Biomedical subjects
Publications and source records attributed to Grant T Gullberg.
We give an overview of the role of Physics in Medicine and Biology in the development of tomographic reconstruction algorithms. We focus on imaging modalities involving ionizing radiation, CT, PET and SPECT, and cover a wide spectrum of reconstruction problems, starting with classical 2D tomography in the 1970s up to 4D and 5D problems involving dynamic imaging of moving organs.
Medical images in nuclear medicine are commonly represented in three dimensions as a stack of two-dimensional images that are reconstructed from tomographic projections. Although natural and straightforward, this may not be an optimal visual representation for performing various diagnostic tasks. A method for three-dimensional (3-D) tomographic reconstruction is developed using a point cloud image representation. A point cloud is a set of points (nodes) in space, where each node of the point cloud is characterized by its position and intensity. The density of the nodes determines the local resolution allowing for the modeling of different parts of the image with different resolution. The reconstructed volume, which in general could be of any resolution, size, shape, and topology, is represented by a set of nonoverlapping tetrahedra defined by the nodes. The intensity at any point within the volume is defined by linearly interpolating inside a tetrahedron from the values at the four nodes that define the tetrahedron. This approach creates a continuous piecewise linear intensity over the reconstruction domain. The reconstruction provides a distinct multiresolution representation, which is designed to accurately and efficiently represent the 3-D image. The method is applicable to the acquisition of any tomographic geometry, such as parallel-, fan-, and cone-beam; and the reconstruction procedure can also model the physics of the image detection process. An efficient method for evaluating the system projection matrix is presented. The system matrix is used in an iterative algorithm to reconstruct both the intensity and location of the distribution of points in the point cloud. Examples of the reconstruction of projection data generated by computer simulations and projection data experimentally acquired using a Jaszczak cardiac torso phantom are presented. This work creates a framework for voxel-less multiresolution representation of images in nuclear medicine.
UNLABELLED: Currently, 2 types of phantoms (physical and computer generated) are used for testing and comparing tomographic reconstruction methods. Data from physical phantoms include all physical effects associated with the detection of radiation. However, with physical phantoms it is difficult to control the number of detected counts, simulate the dynamics of uptake and washout, or create multiple noise realizations of an acquisition. Computer-generated phantoms can overcome some of the disadvantages of physical phantoms, but simulation of all factors affecting the detection of radiation is extremely complex and in some cases impossible. To overcome the problems with both types of phantoms, we developed a physical and computer-generated hybrid phantom that allows the creation of multiple noise realizations of tomographic datasets of the dynamic uptake governed by kinetic models. METHODS: The method is phantom and camera specific. We applied it to an anthropomorphic torso phantom with a cardiac insert, using a SPECT system with attenuation correction. First, real data were acquired. For each compartment (heart, blood pool, liver, and background) of the physical phantom, large numbers of short tomographic projections were acquired separately for each angle. Sinograms were built from a database of projections by summing the projections of each compartment of the phantom. The amount of activity in each phantom compartment was regulated by the number of added projections. Sinograms corresponding to various projection times, configurations and numbers of detector heads, numbers of noise realizations, numbers of phantom compartments, and compartment-specific time-activity curves in MBq/cm3 were assembled from the database. RESULTS: The acquisition produced a database of 120 projection angles ranging over 360 degrees . For each angle, 300 projections of 0.5 s each were stored in 128 x 128 matrices for easy access. The acquired database was successful in the generation of static and dynamic sinograms for which the myocardial uptake and washout was governed by a compartment kinetic model. CONCLUSION: A method has been developed that allows creation of sinograms of physical phantoms with the capacity to control the number of noise realizations, the level of noise, the dynamics of uptake in the phantom compartments, and the acquisition parameters and acquisition modes.
