Volume of distribution

Short description: Measuring the relative affinity of a drug between blood constituents and tissue constituents.

Further information: Distribution (pharmacology)

In pharmacology, the volume of distribution (VD, also known as apparent volume of distribution, literally, 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] In other words, it is the ratio of amount of drug in a body (dose) to concentration of the drug that is measured in blood, plasma, and un-bound in interstitial fluid.[3][4]

The VD of a drug represents the degree to which a drug is distributed in body tissue rather than the plasma. VD is directly proportional with the amount of drug distributed into tissue; a higher VD indicates a greater amount of tissue distribution. A VD greater than the total volume of body water (approximately 42 liters in humans[5]) is possible, and would indicate that the drug is highly distributed into tissue. In other words, the volume of distribution is smaller in the drug staying in the plasma than that of a drug that is widely distributed in tissues.[6]

In rough terms, drugs with a high lipid solubility (non-polar drugs), low rates of ionization, or low plasma protein binding capabilities have higher volumes of distribution than drugs which are more polar, more highly ionized or exhibit high plasma protein binding in the body's environment. Volume of distribution may be increased by kidney 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.

## Contents

* 1 Equations
* 2 Examples
* 3 References
* 4 External links

## Equations

The volume of distribution is given by the following equation:

[math]\displaystyle{ {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 VD for that drug is known. The VD 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, VD decreases.

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

[math]\displaystyle{ {V_{D}} = {V_{P}} + {V_{T}} \left(\frac{fu}{fu_{t}}\right) }[/math]

Where:

* VP = plasma volume
* VT = apparent tissue volume
* fu = fraction unbound in plasma
* fuT = fraction unbound in tissue

## Examples

Main page: Medicine:Table of volume of distribution for drugs

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 [math]\displaystyle{ C_0 }[/math] which directly corresponds to the amount of blood contained in the body [math]\displaystyle{ V_{blood} }[/math]. Mathematically this would be:

[math]\displaystyle{ C_0 = D/V_{blood} }[/math]

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 [math]\displaystyle{ V_D }[/math] 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 [math]\displaystyle{ V_{blood}= }[/math]0.08 L/kg .[7] This gives a [math]\displaystyle{ C_0= }[/math]100 µg/mL if the drug stays in the blood stream only, and thus its volume of distribution is the same as [math]\displaystyle{ V_{blood} }[/math] that is [math]\displaystyle{ V_D= }[/math] 0.08 L/kg. If the drug distributes into all body water the volume of distribution would increase to approximately [math]\displaystyle{ V_D= }[/math]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 [math]\displaystyle{ V_D= }[/math]250-302 L/kg [9]

In the simple mono-compartmental case the volume of distribution is defined as: [math]\displaystyle{ V_D=D/C_0 }[/math], where the [math]\displaystyle{ C_0 }[/math] 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).

Compounds with different VD for a 70 kg man[10] Drug | VD | Comments

|
|

Warfarin | 8 L | Reflects a high degree of plasma protein binding.
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. ↑ "Pharmacokinetics, Pharmacodynamics, and Pharmacogenetics". Avery's Diseases of the Newborn. Elsevier. 2012. pp. 417–428. doi:10.1016/b978-1-4377-0134-0.10034-4. ISBN 978-1-4377-0134-0.
2. ↑ "Volume of distribution". http://sepia.unil.ch/pharmacology/?id=61.
3. ↑ "Pharmacology of Pediatric Anesthesia". Smith's Anesthesia for Infants and Children. Elsevier. 2011. pp. 179–261. doi:10.1016/b978-0-323-06612-9.00007-9. ISBN 978-0-323-06612-9.
4. ↑ "Pharmacokinetic Modeling". Virginia-Maryland Regional College of Veterinary Medicine. http://cpharm.vetmed.vt.edu/VM8314/VM8314PharmaModeling.htm.
5. ↑ "Fluid Physiology: 2.1 Fluid Compartments". http://www.anaesthesiamcq.com/FluidBook/fl2_1.php.
6. ↑ "Pharmacology and Drug Therapy". Textbook of Pediatric Rheumatology. Elsevier. 2011. pp. 71–126. doi:10.1016/b978-1-4160-6581-4.10006-8. ISBN 978-1-4160-6581-4.
7. ↑ "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. 2005. https://www.ncbi.nlm.nih.gov/sites/entrez?cmd=Search&db=books&doptcmdl=GenBookHL&rid=mboc4.table.4143. Retrieved 2007-04-14.
8. ↑ Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. 1976. p. 424. ISBN 0-7216-4393-0. https://archive.org/details/textbookofmedica0005guyt/page/424.
9. ↑ "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". British Journal of Clinical Pharmacology 39 (6): 696–699. June 1995. doi:10.1111/j.1365-2125.1995.tb05731.x. PMID 7654492.
10. ↑ "Distribution and plasma protein binding" (in en). https://www.cambridgemedchemconsulting.com/resources/ADME/distribution.html.

## External links

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

* v
* t
* e

Pharmacology

Ligand (biochemistry)|

| Excitatory|

* Agonist
* Endogenous agonist
* Irreversible agonist
* Partial agonist
* Superagonist
* Physiological agonist

|

Inhibitory|

* Antagonist
* Competitive antagonist
* Irreversible antagonist
* Physiological antagonist
* Inverse agonist
* Enzyme inhibitor

|

* Drug
* Neurotransmitter
* Agonist-antagonist
* Pharmacophore

Pharmacodynamics|

| Activity at receptor|

* Mechanism of action
* Mode of action
* Binding
* Receptor (biochemistry)
* Desensitization (pharmacology)

|

Other effects of ligand|

* Selectivity (Binding, Functional)
* Pleiotropy (drugs)
* Non-specific effect of vaccines
* Adverse effects
* Toxicity (Neurotoxicity)

|

Analysis|

* Dose–response relationship
* Hill equation (biochemistry)
* Schild plot
* Del Castillo Katz model
* Cheng-Prussoff Equation
* Methods (Organ bath, Ligand binding assay, Patch-clamp)

|

Metrics|

* Efficacy
* Intrinsic activity
* Potency (EC50, IC50, ED50, LD50, TD50)
* Therapeutic index
* Affinity

|

Pharmacokinetics|

| Metrics|

* Loading dose
* Volume of distribution (Initial)
* Rate of infusion
* Onset of action
* Biological half-life
* Plasma protein binding
* Bioavailability

|

LADME|

* (L)ADME: (Liberation)
* Absorption
* Distribution
* Metabolism
* Excretion (Clearance)

|

* Compartment
* Bioequivalence

Related
fields|

| Neuroscience and psychology|

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* Neuropharmacology
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Medicine|

* Clinical pharmacology
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Biochemistry and genetics|

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Toxicology|

* Pharmacotoxicology
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Drug discovery|

* Classical pharmacology
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* Photopharmacology
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* Drug tolerance
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Antimicrobial pharmacology|

* Antimicrobial pharmacodynamics
* Minimum inhibitory concentration
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