Optimum momentum transfer arguments for x-ray forward scatter imaging

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.

Evaluation of scatter-to-primary ratio, grid performance and normalized average glandular dose in mammography by Monte Carlo simulation including interference and energy broadening effects

In this work, a computational code for the study of imaging systems and dosimetry in conventional and digital mammography through Monte Carlo simulations is described. The developed code includes interference and Doppler energy broadening for simulation of elastic and inelastic photon scattering, respectively. The code estimates the contribution of scattered radiation to image quality through the spatial distribution of the scatter-to-primary ratio (S/P). It allows the inclusion of different designs of anti-scatter grids (linear or cellular), for evaluation of contrast improvement factor (CIF), Bucky factor (BF) and signal difference-to-noise ratio improvement factor (SIF). It also allows the computation of the normalized average glandular dose, D(g).(N). These quantities were studied for different breast thicknesses and compositions, anode/filter combinations and tube potentials. Results showed that the S/P increases linearly with breast thickness, varying slightly with breast composition or the spectrum used. Evaluation of grid performance showed that the cellular grid provides the highest CIF with smaller BF. The SIF was also greater for the cellular grid, although both grids showed SIF < 1 for thin breasts. Results for D(g).(N) showed that it increases with the half-value layer (HVL) of the spectrum, decreases considerably with breast thickness and has a small dependence on the anode/filter combination. Inclusion of interference effects of breast tissues affected the values of S/P obtained with the grid up to 25%, while the energy broadening effect produced smaller variations on the evaluated quantities.

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.

Human breast cancerin vitro: matching histo-pathology with small-angle x-ray scattering and diffraction enhanced x-ray imaging

Twenty-eight human breast tumour specimens were studied with small-angle x-ray scattering (SAXS), and 10 of those were imaged by the diffraction enhanced x-ray imaging (DEI) technique. The sample diameter was 20 mm and the thickness 1 mm. Two examples of ductal carcinoma are illustrated by histology images, DEI, and maps of the collagen d-spacing and scattered intensity in the Porod regime, which characterize the SAXS patterns from collagen-rich regions of the samples. Histo-pathology reveals the cancer-invaded regions, and the maps of the SAXS parameters show that in these regions the scattering signal differs significantly from scattering by the surrounding tissue, indicating a degradation of the collagen structure in the invaded regions. The DEI images show the borders between collagen and adipose tissue and provide a co-ordinate system for tissue mapping by SAXS. In addition, degradation of the collagen structure in an invaded region is revealed by fading contrast of the DEI refraction image. The 28 samples include fresh, defrosted tissue and formalin-fixed tissue. The d-values with their standard deviations are given. In the fresh samples there is a systematic 0.76% increase of the d-value in the invaded regions, averaged over 11 samples. Only intra-sample comparisons are made for the formalin-fixed samples, and with a long fixation time, the difference in the d-value stabilizes at about 0.7%. The correspondence between the DEI images, the SAXS maps and the histo-pathology suggests that definitive information on tumour growth and malignancy is obtained by combining these x-ray methods.

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.