Parallel Beam Collimators Research Articles

Modulation transfer function assessment in parallel beam and fan beam collimators with square and cylindrical holes

This study investigates modulation transfer function (MTF) in parallel beam (PB) and fan beam (FB) collimators using the Monte Carlo method with full width at half maximum (FWHM), square and circular-shaped holes, and scatter and penetration (S + P) components. A regulation similar to the lead-to-air ratio was used for both collimators to estimate output data. The hole pattern was designed to compare FB by PB parameters. The radioactive source in air and in a water phantom placed in front of the collimators was simulated using MCNP5 code. The test results indicated that the square holes in PB (PBs) had better FWHM than did the cylindrical (PBc) holes. In contrast, the cylindrical holes in the FB (FBc) had better FWHM than the square holes. In general, the resolution of FBc was better than that of the PBc in air and scatter mediums. The S + P decreased for all collimators as the distance from the source to the collimator surface (z) increased. The FBc had a lower S + P than FBs, but PBc had a higher S + P than PBs. Of the FB and PB collimators with the identical hole shapes, PBs had a smaller S + P than FBs, and FBc had a smaller S + P than PBc. The MTF value for the FB was greater than for the PB and had increased spatial frequency; the FBc had higher MTF than the FBs and PB collimators. Estimating the FB using PB parameters and diverse hole shapes may be useful in collimator design to improve the resolution and efficiency of SPECT images.

Revisit of combined parallel‐beam/cone‐beam or fan‐beam/cone‐beam imaging

This aim of this paper is to revisit the parallel-beam/cone-beam or fan-beam/cone-beam imaging configuration, and to investigate whether this configuration has any advantages. Twenty years ago, it was suggested to simultaneously use a parallel-beam (or a fan-beam) collimator and a cone-beam collimator to acquire single photon emission computed tomography data. The motivation was that the parallel-beam (or the fan-beam) collimator can provide sufficient sampling, while the cone-beam collimator is able to provide higher photon counts. Even with higher total counts, this hybrid system does not give significant improvement (if any) in terms of image noise and artifacts reduction. If a conventional iterative maximum-likelihood expectation-maximization algorithm is used to reconstruct the image, the resultant reconstruction may be worse than the parallel-beam-only (or fan-beam-only) system. This paper uses the singular value decomposition (SVD) analysis to explain this phenomenon. The SVD results indicate that the parallel-beam-only and the fan-beam-only system outperform the combined systems. The optimal imaging system does not necessary to be the one that generates the projections with highest signal-to-noise ratio and best resolution.

Design and simulation of a full-ring multi-lofthole collimator for brain SPECT

Currently, clinical brain single photon emission computed tomography (SPECT) is mostly performed using rotating dual-head gamma cameras equipped with low-energy-high-resolution parallel-beam collimators (LEHR PAR). The resolution of these systems is rather poor (8–10 mm) and the rotation of the heavy gamma cameras can introduce misalignment errors. Therefore, we designed a static full-ring multi-lofthole brain SPECT insert for an existing ring of LaBr3 (5% Ce) detectors. The novelty of the design is found in the shutter mechanism that makes the system very flexible and eliminates the need for rotating parts. A stationary SPECT insert is not only more robust, it is also easier to integrate in a magnetic resonance imaging system (MRI) for simultaneous SPECT-MRI. The target spatial resolution of our design is 6 mm. In this study we used analytical calculations to optimize the collimator for an existing ring of LaBr3 (5% Ce) detectors. We fixed the target spatial resolution at 6 mm in the center of the field-of-view and maximized the volume sensitivity by changing the collimator radius, the aperture and the number of loftholes. Based on these optimal parameters we simulated phantom data and evaluated the image quality of our multi-lofthole system. We simulated a noiseless uniform and Defrise phantom to assess artifacts and sampling completeness and a noiseless hot-rod phantom to assess the reconstructed spatial resolution. We visually evaluated a simulated noisy Hoffman phantom with two lesions. Then, we evaluated the non-prewhitening matched filter signal-to-noise ratio (NPW-SNR) in two lesion detectability phantoms: one with hot lesions and one with cold lesions. Finally, a contrast-to-noise (CNR) study was performed on a phantom with both hot and cold lesions of different sizes (6–16 mm). All results were compared to a LEHR PAR system. The optimization resulted in a final collimator design with a volume sensitivity of 1.55 × 10−4 cps Bq−1, which is 2.5 times lower than the sensitivity of a dual-head system with LEHR PAR collimators. Spatial resolution, on the other hand, has clearly improved compared to LEHR PAR: with the multi-lofthole system we successfully reconstructed 4 mm hot rods. Although this improved resolution did not result in an unambiguous improvement in CNR or NPW-SNR, we believe that the flexibility of the shutter mechanism opens interesting perspectives toward time-multiplexing and integration with MRI.

