Biological half-life

Biological half-life (also known as Elimination half-life, Pharmacologic half-life and $T_{\frac {1}{2}}$ ) of a biological substance such as medication is the time it takes from its maximum concentration (C_max) to half maximum concentration in human body,[1][2][3][4][5][6] and is denoted by the abbreviation $t_{\frac {1}{2}}$ . [2][5]

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 cleansing through the function of the liver 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.[7]

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 and pharmacology 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. In contrast, the stability of a substance direct in plasma is described with plasma stability that 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.[8]

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.[9][10] This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). The basis of this decontamination method (used at Harwell) 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. 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

Substance	Biological half-life
Adenosine	Less than 10 seconds
Norepinephrine	2 minutes
Oxaliplatin	14 minutes[11]
Salbutamol	1.6 hours
Zaleplon	1–2 hours
Morphine	2–3 hours
Methotrexate	3–10 hours (lower doses), 8–15 hours (higher doses)[12]
Phenytoin	12–42 hours
Methadone	15–72 hours In rare cases up to 8 days[13]
Buprenorphine	16–72 hours
Clonazepam	30–40 hours[14]
Flurazepam	19–100 hours Active metabolite (desflurazepam): 1.75–10.4 days
Diazepam	20–100 hours Active metabolite (nordazepam): 1.5–8.3 days
Donepezil	3 days (70 hours)[15]
Fluoxetine	4–6 days Active lipophilic metabolite (seproxetine): 4–16 days
Vandetanib	19 days[16]
Amiodarone	25–110 days
Dutasteride	35 days
Bedaquiline	165 days[17]

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.[18]

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.[19][20]
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.[21] 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.[22][23] 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.[24][25] 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.[21]

Rate equations

First-order elimination

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 by

C(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:[26]

{\frac {dC}{dt}}=-kC.

The half-life for this process is[26]

t_{\frac {1}{2}}={\frac {\ln 2}{k}}.\,

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

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 t_½) 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_½ 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.[26] For a more detailed description see Pharmacokinetics § Multi-compartmental models.

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.	$\tau$	$\mathrm {s}$	Design parameter	24 h
C_max	The peak plasma concentration of a drug after administration.	$C_{\text{max}}$	$\mathrm {M}$	Direct measurement	60.9 mmol/L
t_max	Time to reach C_max.	$t_{\text{max}}$	$\mathrm {s}$	Direct measurement	3.9 h
C_min	The lowest (trough) concentration that a drug reaches before the next dose is administered.	$C_{{\text{min}},{\text{ss}}}$	$\mathrm {M}$	Direct measurement	27.7 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).	$V_{\text{d}}$	$\mathrm {m} ^{3}$	${\frac {D}{C_{0}}}$	6.0 L
Concentration	Amount of drug in a given volume of plasma.	$C_{0},C_{\text{ss}}$	$\mathrm {M}$	${\frac {D}{V_{\text{d}}}}$	83.3 mmol/L
Absorption half-life	The time required for the concentration of the drug to double its original value for oral and other extravascular routes.	$t_{{\frac {1}{2}}a}$	$\mathrm {s}$	${\frac {\ln(2)}{k_{\text{a}}}}$	1.0 h
Absorption rate constant	The rate at which a drug enters into the body for oral and other extravascular routes.	$k_{\text{a}}$	$\mathrm {s} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}a}}}$	0.693 ⁻¹
Elimination half-‍life	The time required for the concentration of the drug to reach half of its original value.	$t_{{\frac {1}{2}}b}$	$\mathrm {s}$	${\frac {\ln(2)}{k_{\text{e}}}}$	12 h
Elimination rate constant	The rate at which a drug is removed from the body.	$k_{\text{e}}$	$\mathrm {s} ^{-1}$	${\frac {\ln(2)}{t_{{\frac {1}{2}}b}}}={\frac {CL}{V_{\text{d}}}}$	0.0578 h⁻¹
Infusion rate	Rate of infusion required to balance elimination.	$k_{\text{in}}$	$\mathrm {mol/s}$	$C_{\text{ss}}\cdot CL$	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 mmol/L·h
Area under the curve		$AUC_{\tau ,{\text{ss}}}$	$\mathrm {M} \cdot \mathrm {s}$	$\int _{t}^{t+\tau }C\,\operatorname {d} t$	1,320 mmol/L·h
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.	$\%PTF$	$\%$	${\frac {C_{{\text{max}},{\text{ss}}}-C_{{\text{min}},{\text{ss}}}}{C_{{\text{av}},{\text{ss}}}}}\cdot 100\%$ where $C_{{\text{av}},{\text{ss}}}={\frac {1}{\tau }}AUC_{\tau ,{\text{ss}}}$	41.8%

