Analytical solution of phosphate kinetics for hemodialysis

Abstract

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.

Evaluation of a phosphate kinetics model in hemodialysis therapy—Assessment of the temporal robustness of model predictions

“…Examples include UF, residual renal clearance, and hematocrit values. UF would be relevant to account for the convective flux of phosphate (Andersen & Bangsgaard, 2023;Spalding et al, 2002), whereas residual renal function could play a significant role considering phosphate elimination in patients who still excrete phosphate through the kidneys. For instance, in a study by Iwasawa et al it was found that the amount of phosphate removed by the residual kidney was approximately 1.5-fold greater per week in patients with a glomerular filtration rate >3 mL/min compared to the phosphate removal during one HD treatment (Iwasawa et al, 2013).…”