Use of mathematical modeling to study pressure regimes in normal and Fontan blood flow circulations

TL;DR

This paper introduces mathematical models to analyze blood pressure distribution in Fontan circulation, exploring how pulmonary resistance affects cardiac output through simulations and PDE analysis.

Contribution

It develops novel ODE and PDE models for Fontan blood flow, including conditions for solution existence and effects of pulmonary resistance.

Findings

Pulmonary resistance significantly impacts cardiac output.

Mathematical models predict pressure distribution in Fontan circulation.

Conditions for existence of periodic solutions are established.

Abstract

We develop two mathematical lumped parameter models for blood pressure distribution in the Fontan blood flow circulation: an ODE based spatially homogeneous model and a PDE based spatially inhomogeneous model. We present numerical simulations of the cardiac pressure-volume cycle and study the effect of pulmonary resistance on cardiac output. We analyze solutions of two initial-boundary value problems for a non-linear parabolic partial differential equation (PDE models) with switching in the time dynamic boundary conditions which model blood pressure distribution in the cardiovascular system with and without Fontan surgery. We also obtain necessary conditions for parameter values of the PDE models for existence and uniqueness of non-negative bounded periodic solutions.