Biological half-life explained

Biological half-life (elimination half-life, pharmacological half-life) is the time taken for concentration of a biological substance (such as a medication) to decrease from its maximum concentration (C_max) to half of C_max in the blood plasma.^{[1] [2] [3] [4] [5]} It is denoted by the abbreviation

t _{(1)/(2)} .^{[2] [4]}

This is used to measure the removal of things such as metabolites, drugs, and signalling molecules from the body. Typically, the biological half-life refers to the body's natural detoxification (cleansing) through liver metabolism and through the excretion of the measured substance through the kidneys and intestines. This concept is used when the rate of removal is roughly exponential.

In a medical context, half-life explicitly describes the time it takes for the blood plasma concentration of a substance to halve (plasma half-life) its steady-state when circulating in the full blood of an organism. This measurement is useful in medicine, pharmacology and pharmacokinetics because it helps determine how much of a drug needs to be taken and how frequently it needs to be taken if a certain average amount is needed constantly. By contrast, the stability of a substance in plasma is described as plasma stability. This is essential to ensure accurate analysis of drugs in plasma and for drug discovery.

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.^[6]

Examples

Water

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.^{[7] [8]} This has been used to decontaminate patients who are internally contaminated with tritiated water. The basis of this decontamination method is to increase the rate at which the water in the body is replaced with new water.

Alcohol

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. 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

Substance	Biological half-life
Adenosine	Less than 10 seconds (estimate)^[9]
Norepinephrine	2 minutes^[10]
Oxaliplatin	14 minutes^[11]
Zaleplon	1 hour^[12]
Morphine	1.5–4.5 hours^[13]
Flurazepam	2.3 hours^[14] Active metabolite (N-desalkylflurazepam): 47–100 hours
Methotrexate	3–10 hours (lower doses),8–15 hours (higher doses)^[15]
Methadone	15–72 hoursin rare cases up to 8 days^[16]
Diazepam	20–50 hours^[17] Active metabolite (nordazepam): 30–200 hours
Phenytoin	20–60 hours^[18]
Buprenorphine	28–35 hours^[19]
Clonazepam	30–40 hours^[20]
Donepezil	3 days (70 hours)^[21]
Fluoxetine	4–6 days (under continuous administration)^[22] Active lipophilic metabolite (norfluoxetine): 4–16 days
Amiodarone	14–107 days^[23]
Vandetanib	19 days^[24]
Dutasteride	21–35 days (under continuous administration)^[25]
Bedaquiline	165 days^[26]

Metals

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 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.^[27]

• Polonium in the body has a biological half-life of about 30 to 50 days.
• 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 in the blood has a half life of 28–36 days.^{[28] [29]}
• Lead in bone has a biological half-life of about ten years.
• Cadmium in bone has a biological half-life of about 30 years.
• Plutonium in bone has a biological half-life of about 100 years.
• Plutonium in the liver has a biological half-life of about 40 years.

Peripheral half-life

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.^[30] 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.^{[31] [32]} In addition, unlike the case of peripheral administration, intranasal oxytocin has a central duration of at least 2.25 hours and as long as 4 hours.^{[33] [34]} 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.

Rate equations

See main article: Rate equation.

First-order elimination

Timeline of an exponential decay process^{[35] [36] [37]}

Time (t)	Percent of initial value	Percent completion
t	50%	50%
t × 2	25%	75%
t × 3	12.5%	87.5%
t × 3.322	10.00%	90.00%
t × 4	6.25%	93.75%
t × 4.322	5.00%	95.00%
t × 5	3.125%	96.875%
t × 6	1.5625%	98.4375%
t × 7	0.78125%	99.21875%
t × 10	~0.09766%	~99.90234%

Half-times apply to processes where the elimination rate is exponential. If

C(t) is the concentration of a substance at time t , its time dependence is given byC(t) = C( 0 ) e ^{-kt}

where k is the reaction rate constant. Such a decay rate arises from a first-order reaction where the rate of elimination is proportional to the amount of the substance:^[38]

(d C)/(d t) = - k C.

The half-life for this process is^[38]

t _{(1)/(2)} = (ln2)/(k) .

Alternatively, half-life is given by

t _{(1)/(2)} = (ln2)/(λ _{z})

where λ_z is the slope of the terminal phase of the time–concentration curve for the substance on a semilogarithmic scale.^{[39] [40]}

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

t _{(1)/(2)} = ({ ln2)/(⋅ {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 t) 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 t of about 58 days) are usually started with a loading dose to achieve their desired clinical effect more quickly.

Biphasic half-life

Many drugs follow a biphasic elimination curve — first a steep slope then a shallow slope:

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. The longer half-life is called the terminal half-life and the half-life of the largest component is called the dominant half-life.^[38] For a more detailed description see Pharmacokinetics § Multi-compartmental models.

