Stochastic behavior of the Origin-Ensemble Algorithm – effect on ange verification in proton therapy using Compton-Cameras

Introduction: Origin-Ensemble (OE) image reconstruction recently attracted interest for Compton-camera (CC)- based range verification (RV). OE samples a Markov-chain (MC) to estimate the expected value of the gamma emission distribution. Additionally, it allows to calculate standard deviation values, which depict the intrinsic uncertainty affecting the reconstruction (intra-chain-variability). Considering the low statistics in RV, it is crucial to investigate the effect of intra-chain-variability and initialization of the MC (inter-chain-variability) on reconstructions and range shift detection. Material & Methods: A CC [1] and five-line-sources phantom are simulated in GATE and 104 , 105 and 106 events are reconstructed using 10.000 and 100.000 iterations. OE is implemented following [2,3]. Intra- and interchain variation-coefficient images are calculated from the MC during equilibrium and from 20 reconstructions with different initializations of the random number generator, respectively. Range shifts between a modified phantom are calculated for 25 samples [4]. Results: The inter-chain variation-coefficient is approximately one order of magnitude smaller than the intrachain-variability (Fig.1,2). Variation-coefficients behave inversely with different numbers of eventsper-voxel. For high events-per-voxel the inter-chain-variability is greater and intra-chain-variability smaller and vice versa. Accurate range shift detection with our methods is only possible for 106 events, while it is not for lower statistics due to intra-chain-variability. Inter-chain-variability is reduced by more iterations and intra-chain-variability by better statistics. However, neither is a practical solution for RV. Conclusion: Our experiments indicate that the initialization of the MC has less effect on reconstructions and RV than the MC’s intrinsic variation. Future work focusses on improving OE for low statistics. Additionally, intra-chain-variability obtained by OE could be integrated into RV.