Collimator Response Research Articles

Differences due to collimator blurring in cardiac images with use of circular and elliptic camera orbits

Background. In cardiac imaging systems, an elliptic acquisition orbit about the patient can be used to enhance resolution of single photon emission computed tomography (SPECT) images by minimizing the distance between the object imaged and the rotating detector system. In this study artifacts from images acquired with the standard circular acquisition are compared with those acquired with various elliptic acquisitions. Methods and Results. With the use of elliptic camera orbits of different eccentricities, simulated projection data were generated from a slice through the left ventricle (LV). The projection data included a simulation of the degradation due to the depth-dependent response of the collimator. As is common in many clinical systems, SPECT images were reconstructed with the standard filtered backprojection algorithm without correction for the collimator response. When the ratio of the major-to-minor axis of the acquisition arc is changed from 1 (circular) to 1.5 (elliptic), reconstructed SPECT images show an additional loss of counts (about 10%) in the apical region of the LV. The severity of the apical defect is also dependent on the starting angle of the acquisition arc. When the starting angle is changed from 0° (detector parallel to the major axis of the LV) to 60°, the ratio between the minimum count in the apical region and the maximum count in the left ventricular myocardial wall decreases by as much as 20%. Conclusions. SPECT image artifacts from elliptic acquisitions are significantly more severe than those from circular acquisitions. Because of the significant difference in images reconstructed from circular and elliptic acquisitions, standardized normal files acquired from circular acquisitions should not be used for comparisons with patient data acquired from elliptic acquisitions. (J Nucl Cardiol 2001;8:458-65.)

Absolute activity quantitation from projections using an analytical approach: comparison with iterative methods in Tc-99m and I-123 brain SPECT

Estimates of SPECT activity within certain deep brain structures could be useful for clinical tasks such as early prediction of Alzheimer's disease with Tc-99m or Parkinson's disease with I-123; however, such estimates are biased by poor spatial resolution and inaccurate scatter and attenuation corrections. We compared an analytical approach (AA) of more accurate quantitation to a slower iterative approach (IA). Monte Carlo simulated projections of 12 normal and 12 pathologic Tc-99m perfusion studies, as well as 12, normal and 12 pathologic I-123 neurotransmission studies, were generated using a digital brain phantom and corrected for scatter by a multispectral fitting procedure. The AA included attenuation correction by a modified Metz-Fan algorithm and activity estimation by a technique that incorporated Metz filtering to compensate for variable collimator response (VCR), IA-modeled attenuation, and VCR in the projector/backprojector of an ordered subsets-expectation maximization (OSEM) algorithm. Bias and standard deviation over the 12 normal and 12 pathologic patients were calculated with respect to the reference values in the corpus callosum, caudate nucleus, and putamen. The IA and AA yielded similar quantitation results in both Tc-99m and I-123 studies in all brain structures considered in both normal and pathologic patients. The bias with respect to the reference activity distributions was less than 7% for Tc-99m studies, but greater than 30% for I-123 studies, due to partial volume effect in the striata. Our results were validated using I-123 physical acquisitions of an anthropomorphic brain phantom. The IA yielded quantitation accuracy comparable to that obtained with IA, while requiring much less processing time. However, in most conditions, IA yielded lower noise for the same bias than did AA.

Rotating slant-hole single-photon emission-computed tomography

This dissertation presents a detailed investigation of the use of rotating slant-hole (RSH) collimators in single-photon emission-computed tomography(SPECT). We propose RSH SPECT as an alternative imaging technique, which may have advantages over more traditional SPECT techniques, in certain imaging applications. The basic imaging properties of RSH collimators are derived. This includes the derivation of expressions for the size and location of the common volume of view and the geometric resolution and efficiency. In addition, we derive an analytical expression for the geometric response and transfer functions of RSH collimators. The theoretical expressions for the aforementioned imaging characteristics are verified via Monte Carlo simulations and phantom experiments. Next, we present the development of a three-dimensional (3-D) analytic reconstruction algorithm for RSH SPECT. This includes the derivation of both a backprojection of the filtered projections and a filtering of the simple backprojections (BpjF) algorithm. The relationship between the derived 3-D RSH reconstruction filter and a number of other reconstruction filters is discussed. In addition, the implementation of the BpjF reconstruction algorithm is described and its performance is demonstrated via simulations and phantom experiments. We have also implemented an iterative ordered-subsets expectation-maximization (OS-EM) reconstruction algorithm for RSH SPECT. A detailed description of the development of the projector/backprojector employed by the OS-EM algorithm is provided. Simulation and phantom experiments are again used to demonstrate the performance of the projector/backprojector and the iterative OS-EM reconstruction algorithm. Rotating slant-hole SPECT has potential applications in cardiac and breast imaging. Thus, we demonstrate the feasibility, advantages, and disadvantages of using RSH SPECT via a comparison with conventional SPECT in a cardiac and breast imaging phantom experiment. In conclusion, we summarize the results presented and discuss their implications on the current and future state of RSH SPECT research.

