Breast tissue classification using x-ray scattering measurements and multivariate data analysis

Method of sparse-view coded-aperture x-ray diffraction tomography

Objective.X-ray diffraction (XRD) has been considered as a valuable diagnostic technology providing material specific 'finger-print' information i.e. XRD pattern to distinguish different biological tissues. XRD tomography (XRDT) further obtains spatial-resolved XRD pattern distribution, which has become a frontier biological sample inspection method. Currently, XRD computed tomography (XRD-CT) featured by the conventional CT scan mode with rotation has the best spatial resolution among various XRDT methods, but its scan process takes hours. Meanwhile, snapshot XRDT methods such as coded-aperture XRDT (CA-XRDT) aim at direct imaging without scan movements. With compressed-sensing acquisition applied, CA-XRDT significantly shortens data acquisition time. However, the snapshot acquisition results in a significant drop in spatial resolution. Hence, we need an advanced XRDT method that significantly accelerates XRD-CT acquisition and still maintains an acceptable imaging accuracy for biological sample inspection.Approach.Inspired by the high spatial resolution of XRD-CT from rotational scan and the fast compressed-sensing acquisition in snapshot CA-XRDT (SnapshotCA-XRDT), we proposed a new XRDT imaging method: sparse-view rotational CA-XRDT (RotationCA-XRDT). It takes SnapshotCA-XRDT as a preliminary depth-resolved XRDT method, and combines rotational scan to significantly improve the spatial resolution. A model-based iterative reconstruction (MBIR) method is adopted for RotationCA-XRDT. Moreover, we suggest a refined system model calculation for the RotationCA-XRDT MBIR which is a key factor to improve reconstruction image quality.Main results.We conducted our experimental validation based on Monte-Carlo simulation for a breast sample. The results show that the proposed RotationCA-XRDT method succeeded in producing good images for detecting 2 mm square carcinoma with a 15-view scan. The spatial resolution is significantly improved from current SnapshotCA-XRDT methods. With our refined system model, MBIR can obtain high quality images with little artifacts.Significance.In this work, we proposed a new high spatial resolution XRDT method combining coded-aperture compressed-sensing acquisition and sparse-view scan. The proposed RotationCA-XRDT method obtained significantly better image resolution than current SnapshotCA-XRDT methods in the field. It is of great potential for biological sample XRDT inspection. The proposed RotationCA-XRDT is the fastest millimetre-resolution XRDT method in the field which reduces the scan time from hours to minutes.

Reciprocal-FDK reconstruction for x-ray diffraction computed tomography

Objective. X-ray diffraction (XRD) technology uses x-ray small-angle scattering signal for material analysis, which is highly sensitive to material inter-molecular structure. To meet the high spatial resolution requirement in applications such as medical imaging, XRD computed tomography (XRDCT) has been proposed to provide XRD intensity with improved spatial resolution from point-wise XRD scan. In XRDCT, 2D spatial tomography corresponds to a 3D reconstruction problem with the third dimension being the XRD spectrum dimension, i.e. the momentum transfer dimension. Current works in the field have studied reconstruction methods for either angular-dispersive XRDCT or energy-dispersive XRDCT for small samples. The approximations used are only suitable for regions near the XRDCT iso-center. A new XRDCT reconstruction method is needed for more general imaging applications. Approach. We derive a new FDK-type reconstruction method (Reciprocal-FDK) for XRDCT without limitation on object size. By introducing a set of reciprocal variables, the XRDCT model is transformed into a classical cone-parallel CT model, which is an extension of a circular-trajectory cone-beam CT model, after which the FDK method is applied for XRDCT reconstruction. Main results. Both analytical simulation and Monte Carlo simulation experiments are conducted to validate the XRDCT reconstruction method. The results show that when compared to existing analytical reconstruction methods, there are improvements in the proposed Reciprocal-FDK method with regard to relative structure reconstruction and XRD pattern peak reconstruction. Since cone-parallel CT does not satisfy the data completeness condition, cone-angle effect affects the reconstruction accuracy of XRDCT. The property of cone-angle effect in XRDCT is also analyzed with ablation studies. Significance. We propose a general analytical reconstruction method for XRDCT without constraint on object size. Reciprocal-FDK provides a complete derivation and theoretical support for XRDCT reconstruction by analogy to the well-studied cone-parallel CT model. In addition, the intrinsic problem with the XRDCT data model and the corresponding reconstruction error are discussed for the first time.