References

Pharmacology in one semester
"Half-Life (t½) Definition". AIDSinfo. 2020-02-19. Retrieved 2020-02-20.
"Pharmacokinetics 1 - Introduction" on YouTube
Curry, Stephen H. (1993). "PHARMACOKINETICS OF ANTIPSYCHOTIC DRUGS". Antipsychotic Drugs and their Side-Effects. Elsevier. pp. 127–144. doi:10.1016/b978-0-12-079035-7.50015-4. ISBN 978-0-12-079035-7. The elimination half-life measures the kinetics of loss of drug from the body as a whole once all distribution equilibria have been achieved.
Dasgupta, Amitava; Krasowski, Matthew D. (2020). "Pharmacokinetics and therapeutic drug monitoring". Therapeutic Drug Monitoring Data. Elsevier. pp. 1–17. doi:10.1016/b978-0-12-815849-4.00001-3. ISBN 978-0-12-815849-4. 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.
Toutain, P. L.; Bousquet-Melou, A. (2004). "Plasma terminal half-life" (PDF). Journal of Veterinary Pharmacology and Therapeutics. 27 (6): 427–439. doi:10.1111/j.1365-2885.2004.00600.x. PMID 15601438. Archived from the original (PDF) on 2020-02-20. 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.
IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Biological Half Life". doi:10.1351/goldbook.B00658
Lin VW; Cardenas DD (2003). Spinal Cord Medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1-888799-61-7.
Nordberg, Gunnar (2007). Handbook on the toxicology of metals. Amsterdam: Elsevier. p. 119. ISBN 978-0-12-369413-3.
Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of effective treatments in psychiatry. Cambridge, UK: Cambridge University Press. p. 295. ISBN 978-0-521-84228-0.
Ehrsson, Hans; et al. (Winter 2002). "Pharmacokinetics of oxaliplatin in humans". Medical Oncology. Medical Oncology. 19 (4): 261–5. doi:10.1385/MO:19:4:261. PMID 12512920. 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 for Pain Management in End-of-Life Care". Journal of the American Osteopathic Association. 105 (3 supplement): S18-21. PMID 18154194. Retrieved 2007-01-29.
"Klonopin (clonazepam) Prescribing Guide" (PDF). Genetech USA, Inc. October 2017. Retrieved 2019-01-20.
Asiri, Yousif A.; Mostafa, Gamal A.E. (2010). "Donepezil". Profiles of Drug Substances, Excipients and Related Methodology. 35. Elsevier. pp. 117–150. doi:10.1016/s1871-5125(10)35003-5. ISBN 978-0-12-380884-4. ISSN 1871-5125. PMID 22469221. 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].
"Caprelsa (vandetanib) Tablets, for Oral Use. Full Prescribing Information" (PDF). Sanofi Genzyme, Cambridge, MA, Dec 2016. Retrieved 24 February 2020.
"Sirturo (bedaquiline) Tablets. Full Prescribing Information" (PDF). Janssen Products, Dec 2012. Retrieved 24 February 2020.
Nikolas C Papanikolaou; Eleftheria G Hatzidaki; Stamatis Belivanis; George N Tzanakakis; Aristidis M Tsatsakis (2005). "Lead toxicity update. A brief review". Medical Science Monitor. 11 (10): RA329-36. PMID 16192916.
Griffin et al. 1975 as cited in ATSDR 2005
Rabinowitz et al. 1976 as cited in ATSDR 2005
Baribeau, Danielle A; Anagnostou, Evdokia (2015). "Oxytocin and vasopressin: linking pituitary neuropeptides and their receptors to social neurocircuits". Frontiers in Neuroscience. 9: 335. 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 (eds.). Molecular Neuropharmacology: A Foundation for Clinical Neuroscience (2nd ed.). New York: McGraw-Hill Medical. p. 195. ISBN 9780071481274. 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.
Bonate, Peter L.; Howard, Danny R. (2004). Clinical study design and analysis. Arlington, VA: AAPS Press. pp. 237–239. ISBN 9780971176744.

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[1] Pharmacology in one semester

[AIDSinfo_2020-2] "Half-Life (t½) Definition". AIDSinfo. 2020-02-19. Retrieved 2020-02-20.

[3] "Pharmacokinetics 1 - Introduction" on YouTube

[Curry_1993_pp._127–144-4] Curry, Stephen H. (1993). "PHARMACOKINETICS OF ANTIPSYCHOTIC DRUGS". Antipsychotic Drugs and their Side-Effects. Elsevier. pp. 127–144. doi:10.1016/b978-0-12-079035-7.50015-4. ISBN 978-0-12-079035-7. The elimination half-life measures the kinetics of loss of drug from the body as a whole once all distribution equilibria have been achieved.

