Flat panel detector-based cone beam breast CT (CBBCT) can provide 3D image of the scanned breast with 3D isotropic spatial resolution, overcoming the disadvantage of the structure superimposition associated with X-ray projection mammography. It is very difficult for Mammography to detect a small carcinoma (a few millimeters in size) when the tumor is occult or in dense breast. CBBCT featured with circular scan might be the most desirable mode in breast imaging due to its simple geometrical configuration and potential applications in functional imaging. An inherited large cone angle in CBBCT, however, will yield artifacts in the reconstruction images when only a single circular scan is employed. These artifacts usually manifest themselves as density drop and object geometrical distortion that are more noticeable in the reconstructed image areas that are further away from the circular scanning plane. In order to combat this drawback, a circle plus partial helical scan scheme is proposed. An exact circle plus straight line scan scheme is also conducted in computer simulation for the purpose of comparison. Computer simulations using a numerical breast phantom demonstrated the practical feasibility of this new scheme and correction to those artifacts to a certain degree.
Breast cancer imaging has improved over the last decade with higher and more uniform quality standards for mammography as well as through the increasing use of sonography and magnetic resonance imaging as the adjunct tools. Mammography is still the only screening tool to detect breast cancer for asymptomatic women. Due to the limitations associated with the aforementioned techniques, such as imaging of the overlapping structure with mammography, technician dependent lack of ability to detect calcifications with ultrasound, and low specificity and/or poor detection of the tiny calcium deposits with MRI, there remains an endeavor to explore new ways to better detect breast cancer.
Recently one of the most exciting ways is cone beam breast CT (CBBCT) technology [
Among all CBBCT technologies, FDK [
Recently, Katsevich and Kapralov [
It is well known that a single circular cone beam scan does not provide complete information for an exact reconstruction. This can be appreciated by the 3-D Radon transform of the object function
Illustration of 3-D Radon transform and Radon shell in object space.
Illustration of the radon point in the radon domain within object Radon support.
The light gray volume inside the half Radon ball support is what is called the missing volume, meaning that no Radon points in this volume can be acquired through circular scan. In the spherical coordinates, this missing Radon volume is expressed as
According to Chen and Ning [
There are a couple of proposed “circle plus” trajectories [
For comparison, a CL scanning is also conducted in numerical simulation based on Katsevich’s concept under the less restrictive conditions. During the line scanning, the detector is always fixed at the position where circle scan is conducted, and the X-ray collimation size varied to make sure that X-ray illumination always covers the whole detector as it moves along the line trajectory. In this way, the missing radon volume is filled completely and an exact reconstruction can be achieved through CL scan.
Based on the geometric parameters of current CBBCT, we designed a new scan scheme. The position of the X-ray source is at
The projection angles associated with partial helical scans are uniformly distributed within
Some of the Radon data points acquired from this additional scanning trajectory still can be acquired through a circular scan. This is what is called redundant sampling points in the Radon domain and can be efficiently eliminated by a window function. The geometric setup of the collimation during the partial helical scan is maintained as it is with the circle scan, that is, the half cone illumination geometry. This can avoid the redundant sampling in the missing volume in the Radon domain within the X-ray shots in a helical trajectory. Since the collimation during partial helical scan unavoidably encounters the longitudinal truncation, a geometric dependent truncation window function has to be used to handle this case to remove the incorrect Radon data.
In line scan case, as Figure
Illustration of the straight line scan to achieve exact reconstruction.
Composite reconstruction framework is probably the most preferable algorithm for the CBBCT. The reconstructed object is
Figure
The geometric illustration of a circular scan.
The mathematic equation of
(i) FDK algorithm:
(ii) Hui’s term:
Based on Figure
The Geometrical illustration of the same Radon value defined in object coordinates and reconstruction coordinates associated with the partial helical scan.
This helical reconstruction formula is actually similar to what was presented by Hu [
The final reconstruction is composed of two parts, first one is from circular scan, the second one is from straight line scan, and can be mathematically described by the following equation:
Illustration of straight line scanning.
The implementation of the
Apparently, this is a parabola with its vertex at
Computer simulations are carried out on a mathematic breast phantom that was created for this study. This breast phantom is a half-ellipsoid with three half-axes of 8.8, 8.8, and 16 cm, a large phantom, specifically designed to address the artifacts resulting from the single circular scan. The phantom is wrapped by simulated skin with a thickness of 2 mm. Within the simulated skin, the base material is a compound of adipose and glandular tissues (e.g., 50% adipose and 50% glandular). There are three groups of objects inside the breast phantom. Within first two groups are two sets of spheres: one set of carcinoma spheres with diameters of 1, 2, 4, 6, and 8 mm, respectively, located at the positions where
Partial helical scan parameters.
Iso distance | Magnification factor | Detector pixel pitch | Number of projections | Detector size | Scanning starting position | Scanning ending position | Sampling interval along scanning axis |
---|---|---|---|---|---|---|---|
1.43 | 32 | ||||||
(64) | ( |
Straight line scan parameters.