Energy-based compensation for nonuniform attenuation in Ga-67 SPECT imaging

Describes a method to estimate unattenuated projection images directly from Ga-67 SPECT data acquired over 360/spl deg/ at 3 photopeak energies. The algorithm compensates to third order for the effects of nonuniform attenuation, thereby yielding unattenuated projections with <3% accuracy, provided that scattered photons have been successfully subtracted from each energy window. Previously, the authors demonstrated an approach for using prior information to control noise in the estimated projections. They describe here an accelerated, robust algorithm for implementing these constraints. They have also evaluated the accuracy of the method for a region-of-interest (ROI) activity estimation task as a function of the residual error following scatter subtraction, and under conditions of nonstationary spatial resolution. When the maximum residual scatter subtraction errors at 93, 185, and 300 keV, respectively, were assumed to be 8%, 4%, and 2%, all ROI estimates were biased less than /spl plusmn/7% after attenuation compensation. Projection inconsistencies arising from distance-dependent geometric response and energy-dependent collimator penetration increased the standard deviation of ROI estimates (over location) to /spl sim/10%; however, methods of correcting for distance-dependent collimator response can probably be adapted well to Ga-67 imaging. If scatter can be adequately removed from the 3 Ga-67 photopeak windows, this technique is expected to provide reliable compensation for nonuniform attenuation with no need for an independently measured attenuation map.

Respective roles of scatter, attenuation, depth-dependent collimator response and finite spatial resolution in cardiac single-photon emission tomography quantitation: a Monte Carlo study.

The purpose of this study was to investigate the relative influence of scatter, attenuation, depth-dependent collimator response and finite spatial resolution upon the image characteristics in cardiac single-photon emission tomography (SPET). An acquisition of an anthropomorphic cardiac phantom was performed together with corresponding SPET Monte Carlo simulations. The cardiac phantom and the Monte Carlo simulations were designed so that the effect of scatter, attenuation, depth-dependent collimator response and finite spatial resolution could be studied individually and in combination. The impact of each physical effect and of combinations of effects was studied in terms of absolute and relative quantitative accuracy, spatial resolution and signal-to-noise ratio (SNR) in the resulting images. No corrections for these effects were assessed. Results obtained from Monte Carlo simulations and real acquisitions were in excellent agreement. Attenuation introduced about 90% activity underestimation in a 10-mm-thick left ventricle wall while finite spatial resolution alone introduced about 30% activity underestimation. Scatter had a negligible impact on quantitative accuracy in the recontructed slices when attenuation was present. Neither bull's eye map homogeneity nor contrast between a hot and a cold region were affected by depth-dependent collimator response or finite spatial resolution. Bull's eye map homogeneity was severely affected by attenuation but not by scatter. Attenuation and scatter reduced contrast by about 20% each. Both attenuation and scatter increased the full-width at half-maximum (FWHM) characterizing the spatial resolution of the imaging system by approximately 1 mm each but the main effect responsible for the observed 11-mm FWHM spatial resolution was the depth-dependent collimator response. SNR was reduced by a factor of approximately 2.5 because of attenuation, while scattered counts increased SNR by approximately 10%. In conclusion, the quantification of the relative influence of the different physical effects showed that attenuation is definitely the major phenomenon affecting cardiac SPET imaging accuracy, but that finite spatial resolution, scatter and depth-dependent collimator response also contribute significantly to the errors in absolute and relative quantitation and to the poor spatial resolution.

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.

