Mathematical Model of Potassium Profiling in Chronic Dialysis

Potassium balance is a difficult task in hemodialysis: low potassium in the dialysate is associated with a high risk of sudden cardiac death, whereas excessive dialysate potassium may provoke insufficient removal and hyperkalemia. A better understanding of the problem can be achieved with the use of mathematical models of solute kinetics. This study is aimed at presenting an improved model of solute kinetics and fluid shifts during hemodialysis. It comprises a 2-compartment (intracellular and extracellular) description of sodium, potassium, and urea, including volume fluid shifts induced by osmotic forces. Compared with previous versions, the model also incorporates active Na+ - K+ transport across the cellular membrane via the sodium-potassium pump. Simulations in chronic conditions, concerning both a 4-h standard hemodialysis and the subsequent 20 h interdialytic period, provide values of solute extracellular concentrations, fluid volumes, and potassium Nernst potential, in agreement with literature. The model predicts that the active Na+ - K+ transport decreases during the session (mainly due to a decrease in extracellular potassium) but increases in the inter-dialytic period. Extracellular potassium exhibits a rebound in the interdialytic phase, already evident in the first hours. The model also provides preliminary testable predictions on the patterns of intracellular sodium and potassium concentrations, which require further validation based on in vivo data. Particularly, assuming no residual potassium removal from the organism, the intracellular K+ concentration assumes higher values in the chronic subject compared with the healthy basal conditions. Finally, hemodialysis with profiled potassium (higher in the first half, reduced in the second) is simulated, to point out the advantages compared with the standard session. In perspective, the model can be used to optimize the dialysis treatment on the basis of profiled dialysate concentrations and, with ad hoc in vivo measurements, to provide deeper insight into the mechanisms of internal potassium balance.