Effect of Membrane Permeance and System Parameters on the Removal of Protein-Bound Uremic Toxins in Hemodialysis

Abstract

Inadequate clearance of protein-bound uremic toxins (PBUTs) during dialysis is associated with morbidities in chronic kidney disease patients. The development of high-permeance membranes made from materials such as graphene raises the question whether they could enable the design of dialyzers with improved PBUT clearance. Here, we develop device-level and multi-compartment (body) system-level models that account for PBUT-albumin binding (specifically indoxyl sulfate and p-cresyl sulfate) and diffusive and convective transport of toxins to investigate how the overall membrane permeance (or area) and system parameters including flow rates and ultrafiltration affect PBUT clearance in hemodialysis. Our simulation results indicate that, in contrast to urea clearance, PBUT clearance in current dialyzers is mass-transfer limited: Assuming that the membrane resistance is dominant, raising PBUT permeance from 3 × 10^-6 to 10^-5 m s^-1 (or equivalently, 3.3 × increase in membrane area from ~ 2 to ~ 6 m²) increases PBUT removal by 48% (from 22 to 33%, i.e., ~ 0.15 to ~ 0.22 g per session), whereas increasing dialysate flow rates or adding adsorptive species have no substantial impact on PBUT removal unless permeance is above ~ 10^-5 m s^-1. Our results guide the future development of membranes, dialyzers, and operational parameters that could enhance PBUT clearance and improve patient outcomes.

Keywords: Chronic kidney disease; Dialysis; Indoxyl sulfate; Mass transfer; Modeling; Nanoporous graphene; p-cresyl sulfate.

Fig. 1

Schematics for the a device and b compartment models used in this study

Fig. 2

Effect of increasing dialysate flow rate $Q_{d,\text{in}}$, overall permeance $P_{\text{df}}$, or ultrafiltration rate $Q_{\text{uf}}$ on toxin removal for a PBUTs and b Non-PBUTs, e.g., urea, creatinine. The contour levels and color (note the different scales across sub-figures) denote the device removal ratio (DRR). Dimensionless parameters are plotted. All plots: $x$ = dialysate/plasma flow ratio. Top panels (i): $y$ = ${\text{Pe}}_{\text{df},\text{IS}}^{-1}\propto P_{\text{df},\text{IS}}$, constant $Q_{\text{uf}}$ = 10 mL min⁻¹. Bottom panels (ii): $y$ = ${\text{Pe}}_{\text{uf}}^{-1}\propto$ $Q_{\text{uf}}$, constant $P_{\text{df},\text{IS}}$ = 3 × 10⁻⁶ m s⁻¹. Baseline parameter levels for IS are denoted by the white/black dot and dashed lines for a, and the same dot and lines are presented in b. The transition between the mass-transfer-limited (clear) and dialysate-removal-limited (whiter) regimes is also delineated

Fig. 3

Effect of adding adsorbent (albumin protein, P) to the dialysate inlet (expressed as albumin concentration) on PBUT removal at various permeances as predicted by the equilibrium model. Typical albumin concentration in blood is ~ 600 μM

Fig. 4

a PBUT fractional net removal (indoxyl sulfate) over time during a typical dialysis session as estimated using the multi-compartment model, with parameters set to be same as the device model ($Q_{b,\text{in}}$, $Q_{d,\text{in}}$, $Q_{\text{uf}}$ = 300, 800, 10 mL min⁻¹). The body initially contains ~ 0.66 g of IS. Net removal, ∆q_net, is also presented on the right axis. b Removal performance at 4 h of dialysis as a function of overall permeance. Performance with other metrics is included in Supplementary Material S7

Fig. 5

a Effect of dialysate flow rate on fractional net removal (indoxyl sulfate) during a typical dialysis session for various permeance values. ∞ refers to the limiting case of infinitely high dialysate flow rate. b Same plot for urea, assuming $P_{\text{df},\text{urea}}$ = 2 $P_{\text{df},\text{IS}}$ based on the ratio of diffusivities of urea and IS

Fig. 6

Effect of changing the overall permeance of a indoxyl sulfate and b urea and (i) blood flow rate, (ii) membrane area, (iii) dialysis duration simultaneously on fractional net removal, while keeping other parameters constant ($V_{\text{uf}}$ = 2.4 L). Base case conditions: $A_{\text{m}}$ = 1.87 m², $Q_b$ = 300 mL min⁻¹, $\tau$ = 4 h, $P_{\text{df},\text{IS}}$ = 3 × 10⁻⁶ m s⁻¹ (black dot, dashed lines). Note the different scales for fractional net removal across sub-figures

Fig. 7

Operational parameter space to meet a hypothetical targeted a indoxyl sulfate net removal of 22%, b urea net removal of 64%. $x$: Permeance $P_{\text{df}}$, or overall mass transfer coefficient $K_{o}A$, assuming 1.87 m² membrane area; $y$: Blood flow rate; $z$ (contours): Dialysis duration. The black dots denote the base case conditions