Sodium correction rate in hyponatraemia and hypernatraemia

Clinical background

Correcting severe hyponatraemia or hypernatraemia presents the clinician with a difficult balancing act. Correcting chronic hyponatraemia too quickly can precipitate osmotic demyelination, a serious and sometimes irreversible neurological complication. Correcting severe hyponatraemia too slowly is, on the other hand, associated with increased mortality, as a recent systematic review and meta-analysis of more than 11,000 patients showed [1]. The instrument in this calculator, the Adrogué–Madias formula, provides a mathematical starting point for choosing the infusion fluid and calculating the infusion rate so that correction falls within a safe band. It does not replace frequent sodium measurements, but it gives a structured first estimate rather than an unsystematic guess.

Calculating the rate of sodium correction

The formula estimates the change in serum sodium per litre of infusion fluid given:

$$\Delta S_{\text{Na}} = \frac{[\text{Na}]$${\text{inf}} + [\text{K}]{\text{inf}} - S_{\text{Na}}}{\text{TBW} + 1}

where total body water is calculated as:

$$\text{TBW} = \text{body weight} \times \text{body water fraction}$$

The variables are:

• $S_{\text{Na}}$: the patient's current serum sodium (mEq/L)
• $[\text{Na}]_{\text{inf}}$: the sodium concentration of the infusion fluid (mEq/L). Common values: 0.9% NaCl 154, 3% NaCl 513, Ringer's acetate 130, 0.45% NaCl 77, 5% glucose 0.
• $[\text{K}]_{\text{inf}}$: the potassium concentration of the infusion fluid, where potassium is added (mEq/L). Potassium in the infusion fluid contributes to the effective osmolality in the same way as sodium and is therefore included in the numerator.
• Body water fraction: adult man (0.6), adult woman/older man (0.5), older woman (0.45).
• The +1 in the denominator: the volume infused (1 litre) increases the body water and thereby slightly dilutes the effect.

When the desired change over 24 h has been specified, it is divided by the output of the formula to give the infusion rate (mL/h) required to reach the target.

The formula was presented by Adrogué and Madias in a review article in the New England Journal of Medicine in 2000 [2]. It is not derived from an empirical patient cohort but rests on a simplified physiological model in which body water is assumed to be a closed system and the only change in sodium and water balance is the infusion fluid given. This is a central limitation: the formula does not take account of ongoing renal losses, perspiration, or shifts in ADH level that may occur once treatment begins.

Interpretation in practice

The output of the formula is the expected change in serum sodium per litre of infusion fluid. The concrete decision is to choose a fluid whose sodium concentration gives a suitable ΔS-Na and then calculate the infusion rate from the desired daily target.

For chronic hyponatraemia the desired change over 24 h should be set at approximately 6 to 8 mEq/L. In acute hyponatraemia (duration under 48 hours) a faster correction may be accepted, up to 10 to 12 mEq/L over the first 24 hours, since the risk of osmotic demyelination is negligible when the brain has not had time to adapt.

Take a patient with a serum sodium of 108 mEq/L, weight 70 kg, body water fraction 0.6, to be given 3% NaCl: the formula gives (513 + 0 − 108) / (42 + 1) = 9.4 mEq/L per litre. If the target is 6 mEq/L over 24 hours, the infusion rate is approximately 6/9.4 × 1000/24 ≈ 27 mL/h. This is a starting point, not a prescription: the serum sodium should be checked every two to four hours during active correction.

Validation and performance

Since the formula is theoretically derived and not based on a patient cohort, external validation studies are decisive for judging its clinical reliability.

Mohmand and colleagues carried out a retrospective review of 62 adult patients with hyponatraemia treated with hypertonic saline at an American hospital over five years [3]. Among patients with a serum sodium below 120 mEq/L, the observed rise exceeded that predicted by the formula in 74.2% of cases. The mean actual correction in patients who were overcorrected was 2.4 times higher than predicted. In 11.3% of cases the rise exceeded 12 mEq/L over 24 hours. In 40% of cases the cause of overcorrection was documented water diuresis — that is, the body spontaneously began to excrete dilute urine as the underlying cause of water retention resolved — which the formula cannot anticipate.

