Effective Half Life

The effective half-life of a radionuclide is the time taken for the activity of the sample to reduce to one half of its value in the body of a patient.

Effective half life has two components:

the physical half life (related to the probability of spontaneous decay of the atom – this is fixed and reliably known) and

the biological half life (related to the time taken for half of the radionuclide being expelled from the body by natural biological processes eg. excretion, sweating, respiration etc.). Biological half life varies with the individual and the target organ for the radionuclide as it is dependant on metabolic processes. This makes it less reliably predictable and poses problems for dosage calculations.

l_E = l_P + l_B

Where:-

l_E = effective decay constant = ln 2/T_E( effective half life)

l_p = physical decay constant = ln 2/T_P( physical half life)

l_B = biological decay constant = ln 2/T_B( biological half life)

¹/T_E = ¹/T_P + ¹/T_B

This means that when Technetium 99m is used as a radioactive tracer and is studied with the gamma camera the operator has to take into account not only its 6 hour half life but also the rate at which it will be flushed biologically out of the body. This will depend upon the chemical compound to which it is attached and the way an individual’s metabolism copes with that compound.