Improving on the Adrogue-Madias Formula

The Adrogue-Madias (A-M) formula is correct as written, but technically, it only works when adding 1 L of an intravenous (IV) fluid. For all other volumes, the A-M algorithm gives an approximate answer, one that diverges further from the truth as the IV volume is increased. If 1 L of an IV fluid is calculated to change the serum sodium by some amount, then it was long assumed that giving a fraction of the liter would change the serum sodium by a proportional amount. We challenged that assumption and now prove that the A-M change in [sodium] ([Na]) is not scalable in a linear way. Rather, the Delta[Na] needs to be scaled in a way that accounts for the actual volume of IV fluid being given. This is accomplished by our improved version of the A-M formula in a mathematically rigorous way. Our equation accepts any IV fluid volume, eliminates the illogical infinities, and most importantly, incorporates the scaling step so that it cannot be forgotten. However, the nonlinear scaling makes it harder to obtain a desired Delta[Na]. Therefore, we reversed the equation so that clinicians can enter the desired Delta[Na], keeping the rate of sodium correction safe, and then get an answer in terms of the volume of IV fluid to infuse. The improved equation can also unify the A-M formula with the corollary A-M loss equation wherein 1 L of urine is lost. The method is to treat loss as a negative volume. Because the new equation is just as straightforward as the original formula, we believe that the improved form of A-M is ready for immediate use, alongside frequent [Na] monitoring.

Automated summary

The A-M formula provides an accurate calculation for 1 L of intravenous fluid, but only gives an approximate answer for other volumes due to the non-linear scalability of sodium change. It is important to adjust the Delta[Na] according to the actual volume of IV fluid being given in order to ensure safe sodium correction rates.