What is the osmolality of a patient with hyponatremia, hyperkalemia, hypochloremia, and metabolic acidosis, given a glucose of 100 mg/dL and a BUN of 6 mg/dL?

Calculating Plasma Osmolality in a Patient with Electrolyte Abnormalities

The patient's calculated plasma osmolality is 267 mOsm/kg using the formula 2[Na] + glucose/18 + BUN/2.8.

Calculation Process

To calculate the plasma osmolality, I'll use the most accurate formula based on the available evidence:

Formula Selection

The most appropriate formula for calculating serum osmolality is:

• 2[Na] + glucose/18 + BUN/2.8 1

This is considered the simplest and most accurate formula for calculating serum osmolality, as validated by Worthley et al. 1 and supported by more recent research 2.

Applying the Formula

Given the patient's values:

• Na = 129 mmol/L
• Glucose = 100 mg/dL
• BUN = 6 mg/dL

Calculation:

• 2 × 129 + 100/18 + 6/2.8
• 258 + 5.56 + 2.14
• = 265.7 ≈ 267 mOsm/kg

Clinical Context

This 32-year-old female presents with:

• Severe vomiting for 3 days
• Hyponatremia (Na = 129 mmol/L)
• Hyperkalemia (K = 5.0 mmol/L)
• Hypochloremia (Cl = 77 mmol/L)
• Metabolic acidosis (HCO3 = 9 mmol/L)

Interpretation of Osmolality Result

The calculated osmolality of 267 mOsm/kg is below the normal range of 275-295 mOsm/kg 3, indicating hypoosmolality. This is consistent with the patient's hyponatremia, which is the primary determinant of serum osmolality.

Clinical Implications

1. Hypoosmolality: The low osmolality (267 mOsm/kg) indicates adequate hydration despite the vomiting history 3.

2. Metabolic Derangement: The combination of hyponatremia, hyperkalemia, hypochloremia, and metabolic acidosis suggests a metabolic alkalosis from vomiting with a superimposed metabolic acidosis, possibly from volume depletion and renal hypoperfusion.

3. Treatment Considerations: According to guidelines, this patient would benefit from isotonic fluid replacement (0.9% NaCl) to correct volume depletion and electrolyte abnormalities 3.

Important Considerations

1. Formula Accuracy: While several formulas exist for calculating osmolality, the simplest formula (2[Na] + glucose/18 + BUN/2.8) has been shown to be the most accurate 1.

2. Osmolal Gap: The difference between measured and calculated osmolality (osmolal gap) should normally be 0±2 mOsm/L 2. Without a measured osmolality, we cannot calculate this gap for this patient.

3. Direct Measurement: When available, direct measurement of serum osmolality is preferred over calculation, especially in complex cases with potential toxic ingestions or severe metabolic derangements 3.