Target-filter combination effects on breast tissue characterization using mammographic X-rays: A Monte Carlo simulation study

BACKGROUND

Characterization of normal and malignant breast tissues using X-ray scattering techniques has shown promising results and applications.

OBJECTIVE

To examine possibility of characterizing normal and malignant breast tissues using the scattered photon distribution of polyenergetic beams of 30 kV X-rays.

METHODS

A Monte Carlo simulation is upgraded so that it is capable of simulating input mammographic X-ray spectra from different target-filter combinations, tracing photon transport, and producing the distribution of scattered photons. The target-filter combinations include Mo-Mo, Mo-Al, Mo-Rh, Rh-Rh, Rh-Al, W-Rh, and W-Al. Analysis of obtained scattered photon distribution is carried out by comparing the ratio of count under the peak in the momentum transfer region from 0 to 1.55 nm-1, to that in the region from 1.6 to 9.1 nm-1 (covering the regions of scattering from fat and soft tissue, respectively) for breast samples with different percentages of normal tissue (0-100%).

RESULTS

Mo-Mo target-filter combination shows a high linear dependence of the count under peak ratio on the percentage of normal tissue in breast samples (R2 = 0.9513). Despite slightly less linear than Mo-Mo, target-filter combinations other than Rh-Rh, W-Rh, and W-Al produce high linear responses (R2 > 0.9)CONCLUSION:Mo-Mo target-filter combination would probably be the most relevant in characterizing normal and malignant breast tissues from their scattered photon distribution.

Assessing lesion malignancy by scanning small-angle x-ray scattering of breast tissue with microcalcifications

Scanning small-angle x-ray scattering (SAXS) measurements were performed on 36 formalin-fixed breast tissue biopsies obtained from two patients. All samples contained microcalcifications of type II, i.e. formed by hydroxyapatite. We demonstrate the feasibility of classifying breast lesions by scanning SAXS of tissues containing microcalcifications with a resolution of 35 [Formula: see text]m [Formula: see text] 30 [Formula: see text]m. We report a characteristic Bragg peak found around q  =  1.725 nm^-1 that occurs primarily for malignant lesions. Such a clear SAXS fingerprint is potentially linked to structural changes of breast tissue and corresponds to dimensions of about 3.7 nm. This material property could be used as an early indicator of malignancy development, as it is readily assessed by SAXS. If this fingerprint is combined with other known SAXS features, which also indicate the level of malignancy, such as lipid spacing and collagen periodicity, it could complement traditional pathology-based analyses. To confirm the SAXS-based classification, a histopathological workup and a gold standard histopathological diagnosis were conducted to determine the malignancy level of the lesions. Our aim is to report this SAXS fingerprint, which is clearly related to malignant breast lesions. However, any further conclusion based on our dataset is limited by the low number of patients and samples. Running a broad study to increase the number of samples and patients is of great importance and relevance for the breast-imaging community.

Three-dimensional reciprocal space x-ray coherent scattering tomography of two-dimensional object

PURPOSE

X-ray coherent scattering tomography is a powerful tool in discriminating biological tissues and bio-compatible materials. Conventional x-ray scattering tomography framework can only resolve isotropic scattering profile under the assumption that the material is amorphous or in powder form, which is not true especially for biological samples with orientation-dependent structure. Previous tomography schemes based on x-ray coherent scattering failed to preserve the scattering pattern from samples with preferred orientations, or required elaborated data acquisition scheme, which could limit its application in practical settings. Here, we demonstrate a simple imaging modality to preserve the anisotropic scattering signal in three-dimensional reciprocal (momentum transfer) space of a two-dimensional sample layer.

METHODS

By incorporating detector movement along the direction of x-ray beam, combined with a tomographic data acquisition scheme, we match the five dimensions of the measurements with the five dimensions (three in momentum transfer domain, and two in spatial domain) of the object. We employed a collimated pencil beam of a table-top copper-anode x-ray tube, along with a panel detector to investigate the feasibility of our method.

RESULTS

We have demonstrated x-ray coherent scattering tomographic imaging at a spatial resolution ~2 mm and momentum transfer resolution 0.01 Å^-1 for the rotation-invariant scattering direction. For any arbitrary, non-rotation-invariant direction, the same spatial and momentum transfer resolution can be achieved based on the spatial information from the rotation-invariant direction. The reconstructed scattering profile of each pixel from the experiment is consistent with the x-ray diffraction profile of each material. The three-dimensional scattering pattern recovered from the measurement reveals the partially ordered molecular structure of Teflon wrap in our sample.

