Volume of distribution

In pharmacology, the volume of distribution (V_D, 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 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 proportional 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[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.

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 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, 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 (IV-bolus), 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.

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 $V_{blood}=$ 0.08 L/kg .[7] 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 [8]

If the drug readily diffuses into the body fat the volume of distribution may increase dramatically, an example is chloroquine which has a $V_{D}=$ 250-302 L/kg [9]

In the simple mono-compartmental 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 IV-bolus administration (generally taken around 5 min - 30 min after giving the drug).

Compounds with different V_D for a 70 kg man[10]
Drug	V_D	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.

Sample values and equations

Pharmacokinetic metrics
Characteristic	Description	Symbol	Unit	Formula	Worked example value
Dose	Amount of drug administered.	$D$	$\mathrm {mol}$	Design parameter	500 mmol
Dosing interval	Time between drug dose administrations.	$\tau$	$\mathrm {h}$	Design parameter	24 h
C_max	The peak plasma concentration of a drug after administration.	$C_{\text{max}}$	$\mathrm {mmol/L}$	Direct measurement	60.9 mmol/L
t_max	Time to reach C_max.	$t_{\text{max}}$	$\mathrm {h}$	Direct measurement	3.9 h
C_min	The lowest (trough) concentration that a drug reaches before the next dose is administered.	$C_{{\text{min}},{\text{ss}}}$	$\mathrm {mmol/L}$	Direct measurement	27.7 mmol/L
C_avg	The average plasma concentration of a drug over the dosing interval in steady state.	$C_{{\text{av}},{\text{ss}}}$	$\mathrm {h\times mmol/L}$	${\frac {AUC_{\tau ,{\text{ss}}}}{\tau }}$	55.0 h×mmol/L
Volume of distribution	The apparent volume in which a drug is distributed (i.e., the parameter relating drug concentration in plasma to drug amount in the body).	$V_{\text{d}}$	$\mathrm {L}$	${\frac {D}{C_{0}}}$	6.0 L
Concentration	Amount of drug in a given volume of plasma.	$C_{0},C_{\text{ss}}$	$\mathrm {mmol/L}$	${\frac {D}{V_{\text{d}}}}$	83.3 mmol/L
Absorption half-life	The time required for 50% of a given dose of drug to be absorbed into the systemic circulation.	$t_{{\frac {1}{2}}a}$	$\mathrm {h}$	${\frac {\ln(2)}{k_{\text{a}}}}$	1.0 h
Absorption rate constant	The rate at which a drug enters into the body for oral and other extravascular routes.	$k_{\text{a}}$	$\mathrm {h} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}a}}}$	0.693 h⁻¹
Elimination half-‍life	The time required for the concentration of the drug to reach half of its original value.	$t_{{\frac {1}{2}}b}$	$\mathrm {h}$	${\frac {\ln(2)}{k_{\text{e}}}}$	12 h
Elimination rate constant	The rate at which a drug is removed from the body.	$k_{\text{e}}$	$\mathrm {h} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}b}}}={\frac {CL}{V_{\text{d}}}}$	0.0578 h⁻¹
Infusion rate	Rate of infusion required to balance elimination.	$k_{\text{in}}$	$\mathrm {mol/h}$	$C_{\text{ss}}\cdot CL$	50 mmol/h
Area under the curve	The integral of the concentration-time curve (after a single dose or in steady state).	$AUC_{0-\infty }$	$\mathrm {M} \cdot \mathrm {s}$	$\int _{0}^{\infty }C\,\operatorname {d} t$	1,320 h×mmol/L
Area under the curve		$AUC_{\tau ,{\text{ss}}}$	$\mathrm {M} \cdot \mathrm {s}$	$\int _{t}^{t+\tau }C\,\operatorname {d} t$	1,320 h×mmol/L
Clearance	The volume of plasma cleared of the drug per unit time.	$CL$	$\mathrm {m} ^{3}/\mathrm {s}$	$V_{\text{d}}\cdot k_{\text{e}}={\frac {D}{AUC}}$	0.38 L/h
Bioavailability	The systemically available fraction of a drug.	$f$	Unitless	${\frac {AUC_{\text{po}}\cdot D_{\text{iv}}}{AUC_{\text{iv}}\cdot D_{\text{po}}}}$	0.8
Fluctuation	Peak–trough fluctuation within one dosing interval at steady state.	$\%PTF$	$\%$	$100{\frac {C_{{\text{max}},{\text{ss}}}-C_{{\text{min}},{\text{ss}}}}{C_{{\text{av}},{\text{ss}}}}}$ where $C_{{\text{av}},{\text{ss}}}={\frac {AUC_{\tau ,{\text{ss}}}}{\tau }}$	41.8%

