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Freek J Beekman

Publications and source records attributed to Freek J Beekman.

At least 19 recordsLinked to original sources

Statistical reconstruction for x-ray CT systems with non-continuous detectors.

We analyse the performance of statistical reconstruction (SR) methods when applied to non-continuous x-ray detectors. Robustness to projection gaps is required in x-ray CT systems with multiple detector modules or with defective detector pixels. In such situations, the advantage of statistical reconstruction is that it is able to ignore missing or faulty pixels and that it makes optimal use of the remaining line integrals. This potentially obviates the need to fill the sinogram discontinuities by interpolation or any other approximative pre-processing techniques. In this paper, we apply SR to cone beam projections of (i) a hypothetical modular detector micro-CT scanner and of (ii) a system with randomly located defective detector elements. For the modular-detector system, SR produces reconstruction volumes free of noticeable gap-induced artefacts as long as the location of detector gaps and selection of the scanning range provide complete object sampling in the central imaging plane. When applied to randomly located faulty detector elements, SR produces images free of substantial ring artefacts even for cases where defective pixels cover as much as 3% of the detector area.

Algorithms↗

Hybrid scatter correction applied to quantitative holmium-166 SPECT.

Ho-166 is a combined beta-gamma emitter of which the betas can be used therapeutically. From the 81 keV gammas of Ho-166, SPECT images can be obtained, which give opportunities to guide Ho-166 therapy. Accurate reconstruction of Ho-166 images is currently hampered by photopeak-scatter in the patient, down-scatter in the detector, collimator and patient caused by the 1.4 MeV photons and by bremsstrahlung. We developed and validated a method for quantitative SPECT of Ho-166 that involves correction for both types of scatter plus non-uniform attenuation correction using attenuation maps. Photopeak-scatter (S) is compensated for by a rapid 3D Monte Carlo (MC) method that is incorporated in ordered subset (OS) reconstruction of the emission data, together with simultaneous correction for attenuation (A) and detector response (D); this method is referred to as OS-ADS. Additionally, for correction of down-scatter, we use a 14 keV wide energy window centred at 118 keV (OS-ADSS). Due to a limited number of available energy windows, the same 118 keV energy window was used for down-scatter correction of the simultaneously acquired Gd-153 transmission data. Validations were performed using physical phantom experiments carried out on a dual-head SPECT system; Gd-153 transmission line sources were used for acquiring attenuation maps. For quantitative comparison of OS-ADS and OS-ADSS, bottles filled with Ho-166 were placed in both a cylindrical phantom and an anthropomorphic thorax phantom. Both OS-ADS and OS-ADSS were compared with an ordered subset reconstruction without any scatter correction (OS-AD). Underestimations of about 20% in the attenuation map were reduced to a few per cent after down-scatter correction. The average deviation from the true activity contained in the bottles was +72% with OS-AD. Using OS-ADS, this average overestimation was reduced to +28% and with OS-ADSS the deviation was further reduced to 16%. With OS-AD and OS-ADS, these numbers were more sensitive to the choice of volumes of interest than with OS-ADSS. For the reconstructed activity distributions, erroneous background activity found with OS-AD was reduced by a factor of approximately 2 by applying OS-ADS and reduced by a factor of approximately 4 by applying OS-ADSS. The combined attenuation, photopeak-scatter and down-scatter correction framework proposed here greatly enhanced the quantitative accuracy of Ho-166 imaging, which is of the uppermost importance for image-guided therapies. It is expected that the method, with adapted window settings, also can be applied to other isotopes with high energy peaks that contaminate the photopeak data, such as I-131 or In-111.

Holmium↗

Comparison of methods for suppressing edge and aliasing artefacts in iterative x-ray CT reconstruction.

X-ray CT images obtained with iterative reconstruction (IR) can be hampered by the so-called edge and aliasing artefacts, which appear as interference patterns and severe overshoots in the areas of sharp intensity transitions. Previously, we have demonstrated that these artefacts are caused by discretization errors during the projection simulation step in IR. Although these errors are inherent to IR, they can be adequately suppressed by reconstruction on an image grid that is finer than that typically used for analytical methods such as filtered back-projection. Two other methods that may prevent edge artefacts are: (i) smoothing the projections prior to reconstruction or (ii) using an image representation different from voxels; spherically symmetric Kaiser-Bessel functions are a frequently employed example of such a representation. In this paper, we compare reconstruction on a fine grid with the two above-mentioned alternative strategies for edge artefact reduction. We show that the use of a fine grid results in a more adequate suppression of artefacts than the smoothing of projections or using the Kaiser-Bessel image representation.