CONCLUSIONS

We extend the applicability of conventional x-ray coherent scattering tomography to the reconstruction of two-dimensional samples with anisotropic scattering profile by introducing additional degree of freedom on the detector. The presented method has the potential to achieve low-cost, high-specificity material discrimination based on x-ray coherent scattering.

X-ray diffraction tomography with limited projection information

X-ray diffraction tomography (XDT) records the spatially-resolved X-ray diffraction profile of an extended object. Compared to conventional transmission-based tomography, XDT displays high intrinsic contrast among materials of similar electron density and improves the accuracy in material identification thanks to the molecular structural information carried by diffracted photons. However, due to the weak diffraction signal, a tomographic scan covering the entire object typically requires a synchrotron facility to make the acquisition time more manageable. Imaging applications in medical and industrial settings usually do not require the examination of the entire object. Therefore, a diffraction tomography modality covering only the region of interest (ROI) and subsequent image reconstruction techniques with truncated projections are highly desirable. Here we propose a table-top diffraction tomography system that can resolve the spatially-variant diffraction form factor from internal regions within extended samples. We demonstrate that the interior reconstruction maintains the material contrast while reducing the imaging time by 6 folds. The presented method could accelerate the acquisition of XDT and be applied in portable imaging applications with a reduced radiation dose.

Maximum-likelihood estimation of scatter components algorithm for x-ray coherent scatter computed tomography of the breast

Coherent scatter computed tomography (CSCT) is a reconstructive x-ray imaging technique that yields the spatially resolved coherent-scatter cross section of the investigated object revealing structural information of tissue under investigation. In the original CSCT proposals the reconstruction of images from coherently scattered x-rays is done at each scattering angle separately using analytic reconstruction. In this work we develop a maximum likelihood estimation of scatter components algorithm (ML-ESCA) that iteratively reconstructs images using a few material component basis functions from coherent scatter projection data. The proposed algorithm combines the measured scatter data at different angles into one reconstruction equation with only a few component images. Also, it accounts for data acquisition statistics and physics, modeling effects such as polychromatic energy spectrum and detector response function. We test the algorithm with simulated projection data obtained with a pencil beam setup using a new version of MC-GPU code, a Graphical Processing Unit version of PENELOPE Monte Carlo particle transport simulation code, that incorporates an improved model of x-ray coherent scattering using experimentally measured molecular interference functions. The results obtained for breast imaging phantoms using adipose and glandular tissue cross sections show that the new algorithm can separate imaging data into basic adipose and water components at radiation doses comparable with Breast Computed Tomography. Simulation results also show the potential for imaging microcalcifications. Overall, the component images obtained with ML-ESCA algorithm have a less noisy appearance than the images obtained with the conventional filtered back projection algorithm for each individual scattering angle. An optimization study for x-ray energy range selection for breast CSCT is also presented.

Design and implementation of coded aperture coherent scatter spectral imaging of cancerous and healthy breast tissue samples

A scatter imaging technique for the differentiation of cancerous and healthy breast tissue in a heterogeneous sample is introduced in this work. Such a technique has potential utility in intraoperative margin assessment during lumpectomy procedures. In this work, we investigate the feasibility of the imaging method for tumor classification using Monte Carlo simulations and physical experiments. The coded aperture coherent scatter spectral imaging technique was used to reconstruct three-dimensional (3-D) images of breast tissue samples acquired through a single-position snapshot acquisition, without rotation as is required in coherent scatter computed tomography. We perform a quantitative assessment of the accuracy of the cancerous voxel classification using Monte Carlo simulations of the imaging system; describe our experimental implementation of coded aperture scatter imaging; show the reconstructed images of the breast tissue samples; and present segmentations of the 3-D images in order to identify the cancerous and healthy tissue in the samples. From the Monte Carlo simulations, we find that coded aperture scatter imaging is able to reconstruct images of the samples and identify the distribution of cancerous and healthy tissues (i.e., fibroglandular, adipose, or a mix of the two) inside them with a cancerous voxel identification sensitivity, specificity, and accuracy of 92.4%, 91.9%, and 92.0%, respectively. From the experimental results, we find that the technique is able to identify cancerous and healthy tissue samples and reconstruct differential coherent scatter cross sections that are highly correlated with those measured by other groups using x-ray diffraction. Coded aperture scatter imaging has the potential to provide scatter images that automatically differentiate cancerous and healthy tissue inside samples within a time on the order of a minute per slice.

