Biomedical subjects

G L Zeng

Publications and source records attributed to G L Zeng.

18 recordsLinked to original sources

PubMed2001

Efficient cardiac diffusion tensor MRI by three-dimensional reconstruction of solenoidal tensor fields.

Tensor tomography is being investigated as a technique for reconstruction of in vivo diffusion tensor fields that can potentially be used to reduce the number of magnetic resonance imaging (MRI) measurements. Specifically, assessments are being made of the reconstruction of cardiac diffusion tensor fields from 3D Radon planar projections using a filtered backprojection algorithm in order to specify the helical fiber structure of myocardial tissue. Helmholtz type decomposition is proposed for 3D second order tensor fields. Using this decomposition a Fourier projection theorem is formulated in terms of the solenoidal and irrotational components of the tensor field. From the Fourier projection theorem, two sets of Radon directional measurements, one that reconstructs the solenoidal component and one that reconstructs the irrotational component of the tensor field, are prescribed. Based on these observations filtered backprojection reconstruction formulae are given for the reconstruction of a 3D second order tensor field and its solenoidal and irrotational components from Radon projection measurements. Computer simulations demonstrate the validity of the mathematical formulations and demonstrate that a realistic model of the helical fiber structure of the myocardial tissue specifies a diffusion tensor field for which the first principal vector (the vector associated with the maximum eigenvalue) of the solenoidal component accurately approximates the first principal vector of the diffusion tensor. A priori knowledge of this allows the orientation of the myocardial fiber structure to be specified utilizing one half of the number of MRI measurements of a normal diffusion tensor field study.

Computer Simulation↗

PubMed2001

Cone-beam image reconstruction using spherical harmonics.

Image reconstruction from cone-beam projections is required for both x-ray computed tomography (CT) and single photon emission computed tomography (SPECT). Grangeat's algorithm accurately performs cone-beam reconstruction provided that Tuy's data sufficiency condition is satisfied and projections are complete. The algorithm consists of three stages: (a) Forming weighted plane integrals by calculating the line integrals on the cone-beam detector, and obtaining the first derivative of the plane integrals (3D Radon transform) by taking the derivative of the weighted plane integrals. (b) Rebinning the data and calculating the second derivative with respect to the normal to the plane. (c) Reconstructing the image using the 3D Radon backprojection. A new method for implementing the first stage of Grangeat's algorithm was developed using spherical harmonics. The method assumes that the detector is large enough to image the whole object without truncation. Computer simulations show that if the trajectory of the cone vertex satisfies Tuy's data sufficiency condition, the proposed algorithm provides an exact reconstruction.

Algorithms↗

PubMed2000

A three-dimensional ray-driven attenuation, scatter and geometric response correction technique for SPECT in inhomogeneous media.

The qualitative and quantitative accuracy of SPECT images is degraded by physical factors of attenuation, Compton scatter and spatially varying collimator geometric response. This paper presents a 3D ray-tracing technique for modelling attenuation, scatter and geometric response for SPECT imaging in an inhomogeneous attenuating medium. The model is incorporated into a three-dimensional projector-backprojector and used with the maximum-likelihood expectation-maximization algorithm for reconstruction of parallel-beam data. A transmission map is used to define the inhomogeneous attenuating and scattering object being imaged. The attenuation map defines the probability of photon attenuation between the source and the scattering site, the scattering angle at the scattering site and the probability of attenuation of the scattered photon between the scattering site and the detector. The probability of a photon being scattered through a given angle and being detected in the emission energy window is approximated using a Gaussian function. The parameters of this Gaussian function are determined using physical measurements of parallel-beam scatter line spread functions from a non-uniformly attenuating phantom. The 3D ray-tracing scatter projector-backprojector produces the scatter and primary components. Then, a 3D ray-tracing projector-backprojector is used to model the geometric response of the collimator. From Monte Carlo and physical phantom experiments, it is shown that the best results are obtained by simultaneously correcting attenuation, scatter and geometric response, compared with results obtained with only one or two of the three corrections. It is also shown that a 3D scatter model is more accurate than a 2D model. A transmission map is useful for obtaining measurements of attenuation and scatter in SPECT data, which can be used together with a model of the geometric response of the collimator to obtain corrected images with quantitative and diagnostically accurate information.

Algorithms↗

PubMed2000

A slice-by-slice blurring model and kernel evaluation using the Klein-Nishina formula for 3D scatter compensation in parallel and converging beam SPECT.

