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

Charles Puelz, Zach Danial, Jay S. Raval, Jonathan L. Marinaro, Boyce E. Griffith, Charles S. Peskin

Research output: Contribution to journalArticlepeer-review


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.

Original languageEnglish (US)
Pages (from-to)255-271
Number of pages17
JournalMathematical Medicine and Biology
Issue number2
StatePublished - Jun 1 2021


  • Compartment models
  • Delay differential equations
  • ECMO
  • Plasma kinetics
  • Therapeutic plasma exchange

ASJC Scopus subject areas

  • Neuroscience(all)
  • Modeling and Simulation
  • Immunology and Microbiology(all)
  • Biochemistry, Genetics and Molecular Biology(all)
  • Environmental Science(all)
  • Pharmacology
  • Applied Mathematics


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