What is the estimated serum osmolality with Na 122 mmol/L and glucose 738 mg/dL?

Calculation of Serum Osmolality with Na 122 mmol/L and Glucose 738 mg/dL

The estimated serum osmolality using the standard formula is 285 mOsm/kg, calculated as 2 × Na (mEq/L) + glucose (mg/dL)/18 = 2 × 122 + 738/18 = 244 + 41 = 285 mOsm/kg.

Formula Selection and Calculation

The most accurate and widely accepted formula for calculating serum osmolality is:

Serum osmolality = 2 × [Na⁺] + glucose/18 + BUN/2.8

Since BUN was not provided in this case, we can use the simplified version:

Serum osmolality = 2 × [Na⁺] + glucose/18

Breaking down the calculation:

• Sodium contribution: 2 × 122 = 244 mOsm/kg
• Glucose contribution: 738/18 = 41 mOsm/kg
• Total calculated osmolality: 244 + 41 = 285 mOsm/kg

Clinical Significance and Interpretation

This calculated value of 285 mOsm/kg falls within the normal range of plasma osmolality (275-295 mOsm/kg) 1, despite the presence of:

• Hyponatremia (Na 122 mmol/L, below normal range of 135-145 mmol/L)
• Significant hyperglycemia (738 mg/dL, well above normal)

The normal-appearing osmolality despite hyponatremia can be explained by the osmotic contribution of the markedly elevated glucose, which is compensating for the low sodium level 2.

Corrected Sodium Consideration

It's important to note that the measured sodium is likely factitiously low due to the hyperglycemia. For a more accurate clinical assessment, sodium should be corrected for hyperglycemia:

For each 100 mg/dL glucose above normal, add 1.6 mEq/L to the measured sodium 3.

Assuming normal glucose of 100 mg/dL:

• Glucose elevation: 738 - 100 = 638 mg/dL
• Correction factor: 638 ÷ 100 × 1.6 = 10.2 mEq/L
• Corrected sodium: 122 + 10.2 = 132.2 mEq/L

This corrected sodium of 132.2 mEq/L is still slightly hyponatremic but much closer to normal range.

Clinical Implications

The combination of hyperglycemia (738 mg/dL) and hyponatremia (122 mmol/L) with a calculated osmolality of 285 mOsm/kg suggests:

1. The patient likely has uncontrolled diabetes with significant hyperglycemia
2. The hyponatremia is partially dilutional due to the osmotic effect of glucose drawing water into the extracellular space
3. Despite individual abnormalities in sodium and glucose, the overall osmolality remains within normal range due to their counterbalancing effects

Potential Pitfalls

1. Without BUN values, the calculation may slightly underestimate true osmolality 4
2. Calculated osmolality can sometimes differ from directly measured osmolality, particularly in patients with extreme values 5
3. The formula assumes no significant contribution from unmeasured osmoles (such as alcohols, mannitol, or other substances)

If clinical suspicion warrants, direct measurement of serum osmolality would be recommended to detect any osmolal gap that might indicate the presence of unmeasured osmotically active substances 6.