^{1}, W. Zbijewski

^{2,a)}, A. Badal

^{3}, I. S. Kyprianou

^{3}, J. W. Stayman

^{4}, J. J. Vaquero

^{5}and J. H. Siewerdsen

^{6}

### Abstract

The proliferation of cone-beam CT (CBCT) has created interest in performance optimization, with x-ray scatter identified among the main limitations to image quality. CBCT often contends with elevated scatter, but the wide variety of imaging geometry in different CBCT configurations suggests that not all configurations are affected to the same extent. Graphics processing unit (GPU) accelerated Monte Carlo (MC) simulations are employed over a range of imaging geometries to elucidate the factors governing scatter characteristics, efficacy of antiscatter grids, guide system design, and augment development of scatter correction.

A MC x-ray simulator implemented on GPU was accelerated by inclusion of variance reduction techniques (interaction splitting, forced scattering, and forced detection) and extended to include x-ray spectra and analytical models of antiscatter grids and flat-panel detectors. The simulator was applied to small animal (SA), musculoskeletal (MSK) extremity, otolaryngology (Head), breast, interventional C-arm, and on-board (kilovoltage) linear accelerator (Linac) imaging, with an axis-to-detector distance (ADD) of 5, 12, 22, 32, 60, and 50 cm, respectively. Each configuration was modeled with and without an antiscatter grid and with (i) an elliptical cylinder varying 70–280 mm in major axis; and (ii) digital murine and anthropomorphic models. The effects of scatter were evaluated in terms of the angular distribution of scatter incident upon the detector, scatter-to-primary ratio (SPR), artifact magnitude, contrast, contrast-to-noise ratio (CNR), and visual assessment.

Variance reduction yielded improvements in MC simulation efficiency ranging from ∼17-fold (for SA CBCT) to ∼35-fold (for Head and C-arm), with the most significant acceleration due to interaction splitting (∼6 to ∼10-fold increase in efficiency). The benefit of a more extended geometry was evident by virtue of a larger air gap—e.g., for a 16 cm diameter object, the SPR reduced from 1.5 for ADD = 12 cm (MSK geometry) to 1.1 for ADD = 22 cm (Head) and to 0.5 for ADD = 60 cm (C-arm). Grid efficiency was higher for configurations with shorter air gap due to a broader angular distribution of scattered photons—e.g., scatter rejection factor ∼0.8 for MSK geometry versus ∼0.65 for C-arm. Grids reduced cupping for all configurations but had limited improvement on scatter-induced streaks and resulted in a loss of CNR for the SA, Breast, and C-arm. Relative contribution of forward-directed scatter increased with a grid (e.g., Rayleigh scatter fraction increasing from ∼0.15 without a grid to ∼0.25 with a grid for the MSK configuration), resulting in scatter distributions with greater spatial variation (the form of which depended on grid orientation).

A fast MC simulator combining GPU acceleration with variance reduction provided a systematic examination of a range of CBCT configurations in relation to scatter, highlighting the magnitude and spatial uniformity of individual scatter components, illustrating tradeoffs in CNR and artifacts and identifying the system geometries for which grids are more beneficial (e.g., MSK) from those in which an extended geometry is the better defense (e.g., C-arm head imaging). Compact geometries with an antiscatter grid challenge assumptions of slowly varying scatter distributions due to increased contribution of Rayleigh scatter.

The authors thank Yoshito Otake, Ph. D. (Johns Hopkins University) for assistance with GPU cone-beam reconstruction, and John Boone, Ph. D. (University of California Davis) for providing the digital breast phantom. The research was supported by academic-industry partnership with Carestream Health Inc. (Rochester, NY) and National Institutes of Health (NIH) Grant No. 2R01-CA-112163. A. Sisniega is supported by FPU grant (Spanish Ministry of Education), AMIT project, RECAVA-RETIC Network, Project Nos. TEC2010-21619-C04-01, TEC2011-28972-C02-01, and PI11/00616 (Spanish Ministry of Science and Education), ARTEMIS program (Comunidad de Madrid), and PreDiCT-TB partnership.

