Spatial resolution performance evaluation of a monolithic crystal PET detector with Cramer-Rao lower bound (CRLB)

We have previously reported on continuous miniature crystal element (cMiCE) PET detectors that provide depth of interaction (DOI) positioning capability. A key component of the design is the use of a statistics based positioning (SBP) method for 3D event positioning. The Cramer-Rao lower bound (CRLB) expresses a lower bound on the variance of estimators for a deterministic parameter. Therefore, the CRLB could be used to evaluate whether our SBP algorithm is efficient and to quickly determine the best possible spatial resolution when investigating new detector designs. In this work, the CRLB is first reported based upon experimental results from a PET detector using a 50 mm by 50 mm by 15 mm LYSO crystal readout by a 64-channel PMT on the exit surface of the crystal. The X/Y spatial resolution is very close to the CRLB, while the depth of interaction (DOI) resolution is more than double the CRLB even after correcting for beam size and finite X resolution of the detector. A simulation study was conducted to investigate what causes the difference between measured DOI resolution and the CRLB for DOI. The PET detector was modeled as a 50 mm by 50 mm by 15 mm LYSO crystal readout by a 64-channel SiPM array placed on the entrance surface of the crystal. The results show that Compton scatter in the crystal degrades the DOI resolution. A second interesting result was that the DOI CRLB could not be achieved even when tested using only photoelectric events. This is because of the limitations of the DOI decoding algorithm.