Effective half-life

The effective half-life (Teff) is the time required for the radioactivity of a radiopharmaceutical within an organ or the whole body to fall to half its original value under the combined action of radioactive decay (physical half-life, Tphys) and biological elimination (biological half-life, Tbiol). Because both processes remove activity in parallel and independently, their rate constants add: 1/Teff = 1/Tphys + 1/Tbiol, equivalently Teff = (Tphys x Tbiol)/(Tphys + Tbiol); Teff is always shorter than whichever of Tphys or Tbiol is shorter, and it converges towards the shorter of the two when the two half-lives differ greatly (for a radionuclide with a very long physical half-life and fast biological clearance, Teff approaches Tbiol, and vice versa).

Effective half-life is the quantity that actually appears in dosimetry calculations, because it describes how the true, measurable radioactivity in a source organ declines over time, which is exactly what a time-activity curve records and what must be integrated to obtain the time-integrated activity used in the MIRD formalism. It can be measured directly from serial quantitative imaging without needing to separately determine the physical and biological components.

A practical example: 177Lu has a physical half-life of about 6.65 days; if a PSMA-targeted ligand clears from the kidneys with a biological half-life of a few days, the effective half-life in the kidney will be shorter than 6.65 days, meaning the kidney's radiation exposure is delivered, and finishes, faster than lutetium-177's own decay alone would suggest.