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Bifurcation and dynamics in a mathematical model of early atherosclerosis

How acute inflammation drives lesion development

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Abstract

We present here a mathematical model describing the primary mechanisms that drive the early stages of atherosclerosis. This involves the interactions between modified low density lipoprotein (LDL), monocytes/macrophages, cytokines and foam cells. This model suggests that there is an initial inflammatory phase associated with atherosclerotic lesion development and a longer, quasi-static process of plaque development inside the arterial wall that follows the initial transient. We will show results that show how different LDL concentrations in the blood stream and different immune responses can affect the development of a plaque. Through numerical bifurcation analysis, we show the existence of a fold bifurcation when the flux of LDL from the blood is sufficiently high. By analysing the model presented in this paper, we gain a greater insight into this inflammatory response qualitatively and quantitatively.

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Authors and Affiliations

  1. The University of Sydney, Camperdown, NSW, 2006, Australia

    Alexander D. Chalmers, Anna Cohen & Mary R. Myerscough

  2. Heart Research Institute, 7 Eliza Street, Newtown, NSW, 2042, Australia

    Christina A. Bursill

Authors
  1. Alexander D. Chalmers
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  2. Anna Cohen
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  3. Christina A. Bursill
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  4. Mary R. Myerscough
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Correspondence to Alexander D. Chalmers.

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Chalmers, A.D., Cohen, A., Bursill, C.A. et al. Bifurcation and dynamics in a mathematical model of early atherosclerosis. J. Math. Biol. 71, 1451–1480 (2015). https://doi.org/10.1007/s00285-015-0864-5

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  • DOI: https://doi.org/10.1007/s00285-015-0864-5

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