An Approach for Optimizing Prompt Gamma Photon-Based Range Estimation in Proton Therapy Using Cramér-Rao Theory

Various methods for in vivo range estimation during proton therapy based on the measurement of prompt gamma (PG) photons have been proposed. However, optimizing the method of detection by trial-and-error is a tedious endeavor. Here, we investigate the feasibility of using the Cramér-Rao lower bound (CRLB) to more quickly arrive at an optimum detector design. The CRLB provides the smallest possible variance on the proton range obtained from any unbiased estimator, given a statistical model of the observations. We simulated clinical proton pencil beams targeting a cylindrical, soft-tissue equivalent phantom and scored the PG photons around the phantom. Spatially, temporally, and spectrally resolved PG emission profiles corresponding to different proton ranges were generated. We calculated the proton range estimation uncertainty as a function of several detector setup parameters, such as detector size, bin size, and photon acceptance angle. We found a minimum uncertainty for the proton range estimation based on either spatial, spectral, or temporal information of 2.13, 1.97, and 2.05 mm 2.05 mm, respectively, if the detection parameters were optimized for each case. We conclude that the CRLB is a promising tool for the optimization of the detector setup for PG-based range estimation in particle therapy.