Models for Plasma Kinetics During Simultaneous Therapeutic Plasma Exchange and Extracorporeal Membrane Oxygenation

Authors

Charles Puelz, Department of Pediatrics, Section of Cardiology, Baylor College of Medicine and Texas Children's Hospital, Houston, TX, USA
Zach Danial, Courant Institute of Mathematical Sciences, New York University, New York, NY, USA
Jay S. Raval, Department of Pathology, University of New Mexico, Albuquerque, NM, USA
Jonathan L. Marinaro, Department of Emergency Medicine, University of New Mexico, Albuquerque, NM, USA
Boyce E. Griffith, Departments of Mathematics, Applied Physical Sciences, and Biomedical Engineering, University of North Carolina; Carolina Center for Interdisciplinary Applied Mathematics, University of North Carolina; Computational Medicine Program, University of North Carolina, and McAllister Heart Institute, University of North Carolina, Chapel Hill, NC, USA
Charles S. Peskin, Courant Institute of Mathematical Sciences, New York University, New York, NY, USA

Document Type

Article

Publication Date

6-15-2021

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 (Randerson et al., 1982, Artif. Organs, 6, 43-49). We also show that the algebraic differential 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.

Recommended Citation

Puelz C, Danial Z, Raval JS, Marinaro JL, Griffith BE, Peskin CS. Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation. Math Med Biol. 2021 Jun 15;38(2):255-271. doi: 10.1093/imammb/dqab003. PMID: 33626571.