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:

${\displaystyle {\lambda _{e}}\,={\lambda _{p}}\,+{\lambda _{b}}\,}$ 

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

${\displaystyle t_{1/2}={\frac {\ln(2)}{\lambda _{e}}}}$ 

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]

${\displaystyle {\frac {1}{t_{1/2e}}}={\frac {1}{t_{1/2p}}}+{\frac {1}{t_{1/2b}}}}$  ,
or
${\displaystyle t_{1/2e}={\frac {t_{1/2p}\cdot t_{1/2b}}{t_{1/2p}+t_{1/2b}}}}$ .

• Biological Half-life