CZT detectors are gaining popularity in the medical field. A numerical study of the response of CZT detector pixels to parallel and oblique x rays was conducted. The average k-fluorescence energy generated in a given pixel is 26.0 keV. It is assumed that such x rays travel a mean free path mfp = 0.161 mm in CZT before being absorbed. For applications in nuclear medicine, incident 140 keV photons were used. Each pixel had an area 1.5 mm x 3.3 mm and thickness 5 mm. The spacing between pixels was Δ = 0:3 mm and since Δ >mfp, the model predicts no cross talk between pixels. For parallel photons, the probability of escape is PFesc = 4:0% and the quantum efficiency η = 0:88. Next consider an isotropic source located at a distance 20 cm from the detector plane. For incident angles of 0° to 23° η varied from 0.88 to 0.5 and the fluorescence escape from 3.8 % to 2.0 %. For breast CT applications a typical pixel size is 0.2 mm by 0.2 mm and thickness 0.75 mm. The corresponding values for photons of energy 60 keV are as follows: (i) parallel η = 0:94, PFesc = 30%, oblique η = 0:94, PFesc = 30% at 0°; η = 0:55, PFesc = 18% at 23°. This work provides some quantification of the response of CZT detector pixels to x rays. Cross talk would need to be examined for the breast CT detector.
A numerical study of the wide angle x-ray scatter (WAXS) energy integrated signals (EISs) from breast biopsies was conducted. A benign biopsy was chosen as fibroglandular (fib) tissue whereas biopsies with cancer were approximated as consisting of fib tissue and a cluster of epithelial cells. The grouping of cells represented the malignant portion. The EISs due to scatter were computed for biopsies of thickness dbio = 2 mm, 5 mm, 10 mm and 20 mm. For the malignant biopsies, the fractional volumes of cells (νcell) studied ranged from 0.01 to 0.1. Incident 2 mm diam beams of 30 kV, 50 kV, 80 kV, and 140 kV were considered. The tube current and exposure time were 3 mA and 1 minute, respectively. The WAXS signals were computed by adding the signals from annular detectors subtending scattering angles θ = 2°, 3°, , 23° and solid angles Ωθ = 2.0 x π x [cos(θ - ∆θ/2) - cos(θ + ∆θ/2)] x cos θ where ∆θ = 1°. Let the EIS due to a malignant biopsy be EISms and that of a benign one, EISbs. With these signals, values of SNR were computed. The 30 kV beam provided SNRs < 5 for the lowest entrance exposure, X = 0.0015 C/kg. For biopsies with dbio = 2, 5, 10, 20 mm and νcell = 0.1, the SNRs were 28.0, 38.2, 43.0, and 40.0. The findings suggest that there is potential to use WAXS EISs to diagnose malignancy in breast biopsies.
Dual detector VOI scatter CBCT is similar to dual detector VOI CBCT except that during the high resolution scan, the low resolution flat panel detector is also used to capture the scattered photons. Simulations show a potential use of scatter to diagnose suspicious VOIs. Energy integrated signals due to scatter (EISs) were computed for a specific imaging task involving a malignant lesion and was labelled as a hypothetical experiment (expt) result. The signal was compared to predictions (pred) using benign and malignant lesions. The ΔEISs=EISs|expt - EISs|pred displayed eye catching diffraction structure when the prediction calculation used a benign lesion. The structure occurred even when the phantom compositions were different for prediction and experiment calculations. Since the diffraction structure has a circularly symmetric behaviour because the tissues are amorphous in nature, the 2D ΔEISs patterns were transformed to 1D signals. The 1D signals were obtained by calculating the mean ΔEISs signals in rings. The mean pixel values were a function of the momentum transfer argument q = 4π sin(θ/2)/λ which ranged from 12 to 46 nm-1. The 1D signals correlated well with the 2D profiles. Of particular interest were scatter signatures between q = 20 and 30 nm-1 where malignant tissue is predicted to scatter more than benign fibroglandular tissue. The 1D diffraction signatures could allow a better method to diagnose a suspicious lesion during dual detector scatter VOI CBCT.
Wide-angle x-ray scatter (WAXS) could potentially be used to diagnose ductal carcinoma in situ (DCIS) in breast biopsies. The regions of interest were assumed to consist of fibroglandular tissue and epithelial cells and the model assumed that biopsies with DCIS would have a higher concentration of the latter. The scattered number of photons from a 2-mm diameter column of tissue was simulated using a 110-kV beam and selectively added in terms of momentum transfer. For a 1-min exposure, specificities and sensitivities of unity were obtained for biopsies 2- to 20-mm thick. The impact of sample and tumor cell layer thicknesses was studied. For example, a biopsy erroneously estimated to be 8 mm would be correctly diagnosed if its actual thickness was between 7.3 and 8.7 mm. An 8-mm thick malignant biopsy can be correctly diagnosed provided the malignant cell layer thickness is >0.96 mm. WAXS methods could become a diagnostic tool for DCIS within breast biopsies.
