The use of intravascular contrast provides sufficient enhancement of signal strength to allow for very fast acquisitions. Injecting a large bolus of contrast in a short period of time allowed the subsequent rapid acquisition of diagnostic quality images of most vessels. However, properly triggering the acquisition has proven to be a significant problem. If the acquisition is started too early there is no enhancement and too late results in mostly venous enhancement. The real-time system under development attempts to solve the triggering problem by presenting the operator with two 2-dimensional views through the region of interest. These 2D planes through the ROI are updated at video frame rates (~10-30 fps) allowing the operator or a monitoring algorithm to trigger the 3D acquisition when the bolus arrives. The 2D acquisitions also provide a rare glimpse of the flow dynamics in the ROI. The hardware for this system consists of a 450 MHz Pentium II PC with several expansion cards. A 2 channel, 2 MHz/channel analog-to-digital converter which acquires I and Q from the MRI scanners fast receiver. The data is then processed on a dual TI TMS320C6701 floating-point digital signal processing board (~2 GFLOPs peak performance). Finally, the images are rendered and displayed using a fast graphics board. The software consists of three parts, the host data engine, the DSP module, and GUI to allow the operator to interact with the other two parts. The host data engine is being written in C++ and moves data from the A/D to host memory, then to the DSP and back, and finally to the graphics card. The DSP module must be written in C and performs the pre-contrast frame subtraction, inverse Fourier transform, and scaling and windowing for brightness and contrast. The GUI is being written in Java and will allow the operator to setup and start the acquisition, processing and display of the images.

The assessment of image quality is rigorously defined in terms of an observers ability to extract desired information from the image. For clinical assessment this is a clearly defined but narrow problem: a specific disease is selected and the ability to diagnose the disease with the specified imaging technique is assessed using an ROC experiment. The assessment of technical image quality is a messier problem. Since the image may ultimately be used for a variety of purposes, the technical measure must somehow be related to all the potential tasks. However, as another constraint the technical measure must be relatively simple and inexpensive. Technical assessment typically falls into one of three categories which I will label as (1) image characteristics, (2) observer performance, (3) observer preference. Each of these three approaches have their relative merits and weaknesses. They tend to be complimentary. In this presentation I will examine the usefulness of all three types of measures for the assessment of postprocessing techniques used in our lab for intracranial MRA images.

In this paper a new algorithm is presented for the segmentation and display of blood vessels from images obtained with magnetic resonance angiography (MRA) and other 3D angiographic imaging techniques. The developed algorithm is based on the observation that vessels are strongly evident in the MIP z-buffer as regions of high continuity and low local roughness. Roughness is measured here by the minimum c2 value of a low order local least squares fits in the principal directions through each point in the MIP z-buffer. Although some background pixels in the z-buffer exhibit low local roughness, the size of the connected region is nearly always much smaller than even the very smallest vessels that appear in the MIP image. It is shown that by applying connectivity to the regions of low roughness there is nearly complete separation between vascular detail and background. When connectivity is further applied in the original 3D image, vascular bed segmentation becomes nearly complete. The algorithm consists of three basic steps: (1). determination of the minimum local roughness at each point in the MIP z-buffer. (2). Connection of all neighboring points of low local roughness and (3). Connection of all points in the original 3D image matrix which are connected to the points determined in the MIP z-buffer and which are above an intensity threshold. The algorithm as presented is not optimized, but demonstrates a very strong potential for improved portrayal of vascular detail.

The Finite-Difference Time-Domain (FDTD) method is one of many electromagnetic analysis techniques. Because of its versatility, ease of use and ability to calculate the total electric and magnetic fields, it is becoming an important design and analysis tool in many areas of electromagnetics. With the desire to use higher Magnetic Resonance Imaging (MRI) field strengths combined with the complicated geometry of the human body, FDTD is being used more frequently in MRI Radio Frequency (RF) coil design. FDTD provides significant improvement in RF coil analysis when compared to the cumbersome and complicated methods of experiment and analytical analysis. In particular, FDTD has demonstrated relatively accurate detailed results regarding the Specific Absorption Rate (SAR) or power deposition in the body due to RF coils, and has the ability to provide wide band S-parameter results of a given coil design. Our RF coil lab has recently acquired a commercial FDTD package and is currently using the code to verify and develop experience with FDTD. Several coil designs have been studied including different coil configurations of the same coil. This presentation provides a brief description of the FDTD method. The various RF coil characteristics are also presented in conjunction with a demonstration of the capabilities of the FDTD technique as applied to RF coil design.

