Volume of distribution
In pharmacology, the volume of distribution (V_{D}, also known as apparent volume of distribution) 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.^{[1]} It is defined as the distribution of a medication between plasma and the rest of the body after oral or parenteral dosing.^{[2]}
The V_{D} of a drug represents the degree to which a drug is distributed in body tissue rather than the plasma. V_{D} is directly correlated with the amount of drug distributed into tissue; a higher V_{D} indicates a greater amount of tissue distribution. A V_{D} greater than the total volume of body water (approximately 42 liters in humans^{[3]}) is possible, and would indicate that the drug is highly distributed into tissue.
In rough terms, drugs with a high lipid solubility (nonpolar drugs), low rates of ionization, or low plasma binding capabilities have higher volumes of distribution than drugs which are more polar, more highly ionized or exhibit high plasma binding in the body's environment. 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 1
 Examples 2
 Sample values and equations 3
 References 4
 External links 5
Equations
The volume of distribution is given by the following equation:






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





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 unit for Volume of Distribution is typically reported in liters. 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:






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





Where:
 V_{P} = plasma volume
 V_{T} = apparent tissue volume
 fu = fraction unbound in plasma
 fu_{T} = fraction unbound in tissue
Examples
If you administer a dose D of a drug intravenously in one go (IVbolus), you would naturally 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 the drug 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 .^{[4]} 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 ^{[5]}
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 ^{[6]}
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).
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  Highly charged hydrophilic molecule. 
Sample values and equations
Characteristic  Description  Example value  Symbol  Formula 

Dose  Amount of drug administered.  500 mg  D  Design parameter 
Dosing interval  Time between drug dose administrations.  24 h  \tau  Design parameter 
C_{max}  The peak plasma concentration of a drug after administration.  60.9 mg/L  C_\text{max}  Direct measurement 
t_{max}  Time to reach C_{max}.  3.9 h  t_\text{max}  Direct measurement 
C_{min}  The lowest (trough) concentration that a drug reaches before the next dose is administered.  27.7 mg/L  C_{\text{min}, \text{ss}}  Direct measurement 
Volume of distribution  The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration to drug amount in the body).  6.0 L  V_\text{d}  = \frac{D}{C_0} 
Concentration  Amount of drug in a given volume of plasma.  83.3 mg/L  C_{0}, C_\text{ss}  = \frac{D}{V_\text{d}} 
Elimination halflife  The time required for the concentration of the drug to reach half of its original value.  12 h  t_\frac{1}{2}  = \frac{\ln(2)}{k_\text{e}} 
Elimination rate constant  The rate at which a drug is removed from the body.  0.0578 h^{−1}  k_\text{e}  = \frac{\ln(2)}{t_\frac{1}{2}} = \frac{CL}{V_\text{d}} 
Infusion rate  Rate of infusion required to balance elimination.  50 mg/h  k_\text{in}  = C_\text{ss} \cdot CL 
Area under the curve  The integral of the concentrationtime curve (after a single dose or in steady state).  1,320 mg/L·h  AUC_{0  \infty}  = \int_{0}^{\infty}C\, \operatorname{d}t 
AUC_{\tau, \text{ss}}  = \int_{t}^{t + \tau}C\, \operatorname{d}t  
Clearance  The volume of plasma cleared of the drug per unit time.  0.38 L/h  CL  = V_\text{d} \cdot k_\text{e} = \frac{D}{AUC} 
Bioavailability  The systemically available fraction of a drug.  0.8  f  = \frac{AUC_\text{po} \cdot D_\text{iv}}{AUC_\text{iv} \cdot D_\text{po}} 
Fluctuation  Peak trough fluctuation within one dosing interval at steady state  41.8 %  \%PTF 
= \frac{C_{\text{max}, \text{ss}}  C_{\text{min}, \text{ss}}}{C_{\text{av}, \text{ss}}} \cdot 100 where C_{\text{av},\text{ss}} = \frac{1}{\tau}AUC_{\tau, \text{ss}} 
References
 ^ http://sepia.unil.ch/pharmacology/?id=61
 ^ "vetmed.vt.edu".
 ^ http://www.anaesthesiamcq.com/FluidBook/fl2_1.php
 ^ Alberts, Bruce (2005). "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. NCBI Bookshelf. Retrieved 20070414.
 ^ Guyton, Arthur C. (1976). Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. p. 424.
 ^ Wetsteyn JC (1995). "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". Br J Clinical Pharmacology 39 (6): 696–9.
External links
 Tutorial on volume of distribution
 Overview at icp.org.nz
 Overview at cornell.edu
 Overview at stanford.edu
 Overview at boomer.org