See also

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

Notes and References

1. Web site: Elimination Half-Life . Pharmacology in one semester . 20 February 2020 . 22 October 2020 . https://web.archive.org/web/20201022081736/https://sites.google.com/site/pharmacologyinonesemester/2-drug-distribution-metabolism-and-elimination/2-5-blood-levels/2-5-2-elimination-half-life . dead .
2. Web site: Definition of Half-Life (t) . AIDSinfo . 2020-02-19 . 2020-02-20 . 20 February 2020 . https://web.archive.org/web/20200220040435/https://aidsinfo.nih.gov/understanding-hiv-aids/glossary/286/half-life . dead .
3. Book: Curry, Stephen H. . Antipsychotic Drugs and their Side-Effects . PHARMACOKINETICS OF ANTIPSYCHOTIC DRUGS . Elsevier . 1993 . 978-0-12-079035-7 . 10.1016/b978-0-12-079035-7.50015-4 . 127–144 . The elimination half-life measures the kinetics of loss of drug from the body as a whole once all distribution equilibria have been achieved..
4. Book: Dasgupta . Amitava . Krasowski . Matthew D. . Therapeutic Drug Monitoring Data . Pharmacokinetics and therapeutic drug monitoring . Elsevier . 2020 . 978-0-12-815849-4 . 10.1016/b978-0-12-815849-4.00001-3 . 1–17 . 209258489 . The half-life of a drug is the time required for the serum concentration to be reduced by 50%. Once the half-life of the drug is known, the time required for clearance can be estimated. Approximately 97% of the drug is eliminated by 5 halflives, while ~99% is eliminated by 7 half-lives. .
5. Journal of Veterinary Pharmacology and Therapeutics. 27 . 6 . 427–439 . 2004 . Following i.v. administration, the terminal half-life is the time required for plasma/blood concentration to decrease by 50% after pseudo-equilibrium of distribution has been reached; then, terminal half-life is computed when the decrease in drug plasma concentration is due only to drug elimination, and the term 'elimination half-life' is applicable. Therefore, it is not the time necessary for the amount of the administered drug to fall by one half.. 10.1111/j.1365-2885.2004.00600.x . 15601438 . Plasma terminal half-life . Toutain . P. L. . Bousquet-Melou . A. . https://web.archive.org/web/20200220042629/http://physiologie.envt.fr/wp-content/uploads/2016/06/Plasma_terminal_half-life.pdf . 2020-02-20 .
6. Book: Spinal Cord Medicine. Lin VW. Cardenas DD. Demos Medical Publishing, LLC. 251. 2003. 1-888799-61-7.
7. Book: Nordberg, Gunnar . Handbook on the toxicology of metals . Elsevier . Amsterdam . 2007 . 119 . 978-0-12-369413-3 .
8. Book: Silk, Kenneth R. . Tyrer, Peter J. . Cambridge textbook of effective treatments in psychiatry . Cambridge University Press . Cambridge, UK . 2008 . 295 . 978-0-521-84228-0 .
9. Book: Austria-Codex. Haberfeld H . Adenosin Baxter3 mg/ml Injektionslösung. Österreichischer Apothekerverlag. Vienna. 2020. German.
10. Book: Austria-Codex. Haberfeld H . Noradrenalin Orpha 1 mg/ml Konzentrat zur Herstellung einer Infusionslösung. Österreichischer Apothekerverlag. Vienna. 2020. German.
11. Ehrsson . Hans . Pharmacokinetics of oxaliplatin in humans . Medical Oncology . 19 . 4 . 261–5 . Winter 2002 . 2007-03-28 . etal . dead . https://web.archive.org/web/20070928104657/http://journals.humanapress.com/index.php?option=com_opbookdetails&task=articledetails&category=humanajournals&article_code=MO%3A19%3A4%3A261 . 2007-09-28 . 12512920 . 10.1385/MO:19:4:261 . 1068099 .
12. Zaleplon . Accessed 15 April 2021.
13. Morphine . Accessed 15 April 2021.
14. Flurazepam . Accessed 15 April 2021.
15. Web site: Trexall, Otrexup (methotrexate) dosing, indications, interactions, adverse effects, and more. reference.medscape.com.
16. Manfredonia . John . Prescribing Methadone for Pain Management in End-of-Life Care . Journal of the American Osteopathic Association . 105 . March 2005 . 3 supplement . S18-21 . 2007-01-29 . 18154194 . 20 May 2007 . https://web.archive.org/web/20070520062222/http://www.jaoa.org/cgi/content/full/105/3_suppl/18S . dead .