Artifacts↗

Efficient Monte Carlo based scatter artifact reduction in cone-beam micro-CT.

Cupping and streak artifacts caused by the detection of scattered photons may severely degrade the quantitative accuracy of cone-beam X-ray computed tomography (CT) images. In order to overcome this problem, we propose and validate the following iterative scatter artifact reduction scheme. First, an initial image is reconstructed from the scatter-contaminated projections. Next, the scatter component of the projections is estimated from the initial reconstruction by a Monte Carlo (MC) simulation. The estimate obtained is then utilized during the reconstruction of a scatter-corrected image. The last two steps are repeated until an adequate correction is obtained. The estimation of the noise-free scatter projections in this scheme is accelerated in the following way: first, a rapid (i.e., based on a low number of simulated photon tracks) MC simulation is executed. The noisy result of this simulation is de-noised by a three-dimensional fitting of Gaussian basis functions. We demonstrate that, compared to plain MC, this method shortens the required simulation time by three to four orders of magnitude. Using simulated projections of a small animal phantom, we show that one cycle of the scatter correction scheme is sufficient to produce reconstructed images that barely differ from the reconstructions of scatter-free projections. The reconstructions of data acquired with a charge-coupled device based micro-CT scanner demonstrate a nearly complete removal of the scatter-induced cupping artifact. Quantitative errors in a water phantom are reduced from around 12% for reconstructions without the scatter correction to 1% after the proposed scatter correction has been applied. In conclusion, a general, accurate, and efficient scatter correction algorithm is developed that requires no mechanical modifications of the scanning equipment and results in only a moderate increase in the total reconstruction time.

Algorithms↗

Evaluation of 3D Monte Carlo-based scatter correction for 99mTc cardiac perfusion SPECT.

UNLABELLED: Cardiac SPECT images are degraded by photons scattered in the thorax. Accurate correction for scatter is complicated by the nonuniform density and varied sizes of thoraxes and by the additional attenuation and scatter caused by female patients' breasts. Monte Carlo simulation is a general and accurate method for detailed modeling of scatter. Hence, for 99mTc we compared statistical reconstruction based on Monte Carlo modeling of scatter with statistical reconstruction that incorporates the more commonly used triple-energy-window scatter correction. Both of these scatter correction methods were used in conjunction with attenuation correction and resolution recovery. METHODS: Simultaneous attenuation, detector response, and Monte Carlo-based scatter correction were implemented via the dual-matrix ordered-subset expectation maximization algorithm with a Monte Carlo simulator as part of the forward projector (ADS-MC). ADS-MC was compared to (i) ordered-subset expectation maximization with attenuation correction and with detector response modeling (AD); (ii) like (i) but with scatter correction added using the triple-energy-window method (ADS-TEW). A dual-detector SPECT system equipped with 2 153Gd scanning line sources was used for acquiring 99mTc emission data and attenuation maps. Four clinically realistic phantom configurations (a large thorax and a small thorax, each with and without breasts) with a cardiac insert containing 2 cold defects were used to evaluate the proposed reconstruction algorithms. In these phantom configurations, we compared the performance of the algorithms in terms of noise properties, contrast-to-noise ratios, contrast separability of cold defects, and robustness to anatomic variation. RESULTS: Noise was found to be approximately 14% lower in the ADS-MC images than in the ADS-TEW and AD images. Typically, the contrast obtained with the ADS-MC algorithm was 10%-20% higher than that obtained with the other 2 methods. Furthermore, compared with the other 2 algorithms, the ADS-MC method was less sensitive to anatomic variations. CONCLUSION: Our results indicate that the imaging performance of 99mTc SPECT can be improved more by Monte Carlo-based scatter correction than by window-based scatter correction.

Computer Simulation↗

Photon-counting versus an integrating CCD-based gamma camera: important consequences for spatial resolution.

Charge-coupled devices (CCDs) coupled to scintillation crystals can be used for high resolution imaging with x-rays and gamma-rays. When the CCD images can be read out fast enough, the energy and interaction position of individual gamma quanta can be estimated by real-time image analysis of scintillation light flashes ('photon counting mode'). We tested a set-up in which an electron-multiplying CCD was coupled to a 1 mm thick columnar CsI crystal by means of a fibre-optic taper. We found that, compared to light integration, photon counting improves the intrinsic spatial resolution by a factor of about 3 to 6. Applying our set-up to Tc-99m and I-125 imaging, we were able to obtain intrinsic resolutions below 60 microm (full width at half maximum). Counting losses due to overlapping of light flashes are negligible for event rates typical for biomedical radio-nuclide imaging and do strongly depend on energy window settings. Energy resolution was estimated to be approximately 35 keV FWHM for a 1:1 taper. We conclude that CCD-based gamma cameras have great potential for applications such as in vivo imaging of gamma emitters.

