The effects of fat content on single- and dual-energy CT measurements of bone mineral were quantified using a set of tissue-mimicking phantoms which more accurately represents the in-vivo situation than previous phantoms. The key to performing these measurements in CT is to have a mixture of tissue types within each image voxel, a condition which is not satisfied with standard phantoms. The phantoms used in these studies were solid materials which mimicked 17 different homogeneous mixtures of bone, muscle, and fat. The concept of creating phantoms to mimic different mixtures of these tissues is new. The materials are epoxy-resin based and have different mixtures of phenolic microspheres, polyethylene, and calcium carbonate suspended in them. Single- and dual-energy CT were used to image the phantom materials, and the effects of fat content on bone-mineral measurements were determined. The single-energy CT measurements show how fat content causes an underestimation of the amount of bone mineral present in a specimen, with the underestimation increasing as a function of fat content. With 25% and 50% fat by volume, the single-energy measurements underestimated bone volume percentage by 2.7% and 3.6% respectively. With dual-energy CT, fat content has no effect on the measurement of bone mineral. These results are not surprising. In fact, the effects of fat content on single- and dual-energy CT measurements have been studied many times previously. However, a system of accurately measuring these effects using a set of phantom measurements with physiologically accurate tissue-mimicking materials has not been developed previously. Using these phantoms, dual-energy CT measurements can be accurately calibrated for measurements of bone mineral while the errors possible while measuring bone mineral with single-energy CT can be quantified for any given imaging parameters.
Conventional means of diagnosiing and assessing the progression of osteoporosis, including radiographic absorptiometry and quantitative CT, are directly or indirectly dependent upon bone density. This is, how ever, not always a reliable indicator of fracture risk. Changes in the trabecular structure and bone mineral content (BMC) are thought to provide a better indication of the change of spontaneous fractures occurring. Coherent-scatter CT (CSCT) is a technique which produces images based on the low angle (0 - 10 degrees) x-ray diffraction properties of tissue. Diffraction patterns from an object are acquired using first-generation CT geometry with a diagnostic x-ray image intensifier based system. These patterns are used to reconstruct a series of maps of the angle dependent coherent scatter cross section in a tomographic slice which are dependent upon the molecular structure of the scatterer. Hydroxyapatite has a very different cross section to that of soft tissue, and the CSCT method may, therefore, form the basis for a more direct measure of BMC. Our original CSCT images suffered from a 'cupping' artifact, resulting in increased intensities for pixels at the periphery of the object. This artifact, which is due to self-attenuation of scattered x rays, caused a systematic error of up to 20% in cross-sections measured from a CT image. This effect has been removed by monitoring the transmitted intensity using a photodiode mounted on the primary beam stop, and normalizing the scatter intensity to that of the transmitted beam for each projection. Images reconstructed from data normalized in this way do not exhibit observable attenuation artifacts. Elimination of this artifact enables the determination of accurate quantitative measures of BMC at each pixel in a tomograph.
Conventional computed tomography (CT) images are `maps' of the x ray linear attenuation coefficient within a slice through an object. A novel approach to CT is being developed which instead produces tomographic images based on an object's low-angle (0 - 10 degree(s)) x-ray diffraction properties. The coherent-scatter cross sections of many materials vary greatly, and this coherent-scatter CT (CSCT) system gives material-specific information on this basis. The goal of this research is to produce tomographic maps of bone-mineral content (BMC), first in laboratory specimens, and potentially in patients. The concept of reconstructing tomographic images using coherently scattered x rays was first demonstrated by Harding et al. The approach described here is a modification of their method. First generation CT geometry is used in which a diffraction pattern is acquired for each pencil-beam using a CsI image intensifier coupled to a CCD. Each pattern is sectioned into concentric annular rings so that the integrated signal in each ring gives the scatter intensity at a particular scatter angle, integrated along the path through the object. An image is reconstructed for each ring, resulting in a series of tomographic images corresponding to the scatter intensity at a series of scatter angles. A test phantom was imaged (70 kVp, 50 mAs per exposure, 100 mSv average dose) to demonstrate CSCT. The phantom consists of a water-filled Lucite cylinder containing rods of polyethylene, Lucite, polycarbonate, and nylon. The resulting series of images was used to extract the angular-dependent scatter cross section for every pixel. Using pure material cross sections as basis functions, the cross section from each pixel was fitted using non-negative least squares. The results were used to create material-specific images. These results show that CSCT is feasible with this approach and that if the materials in an object have distinguishable scatter cross sections, the method has the ability to identify the materials. It may be possible to image the BMC distribution as trabecular bone mineral is replaced by lipids.