In this paper, we developed an analytical fan-beam reconstruction algorithm that compensates for uniform attenuation in SPECT. The new fan-beam algorithm is in the form of backprojection first, then filtering, and is mathematically exact. The algorithm is based on three components. The first one is the established generalized central-slice theorem, which relates the 1D Fourier transform of a set of arbitrary data and the 2D Fourier transform of the backprojected image. The second one is the fact that the backprojection of the fan-beam measurements is identical to the backprojection of the parallel measurements of the same object with the same attenuator. The third one is the stable analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan. The fan-beam algorithm is then extended into a cone-beam reconstruction algorithm, where the orbit of the focal point of the cone-beam imaging geometry is a circle. This orbit geometry does not satisfy Tuy's condition and the obtained cone-beam algorithm is an approximation. In the cone-beam algorithm, the cone-beam data are first backprojected into the 3D image volume; then a slice-by-slice filtering is performed. This slice-by-slice filtering procedure is identical to that of the fan-beam algorithm. Both the fan-beam and cone-beam algorithms are efficient, and computer simulations are presented. The new cone-beam algorithm is compared with Bronnikov's cone-beam algorithm, and it is shown to have better performance with noisy projections.
The assessment of regional heart wall motion (local strain) can localize ischemic myocardial disease, evaluate myocardial viability, and identify impaired cardiac function due to hypertrophic or dilated cardiomyopathies. The objectives of this research were to develop and validate a technique known as hyperelastic warping for the measurement of local strains in the left ventricle from clinical cine-magnetic resonance imaging (MRI) image datasets. The technique uses differences in image intensities between template (reference) and target (loaded) image datasets to generate a body force that deforms a finite element (FE) representation of the template so that it registers with the target image. To validate the technique, MRI image datasets representing two deformation states of a left ventricle were created such that the deformation map between the states represented in the images was known. A beginning diastolic cine-MRI image dataset from a normal human subject was defined as the template. A second image dataset (target) was created by mapping the template image using the deformation results obtained from a forward FE model of diastolic filling. Fiber stretch and strain predictions from hyperelastic warping showed good agreement with those of the forward solution (R2=0.67 stretch, R2=0.76 circumferential strain, R2=0.75 radial strain, and R2=0.70 in-plane shear). The technique had low sensitivity to changes in material parameters (deltaR2= -0.023 fiber stretch, deltaR2=-0.020 circumferential strain, deltaR2=-0.005 radial strain, and deltaR2=0.0125 shear strain with little or no change in rms error), with the exception of changes in bulk modulus of the material. The use of an isotropic hyperelastic constitutive model in the warping analyses degraded the predictions of fiber stretch. Results were unaffected by simulated noise down to a signal-to-noise ratio (SNR) of 4.0 (deltaR2= -0.032 fiber stretch, deltaR2=-0.023 circumferential strain, deltaR2=-0.04 radial strain, and deltaAR2=0.0211 shear strain with little or no increase in rms error). This study demonstrates that warping in conjunction with cine-MRI imaging can be used to determine local ventricular strains during diastole.
This paper presents analytical fan-beam and cone-beam reconstruction algorithms that compensate for uniform attenuation in single photon emission computed tomography. First, a fan-beam algorithm is developed by obtaining a relationship between the two-dimensional (2D) Fourier transform of parallel-beam projections and fan-beam projections. Using this relationship, 2D Fourier transforms of equivalent parallel-beam projection data are obtained from the fan-beam projection data. Then a quasioptimal analytical reconstruction algorithm for uniformly attenuated Radon data, developed by Metz and Pan, is used to reconstruct the image. A cone-beam algorithm is developed by extending the fan-beam algorithm to 4pi solid angle geometry. The cone-beam algorithm is also an exact algorithm.
A cone-beam image reconstruction algorithm using spherical harmonic expansions is proposed. The reconstruction algorithm is in the form of a summation of inner products of two discrete arrays of spherical harmonic expansion coefficients at each cone-beam point of acquisition. This form is different from the common filtered backprojection algorithm and the direct Fourier reconstruction algorithm. There is no re-sampling of the data, and spherical harmonic expansions are used instead of Fourier expansions. As a special case, a new fan-beam image reconstruction algorithm is also derived in terms of a circular harmonic expansion. Computer simulation results for both cone-beam and fan-beam algorithms are presented for circular planar orbit acquisitions. The algorithms give accurate reconstructions; however, the implementation of the cone-beam reconstruction algorithm is computationally intensive. A relatively efficient algorithm is proposed for reconstructing the central slice of the image when a circular scanning orbit is used.