KEYWORDS: Breast, Image segmentation, Computer simulations, Photons, Monte Carlo methods, Scattering, Tissues, Breast imaging, Signal attenuation, X-rays
A model based on singly scattered photons could potentially be of use to correct for scatter effects in breast
CBCT applications. Consider a simple phantom consisting of a 14 cm diameter 10.5 cm long cylindrical 50:50
mixture of fibroglandular and fat tissue with 21 cylindrical segments embedded along its central axis. One group
of segments were 2 mm in diameter with compositions 0:100, 20:80, 35:65, 50:50, 65:35, 80:20, and 100:0. The
remaining two groups had diameters of 5 mm and 10 mm. In order to reduce the computational time required,
GEANT4 was used to simulate a scatter profile for a single projection which was then utilized in generating
the large number of unique projections required for CBCT reconstruction. The scatter model was applied in an
attempt to correct the cupping artifact caused by x ray scatter in the reconstructed images. The model assumed
a homogeneous 50:50 phantom. The SPR generated by the model near the phantom center was at most 8%
below that simulated by GEANT4. The scatter corrected images showed an almost complete removal of the
cupping artifact. This simple model shows considerable promise in correcting scatter, though more research is
required to determine its validity in more realistic imaging tasks.
A wide-angle x-ray scatter (WAXS) measurement could potentially be used to determine whether a biopsy of a breast duct is healthy or malignant. A ductal carcinoma in situ (DCIS) occurs when the epithelial cells lining the wall start to replicate and invade the duct interior. Since cells are composed mainly of water a WAXS signal of DCIS could contain a larger component due to water. A model approximates that a breast duct biopsy consists of connective tissue (c.t.) and cells. For a 2 mm diameter 3.81 mm thick healthy duct biopsy, the volumes in cubic mm are 11.56 c.t. and 0.41 cells whereas 6.64 c.t. and 5.33 cells for DCIS. The differential linear scattering coefficients (μs) for both types of biopsies were calculated using the sum vc.t.μsc.t. + vcellμscell where v denotes fractional volume. The cell was assumed to be composed of water, lipids (fat), and other atoms associated with RNA, DNA, proteins, and carbohydrates. The μscell was calculated using the sum 0.771μswater + 0.023μsfat + 0.206μsother. The μs of c.t., water, and fat were available from literature whereas the independent atomic model approximation was used to calculate values for μsother. A WAXS model provided predictions of the number of 6 degree scattered photons Ns for incident 50 kV beams on healthy and malignant ducts. The sum of Ns between 31.5 ≤ E ≤ 45 keV were 1402 and 1529 for respectively the healthy and malignant biopsies. Using Poisson statistics, two Gaussian distributions, and a descision threshold set at their intersection, the false positive and false negative probabilities were 4.7% and 5.0%. This work suggests that DCIS could potentially be diagnosed via energy dispersive WAXS measurements.
The feasibility of cone beam CT (CBCT) for differentiating normal epithelium from invasive carcinoma is investigated
via a simulation study. The phantom consisted of a 5 mm long 5mm diameter cylinder of a 50:50
mixture of fibrous and fatty tissue. Normal epithelium and invasive carcinoma were each modeled as epithelium
and connective tissue compartments with respective cross-sectional dimensions of 158 by 161 μm and 131 by
161 μm . For normal epithelium, 125 cells were placed in the compartments with a higher concentration in the
basal layer. For the invasive carcinoma, 314 cells were spread out sporadically. Cells were modeled as 5.67 μm
diameter spheres. The attenuation coefficients used in the simulation were those of fat for epithelium, 80:20
mixture of fibrous and fat for the connective tissue and water for cells. A point source and 50 μm detector
pixels were assumed. Scatter from the phantom is negligible and was neglected. Three hundred projections were
acquired at magnification 10 in vacuum using a 26 kV spectrum. The preliminary study suggest a potential
application of CBCT for visualizing cell clusters. The contrast was slightly improved by using a 5 to 10 keV
uniform spectrum.
Although scattered radiation is generally regarded as a nuisance in radiological imaging, many innovative imaging concepts that use the scattered field have been demonstrated. A systematic approach, however, for analyzing the medical applications of x-ray scatter imaging has been lacking. We have therefore formulated a simple semi-analytic model that consists of imaging a target object against a background material of the same dimensions when both are situated within a water phantom. The target and background objects have small cross-sectional areas (1.0 mm2) to allow the omission of self-attenuation and multiple scatter within the objects. The incident energy fluence is kept constant so that similar doses are delivered by the various photon beams. For imaging white brain matter versus gray brain matter in a 15 cm thick water phantom, the maximum signal-to-noise ratio, over all photon energies, for images obtained with the forward scatter between 2 degrees - 12 degrees exceeds that of primary images for all object thicknesses less than or equal to 40 mm. The penalty in dose as a result of spectral blur is generally moderate. For example, using an 80 kV beam for the previous imaging task would require approximately a 24% dose increase relative to using a monoenergetic beam. A high-precision experimental apparatus has been assembled to validate our predictions.
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