论文标题
同时治疗血浆交换和体外膜氧合期间血浆动力学的模型
Models for plasma kinetics during simultaneous therapeutic plasma exchange and extracorporeal membrane oxygenation
论文作者
论文摘要
本文重点介绍了数学模型的推导和模拟，这些数学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新的血浆分数。考虑了与静脉或静脉外膜外膜氧合的血浆交换模型。每种情况下都会得出两类模型，一个模型以代数延迟方程的形式得出，另一类是延迟微分方程系统的形式。在特殊情况下，我们的模型将已通过实验数据验证的血浆交换单隔室减少。我们还表明，代数延迟方程是延迟微分方程的前向Euler离散化，时间到通过模型隔室等于运输时间。进行数值模拟以比较不同的模型类型，以研究等离子体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。
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.