A prospective multicentre study in seven critically ill children with acute dysnatraemia found, by contrast, good agreement between predicted and measured serum sodium [4]. The cohort is very small, however, and the results cannot be generalised to adults with chronic hyponatraemia.

Taken together, the evidence suggests that the formula tends to underestimate the correction in hyponatraemia, particularly at low starting values and when the underlying disturbance is reversible. For hypernatraemia, where water losses are more predictable and spontaneous water diuresis does not present the same problem, the formula appears to perform better, although direct validation studies in hypernatraemia are lacking in the literature.

Limitations

The formula presupposes a closed system without ongoing losses or gains. In reality, patients have continuous renal and insensible losses, and the treatment itself can precipitate changes. When the ADH level falls — for example on correction of hypovolaemia, or on withdrawal of a drug that caused SIADH — a sudden water diuresis can arise that drives the serum sodium up independently of the infusion. This is the commonest mechanism behind overcorrection, and the formula cannot capture it [3].

The body water fraction is a rough estimate. In obesity the actual fraction is lower than the standard values used, since adipose tissue contains less water. This leads the formula to underestimate the ΔS-Na in obese patients. Extremes of age, particularly small children, have different fractions that are not covered by the calculator's three categories.

The formula does not apply to patients with renal failure, in whom sodium and water balance is severely disturbed, or to patients receiving large volumes of fluid by other routes (enteral feeds, parenteral nutrition). It must not be used as the sole basis for setting the infusion rate without frequent laboratory checks.

A specific risk exists in patients with a very low serum sodium (below 115 mEq/L) and additional risk factors for osmotic demyelination: alcohol misuse, hypokalaemia, liver disease and malnutrition. Tandukar and colleagues identified 21 published cases of osmotic demyelination despite a correction rate below 10 mEq/L per 24 hours [5]. Twelve of these patients had a starting level below 115 mEq/L, and in all but one of them the correction had been at least 8 mEq/L. The authors recommend that these high-risk patients be limited to below 8 mEq/L per 24 hours, which is stricter than the general limit.

At the same time, a meta-analysis by Ayus and colleagues, comprising 11,811 patients with severe hyponatraemia in 16 studies, shows that slow correction (below 8 mEq/L per 24 hours) was associated with higher in-hospital mortality than faster correction (8 to 10 mEq/L per 24 hours), with 32 fewer deaths per 1,000 patients treated in the faster group [1]. The risk of osmotic demyelination was not significantly increased with faster correction. The tension between these findings means that the rate of correction must be individualised: fast enough to avoid persistent cerebral oedema, slow enough to protect the brain in high-risk patients.

References

1. Ayus JC, Moritz ML, Fuentes NA et al. Correction Rates and Clinical Outcomes in Hospitalized Adults With Severe Hyponatremia: A Systematic Review and Meta-Analysis. JAMA Intern Med 2025. PMID: 39556338
2. Adrogué HJ, Madias NE. Hyponatremia. N Engl J Med 2000;342(21):1581-9. PMID: 10824078
3. Mohmand HK, Issa D, Ahmad Z et al. Hypertonic saline for hyponatremia: risk of inadvertent overcorrection. Clin J Am Soc Nephrol 2007;2(6):1110-7. PMID: 17913972
4. Assadi F, Azarfar A, Bazargani B et al. Validity of the Adrogué-Madias Formula for the Management of Acute Dysnatremias in Critically Ill Children: A Prospective Multicenter Analysis. Pediatr Emerg Care 2023;39(9):707-714. PMID: 37167202
5. Tandukar S, Sterns RH, Rondon-Berrios H. Osmotic Demyelination Syndrome following Correction of Hyponatremia by ≤10 mEq/L per Day. Kidney360 2021;2(9):1415-1423. PMID: 35373113