Volume of distribution

The volume of distribution (V_D) , also known as apparent volume of distribution, is a pharmacological term used to quantify the distribution of a medication between plasma and the rest of the body after oral or parenteral dosing. It is defined as the volume in which the amount of drug would need to be uniformly distributed to produce the observed blood concentration.

Volume of distribution may be increased by renal failure (due to fluid retention) and liver failure (due to altered body fluid and plasma protein binding). Conversely it may be decreased in dehydration.

The initial volume of distribution describes blood concentrations prior to attaining the apparent volume of distribution and uses the same formula.

Equations

The volume of distribution is given by the following equation:

<math>{V_{D}} = \frac{\mathrm{total \ amount \ of \ drug \ in \ the \ body}}{\mathrm{drug \ blood \ plasma \ concentration}}</math>

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 physiologic 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 units for Volume of Distribution are typically reported in (ml or liter)/kg body weight. The fact that V_D is a ratio of a theoretical volume to a fixed unit of body weight explains why the V_D for children is typically higher than that for adults, even though children are smaller and weigh less. 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:

<math>{V_{D}} = {V_{P}} + {V_{T}} \left(\frac{fu}{fu_{t}}\right)</math>

Where:

• V_P = plasma volume

• V_T = apparent tissue volume

• fu = fraction unbound in plasma

• fu_T = fraction unbound in tissue

Examples

Further reading: Table of volume of distribution for drugs

Drug	VD	Comments
Warfarin	8L	Reflects a high degree of plasma protein binding.
Theophylline, Ethanol	30L	Represents distribution in total body water.
Chloroquine	15000L	Shows highly lipophilic molecules which sequester into total body fat.
NXY-059	8L	Highly-charged hydrophilic molecule.

Sample values and equations

Variable	Description	Example value	Abbreviation(s)	Formula
Dose	loading dose (LD), or steady state/maintenance dose (MD)	1000 mg	<math>\textstyle D </math>	<math>\textstyle = V_{d} \times C_{0}</math>
Volume of distribution	The apparent volume in which a drug is distributed immediately after it has been injected intravenously and equilibrated between plasma and the surrounding tissues.	25 L	<math>\textstyle V_d</math>	<math>\textstyle = D / C_0</math>
Concentration	initial or steady-state concentration of drug in plasma	40.0 mg/L	<math>\textstyle C_{0} \ or \ C_{ss}</math>	<math>\textstyle = D / V_d</math>
Biological half-life	The time required for the concentration of the drug to reach half of its original value.	14 hr	<math>\textstyle T_{1/2}</math>	<math>\textstyle = ln (2) / K_{e}</math>
Elimination rate constant	The rate at which drugs are removed from the body.	0.05 /hr	<math>\textstyle K_e</math>	<math>\textstyle = ln (2) / T_{1/2} = Cl / V_{d}</math>
Elimination rate	rate of infusion required to balance elimination	50 mg/hr	<math>\textstyle K_{in}</math>	<math>\textstyle = C_{ss} \times Cl</math>
Area under the curve	The integral of the plasma drug concentration (Cp) after it is administered.	0.1 mg/mL×hr	<math>\textstyle AUC_{0\ \infty}</math>	<math>= \int_{0}^{\infty}C_p\, dt</math>
Clearance	The volume of plasma cleared of the drug per unit time.	1.25 L/hr	<math>\textstyle Cl</math>	<math>\textstyle= V_{d} \times K_{e} = D/AUC</math>
Bioavailability	The fraction of drug that is absorbed.	1	<math>\textstyle F</math>	<math>= \frac{[AUC]_{intravenous}\times dose_{oral}}{[AUC]_{oral}\times dose_{intravenous}}</math>
Cmax	The peak plasma concentration of a drug after oral administration.	40.0 mg/L	<math>\textstyle C_{max}</math>	direct measurement
Cmin	The lowest (trough) concentration that a drug reaches before the next dose is administered.	1.0 mg/L	<math>\textstyle C_{min}</math>	direct measurement

where ln(2) = 0.69315...

External links

• Overview at icp.org.nz
• Overview at cornell.edu
• Overview at stanford.edu
• Overview at boomer.org

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