# Half-life time

##### Physical half-life time (Tp)

The time interval required for an amount of certain radioactive nuclei to decay to half of its original value. Tp 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 (Tb)

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

##### Effective half-life time (Te)

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 Te is calculated using :

Te = (Tp x Tb) / (Tp + Tb) or simply 1/Te = 1/Tp+1/Tb

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

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

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

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