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The free water deficit calculation estimates how much pure (electrolyte-free) water must be administered to correct hypernatraemia — a serum sodium above 145 mEq/L. Hypernatraemia always implies a deficit of free water relative to the body's solute content, because sodium concentration rises when water is lost in excess of sodium, or when sodium is retained in excess of water. The calculation uses total body water (TBW) — estimated from weight, sex, and age — as a surrogate for the body's water compartment, then determines how much additional water would be needed to dilute the existing solute load down to a normal sodium of 140 mEq/L. The formula is based on the conservation of total body osmoles: current TBW × current Na = desired TBW × desired Na, from which the deficit can be derived. This is a minimum estimate — it does not account for ongoing water losses (insensible losses, urine output, fever, sweating) that must be replaced simultaneously. Correction rate is critically important: overly rapid correction (>10–12 mmol/L per day) risks cerebral oedema as brain cells that have adapted to the hyperosmolar environment by accumulating idiogenic osmoles are rapidly re-swollen when osmolality falls too fast. The free water deficit should be replaced gradually over 48–72 hours in most cases of chronic hypernatraemia. Acute hypernatraemia (present for <24 hours) can be corrected more rapidly. The choice of replacement fluid (enteral water, 5% dextrose, or 0.45% saline) depends on the severity of the sodium and associated volume status.
Free water deficit (L) = TBW × (1 - 140 / Serum Na+); where TBW = 0.6 × weight (men), 0.5 × weight (women), 0.45 × weight (elderly women)
- 1Determine total body water (TBW): 0.6 × weight in kg for men; 0.5 × weight in kg for women; 0.45 × weight in kg for elderly women (>65 years). Children use higher fractions (~0.6–0.7). The fraction is lower in women and the elderly because of higher body fat content (fat contains little water).
- 2Apply the formula: Free water deficit = TBW × (1 - 140 / Serum Na+). This gives the litres of pure water needed to correct sodium from its current level to 140 mEq/L.
- 3Calculate the target correction rate: a maximum of 10–12 mmol/L per day (about 0.5 mmol/L per hour) to prevent cerebral oedema. Divide the total deficit by the number of hours needed for correction.
- 4Choose the replacement fluid: enteral free water or 5% dextrose in water (D5W) for pure free water; 0.45% saline (half-normal saline) provides half free water and half isotonic saline, useful when mild volume depletion coexists.
- 5Calculate the infusion rate based on your chosen fluid: for D5W, each litre provides 1 litre of free water; for 0.45% saline, each litre provides approximately 0.5 litres of free water.
- 6Add ongoing losses to the calculated deficit: insensible losses (~500–700 mL/day), urine output (measured hourly), fever (add ~100–150 mL/day per degree Celsius above 37), and any diarrhoea or nasogastric losses.
- 7Monitor serum sodium every 4–6 hours during active correction and adjust the infusion rate accordingly — the formula provides a starting estimate, not a fixed prescription.
Correct no faster than 10–12 mmol/L/day. At current Na 158, target no lower than 146 on day 1. Replace over 48–72 hours.
For chronic hypernatraemia, 4 L of free water deficit should be replaced over 48 hours minimum (≈83 mL/hour of D5W if no ongoing losses). Add insensible losses (~700 mL/day) and measured urine output. Re-check Na every 4–6 hours and titrate.
Deficit alone is 4 L, but ongoing urine losses are 8 L/day — the ongoing losses massively exceed the deficit and must be replaced concurrently.
In DI, the free water deficit underestimates total replacement needs because ongoing losses are enormous. DDAVP should be administered to stop the polyuria. Until DDAVP acts, replace urine output mL-for-mL with D5W or 0.45% saline plus the calculated deficit. After DDAVP, titrate replacement to sodium trend every 2 hours.
Acute hypernatraemia (<24 hours) can be corrected more rapidly than chronic — aim for 1–2 mmol/L/hour, not limited to 0.5 mmol/L/hour.
Because hypernatraemia is acute (idogenic osmoles not yet accumulated), the brain has not adapted and rapid correction carries less cerebral oedema risk. Nonetheless, monitor carefully. Replace 4.64 L over 8–12 hours (D5W at ~500 mL/hour initially) and reassess sodium frequently.
Volume depletion requires partial isotonic resuscitation first, then 0.45% saline for combined electrolyte and free water replacement.
In hypernatraemia with haemodynamic compromise, the priority is restoring circulating volume with normal saline (which, though hypertonic relative to current state, is still hypotonic compared to the patient's plasma). Once haemodynamically stable, switch to 0.45% saline or D5W for free water deficit correction. The 2.3 L deficit should be replaced over 48 hours alongside ongoing losses.
ICU fluid management: guiding the rate and volume of D5W or 0.45% saline replacement in patients with hypernatraemia from sepsis, DI, or decreased fluid intake.