[Dasgupta_Krasowski_2020_pp._1–17-5] Dasgupta, Amitava; Krasowski, Matthew D. (2020). "Pharmacokinetics and therapeutic drug monitoring". Therapeutic Drug Monitoring Data. Elsevier. pp. 1–17. doi:10.1016/b978-0-12-815849-4.00001-3. ISBN 978-0-12-815849-4. 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.

[6] Toutain, P. L.; Bousquet-Melou, A. (2004). "Plasma terminal half-life" (PDF). Journal of Veterinary Pharmacology and Therapeutics. 27 (6): 427–439. doi:10.1111/j.1365-2885.2004.00600.x. PMID 15601438. Archived from the original (PDF) on 2020-02-20. 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.

[7] IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Biological Half Life". doi:10.1351/goldbook.B00658

[SCM-8] Lin VW; Cardenas DD (2003). Spinal Cord Medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1-888799-61-7.

[isbn0-12-369413-2-9] Nordberg, Gunnar (2007). Handbook on the toxicology of metals. Amsterdam: Elsevier. p. 119. ISBN 978-0-12-369413-3.

[isbn0-521-84228-X-10] Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of effective treatments in psychiatry. Cambridge, UK: Cambridge University Press. p. 295. ISBN 978-0-521-84228-0.

[11] Ehrsson, Hans; et al. (Winter 2002). "Pharmacokinetics of oxaliplatin in humans". Medical Oncology. Medical Oncology. 19 (4): 261–5. doi:10.1385/MO:19:4:261. PMID 12512920. Archived from the original on 2007-09-28. Retrieved 2007-03-28.

[12] "Trexall, Otrexup (methotrexate) dosing, indications, interactions, adverse effects, and more". reference.medscape.com.

[13] Manfredonia, John (March 2005). "Prescribing Methadone for Pain Management in End-of-Life Care". Journal of the American Osteopathic Association. 105 (3 supplement): S18-21. PMID 18154194. Retrieved 2007-01-29.

[14] "Klonopin (clonazepam) Prescribing Guide" (PDF). Genetech USA, Inc. October 2017. Retrieved 2019-01-20.

[Asiri_Mostafa_2010_pp._117–150-15] Asiri, Yousif A.; Mostafa, Gamal A.E. (2010). "Donepezil". Profiles of Drug Substances, Excipients and Related Methodology. 35. Elsevier. pp. 117–150. doi:10.1016/s1871-5125(10)35003-5. ISBN 978-0-12-380884-4. ISSN 1871-5125. PMID 22469221. 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].

[16] "Caprelsa (vandetanib) Tablets, for Oral Use. Full Prescribing Information" (PDF). Sanofi Genzyme, Cambridge, MA, Dec 2016. Retrieved 24 February 2020.

[17] "Sirturo (bedaquiline) Tablets. Full Prescribing Information" (PDF). Janssen Products, Dec 2012. Retrieved 24 February 2020.

[18] Nikolas C Papanikolaou; Eleftheria G Hatzidaki; Stamatis Belivanis; George N Tzanakakis; Aristidis M Tsatsakis (2005). "Lead toxicity update. A brief review". Medical Science Monitor. 11 (10): RA329-36. PMID 16192916.

[19] Griffin et al. 1975 as cited in ATSDR 2005

[20] Rabinowitz et al. 1976 as cited in ATSDR 2005

[BaribeauAnagnostou2015-21] Baribeau, Danielle A; Anagnostou, Evdokia (2015). "Oxytocin and vasopressin: linking pituitary neuropeptides and their receptors to social neurocircuits". Frontiers in Neuroscience. 9: 335. doi:10.3389/fnins.2015.00335. ISSN 1662-453X. PMC 4585313. PMID 26441508.

[Oxy_BBB-22] Malenka RC, Nestler EJ, Hyman SE (2009). "Chapter 7: Neuropeptides". In Sydor A, Brown RY (eds.). Molecular Neuropharmacology: A Foundation for Clinical Neuroscience (2nd ed.). New York: McGraw-Hill Medical. p. 195. ISBN 9780071481274. 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.

[Oxytocinergic_circuit-23] 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_2012-24] 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_2012-25] 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.

[Bonate-26] Bonate, Peter L.; Howard, Danny R. (2004). Clinical study design and analysis. Arlington, VA: AAPS Press. pp. 237–239. ISBN 9780971176744.