INTRODUCTION AND AIMS: Magnesium (Mg++) is frequently neglected cation in hemodialysis (HD), even though serum Mg++ is causally associated with cardiovascular outcomes in these patients. Often HD patients are prescribed with dialysate Mg++ (DMg) of 0.5 mM. It is not known if this concentration is adequate in HD patients. In this work, we propose a mathematical model of Mg++ kinetics during HD. The model can assist in optimizing the DMg++ concentration.
METHODS: Two patients were put on 0.5 mM DMg++; pre- and post-HD total Mg++ and albumin concentration were measured. Further, total spent dialysate was collected to quantify the net Mg++ exchange during a session. We assumed that Mg++ is distributed in plasma and interstitial pool. Though Mg++ is also present in intracellular pool, it is assumed that Mg++ there is not available for exchange due to very high Mg++ binding with intracellular proteins. Albumin-Mg++ binding is accounted for in the model - a three-binding site model is assumed. Binding affinity is adjusted to obtain the end-HD Mg++ concentration and keep pre-HD free Mg++ fraction at ~30%. This two-compartmental patient model is connected to a spatiotemporal model representation of a dialyzer where serum Mg++ exchanges with DMg++ (Figure 1A). In dialyzer, we account for the Gibbs-Donnan effect and diffusive-convective exchange.
RESULTS: Dialysis parameters and measured concentration data for two patients are given in Table 1. With an assumed inter-compartmental mass transfer rate of 1000 mL/min and a dialyzer area mass-transfer coefficient 1200 mL/min, we obtained net removal of 259 mg and 72 mg in patient 1 and 2, respectively. The measured removal in spent dialysate is 297 mg and 96 mg in patient 1 and 2, respectively. Time-course of serum Mg++ kinetics is given in Figure 1B.
CONCLUSIONS: HD patients are often prescribed a low DMg++ concentration, resulting in loss of Mg++ during HD. Our model slightly underestimates the total Mg++ loss during single session. Introduction of intracellular Mg++ pool may improve the prediction. To the best of our knowledge this is the first model of Mg++ kinetics during HD with the aim to personalize the DMg++ prescription. Further validation of the model is ongoing.
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