A novel mathematical model of protein-bound uremic toxin kinetics during hemodialysis

Abstract

Protein-bound uremic toxins (PBUTs) are difficult to remove by conventional hemodialysis; a high degree of protein binding reduces the free fraction of toxins and decreases their diffusion across dialyzer membranes. Mechanistic understanding of PBUT kinetics can open new avenues to improve their dialytic removal. We developed a comprehensive model of PBUT kinetics that comprises: (1) a three-compartment patient model, (2) a dialyzer model. The model accounts for dynamic equilibrium between protein, toxin, and the protein-toxin complex. Calibrated and validated using clinical and experimental data from the literature, the model predicts key aspects of PBUT kinetics, including the free and bound concentration profiles for PBUTs and the effects of dialysate flow rate and dialyzer size on PBUT removal. Model simulations suggest that an increase in dialysate flow rate improves the reduction ratio (and removal) of strongly protein-bound toxins, namely, indoxyl sulfate and p-cresyl sulfate, while for weakly bound toxins, namely, indole-3-acetic acid and p-cresyl glucuronide, an increase in blood flow rate is advantageous. With improved dialyzer performance, removal of strongly bound PBUTs improves gradually, but marginally. The proposed model can be used for optimizing the dialysis regimen and for in silico testing of novel approaches to enhance removal of PBUTs.

Conflict of interest statement

PK holds stock in Fresenius Medical Care. ST holds performance shares in Fresenius Medical Care. The remaining authors declare that they have no competing interests.

Figures

Figure 1

Intra-dialytic concentration profiles of protein-bound uremic toxins and urea. Circles depict data published by Eloot et al.; lines represent model fit.

Figure 2

Percentage protein binding at different time points during the course of dialysis; left-to-right for indole-3-acetic acid (IAA), indoxyl sulfate (IS), p-cresyl glucuronide (pCG), and p-cresyl sulfate (pCS). Top row corresponds to in vivo data from 10 HD patients and bottom row shows model simulations.

Figure 3

Percentage protein binding at the dialyzer blood inlet versus blood outlet after 120 min since dialysis start; left-to-right for indole-3-acetic acid (IAA), indoxyl sulfate (IS), p-cresyl glucuronide (pCG), and p-cresyl sulfate (pCS). Top row corresponds to in vivo data from 10 HD patients and bottom row shows model simulations.

Figure 4

Reduction ratio for total () and free () toxin concentration at different time points during an HD session; left-to-right for indole-3-acetic acid (IAA), indoxyl sulfate (IS), p-cresyl glucuronide (pCG), and p-cresyl sulfate (pCS). Top row corresponds to in vivo data from 10 HD patients and bottom row shows model simulations (solid line for total toxin concentration and dashed line for free toxin concentration).

Figure 5

Effect of varying KoA and Qd on removal of phenol red. The left panel shows model predictions by Meyer et al., which closely matched their in vitro results obtained in bench dialysis experiments using artificial plasma (figure reproduced with permission). The blue lines (e–h) describe urea removal and are not part of this discussion. The right panel shows results obtained with our mathematical model by simulating the scenarios studied by Meyer et al.. Line styles and labeling correspond to the same scenarios, which are the following: (a) F6, Qd 300 ml/min, ClPR 11 mL/min; (b) Optiflux F200NR, Qd 300 mL/min, ClPR 14 mL/min; (c) F6, Qd 750 mL/min, ClPR 16 mL/min; (d) Optiflux F200NR, Qd 750 mL/min, ClPR 23 mL/min. The KoA values presented in the right panel are calculated using phenol red clearance values and Meyer et al. clearance expression for PBUTs (reproduced in the Methods section).

Figure 6

Total (top row) and free (bottom row) protein-bound uremic toxin concentrations during and after dialysis; left-to-right for indole-3-acetic acid (IAA), indoxyl sulfate (IS), p-cresyl glucuronide (pCG), and p-cresyl sulfate (pCS). Concentrations are scaled in relation to pre-dialysis plasma concentration. Solid lines denote plasma concentrations, dotted lines interstitial concentrations, and dashed lines free intracellular concentrations. Note that free and total toxin concentrations in the intracellular compartment are identical, as there is no intracellular albumin. Therefore, intracellular concentrations are only shown in the bottom plots.

Figure 7

Effect of blood flow rate (Qb) and dialysate flow rate (Qd) on reduction ratio (RR) calculated for total protein-bound uremic toxin concentration. Clockwise from top left: indole-3-acetic acid (IAA), indoxyl sulfate (IS), p-cresyl sulfate (pCS), and p-cresyl glucuronide (pCG). The simulations were performed for F180NR dialyzer with Qb and Qd were 300 and 700 mL/min, respectively; ultrafiltration volume 2 L. Initial toxin concentrations were same as in model calibration or Figure 1 and corresponding model parameters were taken from Table 3.

Figure 8

Block diagram of the model for protein-bound uremic toxin distribution and removal during dialysis. A three-compartmental model of the patient connected to dialyzer is shown. Here, T, PT, V denote free toxin concentration, protein-bound toxin concentration, and distribution volume in subscripted compartment plasma (pl), interstitial (is) and intracellular (ic); Qp, Qd, and Quf denote plasma flow rate, dialysate flow rate, and ultrafiltration rate, respectively; Cp denote free toxin or protein-bound toxin or toxin free protein concentration in dialyzer blood inlet and Cout in dialyzer blood outlet. A single dialyzer fiber is magnified to depict the counter-current blood and dialysate flow in dialyzer. A small fiber segment Δx is shown through which free toxin transfers from the plasma side to the dialysate side. Here, Qpi and Qdi denote inlet plasma and dialysate flow rate; Qpo and Qdo are outlet plasma and dialysate flow rates; Cpi and Cdi are the molar concentrations at the plasma and dialysate inlet, respectively; Cpo and Cdo are the molar concentrations at the respective outlets.