Derivation of a new formula for calculating urinary electrolyte-free water clearance based on the Edelman equation

In evaluating the renal mechanisms responsible for the generation of the dysnatremias, an analysis of free water clearance (FWC) and electrolyte-free water clearance (EFWC) is often utilized to characterize the rate of urinary free water excretion in these disorders. Previous analyses of FWC and EFWC have failed to consider the relationship among plasma water Na(+) concentration ([Na(+)](pw)), total exchangeable Na(+) (Na(e)), total exchangeable K(+) (K(e)), and total body water (TBW); ( Edelman IS, Leibman J, O'Meara MP, and Birkenfeld LW. J Clin Invest 37: 1236 - 1256, 1958). In their derivations, the classic FWC and EFWC formulas fail to consider the quantitative and physiological significance of the slope and y-intercept in this equation. Consequently, previous EFWC formulas incorrectly assume that urine is isonatric when [Na(+) + K(+)](urine) = [Na(+)](p) or [Na(+) + K(+)](urine) = [Na(+)](p) + [K(+)](p) (where [Na(+)](p) and [K(+)](p) represent plasma Na(+) and K(+) concentrations, respectively). Moreover, previous formulas cannot be utilized in the setting of hyperglycemia. In this article, we have derived a new formula termed modified electrolyte-free water clearance (MEFWC) for determining the electrolyte-free water clearance, taking into consideration the empirical relationship between the [Na(+)](pw) and Na(e), K(e), and TBW: MEFWC = V [1 - 1.03[Na(+) + K(+)](urine)/([Na(+)](p) + 23.8)]. MEFWC, unlike previous formulas, is derived based on the requirement of the Edelman equation that urine is isonatric only when [Na(+) + K(+)](urine) = (Na(e) + K(e))/TBW = 0.97[Na(+)](p) + 23.1. Furthermore, since we have shown that the y-intercept in the Edelman equation varies directly with the plasma glucose concentration, in patients with hyperglycemia, MEFWC = V [1 - 1.03[Na(+) + K(+)](urine)/{[Na(+)](p) + 23.8 + 1.6/100)([glucose](p) - 120)}]. The MEFWC formula will be especially useful in assessing the renal contribution to the generation of the dysnatremias.