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

INTRODUCTION: 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. METHODS: 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. RESULTS: 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). CONCLUSIONS: 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.