# Biology:Biological half-life

The biological half-life of a biological substance is the time it takes for half to be removed by biological processes. This concept is used when the rate of removal is roughly exponential.[1] It is often denoted by the abbreviation $\displaystyle{ t_{\frac{1}{2}} }$. 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. 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.[2]

## 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.[3][4] 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
Norepinephrine 2 minutes
Oxaliplatin 14 minutes[5]
Salbutamol 1.6 hours
Zaleplon 1–2 hours
Morphine 2–3 hours
Methotrexate 3–10 hours (lower doses),

8–15 hours (higher doses)[6]

Phenytoin 12–42 hours

In rare cases up to 8 days[7]

Buprenorphine 16–72 hours
Clonazepam 30-40 hours[8]
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
Fluoxetine 4–6 days

Active lipophilic metabolite 4–16 days

Amiodarone
Dutasteride 35 days
Bedaquiline 165 days

### 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.[9]

• 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.[10][11]
• 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.[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

Main page: Chemistry:Rate equation

### First-order elimination

Half-times apply to processes where the elimination rate is exponential. If $\displaystyle{ C(t) }$ is the concentration of a substance at time $\displaystyle{ t }$, its time dependence is given by

$\displaystyle{ C(t) = C(0) e^{-kt} \, }$

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:[17]

$\displaystyle{ \frac{d C}{d t} = -k C. }$

The half-life for this process is[17]

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

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

$\displaystyle{ t_\frac{1}{2} = \frac{{\ln 2}\cdot{V_D}}{CL} \, }$

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

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.[17] For a more detailed description see Pharmacokinetics § Multi-compartmental models.

## References

1. IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version:  (2006–) "Biological Half Life". doi:10.1351/goldbook.B00658
2. Lin VW; Cardenas DD (2003). Spinal Cord Medicine. Demos Medical Publishing, LLC. p. 251. ISBN 1-888799-61-7.
3. Nordberg, Gunnar (2007). Handbook on the toxicology of metals. Amsterdam: Elsevier. pp. 119. ISBN 978-0-12-369413-3.
4. Silk, Kenneth R.; Tyrer, Peter J. (2008). Cambridge textbook of effective treatments in psychiatry. Cambridge, UK: Cambridge University Press. pp. 295. ISBN 978-0-521-84228-0.
5. Ehrsson, Hans (Winter 2002). Pharmacokinetics of oxaliplatin in humans. Medical Oncology. Archived from the original on 2007-09-28. Retrieved 2007-03-28.
6. Manfredonia, John (March 2005). "Prescribing Methadone for Pain Management in End-of-Life Care". Journal of the American Osteopathic Association 105 (3 supplement): 18S. Retrieved 2007-01-29.
7. "Klonopin (clonazepam) Prescribing Guide". Genetech USA, Inc.. October 2017.
8. 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): RA329-336.
9. Griffin et al. 1975 as cited in ATSDR 2005
10. Rabinowitz et al. 1976 as cited in ATSDR 2005
11. 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. PMID 26441508.
12. "Chapter 7: Neuropeptides". Molecular Neuropharmacology: A Foundation for Clinical Neuroscience (2nd ed.). New York: McGraw-Hill Medical. 2009. 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."
13. "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. doi:10.1038/bjp.2008.132. 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)".
14. "Intranasal oxytocin administration is reflected in human saliva". Psychoneuroendocrinology 37 (9): 1582–6. 2012. doi:10.1016/j.psyneuen.2012.02.014. PMID 22436536.
15. "Salivary levels of oxytocin remain elevated for more than two hours after intranasal oxytocin administration". Neuro Endocrinology Letters 33 (1): 21–5. 2012. PMID 22467107.
16. Bonate, Peter L.; Howard, Danny R. (2004). Clinical study design and analysis. Arlington, VA: AAPS Press. pp. 237–239. ISBN 9780971176744.