I. INTRODUCTION

II. MATERIALS AND METHODS

II.A. GPU-accelerated Monte Carlo simulation platform

II.A.1. Polyenergetic x-ray source model

II.A.2. Photon tracking and variance reduction techniques

II.A.3. Analytical model for the antiscatter grid and flat-panel detector

II.B. CBCT system and object models

II.C. Monte Carlo experiments

II.C.1. Validation of Monte Carlo variance reduction techniques

II.C.2. Effects of system geometry on scatter: Continuously varied SAD and SDD

II.C.3. Specific CBCT configurations: Scatter distributions, image artifacts, and efficacy of an antiscatter grid

II.D. Metrics of scatter assessment

II.D.1. Cupping

II.D.2. Contrast reduction

II.D.3. Contrast-to-noise ratio

III. RESULTS

III.A. Validation of variance reduction techniques

III.B. Effects of system geometry on scatter: Continuously varied SAD and SDD

III.C. Scatter in various CBCT configurations: Cupping, streaks, contrast, and CNR

III.D. Scatter in various CBCT configurations: Scatter components and spatial distribution

III.E. Scatter in various CBCT configurations: Realistic anatomical phantoms

IV. DISCUSSION AND CONCLUSIONS

### Key Topics

- X-ray scattering
- 205.0
- Photons
- 83.0
- Cone beam computed tomography
- 75.0
- Multiple scattering
- 56.0
- Rayleigh scattering
- 50.0

##### A61B6/03

##### G06F15/16

##### G06F19/00

## Figures

Geometric configurations illustrated to scale with the common elliptical phantom.

Geometric configurations illustrated to scale with the common elliptical phantom.

(a) Illustration of the idealized Common Phantom as used in the simulations of the SA, MSK, Head, C-arm, and Linac CBCT. For the Breast configuration (b), the bone inserts were replaced by glandular tissue.

(a) Illustration of the idealized Common Phantom as used in the simulations of the SA, MSK, Head, C-arm, and Linac CBCT. For the Breast configuration (b), the bone inserts were replaced by glandular tissue.

Total scatter distributions computed with and without variance reduction techniques for the Linac geometry. (a) MC-GPU with variance reduction (Variance Red. ON) with 5 × 106 photon histories. (b) MC-GPU with no variance reduction (Variance Red. OFF) and 108 photon histories. (c) “Gold standard” MC-GPU without variance reduction and 1010 photon histories. (d) The relative difference image computed between the distribution obtained with variance reduction (a) and the “gold standard” distribution (c). In each case, the white bar on the colorbar indicates the mean of the respective distributions.

Total scatter distributions computed with and without variance reduction techniques for the Linac geometry. (a) MC-GPU with variance reduction (Variance Red. ON) with 5 × 106 photon histories. (b) MC-GPU with no variance reduction (Variance Red. OFF) and 108 photon histories. (c) “Gold standard” MC-GPU without variance reduction and 1010 photon histories. (d) The relative difference image computed between the distribution obtained with variance reduction (a) and the “gold standard” distribution (c). In each case, the white bar on the colorbar indicates the mean of the respective distributions.

(a) Scatter-to-primary ratio at the center of the detector versus SDD and ADD for systems without a grid. (b) Reduction in SPR due to an antiscatter grid (10:1 grid ratio). (c) Histogram of deflection angles of scattered photons reaching the detector plane for a projection perpendicular to the major axis of the Common Phantom.

(a) Scatter-to-primary ratio at the center of the detector versus SDD and ADD for systems without a grid. (b) Reduction in SPR due to an antiscatter grid (10:1 grid ratio). (c) Histogram of deflection angles of scattered photons reaching the detector plane for a projection perpendicular to the major axis of the Common Phantom.

(i) Axial reconstructions of primary-only projection data for the Common Phantom. (ii) Reconstructions of projections with scatter included in the simulation (without an antiscatter grid). (iii) Reconstructions of primary + scatter projection data with an antiscatter grid.

(i) Axial reconstructions of primary-only projection data for the Common Phantom. (ii) Reconstructions of projections with scatter included in the simulation (without an antiscatter grid). (iii) Reconstructions of primary + scatter projection data with an antiscatter grid.

