Single-photon emission computed tomography

The subject of singl-photon emission computed tomography (SPECT) is generally reviewed. The basic interaction processes of gamma rays in matter are outlined, and the formation of conventional gamma-ray images is described. We then outline the extension of these concepts to the formation of three-dimensional or tomographic images. Of particular concern in emission tomography, the effects of gamma-ray attenuation and scattering are outlined. Several examples are given of practical SPECT systems, and representative results are given.     

Three-dimensional simulation of planar semiconductor diodes

Accurate three-dimensional simulation results are presented, showing the geometry dependence of the current of a planar diode. Comparison of the three-dimensional simulation to one- and two-dimensional results reveals the range of validity of simplified models based on lower-dimensional analysis. The current of square and rectangular junctions is approximated by analytical expressions that provide insight about the bulk and the edge components     

Three-dimensional simulation of inverse narrow-channel effect

Based on a three-dimensional numerical analysis, it is shown that narrow-width MOSFETs of the BOX structure1 exhibit an `inverse? narrow-channel effect whereby their threshold voltages become lower and lower with decreasing channel width. The phenomenon is attributed to a pronounced enhancement of the channel edge region due to a crowding of the fringing field.     

Three-dimensional edge-preserving image enhancement for computed tomography

Computed tomography (CT) images exhibit a variable amount of noise and blur, depending on the physical characteristics of the apparatus and the selected reconstruction method. Standard algorithms tend to favor reconstruction speed over resolution, thereby jeopardizing applications where accuracy is critical. In this paper, we propose to enhance CT images by applying half-quadratic edge-preserving image restoration (or deconvolution) to them. This approach may be used with virtually any CT scanner, provided the overall point-spread function can be roughly estimated. In image restoration, Markov random fields (MRFs) have proven to be very flexible a priori models and to yield impressive results with edge-preserving penalization, but their implementation in clinical routine is limited because they are often viewed as complex and time consuming. For these practical reasons, we focused on numerical efficiency and developed a fast implementation based on a simple three-dimensional MRF model with convex edge-preserving potentials. The resulting restoration method provides good recovery of sharp discontinuities while using convex duality principles yields fairly simple implementation of the optimization. Further reduction of the computational load can be achieved if the point-spread function is assumed to be separable. Synthetic and real data experiments indicate that the method provides significant improvements over standard reconstruction techniques and compares well with convex-potential Markov-based reconstruction, while being more flexible and numerically efficient.     

Maximum likelihood reconstruction for emission tomography

Previous models for emission tomography (ET) do not distinguish the physics of ET from that of transmission tomography. We give a more accurate general mathematical model for ET where an unknown emission density lambda = lambda(x, y, z) generates, and is to be reconstructed from, the number of counts n(*)(d) in each of D detector units d. Within the model, we give an algorithm for determining an estimate lambdainsertion mark of lambda which maximizes the probability p(n(*)|lambda) of observing the actual detector count data n(*) over all possible densities lambda. Let independent Poisson variables n(b) with unknown means lambda(b), b = 1, ..., B represent the number of unobserved emissions in each of B boxes (pixels) partitioning an object containing an emitter. Suppose each emission in box b is detected in detector unit d with probability p(b, d), d = 1, ..., D with p(b,d) a one-step transition matrix, assumed known. We observe the total number n(*) = n(*)(d) of emissions in each detector unit d and want to estimate the unknown lambda = lambda(b), b = 1, ..., B. For each lambda, the observed data n(*) has probability or likelihood p(n(*)|lambda). The EM algorithm of mathematical statistics starts with an initial estimate lambda(0) and gives the following simple iterative procedure for obtaining a new estimate lambdainsertion mark(new), from an old estimate lambdainsertion mark(old), to obtain lambdainsertion mark(k), k = 1, 2, ..., lambdainsertion mark(new)(b)= lambdainsertion mark(old)(b)Sum of (n(*)p(b,d) from d=1 to D/Sum of lambdainsertion mark()old(b('))p(b('),d) from b(')=1 to B), b=1,...B.     

Three-dimensional microwave tomography: initial experimentalimaging of animals

The purpose of this study was to construct a microwave tomographic system capable of conducting experiments with whole scale biological objects and to demonstrate the feasibility of microwave tomography for imaging such objects using a canine model. Experiments were conducted using a three-dimensional (3-D) microwave tomographic system with working chamber dimensions of 120 cm in diameter and 135 cm in height. The operating frequency was 0.9 GHz. The object under study was located in the central area of the tomographic chamber filled with a salt solution. Experimentally measured attenuation of the electromagnetic field through the thorax was about -120 dB. To obtain images, we used various two-dimensional and 3-D reconstruction schemes. Images of the canine were obtained. In spite of imperfections, the images represent a significant milestone in the development of microwave tomography for whole body imaging and demonstrate its feasibility.     