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.

Non Invasive XRF Analysis of Human Hair for Health State Determination of Breast Tissue

Background:

Using hair samples to analyze the trace element concentrations is of interest among many researchers. X-ray fluorescence (XRF) and X-ray diffraction (XRD) are the most common methods in studying the structure and concentration of elements of tissues and also crystalline materials, using low energy X-ray.

Objectives:

In the present study, the detection ability of Wave Length X-ray Fluorescence (WLXRF) of breast cancer at early stages was evaluated and the results were compared with other routine modalities such as mammography.

Materials and Methods:

Hair samples of 54 women (including 27 healthy and 27 patients) with average age of 52.03 ± 11.44 years were analyzed. All the sample donors were Iranian women. For the measurements Wave Length X-ray Fluorescence (WLXRF) method was used.

Results:

Trace elements in healthy individuals were higher than those in cancer patients. In addition, sensitivity of the used method (WLXRF) was 96% compared to mammography (77%) as a gold standard for breast cancer detection.

Conclusions:

Trace elements in healthy individuals were higher than cancer patients and it seems that WLXRF may be used as a safe, low cost and reliable method with sensitivity higher than those of the other two relevant methods, XRD and mammography.

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.

The identification and differentiation of secondary colorectal cancer in human liver tissue using X-ray fluorescence, coherent scatter spectroscopy, and multivariate analysis

Secondary colorectal liver cancer is the most widespread malignancy in patients with colorectal cancer. The aim of this study is to identify and differentiate between normal liver tissue and malignant secondary colorectal liver cancer tissue using X-ray scattering and X-ray fluorescence spectroscopy to investigate the best combination of data that can be used to enable classification of these two tissue types. X-ray fluorescence (XRF) and coherent scatter data were collected for 24 normal and 24 tumor matched pair tissue samples. The levels of 12 elements (P, S, K, Ca, Cr, Fe, Cu, Zn, As, Se, Br, and Rb) were measured in all samples. When comparisons were made between normal and tumor tissues, statistically significant differences were determined for K (p = 0.046), Ca (p = 0.040), Cr (p = 0.011), Fe, Cu, Zn, Br, and Rb (p < 0.01). However, for P, S, As, and Se, no statistically significant differences were found (p > 0.05). For the coherent scatter spectra collected, three peaks due to adipose, fibrous content, and water content of tissue were observed. The amplitude, full width half-maximum, and area under both fibrous content and water content peaks were found to be significantly higher in secondary colorectal liver tumors compared with surrounding normal liver tissue (p < 0.05). However, no significant differences were found for the adipose peak parameters (p > 0.05). Soft independent modeling of class analogy was performed using the XRF, coherent scatter, and elemental ratio data separately, and the accuracy of the classification of 20 unknown samples was found to be 50, 30, and 80%, respectively. Further analysis has shown that using a combination of the XRF and coherent scatter data in a single combined model gave improved normal and tumor liver tissue classification, with an accuracy that was found to be 85%.

X-ray phase-contrast imaging: from pre-clinical applications towards clinics

Phase-contrast x-ray imaging (PCI) is an innovative method that is sensitive to the refraction of the x-rays in matter. PCI is particularly adapted to visualize weakly absorbing details like those often encountered in biology and medicine. In past years, PCI has become one of the most used imaging methods in laboratory and preclinical studies: its unique characteristics allow high contrast 3D visualization of thick and complex samples even at high spatial resolution. Applications have covered a wide range of pathologies and organs, and are more and more often performed in vivo. Several techniques are now available to exploit and visualize the phase-contrast: propagation- and analyzer-based, crystal and grating interferometry and non-interferometric methods like the coded aperture. In this review, covering the last five years, we will give an overview of the main theoretical and experimental developments and of the important steps performed towards the clinical implementation of PCI.

