X-ray forward-scatter imaging: experimental validation of model

Feasibility analysis on simultaneous electron density and attenuation coefficient reconstruction

PURPOSE

Creating a viable reconstruction method for Compton scatter tomography remains challenging. Accounting for scatter attenuation when the underlying attenuation map is not known is particularly challenging, and current mathematical approaches to this vary widely. This work explores a novel approach to joint scatter and attenuation image reconstruction, which leverages the underlying structural similarity between the two images and incorporates a deep learning model in an alternating iterative reconstruction scheme.

METHODS

A single-view computed tomography (CT) imaging procedure for recording Compton scatter is first described. A joint reconstruction model, which iterates between algebraically reconstructing scatter images and estimating the attenuation via deep learning, is then proposed. This model is tested on both a generated dataset of 2D phantom images designed to mimic human tissues as well as a realistically simulated dataset based on real CT images.

RESULTS

Testing results yield convergence of the model and decent reconstruction quality to distinguish crucial features such as tumors and lesions, demonstrating the potential principled utilities of this configuration and deep learning approach. The model achieved a structural similarity index measure of at least 0.82 for scatter and 0.88 for attenuation reconstructions with the realistically simulated dataset.

CONCLUSION

The iterative, deep learning approach outlined in this work shows potential for future efficient medical imaging procedures, reconstructing images with limited scatter information.

WAXS fat subtraction model to estimate differential linear scattering coefficients of fatless breast tissue: phantom materials evaluation

PURPOSE

Develop a method to subtract fat tissue contributions to wide-angle x-ray scatter (WAXS) signals of breast biopsies in order to estimate the differential linear scattering coefficients μ(s) of fatless tissue. Cancerous and fibroglandular tissue can then be compared independent of fat content. In this work phantom materials with known compositions were used to test the efficacy of the WAXS subtraction model.

METHODS

Each sample 5 mm in diameter and 5 mm thick was interrogated by a 50 kV 2.7 mm diameter beam for 3 min. A 25 mm(2) by 1 mm thick CdTe detector allowed measurements of a portion of the θ = 6° scattered field. A scatter technique provided means to estimate the incident spectrum N(0)(E) needed in the calculations of μ(s)[x(E, θ)] where x is the momentum transfer argument. Values of [Formula: see text] for composite phantoms consisting of three plastic layers were estimated and compared to the values obtained via the sum [Formula: see text], where ν(i) is the fractional volume of the ith plastic component. Water, polystyrene, and a volume mixture of 0.6 water + 0.4 polystyrene labelled as fibphan were chosen to mimic cancer, fat, and fibroglandular tissue, respectively. A WAXS subtraction model was used to remove the polystyrene signal from tissue composite phantoms so that the μ(s) of water and fibphan could be estimated. Although the composite samples were layered, simulations were performed to test the models under nonlayered conditions.

RESULTS

The well known μ(s) signal of water was reproduced effectively between 0.5 < x < 1.6 nm(-1). The [Formula: see text] obtained for the heterogeneous samples agreed with [Formula: see text]. Polystyrene signals were subtracted successfully from composite phantoms. The simulations validated the usefulness of the WAXS models for nonlayered biopsies.

CONCLUSIONS

The methodology to measure μ(s) of homogeneous samples was quantitatively accurate. Simple WAXS models predicted the probabilities for specific x-ray scattering to occur from heterogeneous biopsies. The fat subtraction model can allow μ(s) signals of breast cancer and fibroglandular tissue to be compared without the effects of fat provided there is an independent measurement of the fat volume fraction ν(f). Future work will consist of devising a quantitative x-ray digital imaging method to estimate ν(f) in ex vivo breast samples.

An iterative three-dimensional electron density imaging algorithm using uncollimated compton scattered x rays from a polyenergetic primary pencil beam

X-ray film-screen mammography is currently the gold standard for detecting breast cancer. However, one disadvantage is that it projects a three-dimensional (3D) object onto a two-dimensional (2D) image, reducing contrast between small lesions and layers of normal tissue. Another limitation is its reduced sensitivity in women with mammographically dense breasts. Computed tomography (CT) produces a 3D image yet has had a limited role in mammography due to its relatively high dose, low resolution, and low contrast. As a first step towards implementing quantitative 3D mammography, which may improve the ability to detect and specify breast tumors, we have developed an analytical technique that can use Compton scatter to obtain 3D information of an object from a single projection. Imaging material with a pencil beam of polychromatic x rays produces a characteristic scattered photon spectrum at each point on the detector plane. A comparable distribution may be calculated using a known incident x-ray energy spectrum, beam shape, and an initial estimate of the object's 3D mass attenuation and electron density. Our iterative minimization algorithm changes the initially arbitrary electron density voxel matrix to reduce regular differences between the analytically predicted and experimentally measured spectra at each point on the detector plane. The simulated electron density converges to that of the object as the differences are minimized. The reconstruction algorithm has been validated using simulated data produced by the EGSnrc Monte Carlo code system. We applied the imaging algorithm to a cylindrically symmetric breast tissue phantom containing multiple inhomogeneities. A preliminary ROC analysis scores greater than 0.96, which indicate that under the described simplifying conditions, this approach shows promise in identifying and localizing inhomogeneities which simulate 0.5 mm calcifications with an image voxel resolution of 0.25 cm and at a dose comparable to mammography.