Deformable template models for emission tomography

The reconstruction of emission tomography data is an ill-posed inverse problem and, as such, requires some form of regularization. Previous efforts to regularize the restoration process have incorporated rather general assumptions about the isotope distribution within a patient's body. A theoretical and algorithmic framework is presented in which the notion of a deformable template can be used to identify and quantify brain tumors in pediatric patients. Patient data and computer simulation experiments are presented which illustrate the performance of the deformable template approach to single photon emission computed tomography     

Three-dimensional finite-element thermal simulation of GaN-based HEMTs

The aim of this paper is to show and discuss results of three-dimensional finite-element thermal simulation of GaN HEMT structures. HEMTs differing by geometry, substrate material, passivation, and cooling strategy are simulated and compared in order to give a picture of the complex interplay of factors that must be reckoned with for proper thermal modeling and management.     

Three-dimensional method for simulation of multimode interferencecouplers

A three-dimensional (3-D) method for modeling multimode interference devices based on a finite element formulation is presented as an alternative to models having one-dimensional cross-sections only. The method is tested for couplers with two different strongly confined waveguides structures. The results show that full treatment of two-dimensional cross-section is of special importance for design and simulation of waveguide devices for which the effective index approximation is no longer valid. For deep rib waveguide geometries, excess loss greater than 15 dB can be obtained if the 3-D method is not used in the design of the couplers     

Three-dimensional simulation of multistage depressed collectors onmicro-computers

A three-dimensional (3-D) package for simulation of asymmetric and crossed-field multistage depressed collectors for microwave tubes has been developed. This package is based upon the 3-D finite-difference code KOBRA3-INP. The main features of the package are a user-friendly input interface, post-processors for collector analysis and calculation of secondary electron trajectories, and versatile output graphics. Both PC and mainframe versions of the package have been developed. The results of simple benchmark tests and those of simulation and analysis of asymmetric and crossed-field collectors including the effects of secondary electrons are presented. It is found that the asymmetric hyperbolic electric field collector shows very low backstreaming. It is shown that the representation of trajectories in energy space gives a better insight into the behavior of individual trajectories than plotting in coordinate space. The package will be useful for designing novel types of depressed collector     

Three-dimensional numerical simulation of local oxidation ofsilicon

The nitride mask bending stress is modeled in three dimensions by using the beam bending theory. The stress effect on the oxide growth is taken into account for the accurate evaluation of the oxide shape. The three-dimensional behavior of oxide growth is investigated by using three typical mask structures, which are called the hole (contact), island, and line structures. The mask structure effect and narrow mask effect on the bird's beak length are simulated and discussed in comparison with the experimental data obtained by the top-view scanning electron microscopy (SEM) observation. Three-dimensional effects of the oxide thickness of local oxidation of silicon (LOCOS) structures are predicted by comparing simulations with two-dimensional effects obtained by the cross-sectional SEM observation. It is found that the bird's beak length at the corner of the mask edge is much enhanced in the hole structure and retarded in the island structure. This result is explained by the three-dimensional effect on the oxidant diffusion and the nitride bending stress     

Resampling estimates of precision in emission tomography

Methods for estimating the regional variance in emission tomography images which arise from the Poisson nature of the raw data are discussed. The methods are based on the bootstrap and jackknife methods of statistical resampling theory. The bootstrap is implemented in time-of-flight PET (positron emission tomography); the same techniques can be applied to non-time-of-flight PET and SPECT (single-photon-emission computed tomography). The estimates are validated by comparing them to those obtained by repetition of emission scans, using data from a time-of-flight positron emission tomograph. Simple expressions for the accuracy of the estimates are given. The present approach is computationally feasible and can be applied to any reconstruction technique as long as the data are acquired in a raw, uncorrected form.     

Three-dimensional PET emission scan registration and transmissionscan synthesis

The duration of a positron emission tomography (PET) imaging scan can be reduced if the transmission scan of one patient which is used for emission correction can be synthesized by using the reference transmission scan of another patient. In this paper, we propose a new intersubjects PET emission scan registration method and PET transmission synthesis method by using the boundary information of the body or brain scan of the PET emission scans. The PET emission scans have poor image quality and different intensity statistics so that we preprocess the emission scans to have a similar histogram and then apply the point distribution model (PDM) to extract the contours of the emission scan. The extracted boundary contour of every slice is used to reconstruct the three-dimensional (3-D) surface of the reference set and the target set. Our registration is 3-D surface-based which uses the normal flow method to find the correspondence vector field between two 3-D reconstructed surfaces. Since it is difficult to analyze internal organs using PET emission scan imaging without correction, we assume that the deformation of internal organ is homogeneous. With the corresponding vector field between the two emission scans and the transmission scan of the reference set, we can synthesize the transmission scan of the target set     

Three-dimensional topography simulation model: etching andlithography

An etching model in which topography is derived by solving a modified diffusion equation is introduced. This model is simple and makes it possible to simulate three-dimensional (3-D) topography accurately and quickly. Based on this model, a 3-D topography simulator which can be applied in the development of photolithography and isotropic/anisotropic etching has been developed. With this simulator, it is possible to simulate the series processes and multilayer etching, such as contact hole and trench etching. By simulating photolithography, diffraction and standing-wave effects can be found clearly in the 3-D topography of the developed photoresist. In the case of an etching process which is restricted by diffusion, the dependence of the etch front topography on the window width of the mask is examined     

