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.

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.

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.