Vasculitis is a debilitating disease that affects many people. It is thought that the disease is under diagnosed. One of the reasons for this could be that the only diagnostic method is invasive. The goal of our study is to look at the utility of different MR techniques in diagnosing vasculitis. My primary focus in the study is to develop the statistical methods to determine if the MR techniques are useful. There are 3 different statistical methods that are appropriate. The first method uses jackknifing techniques to manipulate the data, and then an ANOVA design to analyze the data. The second method uses generalized estimating equations (GEE) which are an extension of the general linear model that take into account correlation between the covariates. The third method uses an ANOVA design to analyze the data, and a correction to the t-test is proposed to take into account the correlation between the covariates. I have found significant problems with this method and I will discuss possible solutions to these problems. Additionally and with time permitting I would like to run simulations and compare the three different methods. Finally, I would like to talk about issues concerning implementation issues when looking at this problem in ?real life?.

The development of diffusion measurement techniques have found recent clinical utility in mapping axonal white matter trajectories in the brain. This is of importance since the axons are responsible for conducting electrical signals between regions (e.g., cortex) responsible for functional stimulus and reception. In regions of brain tissue where the axons are uniformly and homogeneously organized, the diffusion tensor is highly anisotropic and the direction corresponding to the largest eigenvalue is most likely to be aligned with the fiber tracts. It is well known that the anisotropy decreases when oblique groups of axons are crossing or if there is gray matter or CSF contamination in the voxel. In addition, several measures of diffusion anisotropy with different characteristics have been proposed, which may lead to confusion or conflicting results. To improve our understanding of diffusion anisotropy in brain tissues, we heave developed a method for representing the tensor shape, called the three-phase plot. This plot is a graphical technique based upon a barycentric coordinate system, which weights the tensor shape by a combination of linear, cylindrical and spherical shape factors. This coordinate system can be used to map and segment different tissues based upon the tensor properties. We have used this plot to show the relationships between four well-known anisotropy measures -- the anisotropy index , the fractional anisotropy, the relative anisotropy and the volume fraction. We have also started to examine the effects on diffusion tensor measurements when there are oblique axons or multiple tissue compartments within a voxel. In some cases, it appears that the tensor description of diffusion breaks down, which can lead to inaccuracies in the tensor measurements. These cases will be presented as well as a discussion of an improved model for diffusion tensor MRI.

Water Proton spin self-diffusion tensor MRI imaging may be a useful technique both for assessing pathology and for surgical planning. These techniques may be able to provide information that is not available using conventional T1 and T2 relaxation weighted imaging techniques. Moreover, the directional information in the tensor field has potential applications in white matter axonagraphy. The accuracy of the extracted information depends on many acquistion and model-dependent elements such as motion, gradient cross talk and eddy current artifacts, encoding directions, diffusion time, gradient strength, slice thickness , partial volume effects, multi compartmentalization, echo time, etc. These factors behave like directional "filters" that can affect the interpretation of the extracted data per voxel and may lead to "non physical " under or overestimation of the diffusivities and the corresponding eigen vectors. In the last six months, we have focused on the impact of the choice of encoding directions on the extracted information and tested some procedures to optimize the encoding directions on a cube and a hemisphere with and without prior knowledge of the diffusion tensor and subject to constraints such as minimum propagation error etc. In the search for the optimal encoding and an optimal figure-of-merit , we have made theoretical predictions and performed Monte Carlo simulations. In an attempt to verify these model predictions we have performed an analysis of encoding strategy based on a non parametric bootstrap subsampling procedure with actual diffusion measurements on brain tissues. We applied this bootstrap analysis to compare various encoding strategies on normal volunteers as well as a water phantom.

An in vivo method for assessing fiber tracts in the white matter could provide a better knowledge of brain function and could be used as a tool in the study and diagnosis of the disorders affecting the white matter. We have started to develop methods for fiber bundle visualization and white matter fiber tracking.

