A Control-Theoretic Model of Atherosclerosis

Abstract

We propose a control-theoretic aggregate model of the progression of atherosclerosis plaque, a chronic inflammatory disease of the arterial wall, to study the basic features of this disease. In the model, we exploit the role of inflammation in the disease progression, and use statins—drugs commonly recommended in atherosclerosis—to control this progression. We use a logistic function to allow for constrained growth of plaque. In the model, both the patient’s age and overall health impact the plaque growth and its sensitivity to statins. The model parameters are estimated using original data, or calibrated using published research as well as our own clinical and laboratory studies. We contend that our model helps to gauge the statins’ impact on a patient’s plaque thickness, hence the disease’s progression and cardiovascular risk, without requiring artery scans.

Controlling the thickness of the atherosclerotic plaque by statin medication

“…A figure, similar to Fig 3, was published in [9] using a slightly different model. The trajectories shown in Fig 3 have the same convergence points for t = 90 as those in [9].…”

“…We refer to [9] for a more detailed description of the carotid plaque progression. Here, we highlight only its main features.…”

“…Symbol c-called "carrying capacity" in population dynamics-is determined by the state of health of the patient and represents the terminal (maximum) size of the plaque when they pass away. Examples of solutions to (1) are shown in Fig 1; see [9] for a more detailed description. The lines shown in Fig 1 represent the life-span IMT progression in three representative patients.…”

“…proposed in [9] in that the terminal plaque size is modelled through a static equation (with 6 constants), the current model proposes a differential Eq (3) (with 5 constants) for the terminal plaque size. This equation is coupled with a differential equation for the plaque.…”

“…Those models help understand the dynamics of plaque formation at a micro level. In contrast, [9] propose a macro model. I.e., their model concentrates on patient holistic wellbeing related to atherosclerosis.…”