Crystallography↗

U-SPECT-I: a novel system for submillimeter-resolution tomography with radiolabeled molecules in mice.

UNLABELLED: A major advance in biomedical science and diagnosis was accomplished with the development of in vivo techniques to image radiolabeled molecules, but limited spatial resolution has slowed down applications to small experimental animals. Here, we present a SPECT system (U-SPECT-I) dedicated to radionuclide imaging of murine organs at a submillimeter resolution. METHODS: The high performance of U-SPECT-I is based on a static triangular detector setup, with a cylindric imaging cavity in the center and 75 gold micropinhole apertures in the cavity wall. The pinholes are focused on a small volume of interest such as the mouse heart or spine to maximize the detection yield of gamma-photons. Three-dimensional molecular distributions are iteratively estimated using the detector data and a statistical reconstruction algorithm that takes into account system blurring and data noise to increase resolution and reduce image noise. RESULTS: With 0.6-mm-diameter pinholes, the maximum fraction of detected photons emitted by a point source (peak sensitivity) is 0.22% for a 15%-wide energy window and remains higher than 0.12% in the central 12 mm of the central plane. In a resolution phantom, radioactively filled capillaries as small as 0.5 mm and separated by 0.5 mm can be distinguished clearly in reconstructions. Projection data needed for the reconstruction of cross sections of molecular distributions in mouse organs can readily be obtained without the need for any mechanical movements. Images of a mouse spine show 99mTc-hydroxymethylene diphosphonate uptake down to the level of tiny parts of vertebral processes. These are separated clearly from the vertebral and intervertebral foramina. Using another tracer, one can monitor myocardial perfusion in the left and right ventricular walls, even in structures as small as the papillary muscles. CONCLUSION: U-SPECT-I allows discrimination between molecular concentrations in adjacent volumes of as small as about 0.1 muL, which is significantly smaller than can be imaged by any existing SPECT or PET system. Our initial in vivo images of the mouse heart and spine show that U-SPECT-I can be used for novel applications in the study of dynamic biologic systems with a clear projection to clinical applications. The combination of high resolution and detection efficiency of U-SPECT-I opens up new possibilities for the suborgan-level study of radiotracers in mouse models.

Animals↗

Design and simulation of a high-resolution stationary SPECT system for small animals.

Exciting new SPECT systems can be created by combining pinhole imaging with compact high-resolution gamma cameras. These new systems are able to solve the problem of the limited sensitivity-resolution trade-off that hampers contemporary small animal SPECT. The design presented here (U-SPECT-III) uses a set of detectors placed in a polygonal configuration and a cylindrical collimator that contains 135 pinholes arranged in nine rings. Each ring contains 15 gold pinhole apertures that focus on the centre of the cylinder. A non-overlapping projection is acquired via each pinhole. Consequently, when a mouse brain is placed in the central field-of-view, each voxel in the cerebrum can be observed via 130 to 135 different pinholes simultaneously. A method for high-resolution scintillation detection is described that eliminates the depth-of-interaction problem encountered with pinhole cameras, and is expected to provide intrinsic detector resolutions better than 150 microm. By means of simulations U-SPECT-III is compared to a simulated dual pinhole SPECT (DP-SPECT) system with a pixelated array consisting of 2.0 x 2.0 mm NaI crystals. Analytic calculations indicate that the proposed U-SPECT-III system yields an almost four times higher linear and about sixty times higher volumetric system resolution than DP-SPECT, when the systems are compared at matching system sensitivity. In addition, it should be possible to achieve a 15 up to 30 times higher sensitivity with U-SPECT-III when the systems are compared at equal resolution. Simulated images of a digital mouse-brain phantom show much more detail with U-SPECT-III than with DP-SPECT. In a resolution phantom, 0.3 mm diameter cold rods are clearly visible with U-SPECT-III, whereas with DP-SPECT the smallest visible rods are about 0.6-0.8 mm. Furthermore, with U-SPECT-III, the image deformations outside the central plane of reconstruction that hamper conventional pinhole SPECT are strongly suppressed. Simulation results indicate that future pinhole SPECT systems are likely to bring about significant improvements in radio-molecular imaging of small animals.

