Half-life

The half-life of a substance is the time taken for half of the dose to be eliminated or metabolised.

Half-life

The half-life of a substance, usually denoted by t_1/2, is the time taken for half of the dose to be eliminated or metabolised. The shorter the half-life of a drug, the quicker it is eliminated. The half life of a drug can be influenced by many individual factors, such as metabolic, and genetic.

General

When the drug concentration is around 5% it is said to be negligible, therefore around 4 or 5 half lives must elapse until the drug is eliminated.*



*This is not to say the drug cannot be detected via drug test.
Drug tests will be able to identify trace amounts of a drug even a few days after it has been consumed.

Calculating half-life

T half life	amount of drug	3hr HL	8hr HL	18-50hr HL	4-6day HL
		morphine	MDMA	Clonazepam	Fluoxetine
0	100%	0	0	0	0
1	50%	3	8	18-50	4-6
2	25%	6	16	36-100	8-12
3	12.5%	9	24	54-150	12-18
4	6.25%	12	32	72-200	16-24
5	3.125%	15	40	90-250	20-30
		15 hours	40 hours	~4 to 10 days	3-4 weeks

The above table shows how long it would take to eliminate 4 different drugs from the body. Opiates and stimulants tend to have shorter half lives then benzodiazepines, although there are many exceptions. Anti-depressants and anti-psychotics tend to have very long half lives.

An example using dosages instead of percent: if the half-life of a drug is, say, 4 hours and you ingest 1g (1,000mg), then after 4 hours you'll have 500mg, a half of 1g, in your system, after 8 hours you'll have 250mg, a half of 500mg, and after 12 hours you'll have 125mg, etc.

Mathematics

More formally, the total concentration of a substance in the body can be calculated by

C_t=C₀ e^-kt

Where:
- C_t is the concentration at time t
- C₀ is the initial concentration
- k is the elimination constant, given by k= log(2)/t_1/2. [Where log is taken to base e, giving a value of log(2)=0.693. The value 0.7 can be used without a great deal of loss of precision]

Important things to know about the half-life model

There are several important points to me made here. Firstly, this is a mathematical model, and pharmacological elimination kinetics do not necessarily follow it exactly, although for a large range of substances at a large range of doses it is a good approximation [needs referencing - D]. Some drugs, alcohol and short-acting barbiturates more closely follow zeroth order elimination profiles, i.e. a fixed amount of the drug is metabolised in a unit of time until the drug is totally elimiated. An example of this is that alcohol is metabolised at roughly the rate of one unit (10mg of ethanol) per hour.

Secondly, half-lives can vary wildly between different people. This is especially true, for instance, if an enzyme is involved in metabolism, and the quantity of enzyme present in individuals varies according to genetics.

Thirdly, some drugs are metabolised into active metabolites. Indeed some prodrugs are not pharmacologically active themselves, but are metabolised to pharmacologically active agents. An example of this is heroin which is metabolised to morphine. Other drugs such as the benzodiazepine chlordiazepoxide (Librium) have relatively short half-lives themselves but have metabolites with much longer half-lives.

There are other complications, such as when there are different metabolic pathways to different metabolites, and this is the subject of pharmacokinetics.