Improved estimation of the detector response function for converging beam collimators

Converging beam collimator geometries offer improved tradeoffs between resolution and noise for single photon emission computed tomography (SPECT). The major factor limiting the resolution in SPECT is the collimator-detector response blurring. In order to compensate for this blurring it is useful to be able to calculate the collimator response function. A previous formulation presented a method for calculating the response for parallel and converging beam collimators that assumed that the shape of the holes did not change over the face of the collimator. However, cast collimators are fabricated using pins with a constant cross-section (shape perpendicular to the pin axis). As a result, due to the angulation of the pins, the holes made by these pins have shapes on the front and back faces of the collimator that change with position. This change in hole shape is especially pronounced when the angle between the collimator hole and the collimator normal is large, as is the case for half-fan-beam or short-focal-length collimators. This paper presents a derivation of a modification to the original method that accounts for the change in shape of the collimator holes. The method has been verified by comparing predicted line spread functions to experimentally measured ones for a collimator with a maximum hole angle of with respect to the normal. This formulation is useful for predicting the response of fan-beam collimators in the design process and for use in detector response compensation algorithms.

The effect of radionuclide scatter in emission-transmission CT

In order to assess the relative effect of scatter in comparison to attenuation and collimator blur, the authors imaged concentric cylinder, cold-lesion, and thorax-like phantoms with the emission transmission computed tomography (ETCT) system, a novel device capable of both X-ray CT and SPECT. For these experiments, the ETCT system was outfitted with a single channel of low-noise electronics which permitted acquisition of SPECT data with 3 keV FWHM energy resolution for good scatter rejection. Reference images were reconstructed with object-specific attenuation correction and accurate collimator response compensation These images were then compared to images which were reconstructed without attenuation correction, without collimator response, or with data that had been blurred to simulate 13 keV FWHM energy resolution. The results show that although scatter represents a measurable error, its effect is small compared to the effect of attenuation and collimator blur. As part of this study, the authors have also compared scatter rejection to the well-known dual energy window scatter correction method and to a technique which incorporates an estimate of the scatter distribution directly in the back-projector of the ML-EM algorithm. It is shown that scatter correction may be preferable to scatter rejection due to noise considerations.

The effect of heart motion on kinetic parameter estimates for dynamic cardiac SPECT

Dynamic cardiac SPECT is used to estimate kinetic rate parameters that describe the washin and washout of tracer activity between the blood and the myocardial tissue. These kinetic parameters correlate to myocardial perfusion. There are, however, many physical aspects associated with dynamic SPECT which introduce bias and variance into the estimates. This paper describes a study which investigates the effect of heart motion on kinetic parameter estimates. Dynamic SPECT simulations are performed using a beating version of the MCAT phantom. The amount of blood and background activity in the myocardial tissue regions of interest is shown to vary over the cardiac cycle causing errors in the kinetic parameter estimates, particularly estimates of the washin rate constant. The effect of cardiac motion on kinetic parameter estimates is reduced by bias and variance introduced by photon noise and geometric collimator response. This suggests that techniques used to correct for motion must do so without further reducing photon statistics.

Comparison of Tc-99 tetrofosmin and 511 keV collimated myocardial perfusion SPECT — the effect of collimator response correction

Comparison of Tc-99 tetrofosmin and 511 keV collimated myocardial perfusion SPECT — the effect of collimator response correction

Optimal collimator choice for sequential iodine-123 and technetium-99m imaging

Dual-isotope studies with technetium-99m and iodine-123 may be useful for various organs, including brain and myocardium. For the images obtained with each of the tracers to be comparable, it is important that activity ratios (activity in one part of the image/reference activity in the image) are preserved by the imaging method. We have used a Rollo phantom to study how collimator response affects such ratios. All investigations were performed with 123I(p,5n) and on a Siemens Orbiter 3700 camera fitted with either a low-energy high-resolution (LEHR) or a medium-energy (ME) collimator. Images were made of a Rollo phantom filled with an aqueous solution of either 99Tc or 123I, and placed on the collimator surface with 8 cm of methyl-methacrylate interposed. Count densities were measured in ROIs drawn in each cell of the phantom, and normalised to the maximal ROI value in the image. The mean square error (MSE) was used to assess how well the ratios of count densities approximated the known activity ratios based on the dimensions of the cells of the phantom. For 99mTc, regardless of the collimator used, the count density ratios approximated the activity ratios fairly well (LEHR: MSE=0.008; ME: MSE=0.020). For 123I, count density ratios obtained with the LEHR were consistently higher than activity ratios (MSE=0. 235), whereas the differences between the measured and the theoretical values were less with the ME collimator (MSE=0.013). Contrast fidelity of the 123I images obtained with the LEHR collimator could be improved with Jaszczak scatter correction with k=1, but this led to unfavourable signal-to-noise ratios. For sequential 99mTc/123I studies with extended sources, ME is to be preferred because of its higher contrast accuracy. Spatial resolution is less for the ME than for the LEHR collimator (FWHM with scatter: LEHR/99mTc=6.9 mm, LEHR/123I=7.4 mm, ME/99mTc= 10.1 mm, ME/123I=11.1 mm), but remains similar for both tracers when the ME is used.