Converging collimation increases the geometric efficiency for imaging small organs, such as the heart, but also increases the difficulty of correcting for the physical effects of attenuation, geometric response and scatter in SPECT. In this paper, 3D first-order Compton scatter in non-uniform scattering media is modelled by using an efficient slice by-slice incremental blurring technique in both parallel and converging beam SPECT. The scatter projections are generated by first forming an effective scatter source image (ESSI), then forward-projecting the ESSI. The Compton scatter cross section described by the Klein-Nishina formula is used to obtain spatial scatter response functions (SSRFs) of scattering slices which are parallel to the detector surface. Two SSRFs of neighbouring scattering slices are used to compute two small orthogonal 1D blurring kernels used for the incremental blurring from the slice which is further from the detector surface to the slice which is closer to the detector surface. First-order Compton scatter point response functions (SPRFs) obtained using the proposed model agree well with those of Monte Carlo (MC) simulations for both parallel and fan beam SPECT. Image reconstruction in fan beam SPECT MC simulation studies shows increased left ventricle myocardium-to-chamber contrast (LV contrast) and slightly improved image resolution when performing scatter compensation using the proposed model. Physical torso phantom fan beam SPECT experiments show increased myocardial uniformity and image resolution as well as increased LV contrast. The proposed method efficiently models the 3D first-order Compton scatter effect in parallel and converging beam SPECT.

Biophysical Phenomena↗

PubMed2000

Unmatched projector/backprojector pairs in an iterative reconstruction algorithm.

Computational burden is a major concern when an iterative algorithm is used to reconstruct a three-dimensional (3-D) image with attenuation, detector response, and scatter corrections. Most of the computation time is spent executing the projector and backprojector of an iterative algorithm. Usually, the projector and the backprojector are transposed operators of each other. The projector should model the imaging geometry and physics as accurately as possible. Some researchers have used backprojectors that are computationally less expensive than the projectors to reduce computation time. This paper points out that valid backprojectors should satisfy a condition that the projector/backprojector matrix must not contain negative eigen-values. This paper also investigates the effects when unmatched projector/backprojector pairs are used.

Algorithms↗

PubMed1999

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.

Algorithms↗

PubMed1999

A projector/backprojector with slice-to-slice blurring for efficient three-dimensional scatter modeling.

Scatter correction is an important factor in single photon emission computed tomography (SPECT). Many scatter correction techniques, such as multiple-window subtraction and intrinsic modeling with iterative algorithms, have been under study for many years. Previously, we developed an efficient slice-to-slice blurring technique to model attenuation and system geometric response in a projector/backprojector pair, which was used in an ML-EM algorithm to reconstruct SPECT data. This paper proposes a projector/backprojector that models the three-dimensional (3-D) first-order scatter in SPECT, also using an efficient slice-to-slice blurring technique. The scatter response is estimated from a known nonuniform attenuation distribution map. It is assumed that the probability of detection of a first-order scattered photon from a photon that is emitted in a given source voxel and scattered in a given scatter voxel is proportional to the attenuation coefficient value at that voxel. Monte Carlo simulations of point sources and an MCAT torso phantom were used to verify the accuracy of the proposed projector/backprojector model. An experimental Jaszczak torso/cardiac phantom SPECT study was also performed. For a 64 x 64 x 64 image volume, it took 8.7 s to perform each iteration per slice on a Sun ULTRA Enterprise 3000 (167 MHz, 1 Gbyte RAM) computer, when modeling 3-D scatter, attenuation, and system geometric response functions. The main advantage of the proposed method is its easy implementation and the possibility of performing reconstruction in clinically acceptable time.

Computer Simulation↗

PubMed1998

Iterative and analytical reconstruction algorithms for varying-focal-length cone-beam projections.

In single photon emission computed tomography (SPECT), a varying-focal-length cone-beam collimator can be used to reduce the truncation problem and to maintain sensitivity when imaging the organ of interest. The collimator is constructed so that the collimator holes focus to a circular symmetric, spatially varying, focal point function. The focal length increases radially from the shortest focal length at the centre to the longest focal length at the periphery of the collimator. This paper describes a 3D backprojection-filtering (BF) algorithm for this varying-focal-length cone-beam geometry. The proposed algorithm is compared to an iterative ML-EM (maximum likelihood-expectation maximization) algorithm. The 3D Hoffman brain phantom and Defrise phantom are used in computer simulations. Since the maximum tilt angle of the projection rays is small for most realistic imaging geometries, the proposed algorithm provides a good approximation. When a circular orbit is used, the BF algorithm gives an exact reconstruction of the central slice.

Algorithms↗

PubMed1998

Application of spherical harmonics to image reconstruction for the Compton camera.

The Compton camera can collect SPECT data with high efficiency due to electronic collimation. The data acquired from a Compton camera are projections of source activity along cones and are approximated in this paper by cone-surface integrals. This paper proposes the use of an orthogonal spherical expansion to convert the cone-surface integrals into plane integrals. The conversion technique is efficient. Once the plane integrals are obtained, a 3D image can be reconstructed by the 3D Radon inversion formula. The algorithm is implemented and computer simulations are used to demonstrate the efficiency and accuracy of the proposed reconstruction algorithm.

