An automated optimization strategy to design collimator geometry for small field radiation therapy systems

Abstract

Purpose. To develop an automated optimization strategy to facilitate collimator design for small-field radiotherapy systems. Methods and Materials. We developed an objective function that links the dose profile characteristics (FWHM, penumbra, and central dose rate) and the treatment head geometric parameters (collimator thickness/radii, source-to-distal-collimator distance (SDC)) for small-field radiotherapy systems. We performed optimization using a downhill simplex algorithm. We applied this optimization strategy to a linac-based radiosurgery system to determine the optimal geometry of four pencil-beam collimators to produce 5, 10, 15, and 20 mm diameter photon beams (from a 6.7 MeV, 2.1 mm FWHM electron beam). Two different optimizations were performed to prioritize minimum penumbra or maximum central dose rate for each beam size. We compared the optimized geometric parameters and dose distributions to an existing clinical system (CyberKnife). Results. When minimum penumbra was prioritized, using the same collimator thickness and SDC (40 cm) as a CyberKnife system, the optimized collimator upstream and downstream radii agreed with the CyberKnife system within 3%–14%, the optimized output factors agreed within 0%–8%, and the optimized transverse and percentage depth dose profiles matched those of the CyberKnife with the penumbras agreeing within 2%. However, when maximum dose rate was prioritized, allowing both the collimator thickness and SDC to change, the central dose rate for larger collimator sizes (10, 15, 20 mm) could be increased by about 1.5–2 times at the cost of 1.5–2 times larger penumbras. No further improvement in central dose rate for the 5 mm beam size could be achieved. Conclusions. We developed an automated optimization strategy to design the collimator geometry for small-field radiation therapy systems. Using this strategy, the penumbra-prioritized dose distribution and geometric parameters agree well with the CyberKnife system as an example, suggesting that this system was designed to prioritize sharp penumbra. This represents proof-of-principle that an automated optimization strategy may apply to more complex collimator designs with multiple optimization parameters.

Bayesian optimization to design a novel x‐ray shaping device

“…Previous work on single channel collimator optimization utilized the Nelder-Mead downhill simplex algorithm. 23 Compared with Bayesian optimization, the Nelder-Mead approach is less robust to noise and more likely to become stuck in local minima. Depending on the complexity of the objective function, the latter point may or may not be problematic.…”

“…This is the first work we are aware of to utilize Bayesian optimization in conjunction with Monte Carlo particle transport. Previous work on single channel collimator optimization utilized the Nelder–Mead downhill simplex algorithm 23 . Compared with Bayesian optimization, the Nelder–Mead approach is less robust to noise and more likely to become stuck in local minima.…”

Robust and optimal dose distribution for brain metastases with robotic radiosurgery system: recipe for an inflection point

“…Van Herk et al (2000) noted that a Gaussian distribution represents an idealised dose distribution and suggested that SRT likely offers the closest approximation to this ideal, a hypothesis supported by this study. Further backing this concept is the observation by Wang et al (2021) that CK transverse dose profiles for small fields are well approximated by a Gaussian distribution.…”

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

“…A more efficient approach is the use of formal mathematical optimization algorithms to efficiently find an optimal set of parameters according to a user-defined objective function. 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.…”

“…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 .…”