A feasibility study of multiplexing parallelbeam

Single-photon emission computed tomography (SPECT) is a suitable tool for clinically localizing deep-sited tumors; SPECT with high spatial resolution has the ability to localize deep-sited tumors precisely. However, because of its poor sensitivity, in China SPECT now only plays a complementary role. To improve the sensitivity of the parallel beam collimator mainly used in China, a multiplexing parallel beam collimator is proposed, which can improve sensitivity while maintaining higher spatial resolution by using theoretical prediction and Monte Carlo simulation. The improved sensitivity-to-spatial resolution ratio has an optimal value. In addition, a set of gamma ray channels, introduced only in the transverse direction, did not have any effect in the axial direction. In the transverse direction, the projection data are the sum of the parallel beam and two oblique parallel beams. From visual assessment obtained using computer simulations with equal sensitivity, the reconstructed image at deep-sited was noticeably better than that with the high sensitivity parallelbeam.

SPECT Imaging With Resolution Recovery

Single-photon emission computed tomography (SPECT) is a method of choice for imaging spatial distributions of radioisotopes. Applications of this method are found in medicine, biomedical research and nuclear industry. This paper deals with improving spatial resolution in SPECT by applying correction for the point-spread function (PSF) in the reconstruction algorithm and optimizing the collimator. Several approaches are considered: the use of a depth-dependent PSF model for a parallel-beam collimator derived from experimental data, the extension of this model to a fan-beam collimator, a triangular approximation of the PSF for reconstruction acceleration, and a method for optimal fan-beam collimator design. An unmatched projector/backprojector ordered subsets expectation maximization (OSEM) algorithm is used for image reconstruction. Experimental results with simulated and physical phantom data of a micro-SPECT system show a significant improvement of spatial resolution with the proposed methods.

Slit-Slat Collimator Equipped Gamma Camera for Whole-Mouse SPECT-CT Imaging

A slit-slat collimator was developed for a gamma camera intended for small animal imaging (mice). The gamma camera contains a 10 cm × 10 cm pixelated NaI(Tl) crystal array of individual 1.3 mm × 1.3 mm × 6 mm crystal elements, distanced at 0.2 mm. The housing of the collimator was made of 5 mm tungsten alloy, forming a slit with a 1 mm opening and a 90 degree acceptance angle. The slats were made of lead foils with 0.2 mm in thickness to match the crystal spacing, and possess a length of 40 mm. Individual slats are separated by polyurethane material with a thickness of 1.3 mm corresponding to the size of the crystal elements. Alignment of the collimator with the camera's crystal pattern was performed by adjusting a micrometer screw while monitoring a Co-57 point source for maximum signal intensity. For SPECT, the collimator forms a cylindrical FOV enabling whole mouse imaging with a magnification of 1.9 at COR over the entire AOR (magnification = 1.0). As the gamma camera is part of a bimodal imaging system incorporating also x-ray CT capabilities the collimator had to be co-registered with the other components to yield intrinsically co-registered reconstruction results of both modalities. For this, five parameters corresponding to the geometrical displacements of the collimator as well as the mechanical co-alignment between the gamma camera and the CT subsystem were estimated by means of a dedicated measurement setup involving a number of bimodal calibration sources. To illustrate the performance of the slit-slat collimator and compare its performance to a single pinhole collimator a Derenzo phantom study has been performed. Transversal resolution along the entire long axis is comparable to a pinhole collimator of same pinhole diameter. Axial resolution of the slit-slat collimator is comparable to that of a parallel beam collimator. In addition, a mice study has been performed, as well, with data being presented.