Class modeling analysis of heparin 1H NMR spectral data using the soft independent modeling of class analogy and unequal class modeling techniques

To differentiate heparin samples with varying amounts of dermatan sulfate (DS) impurities and oversulfated chondroitin sulfate (OSCS) contaminants, proton NMR spectral data for heparin sodium active pharmaceutical ingredient samples from different manufacturers were analyzed using multivariate chemometric techniques. A total of 168 samples were divided into three groups: (a) Heparin, [DS] ≤ 1.0% and [OSCS] = 0%; (b) DS, [DS] > 1.0% and [OSCS] = 0%; (c) OSCS, [OSCS] > 0% with any content of DS. The chemometric models were constructed and validated using two well-established methods: soft independent modeling of class analogy (SIMCA) and unequal class modeling (UNEQ). While SIMCA modeling was conducted using the entire set of variables extracted from the NMR spectral data, UNEQ modeling was combined with variable reduction using stepwise linear discriminant analysis to comply with the requirement that the number of samples per class exceed the number of variables in the model by at least 3-fold. Comparison of the results from these two modeling approaches revealed that UNEQ had greater sensitivity (fewer false positives) while SIMCA had greater specificity (fewer false negatives). For Heparin, DS, and OSCS, respectively, the sensitivity was 78% (56/72), 74% (37/50), and 85% (39/46) from SIMCA modeling and 88% (63/72), 90% (45/50), and 91% (42/46) from UNEQ modeling. Importantly, the specificity of both the SIMCA and UNEQ models was 100% (46/46) for Heparin with respect to OSCS; no OSCS-containing sample was misclassified as Heparin. The specificity of the SIMCA model (45/50, or 90%) was superior to that of the UNEQ model (27/50, or 54%) for Heparin with respect to DS samples. However, the overall prediction ability of the UNEQ model (85%) was notably better than that of the SIMCA model (76%) for the Heparin vs DS vs OSCS classes. The models were challenged with blends of heparin spiked with nonsulfated, partially sulfated, or fully oversulfated chondroitin sulfate A, dermatan sulfate, or heparan sulfate at the 1.0, 5.0, and 10.0 wt % levels. The results from the present study indicate that the combination of (1)H NMR spectral data and class modeling techniques (viz., SIMCA and UNEQ) represents a promising strategy for assessing the quality of commercial heparin samples with respect to impurities and contaminants. The methodologies show utility for applications beyond heparin to other complex products.

An active pixel sensor x-ray diffraction (APXRD) system for breast cancer diagnosis

This paper describes the potential application of an active pixel sensor-based x-ray diffraction (APXRD) system in the field of breast cancer diagnosis. The design and initial testing of the system was reported previously (Bohndiek et al 2008b Phys. Med. Biol. 53 655-72). The system has potential both as a 'diffraction enhanced breast imager' (DEBI) and as a probe for quantitative analysis of breast biopsy samples. The resolution of the system in a DEBI arrangement is 1 mm and the contrast available using a material-specific x-ray diffraction image was found to be up to seven times greater than that of a transmission image. Scatter signatures from a series of biopsy-equivalent samples, ranging in composition from 100% fat to 100% fibrous tissue, were acquired with the APXRD system. Multivariate data analysis was used to produce a partial least squares (PLS) model sensitive to sample fat content. The final model is able to accurately predict the fat content of a series of unknown samples and is robust to significant added noise. This suggests that the APXRD system could provide a simple, semi-automated, quantitative measurement system for analysis of breast biopsy samples. Training on a range of scatter signatures from real breast biopsy samples covering various stages of disease is now needed to test this hypothesis.

Automated tremor amplitude and frequency determination from power spectra

Analysis of tremor amplitude and frequency is often done in frequency domain from tremor power spectra. Several methods for tremor amplitude estimation from power spectra were described but have not been systematically compared and evaluated. In addition, current methods for tremor amplitude estimation from power spectra do not correct tremor amplitude when power spectra of adjacent peaks overlap and this could contribute to an overestimation of tremor amplitude. We developed a computer application for automated analysis of tremor power spectra that corrects tremor amplitude, when power spectra of adjacent peaks overlap, with a Gauss curve fitting method. The accuracy of previously described methods and new methods for tremor amplitude estimation from power spectra was evaluated by 78 simulated power spectra and 900 tremor power spectra records of 25 patients with Parkinson's disease. Thus the influence of peak amplitude, number of peaks and degree of peak overlapping on tremor amplitude estimation could be systematically evaluated and compared. We conclude that the Gauss curve fitting method (Gauss 1) enables a more accurate estimation of tremor amplitude than previously described methods.