^{1,a)}, Joseph A. Heanue

^{2}, Tobias Funk

^{2}, Waldo S. Hinshaw

^{3}, Brian P. Wilfley

^{4}, Edward G. Solomon

^{4}and Norbert J. Pelc

^{5}

### Abstract

**Purpose:**

Inverse geometry computed tomography (IGCT) has been proposed as a new system architecture that combines a small detector with a large, distributed source. This geometry can suppress cone-beam artifacts, reduce scatter, and increase dose efficiency. However, the temporal resolution of IGCT is still limited by the gantry rotation time. Large reductions in rotation time are in turn difficult due to the large source array and associated power electronics. We examine the feasibility of using stationary source arrays for IGCT in order to achieve better temporal resolution. We anticipate that multiple source arrays are necessary, with each source array physically separated from adjacent ones.

**Methods:**

Key feasibility issues include spatial resolution, artifacts, flux, noise, collimation, and system timing clashes. The separation between the different source arrays leads to missing views, complicating reconstruction. For the special case of three source arrays, a two-stage reconstruction algorithm is used to estimate the missing views. Collimation is achieved using a rotating collimator with a small number of holes. A set of equally spaced source spots are designated on the source arrays, and a source spot is energized when a collimator hole is aligned with it. System timing clashes occur when multiple source spots are scheduled to be energized simultaneously. We examine flux considerations to evaluate whether sufficient flux is available for clinical applications.

**Results:**

The two-stage reconstruction algorithm suppresses cone-beam artifacts while maintaining resolution and noise characteristics comparable to standard third generation systems. The residual artifacts are much smaller in magnitude than the cone-beam artifacts eliminated. A mathematical condition is given relating collimator hole locations and the number of virtual source spots for which system timing clashes are avoided. With optimization, sufficient flux may be achieved for many clinical applications.

**Conclusions:**

IGCT with stationary source arrays could be an imaging platform potentially capable of imaging a complete 16-cm thick volume within a tenth of a second.

This work is supported by the National Institutes of Health (NIH) Grant No. R01EB006837 and by the National Defense Science and Engineering Fellowship (NDSEG) program. The authors would also like to acknowledge the referees whose comments have improved the clarity and content of this work.

I. INTRODUCTION

II. SYSTEM DESIGN

II.A. Source design

II.B. Volumetric design

II.C. Starting reconstruction

II.D. Detector and collimator design

II.E. Timing

II.F. Virtual bowtie

II.G. Flux

II.H. Other system design issues

III. SIMULATIONS

IV. RESULTS

V. CONCLUSIONS

### Key Topics

- Medical imaging
- 32.0
- Computed tomography
- 28.0
- Collimators
- 27.0
- Image scanners
- 23.0
- Photons
- 15.0

##### A61B6/03

## Figures

Conventional CT, IGCT, and the proposed SS-IGCT. (a) Standard, third-generation CT uses a rotating source and detector to collect a fan beam of data. (b) IGCT inverts the geometry by using a small detector and a series of sources opposite the detector. A fan-like shape of data, analogous to the fan-beam of conventional CT, is collected. Note that these x-ray beams are not illuminated simultaneously, but instead in sequence. The requirements on the rotating source array are very demanding, and the source array itself is very large. (c) The proposed system, SS-IGCT, increases temporal resolution and avoids the complexity of rotating source arrays by using three stationary source arrays. The gaps between the source arrays lead to missing data. Note that the inverted fan beam, beginning at the detector and ending at the source arrays, is missing a portion of the data because of the gap. These missing data prevent the direct use of conventional reconstruction algorithms. (d) The SS-IGCT system shown with additional hardware. In this schematic, the stationary source array is implemented using electron guns. The collimator and detector rotate together. Only a single x-ray beam is shown, corresponding to a single moment in time. The FOV here is the scanner field of view. [Reprinted with permission from S. S. Hsieh and N. J. Pelc, “A volumetric reconstruction algorithm for stationary source inverse-geometry CT,” Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83133N (2012)].

