A patient has the following volumes of distribution: deuterium oxide: 40 liters

Question

A patient has the following volumes of distribution:

deuterium oxide: 40 liters

inulin: 13 liters

Evans blue: 2.8 liters

Her plasma shows a freezing point depression of 0.53 degrees C. For an ideal solution, a 1 OsM solution

depresses the freezing point 1.86 degrees C.

The osmolarity calculated is 0.285 OsM.

Question: The patient ingests 1 L of water containing 0.3 moles of urea, all of which is absorbed. Determine the effects of this procedure on the water and solute in the ECF and ICF after equilibrium has occurred.

Total body

ECF

ICF

Solute

Volume

Osmolarity

Total body

ECF

ICF

Solute

Volume

Osmolarity

Explanation / Answer

Given,

deuterium oxide: 40 liters indicates Total body water (TBW)

inulin: 13 liters indicates Extracellular fluid (ECF)

Evans blue: 2.8 liters indicates plasma volume

Now, Intracellular fluid (ICF) = total body water - ECF = 40-13 = 27 liters

Osmolarity = 0.285 OsM which is same for total body, plasma, ECF and ICF

Now, for urea moles added = 0.3 moles or 0.3 osmoles

Fluid added = 1 liter

For Total Body,

TBW initial = 40 liter

TBW final = 40 + 1 = 41 (because 1 liter water was ingested)

solute initial = 0.285 osmoles/l x 40 l = 11.4 osmoles

solute final = 11.4 + 0.3 = 11.7 osmoles

Final osmolarity = 11.7 osmoles/41 liter = 0.2854 osM

Osmolarity will be same for Total body, ECF and ICF

Urea distributes itself to equilibrium so, 1/3 will add on ECF i.e. 0.1 osmole and 2/3 will add to ICF i.e. 0.2 osmole

For ECF

ECF solute initial = old ECF volume x 0.285 = 13 x 0.285 = 3.705 osmoles

ECF solute final = 3.705 + 0.1 = 3.805 osmoles

ECF volume final = 4.005/0.2854 = 13.33 liter

For ICF

ICF solute initial = 27 x 0.285 = 7.695 osmoles

ICF solute final = 7.695 + 0.2 = 7.895 osmoles

ICF final volume = 7.895/0.2854 = 27.66 liter

Now, the table can be filled as

Total body

ECF

ICF

Solute

11.7 osmoles

3.805 osmoles

7.895 osmoles

Volume

41 liter

13.33 liter

27.66 liter

Osmolarity

0.2854 OsM

0.2854 OsM

   0.2854 OsM

Total body

ECF

ICF

Solute

11.7 osmoles

3.805 osmoles

7.895 osmoles

Volume

41 liter

13.33 liter

27.66 liter

Osmolarity

0.2854 OsM

0.2854 OsM

   0.2854 OsM

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