  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.
