Phosphate kinetics during hemodialysis: Evidence for biphasic regulation  Elaine M. Spalding, Paul W. Chamney, Ken Farrington  Kidney International  Volume 61, Issue 2, Pages 655-667 (February 2002) DOI: 10.1046/j.1523-1755.2002.00146.x Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 1 Model A: Schematic representation of two-pool kinetics. Abbreviations are: Me, extracellular mass of solute; Ce, extracellular concentration of solute; Ve, extracellular volume; Mi, intracellular mass of solute; Ci, intracellular concentration of solute; Vi, intracellular volume; F1, intercompartmental flux; Fd, diffusive flux across dialyzer membrane; Fc, convective flux across dialyser membrane; Kd, dialyzer clearance; Kie, cell membrane mass transfer coefficient. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 2 Graphic representation of two-pool kinetics. Symbols are: (solid line) extracellular concentration according to the model; (dotted line) intracellular concentration according to the model. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 3 Model B: Schematic representation of three-pool kinetics. The two-pool kinetic model of model A Figure 1 forms the basis of this model with additional phosphate flux (F3) into the extracellular space from a third pool. This occurs in proportion to the phosphate error (Σ) or the difference between the momentary intracellular phosphate concentration and an intrinsic intracellular phosphate target concentration. The magnitude of phosphate generation is dependent on a constant factor termed the gain. Abbreviations are in the legend to Figure 1. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 4 Representative treatment exhibiting features of model B. Two-pool kinetics are operational beyond the duration of dialysis. When the prevailing phosphate concentration falls below the target point phosphate is released from the third pool. The critically low limit is not reached in this treatment. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 5 Representative treatment exhibiting features of model C. Kinetics are as for model B Figure 4 but, in addition, when the critically low limit is exceeded, fourth pool kinetics become operational. The influx from this pool switches off when a safe phosphate level has been re-established. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 6 Representative treatment exhibiting features of model C with repeated activation of fourth pool kinetics. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 7 Model C: Addition of hysteresis element to model B. In addition to the proportional control mechanism shown in the three-pool model Figure 3, critically low intracellular phosphate levels trigger immediate release of phosphate from a fourth pool local to the intracellular space (F4). This independent mechanism serves to protect the intracellular environment from dangerously low phosphate concentrations. Abbreviations are in the legend to Figures 1 and 3. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 8 Representative data from one patient showing observed urea levels during dialysis (•) versus urea levels predicted by two-pool model (represented by the line) in (A) long dialysis and (B) short dialysis. Allowing for cardiopulmonary recirculation (CPR) and for a degree of peripheral compartmentalization in the short dialysis, it was possible to achieve excellent fits between the observed urea data and the two-pool model, assuming an intracellular to extracellular transfer coefficient (Kie). In A, Kie = 750mL/min; CPR = 4%; volume = 100%. In B, Kie = 413mL/min; CPR = 4%; volume = 57.5%. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 9 Mean observed phosphate levels during dialysis for all 58 treatments versus phosphate levels predicted by two-pool model. A clear discontinuity exists where the phosphate data plateaus and deviates from the two-pool model. The degree of rebound can also be seen to be greater in the observed data than the two-pool prediction. Symbols are: (▪) observed phosphate data; (•) two-pool model. Observed phosphate data are mean ± 95% confidence intervals. For the key to the time differential axis, see “Sampling and assay techniques.” Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 10 Serial mean plasma bicarbonate measurements throughout dialysis. Bicarbonate levels increase throughout dialysis. No plateau is seen during dialysis in the bicarbonate data in contrast to the phosphate data Figure 9. Data are mean ± 95% confidence intervals. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 11 (A) Target phosphate concentration. The majority of values fell within the physiological range (0.75 to 1.40mmol/L) and those that did not tended to have higher pre-dialysis phosphate concentrations (shown in parenthesis). (B) Correlation between pre-dialysis serum phosphate concentration and target extracellular phosphate concentration according to the model (r = 0.47, P < 0.001). Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 12 (A) Representative treatment exhibiting three-pool kinetics. Symbols are: (•) extracellular phosphate data. Lines are: dotted, two-pool kinetics; solid, three-pool kinetics. (B) Cumulative standard deviation curves for panel A. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 13 Correlation between pre-dialysis serum phosphate concentration and critically low extracellular phosphate concentration according to the model (r = 0.67, P < 0.0001). Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 14 Two representative treatments (A and B) exhibiting four-pool kinetics with corresponding cumulative standard deviation curves (C and D). (A) The pre-hemodialysis serum phosphate concentration is 1.07mmol/L and there is a substantial contribution toward regulation from both the third and fourth pools. (C) The pre-hemodialysis serum phosphate concentration is 0.88mmol/L and the contribution toward regulation from the third pool is minimal. This is presumably because this individual has little in the way of third-pool phosphate stores. Symbols are: (•) extracellular phosphate data; (dotted line) two-pool kinetics; (dashed line) three-pool kinetics; (solid line) four-pool kinetics. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions

Figure 15 Comparison of observed serum phosphate concentrations in long and short dialysis for all 58 treatments. Symbols are: (▪) short dialysis; (•) long dialysis; *P < 0.001 and **P < 0.01, paired t test. Data are mean ± SEM values. Kidney International 2002 61, 655-667DOI: (10.1046/j.1523-1755.2002.00146.x) Copyright © 2002 International Society of Nephrology Terms and Conditions