5 g mannitol was injected intravenously. 40% of mannitol is excreted. After equilibrium, plasma concentration of mannitol is 30 mg%. Calculate extracellular fluid volume.
## Core Concept
The problem involves calculating the extracellular fluid volume using the concept of mannitol distribution. Mannitol is a substance that distributes primarily within the extracellular fluid (ECF) compartment and is often used to measure ECF volume. It is not significantly metabolized and is freely filtered by the kidneys.
## Why the Correct Answer is Right
To calculate the extracellular fluid volume, we first need to understand that mannitol distributes throughout the extracellular space. Given that 5 g of mannitol was injected and 40% of it is excreted, 60% remains in the body. The amount remaining is 5 g * 0.6 = 3 g. The plasma concentration of mannitol after equilibrium is 30 mg%, or 30 mg/dL. To find the volume of distribution of mannitol (which approximates the extracellular fluid volume), we use the formula: Volume = Amount / Concentration. First, convert the amount to milligrams: 3 g = 3000 mg. The concentration is 30 mg/dL.
## Why Each Wrong Option is Incorrect
**Option A:** This option would be incorrect based on miscalculation or incorrect application of the formula.
**Option B:** Similarly, this would be incorrect for the same reasons as option A, likely due to a calculation error.
**Option C:** This option suggests a calculation that does not match the provided numbers and correct physiological application.
**Option D:** This is the correct calculation: if 3000 mg of mannitol results in a concentration of 30 mg/dL, then the volume is 3000 mg / 30 mg/dL = 100 dL or 10 liters.
## Clinical Pearl / High-Yield Fact
A key point to remember is that mannitol is used clinically to reduce intracranial pressure and to promote diuresis. Its distribution primarily in the extracellular space makes it useful for measuring ECF volume. The typical ECF volume in an adult is approximately 12-15 liters, which can vary based on body size and composition.
## Correct Answer: D. 10 liters