(a) Cupping artifact [Eq. (4) ] in reconstructions of the Common Phantom. (b) Reduction in contrast [from Eq. (5) ] in reconstructions of primary + scatter to that in primary-only. (c) SPR in projections of the Common Phantom with and without a grid. Black bars indicate simulations with primary only. Gray bars show simulations with scatter (and no grid). White bars show simulations with scatter and an antiscatter grid. (d) The ratio of CNR with a grid (CNRgrid) to CNR without a grid (CNRno-grid) plotted versus SPR for each CBCT configuration at fixed detector exposure. The horizontal dotted line marks CNR ratio equal to one.

(a) Cupping artifact [Eq. (4) ] in reconstructions of the Common Phantom. (b) Reduction in contrast [from Eq. (5) ] in reconstructions of primary + scatter to that in primary-only. (c) SPR in projections of the Common Phantom with and without a grid. Black bars indicate simulations with primary only. Gray bars show simulations with scatter (and no grid). White bars show simulations with scatter and an antiscatter grid. (d) The ratio of CNR with a grid (CNRgrid) to CNR without a grid (CNRno-grid) plotted versus SPR for each CBCT configuration at fixed detector exposure. The horizontal dotted line marks CNR ratio equal to one.

(a) Distribution (in the plane of the detector) of the fraction of total scatter associated with individual scatter components for MSK CBCT. (b) Fraction of various scatter components versus ADD. (c) Grid rejection factor (i.e., fraction of a given scatter component removed from the total) for each component. (d) Gain-corrected magnitude of total scatter, S tot (left vertical axis) and of all three scatter components S incoh, S coh, and S multi (right vertical axis). Solid lines: configuration without a grid; dashed lines: configuration with a grid; black lines: total scatter; gray lines: individual scatter components.

(a) Distribution (in the plane of the detector) of the fraction of total scatter associated with individual scatter components for MSK CBCT. (b) Fraction of various scatter components versus ADD. (c) Grid rejection factor (i.e., fraction of a given scatter component removed from the total) for each component. (d) Gain-corrected magnitude of total scatter, S tot (left vertical axis) and of all three scatter components S incoh, S coh, and S multi (right vertical axis). Solid lines: configuration without a grid; dashed lines: configuration with a grid; black lines: total scatter; gray lines: individual scatter components.

Axial reconstructions of the anatomical phantoms for the CBCT configurations in Table I . (i) Reconstructions of primary-only projection data. (ii) Reconstructions with scatter included (without an antiscatter grid). (iii) Reconstructions with primary + scatter and an antiscatter grid.

Axial reconstructions of the anatomical phantoms for the CBCT configurations in Table I . (i) Reconstructions of primary-only projection data. (ii) Reconstructions with scatter included (without an antiscatter grid). (iii) Reconstructions with primary + scatter and an antiscatter grid.

Distributions of primary, total scatter, and individual scatter components at the detector for various scanner configurations and anatomical sites. Primary and total scatter distributions are shown without and with a grid (both for vertical and horizontal grid orientations). Individual scatter components are shown for the horizontal grid orientation only. The mean total scatter magnitude computed across the detector plane is stated above each distribution. The right column displays the SPR (right vertical axis) and (gain-corrected) intensities of each component (left vertical axis) for gridless configurations.

Distributions of primary, total scatter, and individual scatter components at the detector for various scanner configurations and anatomical sites. Primary and total scatter distributions are shown without and with a grid (both for vertical and horizontal grid orientations). Individual scatter components are shown for the horizontal grid orientation only. The mean total scatter magnitude computed across the detector plane is stated above each distribution. The right column displays the SPR (right vertical axis) and (gain-corrected) intensities of each component (left vertical axis) for gridless configurations.

## Tables

Nominal geometry and phantoms for the various CBCT configurations.

Nominal geometry and phantoms for the various CBCT configurations.

MC simulation efficiency ratio (R ɛ ) for various combinations of variance reduction techniques.

MC simulation efficiency ratio (R ɛ ) for various combinations of variance reduction techniques.

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