#### Volume of distribution

##### Volume of distribution

As shown under therapeutic drug concentrations, drug action depends upon the concentration of the drug in the body. How do we determine the concentration when we administer a specific dose? If the human body would have been a single compartment (e.g. a 'bucket with water'), the concentration would be simply calculated via:

Concentration_{bucket} = Dose / Volume_{bucket}. However, the human body contains countless 'compartments' over which the drug can distribute. The concentration in all of these compartments will differ, depending on physicochemical properties like the size and lipophilicity of the drug (as explained in Transport over barriers).

Thus, in order to make any predictions on proper therapeutic drug concentrations, we need to know over which volume a drug can distribute, and how this compares to the concentation that is measured from a sample from one of these 'compartments'. Commonly, blood samples are withdrawn to obtain the concentration in the blood, and therefore we need to know how this concentration in the blood reflects the total dose in the body, and this can be determined if we know over ratio the drug is distributed in relation to the blood (plasma).

In example: if two drugs are administered in the same dose, but one drug has a lower plasma concentration, it is distributed more over other tissues. So this distribution factor is called the **Volume of distribution**, with units Liter (or Liter/kg). The unit Liter may seem misleading, as it is not an actual Volume. Instead it explains how much of a drug will be located in the plasma compared to other tissues. In other words (and a more exact definition): the volume of distribution (V_{d}) of a drug is the volume of fluid required to contain the total amount of drug in the body at the same concentration as that of the plasma.

V_{d} is a mathematically determined value and in general, the greater the V_{d}, the greater the diffusibility of the drug. It is impossible to measure the volume of distribution of a drug, but it can be calculated. This volume comes from the division of the administered dose by the concentration measured in a certain body fluid, usually plasma:

**V _{d} = Dose / C and C = Dose / V_{d}**

*In example:*

- If a drug with dose 25 units are dissolved in 100 litres. If the distribution would be equal among the whole volume we find the concentration to be 0,25 units/litre. The volume of distribution is then 25 / 0,25 = 100 litres.
- Now, the drug with dose 25 units is not equally dissolved among all 'compartments'. Instead (see the Figure) only 5 units can are found in the red/plasma compartment, which we will put on 5 litres. Then, the plasma concentration of drug is:
*C = 5 / 5 = 1 unit/litre*Now we can calculate Vd:

*V*_{d}= Dose / C = 25 / 1 = 25 litreIn other words, we would need 25 litres of plasma to have the full dose of 25 units at the same concentration of that measured in the plasma.

See how different volumes will effect drug concentrations by clicking here and selecting the simple container model (module 1).

Although everybody has a different Vd for different drugs, an average apparent Vd is determined for new drugs during development. This can help with the dosing of new drugs in new patients.

#### Volume of distribution

##### Volume of distribution

Although everybody has a different Vd for different drugs, an average apparent Vd is determined for new drugs during development. This can help with the dosing of new drugs in new patients. Example:Gentamicin: a dose of 180 mg is given by IV bolus to a person with a weight of 70 kg. The apparent volume of distribution of gentamicin is 0,31 L/kg. What is the initial concentration likely to be immediately after injection? 8.29 mg/L

Arithmetic Example - Gentamicin:

A dose of 180 mg is given by IV bolus to a person with a weight of 70 kg. The apparent volume of distribution of gentamicin is 0.31 L/kg. What is the initial concentration likely to be immediately after injection? (provide the answer in two decimals in mg/L)

Extra info: The Volume of Distribution of gentamicin in this person is 70 kg · 0.31 L/kg = 21.7 L. The initial concentration can be calculated according to: C = Dose / Vd = 180 · 21.7 L = 8.29 mg/L