Prediction of dysnatremias in critically ill patients based on the law of conservation of mass. Comparison of existing formulae

Background: We aimed to examine the predictive value of a novel mathematical formula based on the law of conservation of mass in calculating sodium changes in intensive care unit patients and compare its performance with previously published formulae. Methods: 178 patients were enrolled from 01/2010 to 10/2013. Plasma and urine were collected in two consecutive 8-hour intervals and the sodium was measured. The predicted sodium concentration was calculated based on previous equations and our formula. The two 8-hour period (epoch 1 and 2) results were compared. Variability of predicted values among the measured range of serum sodium levels were provided by Bland-Altman plots with bias and precision statistics. Comparison of the results was performed with the statistical model of the Percentage Similarity. Results: 47.19% patients had dysnatremias. The bias ± SD with 95% limits of agreement for sodium levels were -1.395±3.491 for epoch 1 and -1.623 ±11.1 for epoch 2 period. Bland-Altman analysis for the epoch 1 study period had the following results: -0.8079±3.447 for Adrogué–Madias, 0.56±9.687 for Barsoum–Levine, 0.1412±3.824 for EFWC and 0.294±4.789 for Kurtz–Nguyen formula. The mean similarity, SD and coefficient variation for the methods compared with the measured sodium are: 99.56%, 3.873, 3.89% epoch 1, 99.56%, 1.255, 1.26% for epoch 2, 99.77%, 1.245, 1.26% for Adrogue-Madias, 100.1%, 1.337, 1.34% for Barsoum-Levine, 100.1%, 1.704, 1.7% for Nguyen, 100.1%, 1.370, 1.37% for ECFW formula. Conclusions: The law of conservation of mass can be successfully applied for the prediction of sodium changes in critically ill patients.