High resolution diffusion tensor images are used for estimating the principal diffusivity directions for every voxel. For anisotropic (white matter) voxels, this describes the fiber tract direction. Voxel connectivity was obtained by considering the possible pathways in a conic neighborhood of each voxel. We present a series of images in the axial, coronal and sagittal plane in which the connections of fibers in corpus callosum, internal capsule and radiation fibers are clearly visible.

In Real-Time MRI, phase-encoding (PE) methods may not only affect the temporal resolution, but also the appearance of flow and patient movement in the sliding-window reconstructions. Our objective is to find the optimum sampling strategy (PE order) for contrast-enhanced MRA that has high temporal resolution while demonstrating a relatively smooth appearance of motion between image frames. To accomplish this objective, we have developed IDL programs to simulate dynamic objects changing in intensity, moving in one-dimension, moving in two-dimension, and a bolus moving in vessels. Then we used these dynamic phantoms to simulate different sampling strategies such as Keyhole, BRISK (block regional interpolation scheme for k-space), TRICKS (time-resolved imaging of contrast kinetics), CURE (continuous update with random encoding), and glimpse. Currently, we are exploring general properties of dynamic images in the temporal frequency domain to determine the optimum sampling strategy so that both the temporal resolution and the image quality can be improved.

The phase-encoding scheme can significantly affect the quality of fast spin-echo (FSE) images because the echo amplitude is modulated as a function of the echo position in k-space. The effect of the modulation in two-dimensional FSE imaging is ghosting and blurring artifacts and resolution loss in the phase-encoding (PE) direction. These problems are particularly severe for imaging small structures with short T2 or for long echo train length (ETL) pulse sequences. In 3D FSE imaging, the use of two phase-encoding directions presents the opportunity for improved PE schemes. A new scheme for assignment of echoes to views in 3D FSE, termed generalized, has been developed. This scheme distributes T2 effects along both PE directions allowing considerable flexibility in the selection of blurring artifacts appearance. In a set of simulation, phantom and in vivo experiments, the performance of the generalized PE scheme for 3D FSE imaging was compared with that of existing PE schemes. The results demonstrate the flexibility of the generalized PE scheme and its superiority over other PE techniques that are presently in use. This superiority manifests itself in reduced blurring, improved small object visualization, and optimized acquisition time. All these make the generalized PE 3D FSE sequence is a promising alternative to conventional 3D FSE sequences.

Introduction

Rutt and Liu developed the Sliding Interleaved ky (SLINKY)[1] technique to eliminate the slab boundary artifact (SBA) from multi-slab imaging. Proper reconstruction of SLINKY data requires preventing or removing k-space data inconsistencies.

Methods

We acquired fully sampled, highly overlapped datasets of both phantoms and volunteers. Proper sorting of the data enabled us to isolate and study possible sources of error which might lead to residual artifacts in SLINKY images. We made use of the data redundancy to remove the supposed errors and generate SLINKY reconstructions. We compared various reconstructions to determine the main source of residual SBA errors.

Results

SLINKY reconstructions currently assume a uniform response by tissues to the RF-excitation. Correction requires only simple multiplicative operations in k-space. Our results show that in regions with several tissue types, magnitude variations in the resulting excitation profiles would require deconvolution rather than multiplicative operations in k-space.

Discussion

We are now in a better position to state why the Highly Overlapped Thin Slab Acquisition (HOTSA) sequence is effective and in what cases it might fail to correct the residual SBA. These findings have implications for other implementations and uses of SLINKY: SLINKY phased array studies, navigator-free SLINKY, Sliding Interleaved Projection Reconstruction (SLIPR) [2] and Fast Spin Echo SLIPR (FSESLIPR).

References

[1] Liu K, Rutt BK: Sliding Interleaved ky (SLINKY) Acquisition: A Novel 3-D MRA Technique with Suppressed Slab Boundary Artifact. J Magn Reson Imag, 8:905:911, 1998

[2] Roberts J et. al. Sliding Interleaved Projection Reconstruction Acquisition (SLIPR) Proc. ISMRM 99 pg 159 Supported by NIH 1R01 HL48223, GE Medical Systems, Eccles Foundation