Animals↗

Photon penetration and scatter in micro-pinhole imaging: a Monte Carlo investigation.

Pinhole SPECT is rapidly gaining popularity for imaging laboratory animals using gamma-emitting molecules. Penetration and scattering of gamma radiation in the pinhole edge material can account for a significant fraction of the total number of photons detected, particularly if the pinholes have small diameters. This study characterizes the effects of penetration and scatter with micro-pinholes made of lead, tungsten, gold and platinum. Monte Carlo simulations are performed for 1-125 (27-35 keV) and Tc-99m (140 keV) point sources with pinhole diameters ranging from 50 to 500 microm. The simulations account for the effects of photo-electric interaction, Rayleigh scattering, Compton scattering, ionization, bremsstrahlung and electron multiple scattering. As a typical example, in the case of a Tc-99m point source and pinholes with a diameter of 300 microm in gold or platinum, approximately 55% of the photons detected resulted from penetration and approximately 3% from scatter. For pinhole diameters ranging from 100 to 500 microm, the penetration fraction for tungsten and lead was approx a factor of 1.0 to 1.6 higher and the scatter fraction was 1.0 to 1.8 times higher than in case of gold or platinum. Using I-125 instead of Tc-99m decreases the penetration fraction by a factor ranging from 3 to 11 and the scatter fraction by a factor ranging from 12 to 40. For all materials studied, the total amounts of penetrated and scattered photons changed approximately linearly with respect to the pinhole diameter.

Electrons↗

Monte Carlo-based down-scatter correction of SPECT attenuation maps.

Combined acquisition of transmission and emission data in single-photon emission computed tomography (SPECT) can be used for correction of non-uniform photon attenuation. However, down-scatter from a higher energy isotope (e.g. 99mTc) contaminates lower energy transmission data (e.g. 153Gd, 100 keV), resulting in underestimation of reconstructed attenuation coefficients. Window-based corrections are often not very accurate and increase noise in attenuation maps. We have developed a new correction scheme. It uses accurate scatter modelling to avoid noise amplification and does not require additional energy windows. The correction works as follows: Initially, an approximate attenuation map is reconstructed using down-scatter contaminated transmission data (step 1). An emission map is reconstructed based on the contaminated attenuation map (step 2). Based on this approximate 99mTc reconstruction and attenuation map, down-scatter in the 153Gd window is simulated using accelerated Monte Carlo simulation (step 3). This down-scatter estimate is used during reconstruction of a corrected attenuation map (step 4). Based on the corrected attenuation map, an improved 99mTc image is reconstructed (step 5). Steps 3-5 are repeated to incrementally improve the down-scatter estimate. The Monte Carlo simulator provides accurate down-scatter estimation with significantly less noise than down-scatter estimates acquired in an additional window. Errors in the reconstructed attenuation coefficients are reduced from ca. 40% to less than 5%. Furthermore, artefacts in 99mTc emission reconstructions are almost completely removed. These results are better than for window-based correction, both in simulation experiments and in physical phantom experiments. Monte Carlo down-scatter simulation in concert with statistical reconstruction provides accurate down-scatter correction of attenuation maps.

Algorithms↗

Characterization and suppression of edge and aliasing artefacts in iterative x-ray CT reconstruction.

For the purpose of obtaining x-ray tomographic images, statistical reconstruction (SR) provides a general framework with possible advantages over analytical algorithms such as filtered backprojection (FBP) in terms of flexibility, resolution, contrast and image noise. However, SR images may be seriously affected by some artefacts that are not present in FBP images. These artefacts appear as aliasing patterns and as severe overshoots in the areas of sharp intensity transitions ('edge artefacts'). We characterize this inherent property of iterative reconstructions and hypothesize how discretization errors during reconstruction contribute to the formation of the artefacts. An adequate solution to the problem is to perform the reconstructions on an image grid that is finer than that typically employed for FBP reconstruction, followed by a downsampling of the resulting image to a granularity normally used for display. Furthermore, it is shown that such a procedure is much more effective than post-filtering of the reconstructions. Resulting SR images have superior noise-resolution trade-off compared to FBP, which may facilitate dose reduction during CT examinations.

Algorithms↗

Suppression of intensity transition artifacts in statistical x-ray computer tomography reconstruction through radon inversion initialization.

