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 theoretical volume in which the total amount of drug would need to be uniformly distributed to produce the desired blood concentration of a drug.^{[1]} ^{[2]}
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.
Contents
Equations
The volume of distribution is given by the following equation:
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:
Where:
 V_{P} = plasma volume
 V_{T} = apparent tissue volume
 fu = fraction unbound in plasma
 fu_{T} = fraction unbound in tissue
Examples
Understanding volume of distribution
If you administer a dose D of a drug intravenously in one go (IVbolus), you would naively expect it to have an immediate blood concentration C_{0} which directly corresponds to the amount of blood contained in the body V_{blood}. Mathematically this would be:
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 it is no longer in the blood stream? The volume of distribution V_{D} quantifies just that by specifying how big a volume you would need in order to observe the blood concentration actually measured.
A practical example for a simple case (monocompartmental) would be to administer D=8 mg/kg to a human. A human has a blood volume of around V_{blood} = 0.08 l/kg ^{[3]}. This gives a C_{0} = 100 µg/ml if the drug stays in the blood stream only, and thus its volume of distribution is the same as V_{blood} that is V_{D} = 0.08 l/kg. If the drug distributes into all body water the volume of distribution would increase to approximately V_{D} = 0.57 l/kg ^{[4]}
If the drug readily diffuses into the body fat the volume of distribution may increase dramatically, an example is chloroquine which has a V_{D} = 250302 l/kg ^{[5]}
In the simple monocompartmental case the volume of distribution is defined as: V_{D} = D / C_{0}, where the C_{0} in practice is an extrapolated concentration at time=0 from the first early plasma concentrations after an IVbolus administration (generally taken around 5min  30min after giving the drug).
Further reading:Table of volume of distribution for drugs
Drug V_{D} 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. NXY059 8L Highlycharged hydrophilic molecule. Sample values and equations
Characteristic Description Example value Abbreviation(s) Formula Dose Loading dose (LD), or steady state / maintenance dose (MD). 500 mg design parameter τ Dosing interval. 24 h design parameter 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. 6.0 L Concentration Initial or steadystate concentration of drug in plasma. 83.3 µg/mL Biological halflife The time required for the concentration of the drug to reach half of its original value. 12 h Elimination rate constant The rate at which drugs are removed from the body. 0.0578 h^{1} Elimination rate Rate of infusion required to balance elimination. 50 mg/h Area under the curve The integral of the concentrationtime curve (after a single dose or in steady state). 1320 µg/mL×h
Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h Bioavailability The fraction of drug that is absorbed. 0.8 C_{max} The peak plasma concentration of a drug after oral administration. 60.9 µg/mL direct measurement t_{max} Time to reach C_{max}. 3.9 h direct measurement C_{min} The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 µg/mL direct measurement Fluctuation Peak trough fluctuation within one dosing interval at steady state 41.8 %
where
edit References
 ^ http://www.merckmanuals.com/professional/sec21/ch324/ch324d.html
 ^ "vetmed.vt.edu". http://cpharm.vetmed.vt.edu/VM8314/VM8314PharmaModeling.htm.
 ^ Alberts, Bruce (2005). "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. NCBI Bookshelf. http://www.ncbi.nlm.nih.gov/sites/entrez?cmd=Search&db=books&doptcmdl=GenBookHL&rid=mboc4.table.4143. Retrieved 20070414.
 ^ Guyton, Arthur C. (1976). Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. p. 424. ISBN 0721643930.
 ^ Wetsteyn JC (1995). "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". Br J Clinical Pharmacology 39 (6): 696–9. PMID 7654492.
External links
 Tutorial on volume of distribution
 Overview at icp.org.nz
 Overview at cornell.edu
 Overview at stanford.edu
 Overview at boomer.org
Medication > Pharmacology Pharmacokinetics ADME: Absorption • Distribution • Metabolism • Excretion (Clearance)
Loading dose • Volume of distribution (Initial) • Rate of infusion
Compartment • Bioequivalence • Bioavailability
Onset of action • Biological halflife • Plasma protein binding
Therapeutic index (LD_{50}/ED_{50})Pharmacodynamics Agonism and antagonism Agonist: Inverse agonist • Irreversible agonist • Partial agonist • Superagonist • Physiological agonist
Antagonist: Competitive antagonist • Irreversible antagonist • Physiological antagonist
Other: Binding • Affinity • Binding selectivity • Functional selectivityOther Related fields/subfields Categories: 
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