Numerical optimization of longitudinal collimator geometry for novel x-ray field

OBJECTIVE

A novel X-ray field produced by an ultrathin conical target is described in the literature. However, the optimal design for an associated collimator remains ambiguous. Current optimization methods using Monte Carlo calculations restrict the efficiency and robustness of the design process. A more generic optimization method that reduces parameter constraints while minimizing computational load is necessary. A numerical method for optimizing the longitudinal collimator hole geometry for a cylindrically-symmetrical X-ray tube is demonstrated and compared to Monte Carlo calculations. Approach: The X-ray phase space was modelled as a four-dimensional histogram differential in photon initial position, final position, and photon energy. The collimator was modelled as a stack of thin washers with varying inner radii. Simulated annealing was employed to optimize this set of inner radii according to various objective functions calculated on the photon flux at a specified plane. Main results: The analytical transport model used for optimization was validated against Monte Carlo calculations using Geant4 via its wrapper, TOPAS. Optimized collimators and the resulting photon flux profiles are presented for three focal spot sizes and five positions of the source. Optimizations were performed with multiple objective functions based on various weightings of precision, intensity, and field flatness metrics. Finally, a select set of these optimized collimators, plus a parallel-hole collimator for comparison, were modelled in TOPAS. The evolution of the radiation field profiles are presented for various positions of the source for each collimator. Significance: This novel optimization strategy proved consistent and robust across the range of X-ray tube settings regardless of the optimization starting point. Common collimator geometries were re-derived using this algorithm while simultaneously optimizing geometry-specific parameters. The advantages of this strategy over iterative Monte Carlo-based techniques, including computational efficiency, radiation source-specificity, and solution flexibility, make it a desirable optimization method for complex irradiation geometries. .

Technical Note: Dose voxel resolution determination for Monte Carlo electron beam simulation in thin targets

BACKGROUND

Monte Carlo particle simulation has become the primary tool for designing low-energy miniature x-ray tubes due to the difficulties of physically prototyping these devices and characterizing their radiation fields. Accurate simulation of electronic interactions within their targets is necessary for modeling both photon production and heat transfer. Voxel-averaging can conceal hot spots in the target heat deposition profile that can threaten the integrity of the tube.

PURPOSE

This research seeks a computationally-efficient method of estimating voxel-averaging error in energy deposition simulations of electron beams penetrating thin targets to inform the appropriate scoring resolution for a desired accuracy level.

METHODS

An analytical model to estimate voxel-averaging along the target depth was developed and compared to results from Geant4 via its wrapper, TOPAS. A 200 keV planar electron beam was simulated to impinge tungsten targets of thicknesses between 1.5- and 12.5- μ m ${{\umu {\rm m}}}$ . For each target, the model was used to calculate the energy deposition ratio between voxels of varying sizes centered on the longitudinal midpoint of the target. Model-calculated ratios were compared to simulation outputs to gauge the model's accuracy. Then, the model was used to approximate the error between the point value of electron energy deposition and a voxel-based measurement.

RESULTS

The model underestimates error to within 5% for targets less than 7.5- μ m ${{\umu {\rm m}}}$ in thickness with increasing error for greater thicknesses. For the 1.5- μ m ${{\umu {\rm m}}}$ target, calculations of the point-vs.-voxel energy deposition show an 11% averaging effect between the midpoint and a 1.5- μ m ${{\umu {\rm m}}}$ voxel. Energy deposition profiles along the target depth were also calculated in the Monte Carlo for reference.

CONCLUSION

A simple analytical model was developed with reasonable accuracy to guide Monte Carlo users in estimating the appropriate depth-voxel size for thin-target x-ray tube simulations. This methodology can be adapted for other radiological contexts to increase robustness in point-value estimations.