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

Abstract

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.

Fast multipurpose Monte Carlo simulation for proton therapy using multi‐ and many‐core CPU architectures

“…For comparison purposes, modularity in MCsquare allows the user to choose among several models and hence to reach his own trade-off between speed and accuracy. Moreover, MCsquare can simulate the emission of prompt gamma (PG), which can be used for in vivo range verification [14][15][16] before and/or during treatment delivery.…”

Classification of the source of treatment deviation in proton therapy using prompt‐gamma imaging information

“…It detects energy depositions of gamma rays between 3 and 6 MeV. The response of this camera to prompt‐gamma rays according to a specific treatment case, given in form of one prompt‐gamma profile per PBS spot, is modeled with the REGGUI software 31 utilizing an analytical model based on Monte Carlo simulations. The treatment plan and the corresponding pCT were used as input to simulate the reference prompt‐gamma profiles for each PBS spots.…”

Experimental Comparison of Knife-Edge and Multi-Parallel Slit Collimators for Prompt Gamma Imaging of Proton Pencil Beams

“…As a consequence, the spatial resolution of the collimator needs to be compromised in order to favor the counting statistics and achieve a clinically viable efficiency of the order of 1 prompt gamma detected every 10 5 protons ( 13 ). The subsequent, poor spatial resolution as well as the significant statistical fluctuations of the signal of a single spot is then compensated for by the use of a priori information when comparing the actually measured profile to a reference computed one reflecting the treatment plan hypotheses ( 14 ).…”