Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation

TL;DR

This paper develops and compares mathematical models for plasma kinetics during simultaneous plasma exchange and ECMO, including delay equations and differential equations, validated with experimental data and numerical simulations.

Contribution

It introduces new delay and differential equation models for plasma exchange during ECMO, linking algebraic delay equations to discretized delay differential equations.

Findings

Models reduce to validated single compartment forms in special cases

Delay equations are Euler discretizations of delay differential equations

Simulations show impact of port switching and parameter sensitivity

Abstract

This paper focuses on the derivation and simulation of mathematical models describing new plasma fraction in blood for patients undergoing simultaneous extracorporeal membrane oxygenation and therapeutic plasma exchange. Models for plasma exchange with either veno-arterial or veno-venous extracorporeal membrane oxygenation are considered. Two classes of models are derived for each case, one in the form of an algebraic delay equation and another in the form of a system of delay differential equations. In special cases, our models reduce to single compartment ones for plasma exchange that have been validated with experimental data. We also show that the algebraic delay equations are forward Euler discretizations of the delay differential equations, with timesteps equal to transit times through model compartments. Numerical simulations are performed to compare different model types, to investigate the impact of plasma device port switching on the efficiency of the exchange process, and to study the sensitivity of the models to their parameters.