MRI diffusion imaging is effective in measuring the diffusion tensor in brain, cardiac, liver, and spinal tissue. Diffusion tensor tomography MRI (DTT MRI) method is based on reconstructing the diffusion tensor field from measurements of projections of the tensor field. Projections are obtained by appropriate application of rotated diffusion gradients. In the present paper, the potential of a novel data acquisition scheme, PROPELLER (Periodically Rotated Overlapping ParallEL Lines with Enhanced Reconstruction), is examined in combination with DTT MRI for its capability and sufficiency for diffusion imaging. An iterative reconstruction algorithm is used to reconstruct the diffusion tensor field from rotated diffusion weighted blades by appropriate rotated diffusion gradients. DTT MRI with PROPELLER data acquisition shows significant potential to reduce the number of weighted measurements, avoid ambiguity in reconstructing diffusion tensor parameters, increase signal-to-noise ratio, and decrease the influence of signal distortion.
A novel approach to reconstructing the principal directions of a diffusion tensor field directly from magnetic resonance imaging (MRI) data using a tensor tomography data acquisition approach was developed. If tensor eigenvalues are assumed to be known, the reconstruction of principal directions requires fewer measurements than the reconstruction of the full tensor field. The tensor tomography data acquisition method (rotating diffusion gradients) leads to a unique reconstruction of principal directions, whereas the conventional MRI acquisition technique (stationary diffusion gradients) leads to an ambiguous reconstruction of principal directions when the same number of measurements are used. A computer-generated phantom was used to simulate the diffusion tensor field in the mid-ventricular region of the myocardium. The principal directions of the diffusion tensor field were assumed to align with the fibre structure of the myocardium. An iterative algorithm was used to reconstruct the principal directions. Computer simulations verify that the proposed method provides accurate reconstruction of the principal directions of a diffusion tensor field.
Factor analysis is a powerful tool used for the analysis of dynamic studies. One of the major drawbacks of factor analysis of dynamic structures (FADS) is that the solution is not mathematically unique when only nonnegativity constraints are used to determine factors and factor coefficients. In this paper, a method to correct for ambiguous FADS solutions has been developed. A nonambiguous solution (to within certain scaling factors) is obtained by constructing and minimizing a new objective function. The most common objective function consists of a least squares term that when minimized with nonnegativity constraints, forces agreement between the applied factor model and the measured data. In our method, this objective function is modified by adding a term that penalizes multiple components in the images of the factor coefficients. Due to nonuniqueness effects, these factor coefficients consist of more than one physiological component. The technique was tested on computer simulations, an experimental canine cardiac study using 99mTc-teboroxime, and a patient planar 99mTc-MAG3 renal study. The results show that the technique works well in comparison to the truth in computer simulations and to region of interest (ROI) measurements in the experimental studies.
Atherosclerotic plaque rupture is responsible for the majority of myocardial infarctions and acute coronary syndromes. Rupture is initiated by mechanical failure of the plaque cap, and thus study of the deformation of the plaque in the artery can elucidate the events that lead to myocardial infarction. Intravascular ultrasound (IVUS) provides high resolution in vitro and in vivo cross-sectional images of blood vessels. To extract the deformation field from sequences of IVUS images, a registration process must be performed to correlate material points between image pairs. The objective of this study was to determine the efficacy of an image registration technique termed Warping to determine strains in plaques and coronary arteries from paired IVUS images representing two different states of deformation. The Warping technique uses pointwise differences in pixel intensities between image pairs to generate a distributed body force that acts to deform a finite element model. The strain distribution estimated by image-based Warping showed excellent agreement with a known forward finite element solution, representing the gold standard, from which the displaced image was created. The Warping technique had a low sensitivity to changes in material parameters or material model and had a low dependency on the noise present in the images. The Warping analysis was also able to produce accurate strain distributions when the constitutive model used for the Warping analysis and the forward analysis was different. The results of this study demonstrate that Warping in conjunction with in vivo IVUS imaging will determine the change in the strain distribution resulting from physiological loading and may be useful as a diagnostic tool for predicting the likelihood of plaque rupture through the determination of the relative stiffness of the plaque constituents.
