This report presents analytical formulas for the image-forming and background event rates seen by circular positron-emission tomographs with parallel side shielding. These formulas include deadtime losses, detector efficiency, coincidence resolving time, amount of activity, patient port diameter, shielding gap, and shielding depth. A figure of merit, defined in terms of these quantitites, describes the signal-to-noise ratio in the reconstructed image of a 20-cm cylinder of water with uniformly dispersed activity. For 1-cm-wide nal (TI) detectors, a 50-cm patient port, an activity of 200 microCi per axial centimeter, and a shielding gap of 2 cm, the optimum shielding depth is 20 cm, which requires a detector circle diameter of 90 cm. For a 25-cm patient port and other conditions as above, the optimum shielding depth is 14 cm. Results are presented for the scintillators Nal(TI), bismuth germanate (BGO), CsF, and plastic; and for Ge(Li) and wire chambers with converters. In these examples, BGO provided the best signal-to-noise activity levels below 1000 microCi per cm, and CsF had the advantage for higher activity levels.
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Stephen E. Derenzo (1981) studied this question.