PSF, LSF and S/P in mammography: GEANT4 validation

The main goal of this study was to validate the predictions of GEANT4, a Monte Carlo code originally developed for high-energy physics, for low-energy (10-40 keV) photon transmission and scattering through matter similar to biological tissue. We compared GEANT4 calculations with existing phantom data relevant for the mammographic imaging technique. This work showed that scattered-to-primary ratio data can be simulated using GEANT4 with a deviation smaller than 5%. At the same time, we encountered a limitation in the small-angle region description by the code, which is important for point- and line-spread function calculations. The comparison with forward angle data showed that the GEANT4 models, known as "G4 Low Energy" and "G4 Penelope", describe the measurements for X-ray beams typically used in mammography better than 10% for angles above 10 degrees, and that "G4 Low Energy" is preferable to "G4 Penelope ". The results confirm the possible use of GEANT4 for the optimization of applications based on low-energy photon transmission and scattering.

An analytic model for the response of a CZT detector in diagnostic energy dispersive x-ray spectroscopy

A CdZnTe detector (CZTD) can be very useful for measuring diagnostic x-ray spectra. The semiconductor detector does, however, exhibit poor hole transport properties and fluorescence generation upon atomic de-excitations. This article describes an analytic model to characterize these two phenomena that occur when a CZTD is exposed to diagnostic x rays. The analytical detector response functions compare well with those obtained via Monte Carlo calculations. The response functions were applied to 50, 80, and 110 kV x-ray spectra. Two 50 kV spectra were measured; one with no filtration and the other with 1.35 mm Al filtration. The unfiltered spectrum was numerically filtered with 1.35 mm of Al in order to see whether the recovered spectrum resembled the filtered spectrum actually measured. A deviation curve was obtained by subtracting one curve from the other on an energy bin by bin basis. The deviation pattern fluctuated around the zero line when corrections were applied to both spectra. Significant deviations from zero towards the lower energies were observed when the uncorrected spectra were used. Beside visual observations, the exposure obtained using the numerically attenuated unfiltered beam was compared to the exposure calculated with the actual filtered beam. The percent differences were 0.8% when corrections were applied and 25% for no corrections. The model can be used to correct diagnostic x-ray spectra measured with a CdZnTe detector.

A semianalytic model to extract differential linear scattering coefficients of breast tissue from energy dispersive x-ray diffraction measurements

The goal of this work is to develop a technique to measure the x-ray diffraction signals of breast biopsy specimens. A biomedical x-ray diffraction technology capable of measuring such signals may prove to be of diagnostic use to the medical field. Energy dispersive x-ray diffraction measurements coupled with a semianalytical model were used to extract the differential linear scattering coefficients [mus(x)] of breast tissues on absolute scales. The coefficients describe the probabilities of scatter events occuring per unit length of tissue per unit solid angle of detection. They are a function of the momentum transfer argument, x=sin(theta/2)/X, where theta=scatter angle and lambda=incident wavelength. The technique was validated by using a 3 mm diameter 50 kV polychromatic x-ray beam incident on a 5 mm diameter 5 mm thick sample of water. Water was used because good x-ray diffraction data are available in the literature. The scatter profiles from 6 degrees to 15 degrees in increments of 1 degrees were measured with a 3 mm x 3 mm x 2 mm thick cadmium zinc telluride detector. A 2 mm diameter Pb aperture was placed on top of the detector. The target to detector distance was 29 cm and the duration of each measurement was 10 min. Ensemble averages of the results compare well with the gold standard data of A. H. Narten ["X-ray diffraction data on liquid water in the temperature range 4 degrees C-200 degrees C," ORNL Report No. 4578 (1970)]. An average 7.68% difference for which most of the discrepancies can be attributed to the background noise at low angles was obtained. The preliminary measurements of breast tissue are also encouraging.

Measurement of coherent x-ray scatter form factors for amorphous materials using diffractometers

The feasibility of measuring the coherent x-ray scatter form factors of amorphous materials using powder diffractometers has been assessed. A five-step procedure was developed: (i) Low-angle background, consisting of a portion of the incident x-ray beam that passes directly to the detector, is measured using a specially designed replacement for the sample holder which absorbs most of the photons that otherwise would scatter off the sample holder cavity. (ii) Angle-dependent effects including monochromator efficiency and projected beam area are characterized by extracting the incoherent signal from the diffraction pattern of powdered graphite. The incoherent signal divided by the calculated incoherent cross section gives a correction factor as a function of scattering angle theta. (iii) Diffraction patterns are measured for the samples for theta = 2 degrees -150 degrees. (iv) The scattering data are corrected for background and then for angle-dependent effects. (v) The data are normalized to calculated free atom form factors at high theta, and the coherent form factor extracted. The method was implemented on two diffractometers at different energies (Co Kalpha and Cu Kalpha), and the results compared for water and plastics. Over the range 0.117 < x < 5.39 nm(-1), where x = lambda(-1) sin(theta/2), the average form factor ratio for water was 0.93. Systematic errors are difficult to eliminate. While this x-ray powder diffractometer technique suffices for a survey measurement of the form factor of a material, its accuracy is probably insufficient for detailed studies.

