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The biological half-life or terminal half-life of a substance is the time it takes for a substance (for example a metabolite, drug, signalling molecule, radioactive nuclide, or other substance) to lose half of its pharmacologic, physiologic, or radiologic activity.[1] Typically, this refers to the body's cleansing through the function of kidneys and liver in addition to excretion functions to eliminate a substance from the body. In a medical context, half-life may also describe the time it takes for the blood plasma concentration of a substance to halve (plasma half-life) its steady-state. The relationship between the biological and plasma half-lives of a substance can be complex depending on the substance in question, due to factors including accumulation in tissues (protein binding), active metabolites, and receptor interactions.[2] Biological half-life is an important pharmacokinetic parameter and is usually denoted by the abbreviation

t

1 2

displaystyle t_ frac 1 2

.[3] While a radioactive isotope decays perfectly according to first order kinetics where the rate constant is fixed, the elimination of a substance from a living organism follows more complex chemical kinetics. See Rate equation.

Contents

1 Examples

1.1 Water 1.2 Alcohol 1.3 Common prescription medications 1.4 Metals 1.5 Peripheral half-life

2 Rate equations

2.1 First-order elimination 2.2 Biphasic half-life

3 Sample values and equations 4 See also 5 References

Examples[edit] Water[edit] The biological half-life of water in a human is about 7 to 14 days. It can be altered by behavior. Drinking large amounts of alcohol will reduce the biological half-life of water in the body.[4][5] This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). The basis of this decontamination method (used at Harwell)[citation needed] is to increase the rate at which the water in the body is replaced with new water. Alcohol[edit] The removal of ethanol (drinking alcohol) through oxidation by alcohol dehydrogenase in the liver from the human body is limited. Hence the removal of a large concentration of alcohol from blood may follow zero-order kinetics. Also the rate-limiting steps for one substance may be in common with other substances. For instance, the blood alcohol concentration can be used to modify the biochemistry of methanol and ethylene glycol. In this way the oxidation of methanol to the toxic formaldehyde and formic acid in the human body can be prevented by giving an appropriate amount of ethanol to a person who has ingested methanol. Note that methanol is very toxic and causes blindness and death. A person who has ingested ethylene glycol can be treated in the same way. Half life is also relative to the subjective metabolic rate of the individual in question. Common prescription medications[edit]

Substance Biological half-life

Adenosine <10 seconds

Norepinephrine 2 minutes

Oxaliplatin 14 minutes[6]

Salbutamol 1.6 hours

Zaleplon 1–2 hours

Morphine 2–3 hours

Methotrexate 3–10 hours (lower doses), 8–15 hours (higher doses)[7]

Phenytoin 12–42 hours

Methadone 15 hours to 3 days, in rare cases up to 8 days[8]

Buprenorphine 16–72 hours

Clonazepam 18–50 hours

Diazepam 20–100 hours (active metabolite, nordazepam 1.5–8.3 days)

Flurazepam 0.8–4.2 days (active metabolite, desflurazepam 1.75–10.4 days)

Donepezil 70 hours (approx.)

Fluoxetine 4–6 days (active lipophilic metabolite 4–16 days)

Dutasteride 5 weeks

Amiodarone 25–110 days

Bedaquiline 5.5 months

Metals[edit] The biological half-life of caesium in humans is between one and four months. This can be shortened by feeding the person prussian blue. The prussian blue in the digestive system acts as a solid ion exchanger which absorbs the caesium while releasing potassium ions. For some substances, it is important to think of the human or animal body as being made up of several parts, each with their own affinity for the substance, and each part with a different biological half-life (physiologically-based pharmacokinetic modelling). Attempts to remove a substance from the whole organism may have the effect of increasing the burden present in one part of the organism. For instance, if a person who is contaminated with lead is given EDTA
EDTA
in a chelation therapy, then while the rate at which lead is lost from the body will be increased, the lead within the body tends to relocate into the brain where it can do the most harm.[9]

