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

Model predictions for the wide-angle x-ray scatter signals of healthy and malignant breast duct biopsies

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 [Formula: see text]. WAXS methods could become a diagnostic tool for DCIS within breast biopsies.

A method to estimate the fractional fat volume within a ROI of a breast biopsy for WAXS applications: animal tissue evaluation

PURPOSE

To develop a method to estimate the mean fractional volume of fat (ν¯fat) within a region of interest (ROI) of a tissue sample for wide-angle x-ray scatter (WAXS) applications. A scatter signal from the ROI was obtained and use of ν¯fat in a WAXS fat subtraction model provided a way to estimate the differential linear scattering coefficient μs of the remaining fatless tissue.

METHODS

The efficacy of the method was tested using animal tissue from a local butcher shop. Formalin fixed samples, 5 mm in diameter 4 mm thick, were prepared. The two main tissue types were fat and meat (fibrous). Pure as well as composite samples consisting of a mixture of the two tissue types were analyzed. For the latter samples, νfat for the tissue columns of interest were extracted from corresponding pixels in CCD digital x-ray images using a calibration curve. The means ν¯fat were then calculated for use in a WAXS fat subtraction model. For the WAXS measurements, the samples were interrogated with a 2.7 mm diameter 50 kV beam and the 6° scattered photons were detected with a CdTe detector subtending a solid angle of 7.75 × 10(-5) sr. Using the scatter spectrum, an estimate of the incident spectrum, and a scatter model, μs was determined for the tissue in the ROI. For the composite samples, a WAXS fat subtraction model was used to estimate the μs of the fibrous tissue in the ROI. This signal was compared to μs of fibrous tissue obtained using a pure fibrous sample.

RESULTS

For chicken and beef composites, ν¯fat=0.33±0.05 and 0.32 ± 0.05, respectively. The subtractions of these fat components from the WAXS composite signals provided estimates of μs for chicken and beef fibrous tissue. The differences between the estimates and μs of fibrous obtained with a pure sample were calculated as a function of the momentum transfer x. A t-test showed that the mean of the differences did not vary from zero in a statistically significant way thereby validating the methods.

CONCLUSIONS

The methodology to estimate ν¯fat in a ROI of a tissue sample via CCD x-ray imaging was quantitatively accurate. The WAXS fat subtraction model allowed μs of fibrous tissue to be obtained from a ROI which had some fat. The fat estimation method coupled with the WAXS models can be used to compare μs coefficients of fibroglandular and cancerous breast tissue.

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.

Synchrotron-based coherent scatter x-ray projection imaging using an array of monoenergetic pencil beams

Traditional projection x-ray imaging utilizes only the information from the primary photons. Low-angle coherent scatter images can be acquired simultaneous to the primary images and provide additional information. In medical applications scatter imaging can improve x-ray contrast or reduce dose using information that is currently discarded in radiological images to augment the transmitted radiation information. Other applications include non-destructive testing and security. A system at the Canadian Light Source synchrotron was configured which utilizes multiple pencil beams (up to five) to create both primary and coherent scatter projection images, simultaneously. The sample was scanned through the beams using an automated step-and-shoot setup. Pixels were acquired in a hexagonal lattice to maximize packing efficiency. The typical pitch was between 1.0 and 1.6 mm. A Maximum Likelihood-Expectation Maximization-based iterative method was used to disentangle the overlapping information from the flat panel digital x-ray detector. The pixel value of the coherent scatter image was generated by integrating the radial profile (scatter intensity versus scattering angle) over an angular range. Different angular ranges maximize the contrast between different materials of interest. A five-beam primary and scatter image set (which had a pixel beam time of 990 ms and total scan time of 56 min) of a porcine phantom is included. For comparison a single-beam coherent scatter image of the same phantom is included. The muscle-fat contrast was 0.10 ± 0.01 and 1.16 ± 0.03 for the five-beam primary and scatter images, respectively. The air kerma was measured free in air using aluminum oxide optically stimulated luminescent dosimeters. The total area-averaged air kerma for the scan was measured to be 7.2 ± 0.4 cGy although due to difficulties in small-beam dosimetry this number could be inaccurate.

The optimization of an energy-dispersive X-ray diffraction system for potential clinical application

In the past decade, energy-dispersive X-ray diffraction (EDXRD) has been used to identify the nature of tissues. However, these systems have limited clinical use because of problems such as the long measurement times. In this study, the relation between various setup parameters and some performance specifications such as sensitivity, spatial resolution and momentum transfer resolution were assessed using both geometrical calculations and modeling. Accuracy of the derived relations was also confirmed by means of experimental measurements. As an example, the optimum parameters were determined for obtaining diffraction patterns of breast tissue for an efficient acquisition time. Accordingly, the results of this study could introduce a useful tool for EDXRD optimization in clinical application.

An energy-dispersive technique to measure x-ray coherent scattering form factors of amorphous materials

The material-dependent x-ray scattering properties of amorphous substances such as tissues and phantom materials used in imaging are determined by their scattering form factors, measured as a function of the momentum transfer argument, x. Incoherent scattering form factors, F(inc), are calculable for all values of x while coherent scattering form factors, F(coh), cannot be calculated except at large x because of their dependence on long-range order. As a result, measuring F(coh) is very important to the developing field of x-ray scatter imaging. Previous measurements of F(coh), based on crystallographic techniques, have shown significant variability, as these techniques are not optimal for amorphous materials. We have developed an energy-dispersive technique that uses a polychromatic x-ray beam and an energy-sensitive detector. We show that F(coh) can be measured directly, with no scaling parameters, by computing the ratio of two spectra: the first, measured at a given scattering angle and the second, the direct transmission spectrum with no scattering. Experiments have been constructed on this principle and used to measure F(coh) for water and polyethylene to explore the reliability of the technique. A 121 kVp x-ray spectrum and seven different scattering angles between 1.67 and 15.09 degrees were used, resulting in a measurable range of x between 0.5 and 9.5 nm(-1). These are the first measurements of F(coh) made without the need for a scaling factor. Resolution in x varies between 10% for small scattering angles and 2% for large scattering angles. Accuracy in F(coh) is shown to be strongly dependent on the precision of the experimental geometry and varies between 5% and 15%. Comparison with previous published measurements for water shows values of the average absolute relative difference between 8% and 14%.

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.