Biological half-life

The biological half-life of a substance is the time required for half of that substance to be removed from an organism by either a physical or a chemical process.

While a radioactive substance 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.

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 behaviour. Drinking large amounts of beer 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 as Harwell) is to increase the rate at which the water in the body is replaced with new water.

Alcohol

For instance, 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 a person who has ingested methanol an alcoholic drink. 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.

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:

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

Frst-order elimination

This process is usually a first-order 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:

C_{t} = C_{0} e^{-kt} \,

C_t 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 = \frac{\ln 2}{t_{1/2}} \,

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} = \frac{CL} \,

A prescription medication

Some substances migrate slowly from the brain to the blood. Prozac, a prescription antidepressant, remains a long time in the brain because it is lipophilic.

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 substance, is it 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.

Cesium 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.

A substance can have an effect on the health of a person long after the substance has left the body. For example, a car crash under the influence of chemicals may have consequences long into the future. A carcinogenic substance may cause cancer cells to appear, which may continue to multiply even after exposure to the carcinogen has stopped.

References

Birkett DJ (2002). Pharmacokinetics Made Easy (Revised Edition). Sydney: McGraw-Hill Australia. ISBN 0-07-471072-9.

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