Polonium
Polonium
in the body has a biological half-life of about 30 to 50 days. Caesium
Caesium
in the body has a biological half-life of about one to four months. Mercury (as methylmercury) in the body has a half-life of about 65 days. Lead
Lead
in the blood has a half life of 28–36 days.[10][11] Lead
Lead
in bone has a biological half-life of about ten years. Cadmium
Cadmium
in bone has a biological half-life of about 30 years. Plutonium
Plutonium
in bone has a biological half-life of about 100 years. Plutonium
Plutonium
in the liver has a biological half-life of about 40 years.

Peripheral half-life[edit] Some substances may have different half-lives in different parts of the body. For example, oxytocin has a half-life of typically about three minutes in the blood when given intravenously. Peripherally administered (e.g. intravenous) peptides like oxytocin cross the blood-brain-barrier very poorly, although very small amounts (< 1%) do appear to enter the central nervous system in humans when given via this route.[12] In contrast to peripheral administration, when administered intranasally via a nasal spray, oxytocin reliably crosses the blood–brain barrier and exhibits psychoactive effects in humans.[13][14] In addition, also unlike the case of peripheral administration, intranasal oxytocin has a central duration of at least 2.25 hours and as long as 4 hours.[15][16] In likely relation to this fact, endogenous oxytocin concentrations in the brain have been found to be as much as 1000-fold higher than peripheral levels.[12] Rate equations[edit] First-order elimination[edit] There are circumstances where the half-life varies with the concentration of the drug. Thus the half-life, under these circumstances, is proportional to[dubious – discuss] the initial concentration of the drug A0 and inversely proportional to the zero-order rate constant k0 where:

t

1 2

=

0.5

A

0

k

0

displaystyle t_ frac 1 2 = frac 0.5A_ 0 k_ 0 ,

This process[clarification needed] is usually a logarithmic process - that is, a constant proportion of the agent is eliminated per unit time.[17] Thus the fall in plasma concentration after the administration of a single dose is described by the following equation:

C

t

=

C

0

e

− k t

displaystyle C_ t =C_ 0 e^ -kt ,

Ct is concentration after time t C0 is the initial concentration (t=0) k is the elimination rate constant

The relationship between the elimination rate constant and half-life is given by the following equation:

k =

ln ⁡ 2

t

1 2

displaystyle k= frac ln 2 t_ frac 1 2 ,

Half-life
Half-life
is determined by clearance (CL) and volume of distribution (VD) and the relationship is described by the following equation:

t

1 2

=

ln ⁡ 2

V

D

C L

displaystyle t_ frac 1 2 = frac ln 2 cdot V_ D CL ,

In clinical practice, this means that it takes 4 to 5 times the half-life for a drug's serum concentration to reach steady state after regular dosing is started, stopped, or the dose changed. So, for example, digoxin has a half-life (or t½) of 24–36 h; this means that a change in the dose will take the best part of a week to take full effect. For this reason, drugs with a long half-life (e.g., amiodarone, elimination t½ of about 58 days) are usually started with a loading dose to achieve their desired clinical effect more quickly. Biphasic half-life[edit] Many drugs follow a biphasic elimination curve — first a steep slope then a shallow slope:[18]

STEEP (initial) part of curve —> initial distribution of the drug in the body. SHALLOW part of curve —> ultimate excretion of drug, which is dependent on the release of the drug from tissue compartments into the blood.

