardiology and Department of Pediatrics, Division of Endocrinology, Department of Internal Medicine, Scott and White, Temple, TX, USA
3Department of Mathematics, Southern Polytechnic State University, Marietta, GA, USA
4Department of Mathematics, Texas A & M University, College Station, TX, USA
Received 29 August 2007; Accepted 12 December 2007
Copyright © 2008 Hindawi Publishing Corporation. This is an open access article distributed under the
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Abstract
Atherosclerosis is a disease of the vasculature that is characterized by chronic inflammation and the accumulation of lipids and apoptotic cells in the walls of large arteries. This disease results in plaque growth in an infected artery typically leading to occlusion of the artery. Atherosclerosis is the leading cause of human mortality in the US, much of Europe, and parts of Asia. In a previous work, we introduced a mathematical model of the biochemical aspects of the disease, in particular the inflammatory response of macrophages in the presence of chemoattractants and modified low density lipoproteins. Herein, we consider the onset of a lesion as resulting from an instability in an equilibrium configuration of cells and chemical species. We derive an appropriate norm by taking an energy estimate approach and present stability criteria. A bio-physical analysis of the mathematical results is presented.