Evaluation of a stochastic reconstruction algorithm for use in Compton camera imaging and beam range verification from secondary gamma emission during proton therapy

In this paper, we study the feasibility of using the stochastic origin ensemble (SOE) algorithm for reconstructing images of secondary gammas emitted during proton radiotherapy from data measured with a three-stage Compton camera. The purpose of this study was to evaluate the quality of the images of the gamma rays emitted during proton irradiation produced using the SOE algorithm and to measure how well the images reproduce the distal falloff of the beam. For our evaluation, we performed a Monte Carlo simulation of an ideal three-stage Compton camera positioned above and orthogonal to a proton pencil beam irradiating a tissue phantom. Scattering of beam protons with nuclei in the phantom produces secondary gamma rays, which are detected by the Compton camera and used as input to the SOE algorithm. We studied the SOE reconstructed images as a function of the number of iterations, the voxel probability parameter, and the number of detected gammas used by the SOE algorithm. We quantitatively evaluated the capabilities of the SOE algorithm by calculating and comparing the normalized mean square error (NMSE) of SOE reconstructed images. We also studied the ability of the SOE reconstructed images to predict the distal falloff of the secondary gamma production in the irradiated tissue. Our results show that the images produced with the SOE algorithm converge in ∼10 000 iterations, with little improvement to the image NMSE for iterations above this number. We found that the statistical noise of the images is inversely proportional to the ratio of the number of gammas detected to the SOE voxel probability parameter value. In our study, the SOE predicted distal falloff of the reconstructed images agrees with the Monte Carlo calculated distal falloff of the gamma emission profile in the phantom to within ±0.6 mm for the positions of maximum emission (100%) and 90%, 50% and 20% distal falloff of the gamma emission profile. We conclude that the SOE algorithm is an effective method for reconstructing images of a proton pencil beam from the data collected by an ideal Compton camera and that these images accurately model the distal falloff of secondary gamma emission during proton irradiation.