Decay correction

Decay correction is the mathematical adjustment of a measured activity or image intensity to remove the effect of ongoing radioactive decay between the time of measurement and a chosen reference time, using the standard exponential decay law At = A0 x e^(-λt), where λ = ln(2)/T-half is the decay constant and t is the elapsed time. Without this correction, any comparison of activity across two different times, whether it is checking the activity in a dose calibrator against the time of patient injection, or comparing two frames of a dynamic PET scan, or comparing organ uptake on serial post-therapy SPECT images taken days apart, would confound genuine biological change with the trivial fact that the radionuclide has simply decayed further by the later time point.

In practice, decay correction is applied both to individual imaging frames (each PET or SPECT frame is corrected back to a common reference time, commonly either the frame start time, its mid-point, or the injection time) and to any activity measurement recorded away from the time it is needed, such as calculating the percentage of injected activity present in an organ, which requires decay-correcting the measured organ activity back to, or the injected activity forward to, a common time point. For dynamic and quantitative studies, the correction must also account for decay occurring during the frame acquisition itself, not just between frames, particularly for short-half-life radionuclides such as rubidium-82 or oxygen-15 relative to the scan duration.

Getting the decay-correction convention wrong, or applying it inconsistently between the dose calibrator, the scanner and the dosimetry software, is a recognised, easily overlooked source of quantitative error in both diagnostic quantification (SUV, kinetic modelling) and therapeutic dosimetry.