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.