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: 1) Ray tracing photons from the x-ray source into the object where they experience their first scattering event and form scattering sources. 2) 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 by using the Source Iteration method. 3) 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 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: 1) a water phantom containing lung, air, and bone inserts (WLAB phantom) and 2) a pelvis phantom derived from a clinical CT data set. For these studies, we modeled the TrueBeam ^® (Varian Medical Systems, Palo Alto, CA) kV imaging system with a source energy of 125kVp. 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 second 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.