Stability analysis of a model of atherogenesis: An energy estimate approach

A. I. Ibragimov, C. J. McNeal, L. R. Ritter, J. R. Walton

Research output: Contribution to journalArticlepeer-review

5 Scopus citations

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.

Original languageEnglish
Pages (from-to)121-142
Number of pages22
JournalComputational and Mathematical Methods in Medicine
Volume9
Issue number2
DOIs
StatePublished - Jun 2008

Keywords

  • Atherogenesis
  • Atherosclerosis
  • Chemotaxis
  • Energy estimate
  • Stability analysis

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