Correct Answer: A. 840 mEq
Sodium deficit calculation requires understanding total body water (TBW) distribution and the normal sodium concentration gradient. In a 70 kg adult male, TBW is approximately 60% of body weight = 70 × 0.60 = 42 L. Normal serum sodium is 135–145 mEq/L; here it is 120 mEq/L (hyponatremia). The sodium deficit formula is: Sodium deficit = TBW × (Normal Na – Actual Na) = 42 L × (140 – 120) = 42 × 20 = 840 mEq. This calculation assumes we use a normal reference sodium of 140 mEq/L (the midpoint of the normal range). The 42 L represents the volume in which sodium is distributed—primarily the extracellular and intracellular compartments. This is the standard approach taught in Indian medical schools (Harrison, Guyton) and used in clinical practice to guide hypertonic saline replacement in symptomatic hyponatremia. The answer reflects the total mEq of sodium needed to restore serum concentration to normal, though actual replacement is done cautiously to avoid osmotic demyelination syndrome.
Why the other options are wrong
B. 480 mEq — This results from using only extracellular fluid volume (ECF ≈ 14 L, or 20% of body weight) instead of total body water. The trap is confusing the compartment in which sodium is measured (plasma) with the compartment in which it is distributed (total body water). While sodium concentration is measured in plasma, the deficit calculation must account for the entire TBW volume to determine total replacement needed. C. 1400 mEq — This results from using 70 L (incorrectly assuming 100% of body weight as water) or from doubling the correct answer. This overestimation would lead to excessive sodium replacement, risking hypernatremia and osmotic complications. The error reflects misunderstanding that TBW is 60% (not 100%) of body weight in adult males. D. 280 mEq — This results from using only 14 L (plasma volume, ~20% of 70 kg) or from halving the correct answer. This underestimation would provide insufficient sodium replacement and fail to correct symptomatic hyponatremia. The trap is using plasma volume alone rather than the physiologically relevant TBW distribution volume.
High-Yield Facts
- Sodium deficit formula: TBW (L) × (Normal Na – Actual Na) mEq/L; use 140 mEq/L as normal reference
- TBW in adult males = 60% of body weight; in females and elderly = 50% due to higher fat content
- Normal serum sodium range = 135–145 mEq/L; values <120 mEq/L indicate severe hyponatremia requiring careful correction
- Correction rate limit = 8–10 mEq/L per 24 hours to avoid osmotic demyelination syndrome (ODS), a serious complication of rapid correction
- Hypertonic saline (3%) contains 513 mEq/L sodium; used only for symptomatic hyponatremia (seizures, altered mental status) with careful monitoring
Mnemonics
TBW-60-40 Rule Adult males: 60% TBW. Females/elderly: 50% TBW. Children: 70% TBW. Remember: more fat = less water. Deficit = TBW × ΔNa Sodium deficit (mEq) = Total Body Water (L) × (140 − current Na). Always use 140 as the target normal sodium for calculation.
NBE Trap
NBE pairs this calculation with compartment confusion—students often use plasma volume (14 L) or ECF (14 L) instead of TBW (42 L), leading to answers B and D. The trap tests whether students understand that sodium distributes across total body water, not just the measured plasma compartment.
Clinical Pearl
In Indian ICUs, hyponatremia is common in sepsis, SIADH (TB meningitis), and post-operative states. Calculating the deficit guides safe replacement—too fast causes ODS (permanent neurological damage), too slow risks cerebral edema. This formula is bedside essential for any physician managing critically ill patients.
_Reference: Guyton & Hall Textbook of Medical Physiology, Ch. 25 (Body Fluid Compartments); Harrison Principles of Internal Medicine, Ch. 297 (Hyponatremia)_