The relative importance of energy resolution for quantitative /sup 99m/Tc SPECT imaging

The authors seek to determine the desired energy resolution for quantitative SPECT imaging. As the energy resolution of the system is improved, the relative error due to scatter decreases. Yet, at some point the improvement becomes inconsequential since the scatter error is small compared to the other physical perturbations in the radionuclide measurement. In order to estimate the energy resolution at which this condition becomes true, the authors used a Monte Carlo code to simulate the emission data from a myocardial perfusion phantom. The data were reconstructed using a maximum likelihood code, and the images were analyzed to determine the relative effects of attenuation correction, collimator response compensation, noise, and scatter rejection on image quantitation. The simulations showed that improving the system energy resolution beyond 5 keV offers little benefit for myocardial perfusion studies as judged by the noise in a 9-pixel ROI. The relevance of this result to other applications is also discussed.

Quantitative small field-of-view pinhole SPECT imaging: initial evaluation

A quantitative filtered backprojection (FBP) algorithm for small field-of-view pinhole SPECT has been implemented and evaluated. This algorithm compensates for attenuation, scatter, geometric collimator response and system misalignment. Pinhole SPECT quantification with three different pinhole collimators was evaluated using experimentally acquired phantom data. SPECT scans using both in-air and in-water point sources located at different places and a cylinder filled with uniform activity were acquired. Planar scans of an in-air point source from different incident angles were acquired to determine the angular dependence of the geometric collimator response. Images were reconstructed using the FBP algorithm, with geometric response correction, dual-window scatter subtraction (c=0.4), single iteration Chang attenuation compensation, and system misalignment correction. Total activities in point source experiments and concentrations in cylindrical phantom experiments were measured. Accurate quantitative results (<7%) were obtained using the pinhole FBP algorithm.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

A practical method for incorporating scatter in a projector-backprojector for accurate scatter compensation in SPECT

A projector-backprojector pair has been developed that models attenuation and the spatially variant collimator and scatter response functions in a uniformly attenuating object for single photon emission computed tomography (SPECT). The scatter response function (SRF) is modeled using a scheme based on the scatter responses of point sources in a large slab phantom. This scheme, slab derived scatter estimation, allows efficient and accurate modeling of the asymmetric and spatially variant properties of the scatter response during the projection and backprojection operations. The scatter model is verified by comparison of scatter line source response functions, scatter/primary ratios, and projection data from extended source distributions obtained using this method and direct Monte Carlo simulations. Combined with iterative reconstruction techniques, this projector-backprojector provides a practical and accurate means for scatter compensation in SPECT. Preliminary results of combining this projector-backprojector with the maximum-likelihood-expectation-maximization algorithm show a significant increase in quantitative accuracy as compared to compensation for only attenuation and the spatially variant collimator response function.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Implementation and evaluation of an analytical solution to the photon attenuation and nonstationary resolution reconstruction problem in SPECT

The implementation and evaluation of an analytical solution to the photon attenuation and nonstationary resolution reconstruction problem in single photon emission computed tomography (SPECT) are presented. The method is based on a combination of the Bellini attenuation compensation and the Appledorn nonstationary resolution correction algorithms. It is termed the simultaneous correction algorithm (SCA). The results of testing the method with point source acquisitions showed a significant improvement in reducing the nonstationary behavior of the collimator response. The ratios of the FWHMs showed better agreement with the ideal value of 1.0, and the modulation transfer functions (MTFs) of the point spread functions exhibited less positional variation when using the SCA over other methods. In addition, the initial quantitative values were restored to acceptable levels. >