Algorithms↗

PubMed1998

Kinetic parameter estimation from SPECT cone-beam projection measurements.

Kinetic parameters are commonly estimated from dynamically acquired nuclear medicine data by first reconstructing a dynamic sequence of images and subsequently fitting the parameters to time-activity curves generated from regions of interest overlaid upon the image sequence. Biased estimates can result from images reconstructed using inconsistent projections of a time-varying distribution of radiopharmaceutical acquired by a rotating SPECT system. If the SPECT data are acquired using cone-beam collimators wherein the gantry rotates so that the focal point of the collimators always remains in a plane, additional biases can arise from images reconstructed using insufficient, as well as truncated, projection samples. To overcome these problems we have investigated the estimation of kinetic parameters directly from SPECT cone-beam projection data by modelling the data acquisition process. To accomplish this it was necessary to parametrize the spatial and temporal distribution of the radiopharmaceutical within the SPECT field of view. In a simulated chest image volume, kinetic parameters were estimated for simple one-compartment models for four myocardial regions of interest. Myocardial uptake and washout parameters estimated by conventional analysis of noiseless simulated cone-beam data had biases ranging between 3-26% and 0-28%, respectively. Parameters estimated directly from the noiseless projection data were unbiased as expected, since the model used for fitting was faithful to the simulation. Statistical uncertainties of parameter estimates for 10,000,000 events ranged between 0.2-9% for the uptake parameters and between 0.3-6% for the washout parameters.

Heart↗

PubMed1998

Projection space image reconstruction using strip functions to calculate pixels more "natural" for modeling the geometric response of the SPECT collimator.

The spatially varying geometric response of the collimator-detector system in single photon emission computed tomography (SPECT) causes loss in resolution, shape distortions, reconstructed density nonuniformity, and quantitative inaccuracies. A projection space image reconstruction algorithm is used to correct these reconstruction artifacts. The projectors F use strip functions to calculate pixels more "natural" for modeling the two-dimensional (2-D) geometric response of the SPECT collimator transaxially to the axis of rotation. These projectors are defined by summing the intersection of an array of multiple strips rotated at equal angles to approximate the ideal system geometric response of the collimator. Two projection models were evaluated for modeling the system geometric response function. For one projector each strip is of equal weight, for the other projector a Gaussian weighting is used. Parallel beam and fan beam projections of a physical three-dimensional (3-D) Hoffman brain phantom and a Jaszczak cold rod phantom were used to evaluate the geometric response correction. Reconstructions were obtained by using the singular value decomposition (SVD) method and the iterative conjugate gradient algorithm to solve for q in the imaging equation FGq = p, where p is the projection measurement. The projector F included the new models for the geometric response, whereas, the backprojector G did not always model the geometric response in order to increase the computational speed. The final reconstruction was obtained by sampling the backprojection Gq at a discrete array of points. Reconstructions produced by the two proposed projectors showed improved resolution when compared against a unit-strip "natural" pixel model, the conventional image pixelized model with ray tracing to calculate the geometric response, and the filtered backprojection algorithm. When the reconstruction is displayed on fine grid points, the continuity and resolution of the image is preserved without the ring artifacts seen in the unit-strip "natural" pixel model. With present computing power, the geometric response correction using the proposed projection space reconstruction approach is not yet feasible for routine clinical use.

Algorithms↗

PubMed1998

Iterative reconstruction of fluorine-18 SPECT using geometric point response correction.

UNLABELLED: This article demonstrates resolution recovery in 18F SPECT image reconstruction by using an iterative algorithm that corrects for the system geometric response. METHODS: Patient and phantom studies were performed using a Picker PRISM 3000 three-detector SPECT system (Picker International, Inc., Cleveland, OH) to image 18F with 511 keV collimators. A measured point response function of the imaging system was used in an iterative reconstruction algorithm in which the projector and backprojector modeled the system point response function by using an efficient layer-by-layer blurring technique. The blurring function was a five-element kernel in the shape of a cross. The iterative reconstruction algorithm was an ordered-subset maximum-likelihood expectation maximization algorithm. RESULTS: The iterative reconstruction algorithm with geometric response correction showed an improvement in resolution over the filtered backprojection reconstruction and the iterative reconstruction without correction. CONCLUSION: The proposed iterative reconstruction algorithm with geometric response correction is efficient and effective with significant resolution recovery.

Aged↗

PubMed1997

Reduction of geometric and intensity distortions in echo-planar imaging using a multireference scan.

