The simulation of continuous arteriovenous hemodialysis with a mathematical model

Abstract

We have developed a mathematical model that predicts the performance of continuous arteriovenous hemodialysis. Given patient (plasma protein concentration, hematocrit, mean arterial pressure, central venous pressure) and circuit (flow resistance, membrane hydraulic permeability, dialyzer mass transfer coefficient, ultrafiltrate column height, dialysate flow rate) characteristics as inputs, predictions of hydraulic and oncotic pressure distribution, filtration rate, blood flow, total, diffusive, and convective urea clearances are provided. The model was tested by perfusing a circuit with bovine blood under conditions of pure ultrafiltration, zero net ultrafiltration and dialysis, or combined ultrafiltration and dialysis (countercurrent dialysate flow at rates of 10, 20, and 30 ml/min). In order to permit computation, membrane hydraulic permeability and flow resistances were measured. Dialyzer mass transfer coefficient for urea could not be measured directly and so was determined by fitting model predictions to measured urea clearances. For all conditions of operation, a urea mass transfer coefficient of 0.014 cm/min successfully simulated the data. Predictions of blood flow, filtrate generation rate, and circuit pressure distribution were accurate. At lower dialysate flow rates, urea clearance approximated the sum of dialysate flow and filtration rate. At higher dialysate flows, however, departure from this ideal blood-dialysate equilibrium was observed. Model predictions regarding the relative contributions of diffusion and convection to urea clearance were explored. Under conditions of nearly perfect equilibration of urea between blood and dialysate at the blood inlet, the model predicts that the diffusive clearance of urea will increase with increasing rate of filtration and may exceed the rate of dialysate inflow.