# RLO: Volume of Distribution

## Sample calculations

A patient weighing 60 kilograms is given a 1000 microgram dose of Drug A. Drug A distributes extensively into tissues, so that only a fraction of the original dose remains within the plasma. On measuring the plasma concentration, we get a value of 2 micrograms per litre. Because of the distribution into tissues, it appears that we have diluted the dose into a much larger volume of plasma than is actually there. In order to account for the entire initial drug dose and the 2 micrograms per litre plasma concentration, in this patient we would need a plasma volume of 1000 micrograms divided by 2 micrograms per litre or 500 litres. if this volume is further divided by the patient's body weight, the result is a value that can be useful in calculations for other patients: 500 litres divided by 60 kilograms equals 8.33 litres per kilogram.

In another example, the same patient is given 350 milligrams of Drug B, which distributes throughout extracellular fluid, but not readily into tissues. On measuring a peak level, we may get a value of 20 milligrams per litre. Dividing the 350 milligram dose by 20 milligrams per litre gives us 17.5 litres of plasma. Further dividing this by the patient's weight gives us an apparent volume of distribution for Drug B of 0.29 litres per kilogram.

The difference between the apparent volumes of distribution of these two drugs is due to their differing lipid vs water solubilities and plasma protein vs tissue binding characteristics. Drug A has high lipid solubility and exhibits extensive tissue binding while Drug B is more water soluble, less lipid soluble, and therefore distributes into the extracellular fluid only.

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