IMFUFA, Centre for Mathematical Modeling, Human Health and Disease, Roskilde University, Roskilde, Denmark.
DTU Compute, Technical University of Denmark, Kongens Lyngby, Denmark.
J Math Biol. 2023 Jun 18;87(1):11. doi: 10.1007/s00285-023-01942-4.
Chronic kidney diseases imply an ongoing need to remove toxins, with hemodialysis as the preferred treatment modality. We derive analytical expressions for phosphate clearance during dialysis, the single pass (SP) model corresponding to a standard clinical hemodialysis and the multi pass (MP) model, where dialysate is recycled and therefore makes a smaller clinical setting possible such as a transportable dialysis suitcase. For both cases we show that the convective contribution to the dialysate is negligible for the phosphate kinetics and derive simpler expressions. The SP and MP models are calibrated to clinical data of ten patients showing consistency between the models and provide estimates of the kinetic parameters. Immediately after dialysis a rebound effect is observed. We derive a simple formula describing this effect which is valid both posterior to SP or MP dialysis. The analytical formulas provide explanations to observations of previous clinical studies.
慢性肾脏疾病意味着需要持续清除毒素，血液透析是首选的治疗方式。我们推导出了透析过程中磷酸盐清除率的解析表达式，单次通过 (SP) 模型对应于标准的临床血液透析，而多通道 (MP) 模型则是回收透析液的，因此可以在更小的临床环境中进行，例如便携式透析箱。对于这两种情况，我们都表明，对流对磷酸盐动力学的贡献可以忽略不计，并推导出了更简单的表达式。SP 和 MP 模型根据十名患者的临床数据进行了校准，结果表明模型之间具有一致性，并提供了动力学参数的估计值。透析后立即观察到反弹效应。我们推导出了一个简单的公式来描述这种效应，它在 SP 或 MP 透析后都有效。解析公式为以前的临床研究的观察结果提供了解释。
