Abstract
Atherosclerosis, a chronic inflammatory disorder of the arterial wall, is a complex process whose dynamics are affected by multiple factors. The disease control consists of restraining it by administering statins. Slowing down or halting the plaque growth depends on the patient age at which the statin treatment begins and on the thickness of the intima-media (IMT) at that time. In this paper, we propose a mathematical model to estimate the sets of atherosclerosis states, from which the use of statins can restrain the disease. Our model is control-theoretic, and the estimated sets are the viability kernels, in the parlance of viability theory. To our best knowledge, this way of modelling the atherosclerosis progression is original. We compute two viability kernels, each for a different statin-treatment dose. Each kernel is composed of the vector [age, IMT] from which the disease can be restrained. By extension, the disease can't be restrained from the kernel complements, this being mainly because of the disease and patient-age advancement. The kernels visualise tradeoffs between early and late treatments, which helps the clinician to decide when to start the statin treatment and which statin dose may be sufficient.
Highlights
The aim of this paper is to use a control-theoretic aggregate model of the progression of atherosclerotic plaque to assess viability of the process of restraining it
Our aim is to estimate the disease states [age, intima-media thickness (IMT)], from which the statin treatment is advantageous to patients’ wellbeing
We present atherosclerosis as a dynamic process and propose a mathematical model that captures the basic features of atherosclerosis progression and the role of statins in slowing down this progression
Summary
The aim of this paper is to use a control-theoretic aggregate model of the progression of atherosclerotic plaque to assess viability of the process of restraining it. Therapy consists of treating patients with statins to achieve stabilisation of the plaque at a survival level. The treatment may not improve, or stabilise, the patient’s wellbeing if the plaque is thick or if the patient is at an advanced age. The treatment may be nonessential for young patients, or when the plaque is thin. Our aim is to estimate the disease states [age, IMT] (where IMT is the obvious abbreviation for intima-media thickness), from which the statin treatment is advantageous to patients’ wellbeing. We call these sets the viability kernels
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