Reconstruction methods for quantitative brain SPECT

The effects of various reconstruction algorithms and compensation techniques for brain SPECT (single-photon-emission computed tomography) reconstruction are investigated. The conventional FB (filtered backprojection) and iterative ML-EM (maximum-likelihood estimation-maximization) algorithms are used. Projection data were acquired via dual energy windows for use in scatter compensation. Assuming uniform attenuation, the Chang attenuation compensation algorithm is applied. Restoration filters are used with the FB algorithms to compensate for the average effects of collimator and scatter response functions. Two-dimensional (2-D) and three-dimensional (3-D) compensation methods are compared. Compensation for the one-dimensional spatially variant collimator response, using an iterative reconstruction method, is shown. The results show that conventional reconstruction and compensation methods provide substantial improvement in reconstructed image quality and quantitative accuracy compared with no compensation. 3-D processing gives better results than 2-D processing. Iterative reconstruction provided more accurate quantitation with a substantial increase in computational cost.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

(5) Compton Scatter Distribution Function in Non-Uniform Attenuation in SPECT(2. Tomographic Imaging)

(Introduction) Major problems of single photon emission computed tomography (SPECT) which degrade images both qualitatively and quantitatively include attenuation, camera uniformity geometric collimator response, and scattered photons. Compton scattered photons degrade spatial resolution and reduce the accuracy and precison of quantiation in SPECT images. The majority of correction methods introduced to reduce influence of compton scatter component consider the scatter distribution function to be a symmetrical, monoexponential function of distance from source position. Here a more realistic approach has been taken to derive scatter distribution functions for usiform and nonuniform scattering geometries. (Method) Monte Carlo simulations of Tc-99m point and line sources were used to obtain detailed information on the spatial and energy distribution of scattered and non-scattered events in SPECT images. EGS4 simulation code was adapted for use with planar and SPECT imaging geometries and detection devices. Simulations were carried out in two steps : 1) photons were followed in attenuation media until they were completely absorbed or emerged. Photon energy, input and output coordinates, direction and scatter order were recorded for photons that emerged within the detector field of view. 2) The detection process was simulated in a second step which gave greater flexibility in changing detection parameters (collimator geometry, intrinsic spatial resolution, energy resolution, energy window settings etc.). Scatter in the collimator and septal penetration were not included. Energy resolution of the system was simulated by sampling from an energydependent Gaussian function. The data shown were obtained from a simulation of SPECT system with a LEHR collimator, radius of rotation of 13cm, an energy resolution of 13%, intrinsic spatial resolution of 3.6mm, an energy window of 20% centered at 140KeV and a pixel size of 1mm. Seperate images were obtained for nonscattered events and events of scatter order n=1-3, a single image was obtained for n>4. (Results) The scatter distribution function in non-uniform density media indicates that scatter correction techniqes based on single exponential scatter distribution function do not provide a valid correction for non-uniform scattering geometries. Further investigations of SDF in more complex non-uniform geometries are needed to develop accurate correction method for Compton scatter reduction in SPECT images. My results suggest that 3-D scatter correction function and reconstruction methods need to be applied.

A new approach to evaluate the response functions for conical and cylindrical collimators

A new approach to the evaluation of the conical collimator response function is shown. The basic collimator formulae are reviewed. The collimator response function has been found in a very easy way. An approximate solution has been introduced. Studying the response of a measuring system, the use of this approximation strongly reduces the complexity of the relations to be used; therefore it would provide a useful starting point for a Monte Carlo calculation. The errors introduced are less than 10%. Approximate relations that allow the evaluation of the response of conical and cylindrical collimators to plane and line sources are also given.

Collimator Design Using Ray-Tracing Techniques

A new computer program, RAYTRC, has been written to analyze and design collimators for high-energy gamma-ray cameras used in nuclear medicine. The program finds collimator sensitivity, and geometric and penetration point source response functions. The results of this program are presented for a number of commercial collimators and for a new experimental design used to image with 511 keV gamma-rays. Collimators designed for such high-energy gamma-rays often produce bothersome hole pattern in the images due to thick septa. In order to analyze this problem we introduce a 'generalized collimator transfer function' which characterizes not only the averaged collimator response, but also the effect of hole pattern on the images.

Evaluation and Comparison Between the Collimator and the Detector Responses in a Scintillation Camera

A method to study the relative influences of the collimator and the detector on the final image of a scintillation camera is proposed. The collimator response is studied by applying a technique based on the Fourier analysis for evaluating the point spread function (PSF) of parallel holes collimators. A mathematical expression for the PSF is obtained and from it the collimator MTF and plane sensitivity are evaluated. The scintillation camera response is obtained from the LSF measured experimentally. The detector response is obtained from these results. The method is applied to a Toshiba GCA 102 scintillation camera and from the results obtained the relative influences of the collimator and the detector on the image deterioration as a function of the object distance are discussed.