A ptototype compartmental model of blood pressure distribution

TL;DR

This paper introduces a compartmental differential equation model simulating blood pressure distribution, capturing periodic and almost periodic behaviors based on heart contraction timings, with numerical validation.

Contribution

It presents a novel compartmental model for blood pressure distribution that accounts for periodic and almost periodic dynamics, supported by numerical simulations.

Findings

Model admits unique bounded solutions

Solutions are periodic or almost periodic depending on heart contractions

Numerical simulations validate the model's behavior

Abstract

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.