Neurosurgical wards: managing hypernatraemia after pituitary surgery or traumatic brain injury where central DI is common and ongoing losses dominate the clinical picture.
Geriatric medicine: estimating free water replacement needs in nursing home residents with chronic hypernatraemia from inadequate fluid intake, dementia-related dipsia impairment, or diuretic overuse.
Neonatal and paediatric intensive care: calculating careful correction volumes in neonatal hypernatraemia from inadequate breastfeeding or congenital DI, where brain vulnerability is highest.
Endocrinology clinics: used alongside desmopressin dosing in outpatients with central DI to estimate daily free water requirements and guide DDAVP titration based on urine osmolality and serum sodium trends.
Central Diabetes Insipidus — Ongoing Losses Dominate
In complete central DI (e.g., post-neurosurgical or traumatic brain injury), urine output can reach 10–20 litres per day of dilute urine. The free water deficit formula captures the static historical deficit but the ongoing losses vastly exceed it. The priority is immediate DDAVP administration alongside hourly urine output replacement with D5W or 0.45% saline. Serum sodium can rise by 10–20 mmol/L per hour if losses are not replaced. These patients require ICU monitoring with a urinary catheter and sodium checked every 1–2 hours until DDAVP takes effect.
Hypernatraemia in Burns Patients
Major burns cause massive evaporative water loss from denuded skin surfaces. Standard burn formulae (Parkland, Brooke) calculate isotonic fluid resuscitation for the first 24–48 hours, but do not fully account for the subsequent free water loss phase. Hypernatraemia is common in burn patients beyond the resuscitation phase. Replacement requires D5W or 0.45% saline in addition to the ongoing burn wound fluid losses, which can be estimated as 1 mL/kg/% burn area/hour of evaporative loss using specialised burn care protocols.
Osmotic Diuresis from Uncontrolled Diabetes
In hyperglycaemic hyperosmolar state (HHS), glucosuria drives an enormous osmotic diuresis. Patients lose hypotonic urine (urine Na typically 40–70 mEq/L) relative to plasma, causing hypernatraemia on top of the hyperosmolality from glucose. The free water deficit must be calculated accounting for the effect of glucose on plasma osmolality. Additionally, as insulin is given and glucose normalises, sodium will rise further (glucose was diluting the effective sodium) — the corrected sodium (add 1.6 mEq/L Na per 100 mg/dL glucose above 100) should be calculated to anticipate this.
Hypernatraemia After Resuscitation with Hypertonic Sodium Bicarbonate
Cardiac arrest resuscitation sometimes involves multiple ampules of 8.4% sodium bicarbonate (each 50 mL ampule contains ~50 mEq of NaHCO3 — approximately 1000 mEq/L sodium). This is a frequent iatrogenic cause of acute hypernatraemia in the ICU. Unlike chronic hypernatraemia, this is acute (no idiogenic osmole accumulation), so correction can be more rapid (1–2 mmol/L/hour) but still requires careful monitoring. The formula applies, but TBW should use lean body weight in post-resuscitation patients who may have received large volumes of isotonic fluids, diluting lean mass estimates.
Breastfeeding Hypernatraemia in Neonates
Neonatal hypernatraemia from insufficient breastfeeding is a paediatric emergency. Neonates have high TBW fractions (0.75–0.80) and high insensible losses relative to body size. Hypernatraemia develops rapidly when milk intake is inadequate. Correction must be exceptionally gradual (target <10–12 mmol/L per day, ideally 8 mmol/L per day) because neonatal brains are particularly vulnerable to cerebral oedema from rapid correction. Supplemental feeding (formula or expressed breast milk) alongside close monitoring is the mainstay of treatment.
| Population | TBW Fraction | Example: 70 kg | Notes |
|---|---|---|---|
| Adult men (18–64) | 0.60 | 42 L | Standard male fraction |
| Adult women (18–64) | 0.50 | 35 L | Lower due to higher adipose proportion |
| Elderly men (>65) | 0.50 | 35 L | Reduced lean mass with age |
| Elderly women (>65) | 0.45 | 31.5 L | Lowest fraction — highest fat-to-lean ratio |
| Children (approx) | 0.60–0.70 | Varies | Consult paediatric tables; higher in infants |
| Obese patients | Use lean/adjusted BW | Varies | Standard fraction overestimates TBW if applied to total weight |
Why is the maximum correction rate 10–12 mmol/L per day?
When plasma sodium rises chronically above normal, brain cells lose water osmotically and compensate by accumulating intracellular organic osmoles (idiogenic osmoles — taurine, glutamate, myo-inositol, betaine). This adaptation prevents brain shrinkage. If sodium is corrected too rapidly, plasma osmolality falls faster than brain cells can export these idiogenic osmoles, causing water to rush into brain cells — leading to cerebral oedema, seizures, and herniation. Limiting correction to 10–12 mmol/L per day (or 0.5 mmol/L per hour) gives brain cells time to adjust safely.