Super-resolution in respiratory synchronized positron emission tomography

Respiratory motion is a major source of reduced quality in positron emission tomography (PET). In order to minimize its effects, the use of respiratory synchronized acquisitions, leading to gated frames, has been suggested. Such frames, however, are of low signal-to-noise ratio (SNR) as they contain reduced statistics. Super-resolution (SR) techniques make use of the motion in a sequence of images in order to improve their quality. They aim at enhancing a low-resolution image belonging to a sequence of images representing different views of the same scene. In this work, a maximum a posteriori (MAP) super-resolution algorithm has been implemented and applied to respiratory gated PET images for motion compensation. An edge preserving Huber regularization term was used to ensure convergence. Motion fields were recovered using a B-spline based elastic registration algorithm. The performance of the SR algorithm was evaluated through the use of both simulated and clinical datasets by assessing image SNR, as well as the contrast, position and extent of the different lesions. Results were compared to summing the registered synchronized frames on both simulated and clinical datasets. The super-resolution image had higher SNR (by a factor of over 4 on average) and lesion contrast (by a factor of 2) than the single respiratory synchronized frame using the same reconstruction matrix size. In comparison to the motion corrected or the motion free images a similar SNR was obtained, while improvements of up to 20% in the recovered lesion size and contrast were measured. Finally, the recovered lesion locations on the SR images were systematically closer to the true simulated lesion positions. These observations concerning the SNR, lesion contrast and size were confirmed on two clinical datasets included in the study. In conclusion, the use of SR techniques applied to respiratory motion synchronized images lead to motion compensation combined with improved image SNR and contrast, without any increase in the overall acquisition times.     

Three-gamma annihilation imaging in positron emission tomography

It is argued that positron annihilation into three photons, although quite rare, could still be used as a new imaging modality of positron emission tomography. The information gained when the three decay photons are detected is significantly higher than in the case of 511 keV two-gamma annihilation. The performance of three-gamma imaging in terms of the required detector properties, spatial resolution and counting rates is discussed. A simple proof-of-principle experiment confirms the feasibility of the new imaging method.     

Three-dimensional head model simulation of transcranial magnetic stimulation

This paper presents a finite element method used to evaluate the induced current density in a realistic model of the human head exposed to a time varying magnetic field. The tissue electric properties were varied to ascertain their influence on the induced currents. Current density magnitude and vector plots were generated throughout the tissue layers to determine the effects of tissue boundaries on the field. The current density magnitude correlated to the conductivity of the tissue in all the cases tested except where the tissue permittivity was raised to a level to allow for displacement currents. In this case, the permittivity of the tissue was the dominant factor. Current density components normal to the tissue interface were shown to exist in all solutions within the cortex contrary to the predictions of present models that rely on symmetrical geometries. Additionally, modifications in the cortical geometry were shown to perturb the field so that the site of activation could be altered in diseased patient populations. Finally, by varying the tissue permittivity values and the source frequency, we tested the effects of alpha dispersion theories on transcranial magnetic stimulation.     

Reconstruction of emission tomography data using origin ensembles

A new statistical reconstruction method based on origin ensembles (OE) for emission tomography (ET) is examined. Using a probability density function (pdf) derived from first principles, an ensemble expectation of numbers of detected event origins per voxel is determined. These numbers divided by sensitivities of voxels and acquisition time provide OE estimates of the voxel activities. The OE expectations are shown to be the same as expectations calculated using the complete-data space. The properties of the OE estimate are examined. It is shown that OE estimate approximates maximum likelihood (ML) estimate for conditions usually achieved in practical applications in emission tomography. Three numerical experiments with increasing complexity are used to validate theoretical findings and demonstrate similarities of ML and OE estimates. Recommendations for achieving improved accuracy and speed of OE reconstructions are provided.     

Three-dimensional electrical impedance tomography based on thecomplete electrode model

In electrical impedance tomography an approximation for the internal resistivity distribution is computed based on the knowledge of the injected currents and measured voltages on the surface of the body. It is often assumed that the injected currents are confined to the two-dimensional (2-D) electrode plane and the reconstruction is based on 2-D assumptions. However, the currents spread out in three dimensions and, therefore, off-plane structures have significant effect on the reconstructed images. In this paper we propose a finite element-based method for the reconstruction of three-dimensional resistivity distributions. The proposed method is based on the so-called complete electrode model that takes into account the presence of the electrodes and the contact impedances. Both the forward and the inverse problems are discussed and results from static and dynamic (difference) reconstructions with real measurement data are given. It is shown that in phantom experiments with accurate finite element computations it is possible to obtain static images that are comparable with difference images that are reconstructed from the same object with the empty (saline filled) tank as a reference.