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

Hypertonic Saline Infusion for Hyponatremia: Limitations of the Adrogué-Madias and Other Formulas

Hypertonic saline infusion is used to correct hyponatremia with severe symptoms. The selection of the volume of infused hypertonic saline ( VInf ) should address prevention of overcorrection or undercorrection. Several formulas computing this VInf have been proposed. The limitations common to these formulas consist of (1) failure to include potential determinants of change in serum sodium concentration ([ Na ]) including exchanges between osmotically active and inactive sodium compartments, changes in hydrogen binding of body water to hydrophilic compounds, and genetic influences and (2) inaccurate estimates of baseline body water entered in any formula and of gains or losses of water, sodium, and potassium during treatment entered in formulas that account for such gains or losses. In addition, computing VInf from the Adrogué-Madias formula by a calculation assuming a linear relation between VInf and increase in [ Na ] is a source of errors because the relation between these two variables was proven to be curvilinear. However, these errors were shown to be negligible by a comparison of estimates of VInf by the Adrogué-Madias formula and by a formula using the same determinants of the change in [ Na ] and the curvilinear relation between this change and VInf . Regardless of the method used to correct hyponatremia, monitoring [ Na ] and changes in external balances of water, sodium, and potassium during treatment remain imperative.

Ratio Profile: Physiologic Approach to Estimating Appropriate Intravenous Fluid Rate to Manage Hyponatremia in the Syndrome of Inappropriate Antidiuresis

A hyponatremic patient with the syndrome of inappropriate antidiuresis (SIAD) gets normal saline (NS), and the plasma sodium decreases, paradoxically. To explain, desalination is often invoked: if urine is more concentrated than NS, the fluid's salts are excreted while some water is reabsorbed, exacerbating hyponatremia. But comparing concentrations can be deceiving. They should be converted to quantities because mass balance is key to unlocking the paradox. The [sodium] equation can legitimately be used to track all of the sodium, potassium, and water entering and leaving the body. Each input or output "module" can be counterbalanced by a chosen iv fluid so that the plasma sodium stays stable. This equipoise is expressed in terms of the iv fluid's infusion rate, an easy calculation called the ratio profile. Knowing the infusion rate that maintains steady state, we can prescribe the iv fluid at a faster rate in order to raise the plasma sodium. Rates less than the ratio profile may risk a paradox, which essentially is caused by an iv fluid underdosing. Selecting an iv fluid that is more concentrated than urine is not enough to prevent paradoxes; even 3% saline can be underdosed. Drinking water adds to the ratio profile and is underestimated in its ability to provoke a paradox. In conclusion, the quantitative approach demystifies the paradoxical worsening of hyponatremia in SIAD and offers a prescriptive guide to keep the paradox from happening. The ratio profile method is objective and quickly deployable on rounds, where it may change patient management for the better.

Edelman Revisited: Concepts, Achievements, and Challenges

The key message from the 1958 Edelman study states that combinations of external gains or losses of sodium, potassium and water leading to an increase of the fraction (total body sodium plus total body potassium) over total body water will raise the serum sodium concentration ([Na]_S), while external gains or losses leading to a decrease in this fraction will lower [Na]_S. A variety of studies have supported this concept and current quantitative methods for correcting dysnatremias, including formulas calculating the volume of saline needed for a change in [Na]_S are based on it. Not accounting for external losses of sodium, potassium and water during treatment and faulty values for body water inserted in the formulas predicting the change in [Na]_S affect the accuracy of these formulas. Newly described factors potentially affecting the change in [Na]_S during treatment of dysnatremias include the following: (a) exchanges during development or correction of dysnatremias between osmotically inactive sodium stored in tissues and osmotically active sodium in solution in body fluids; (b) chemical binding of part of body water to macromolecules which would decrease the amount of body water available for osmotic exchanges; and (c) genetic influences on the determination of sodium concentration in body fluids. The effects of these newer developments on the methods of treatment of dysnatremias are not well-established and will need extensive studying. Currently, monitoring of serum sodium concentration remains a critical step during treatment of dysnatremias.

Improving on the Adrogué-Madias Formula

The Adrogué-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 Δ[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 Δ[Na]. Therefore, we reversed the equation so that clinicians can enter the desired Δ[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.