Analytical solution of phosphate kinetics for hemodialysis

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,...

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Bibliographic Details
Published in:Journal of mathematical biology 2023-07, Vol.87 (1), p.11-11, Article 11
Main Authors: Andersen, M., Bangsgaard, K. O., Heaf, J. G., Ottesen, J. T.
Format: Article
Language:English
Subjects:
Applications of Mathematics
Dialysate
Dialysis
Dialysis Solutions
Dialyzers
Exact solutions
Hemodialysis
Humans
Kidney diseases
Kidney Failure, Chronic - therapy
Kinetics
Mathematical and Computational Biology
Mathematical models
Mathematics
Mathematics and Statistics
Ordinary differential equations
Patients
Phosphates
Plasma
Renal Dialysis
Toxins
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Summary: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.
ISSN:0303-6812
1432-1416
DOI:10.1007/s00285-023-01942-4