Iso distance | Magnification factor | Detector pixel pitch | Number of projection | Detector size | Scanning starting position | Scanning ending position | Sampling interval along scanning axis |
---|---|---|---|---|---|---|---|
650 mm | 1.43 | 0.388 mm | 556 | ||||
(210) | ( | ||||||
(64) | ( |
The simulation was conducted in several settings as discussed in Section
Central sagittal image comparison between MFDK, phantom, and circle plus partial helical term with different sampling intervals. (a) Circular FDK reconstruction; (b) circular Hui’s term; (c) MFDK reconstruction (circle FDK + Hui term); (d) partial helical reconstruction (32 X-ray shots during helix scan); (e) MFDK + Helix reconstruction (32 shots for helical scan); (f) partial helical reconstruction (64 X-ray shots during helix scan); (g) MFDK + Helix reconstruction (64 shots for helical scan); (h) phantom image of the same sagittal slice.
FDK
Hui term
MFDK
Helix recon (32 shots)
MFDK + Helix (32 shots)
Helix recon (64 shots)
MFDK + Helix (64 shots)
Phantom image
The contribution from straight line scan was reconstructed using Katsevich’s algorithm. Figure
The central sagittal image comparison between phantom and CL scan scheme with different sampling intervals along straight line trajectory. (a) Circular FDK reconstruction; (b) straight line scan reconstruction (556 shots); (c) FDK + Line reconstruction (556 shots for line scan); (d) straight line scan reconstruction (210 shots); (e) FDK + Line reconstruction (210 shots for line scan); (f) straight line scan reconstruction (64 shots); (g) FDK + Line reconstruction (64 shots for line scan); (h) phantom image of the same sagittal slice.
FDK
Line scan (556 shots)
FDK + Line scan (556 shots)
Line scan (210 shots)
FDK + Line scan (210 shots)
Line scan (64 shots)
FDK + Line scan (64 shots)
Phantom
Figure
Profile comparison between phantom, MFDK, MFDK plus helical scan, and FDK plus straight line scan schemes. (a) Phantom image with three profile lines; (b) profile comparison along the middle vertical line in (a); (c) profile comparison along the left vertical line in (a); (d) profile comparison along the horizontal line in (a).
Phantom image with three profile lines
Profile comparison along the middle vertical line in (a)
Profile comparison along the left vertical line in (a)
Profile comparison along the horizontal line in (a)
A quantitative measurement of reconstruction error (
Scan scheme | MFDK (circle) | CH (64 shots in Helix scan) | CL (556 shots in Line scan) |
---|---|---|---|
2.1 | 0.70 | 0.70 |
In order to test the performance of this new scheme over the quantum noise that is commonly encountered in practical CBBCT data acquisition, we generated quantum noise contaminated data. An X-ray with 60 kVp was selected which corresponds to an effective photon fluence of 2.65*107 photons
The Central sagittal image comparison between different scanning schemes based on simulated quantum noise in the projection data. (a) Circular FDK; (b) MFDK + Helix reconstruction (64 shots for helical scan); (c) FDK + Line reconstruction (556 shots for line scan).
FDK
MFDK + Helix (64 shots)
FDK + Line (556 shots)
The new scanning scheme of CH scan works better than a single circular scan in terms of image uniformity and geometrical correctness based on the computer simulations of a mathematic breast phantom and a simulated breast phantom on CBBCT prototype study. Partial helical scan with different sampling intervals showed that the number of X-ray shootings between 32 and 64 could provide acceptable reconstructed images in terms of correction to the intensity drop along the scanning axis and geometrical distortion around the nipple area based on the scanning geometrical parameters and breast size. This is encouraging, since the quality of reconstructed images could improve without too much additional radiation exposure to the patient. Also note that the smaller the sampling interval (the larger the number of projections) in helical scan, the less the streak artifacts in the corrected area. However, these streak artifacts are faintly visible. In practical situation, the image quality should be balanced with the sampling interval in helical scan. This new scanning scheme is not intended to conduct an exact reconstruction. Theoretically, when the missing volume in Radon domain is completely filled and at least as densely sampled as those accessed by circle scan, the combined reconstruction is exact. By sparsely sampling the missing volume through a proposed scanning scheme, it suffices to correct the artifacts occurring in a single circular scan. On the other hand, the new scanning scheme is easy to operate in practice without complicated mechanical modification on the current prototype CBBCT system.
As was mentioned in Section
Visually, the reconstruction from CL scheme looks smoother than that from CH scheme; all the streak artifacts noticed in CH are gone in CL. This can also be appreciated from the profile comparison. The profile comparison in Figure
In conclusion, by incorporating a sparse partial helical scanning trajectory into an FDK-based single circular scanning scheme, a new circle plus partial helical scanning scheme was proposed to compensate for the artifacts inherited by a single circular scan for CBBCT prototype system. The numerical simulation study has demonstrated its feasibility.
This project was supported in part by NIH Grants 8 R01 EB 002775, R01 9 HL078181, 4 R33 CA94300, and 1R44CA103236. The authors also express their thanks to Dr. Delphines for her proofreading of this manuscript.