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Studies on Atherosclerotic Plaque Formation: A Mathematical Approach

  • Debasmita MukherjeeEmail author
  • Lakshmi Narayan Guin
  • Santabrata Chakravarty
Conference paper
  • 38 Downloads
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 302)

Abstract

Atherosclerosis is one of the main causes behind several cardiovascular diseases (CVDs). It occurs due to plaque accumulation in the innermost layer of artery, known as intima. The present study deals with a qualitative mathematical model consisting of a system of ten nonlinear ordinary differential equations (ODEs) involving ten important interacting cellular components coming into play namely, low density lipoprotein, free radicals, chemoattractants, monocytes, macrophages, T-cells, smooth muscle cells, foam cells and collagen in order to describe the evolution of atherosclerotic plaque. Numerical results obtained for this model are shown through several plots represented by phase portraits of some subsystems. As the present model is encountered with various important cellular components involving atherosclerosis, so it is believed to provide a platform for in silico treatment of this pernicious disease.

Keywords

Atherosclerosis Non-linear ODE system Routh-Hurwitz criterion 

Notes

Acknowledgements

This paper was presented in ICMAAM-2018. The authors gratefully acknowledge the financial support by Special Assistance Programme (SAP-III) sponsored by the University Grants Commission (UGC), New Delhi, India [Grants no. F.510/3/DRS-III/2015(SAP-I)].

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Copyright information

© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  • Debasmita Mukherjee
    • 1
    Email author
  • Lakshmi Narayan Guin
    • 1
  • Santabrata Chakravarty
    • 1
  1. 1.Department of MathematicsVisva BharatiSantiniketanIndia

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