Volume of distribution

The volume of distribution is given by the following equation:

${\displaystyle {V_{D}}={\frac {\mathrm {total\ amount\ of\ drug\ in\ the\ body} }{\mathrm {drug\ blood\ plasma\ concentration} }}}$

Therefore, the dose required to give a certain plasma concentration can be determined if the V_D for that drug is known. The V_D is not a physiological value; it is more a reflection of how a drug will distribute throughout the body depending on several physicochemical properties, e.g. solubility, charge, size, etc.

The unit for Volume of Distribution is typically reported in litres. As body composition changes with age, V_D decreases.

The V_D may also be used to determine how readily a drug will displace into the body tissue compartments relative to the blood:

${\displaystyle {V_{D}}={V_{P}}+{V_{T}}\left({\frac {fu}{fu_{t}}}\right)}$

Where:

• V_P = plasma volume
• V_T = apparent tissue volume
• fu = fraction unbound in plasma
• fu_T = fraction unbound in tissue

If you administer a dose D of a drug intravenously in one go (IV-bolus), you would naturally expect it to have an immediate blood concentration ${\displaystyle C_{0}}$ which directly corresponds to the amount of blood contained in the body ${\displaystyle V_{blood}}$. Mathematically this would be:

${\displaystyle C_{0}=D/V_{blood}}$

But this is generally not what happens. Instead you observe that the drug has distributed out into some other volume (read organs/tissue). So probably the first question you want to ask is: how much of the drug is no longer in the blood stream? The volume of distribution ${\displaystyle V_{D}}$ quantifies just that by specifying how big a volume you would need in order to observe the blood concentration actually measured.

An example for a simple case (mono-compartmental) would be to administer D=8 mg/kg to a human. A human has a blood volume of around ${\displaystyle V_{blood}=}$0.08 L/kg .[7] This gives a ${\displaystyle C_{0}=}$100 µg/mL if the drug stays in the blood stream only, and thus its volume of distribution is the same as ${\displaystyle V_{blood}}$ that is ${\displaystyle V_{D}=}$ 0.08 L/kg. If the drug distributes into all body water the volume of distribution would increase to approximately ${\displaystyle V_{D}=}$0.57 L/kg [8]

If the drug readily diffuses into the body fat the volume of distribution may increase dramatically, an example is chloroquine which has a ${\displaystyle V_{D}=}$250-302 L/kg [9]

In the simple mono-compartmental case the volume of distribution is defined as: ${\displaystyle V_{D}=D/C_{0}}$, where the ${\displaystyle C_{0}}$ in practice is an extrapolated concentration at time = 0 from the first early plasma concentrations after an IV-bolus administration (generally taken around 5 min - 30 min after giving the drug).

• Tutorial on volume of distribution
• Overview at icp.org.nz
• Overview at cornell.edu
• Overview at stanford.edu
• Overview at boomer.org