Bulletin of Mathematical Biology

, Volume 76, Issue 5, pp 1117–1142

Athero-protective Effects of High Density Lipoproteins (HDL): An ODE Model of the Early Stages of Atherosclerosis


  • Anna Cohen
    • School of Mathematics and StatisticsUniversity of Sydney
    • School of Mathematics and StatisticsUniversity of Sydney
  • Rosemary S. Thompson
    • School of Mathematics and StatisticsUniversity of Sydney
Original Article

DOI: 10.1007/s11538-014-9948-4

Cite this article as:
Cohen, A., Myerscough, M.R. & Thompson, R.S. Bull Math Biol (2014) 76: 1117. doi:10.1007/s11538-014-9948-4


We present an ODE model which we use to investigate how High Density Lipoproteins (HDL) reduce the inflammatory response in atherosclerosis. HDL causes atherosclerotic plaque stabilisation and regression, and is an important potential marker and prevention target for cardiovascular disease. HDL enables cholesterol efflux from the arterial wall, macrophage and foam cell emigration, and has other athero-protective effects. Our basic inflammatory model is augmented to include several different ways that HDL can act in early atherosclerosis. In each case, the action of HDL is represented via a parameter in the model. The long-term model behaviour is investigated through phase plane analysis and simulations. Our results indicate that only HDL-enabled cholesterol efflux can stabilise the internalised lipid content in the lesion so that it does not continue to grow, but this does not reduce macrophage numbers which is required to stabilise the lesion or prevent rupture. HDL-enabled macrophage emigration guarantees lesion stabilisation by maintaining stable macrophage content.


Cardiovascular diseaseDynamical systems

Copyright information

© Society for Mathematical Biology 2014