Being able to provide relatively high resolution in-vivo quantitative measurements of myocardial perfusion in ml/min/g with a standard MRI scanner could be extremely valuable clinically. Recently, this has been shown by others to be possible in a single slice with MRI using a Gd-DTPA bolus injection. The method involves mapping measured signal intensities to Gd-DTPA concentrations and then fitting concentration curves over time to compartmental models. We are attempting to extend this work to multiple slices, using a spoiled gradient echo pulse sequence recently developed by Picker. We have imaged a Gd-DTPA vial phantom to relate signal intensities to Gd-DTPA concentrations, and have acquired data from a normal volunteer (see Figure). The data is currently being analyzed by choosing regions of interest separately in each time frame to compensate for respiratory motion. Automation of the region of interest selection is planned. We also plan to improve this approach by developing further our methods that estimate compartmental model parameters without use of an input function. This would enable using larger Gd-DTPA doses which would improve SNR, and allow acquisition of the entire left ventricle, since temporal sampling could be reduced. A concern with these sequences is that with respiration, the single slice imaged actually reflects different spatial locations, including tissue from other slices, over time. Ideally, all of the necessary data could be acquired in a single breath hold. Alternatively, ways of warping the myocardium in different phases of respiration to a single ECG-gated slice may need to be explored.

If we know the general form of a impulse response function for several signal channels, but the impulse response has some unknown parameters individual to each channel, it may be possible to recover the original input signal and these parameters given the measured signals from each of the channels.

This method can be applied for estimating physiological parameters from dynamic PET, SPECT, or MRI images. In all of these cases, taking tissue time activity curves extracted from regions of interest as separate signal channels, we can potentially recover the blood input function needed

for parameter estimation. The conventional method of blood input function measurement is done by direct arterial blood sampling, which is invasive, time-consuming, requires extra staff and additional radiation exposure to clinical personnel.

The main difficulty of blind deconvolution is that if the channels have significant noise levels the method gives significant errors too. Efforts were made to denoise measured signals by decomposing them in the basis of Chebyshev polynomials and applying blind deconvolution to the modeled signals.

Preliminary results with noisy simulations show that the approach can work in certain cases. The blood input function found using this approach shows much better accuracy in some cases, but in some cases the issue of accuracy is still unresolved. In order to determine the range of applications of this method, necessary and sufficient conditions in terms of the parameters and the signals need to be defined.

Another approach we are pursuing is to find appropriate orthonormal bases for decomposition of the signals so as to improve the accuracy by reducing noise.

Adenosine is used as a vasodilator in animal and patient studies. It is used in stress studies to get enhanced contrast between the regions perfused by the stenosed artery and normal regions. The parameters estimated after using adenosine stress protocol will thus give a rough estimate of the coronary flow reserve. Dynamic teboroxime studies can be done by using continuous infusion of adenosine throughout the study, so that the flows are held constant, which is assumed in case of compartmental modeling methods. In patients however, 6 minute infusion of adenosine is given. The parameters estimated with these protocols can likely be different from each other. In order to verify this, canine data using continuous and 6 minute stress protocol are processed and the occlusion to normal ratios were compared. In addition to this, simulations were done for both protocols and the parameters were calculated for each.

In the canine study performed, adenosine was first administered with the standard patient protocol (0.14mg/kg/min infusion for 6 minutes with radionuclide injection at 3 minutes) and then 53 minutes later another study was done with adenosine infusion held constant at 0.14mg/kg/min. Also a computer simulation was done to see the effects of changing flows on the kinetic parameters.

The estimation of parameters using dynamic teboroxime data requires constant blood flow. In case of changes in blood flow, as in the 6 minute stress protocol, the parameters are underestimated and hence give inaccurate occluded to normal ratios. If the adenosine interval is increased then the parameters might be more similar to the continuous stress parameters.

A three dimensional finite element method is developed for large non-linear deformations of ventricular myocardium. To model the heart tissue, the incompressible, transversely isotropic hyper-elastic material is implemented. This method utilizes gated SPECT or gated MRI data by creating image driven external force in finite element governing equations. The method is developed to better and more realistically estimate the strain and stress of the myocardium by using imaging data in conjunction with the laws of continuum mechanics physics. The better estimation of the strains especially important in the case of gated SPECT where the estimation of the heart movement is very poor due to low resolution and noise. Also, with this method the estimation of stresses in the myocardial wall can be performed. The strains and stresses in myocardial wall are important determinants of heart performance.