For a more detailed description see Pharmacokinetics--Multi-compartmental_models. Sample values and equations[edit]

Characteristic Description Example value Symbol Formula

Dose Amount of drug administered. 500 mg

D

displaystyle D

Design parameter

Dosing interval Time between drug dose administrations. 24 h

τ

displaystyle tau

Design parameter

Cmax The peak plasma concentration of a drug after administration. 60.9 mg/L

C

max

displaystyle C_ text max

Direct measurement

tmax Time to reach Cmax. 3.9 h

t

max

displaystyle t_ text max

Direct measurement

Cmin The lowest (trough) concentration that a drug reaches before the next dose is administered. 27.7 mg/L

C

min

,

ss

displaystyle 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 in plasma to drug amount in the body). 6.0 L

V

d

displaystyle V_ text d

=

D

C

0

displaystyle = frac D C_ 0

Concentration Amount of drug in a given volume of plasma. 83.3 mg/L

C

0

,

C

ss

displaystyle C_ 0 ,C_ text ss

=

D

V

d

displaystyle = frac D V_ text d

Elimination half-life The time required for the concentration of the drug to reach half of its original value. 12 h

t

1 2

displaystyle t_ frac 1 2

=

ln ⁡ ( 2 )

k

e

displaystyle = 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

e

displaystyle k_ text e

=

ln ⁡ ( 2 )

t

1 2

=

C L

V

d

displaystyle = 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

in

displaystyle k_ text in

=

C

ss

⋅ C L

displaystyle =C_ text ss cdot CL

Area under the curve The integral of the concentration-time curve (after a single dose or in steady state). 1,320 mg/L·h

A U

C

0 − ∞

displaystyle AUC_ 0-infty

=

0

C

d ⁡ t

displaystyle =int _ 0 ^ infty C,operatorname d t

A U

C

τ ,

ss

displaystyle AUC_ tau , text ss

=

t

t + τ

C

d ⁡ t

displaystyle =int _ t ^ t+tau C,operatorname d t

Clearance The volume of plasma cleared of the drug per unit time. 0.38 L/h

C L

displaystyle CL

=

V

d

k

e

=

D

A U C

displaystyle =V_ text d cdot k_ text e = frac D AUC

Bioavailability The systemically available fraction of a drug. 0.8

f

displaystyle f

=

A U

C

po

D

iv

A U

C

iv

D

po

displaystyle = 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 %

% P T F

displaystyle %PTF

=

C

max

,

ss

C

min

,

ss

C

av

,

ss

⋅ 100

displaystyle = frac C_ text max , text ss -C_ text min , text ss C_ text av , text ss cdot 100

where

C

av

,

ss

=

1 τ

A U

C

τ ,

ss

displaystyle C_ text av , text ss = frac 1 tau AUC_ tau , text ss

[

v t e

]

See also[edit]

Half-life, pertaining to the general mathematical concept in physics or pharmacology. Effective half-life

References[edit]