References

Ward, Robert M.; Kern, Steven E.; Lugo, Ralph A. (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.
"Volume of distribution". sepia.unil.ch. Retrieved 19 April 2018.
Davis, Peter J.; Bosenberg, Adrian; Davidson, Andrew; Jimenez, Nathalia; Kharasch, Evan; Lynn, Anne M.; Tofovic, Stevan P.; Woelfel, Susan (2011). "Pharmacology of Pediatric Anesthesia". Smith's Anesthesia for Infants and Children. Elsevier. pp. 179–261. doi:10.1016/b978-0-323-06612-9.00007-9. ISBN 978-0-323-06612-9.
"vetmed.vt.edu".
"Fluid Physiology: 2.1 Fluid Compartments". www.anaesthesiamcq.com. Retrieved 19 April 2018.
Ilowite, Norman T.; Laxer, Ronald M. (2011). "PHARMACOLOGY AND DRUG THERAPY". Textbook of Pediatric Rheumatology. Elsevier. pp. 71–126. doi:10.1016/b978-1-4160-6581-4.10006-8. ISBN 978-1-4160-6581-4.
Alberts, Bruce (2005). "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. NCBI Bookshelf. Retrieved 2007-04-14.
Guyton, Arthur C. (1976). Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. p. 424. ISBN 0-7216-4393-0.
Wetsteyn JC (1995). "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". Br J Clin Pharmacol. 39 (6): 696–9. doi:10.1111/j.1365-2125.1995.tb05731.x. PMC 1365086. PMID 7654492.
Swain, Chris. "Distribution and plasma protein binding". Cambridge MedChem Consulting. Retrieved 2020-04-02.

External links

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[Ward_Kern_Lugo_2012_pp._417–428-1] Ward, Robert M.; Kern, Steven E.; Lugo, Ralph A. (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.

[Davis_Bosenberg_Davidson_Jimenez_2011_pp._179–261-3] Davis, Peter J.; Bosenberg, Adrian; Davidson, Andrew; Jimenez, Nathalia; Kharasch, Evan; Lynn, Anne M.; Tofovic, Stevan P.; Woelfel, Susan (2011). "Pharmacology of Pediatric Anesthesia". Smith's Anesthesia for Infants and Children. Elsevier. pp. 179–261. doi:10.1016/b978-0-323-06612-9.00007-9. ISBN 978-0-323-06612-9.

[urlUntitled_Document-4] "vetmed.vt.edu".

[5] "Fluid Physiology: 2.1 Fluid Compartments". www.anaesthesiamcq.com. Retrieved 19 April 2018.

[Ilowite_Laxer_2011_pp._71–126-6] Ilowite, Norman T.; Laxer, Ronald M. (2011). "PHARMACOLOGY AND DRUG THERAPY". Textbook of Pediatric Rheumatology. Elsevier. pp. 71–126. doi:10.1016/b978-1-4160-6581-4.10006-8. ISBN 978-1-4160-6581-4.

[alberts_table-7] Alberts, Bruce (2005). "Leukocyte functions and percentage breakdown". Molecular Biology of the Cell. NCBI Bookshelf. Retrieved 2007-04-14.

[textbookofmedicalphysiology5thed-8] Guyton, Arthur C. (1976). Textbook of Medical Physiology (5th ed.). Philadelphia: W.B. Saunders. p. 424. ISBN 0-7216-4393-0.

[9] Wetsteyn JC (1995). "The pharmacokinetics of three multiple dose regimens of chloroquine: implications for malaria chemoprophylaxis". Br J Clin Pharmacol. 39 (6): 696–9. doi:10.1111/j.1365-2125.1995.tb05731.x. PMC 1365086. PMID 7654492.

[10] Swain, Chris. "Distribution and plasma protein binding". Cambridge MedChem Consulting. Retrieved 2020-04-02.