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Dynamic Response of Evolved Atherosclerotic Plaque Model and its Stability

Debasmita Mukherjee, Lakshmi Narayan Guin, Santabrata Chakravarty

Abstract



The present study is dealt with the formation of a mathematical model of atherosclerotic plaque evolved through the interactions among various cellular species in the biochemical process causing concern of health hazard for impairment of the cardiovascular system. Of many participating species several important species like LDLs, HDLs, radicals, oxidized LDLs, chemo-attractants, monocytes, macrophages, T-cells, smooth muscle cells (SMCs) and the necrotic core are selected to interact in the process. As the proposed model admits global stability, it can cater for larger range of parameter values towards acceptability for in silico studies on atherosclerotic plaque formation. The large system of differential equations (ODEs) emerging from the dynamics of all the cellular components forming plaque in the arterial lumen is reduced to smaller system for an in-depth study on the characteristics of the participating cellular species including their individual contributions to the association or dissociation of plaque. The quasi steady state approximation theory (QSSA) is inducted for the purpose of reduction of the primal system into a smaller ones (Model A and Model B) by way of protecting contributions of those nonexistent species in terms of the concentrations of the participating species in the reduced system. The present model system experiences bifurcation with respect to a couple of parameters of significance. The applicability of the proposed plaque model is validated through a comparison of the present results with those of the existing experimental data.

Keywords


Atherosclerosis, Cholesterol efflux, Quasi Steady State Approximation (QSSA), Global Stability, Saddle Node Bifurcation.

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