Detection limit of a lutetium based non-paralizable PET detector

The effect of the intrinsic lutetium radioactivity on the detection performances of a LYSO based in-beam PET prototype used for quality control of hadron therapy treatments is studied. This radioactivity leads to a background that degrades the measurement of the $\beta$ + signal. In particular, it prevents the measurement of faint signals originating from low activity $\beta$ + sources. This paper presents a method to estimate the minimum $\beta$ + activity that can be measured for any acquisition time taking into account the non-extensible dead time of the detector. This method is illustrated with experimental data collected with the in-beam PET prototype. The results presented in this paper are therefore specific to this detector. The method can however be applied in other contexts, either to other lutetium based PET detectors or even to non-PET detectors affected by lutetium radioactivity. The dead time correction formalism can also be used generally to scale signal and background yields in any non-paralizable detector, even those in which the background is not due to the presence of intrinsic radioactivity.