Statistical reconstruction (SR) methods provide a general and flexible framework for obtaining tomographic images from projections. For several applications SR has been shown to outperform analytical algorithms in terms of resolution-noise trade-off achieved in the reconstructions. A disadvantage of SR is the long computational time required to obtain the reconstructions, in particular when large data sets characteristic for x-ray computer tomography (CT) are involved. As was shown recently, by combining statistical methods with block iterative acceleration schemes [e.g., like in the ordered subsets convex (OSC) algorithm], the reconstruction time for x-ray CT applications can be reduced by about two orders of magnitude. There are, however, some factors lengthening the reconstruction process that hamper both accelerated and standard statistical algorithms to similar degree. In this simulation study based on monoenergetic and scatter-free projection data, we demonstrate that one of these factors is the extremely high number of iterations needed to remove artifacts that can appear around high-contrast structures. We also show (using the OSC method) that these artifacts can be adequately suppressed if statistical reconstruction is initialized with images generated by means of Radon inversion algorithms like filtered back projection (FBP). This allows the reconstruction time to be shortened by even as much as one order of magnitude. Although the initialization of the statistical algorithm with FBP image introduces some additional noise into the first iteration of OSC reconstruction, the resolution-noise trade-off and the contrast-to-noise ratio of final images are not markedly compromised.

Algorithms↗

Comparison of methods for thyroid volume estimation in patients with Graves' disease.

Individualised dosage models are frequently applied for radioiodine therapy in patients with Graves' hyperthyroidism, especially in Europe. In these dosage schemes the thyroid volume is an important parameter. Thyroid volume determinations are usually made with ultrasonography or with thyroid scintigraphy, although the accuracy of planar scintigraphy for this purpose is not well established. The aim of this study was to compare the accuracy of three modalities for the determination of the thyroid volume in patients with Graves' disease: planar scintigraphy (PS), single-photon emission tomography (SPET) and ultrasonography (US). These three modalities were compared with magnetic resonance imaging (MRI) as the gold standard. Thyroid volume estimations were performed in 25 patients with Graves' disease. The PS images were subjected to filtering and thresholding, and a standard surface formula was used to calculate the thyroid volume. With SPET the iteratively reconstructed thyroid images were filtered, and after applying a threshold method an automatic segmentation algorithm was used for the volume determinations. Thyroid volumes were estimated from the US images using the ellipsoid volume model for multiple two-dimensional measurements. For MRI, thyroid segmentation was performed manually in gadolinium-enhanced T1-weighted images and a summation-of-areas technique was used for the volume measurements. The thyroid volumes calculated with MRI were 25.0+/-13.8 ml (mean+/-SD, range 7.0-56.3 ml). PS correlated poorly with MRI ( R(2)=0.61) and suffered from a considerable bias (-4.0+/-17.6 ml). The differences between PS and MRI volume estimations had a very large spread (33+/-58%). For SPET both the correlation with MRI ( R(2)=0.84) and the bias (1.8+/-11.9 ml) were better than for PS. US had by far the best correlation with MRI ( R(2)=0.97) and the best precision, but the bias (6.8+/-7.5 ml) was not negligible. In conclusion, SPET is preferred over PS for accurate measurements of thyroid volume. US is the most accurate of the three modalities, if a correction is made for bias.

Adult↗

Monte Carlo simulations of pinhole imaging accelerated by kernel-based forced detection.

Pinhole collimation can provide both higher sensitivity and resolution than parallel hole collimation when used to image small objects. When objects are placed close to the pinhole, small pinhole diameters combined with high-magnification pinhole geometries yield ultra high resolution images. With Monte Carlo (MC) calculations it is possible to simulate accurately a wide range of features of pinhole imaging. The aim of the present work is to accelerate MC simulations of pinhole SPECT projections. To achieve speed-up, forced detection (FD), a commonly used acceleration technique, is replaced by a kernel-based forced detection (KFD) step. In KFD, instead of tracing individual photons from the source or last scatter position to the detector, a position dependent kernel (point spread function (PSF)) is projected on the detector. The PSFs for channel and knife edge pinhole apertures model the penetration effects through the aperture material. For simulations, the PSFs are pre-calculated and stored in tables. The speed-up and accuracy achieved by using KFD were validated by means of digital phantoms. MC simulations with FD and with KFD converge to almost identical images. However, KFD converges to an equal image noise level one to four orders of magnitude faster than FD, depending on the number of photons simulated. A simulator accelerated by KFD could serve as a practical tool to improve iterative image reconstruction.

Monte Carlo Method↗

Towards in vivo nuclear microscopy: iodine-125 imaging in mice using micro-pinholes.