Estimation of Fan Beam and Parallel Beam Parameters in a Wire Mesh Design

Special collimators used in imaging systems play an important part in obtaining qualified images to improve diagnosis in medicine. The primary aim of this study was to compare resolution between fan beam and parallel beam collimators using Monte Carlo simulation in the shape of cubic holes. Also, parameters such as geometric efficiency, geometric resolution, scatter, penetration, and full width at half maximum were studied to compare their special characteristics. The simulation results demonstrated that the geometry efficiency of a fan beam collimator increased as the angle of the slant hole increased, and the geometric resolution decreased as the angle of the slant hole increased, at a distinct distance from a monoenergetic source of γ-rays. In contrast, at a distinct angle, geometric resolution increased as the distance between the source and the collimator surface increased. For both collimators, scatter and penetration decreased as the distance increased. These results were in agreement with ADAC company data. Finally, fan beam collimators were found to have better resolution than parallel beam collimators with a cubic hole shape in a wire mesh design. Estimation of the fan beam by parallel beam parameters as cubic holes can be suitable in collimator design to improve resolution and efficiency.

SPECT using asymmetric pinholes with truncated projections

Tomographic systems employing truncated projections have been developed for parallel and fan beam collimation and for cone beam CT but the idea has not been extensively explored in pinhole single photon emission computed tomography (SPECT). In this paper, we explore the sampling requirements and system performance of SPECT systems with asymmetric pinhole collimators and truncated projections. We demonstrate that complete 3D sampling can be achieved by using multiple detectors with truncated asymmetric pinholes, offset axially from each other, and a spiral orbit. The use of truncated projections can be exploited in the design of pinhole SPECT systems by moving the pinholes closer to the subject, resulting in increased sensitivity and improved spatial resolution. Truncated and untruncated pinhole systems were evaluated using the contrast-to-noise ratio (CNR) calculated from the linearized local impulse response as a figure of merit. The CNR for the truncated pinhole system was up to 60% greater than that for the untruncated system at matched resolution for a source voxel near the centre of a uniform phantom and 30% greater at the edge. We conclude that an object can be reconstructed from asymmetric pinholes with truncated projections, which leads to potentially important design considerations and applications in single- and multi-pinhole SPECT.

A 3D point-kernel multiple scatter model for parallel-beam SPECT based on a gamma-ray buildup factor

A three-dimensional (3D) point-kernel multiple scatter model for point spread function (PSF) determination in parallel-beam single-photon emission computed tomography (SPECT), based on a dose gamma-ray buildup factor, is proposed. This model embraces nonuniform attenuation in a voxelized object of imaging (patient body) and multiple scattering that is treated as in the point-kernel integration gamma-ray shielding problems. First-order Compton scattering is done by means of the Klein–Nishina formula, but the multiple scattering is accounted for by making use of a dose buildup factor. An asset of the present model is the possibility of generating a complete two-dimensional (2D) PSF that can be used for 3D SPECT reconstruction by means of iterative algorithms. The proposed model is convenient in those situations where more exact techniques are not economical. For the proposed model's testing purpose calculations (for the point source in a nonuniform scattering object for parallel beam collimator geometry), the multiple-order scatter PSF generated by means of the proposed model matched well with those using Monte Carlo (MC) simulations. Discrepancies are observed only at the exponential tails mostly due to the high statistic uncertainty of MC simulations in this area, but not because of the inappropriateness of the model.

