# Biological half-life

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Editor-In-Chief: C. Michael Gibson, M.S., M.D. [1]

The biological half-life of a substance is the time it takes for a substance (drug, radioactive nuclide, or other) to lose half of its pharmacologic, physiologic, or radiologic activity, as per the MeSH definition.

Biological half-life is an important pharmacokinetic parameter and is usually denoted by the abbreviation t1/2.[1]

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 kinetics. See the article rate equation.

## Examples of biological half-lives

### Water

The biological half-life of water in a human is about 7 to 10 days. It can be altered by behavior. Drinking large amounts of alcohol will reduce the biological half-life of water in the body. This has been used to decontaminate humans who are internally contaminated with tritiated water (tritium). Drinking the same amount of water would have a similar effect, but many would find it difficult to drink a large volume of water. 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 (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.

### Prescription medications

Substance Half-life Notes
Amiodarone 25 days
Cisplatin 20 to 30 minutes
Chlorambucil 1.53 hours
Digoxin 24 to 36 hours
Fluoxetine 1 to 6 days

The active metabolite of fluoxetine is lipophilic and migrates slowly from the brain to the blood. The metabolite has a biological half-life of 4 to 16 days.

Methadone 15 to 60 hours, in rare cases up to 190 hours.[2]
Oxaliplatin 14 minutes[3]
Salbutamol 7 hours

### 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. 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.

• 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.
• 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.

## Rate equations

### Zero-order elimination

There are circumstances where the half-life varies with the concentration of the drug. 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). Thus the half-life, under these circumstances, is proportional to the initial concentration of the drug A0 and inversely proportional to the zero-order rate constant k0 where:

${\displaystyle t_{1/2}={\frac {0.5A_{0}}{k_{0}}}\,}$

### First-order elimination

This process is usually a logarithmic process - that is, a constant proportion of the agent is eliminated per unit time (Birkett, 2002). Thus the fall in plasma concentration after the administration of a single dose is described by the following equation:

${\displaystyle C_{t}=C_{0}e^{-kt}\,}$
• 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:

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

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

${\displaystyle t_{1/2}={\frac {{\ln 2}.{V_{D}}}{CL}}\,}$

In clinical practice, this means that it takes just over 4.7 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 hours; 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 90 days) are usually started with a loading dose to achieve their desired clinical effect more quickly.

## See also

• Browsing MeSH:
• Half-life, pertaining to the general mathematical concept in physics or pharmacology.
• Kinetics

## References

• Birkett DJ (2002). Pharmacokinetics Made Easy (Revised Edition). Sydney: McGraw-Hill Australia. ISBN 0-07-471072-9.
1. Template:GoldBookRef
2. Manfredonia, John (March 2005). "Prescribing Methadone for Pain Management in End-of-Life Care". JAOA—The Journal of the American Osteopathic Association. Retrieved 2007-01-29.
3. Ehrsson, Hans; et al. (Winter 2002). "Pharmacokinetics of oxaliplatin in humans". Medical Oncology. Retrieved 2007-03-28.