Monte Carlo simulation of prompt-γ emission in proton therapy using a track length estimator
Résumé
Purpose: Online in vivo control of the ion range in a patient during proton therapy is a major challenge for quality assurance of treatments. After measurements showed that prompt-γ emission is correlated to the ion range (Min et al 2006, Testa et al 2008), prompt-γ imaging emerged as apromising method (Verburg et al 2013). Fast methods are required to compute accurate prompt-γ emission maps to design and predict the camera response from treatment plans. An analytic computation method based on the structure of the dose calculation engines in treatment planning system has recently been proposed (Sterpin et al 2015). An alternative technique based on variance reduction in Monte Carlo (MC) calculations is developed here for computing prompt-γ emission maps in proton therapy.Materials/Methods: The track length estimator (TLE) method is a standard variance reduction technique in voxel-based dose computation in the kerma approximation (Williamson 1987), and similar approaches have also been developed for positron emitter distributions in proton therapy (Parodi et al 2007). A specific track length estimator has been developed here to design a continuous process along the proton track that locally deposits the expected value of the prompt-γ emission (induced by proton inelastic scattering) that would have occurred if a large number of protons with the same incident energy had followed the same step (i.e. track element). First an elemental database of prompt-γ emission spectra is established in the clinical energy range of incident protons for all elements in the composition of human tissues. This database of the prompt-γ spectra is built offline with high statistics. Regarding the implementation of the prompt-γ TLE MC tally, each proton deposits along its track the expectation of the prompt-γ spectra from the database according to the proton kinetic energy and the local material density and composition. All software developments have been carried out with the Gate/Geant4 toolkit.Results: A detailed statistical analysis is reported to characterize the dependency of the variance reduction on the geometrical (track length distribution) and physical (linear prompt-γ spectrum database) parameters. Benchmarking of the proposed technique with respect to an analogous MC technique is carried out. A large relative efficiency gain is reported, ca. 105. Such an efficiency gain could reduce the MC computing time of a full treatment from some weeks to less than one hour. Implementation issues are also addressed.Conclusions: This MC-based technique makes it possible to deal with complex situations such as heterogeneities for which proton straggling and secondary protons may have a decisive contribution. When considering translation to clinic, measurements for the prompt-γ s pectrum d atabase, or at least a sound calibration protocol of the simulated prompt-γ spectra, will have to be carried out.