Comparing the Voets equation and the Adrogue-Madias equation for predicting the plasma sodium response to intravenous fluid therapy in SIADH patients

Abstract

Background The syndrome of inappropriate antidiuretic hormone secretion (SIADH) is one of the most common causes of hypotonic hyponatremia. In our previous work, we have derived a novel model (Voets equation) that can be used by clinicians to predict the effect of crystalloid intravenous fluid therapy on the plasma sodium concentration in SIADH. Methods In this retrospective chart review, the predictive accuracy of the Voets equation and the Adrogue-Madias equation for the plasma sodium response to crystalloid infusate was compared for fifteen plasma sodium response measurements (n = 15) in twelve SIADH patients. The medical records of these patients were accessed anonymously and none of the authors were their treating physicians. The Pearson correlation coefficient r and corresponding p-value were calculated for the predictions by the Voets model compared to the measured plasma sodium response and for the predictions by the Adrogue-Madias model compared to the measured plasma sodium response. Results and conclusion The presented results show that the Voets model (r = 0.94, p < 0.001) predicted the aforementioned plasma sodium response significantly more accurately than the Adrogue-Madias model (r = 0.49, p = 0.07) in SIADH patients and could therefore be a clinically useful addition to the existing prediction models.

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“…For this particular scenario, we believe that the Voets equation-Eq. (1) below-is conceptually better suited than the Adrogue-Madias model, as previously shown for SIADH patients: [8,9] Here, the parameters Δ[Na + ] p , [Na + ] p , V i , TBW , O i , and O u represent the predicted change in plasma sodium concentration, initial plasma sodium concentration, infusate volume, total body water, infusate osmolarity (which equals infusate tonicity for crystalloid fluids), and urine osmolarity, respectively [8]. Suppose that a PDC is applied to the previously presented patient with total body water of 31 L, as estimated from her body weight, and that her urine osmolarity is clamped at approximately 250 mOsmol/L, which corresponds to her urine osmolarity on admission.…”

“…For this particular scenario, we believe that the Voets equation—Eq. ( 1 ) below—is conceptually better suited than the Adrogue-Madias model, as previously shown for SIADH patients: [ 8 , 9 ] …”

“…This is desirable as PDC merely sets the stage for a controlled correction of the plasma sodium concentration; it should not in itself induce significant changes in free water clearance. According to the Voets equation, her predicted change in plasma sodium concentration in response to a 0.50L 3.0%-NaCl bolus (osmolarity: 1,026 mOsmol/L) would be 9.1 mmol/L: [8] By contrast, the modified Adrogue-Madias equation estimates the net effect of a 0.50L 3.0%-NaCl bolus (sodium concentration: 513 mmol/L) on the plasma sodium concentration as follows: [4,9] Although no prediction model is infallible and a margin of error is inevitable, this relative underestimation of 2.5 mmol/L could encourage physicians to administer larger volumes of saline to the patient than the Voets equation suggests, potentially causing an overly rapid correction of the plasma sodium concentration. In a similar vein, a 3.0%-NaCl bolus of 0.75L, required to increase this patient's plasma sodium concentration with 10 mmol/L according to the…”

“…A major and frequently cited issue with this model is that it solely looks at the redistribution of crystalloid infusate and disregards any subsequent renal water and solute handling. Therefore, calculations according to the Adrogue-Madias equation are short-term predictions, and their accuracy quickly breaks down as time passes [ 8 , 9 ]. Ignoring renal infusate handling will lead to an imprecise prediction of the “net”—clinically relevant—effect of saline infusion on the plasma sodium concentration.…”

“…This model is based on the electrolyte-free water balance that considers both infusate input and renal output under the condition of relatively fixed urine osmolarity. Therefore, it is an ideally suited model to predict the net change in plasma sodium concentration in response to crystalloid infusate boluses with a PDC (dubbed “therapeutic SIADH”) [ 8 , 9 ]. Because sudden changes in endogenous ADH release are not an issue with a PDC, the patient essentially has a fixed urine osmolarity.…”