Volume of distribution.html



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. ¹

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:

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 real volume; 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.

It is important to note that the volume of distribution cannot be smaller than the physiological volume of intravascular plasma, which is approximately 3L in humans.

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

Further reading: Table of volume of distribution for drugs

Sample values and equations

Variable	Abbreviation(s)	Example value	Formula
Dose (loading dose, or steady state/maintenance)	D (LD or MD)	1000 mg	=Vd*C0
Volume of distribution	Vd	25 L	=D/C0
Concentration (initial or steady-state)	C0 or Css	40.0 mg/L	=D/Vd
Biological half-life	T½	14 hr	=0.7/Ke
Elimination rate constant	Ke	0.05/hr	=0.7/(T½) =Cl/Vd
Elimination rate, or rate of infusion to balance elimination	Kin	50 mg/hr	=Css*Cl
Clearance	Cl	1.25 L/hr	=Vd*Ke
Bioavailability	F	1

Note that the "0.7" constant is a commonly used log approximation, but not the actual value. Another commonly used approximation is 0.693. -(ln(0.5)) = 0.69315.

References

External links

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