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. 2012 Jun 7;57(11):3281-93.
doi: 10.1088/0031-9155/57/11/3281. Epub 2012 May 9.

Efficient Voxel Navigation for Proton Therapy Dose Calculation in TOPAS and Geant4

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Free PMC article

Efficient Voxel Navigation for Proton Therapy Dose Calculation in TOPAS and Geant4

J Schümann et al. Phys Med Biol. .
Free PMC article

Abstract

A key task within all Monte Carlo particle transport codes is 'navigation', the calculation to determine at each particle step what volume the particle may be leaving and what volume the particle may be entering. Navigation should be optimized to the specific geometry at hand. For patient dose calculation, this geometry generally involves voxelized computed tomography (CT) data. We investigated the efficiency of navigation algorithms on currently available voxel geometry parameterizations in the Monte Carlo simulation package Geant4: G4VPVParameterisation, G4VNestedParameterisation and G4PhantomParameterisation, the last with and without boundary skipping, a method where neighboring voxels with the same Hounsfield unit are combined into one larger voxel. A fourth parameterization approach (MGHParameterization), developed in-house before the latter two parameterizations became available in Geant4, was also included in this study. All simulations were performed using TOPAS, a tool for particle simulations layered on top of Geant4. Runtime comparisons were made on three distinct patient CT data sets: a head and neck, a liver and a prostate patient. We included an additional version of these three patients where all voxels, including the air voxels outside of the patient, were uniformly set to water in the runtime study. The G4VPVParameterisation offers two optimization options. One option has a 60-150 times slower simulation speed. The other is compatible in speed but requires 15-19 times more memory compared to the other parameterizations. We found the average CPU time used for the simulation relative to G4VNestedParameterisation to be 1.014 for G4PhantomParameterisation without boundary skipping and 1.015 for MGHParameterization. The average runtime ratio for G4PhantomParameterisation with and without boundary skipping for our heterogeneous data was equal to 0.97: 1. The calculated dose distributions agreed with the reference distribution for all but the G4PhantomParameterisation with boundary skipping for the head and neck patient. The maximum memory usage ranged from 0.8 to 1.8 GB depending on the CT volume independent of parameterizations, except for the 15-19 times greater memory usage with the G4VPVParameterisation when using the option with a higher simulation speed. The G4VNestedParameterisation was selected as the preferred choice for the patient geometries and treatment plans studied.

Figures

Figure 1
Figure 1
The four parameterization methods in a schematic display. For a detailed description see section 2.1. a) is a parameterization where each voxel is created one by one without knowledge of the intrinsic geometry patterns of CT volumes, b) a parameterization along one axis (green) followed by replication of this line of voxels along another axis and a replication of the whole slice along the third axis, c) indicates how G4Phantom calculates the position of each voxel by taking advantage of the knowledge of the pattern of CT volumes, where N is the “copy number”, the index of the voxel, dx, dy and dz (nx, ny and nz) are the dimensions (number) of a voxel in x,y and z, respectively, and d) shows the voxel numbers that the MGHParameterization associates with each voxel to find the next voxel a particle would enter when traversing the CT volume.
Figure 2
Figure 2
Percent difference of the CPU timing results compared to G4VNestedParameterisation (G4Nested). Shown are G4PhantomParameterisation (G4Phantom) and MGHParameterization (G4MGH) for the nominal CT volume and the CT volume with all voxels set to be made of water (water). Timing results for a liver, a head and neck, and a prostate patient are shown. CPU times are for a) 1 million particles (γ, e, e+, p and n, for a list of the percentages refer to Table 2), and b) for 1 million protons.
Figure 3
Figure 3
Gamma index distributions with G4MGH as the reference dose distribution. The distributions are for a) head and neck, b) prostate and c) liver patients. Shown are G4Nested (blue, solid), G4Phantom without (green, dashed) and with (red, thin dashes) boundary skipping. The light blue dashed line indicates the 5% line. The numbers in the legend are the values of each parameterization at a gamma value of unity.
Figure 4
Figure 4
Dose difference plots. a-b: Head and neck patient, slice with air cavities from the nose. Dose difference plots are obtained by subtracting the dose distribution from G4MGH from G4Nested (a) and G4Phantom (b). Statistical fluctuations can be seen together with the systematic lower dose in the air cavities in (b). c-d: Fabricated head and neck CT that was composed of arrays of 20 voxels where 4 voxels with HU=3000 are followed by 16 voxels of air. Differences between G4MGH and G4Nested (c) and G4Phantom (d). The distribution in (d) is systematically different.

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