# Medicine:Effective half-life

In pharmacokinetics, the **effective half-life** is the rate of accumulation or elimination of a biochemical or pharmacological substance in an organism; it is the analogue of biological half-life when the kinetics are governed by multiple independent mechanisms. This is seen when there are multiple mechanisms of elimination, or when a drug occupies multiple pharmacological compartments. It reflects the cumulative effect of the individual half-lives, as observed by the changes in the actual serum concentration of a drug under a given dosing regimen. The complexity of biological systems means that most pharmacological substances do not have a single mechanism of elimination, and hence the observed or effective half-life does not reflect that of a single process, but rather the summation of multiple independent processes.

## Radionuclides

When radionuclides are used pharmacologically, for example in radiation therapy, they are eliminated through a combination of radioactive decay and biological excretion. An effective half-life of the drug will involve a decay constant that represents the sum of the biological and physical decay constants, as in the formula:

- [math]\displaystyle{ {\lambda_e} \, = {\lambda_p} \, + {\lambda_b} \, }[/math]

With the decay constant it is possible to calculate the effective half-life using the formula:

- [math]\displaystyle{ t_{1/2} = \frac{\ln (2)}{\lambda_e} }[/math]

The biological decay constant is often approximated as it is more difficult to accurately determine than the physical decay constant.

Alternatively, since the radioactive decay contributes to the "*physical* (i.e. *radioactive*)" half-life, while the metabolic elimination processes determines the "*biological*" half-life of the radionuclide, the two act as parallel paths for elimination of the radioactivity, the effective half-life could also be represented by the formula:^{[1]}^{[2]}

- [math]\displaystyle{
\frac{1}{t_{1/2e}} = \frac{1}{t_{1/2p}} + \frac{1}{t_{1/2b}} }[/math] ,

or

[math]\displaystyle{ t_{1/2e} = \frac{t_{1/2p}\cdot t_{1/2b}} {t_{1/2p} + t_{1/2b}} }[/math].

## External links

## References

- ↑ Biological Effects of Radiation ©1996, Kenneth R. Koehler.
- ↑ Half-life, effective, European Nuclear Society

Original source: https://en.wikipedia.org/wiki/Effective half-life.
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