A 20 year old female presents to your emergency service with severe head trauma

Question

A 20 year old female presents to your emergency service with severe head trauma from a fall. An MRI reveals swelling of her brain, but no sign of hemorrhage. You determine that removing 100 ml of intracellular fluid from her brain will greatly relieve the increasing intracranial pressure. Assuming she was isotonic upon presentation, what osmolarity would you need to achieve in her body to accomplish this? She weighs 60 kg and assume that her brain weighs 3 kg and is 70% water. 2) What volume of 10% mannitol would you need to add to get her to this osmolarity? The molecular weight of mannitol is 182.

Explanation / Answer

You have to assume that since the removal of 100 ml of fluid was already determined, the osmolarity was determined before arriving at the conclusion to remove the 100 ml. Also, you must assume that the number of particles in the brain before and after removing fluids would remain constant.

First you have to determine how much fluid is in the brain. Multiply 3 kg x 0.7 to get 2.1 kg, which is also equal to 2.1 L of fluid. Then you use this determine the number of particles present in the brain under isotonic conditions. If you use m/v=c, and v=2.1 L and c=300 mOsm/L, you get 630 mOsm of particles in the brain, which will remain constant.

Next, you have to determine what the osmolarity after you remove the 100 ml. So, using the same formula, m=630 mOsm, v=2.1 L - 0.1 L, you get 630 mOsm/2.0 L = 315 mOsm/L. This is your answer for the first part. This makes sense because the osmolarity is hypertonic. By making the fluid surrounding the brain hypertonic, it will draw out fluid from the brain cells, effectively reducing the swelling.

Then, for part two, you must figure out how many Osmoles are in the 10% mannitol solution. So there is 100 g mannitol / L. Then divide by the molecular weight to get 0.549 mol or 549 mmol in the solution. Then there is 1 mOsm/1 mmol, so there are 549 mOsm in the 10% solution.

Once you have this, you go back to the equation m/v=c and use the osmolarity you figured out in part 1 to determine the volume needed to achieve this osmolarity. so, 549 mOsm/ 315 mOsm/L = 1.74 L of mannitol solution needed.

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