Limitations of Poisson statistics in describing radioactive decay.
OBJECTIVE
The assumption that nuclear decays are governed by Poisson statistics is an approximation. This approximation becomes unjustified when data acquisition times longer than or even comparable with the half-lives of the radioisotope in the sample are considered. In this work, the limits of the Poisson-statistics approximation are investigated.


METHODS
The formalism for the statistics of radioactive decay based on binomial distribution is derived. The theoretical factor describing the deviation of variance of the number of decays predicated by the Poisson distribution from the true variance is defined and investigated for several commonly used radiotracers such as (18)F, (15)O, (82)Rb, (13)N, (99m)Tc, (123)I, and (201)Tl.


RESULTS
The variance of the number of decays estimated using the Poisson distribution is significantly different than the true variance for a 5-minute observation time of (11)C, (15)O, (13)N, and (82)Rb.


CONCLUSIONS
Durations of nuclear medicine studies often are relatively long; they may be even a few times longer than the half-lives of some short-lived radiotracers. Our study shows that in such situations the Poisson statistics is unsuitable and should not be applied to describe the statistics of the number of decays in radioactive samples. However, the above statement does not directly apply to counting statistics at the level of event detection. Low sensitivities of detectors which are used in imaging studies make the Poisson approximation near perfect.
Radiology Department, Center for Advanced Medical Imaging Sciences, Massachusetts General Hospital and Harvard Medical School, 55 Fruit Street, Boston, MA 01721, USA. Electronic address: arkadiusz.sitek@philips.com.
Arkadiusz
A
Sitek
Department of Radiology, Medical Imaging Research Group, University of British Columbia and Vancouver Coastal Health Research Institute, VGH Research Pavilion, #366-828 West 10th Avenue, V5Z 1L8 Vancouver, BC, Canada.
Anna M
AM
Celler
D009683:Nuclear Medicine; D016012:Poisson Distribution; D011851:Radioactivity; D011868:Radioisotopes
D011868:Radioisotopes
Poisson distribution; Radioactive decay; Statistics