Echo-planar imaging (EPI) is very sensitive to patient-induced field inhomogeneity caused by susceptibility changes between different anatomical regions. This results in geometric and intensity distortions in the image, especially near tissue/air and tissue/bone interfaces. A new approach is presented to reduce geometric and intensity distortions in EPI. A phase-encoded multireference scan is used to estimate the amplitude and phase errors in the measured signals due to the field inhomogeneity. The EPI data is corrected using both the amplitude and phase of the measured errors. This technique has been evaluated using EPI pulse sequences implemented with conventional gradients and implemented with imaging systems that have special resonating gradients and fast analog to digital converters. The results in both phantom and human studies show that in the absence of object motion the new correction technique can effectively reduce the geometric and intensity distortions.

Cerebellum↗

PubMed1994

Application of convergent-beam collimation and simultaneous transmission emission tomography to cardiac single-photon emission computed tomography.

Single-photon emission computed tomography (SPECT) is the most commonly performed imaging technique for perfusion studies of the heart and brain. However, these organs are much smaller than the crystal surface of gamma cameras. SPECT sensitivity and resolution can be improved by using fan- and cone-beam collimators to magnify the image of these organs over a larger portion of the crystal face. Special orbits and reconstruction algorithms must be used with convergent-beam acquisitions to prevent image distortion. Differential attenuation of source activity in the chest is one of the most vexing problems in cardiac SPECT, especially with Thallium-201. Multi-headed cameras equipped with convergent-beam collimators allow a transmission image to be obtained at the same time as emission images. Applying a transmission map of the chest attenuation values to the emission images produces a truer picture of source distribution in the heart. This article reviews the technical problems associated with convergent-beam geometry and simultaneous transmission emission tomography SPECT imaging of the heart.

Algorithms↗

PubMed1992

Review of convergent beam tomography in single photon emission computed tomography.

Investigation of convergent-beam single photon emission computed tomography (SPECT) is actively being pursued to evaluate its clinical potentials. Fan-beam, cone-beam, pin-hole and astigmatic collimators are being used with rotating gamma cameras having large crystal areas, to increase the sensitivity for emission and transmission computed tomography of small organs such as the thyroid, brain or heart. With new multi-detector SPECT systems, convergent-beam geometry offers the ability to simultaneously obtain emission and transmission data necessary to quantify uptake of radiopharmaceutical distributions in the heart. The development of convergent-beam geometry in SPECT requires the integration of hardware and software. In considering hardware, the optimum detector system for cone-beam tomography is a system that satisfies the data sufficiency condition for which the scanning trajectory intersects any plane passing through the reconstructed region of interest. However, the major development of algorithms has been for the data insufficient case of single planar orbit acquisitions. The development of these algorithms have made possible the preliminary evaluation of this technology and the imaging of brain and heart are showing significant potential for the clinical application of cone-beam tomography. Presently, significant research activity is pursuing the development of algorithms for data acquisitions that satisfy the data sufficiency condition and that can be implemented easily and inexpensively on clinical SPECT systems.

Brain↗

PubMed1992

A cone-beam tomography algorithm for orthogonal circle-and-line orbit.

A cone-beam algorithm which provides a practical implementation of B D Smith's cone-beam inversion formula is presented. For a cone-beam vertex orbit consisting of a circle and an orthogonal line. This geometry is easy to implement in a SPECT system, and it satisfies the cone-beam data sufficiency condition. The proposed algorithm is in the form of a convolution-back projection, and requires a pre-filtering procedure. Computer simulations show a reduction of the artifacts that are found with the Feldkamp algorithm where the cone-beam vertex orbit is a circle.

Algorithms↗

PubMed1991

Cone beam tomography of the heart using single-photon emission-computed tomography.

The authors evaluated cone beam single-photon emission-computed tomography (SPECT) of the heart. A new cone beam reconstruction algorithm was used to reconstruct data collected from "short scan" acquisitions (of slightly more than 180 degrees) of a detector anteriorally traversing a noncircular orbit. The less than 360 degrees acquisition was used to minimize the attenuation artifacts that result from reconstructing posterior projections of 201T1 emissions from the heart. The algorithm includes a new method for reconstructing truncated projections of background tissue activity that eliminates reconstruction ring artifacts. Phantom and patient results are presented which compare a high-resolution cone beam collimator (50-cm focal length; 6.0-mm full width at half maximum [FWHM] at 10 cm) to a low-energy general purpose (LEGP) parallel hole collimator (8.2-mm FWHM at 10 cm) which is 1.33 times more sensitive. The cone beam tomographic results are free of reconstruction artifacts and show improved spatial and contrast resolution over that obtained with the LEGP parallel hole collimator. The limited angular sampling restrictions and truncation problems associated with cone beam tomography do not deter from obtaining diagnostic information. However, even though these preliminary results are encouraging, a thorough clinical study is still needed to investigate the specificity and sensitivity of cone beam tomography.

Algorithms↗

PubMedDate not supplied

Image reconstruction--a tutorial.

This paper is written for physicians and presents basic principles of image reconstruction in nuclear medicine. Both analytical and iterative methods are discussed without rigorous mathematics.

Algorithms↗