KEYWORDS: Sensors, Convolution, Stochastic processes, Modulation transfer functions, Signal to noise ratio, Signal detection, Digital imaging, Quantum efficiency, Imaging systems, Image processing
Image blur in digital imaging systems results from both the spatial spreading of quanta representing the image in the detector system and from the integration of quanta over the finite detector element width. Linear-systems theory has often been used to describe these blurring mechanisms as a convolution, implying the existence of a corresponding modulation transfer function (MTF) in the spatial-frequency domain. This also implies that the resulting noise- power spectrum (NPS) is modified by the square of the blurring MTF. This deterministic approach correctly describes the effect of each blurring mechanism on the overall system MTF, but does not correctly describe image noise characteristics. This is because the convolution is a deterministic calculation, and neglects the statistical properties of the image quanta. Rabbani et al. developed an expression for the NPS following a stochastic spreading mechanism that correctly accounts for these statistical properties. Use of their results requires a modification in how we should interpret the convolution theorem. We suggest the use of a `stochastic' convolution operator, that uses the Rabbani equation for the NPS rather than the deterministic result. This approach unifies the description of both image blur and image noise into a single linear-systems framework. This method is then used to develop expressions for the signal, NPS, DQE, and pixel SNR for a hypothetical digital detector design that includes the effects of conversion to secondary quanta, stochastic spreading of the secondary quanta, and a finite detector-element width.
KEYWORDS: X-ray optics, X-rays, Visualization, Spatial frequencies, Quantum efficiency, Monte Carlo methods, Modulation transfer functions, Signal to noise ratio, X-ray imaging, Imaging systems
Medical x-ray imaging systems must be carefully designed to ensure that images can be produced with the highest possible signal-to-noise ratio (SNR) for a given x-ray dose to the patient. In most practical systems, images result from the conversion of primary x-rays into secondary quanta such as optical photons or electrical charge, in multiple cascaded stages. The average number of quanta at each stage (per incident x ray) is often evaluated as the product of all preceding system gain factors and displayed graphically as a "quantum-accounting diagram" (QAD). The stage with the fewest quanta forms the quantum sink, and is generally the noise-determining stage. This "zero spatial-frequency" type analysis is simplistic, however, as it ignores the spatial spreading of secondary quanta that will further degrade image noise. We have recently extended the above approach by introducing a spatial-frequency dependent QAD, in which the number of quanta at each stage is expressed by the product of all preceding system gains and squared modulation transfer functions (MTFs). The results are displayed graphically and used to determine the quantum-sink stage as a function of spatial frequency. The visual impact of the non-zero spatial frequency quantum sink is illustrated in a Monte Carlo simulation of the cascading process. A hypothetical system consisting of a scintillating phosphor optically coupled to a CCD camera is used for illustrative purposes. It is shown that an inefficient optical system results in the addition of a quantum mottle to the images due to a secondary quantum sink in the number of optical quanta. The mottle appears to be uniform in frequencies, but in combination with the effect of the screen MTF masks high-frequency detail more than low-frequency detail. This secondary quantum sink can be minimized both by: i) increasing the efficiency of the optical system; and, ii) improving the highfrequency response of the screen. Increasing the optical efficiency reduces the secondary quantum mottle, thus improving visualization particularly at high frequencies. Improving the high-frequency response makes a slight improvement on the quantum mottle, and also increases the contrast of the high-frequency patterns. The combination improves visualization at high spatial frequencies. Interpretation of the QAD is assisted by a direct comparison with the corresponding Monte Carlo images. It is concluded that the secondary quantum sink results in a visible deterioration of image quality at any specified frequency when the QAD at that frequency is less than approximately five times the primary quantum sink QAD value.
We are developing an x-ray microtomographic imaging system ((mu) CT) for imaging small objects at very high (approximately 25 micrometers ) spatial resolution. The detector for this system consists of a CCD array coupled to a phosphor screen through a fiber-optic faceplate. For the purposes of signal and noise analysis, this system is modeled as a multi-stage cascaded imaging system consisting of: (a) conversion of x-ray quanta to optical quanta in the phosphor; (b) collection and transfer of optical quanta from the phosphor to the CCD; and (c) detection of optical quanta by the CCD. We use the model of Rabbani et al. for cascaded systems to theoretically calculate the detective quantum efficiency (DQE) as a function of spatial frequency. We have developed the theoretical basis of a spatial-frequency dependent nomogram in terms of the system DQE. This approach is used to identify any sources of image degradation, and to make optimal design decisions of system parameters such as optical gains or numerical apertures. Using this approach, we show that the spreading of optical photons in the phosphor screen is the most significant factor degrading the MTF.
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