The Z-buffer Segmentation Algorithm (ZBS) that we presented previously performed image segmentation based upon positional smoothness and continuity of objects that appear in the maximum intensity projection (MIP) of the MRA image data. The MIP Z-buffer, consisting of the original "Z" positions of each point that projects into the MIP image, provides a 2D image that is processed to look for positional smoothness around every point in the MIP image. In this presentation we will review several improvements that have been made since the initial description of the algorithm. These include improvement to the display, the segmentation algorithm, and the acquisition technique. 1) Display improvements: working with our Neurosurgery and Neuroradiology collaborators, we have developed a reduced dynamic range display with a rapid and intuitive user interface, and a variety of options to view the original image data (or MIP of the original data) in conjunction with the ZBS structure. 2) Segmentation algorithm improvements: we have also developed and are evaluating a multiple-MIP (multiple-direction, multiple overlapping slab) segmentation algorithm. The original algorithm operated on the Z-buffer from a single axial collapse MIP image. The new algorithm allows multiple directions and multiple thicknesses of the MIP algorithm to be investigated. 3) Finally, we have found the segmentation to be somewhat sensitive to ghosting artifacts related to the flow in the circle of Willis of some patients. We hypothesize that this artifact is related to the difference in timing between the phase and frequency encoding pulses. This timing difference in conjunction with the pulsatile motion of the blood results in pseudo motion of the blood vessels. The artifact is reduced by either bipolar 1st order gradient nulling of the phase encoding pulses or an elliptical centric acquisition, or both.

Diffusion Tensor Imaging can provide information about the degree of anisotropy and the orientation of the fibrous tissues. Of special interest is the possibility of using this information in order to construct maps of white matter connectivity in the human brain. Assessment of white matter projections in the human brain in vivo may enlarge the understanding of the functional integration process of the brain and may be of clinical use. Previous studies [1,2] have demonstrated the reconstruction of specific white matter tracts by using the major tensor eigenvector as the most probable fiber direction. Even this method gives good results for white matter bundles with high anisotropy, there are few limitations that will be addressed. The difficulties in fiber tracking arise from the high complexity of the brain white matter organization as well as from the limitations of the imaging experiment such as image noise and partial voluming. In this study we have investigated the tensorline algorithm [3], a recently described method for white mater tracking in diffusion tensor fields. The tensorline technique employs the entire diffusion tensor for the propagation of streamlines in the tensor field. This approach appears to demonstrate better results than the regular approach in white matter regions of

relatively low anisotropy (such as crossing fibers regions). Using tensorline method some of the major white matter tracts of the brain were reconstructed. In order to verify how the noise and partial voluming affects the accuracy of the fiber tracking we simulated diffusion tensor data. The deviation from the ideal path increases with the distance from the seed points and the higher level of noise. In the case of low anisotropy data sets, tensorline algorithm exhibits significantly lower deviation than the regular streamline approach.

[1] Mori, S. , Crain,B.J.,Chacko,V.P. & van Zijl, P.C., Ann.Neurol. 45, 265-269, 1999

[2] Conturo, E.T. at al. Proc.Natl.Acad.Sci. , 96, 10422-10427, 1999

[3] Weinstein, D. and Kindlmann,G., Proc. IEEE Visualization, 1999

Diffusion tensor magnetic resonance imaging (DT-MRI) is a promising tool for analyzing the structure of nerve bundles in white matter. Previously, we have proposed a method for detecting nerve fiber bundles in white matter using diffusion tensor images. This method was used to analyze human brain data. However, there are still problems in the investigation of the connectivity of nerve bundles. The main problem encountered is the noise contamination. To solve such problems, we considered a scalar potential field using several attributes of the diffusion tensor. The goal of this study is to obtain a qualitative map of the connectivity of the nerve bundles in vivo using scalar field formalism. The scalar fields include fractional anisotropy (FA), and the similarity of the principal axis of the diffusion tensor combined with FA. To construct the scalar potential field, we multiply the magnitude of these fields. The feasibility of the scalar potential field approach is tested by comparing it with the conventional FA maps. The proposed method can also be used to calculate the connectivity of nerve bundles between any two points in the field and shows less sensitivity to measurement noise. Recently this procedure has been extended to estimate brain tissue connectivity by including the whole decoded diffusion tensor. This approach may be more robust in determining brain connection patterns.

