Analytical computation of prompt gamma ray emission and detection for proton range verification.

A prompt gamma (PG) slit camera prototype recently demonstrated that Bragg Peak position in a clinical proton scanned beam could be measured with 1-2 mm accuracy by comparing an expected PG detection profile to a measured one. The computation of the expected PG detection profile in the context of a clinical framework is challenging but must be solved before clinical implementation. Obviously, Monte Carlo methods (MC) can simulate the expected PG profile but at prohibitively long calculation times. We implemented a much faster method that is based on analytical processing of precomputed MC data that would allow practical evaluation of this range monitoring approach in clinical conditions. Reference PG emission profiles were generated with MC simulations (PENH) in targets consisting of either (12)C, (14)N, (16)O, (31)P or (40)Ca, with 10% of (1)H. In a given geometry, the local PG emission can then be derived by adding the contribution of each element, according to the local energy of the proton obtained by continuous slowing down approximation and the local composition. The actual incident spot size is taken into account using an optical model fitted to measurements and by super sampling the spot with several rays (up to 113). PG transport in the patient/camera geometries and the detector response are modelled by convolving the PG production profile with a transfer function. The latter is interpolated from a database of transfer functions fitted to MC data (PENELOPE) generated for a photon source in a cylindrical phantom with various radiuses and a camera placed at various positions. As a benchmark, the analytical model was compared to MC and experiments in homogeneous and heterogeneous phantoms. Comparisons with MC were also performed in a thoracic CT. For all cases, the analytical model reproduced the prediction of the position of the Bragg peak computed with MC within 1 mm for the camera in nominal configuration. When compared to measurements, the shape of the profiles was well reproduced and agreement for the estimation of the position of the Bragg peak was within 2.7 mm on average (1.4 mm standard deviation). On a non-optimized MATLAB code, computation time with the analytical model is between 0.3 to 10 s depending on the number of rays simulated per spot. The analytical model can be further used to determine which spots are the best candidates to evaluate the range in clinical conditions and eventually correct for over- and under-shoots depending on the acquired PG profiles.