Developing an Analytical Model for Knife-Edge Slit Collimator Optimization for Prompt Gamma Imaging in Proton Therapy

Purpose: Gamma cameras are one of the most promising technologies for in-vivo range monitoring in proton therapy. Monte Carlo (MC) simulation is a common calculation-based technique to design and optimize gamma cameras. However, it is prohibitively time-consuming. Analytical modeling speeds up the process of finding the optimal design. Materials and Methods: We proposed an analytical method using the efficiency-resolution trade-off for optimizing a knife-edge collimator based on the range retrieval precision of protons. Monte Carlo simulation was used for validation of obtained collimator efficiencies. Results: The model predicts that for the optimal range retrieval precision, the ratio of the source-to-detector distance to the source-to-collimator distance should be ranging from . For a special case, it was found that assuming an ideal detector , the falloff retrieval precision is optimal at independent of the collimator resolution. Moreover, using the optimized camera, the difference between the MC calculated range and the absolute range was 0.5 cm (the relative error is about 3%). Conclusion: It was found that the collimator parameters are in good agreement in comparison with that of the MC results reported in the literature. The analytical method studied in this work can be used to design and optimize imaging systems based on KE collimators in combination with new detectors in a fast and reliable way.