^ "Half-Life". Medical Subject Headings. United States National Library of Medicine. 2016. Tree No. G01.910.405. Retrieved June 3, 2016.  ^ Lin VW; Cardenas DD (2003). Spinal Cord Medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1-888799-61-7.  ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Biological Half Life". ^ Nordberg, Gunnar (2007). Handbook on the toxicology of metals. Amsterdam: Elsevier. p. 119. ISBN 0-12-369413-2.  ^ Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of effective treatments in psychiatry. Cambridge, UK: Cambridge University Press. p. 295. ISBN 0-521-84228-X.  ^ Ehrsson, Hans; et al. (Winter 2002). " Pharmacokinetics
Pharmacokinetics
of oxaliplatin in humans". Medical Oncology. Archived from the original on 2007-09-28. Retrieved 2007-03-28.  ^ "Trexall, Otrexup (methotrexate) dosing, indications, interactions, adverse effects, and more". reference.medscape.com.  ^ Manfredonia, John (March 2005). "Prescribing Methadone
Methadone
for Pain Management in End-of-Life Care". JAOA—The Journal of the American Osteopathic Association. 105 (3 supplement): 18S. Retrieved 2007-01-29.  ^ Nikolas C Papanikolaou; Eleftheria G Hatzidaki; Stamatis Belivanis; George N Tzanakakis; Aristidis M Tsatsakis (2005). " Lead
Lead
toxicity update. A brief review". Medical Science Monitor. 11 (10): RA329-336.  ^ Griffin et al. 1975 as cited in ATSDR 2005 ^ Rabinowitz et al. 1976 as cited in ATSDR 2005 ^ a b Baribeau, Danielle A; Anagnostou, Evdokia (2015). " Oxytocin
Oxytocin
and vasopressin: linking pituitary neuropeptides and their receptors to social neurocircuits". Frontiers in Neuroscience. 9. doi:10.3389/fnins.2015.00335. ISSN 1662-453X. PMC 4585313 . PMID 26441508.  ^ Malenka RC, Nestler EJ, Hyman SE (2009). "Chapter 7: Neuropeptides". In Sydor A, Brown RY. Molecular Neuropharmacology: A Foundation for Clinical Neuroscience (2nd ed.). New York: McGraw-Hill Medical. p. 195. ISBN 9780071481274. Oxytocin
Oxytocin
can be delivered to humans via nasal spray following which it crosses the blood–brain barrier. ... In a double-blind experiment, oxytocin spray increased trusting behavior compared to a placebo spray in a monetary game with real money at stake.  ^ McGregor IS, Callaghan PD, Hunt GE (May 2008). "From ultrasocial to antisocial: a role for oxytocin in the acute reinforcing effects and long-term adverse consequences of drug use?". British Journal of Pharmacology. 154 (2): 358–68. doi:10.1038/bjp.2008.132. PMC 2442436 . PMID 18475254. Recent studies also highlight remarkable anxiolytic and prosocial effects of intranasally administered OT in humans, including increased ‘trust’, decreased amygdala activation towards fear-inducing stimuli, improved recognition of social cues and increased gaze directed towards the eye regions of others (Kirsch et al., 2005; Kosfeld et al., 2005; Domes et al., 2006; Guastella et al., 2008)  ^ Weisman O, Zagoory-Sharon O, Feldman R (2012). "Intranasal oxytocin administration is reflected in human saliva". Psychoneuroendocrinology. 37 (9): 1582–6. doi:10.1016/j.psyneuen.2012.02.014. PMID 22436536.  ^ Huffmeijer R, Alink LR, Tops M, Grewen KM, Light KC, Bakermans-Kranenburg MJ, Ijzendoorn MH (2012). "Salivary levels of oxytocin remain elevated for more than two hours after intranasal oxytocin administration". Neuro Endocrinology Letters. 33 (1): 21–5. PMID 22467107.  ^ Birkett DJ (2002). For example, ethanol may be consumed in sufficient quantity to saturate the metabolic enzymes in the liver, and so is eliminated from the body at an approximately constant rate (zero-order elimination Pharmacokinetics
Pharmacokinetics
Made Easy (Revised Edition). Sydney: McGraw-Hill Australia. ISBN 0-07-471072-9. ^ "Basic Pharmacology". www.valuemd.com. 

v t e

Concepts in pharmacology

Pharmacokinetics

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

Loading dose Volume of distribution (Initial) Rate of infusion

Compartment Bioequivalence Bioavailability

Onset of action Biological half-life Mean residence time Plasma protein binding

Therapeutic index (Median lethal dose, Effective dose)

Pharmacodynamics

Mechanism of action Toxicity
Toxicity
(Neurotoxicology) Dose–response relationship
Dose–response relationship
(Efficacy, Potency)

Antimicrobial pharmacodynamics: Minimum inhibitory concentration (Bacteriostatic) Minimum bactericidal concentration (Bactericide)

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 selectivity

Other

Drug
Drug
tolerance: Tachyphylaxis

Drug
Drug
resistance: Antibiotic resistance Multiple drug resistance

Drug
Drug
discovery strategies

Classical pharmacology

Reverse pharmacology

Related fields/subfields

Pharmacogenetics Pharmacogenomics

Neuropsychopharmacology (Neuropharmacology, P

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