Half-life time

The half-life time is the duration it takes for any physical process to reduce the initial amount to fifty percent of its initial value.

Physical half-life time (T_p)

The time interval required for an amount of certain radioactive nuclei to decay to half of its original value. T_p is always a constant for a particular radioactive isotope and is unaffected by changes in surrounding such as temperature or pressure.

Biological half-life time (T_b) 

The time interval required for the body to eliminate 50% of any substance by normal routes of elimination: metabolic turnover and excretion. T_b is affected by many external factors such as hydration, hepatic function and renal function.

Effective half-life time (T_e)

The time interval required for the radioactivity of a certain amount of radioactive substance distributed in tissues and organs to decrease to half its original value due to radioactive decay and biological elimination.

In most cases T_e is calculated using:

T_e = (T_p x T_b) / (T_p + T_b) or simply 1/T_e = 1/T_p+1/T_b

However, there are three special situations described below to understand T_e better ².

1) T_p >>> T_b then T_e ~ T_b. An example would be Xe-133 which is used for pulmonary ventilation studies. It has a T_p of 5.3 days and T_b of 15 seconds. T_e of Xe-133 is equal to T_b which is 15 seconds

2) T_b >>> T_p then T_e ~ T_p. An example would be Tc-99m sulfur colloid used for liver scans which has a T_p of 6 hours and T_b which is indefinitely long. The T_e for Tc-99m sulfur colloid is therefore equal to T_p which is 6 hours

3) T_p = T_b then T_e = 1/2 T_p = 1/2 T_b. An example would be Tc-99m MAA (macroaggregated albumin) used for pulmonary perfusion studies where T_p = 6 hours and T_b = 6 hours and therefore T_e = 3 hours