The main performance parameters in positron camera system design are sensitivity and spatial resolution. This paper concerns sensitivity, which is a function of the scintillation material, the solid angle subtended by the detector array, and the scintillator packing fraction. The solid angle can be increased by extending the axial extent of cylindrical detector systems. Most commercial positron camera systems are usually based on rings of detector blocks with lutetium oxyorthosilicate, LSO:Ce or LYSO:Ce, as the scintillator of choice. By adding more block detector rings, the solid angle increases while the detection efficiency remains fairly constant assuming the same crystal thickness. It has been shown that Ca co-doping of LSO:Ce reduces the scintillation decay time to ~ 30 ns with a light output over 30000 ph/MeV. This improvement may give a time-of-flight (TOF) advantage with time resolution of 500 to 600 ps or less. If we couple the count rate sensitivity of a large axial field-of-view (AFOV) system to the TOF sensitivity increase, we have the means to create examination times in the sub-minute range with no compromise in image quality. In the present study we have compared the existing Siemens molecular CT (mCT) systems to future 6, 8, 12, 20 and higher block ring systems with and without the TOF advantage. The mCT 4 block ring system has been used as a reference. The time for acceptable image quality with this system is then extrapolated to other systems based on planar sensitivity. However, the planar sensitivity is related to the solid angle, and reaches saturation for large AFOVs. This implies that there is an upper count rate sensitivity limit. A 20 block ring system may cover a 70 cm examination range at a certain planar count rate and could provide acceptable quality images in approximately 10 seconds by combining a high planar sensitivity count rate provided by the multi-ring feature, the high stopping power of LSO and the TOF gain due to the improved timing resolution.