Mathematical Analysis on Stroke Risk Progression through the Dynamics of Metabolic and Hemodynamic Factors

Stroke is a severe and escalating global health threat, responsible for substantial mortality and long-term disability across all age groups. Under these circumstances, we developed a non-linear mathematical model to examine stroke risk progression arising from the coupled interactions of metabolic dysfunction and hemodynamic factors. The analysis focuses on key physiological variables, including body mass index (BMI), insulin concentration, low-density lipoprotein (LDL) cholesterol, blood pressure, and cerebral blood flow, incorporating the effects of atherosclerosis and cerebral autoregulation. The governing relationships are formulated using a system of ordinary differential equations to capture the nonlinear dynamics underlying metabolic vascular interactions. Numerical investigations reveal that persistent metabolic imbalance promotes elevated LDL cholesterol and blood pressure, accelerates atherosclerotic vascular damage, and progressively impairs cerebral autoregulatory capacity. As a result, cerebral blood flow declines over time, significantly increasing stroke risk. These findings highlight the critical role of metabolic and hemodynamic control in mitigating long term cerebrovascular complications.

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