Does the formula account for ongoing losses?
No. The free water deficit formula calculates only the static deficit needed to raise TBW to normalise serum sodium. It does not include ongoing insensible losses (~500–700 mL/day in a calm, afebrile adult), urine output (which must be measured and replaced hourly in DI), fever losses (~100–150 mL/day per degree above 37°C), or GI losses. All ongoing losses must be added to the total fluid replacement plan.
What fluid should be used to correct hypernatraemia?
The fluid choice depends on severity and coexisting volume status. Pure free water: enteral (nasogastric or oral water) if gut is accessible — most physiological and avoids IV complications. IV options: 5% dextrose in water (D5W) provides free water once glucose is metabolised; 0.45% normal saline (half-normal saline) provides approximately 50% free water and 50% isotonic saline — useful when mild volume depletion coexists. Normal (0.9%) saline is used only in haemodynamic compromise and does not correct hypernatraemia effectively — it is still hypertonic relative to the elevated serum sodium in most patients.
How should I monitor during correction?
Check serum sodium every 4–6 hours initially during active correction. If sodium is falling faster than 0.5 mmol/L per hour, slow the infusion rate. If sodium is falling slower than planned, ensure ongoing losses are being replaced adequately. Urine output should be monitored hourly — especially in DI. Neurological status should be assessed regularly for signs of cerebral oedema (headache, nausea, seizures) which would indicate over-rapid correction.
What is the aetiology of hypernatraemia — what causes free water loss?
Hypernatraemia develops from inadequate free water intake relative to losses. Common causes: (1) Insensible losses — fever, burns, hyperventilation, hot environment. (2) Renal free water loss — central DI (ADH deficiency), nephrogenic DI (ADH resistance), osmotic diuresis (glucose, urea, mannitol). (3) GI losses — osmotic diarrhoea, lactulose use, vomiting (water lost relative to sodium). (4) Iatrogenic — hypertonic saline, sodium bicarbonate infusion. (5) Inadequate access to water — unconscious patients, frail elderly, infants.
Is the TBW fraction different in obese patients?
Yes. Adipose tissue contains very little water (~10% water content vs ~70% for lean tissue). In morbidly obese patients, using the standard TBW fraction (0.6 for men, 0.5 for women) based on total body weight significantly overestimates TBW. Some guidelines recommend using lean body weight or an adjusted body weight for TBW calculation in obese patients, which gives a smaller (and more accurate) TBW estimate.
Can I use this formula in children?
The formula applies in children but TBW fractions differ: neonates have ~0.75–0.80 of body weight as water; infants ~0.65; young children ~0.60. Children are at higher risk of rapid sodium changes due to their smaller TBW reserve. Paediatric nephrology guidelines recommend conservative correction rates of ≤10 mmol/L per day (ideally ~8 mmol/L per day) and more frequent monitoring. Always consult paediatric-specific references for management in this age group.
What if the hypernatraemia is from sodium excess rather than water deficit?
The free water deficit formula assumes hypernatraemia is due to water loss. In the rare scenario of sodium excess (e.g., iatrogenic hypertonic saline administration, saltwater near-drowning, hyperaldosteronism), the patient may not have a true TBW deficit — they have excess sodium with normal or elevated TBW. In these cases, the priority is promoting renal sodium excretion (using loop diuretics) alongside free water or D5W replacement. The formula still provides a useful starting estimate of replacement volume, but the approach must account for the sodium overload rather than pure water deficit.
プロのヒント
Never use the free water deficit formula as a set-and-forget prescription. It gives a starting point. Recalculate the remaining deficit every 4–6 hours using the new serum sodium and current TBW. Clinical reassessment and serial sodium checks are non-negotiable. A useful practical rule: lower the sodium by no more than 10–12 mEq/day; if you start at Na 160, aim for Na 148–150 by end of day 1, then 138–140 by end of day 2.
ご存知でしたか？
The term 'idiogenic osmoles' was coined to describe the brain's survival strategy during hypernatraemia. These tiny organic molecules — including taurine, myo-inositol, and glutamine — are synthesised or imported into brain cells to prevent dangerous cellular dehydration. They are so effective that patients with chronic sodium levels of 170–180 mEq/L can be surprisingly alert — a level that would cause coma if reached acutely. These same molecules become the brain's enemy during correction, retaining water in brain cells if sodium falls too fast.
参考文献
- ›Adrogue HJ, Madias NE — Hypernatraemia. NEJM 2000
- ›Spasovski G et al. — Clinical practice guideline on hyponatraemia. Eur J Endocrinol 2014
- ›UpToDate — Treatment of hypernatraemia in adults
- ›Sterns RH — Disorders of plasma sodium. NEJM 2015
- ›NICE — Intravenous fluid therapy in adults in hospital (CG174)