Tensor tomography is being developed as an imaging technique that may aid in characterizing disease states by measuring in vivo tensor quantities such as diffusion, deformation (stress and strain), and conductivity. Of special interest is the possibility of using magnetic resonance imaging (MRI) to obtain in vivo estimates of 3D distributions of diffusion, strain, and stress tensor fields in the myocardium. It is interesting to note that various non-tomographic techniques using MRI to measure 3D distributions of diffusion and strain tensor fields have already been developed. The motivation behind this work is to determine if, for specific applications, tensor tomography could provide a more accurate and more efficient method of measuring tensor fields than the more direct techniques that have already been developed in MRI.

In previous work it has been shown that a symmetric tensor field can be decomposed into the sum of a solenoidal (symmetric and divergence-free) tensor field and an irrotational (symmetric and curl-free) tensor field. Three-dimensional reconstruction formulae (both filter-then-backproject [FBP] and backproject-then-filter [BPF] types) have been developed for reconstruction of the solenoidal and irrotational components of tensor fields that approach zero on their boundaries (i.e., are uniquely determined by a divergence-free and curl-free component). It has been shown that solenoidal measurements which include either one set of X-ray directional measurements (sampled over the entire sphere or on three separate Orlov circles), one set of X-ray directional measurements on one Orlov circle plus two sets of Radon directional measurements, or three sets of Radon directional measurements are sufficient for reconstructing the solenoidal component. It has also been shown that irrotational measurements, which include three sets of directional Radon measurements, are sufficient to reconstruct the irrotational component. The aim of this paper is to extend this work and develop general inversion formulae for the computed tomography of tensor fields on bounded domains with harmonic components.

If a tensor field is not zero on its boundary it may have a harmonic component which is both divergence-free and curl-free. The value of the field on the boundary contributes to both the irrotational and solenoidal measurements. Therefore, the reconstructed potential functions will include a contribution that arises from the harmonic field component. Through decomposition of the tensor field into homogeneous irrotational, homogeneous solenoidal, and harmonic fields we will show by extending Osman and Prince?s work for vector fields that: (i) the irrotational measurements can be used to image the homogeneous irrotational component (the curl-free component) and the harmonic component; and (ii) the solenoidal measurements can be used to image the homogeneous solenoidal component (the divergence-free component) and the harmonic component.

Due to finite system resolution of a SPECT detecting system, it is only necessary to sample the projection data in a coarse grid. Usually the projections are acquired in a 64x64 or 128x128 array, and the detector pixel size is about 0.90 or 0.45 cm, respectively. If one uses a 256x256 or 512x512 array to acquire data with a pixel size of 0.225 or 0.1125 cm, one does not gain any image resolution, but wastes computer memory. The detection resolution cannot be increased by using a finer sampling scheme. However, by using finer sampling, that is, oversampling, one can gain signal-to-noise ratio.

For example, when one samples 2 times finer than it is required according to the Nyquist principle, one can always obtain the "regularly" sampled image by summing 4 neighboring pixels into one. Nothing is lost and nothing is gained. If one can do something smarter than summing up 4 pixels, the signal-to-noise ratio can be increased by paying the price of oversampling.

If the "regularly" sampled image consists of N pixels, and the oversampled image consists of 4N pixels. A small N-dimensional subspace in the 4N-dimensional space contains the true (noise-less, but blurred) images. By "projecting" the oversampled image into the small subspace, the noise can be reduced. A maximum likelihood technique is proposed to perform this "projection". Applications in planar and SPECT imaging will be investigated.

In the cardiac model developed by Beyar and Sideman, the left ventricle (LV) was assumed to be a thick-walled ellipsoid. In our previous work, we applied the ellipsoid model to MCAT phantom data, and observed that the cardiac motion could be easily parameterized. For noisy cardiac SPECT data, large efforts should be made to preprocess the data in order to achieve possible success. In this work, the ellipsoid model was applied to a set of patient cardiac data. By performing the prolate spheroidal transformation, the endocardial and epicardial surfaces were transformed to approximately two straight lines, which could be tracked more easily at different time frames. This transformation makes it possible to quantitatively parameterize the motion of LV. The LV wall can be defined more reliably. In the transformed coordinate system, the generation of finite-element meshes gives better and finer meshes at the apical region of the left ventricle wall, and the generation process is simple and fast.