Conventional CT, IGCT, and the proposed SS-IGCT. (a) Standard, third-generation CT uses a rotating source and detector to collect a fan beam of data. (b) IGCT inverts the geometry by using a small detector and a series of sources opposite the detector. A fan-like shape of data, analogous to the fan-beam of conventional CT, is collected. Note that these x-ray beams are not illuminated simultaneously, but instead in sequence. The requirements on the rotating source array are very demanding, and the source array itself is very large. (c) The proposed system, SS-IGCT, increases temporal resolution and avoids the complexity of rotating source arrays by using three stationary source arrays. The gaps between the source arrays lead to missing data. Note that the inverted fan beam, beginning at the detector and ending at the source arrays, is missing a portion of the data because of the gap. These missing data prevent the direct use of conventional reconstruction algorithms. (d) The SS-IGCT system shown with additional hardware. In this schematic, the stationary source array is implemented using electron guns. The collimator and detector rotate together. Only a single x-ray beam is shown, corresponding to a single moment in time. The FOV here is the scanner field of view. [Reprinted with permission from S. S. Hsieh and N. J. Pelc, “A volumetric reconstruction algorithm for stationary source inverse-geometry CT,” Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83133N (2012)].

Volumetric depiction of SS-IGCT, showing the detector, source arrays, source trajectory and the x-ray beam. The five source rows, which constitute the source trajectory of the system, are drawn on the source array as circular stripes. Some elements, such as the collimator, have been omitted in this schematic. (a) Two x-ray beams are emitted from two different source rows. (b) The triangular field of view is shown.

Volumetric depiction of SS-IGCT, showing the detector, source arrays, source trajectory and the x-ray beam. The five source rows, which constitute the source trajectory of the system, are drawn on the source array as circular stripes. Some elements, such as the collimator, have been omitted in this schematic. (a) Two x-ray beams are emitted from two different source rows. (b) The triangular field of view is shown.

(a) The voxel-by-voxel conjugate ray. Typically, the standard conjugate ray would be used as a substitute for the missing ray. The standard conjugate ray is symmetric to the missing ray. In the starting reconstruction, we choose to use a voxel-by-voxel conjugate ray. For Voxel A, which lies on the axis of rotation (the black dotted line), the voxel-by-voxel conjugate ray is equivalent to the standard conjugate ray. For Voxel B, which lies off the axis of rotation, the voxel-by-voxel conjugate ray is coplanar to the missing ray and the standard conjugate ray but also passes through Voxel B. (b) Reconstruction using the standard conjugate ray as a substitute for the missing ray. A longitudinal slice is shown of four water spheres, each 1 cm in diameter and 10 cm from the isocenter. The top sphere is in the plane of the source row, and the bottom sphere is 4 cm from the isocenter. (c) Reconstruction using the voxel-by-voxel conjugate ray as a substitute for the missing ray. The voxel-by-voxel conjugate ray reduces artifacts and the faint, ghost spheres that appeared with the standard conjugate ray. [WL, WW] = [−1000, 80].

(a) The voxel-by-voxel conjugate ray. Typically, the standard conjugate ray would be used as a substitute for the missing ray. The standard conjugate ray is symmetric to the missing ray. In the starting reconstruction, we choose to use a voxel-by-voxel conjugate ray. For Voxel A, which lies on the axis of rotation (the black dotted line), the voxel-by-voxel conjugate ray is equivalent to the standard conjugate ray. For Voxel B, which lies off the axis of rotation, the voxel-by-voxel conjugate ray is coplanar to the missing ray and the standard conjugate ray but also passes through Voxel B. (b) Reconstruction using the standard conjugate ray as a substitute for the missing ray. A longitudinal slice is shown of four water spheres, each 1 cm in diameter and 10 cm from the isocenter. The top sphere is in the plane of the source row, and the bottom sphere is 4 cm from the isocenter. (c) Reconstruction using the voxel-by-voxel conjugate ray as a substitute for the missing ray. The voxel-by-voxel conjugate ray reduces artifacts and the faint, ghost spheres that appeared with the standard conjugate ray. [WL, WW] = [−1000, 80].

Detector stitching, the collimator, and the set of angles Φ. (a) A conventional system is shown with a large detector, collimator, and x-ray source emitting a fan beam of radiation directed toward the detector. (b) The SS-IGCT system is shown with a smaller detector and the collimator. The collimator (drawn thick) lies just within the source ring, and the collimator itself has three holes. To minimize confusion, gaps between source arrays are not shown. We use . A source spot lies on one of the three stationary source arrays, which illuminates the detector through a hole in the collimator. (c) and (d) The collimator and detector have rotated such that another collimator hole is present in front of the same source spot. The source spot is re-energized. The data collected from the three source firings, illustrated in (b)–(d), are equivalent to the single image with the large detector in (a). The thickness of the collimator has been exaggerated in these figures to show more clearly the directionality of each collimator hole, which allows the collimator to filter out radiation which is not directed toward the detector.

