Application of the mathematical theory of sequential sampling to gamma scanning in nuclear medicine

Abstract

To minimize the time for performing a gamma scan in nuclear medicine, optimum use must be made of the statistical data from the scan to control the time of observation at any given point. In the work described, the sequential sampling technique has been applied to the problem of proportioning observation time on the basis of observed counts. In the limit of both very high and very low count rates, advantagesis taken of the rapid decision time afforded by the good statistics of high rates and the a priori rejection of areas exhibiting low rates. Areas of intermediate activity require longer times to obtain a statistically significant estimate of activity. In this scanning method, accumulated counts from a stationary sensor are compared with two (linearly) time- varying thresholds: upon crossing either threshold an intensity estimate is made (which may be binary) and the scan continued to the next point. This procedure is well known in sequential hypothesis testing and the theory developed is pertinent to the gamma scanning application. An analysis of the system as compared to a fixed observation- time-in-scanning has been made. For a two-level detection system, with a given error probability and a given ratio of decay rate for a high-activity region to that for a low-activity region, it has been found that the average observation time for a variable threshold scanning is approximately half that for fixed-time scanning.