Finite volume scheme for double convection-diffusion exchange of solutes in bicarbonate high-flux hollow-fiber dialyzer therapy

Mechanisms of Peritoneal Acid-Base Kinetics During Peritoneal Dialysis: A Mathematical Model Study

To investigate mechanisms of acid-base changes during peritoneal dialysis (PD), a mathematical model was developed that describes kinetics of peritoneal bicarbonate, CO2, and pH during the dwell with both high and low lactate-containing dialysis fluids. The model was based on a previous modification of the Rippe 3-Pore model of water and solute kinetic transport across the peritoneal membrane during the PD dwell. A central feature of the present modification is an electroneutrality constraint on peritoneal-fluid ion concentrations, which results in the conclusion that peritoneal bicarbonate-concentration kinetics are entirely dependent on the kinetics of the other ions. This new model was able to closely predict peritoneal bicarbonate-concentration kinetics during the dwell. Predictions of total peritoneal bicarbonate-mass kinetics were greater than those of porous, transmembrane bicarbonate transport, suggesting that a portion of bicarbonate comes from CO2 transport, both porous and nonporous and then a partial conversion to bicarbonate. Fitting the model to experimental pH data during the dwell, required addition of a peritoneal CO2 mass-conservation constraint, coupled with the description for peritoneal bicarbonate kinetics. Predicted pH kinetics during the dwell, closely mimicked the experimental data. The conclusion was that the mechanisms describing peritoneal bicarbonate and pH kinetics during PD must include 1) electroneutrality of peritoneal fluid, 2) porous transport of bicarbonate and CO2, 3) nonporous transport of CO2, and 4) CO2 conversion to bicarbonate. These mechanisms are quite different and more complex than the bicarbonate-centered, lactate to acid-generation mechanisms previously proposed.

Mathematical model of calcium exchange during haemodialysis using a citrate containing dialysate

Calcium has two important roles in haemodialysis. It participates in the activation of blood coagulation and calcium intakes have a major impact on patient mineral and bone metabolism. The aim of this article is to propose a mathematical model for calcium ions concentration in a dialyzer during haemodialysis using a citrate dialysate. The model is composed of two elements. The first describes the flows of blood and dialysate in a dialyzer fibre. It was obtained by asymptotic analysis and takes into account the anisotropy of the fibres forming a dialyzer. Newtonian and non-Newtonian blood rheologies were tested. The second part of the model predicts the evolution of the concentration of five chemical species present in these fluids. The fluid velocity field drives the convective part of a convection-reaction-diffusion system that models the exchange of free and complexed calcium. We performed several numerical experiments to calculate the free calcium concentration in the blood in a dialyzer using dialysates with or without citrate. The choice of blood rheology had little effect on the fluid velocity field. Our model predicts that only a citrate based dialysate without calcium can decrease free calcium concentration at the blood membrane interface low enough to inhibit blood coagulation. Moreover for a given calcium dialysate concentration, adding citrate to the dialysate decreases total calcium concentration in the blood at the dialyzer outlet. This decrease of the calcium concentration can be compensated by infusing in the dialyzed blood a quantity of calcium computed from the model.

Acid-base alterations in ESRD and effects of hemodialysis

Acid-base alterations in patients with kidney failure and on hemodialysis (HD) treatment contribute to (1) intradialytic hypercapnia and hypoxia, (2) hemodynamic instability and cardiac arrhythmia, (3) systemic inflammation, and (4) a number of associated electrolyte alterations including potentiating effects of hypokalemia, hypocalcemia and, chronically, soft-tissue and vascular calcification, imparting poor prognosis and mortality. This paper discusses acid-base regulation and pathogenesis of dysregulation in patients with kidney failure. Major organ and systemic effects of acid-base perturbations with a specific focus on kidney failure patients on HD are emphasized, and potential mitigating strategies proposed. The high rate of HD-related complications, specifically those that can be accounted for by rapid and steep acid-base perturbations imposed by HD treatment, attests to the pressing need for investigations to establish a better dialysis regimen.