Bayesian optimization to design a novel x‐ray shaping device

Abstract

Purpose In radiation therapy, x‐ray dose must be precisely sculpted to the tumor, while simultaneously avoiding surrounding organs at risk. This requires modulation of x‐ray intensity in space and/or time. Typically, this is achieved using a multi leaf collimator (MLC)—a complex mechatronic device comprising over one hundred individually powered tungsten ‘leaves’ that move in or out of the radiation field as required. Here, an all‐electronic x‐ray collimation concept with no moving parts is presented, termed “SPHINX”: Scanning Pencil‐beam High‐speed Intensity‐modulated X‐ray source. SPHINX utilizes a spatially distributed bremsstrahlung target and collimator array in conjunction with magnetic scanning of a high energy electron beam to generate a plurality of small x‐ray “beamlets.” Methods A simulation framework was developed in Topas Monte Carlo incorporating a phase space electron source, transport through user defined magnetic fields, bremsstrahlung x‐ray production, transport through a SPHINX collimator, and dose in water. This framework was completely parametric, meaning a simulation could be built and run for any supplied geometric parameters. This functionality was coupled with Bayesian optimization to find the best parameter set based on an objective function which included terms to maximize dose rate for a user defined beamlet width while constraining inter‐channel cross talk and electron contamination. Designs for beamlet widths of 5, 7, and 10 mm2 were generated. Each optimization was run for 300 iterations and took approximately 40 h on a 24‐core computer. For the optimized 7‐mm model, a simulation of all beamlets in water was carried out including a linear scanning magnet calibration simulation. Finally, a back‐of‐envelope dose rate formalism was developed and used to estimate dose rate under various conditions. Results The optimized 5–, 7–, and 10‐mm models had beamlet widths of 5.1 , 7.2 , and 10.1 mm2 and dose rates of 3574, 6351, and 10 015 Gy/C, respectively. The reduction in dose rate for smaller beamlet widths is a result of both increased collimation and source occlusion. For the simulation of all beamlets in water, the scanning magnet calibration reduced the offset between the collimator channels and beam centroids from 2.9 ±1.9 mm to 0.01 ±0.03 mm. A slight reduction in dose rate of approximately 2% per degree of scanning angle was observed. Based on a back‐of‐envelope dose rate formalism, SPHINX in conjunction with next‐generation linear accelerators has the potential to achieve substantially higher dose rates than conventional MLC‐based delivery, with delivery of an intensity modulated 100 × 100 mm2 field achievable in 0.9 to 10.6 s depending on the beamlet widths used. Conclusions Bayesian optimization was coupled with Monte Carlo modeling to generate SPHINX geometries for various beamlet widths. A complete Monte Carlo simulation for one of these designs was developed, including electron beam transport of all beamlets through scanning magnets, x‐ray production and collimation, a...

ParticlePhaseSpace: A python package for streamlined import, analysis, and export of particle phase space data

“…The particles which are handled by this code are defined inside ParticleConfig which enables simple extension to arbitrary particles. Figure 2 shows examples of some of the plots which can be generated using ParticlePhaseSpace using data from the X-ray collimator described in Whelan et al (2022). There are some additional open source codes providing similar functionality to this code, including p2sat (Esnault (2021)) and postpic (Kuschel (2014)).…”

TopasOpt: An open‐source library for optimization with Topas Monte Carlo

“…implemented the Nelder‐Mead method in conjunction with MCNP and to perform single channel collimator design, 4 while Whelan et al. used Bayesian Optimization in conjunction with Topas to optimize a novel collimator array 5 . However, at present there is no simple and general‐purpose method to incorporate formal optimization routines into Monte Carlo simulation.…”

“…There are some examples in the literature of this approach: Wang et al implemented the Nelder-Mead method in conjunction with MCNP and to perform single channel collimator design, 4 while Whelan et al used Bayesian Optimization in conjunction with Topas to optimize a novel collimator array. 5 However, at present there is no simple and general-purpose method to incorporate formal optimization routines into Monte Carlo simulation. Several toolkits exist for performing Monte Carlo simulations; of note are Fluka, EGS, and Geant4.…”

“…used Bayesian Optimization in conjunction with Topas to optimize a novel collimator array. 5 However, at present there is no simple and general‐purpose method to incorporate formal optimization routines into Monte Carlo simulation.…”