17. Diazepam . Accessed 15 April 2021.
18. Book: Austria-Codex. Haberfeld H . Epilan D 100 mg-Tabletten. Österreichischer Apothekerverlag. Vienna. 2020. German.
19. Buprenorphine . Accessed 15 April 2021.
20. Web site: Klonopin (clonazepam) Prescribing Guide . October 2017 . Genentech USA, Inc. . 2019-01-20.
21. Book: Asiri . Yousif A. . Mostafa . Gamal A.E. . Profiles of Drug Substances, Excipients and Related Methodology . 35 . Donepezil . Elsevier . 2010 . 978-0-12-380884-4 . 1871-5125 . 10.1016/s1871-5125(10)35003-5 . 22469221 . 117–150 . Plasma donepezil concentrations decline with a half-life of approximately 70 h. Sex, race, and smoking history have no clinically significant influence on plasma concentrations of donepezil [46–51]..
22. Fluoxetine . Accessed 15 April 2021.
23. Book: Austria-Codex. Haberfeld H . Sedacoron 200 mg-Tabletten. Österreichischer Apothekerverlag. Vienna. 2020. German.
24. Web site: Caprelsa (vandetanib) Tablets, for Oral Use. Full Prescribing Information . Sanofi Genzyme, Cambridge, MA, Dec 2016. . 24 February 2020.
25. Book: Austria-Codex. Haberfeld H . Avodart 0,5 mg Weichkapseln. Österreichischer Apothekerverlag. Vienna. 2020. German.
26. Web site: Sirturo (bedaquiline) Tablets. Full Prescribing Information . Janssen Products, Dec 2012. . 24 February 2020.
27. Lead toxicity update. A brief review.. Nikolas C Papanikolaou . Eleftheria G Hatzidaki . Stamatis Belivanis . George N Tzanakakis . Aristidis M Tsatsakis . Medical Science Monitor. 2005. 11. 10. RA329-36 . 16192916 .
28. Griffin et al. 1975 as cited in ATSDR 2005
29. Rabinowitz et al. 1976 as cited in ATSDR 2005
30. Baribeau . Danielle A . Anagnostou . Evdokia . Oxytocin and vasopressin: linking pituitary neuropeptides and their receptors to social neurocircuits . Frontiers in Neuroscience . 9 . 335 . 2015 . 1662-453X . 10.3389/fnins.2015.00335 . 26441508 . 4585313. free .
31. Book: Malenka RC, Nestler EJ, Hyman SE . Sydor A, Brown RY . Molecular Neuropharmacology: A Foundation for Clinical Neuroscience . 2009 . McGraw-Hill Medical . New York . 9780071481274 . 195 . 2nd . Chapter 7: Neuropeptides . 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..
32. McGregor IS, Callaghan PD, Hunt GE . 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 . May 2008 . 18475254 . 2442436 . 10.1038/bjp.2008.132 . 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).
33. Weisman O, Zagoory-Sharon O, Feldman R . Intranasal oxytocin administration is reflected in human saliva . . 37 . 9 . 1582–6 . 2012 . 22436536 . 10.1016/j.psyneuen.2012.02.014 . 25253083 .
34. Huffmeijer R, Alink LR, Tops M, Grewen KM, Light KC, Bakermans-Kranenburg MJ, Ijzendoorn MH . Salivary levels of oxytocin remain elevated for more than two hours after intranasal oxytocin administration . . 33 . 1 . 21–5 . 2012 . 22467107.
35. Book: Miles Hacker. William S. Messer. Kenneth A. Bachmann. Pharmacology: Principles and Practice. 19 June 2009. Academic Press. 978-0-08-091922-5. 205.
36. Book: Frymoyer. Adam. Infectious Disease and Pharmacology. Pharmacokinetic Considerations in Neonates. 2019. 123–139. 10.1016/B978-0-323-54391-0.00011-4. 9780323543910. 57512164 .
37. Book: Chan. Patrick. Uchizono. James A.. Essentials of Pharmacology for Anesthesia, Pain Medicine, and Critical Care. Pharmacokinetics and Pharmacodynamics of Anesthetics. 2015. 3–47. 10.1007/978-1-4614-8948-1_1. 978-1-4614-8947-4.
38. Book: Bonate. Peter L.. Howard. Danny R.. Clinical study design and analysis. 2004. AAPS Press. Arlington, VA. 9780971176744. 237 - 239.
39. Toutain. P. L.. Bousquet-Melou. A.. Plasma terminal half-life. Journal of Veterinary Pharmacology and Therapeutics. 27. 6. 2004. 427–439. 0140-7783. 10.1111/j.1365-2885.2004.00600.x. 15601438.
40. Book: Younggil Kwon. Handbook of Essential Pharmacokinetics, Pharmacodynamics and Drug Metabolism for Industrial Scientists. 8 May 2007. Springer Science & Business Media. 978-0-306-46820-9. 24–.