SPECT attenuation correction by transmission imaging has had only modest clinical acceptance as a viable technique to assist physicians in artifact reduction in scintigraphy. Expensive transmission sources and quality control requirements have been issues related to acceptance. Using a new moving point source design, the technical demands for routine clinical use have been reduced and additional clinical applications are being evaluated.

A pair of collimated Ba-133 point sources in fan beam geometry sweep across the crystal field to measure attenuation paths; followed by a blank reference calibration scan. The 350 keV photons from Ba-133 penetrate the septa of low energy collimators providing a fan beam transmission scan even with parallel hole collimators. Improved acquisition software allows both transmission scanning and cardiac gated data to be acquired by sequentially performing emission, then transmission data acquisition. Transmission and attenuation corrected emission reconstruction uses either MLEM or OSMLEM algorithms. The effect of scatter avoidance energy windowed data is being evaluated within this technique.

This new transmission imaging scheme allows the application of measured attenuation correction maps to SPECT imaging, with emphasis for cardiac imaging, or PET coincidence imaging. Compensation for attenuation, Compton scatter and spatially varying resolution in both SPECT and PET are integral components toward improved quantitation.

In cardiac SPECT imaging, it has been shown that the simultaneous transmission and emission protocol (STEP) has the advantage that the quantitative accuracy of the reconstructed images can be significantly improved by performing non-uniform attenuation correction (AC). However, it has been shown that AC sometimes results in an apparent apical defect in the reconstructed images. A set of clinical studies show that AC significantly affects the visual interpretation of Tl-201 stress/4 h-delay SPECT images. With AC, the specificity is increased in the right coronary artery (RCA) region, but the sensitivity in the left anterior descending artery (LAD) region is significantly decreased. In this work, we will study the effects of AC, detector response compensation (DRC), and scatter compensation (SC) in patient studies using fan beam STEP. It is shown that DRC in addition to AC significantly decreases the severity of the apparent apical defect, compared with AC. The visual quality of the reconstructed cardiac SPECT images is significantly improved. And quantitatively, the intensity at the apical region relative to that at the rest of the left ventricle (LV) wall (RI) is increased. SC in addition to both AC and DRC increases the LV wall-to-chucair contrast and increases the RI. Further work will be carried out to study the effects of DRC and SC, in addition to AC, on the detection of coronary artery diseases (CAD) in cardiac SPECT imaging in converging beam STEP, using ROC studies.

An iterative algorithm that reconstructs of attenuation map and emission activity distribution from emission data only is proposed based on semi-linearized attenuated Radon. At each step of the algorithm, emission activity distribution is first reconstructed, using the ML-EM algorithm and the attenuation map from previous iteration. Then the attenuation map is estimated by using obtained emission distribution and the emission projections. To find the attenuation map effectively in a possible class of solutions the attenuation map is constrained by an optimal basis set, derived from cross-correlation of a priory images or "knowledge set." Computer simulations show that the proposed algorithm has the capacity to effectively evaluate emission activity distribution and transmission map without transmission measurements.

Image reconstruction from cone-beam projection is desired both for single photon emission computed tomography (SPECT) and for X-ray computed tomography (CT). We have developed a novel image reconstruction method from cone-beam projections using spherical harmonics. The algorithm consists of three parts: 1) obtaining the first derivative of the plane integral (3D Radon transform) from cone-beam projections using harmonic expansion for each cone vertex position, 2) rebinning the data and calculating the second derivative, and 3) reconstructing the image by 3D Radon backprojection.

RSH uses segmented collimators that acquire multiple projections, from the region of interest, for each location of the detector. This increases the sensitivity of the system proportional to the number of segments used. The geometric point response function is the distribution of the number of photons striking the detector and depends on the aperture of the collimator holes, distance of the point source and collimator geometry. In most collimators the geometric point response function is symmetric about the central axis. It can be derived by considering only one collimator hole. For RSH the geometric point response is asymmetric and varies with the distance from the collimator. It was however observed to be shift invariant for a given depth. We used the frequency domain implementation to correct for the geometric response. In this method the 2D fourier transform of the geometric point response and the image plane of the same depth are multiplied. The 2D inverse fourier transform of the above plane is then projected in the conventional way.

