Finite-element modeling of time-dependent sodium exchange across the hollow fiber of a hemodialyzer by coupling with a blood pool model.

Abstract

Hollow fiber models describe the exchange of solutes between blood and dialysate across the membrane of a single fiber of the hemodialysis filter (hemodialyzer). This work aims to develop a new approach to simulate the solute exchange in a hollow fiber in a dynamic and realistic way. Sodium was chosen as our solute of interest due to its importance in hemodialysis as an osmotic regulator. A 2-dimensional (2D) hollow fiber model based on the finite element method (FEM) is coupled to a simple blood pool model to dynamically update the concentration of the solute entering the dialyzer. The resulting coupled model maintains the geometrical detail of the 2D fiber representation and gains a dynamic, blood-side inlet solute concentration. In vitro dialysis sessions were carried out for model validation, by implementing a combination of blood volume loss and/or sodium concentration steps. Plasmatic sodium concentration was recorded by blood gas sampling. Dialysate inlet and outlet conductivities were continuously recorded. Simulated plasmatic sodium concentration was compared with data from the blood gas samples. A mean error of 1.76 ± 1.03 mM was found for the complete dataset, along with a 3.87 mM maximum error. The simulated outlet dialysate sodium concentration was compared with the recorded outlet dialysate conductivity: a very high correlation was found on the whole dataset (R2 = 0.992). Coupling our FEM hollow fiber model to a simple blood pool model proved to be an effective approach for dynamical analysis of the properties of the hemodialyzer.