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Analytical Solutions of a Two-Compartment Model Based on the Volume-Average Theory for Blood Toxin Concentration during and after Dialysis

Authors :
Yoshihiko Sano
Kentaro Sato
Ryusei Iida
Narutoshi Kabashima
Toyomu Ugawa
Source :
Membranes, Vol 11, Iss 7, p 506 (2021)
Publication Year :
2021
Publisher :
MDPI AG, 2021.

Abstract

Accurate prediction of blood toxin concentration during and after dialysis will greatly contribute to the determination of dialysis treatment conditions. Conventional models, namely single-compartment model and two-compartment model, have advantages and disadvantages in terms of accuracy and practical application. In this study, we attempted to derive the mathematical model that predicts blood toxin concentrations during and after dialysis, which has both accuracy and practicality. To propose the accurate model, a new two-compartment model was mathematically derived by adapting volume-averaging theory to the mass transfer around peripheral tissues. Subsequently, to propose a practical model for predicting the blood toxin concentration during dialysis, an analytical solution expressed as algebraic expression was derived by adopting variable transformation. Furthermore, the other analytical solution that predicts rebound phenomena after dialysis was also derived through similar steps. The comparisons with the clinical data revealed that the proposed analytical solutions can reproduce the behavior of the measured blood urea concentration during and after dialysis. The analytical solutions proposed as algebraic expressions will allow a doctor to estimate the blood toxin concentration of a patient during and after dialysis. The proposed analytical solutions may be useful to consider the treatment conditions for dialysis, including the rebound phenomenon.

Details

Language :
English
ISSN :
20770375
Volume :
11
Issue :
7
Database :
Directory of Open Access Journals
Journal :
Membranes
Publication Type :
Academic Journal
Accession number :
edsdoj.4c13f61671014fb395afc51c75681145
Document Type :
article
Full Text :
https://doi.org/10.3390/membranes11070506