Characterization of cirrhosis and hepatocellular carcinoma using low-angle x-ray scattering signatures of serum

The diagnosis of hepatocellular carcinoma (HCC) usually occurs at late stages in the disease when there are few effective treatment options. The measurement of the concentration of tumour markers in the serum of patients is a complementary tool frequently used for the interpretation of diagnostic imaging results. It is also used as a prognostic tool for the detection of cancer. Unfortunately, the sensitivity of tumour markers is still low and many times it yields normal results for cirrhotic and HCC patients. In the current work, the detection possibility of the structural changes in serum proteins accompanying cirrhosis and HCC is investigated using a low-angle x-ray scattering (LAXS) technique. The results show that there are significant differences in the LAXS profiles of cirrhosis and HCC lyophilized serum samples compared to normal. The changes in shape, total counts and position of the first scattering peak at 4.8 degrees, which was previously reported to be sensitive to the structural changes in protein, showed the most characteristic deviations from normal serum. The present results are promising and would offer a potentially helpful complementary tool for monitoring cirrhosis and HCC.

Optimum momentum transfer arguments for x-ray forward scatter imaging

In our research program we have shown through modeling, related numerical calculations, and experimental measurements that there exists a potential use of scattered radiation for medical x-ray imaging. Each incident photon of wavelength lambda which scatters at a small angle theta with respect to its initial direction of travel has a change in momentum characterized by the photon momentum transfer argument x = lambda(-1) sin(theta/2). In this work, we show that in order to maximize the signal-to-noise ratio (SNR) obtained with scattered x rays, one must detect photons with specific x values. Using a photon counting detector to distinguish 2-cm-thick polymethyl methacrylate and nylon targets situated within a 15-cm-diam spherical water phantom with an 80 kV beam yields experimentally SNR/square root(K(air)c) = 12.8 +/- 0.2 (mJ/kg)(-1/2) when using the photons between x = 0.5 and 0.7 nm(-1). Here K(air)c is the air collision kerma and the average momentum transfer argument, x, is calculated by weighting x by the incident photon fluence distribution. The model predicts a value of SNR/square root(K(air)c) = 12.9 (mJ/kg)(-1/2). If we choose to form the signal with the range in x extended to be from 0.5 to 1.0 nm(-1) then, despite the detection of more scattered photons, experimentally SNR/square root(K(air)c) decreases by 38% to 7.9 +/- 0.3 (mJ/kg)(-1/2). The model predicts a value of 9.46 (mJ/kg)(-1/2). Results for energy integrating detectors are in general similar to those for photon counters, but there exist cases where a significant decrease in SNR can occur. For example, for measurements in air with the two plastics at theta = 3 degrees the SNR for an energy integrator was found to be 52% that of a photon counter. Numerical calculations predict that the effects of spectral blur can be significant when a narrow angular range is used for detection. Preliminary numerical predictions for breast tissues suggest a potential use of x-ray scatter in the field of mammography.

Updating of form factor tabulations for coherent scattering of photons in tissues

An updating of photon transport modelling in tissues is carried out by including the effect of molecular interference in the coherent (Rayleigh) scattering. To this end, the present tabulations--which permit us to obtain the linear differential scattering coefficient of compounds from a simple weighted sum of the elemental components--are integrated by adding files for a limited set of molecular interference functions. This set originates from a four-component model which is found to be capable of reproducing human tissues in situations involving bony and soft tissues. The proposed procedure overcomes, in the computation, the hindrance that the dependence on molecular interference effects leads every tissue to have its own diffraction pattern, which is not easily obtained by means of measurements or calculations.

Analysis of low-angle x-ray scattering peaks from lyophilized biological samples

Low-angle x-ray scattering (LAXS) from lyophilized blood and its constituents is characterized by the presence of two peaks in the forward direction of scattering. These peaks are found to be sensitive to the variations in the molecular structure of a given sample. The present work aims to explore the nature of LAXS from a variety of lyophilized biological samples. It also aims to investigate the possibility that a certain biological macromolecule is responsible of the production of LAXS peaks. This is carried out through measurements of LAXS from complex biological samples and their basic constituents. Among the measured samples are haemoglobin (Hb), globin, haem, packed red blood cells, bovine albumin, egg albumin, milk, casein, glutamine, alanine, fat, muscle and DNA. A table containing some characteristic parameters of the LAXS profiles of these samples is also presented. Analysis of measured profiles shows that all lyophilized samples produce at least one relatively broad peak at a scattering angle around 10.35 degrees. The full width at half maximum (FWHM) of this peak varies considerably among the measured samples. Except for milk and casein. one additional peak at a scattering angle around 4.65 degrees is observed only in the LAXS profiles of proteins or protein-rich samples. This fact strongly suggests protein to be the biological macromolecule from which this characteristic peak originates. The same idea is further strengthened through discussion of some previous observations.