Immediately after mannitol administration and before osmotic diuresis takes place, the following profile is created in the serum: Na 120 mmol/L, Glucose 5 mmol/L, Urea 5 mmol/L, Mannitol 75 mmol/L, Osmolality 325 mOsmo/kg. Which of the following is true?
A. The calculated osmolarity (mOsmo/L) is 120×2 + 5/18 + 5/2.8 = 242 mOsmo/L; and as the measured osmolality is 325 mOsmo/kg, the osmol gap is 325 – 242 = 83 mOsmo/kg
B. The risk of cerebral edema is transiently increased before osmotic diuresis occurs because of the hyponatremia
C. Tonicity is the same as the calculated osmolarity, and in this case it is low.
D. Effective osmolality in this case is high, and so the risk of cerebral edema is decreased.
Answer: D is correct
Editor’s comment
In the calculation of osmolarity, division by 18 to glucose and 2.8 to urea is only necessary if they are expressed in mg/dL. If they are expressed in mmol/L, direct addition is enough. The calculated osmolarity is therefore 120×2 + 5 + 5 = 250 mOsmo/kg. The osmol gap is 325 – 250 = 75 mOsmo/kg. This gap is numerically exactly the mannitol concentration (i.e. 75 mmol/L) not involved in the calculation of osmolarity, but is measured by the osmometer (freezing point depression method), and hence the osmol gap. Note that strictly speaking, osmolality is measured by the osmometer, expressed in mOsmo/kg solvent, and weight of any solute content excluded. Osmolarity is calculated, expressed in mOsmo/L of solution, and solute content is included. It was found that a serum mannitol concentration of 75mmol/L (1365 mg/dL) might be expected to be associated with a serum sodium level of approximately 120 mmol/L. Because of this difference in the methodology of derivation, though the gap is numerically measured osmolality minus calculated osmolarity, it cannot be standardized to call this gap the osmolal gap or osmolar gap, and the term osmol gap has been suggested to evade the confusion.
It is not the hyponatremia per se that increases the risk of cerebral edema, nor is the measured osmolality or calculated osmolarity. It is the tonicity that is really related to the risk of cerebral edema. Another name for tonicity is effective osmolality, which is a measure of the ability of a solution to exert an osmotic pressure upon the membrane, and is numerically the concentration of the solutes that cannot cross the membrane. Only solutes that cannot cross the membrane (i.e. non-penetrating solutes) separating the two compartments generate an effective osmotic pressure (tonicity). Urea crosses the cell membrane easily and does not contribute to osmotic pressure (a penetrating solute, or an ineffective solute, another example is ethanol), but will be measured as part of the plasma osmolality by the osmometer, while effective solutes (such as sodium, glucose and mannitol) are confined largely to the extracellular fluid (ECF) compartment and contribute to both measured osmolality and effective osmolality (tonicity). In this case, the effective osmolality (tonicity) is 120×2 + 5 (glucose) + 75 (mannitol) = 320 mOsmo/kg (high), i.e. urea is not included. Because of this high tonicity, risk of cerebral edema is decreased, so D is the correct answer.
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