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.

中文翻译：

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同时治疗性血浆交换和体外膜氧合期间的血浆动力学模型

本文重点介绍了数学模型的推导和模拟，这些模型描述了同时进行体外膜氧合和治疗性血浆交换的患者血液中的新血浆分数。考虑使用静脉-动脉或静脉-静脉体外膜氧合进行血浆交换的模型。每种情况都导出了两类模型，一类是代数延迟方程的形式，另一类是延迟微分方程组的形式。在特殊情况下，我们的模型简化为用于血浆交换的单隔室模型，这些模型已经通过实验数据进行了验证（Randerson 等人，1982，Artif. Organs，6、43-49）。我们还证明了代数微分方程是延迟微分方程的正向欧拉离散，时间步长等于通过模型隔间的传输时间。进行数值模拟以比较不同的模型类型，研究等离子设备端口切换对交换过程效率的影响，并研究模型对其参数的敏感性。