An inversion formula for the exponential radon transform in spatial domain with variable focal-length fan-beam collimation geometry.

Inverting the exponential Radon transform has a potential use for SPECT (single photon emission computed tomography) imaging in cases where a uniform attenuation can be approximated, such as in brain and abdominal imaging. Tretiak and Metz derived in the frequency domain an explicit inversion formula for the exponential Radon transform in two dimensions for parallel-beam collimator geometry. Progress has been made to extend the inversion formula for fan-beam and varying focal-length fan-beam (VFF) collimator geometries. These previous fan-beam and VFF inversion formulas require a spatially variant filtering operation, which complicates the implementation and imposes a heavy computing burden. In this paper, we present an explicit inversion formula, in which a spatially invariant filter is involved. The formula is derived and implemented in the spatial domain for VFF geometry (where parallel-beam and fan-beam geometries are two special cases). Phantom simulations mimicking SPECT studies demonstrate its accuracy in reconstructing the phantom images and efficiency in computation for the considered collimator geometries.

A study on attenuation correction using Tc-99m external TCT source in Tc-99m GSA liver SPECT

In attenuation correction of ECT images by transmission CT (TCT) with an external 99mTc gamma-ray source, simultaneous TCT/ECT data acquisition is difficult, when the same radionuclide such as 99mTc-tetrofosmin or 99mTc-GSA is used as the tracer. In this case, TCT is usually acquired before administration of the tracer, and ECT is acquired separately after the tracer injection. However, misregistration may occur between the TCT and ECT images, and the repetition of examinations add to the mental and physical stress of the patients. In this study, to eliminate this problem, we evaluated whether attenuation correction of ECT images can be achieved by acquiring TCT and ECT simultaneously, then acquiring ECT alone, and preparing an attenuation map by subtracting the latter from the former using 99mTc-GSA liver ECT. The ECT system used was a three-head gamma camera equipped with one cardiac fan beam collimator and two parallel beam collimators. External gamma-ray source for TCT of 99mTc was 740 MBq, and ECT of 99mTc-GSA was 185 MBq. First, pure TCT data were acquired for the original TCT-map, then, ECT/TCT data were acquired for the subtracted TCT-map, and finally, pure ECT data were acquired. The subtracted attenuation map was produced by subtracting the pure ECT image from the TCT/ECT image, and attenuation correction of the ECT image was done using both this subtracted TCT map and attenuation map from pure TCT. These two attenuation corrected images and non-corrected images were compared. Hot rods phantom, a liver phantom with a defect, and 10 patients were evaluated. Attenuation corrected ECT values using the subtraction attenuation map showed an error of about 5% underestimation compared with ECT values of the images corrected by original attenuation map at the defect in the liver phantom. A good correlation of y = 22.65 + 1.06x, r = 0.958 was observed also in clinical evaluation. By means of the method proposed in this study, it is possible to perform simultaneous TCT/ECT data acquisition for attenuation correction using Tc-99m external source in Tc-99m GSA liver SPECT. Moreover, it is thought that this method decreases the mental and physical stress of the patients.

Hybrid parallel-slant hole collimators for SPECT imaging

We propose a new collimator geometry, the hybrid parallel-slant (HPS) hole geometry, to improve sensitivity for SPECT imaging with large field of view (LFOV) gamma cameras. A HPS collimator has one segment with parallel holes and one or more segments with slant holes. The collimator can be mounted on a conventional SPECT LFOV system that uses parallel-beam collimators, and no additional detector or collimator motion is required for data acquisition. The parallel segment of the collimator allows for the acquisition of a complete data set of the organs-of-interest and the slant segments provide additional data. In this work, simulation studies of an MCAT phantom were performed with a HPS collimator with one slant segment. The slant direction points from patient head to patient feet with a slant angle of 30/spl deg/. We simulated 64 projection views over 180/spl deg/ with the modeling of nonuniform attenuation effect, and then reconstructed images using an MLEM algorithm that incorporated the hybrid geometry. It was shown that sensitivity to the cardiac region of the phantom was increased by approximately 50% when using the HPS collimator compared with a parallel-hole collimator. No visible artifacts were observed in the myocardium and the signal-to-noise ratio (SNR) of the myocardium walls was improved. Compared with collimators with other geometries, using a HPS collimator has the following advantages: (a) significant sensitivity increase; (b) a complete data set obtained from the parallel segment that allows for artifact-free image reconstruction; and (c) no additional collimator or detector motion. This work demonstrates the potential value of hybrid geometry in collimator design for LFOV SPECT imaging.