Position-sensitive gamma-radiation detectors equipped with collimators have been used for in vivo imaging of the distribution of radiolabelled molecules in laboratory animals and humans for several decades. To date, the best image resolution achieved in a rodent is on the order of 1 mm. Here we demonstrate how a basic and compact gamma camera can be constructed for in vivo radionuclide imaging in small animals, at much higher spatial resolution. Resolution improvements were obtained by combining dense, shaped, micro-pinhole apertures with iodine-125, an isotope with low energy emissions, ease of incorporation into a wide range of molecules, and straightforward translation into the clinic via other isotopes of iodine that are suitable for nuclear medicine imaging. (125)I images of test distributions and a mouse thyroid have been obtained at a resolution of as high as 200 microm using this simple bench-top camera. Possible future applications and extension to ultra-high-resolution emission tomography are discussed.

Animals↗

Introduction to the physics of molecular imaging with radioactive tracers in small animals.

Recent advances have greatly enhanced the three-dimensional (3D) imaging of radioactive tracers in living animals. this article introduces the physics of imaging behind the imaging methods. The article first discusses the selection of the radiation emitted from the tracer and then the process of tomographic reconstruction or how 3D images are made from imaging around the outside of the animal. The technique of single photon emission computed tomography (SPECT) in which the detection of one X-ray or gamma ray at a time is employed for image formation is then described. Finally, positron emission tomography (PET) which relies on the simultaneous detection of the pair of gamma-rays formed when the positron annihilates is presented.

Animals↗

Efficient fully 3-D iterative SPECT reconstruction with Monte Carlo-based scatter compensation.

Quantitative accuracy of single photon emission computed tomography (SPECT) images is highly dependent on the photon scatter model used for image reconstruction. Monte Carlo simulation (MCS) is the most general method for detailed modeling of scatter, but to date, fully three-dimensional (3-D) MCS-based statistical SPECT reconstruction approaches have not been realized, due to prohibitively long computation times and excessive computer memory requirements. MCS-based reconstruction has previously been restricted to two-dimensional approaches that are vastly inferior to fully 3-D reconstruction. Instead of MCS, scatter calculations based on simplified but less accurate models are sometimes incorporated in fully 3-D SPECT reconstruction algorithms. We developed a computationally efficient fully 3-D MCS-based reconstruction architecture by combining the following methods: 1) a dual matrix ordered subset (DM-OS) reconstruction algorithm to accelerate the reconstruction and avoid massive transition matrix precalculation and storage; 2) a stochastic photon transport calculation in MCS is combined with an analytic detector modeling step to reduce noise in the Monte Carlo (MC)-based reprojection after only a small number of photon histories have been tracked; and 3) the number of photon histories simulated is reduced by an order of magnitude in early iterations, or photon histories calculated in an early iteration are reused. For a 64 x 64 x 64 image array, the reconstruction time required for ten DM-OS iterations is approximately 30 min on a dual processor (AMD 1.4 GHz) PC, in which case the stochastic nature of MCS modeling is found to have a negligible effect on noise in reconstructions. Since MCS can calculate photon transport for any clinically used photon energy and patient attenuation distribution, the proposed methodology is expected to be useful for obtaining highly accurate quantitative SPECT images within clinically acceptable computation times.

Algorithms↗

Effect of phantom voxelization in CT simulations.

In computer simulations of x-ray CT systems one can either use continuous geometrical descriptions for phantoms or a voxelized representation. The voxelized approach allows arbitrary phantoms to be defined without being confined to geometrical shapes. The disadvantage of the voxelized approach is that inherent errors are introduced due to the phantom voxelization. To study effects of phantom discretization, analytical CT simulations were run for a fan-beam geometry with phantom voxel sizes ranging from 0.0625 to 2 times the reconstructed pixel size and noise levels corresponding to 10(3) - 10(7) photons per detector pixel prior to attenuation. The number of rays traced per detector element was varied from 1 to 16. Differences in the filtered backprojection images caused by changing the phantom matrix sizes and number of rays traced were assessed by calculating the difference between reconstructions based on the finest matrix and coarser matrix simulations. In noise free simulations, all phantom matrix sizes produced a measurable difference in comparison with the finest phantom matrix used. When even a small amount of noise was added to the projection data, the differences due to the phantom discretization were masked by the noise, and in all cases there was almost no improvement by using a phantom matrix that was more than twice as fine as the reconstruction matrix. No substantial improvement was achieved by tracing more than 4 rays per detector pixel.

Algorithms↗