A ptototype compartmental model of blood pressure distribution

We consider a system of differential equations the behavior of which solutions possesses several properties characteristic of the blood pressure distribution. The system can be used for a compartmental modeling of the cardiovascular system. It admits a unique bounded solution such that all coordinates of the solution are separated from zero by positive numbers, and which is periodic, eventually periodic or almost periodic depending on the moments of heart contraction. Appropriate numerical simulations are provided.

💡 Research Summary

The paper introduces a prototype compartmental model designed to capture the essential dynamics of blood‑pressure distribution throughout the cardiovascular system. By partitioning the circulatory loop into a finite number of compartments, each representing a vascular segment (e.g., aorta, peripheral artery, capillary bed, vein), the authors translate the fluid‑mechanical interactions into a system of first‑order ordinary differential equations that resemble electrical resistor‑capacitor networks. The state variable (x_i(t)) denotes the pressure in compartment (i); the flow between adjacent compartments follows a linear resistance law, while each compartment stores blood according to a compliance (capacity) term (C_i). The governing equation for compartment (i) can be written as

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