Speed up of an analytical algorithm for nonuniform attenuation correction by using PC video/graphics card architecture

A major task in quantitative SPECT (single photon emission computed tomography) reconstruction is compensation for object-specific attenuation, which is usually nonuniform. Mathematically this task is expressed as the inversion of the attenuated Radon transform. Novikov had derived an explicit inversion formula for the attenuated Radon transform for parallel-beam collimation geometry. In our previous work, we extended his work to variable focusing fan-beam (VFF) collimators. A ray-driven analytical inversion formula for VFF reconstruction with nonuniform attenuation was derived. The drawback of ray-driven methods is that they are time consuming. In this work, we proposed a fast implementation method, which includes algorithm optimization and acceleration by the texture-mapping architecture of PC graphics/video card. We further investigated the noise properties and associated artifacts of the analytical inversion formula. The artifacts were remarkably reduced when more projections were sampled to mitigate the problem of wide bandwidth of the discrete Hilbert transform. The reconstruction from noisy data demonstrated the accuracy and robustness of the presented ray-driven analytical inversion formula with dramatic speed acceleration by the PC graphics/video card.

An analytical inversion of the nonuniformly attenuated Radon transform with variable focal-length fan-beam collimators

Single photon emission computed tomography (SPECT) is based on the measurement of radiation emitted by a radiotracer injected into the patient. Because of photoelectric absorption and Compton scatter, the gamma photons are attenuated inside the body before arriving at the detector. A quantitative reconstruction must consider the attenuation, which is usually nonuniform. Novikov has derived an explicit inversion formula for the nonuniformly attenuated Radon transform for SPECT reconstruction of parallel-beam collimated projections. In this paper, we extend his research to variable focal-length fan-beam VFF collimator geometry. A ray-driven analytical formula for VFF reconstruction with nonuniform attenuation was derived. As a unified framework, this formula can be used for parallel-beam, fan-beam, and VFF collimators. Its accuracy is demonstrated by computer simulation experiments.

Geometrical similarities of the Orlov and Tuy sampling criteria and a numerical algorithm for assessing sampling completeness

Tuy and others have derived a sufficiency condition for complete sampling using a cone-beam geometry. Herein, we express Tuy's cone-beam condition in the language and geometry of Orlov's condition for parallel-beam collimation. One may determine from this condition what volume is completely sampled. This inversion has been implemented in software. The software determines a lower bound on the completely sampled volume for arbitrary orbits.

Optimization technique for a Prompt Gamma-ray SPECT collimator system.

Because background radiation in an irradiation room creates a problem with the PG-SPECT (Prompt Gamma-ray Single Photon Emission Computed Tomography) system, which evaluates the absorbed dose for the Boron Neutron Capture Therapy treatment, optimization of a collimator system was performed while taking the shielding of background gamma-rays into consideration. Assuming that a parallel-beam collimator is used, three parameters--the diameter of a hole, the length of the collimator, and the number of detectors (the number of holes of the collimator)--were selected for optimization. Because the combinations of these parameters are limitless, it is difficult to determine them simultaneously. Therefore, a statistically derived Optimization Criterion has been proposed to optimize these parameters. When the spatial resolution was 1 cm-FWHM (full width at half maximum), the optimal diameter of the collimator was 5.4 mm, the optimal length was 321 mm, and the optimal number of detectors was 31 x 31.