The RSH collimator has three active regions depending on the center of the common volume and they were found to be:

Case 1: xq1 = (xn *C + 0.5 *S)(L +B) /Z

xr1 = ([Z +L +(xn+1)B]C + (L tan(30°) -0.5*S)(Z +L +B))/(Z +L)

Case 2: xq2 = (xn *C *B + (L *tan30° +0.5 *S)(Z +L +B))/(Z +L)

xr2 = (C[Z + (xn +1)L + (xn +1)B] - 0.5 *S(Z +L +B)) /Z

Case 3: xq3 = (xn*(L +B) + 0.5 *S(Z +L +B))/Z

xr3 = (C[Z + L + (xn+1)B] - (L *tan(30°) +0.5 *S) (Z +L +B)) /(Z +L)

Y- axis : yq = (yn *C *(L+B) + 0.5 *S *(Z+L+B))/Z;

yr = ((Z +L +(yn+1)*B) *C - (Z +L +B) *0.5 *S)/(Z +L);

where xq1, xq2 and xq3 represent the shadow or dead space where as xr1, xr2 and xr3 represent the sum of the active region and the shadow corresponding to the collimator hole under consideration in the X-direction, yq and yr is the corresponding regions in the Y-direction, Z is the distance of the point source from the collimator, L is the collimator thickness, B is the distance of the crystal from the collimator, S is the thickness of the septa, xn*C and yn*C are the distance from the center of the collimator, 30° is the slant angle of the collimator, D is the length of the detector, F is the center of the common volume and equals D/(4*tan(30°))and Xoff is the difference between the F and the point source Z.

The linogram is now a familiar concept to experts in the field of Image Reconstruction from Projections. Linograms were invented by Paul Edholm of Linköping University. The basic idea is that rather than the conventional (f ,s) parameters used to describe the collection of line integrals measured by a scanner ("sinogram" sampling), a special choice of parameters ("linogram" parameters (u,v)) is used, leading to a more convenient and faster backprojection operation. Backprojection is usually the rate determining step in reconstruction algorithms, and this is particularly true when fully three-dimensional (3D) backprojection is required. The planogram is a 3D extension, masterminded by Paul Kinahan of the University of Pittsburgh, of the linogram concept and it is the basis for a novel, fast, and accurate method of performing the time-consuming 3D backprojection needed for 3D PET reconstructions. Improvements in reconstruction times of about 2 orders of magnitude are anticipated for conventional 3D PET geometries, and even more improvement is expected for dual SPECT/PET systems.

This research project consists of an investigation and implementation of the planogram concept, with applications directed at PET systems that use large-area detectors. Since many two-headed SPECT cameras are being enhanced with coincidence detection capability, the advance anticipated by using planograms is particularly timely. The presentation will focus on planogram concepts, and illustrate the steps involved to perform fully 3D backprojection and image reconstruction for a generic planar-detector 3D PET system. The research project involves theoretical developments and implementation for proof-of-concept. The resulting algorithm will be tested using simulated data and PCD data measured on the IRIX SPECT camera. Comparisons will be made against standard 3D PET algorithms to verify accurate reconstruction and to measure improvements in reconstruction speed.

A ?partial-rebinning? scheme and iterative reconstruction algorithm are described for fully 3D nuclear medicine imaging. The reconstruction framework is developed in the context of positron emission tomographic imaging performed with rotating planar detectors acting in coincidence-mode. The data are binned into series of direct and oblique 3D sinograms using coarse sampling in polar angles ("tilts") in order to reduce the size of the data set and computational burden of the reconstruction. This binning results in depth-dependent axial blurring, but the coarse polar sampling reduces this blurring relative to single-slice rebinning. There is a tradeoff between the number of tilts used, the degree of axial blurring, and the reconstruction time, and the number of tilts can be tuned for specific applications. Compensation for axial blurring can be performed by modeling the binning kernel and point response function during iterative reconstruction. Using this binning procedure, the fully 3D reconstruction problem can be broken into a series of subsets of multi-slice 2D reconstructions. A rotation-based projector is used, which has the benefit that reconstruction models and compensation methods developed for 2D reconstruction can be easily adapted to the fully 3D problem. The approach also brings potential benefits by preserving the Poisson statistical nature of the data, providing user-defined choice of axial resolution vs. reconstruction time tradeoff, potentially providing very accurate attenuation compensation, and retaining the fully 3D sampling qualities of the acquired data.