UNLABELLED: Quantitative gated SPECT (QGS) software has been reported to overestimate the left ventricular ejection fraction (LVEF) in patients with small hearts. This finding is caused by the inaccurate detection of the endocardial surface of the left ventricle (LV) due to low resolution and partial-volume effects. In this article we develop a method to calculate the LVEF from gated SPECT data without edge detection and compare it with the QGS method of calculating the LVEF. METHODS: The short-axis images were transformed to the prolate spheroid coordinate system, and detection of the layer of maximum counts (a surface area of maximum counts) was made. First, the volume enclosed by the layer of maximum counts (V(max)) was calculated; then the corresponding ejection fraction [(LVEF)(max)] was calculated. The LVEF was calculated by multiplying the (LVEF)(max) by a constant factor, which was determined from a series of calculations made using QGS on larger hearts. In computer simulations the end-diastolic left ventricular volume (EDV) and the targeted LVEF (tLVEF) were varied to produce LVs of different sizes. The LVs were modeled by 2 confocal hemiellipsoids with 7 different EDVs. The tLVEF was increased from 25% to 75%, in 5% step-size increments, for a total of 11 different ejection fractions. These datasets were then smoothed, creating a total of 77 smoothed sets. The smoothed images were processed by the QGS method and by our method. In patient studies, 58 patient datasets were processed by the QGS method and by our method. No attenuation correction was performed on these datasets. The patients were divided into 2 groups: 44 patients with large hearts (EDV > or = 80 mL) and 14 patients with small hearts (EDV < 80 mL). RESULTS: In computer simulations, the QGS method and our method performed well when imaging large EDVs (EDV > or = 80 mL). Our method derived better results than did the QGS method for small EDVs. In patient studies the LVEF calculated by our method matched well with the QGS LVEF in the 44 patients with large hearts. The correlation coefficient between them was found to be 0.957. Of the 14 patients with small hearts, the LVEFs of 5 patients were severely overestimated by the QGS method compared with the results obtained with our method. CONCLUSION: It is possible to calculate the LVEF without edge detection. Compared with QGS LVEF, our method gave better results for small LVs in computer simulations.
BACKGROUND: One of the major problems associated with technetium 99m teboroxime cardiac imaging is the high concentration of activity in the liver. In some cases it is impossible to diagnose defects on the inferior wall because of the finite resolution and scatter that cause images of the inferior wall and the liver to overlap. METHODS AND RESULTS: The least-squares factor analysis of dynamic structures method, with correction for non-unique solutions, was used to remove the liver activity from the image. The method was applied to dynamically acquired Tc-99m teboroxime data. The liver activity removal method was tested through use of computer simulations and tomographically acquired canine and patient cardiac studies. In all studies the least-squares factor analysis of dynamic structures method was able to extract the liver activity from the series of dynamic images, thereby making it possible to remove it quantitatively from the entire series. The method was used successfully to remove the liver activity that partially overlapped the inferior wall in normal hearts. The method tends to increase the contrast between defects and normal myocardial tissue in abnormal hearts. CONCLUSIONS: The method presented can be used to assist in diagnosis of cardiac disease when dynamically acquired teboroxime data are used. Because the contrast between the defect and normal myocardial tissue can be changed, the processed image cannot be used by itself to make an accurate diagnosis. However, with the liver activity removed, the image provides additional information that is very useful in the imaging of patients whose liver activity overlaps the inferior heart wall.