Volume of distribution

Further information: Distribution (pharmacology)

In pharmacology, the volume of distribution (${\displaystyle V_{D}}$, also known as apparent volume of distribution or volume of dilution^[1]) is the theoretical volume that would be necessary to contain the total amount of an administered drug at the same concentration that it is observed in the blood plasma.^[2]

Roughly speaking, the ${\displaystyle V_{D}}$, as a property of a drug, measures the degree to which it is distributed in body tissue rather than the blood plasma. Drug properties which cause high ${\displaystyle V_{D}}$ include high lipid solubility (non-polarity), low rates of ionization, or low plasma protein binding capabilities. Disease states which increase ${\displaystyle V_{D}}$ include kidney failure (due to fluid retention) and liver failure (due to altered body fluid and plasma protein binding). Conversely, dehydration may decrease ${\displaystyle V_{D}}$.

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

Motivation and equation

Suppose one administers an amount of drug ${\displaystyle D}$  intravascularly, then measures the drug concentration in blood ${\displaystyle C_{0}}$  (assuming enough time has elapsed for the drug to distribute, but not enough time for elimination). The volume of distribution is the quotient:

${\displaystyle V_{D}={\frac {D}{C_{0}}}}$ 

If the drug remains entirely intravascularly, ${\displaystyle V_{D}}$  will be identical to the blood volume ${\displaystyle V_{blood}}$ . However, if a drug diffuses out of the intravascular space into the tissues or interstitium, the measured concentration will be lower-than-expected compared to a hypothetical intravascular-only drug. Therefore, ${\displaystyle V_{D}>V_{blood}}$ , with a higher ${\displaystyle V_{D}}$  value corresponding to a greater tendency for the drug to exit the intravascular space.

One clinical utility is that the dose required ${\displaystyle D}$  to achieve a target plasma concentration ${\displaystyle C_{0}}$  can be determined if the ${\displaystyle V_{D}}$  for that drug is known.

The ${\displaystyle V_{D}}$  is not a physiological value; it is more a reflection of how a drug will distribute throughout the body depending on several physicochemical properties such as solubility, charge, size, etc.

The unit for ${\displaystyle V_{D}}$  may be reported extensively in litres (for a patient of given weight), or intensively as litres-per-kilogram.

The ${\displaystyle V_{D}}$  may also be used to determine how readily a drug will displace into the body tissue compartments relative to the blood:

${\displaystyle {V_{D}}={V_{P}}+{V_{T}}\left({\frac {f_{u_{P}}}{f_{u_{T}}}}\right)}$ 

Where:

• ${\displaystyle V_{P}}$ : plasma volume
• ${\displaystyle V_{T}}$ : apparent tissue volume
• ${\displaystyle f_{u_{P}}}$ : fraction unbound in plasma
• ${\displaystyle f_{u_{T}}}$ : fraction unbound in tissue

Examples

Main article: Table of volume of distribution for drugs

See also: Pharmacokinetics § Metrics

For example, chloroquine has much greater affinity for body fat than blood, resulting in a ${\displaystyle V_{D}\approx 250L/kg}$  ^[3] compared to ${\displaystyle V_{blood}\approx 0.08L/kg}$ ^[4].

Example ${\displaystyle V_{D}}$  values for a 70 kg man^[5], with approximate blood volume 5-6L.

Drug	${\displaystyle V_{D}}$	Comments
Warfarin	8 L	Reflects a high degree of plasma protein binding, which sequesters the drug in the intravascular space.
Theophylline, Ethanol	30 L	Represents distribution in total body water.
Chloroquine	15000 L	Shows highly lipophilic molecules which sequester into total body fat.
NXY-059	8 L	Highly charged hydrophilic molecule.

References

1. Ward RM, Kern SE, Lugo RA (2012). "Pharmacokinetics, Pharmacodynamics, and Pharmacogenetics". Avery's Diseases of the Newborn. Elsevier. pp. 417–428. doi:10.1016/b978-1-4377-0134-0.10034-4. ISBN 978-1-4377-0134-0.
2. "Volume of distribution". sepia.unil.ch. Retrieved 19 April 2018.
3. Wetsteyn JC, De Vries PJ, Oosterhuis B, Van Boxtel CJ (June 1995). "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". British Journal of Clinical Pharmacology. 39 (6): 696–699. doi:10.1111/j.1365-2125.1995.tb05731.x. PMC 1365086. PMID 7654492.
4. Alberts B (2005). "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. Retrieved 2007-04-14 – via NCBI Bookshelf.
5. Swain C. "Distribution and plasma protein binding". Cambridge MedChem Consulting. Retrieved 2020-04-02.

External links

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