A simple model for the efficient correction of collimator blur in 3D SPECT imaging

The problem of performing an efficient compensation of collimator blur in the three-dimensional (3D) reconstruction of SPECT data acquired in parallel beam geometry is tackled. An approximate model for data acquisition is developed, which leads to the construction of the corresponding projector-backprojector pair. In order to perform some numerical tests, the model is customized to a state-of-the-art neuro-SPECT scanner, which is supplied with a three-segmented parallel beam collimator. Some reconstruction algorithms based on this customization are presented and their results are compared, in terms of quality and timing requirements, with the outcome generated by the corresponding fully 3D model. According to this numerical simulation, where voxel-driven (back-)projectors are used, the conclusion can be drawn that the approximate model produces reconstructions as good as the ones generated by the fully 3D model in a time which is one order of magnitude shorter. In the case that (back-)projectors based on the rotation of the emission matrix are used, the proposed approximate model is evaluated to be about four times faster than the corresponding fully 3D model.

Design and experimental validation of a quantitative myocardial /sup 201/Tl SPECT system

We have developed a quantitative SPECT system, and evaluated its potential for quantitative assessment of bio-physiological functions in the myocardium particularly with /sup 201/Tl. Our approach included development of a transmission system that provides accurate attenuation /spl mu/ maps, and implementation of ordered-subset EM reconstruction with transmission data based attenuation correction in addition to scatter correction using the transmission-dependent convolution subtraction (TDCS) technique. The transmission system was designed using Monte Carlo simulation to minimize the scatter in the transmission projection data while keeping loss of sensitivity minimal, and was attached to an opposing 2-head gamma camera fitted with parallel beam collimators. Observed /spl mu/ values agreed quantitatively well with the theoretical expected values in both phantoms and human thorax. Phantom experiments with /sup 201/Tl also demonstrated that, with both corrections for attenuation and scatter, observed images were directly proportional to the actual radioactivity distribution for various phantom geometries. Attenuation correction without scatter correction improved images in deep structure, but resulted in significant artifacts in the chest phantom in addition to dependency of observed radioactivity concentrations on the diameter of cylindrical phantoms. Absolute quantitation of bio-physiological functions, which is well established in PET, is shown to be feasible using SPECT, if both quantitative attenuation and scatter corrections are employed.

A unified reconstruction framework for both parallel-beam and variable focal-length fan-beam collimators by a Cormack-type inversion of exponential radon transform.

A variety of inversions of exponential Radon transform has been derived based on the circular harmonic transform in Fourier space by several research groups. However, these inversions cannot be directly applied to deal with the reconstruction for fan-beam or variable-focal-length fan-beam collimator geometries in single photon emission computed tomography (SPECT). In this paper, we derived a Cormack-type inversion of the exponential Radon transform by employing the circular harmonic transform directly in the projection space and the image space instead of the Fourier space. Thus, a unified reconstruction framework is established for parallel-, fan-, and variable-focal-length fan-beam collimator geometries. Compared to many existing algorithms, the presented one greatly mitigates the difficulty of image reconstruction due to the complicated collimator geometry and significantly reduces the computational burden of the special functions, such as Chebyshev or Bessel functions. By the well-established fast-Fourier transform (FFT), our algorithm is very efficient, as demonstrated by several numerical simulations.

Geometrical response of multihole collimators

A complete theory of camera multihole collimators is presented. The geometrical system response is determined in closed form in frequency space. This closed form accounts for the known efficiency and resolution formulae for parallel beam, fan beam, cone beam and astigmatic collimators as well as for the most frequent hole array patterns and hole shapes. The point spread function in the space domain for a certain collimator and source position can be calculated via a discrete fast Fourier transform. Beside the complete theoretical definition of the response of multihole collimators, this theory allows the definition of accurate models of the geometrical response for SPECT reconstruction and it is suitable for designing new collimators.