What is the expression to calculate the effective half-life?

The effective half-life is determined by the interaction between the physical half-life and the biological half-life of a radioactive substance. The expression that correctly calculates the effective half-life is obtained through the relationship of these two half-lives, which are represented by Tp (physical half-life) and Tb (biological half-life).

The formula for calculating the effective half-life incorporates both the physical and biological half-lives, reflecting how both processes collectively affect the decay of the radionuclide in a biological system. This is captured in the expression [(TpxTb)/(Tp+TB)], which gives a weighted average of the two half-lives. This calculation is critical in PET imaging because knowing the effective half-life allows for accurate timing in imaging protocols and enhances the reliability of quantifying tracer uptake in tissues.

The other expressions do not accurately represent the relationship necessary for calculating the effective half-life in a biological context. For instance, multiplying or averaging the two half-lives without the appropriate relationships will not yield the effective decay time of the substance within a biological system, thus reaffirming why the selected expression is fundamental to understanding the dynamics of radiotracer behavior in PET imaging.