Effective Half-life

Ideally, a radiopharmaceutical's effective half­life equals approximately 1.5 times the duration of the diagnostic procedure. This provides a good compromise between our desire to minimize radiation dose to the patient and to maximize the dose to be injected so counting statistics are good and image quality is optimal. With the sole exception of Xe­133 or another noble gas used for a ventilation study, there is no other procedure in which images are acquired and the radiopharmaceutical is expelled from the body almost quantitatively within a few minutes of completing the study. Most compounds exhibit exponential clearance patterns so their effective half-life is moderately long (measured in hours or days as opposed to seconds or minutes).

The relationship between effective half-life, biological half-life, and physical half-life is shown in the equation below:

1 / t(eff) = 1 / t(biol) + 1 / t(phys )

In the special case where the biological half-life of a particular compound is very long compared to the physical half-life (e.g., Tc­99m sulfur colloid in the liver), 1 / t(biol) is a very small number, approximating 0, and the effective half-life therefore equals the physical half-life.

Similarly, where the physical half-life is very long compared to the biological half-life (e.g., Xe­133 gas in the lungs), 1 / t(phys) is a very small number, approximating 0, and the effective half-life equals the biological half-life.

The classical example of an ideal effective half-life is that of Tc­99m MDP, which has an effective half-life = 6 hr; since bone imaging is a 4 hr procedure, the ratio of effective half-life to duration of the test is 1.5:1, considered ideal. On the other hand, Tc­99m sulfur colloid has a effective half-life of 6 hr in the liver, but the procedure takes only 1 hr. This 6:1 ratio doesn't mean that a liver scan is a bad procedure to perform, but rather that the compound has a residence time in the liver that is longer than desirable, resulting in an increase in the radiation dose to the target organ. In this particular case, simply switching from Tc­99m sulfur colloid to Tc­99m microaggregated albumin decreases the t_eff from 6 hr to approximately 3 hr, lowering the ratio of effective half-life to procedure length to 3:1 and decreasing the radiation dose by 50%.