A Kinetic Model of Inorganic Phosphorus Mass Balance in Hemodialysis Therapy

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Abstract

Background: There is growing evidence that inorganic phosphorus (iP) accumulation in tissues (dTiP/dt) is a risk factor for cardiac death in hemodialysis therapy (HD). The factors controlling iP mass balance in HD are dietary intake (GiP), removal by binders (JbiP) and removal by dialysis (JdiP). If iP accumulation is to be minimized, it will be necessary to regularly monitor and optimize GiP, JbiP and JdiP in individual patients. We have developed a kinetic model (iPKM) designed to monitor these three parameters of iP mass balance in individual patients and report here preliminary evaluation of the model in 23 HD patients. Methods: GiP was calculated from PCR measured with urea kinetics; JdiP was calculated from the product of dialyzer plasma water clearance (KpwiP) and time average plasma iP concentration (TACiP) and treatment time (t); a new iP concentration parameter (nTACiP, the TACiP normalized to predialysis CoiP) was devised and shown to be a highly predictable function of the form nTACiP = 1 – α(1 – exp[–βKpwiP· t/ViP]), where the coefficients α and β are calculated for each patient from 2 measure values for nTACiP, KpwiP·t/ViP early and late in dialysis; we measured 8–10 serial values for nTACiP, KpwiP· t/ViP over a single dialysis in 23 patients; the expression derived for iP mass balance is ΔTiP = 12(PCR) – [KpwiP(t) (N/7)][CoiP(1 – α(1 – exp[–β(Kt/ViP)]))] – kb·Nb. Results: Calculated nTACiP = 1.01(measured nTACiP), r = 0.98, n = 213; calculated JdiP = 0.66(measured total dialysate iP) + 358, n = 23, r = 0.88, p < 0.001. Evaluation of 10 daily HD patients (DD) and 13 3 times weekly patients with the model predicted the number of binders required very well and showed that the much higher binder requirement observed in these DD patients was due to much higher NPCR (1.3 vs. 0.96). Conclusion: These results are very encouraging that it may be possible to monitor the individual effects of diet, dialysis and binders in HD and thus optimize these parameters of iP mass balance and reduce phosphate accumulation in tissues.

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Phosphate kinetics during hemodialysis: Evidence for biphasic regulation.

Ken Farrington, Paul W Chamney, Peter Spalding (2002)

Hyperphosphatemia in the hemodialysis population is ubiquitous, but phosphate kinetics during hemodialysis is poorly understood. Twenty-nine hemodialysis patients each received one long and one short dialysis, equivalent in terms of urea clearance. Phosphate concentrations were measured during each treatment and for one hour thereafter. A new model of phosphate kinetics was developed and implemented in VisSim. This model characterized additional processes involved in phosphate kinetics explaining the departure of the measured data from a standard two-pool model. Pre-dialysis phosphate concentrations were similar in long and short dialysis groups. Post-dialysis phosphate concentrations in long dialysis were higher than in short dialysis (P < 0.02) despite removal of a greater mass of phosphate (P < 0.001). In both long and short dialysis serum phosphate concentrations initially fell in accordance with two-pool kinetics, but thereafter plateaued or increased despite continuing phosphate removal. Implementation of an additional regulatory mechanism such that a third pool liberates phosphate to maintain an intrinsic target concentration (1.18 +/- 0.06 mmol/L; 95% confidence intervals, CI) explained the data in 24% of treatments. The further addition of a fourth pool hysteresis element triggered by critically low phosphate levels (0.80 +/- 0.07 mmol/L, CI) yielded an excellent correlation with the observed data in the remaining 76% of treatments (cumulative standard deviation 0.027 +/- 0.004 mmol/L, CI). The critically low concentration correlated with pre-dialysis phosphate levels (r=0.67, P < 0.0001). Modeling of phosphate kinetics during hemodialysis implies regulation involving up to four phosphate pools. The accuracy of this model suggests that the proposed mechanisms have physiological validity.