Cramér–Rao Bound Evaluations of Compton Imager Designs for Proton Beam Range Verification

Abstract

Compton imaging is an attractive tool for range verification and dose estimation in proton therapy. To investigate the application of CdZnTe-based cameras for this task, we apply the uniform Cram&#x00E9;r&#x2013;Rao bound (UCRB) to dual-plane-based designs with various interplane spacings and evaluate their bias-variance tradeoff. The investigation focuses on the 718-keV and 4.4-MeV prompt gammas emitted from proton interactions with ¹²C, and focuses on a detector geometry having two planes of <inline-formula> <tex-math notation="LaTeX">$3 \times 3$ </tex-math></inline-formula> CdZnTe crystals with a volume of <inline-formula> <tex-math notation="LaTeX">$2 \times 2 \times 1.5 \,\,\mathrm {cm}^{3}$ </tex-math></inline-formula>. When considering only interplane events, the improvement in minimum variance plateaus at 8 cm. However, when considering both intraplane and interplane events with an efficiency factor, the optimum spacing is calculated to be around 4 cm as larger spacings degrade the performance with poorer efficiency and a lower interplane to intraplane fraction. In addition, the study uses the modified UCRB based on a simulated distribution of prompt gamma rays expected from proton irradiation. The results show that the optimum spacing may be between 2 and 4 cm, depending on the specific bias-gradient norm.