Acuros CTS: A fast, linear Boltzmann transport equation solver for computed tomography scatter - Part I: Core algorithms and validation

Abstract

Purpose: To describe Acuros^® CTS, a new software tool for rapidly and accurately estimating scatter in x-ray projection images by deterministically solving the linear Boltzmann transport equation (LBTE).

Methods: The LBTE describes the behavior of particles as they interact with an object across spatial, energy, and directional (propagation) domains. Acuros CTS deterministically solves the LBTE by modeling photon transport associated with an x-ray projection in three main steps: (a) Ray tracing photons from the x-ray source into the object where they experience their first scattering event and form scattering sources. (b) Propagating photons from their first scattering sources across the object in all directions to form second scattering sources, then repeating this process until all high-order scattering sources are computed using the source iteration method. (c) Ray-tracing photons from scattering sources within the object to the detector, accounting for the detector's energy and anti-scatter grid responses. To make this process computationally tractable, a combination of analytical and discrete methods is applied. The three domains are discretized using the Linear Discontinuous Finite Elements, Multigroup, and Discrete Ordinates methods, respectively, which confer the ability to maintain the accuracy of a continuous solution. Furthermore, through the implementation in CUDA, we sought to exploit the parallel computing capabilities of graphics processing units (GPUs) to achieve the speeds required for clinical utilization. Acuros CTS was validated against Geant4 Monte Carlo simulations using two digital phantoms: (a) a water phantom containing lung, air, and bone inserts (WLAB phantom) and (b) a pelvis phantom derived from a clinical CT dataset. For these studies, we modeled the TrueBeam^® (Varian Medical Systems, Palo Alto, CA) kV imaging system with a source energy of 125 kVp. The imager comprised a 600 μm-thick Cesium Iodide (CsI) scintillator and a 10:1 one-dimensional anti-scatter grid. For the WLAB studies, the full-fan geometry without a bowtie filter was used (with and without the anti-scatter grid). For the pelvis phantom studies, a half-fan geometry with bowtie was used (with the anti-scatter grid). Scattered and primary photon fluences and energies deposited in the detector were recorded.

Results: The Acuros CTS and Monte Carlo results demonstrated excellent agreement. For the WLAB studies, the average percent difference between the Monte Carlo- and Acuros-generated scattered photon fluences at the face of the detector was -0.7%. After including the detector response, the average percent differences between the Monte Carlo- and Acuros-generated scatter fractions (SF) were -0.1% without the grid and 0.6% with the grid. For the digital pelvis simulation, the Monte Carlo- and Acuros-generated SFs agreed to within 0.1% on average, despite the scatter-to-primary ratios (SPRs) being as high as 5.5. The Acuros CTS computation time for each scatter image was ~1 s using a single GPU.

Conclusions: Acuros CTS enables a fast and accurate calculation of scatter images by deterministically solving the LBTE thus offering a computationally attractive alternative to Monte Carlo methods. Part II describes the application of Acuros CTS to scatter correction of CBCT scans on the TrueBeam system.

Keywords: Monte Carlo; cone-beam CT; deterministic calculation; discrete ordinates; finite element; scatter.

Figure 1

Reconstructed cone‐beam CT images of a clinical pelvis scan. Severe shading is seen when no scatter correction is applied. Even after kernel‐based (fASKS) scatter correction, some residual scatter artifact remains, including shading in the bladder (arrows). Display window [−300, 300] HU. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 2

Overview of the computational algorithm in Acuros CTS. Photons depart the source and arrive into the object in step 1 (red), where they scatter one or multiple times in step 2 (orange) to finally arrive at the detector panel in step 3 (green). [Color figure can be viewed at wileyonlinelibrary.com]

Figure 3

(a) Simplified grid response for focused 1D grid and (b) simplified detector response. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 4

(a) Digital WLAB phantom showing dimensions of water (W) and lung (L), air (A), and bone (B) inserts. (b) Imaging geometry, as viewed from above. All dimensions are in centimeters. The phantom extends ±20 cm in/out of the page, while the detector extends ±15 cm in/out of the page. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 5

Multiplanar reformat of a digital pelvis phantom on an IGRT table, showing water and bone densities. Display window [0, 2] g/cm³.

Figure 6

WLAB phantom primary and scatter images of fluence at the detector, comparing Geant4 and Acuros. Primary images shown on [0, 2 × 10⁻⁸] photons/mm², scatter images shown on [4 × 10⁻⁹, 8 × 10⁻⁹] photons/mm² window. Horizontal line profiles are taken across the central row. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 7

Scatter fraction line profiles for WLAB phantom, using energy deposited in the CsI scintillator, for cases without and with a 10:1 grid. [Color figure can be viewed at wileyonlinelibrary.com]

Figure 8

(a) Orientation of 0° (AP) and 270° (lateral) projections relative to patient. Geometry not to scale. (b) Primary and scatter images of energy deposited in the detector for Geant4 and Acuros for the 0° projection. Primary images are shown on the same log scale, while the scatter images are shown on the same linear scale. (c) Horizontal line profiles of scatter fraction across central row. [Color figure can be viewed at wileyonlinelibrary.com]