Detector stitching, the collimator, and the set of angles Φ. (a) A conventional system is shown with a large detector, collimator, and x-ray source emitting a fan beam of radiation directed toward the detector. (b) The SS-IGCT system is shown with a smaller detector and the collimator. The collimator (drawn thick) lies just within the source ring, and the collimator itself has three holes. To minimize confusion, gaps between source arrays are not shown. We use . A source spot lies on one of the three stationary source arrays, which illuminates the detector through a hole in the collimator. (c) and (d) The collimator and detector have rotated such that another collimator hole is present in front of the same source spot. The source spot is re-energized. The data collected from the three source firings, illustrated in (b)–(d), are equivalent to the single image with the large detector in (a). The thickness of the collimator has been exaggerated in these figures to show more clearly the directionality of each collimator hole, which allows the collimator to filter out radiation which is not directed toward the detector.

Sampling in a longitudinal (for example, a coronal) plane with the proposed system parameters. (a) The SS-IGCT system, with five source rows and with maximum cone angle α. (b) A reference, conventional CT system with 4 cm of coverage in the axial direction. Its worst case minimum tilt angle (equivalently, the half-cone angle) is α.

Sampling in a longitudinal (for example, a coronal) plane with the proposed system parameters. (a) The SS-IGCT system, with five source rows and with maximum cone angle α. (b) A reference, conventional CT system with 4 cm of coverage in the axial direction. Its worst case minimum tilt angle (equivalently, the half-cone angle) is α.

Modulation transfer function of the proposed system as compared to the FDK reference.

Modulation transfer function of the proposed system as compared to the FDK reference.

Noise performance of (a) the reference FDK system and (b) our proposed system. Window width is 800 and level is 0. The standard deviations in the water spheres were measured to be 320 HU for the reference system, and 301 HU for our proposed system.

Noise performance of (a) the reference FDK system and (b) our proposed system. Window width is 800 and level is 0. The standard deviations in the water spheres were measured to be 320 HU for the reference system, and 301 HU for our proposed system.

Sagittal slices of the (a) reference system and (b) the proposed system, and axial slices through the (c) reference system and (d) the proposed system for a FORBILD thorax phantom. Window width is 200 and level is 0. [Reprinted with permission from S. S. Hsieh and N. J. Pelc, “A volumetric reconstruction algorithm for stationary source inverse-geometry CT,” Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83133N (2012)].

Sagittal slices of the (a) reference system and (b) the proposed system, and axial slices through the (c) reference system and (d) the proposed system for a FORBILD thorax phantom. Window width is 200 and level is 0. [Reprinted with permission from S. S. Hsieh and N. J. Pelc, “A volumetric reconstruction algorithm for stationary source inverse-geometry CT,” Proc. SPIE 8313, Medical Imaging 2012: Physics of Medical Imaging, 83133N (2012)].

## Tables

System flux comparison to a wide-cone reference scanner for imaging tasks requiring wide, volumetric scanning. SS-IGCT may produce flux sufficient for many clinical applications, such as whole-organ perfusion.

System flux comparison to a wide-cone reference scanner for imaging tasks requiring wide, volumetric scanning. SS-IGCT may produce flux sufficient for many clinical applications, such as whole-organ perfusion.

System flux comparison to a standard clinical scanner operating in helical mode to capture a 16 cm volume. SS-IGCT captures the volume in a single axial scan and with increased temporal resolution.

System flux comparison to a standard clinical scanner operating in helical mode to capture a 16 cm volume. SS-IGCT captures the volume in a single axial scan and with increased temporal resolution.

Proposed system parameters. The “worst case minimum cone angle” refers to the smallest tilt angle for which any voxel along isocenter will be seen by at least one source row. This is diagrammed in Fig. 5 .

Proposed system parameters. The “worst case minimum cone angle” refers to the smallest tilt angle for which any voxel along isocenter will be seen by at least one source row. This is diagrammed in Fig. 5 .

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