A fast, linear Boltzmann transport equation solver for computed tomography dose calculation (Acuros CTD)

Abstract

Purpose: To improve dose reporting of CT scans, patient-specific organ doses are highly desired. However, estimating the dose distribution in a fast and accurate manner remains challenging, despite advances in Monte Carlo methods. In this work, we present an alternative method that deterministically solves the linear Boltzmann transport equation (LBTE), which governs the behavior of x-ray photon transport through an object.

Methods: Our deterministic solver for CT dose (Acuros CTD) is based on the same approach used to estimate scatter in projection images of a CT scan (Acuros CTS). A deterministic method is used to compute photon fluence within the object, which is then converted to deposited energy by multiplying by known, material-specific conversion factors. To benchmark Acuros CTD, we used the AAPM Task Group 195 test for CT dose, which models an axial, fan beam scan (10 mm thick beam) and calculates energy deposited in each organ of an anthropomorphic phantom. We also validated our own Monte Carlo implementation of Geant4 to use as a reference to compare Acuros against for other common geometries like an axial, cone beam scan (160 mm thick beam) and a helical scan (40 mm thick beam with table motion for a pitch of 1).

Results: For the fan beam scan, Acuros CTD accurately estimated organ dose, with a maximum error of 2.7% and RMSE of 1.4% when excluding organs with <0.1% of the total energy deposited. The cone beam and helical scans yielded similar levels of accuracy compared to Geant4. Increasing the number of source positions beyond 18 or decreasing the voxel size below 5 × 5 × 5 mm³ provided marginal improvement to the accuracy for the cone beam scan but came at the expense of increased run time. Across the different scan geometries, run time of Acuros CTD ranged from 8 to 23 s.

Conclusions: In this digital phantom study, a deterministic LBTE solver was capable of fast and accurate organ dose estimates.

Keywords: CT dose; Monte Carlo; deterministic solver; discrete ordinates; organ dose.

Figure 1

The uncollided fluence at each voxel is determined by ray tracing from the source. If there are multiple sources, it is the sum of all sources. The collided fluence is the solution of the LBTE and represents the secondary (scattered) fluence. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Overview of CT dose simulation with a voxelized phantom, as described in Ref. .Not drawn to scale.

Figure 3

Energy deposited in axial fan beam scan simulation. The top row shows Geant4 results, the middle row shows Acuros, and the bottom row shows the difference. From left to right, the central axial, coronal, and sagittal slices are shown. The jet colormap spans [0 0.05] eV/mm³/photon for the first two rows and [−0.025 0.025] eV/mm³/photon for the last row. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4

Energy deposited in each organ for the axial fan beam scan simulation. The Geant4 and Acuros results are superimposed on the TG 195 results. Note the log scale of the y‐axis. Organs below the dashed line absorb <0.1% of the total energy absorbed. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

Energy deposited in axial cone beam scan simulation. The jet colormap spans [0 0.005] eV/mm³/photon for the top two rows and [−0.0025 0.0025] eV/mm³/photon for the bottom row. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 6

Energy deposited in each organ for the axial cone beam scan simulation. Note the log scale of the y‐axis. Organs below the dashed line absorb <0.1% of the total energy absorbed. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7

Impact of parameter selection on run time and RMSE. (a) Number of uniformly spaced source angles, using 5 mm isotropic voxels. (b) In‐plane voxel size, using 18 sources. The longitudinal voxel size was kept to a maximum of 5 mm. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 8

Energy deposited in helical scan simulation. The jet colormap spans [0 0.005] eV/mm³/photon for the top two rows and [−0.0025 0.0025] eV/mm³/photon for the bottom row. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 9

Energy deposited in each organ for the helical scan simulation. Note the log scale of the y‐axis. Organs below the dashed line absorb <0.1% of the total energy absorbed. [Color figure can be viewed at wileyonlinelibrary.com]