MR images that are reconstructed by standard Fourier techniques have uniform spatial resolution and noise distribution throughout the image. This type of reconstruction is reasonable when all imaged objects have the same or close signal-to-noise ratios (SNRs). However, when SNRs of imaged objects are distributed in a wide range of values (from high SNR to very low SNR) the standard reconstruction may not be ideal. Images of low SNR (low intensity) objects could be completely degraded by noise. The noise power is proportional to the percent of

k-space used for reconstruction, therefore, it is reasonable to reconstruct images with low intensity objects using only part of k-space. In this case, the SNR and the noise-limited resolution of these objects would be improved but the theoretical image resolution for these images would be decreased everywhere. Therefore, the ideal MRI reconstruction technique should use different percentage of k-space to reconstruct pixels with different SNR values. The technique requires the knowledge of SNR for each pixel which may be estimated by using phase images. A variable percent k-space reconstruction technique using these principles has been developed. The technique uses the estimated value of SNR for each pixel to determine how large part of k-space should be used to reconstruct the pixel. The application of this reconstruction technique for data acquired by phase-array coil demonstrated improved image contrast and noise suppression.

In the analysis of MR angiographic data, our group has developed a set of quantitative measures that can be applied along the length of a vessel. Two common measures include the signal to noise ratio and the signal difference to noise ratio. The application of a measure along the length of a vessel requires the segmentation of the vessel and the determination of the "centerline" of the vessel. Definitions of the vessel centerline vary, but in general depend upon voxel intensities in the vessel cross section. The development of the Z-Buffer Segmentation Algorithm for segmenting vessel data from the MR volume makes it possible to consider automating segmentation, centerline extraction and subsequent data analysis. To this end, we have been exploring what is referred to in computer graphics literature as object skeletonization. An object skeleton may be thought of as a very compact topology- (or shape-) preserving representation of the original object. We propose to apply automated skeletonization techniques to the segmented vessel data to extract the underlying vessel "skeleton." With the skeleton as reference we will then determine the centerlines using voxel intensities. The skeletonization algorithms may also provide a very convenient means for determining vessel lengths and detecting and locating bifurcations. Such information may be readily used for compact data representation and registration between datasets. We will give a basic introduction to skeletonization and discuss its application to our own data.

In this paper, we developed a semi-automatic algorithm to segment the left ventricle (LV) from gated SPECT data and to generate a finite element mesh for the finite element software package ABAQUS. The LV can approximately be treated as a hollow cylinder sealed at the apex. To detect the surfaces of the LV, the apex should be treated differently from the rest. A combination of polar coordinates (for the apex region) and cylindrical coordinates (for the base region) has been used to transform the images of the LV into approximate planes. The segmentation was performed on the transformed images. Different edge detection algorithms can be implemented by the user. Upon the successful segmentation of the LV, the finite element mesh is generated in ABAQUS format. The whole process is automatic except for initially locating the origin of the polar-cylindrical coordinate system in the LV cavity. Global parameters of the LV such as volume of the cavity, volume of the myocardium, and the ejection fraction can be calculated upon the successful segmentation of the LV. The method has been applied to the MCAT phantom and several patient studies. It works well for the MCAT phantom and needs further validation for SPECT data.

Image based finite element analysis of the left ventricle will be used to quantify the effects of myocardial infarction, dilated and hypertrophic cardiomyopathy on the passive and active behavior of the humen left ventricle (LV). Initially, the passive behavior of the normal heart will be studied using a image based finite element program. This method, called Warping, uses the image data to create a body force that deforms the finite element model and track tissue deformation. This body force is based on the pointwise difference in pixel intensities between the reference and the loaded images.

Since the passive behavior of the left ventricle was of interest, the image corresponding to the beginning of passive filling, was designated as the reference image and the image corresponding to the end of diastole was designated the loaded image. The left ventricular wall shown in the reference image was manually segmented and a two dimensional finite element mesh was created. The Warping version of the non-linear finite element program NIKE3D (NIKE3Di, Lawrence Livermore National Laboratory) was used to analyze the images. No other loads were placed on the LV model.

Comparison of average stretch as determined by Warping and measured by macromechanical measurements of the images showed excellent agreement (<5% error) for both the average lumen circumferential stretch and the average stretch of the external boundary.

The results indicate that this technique may be appropriate for high-resolution analysis of effects of myocardial infarction, dilated and hypertrophic cardiomyopathy on the passive and active behavior of the human left ventricle.

Many MRI applications such as cardiac imaging, functional MRI (fMRI), contrast-enhanced dynamic imaging, time-resolved angiography involve the collection of a time series of images of the same slice or volume to monitor a dynamic process. To capture the details of the dynamic process, it is important to obtain both high temporal resolution and high spatial resolution. However, there is typically a trade-off between imaging speed and spatial resolution. Several sampling strategies have been proposed to improve both the temporal and spatial resolution. Such methods include Keyhole imaging, Reduced-Encoding Imaging through Generalized-Series Reconstruction (RIGR), Time Resolved Imaging of Contrast Kinetics (TRICKS), and Glimpse. These methods share the same goal: to reduce the amount of data needed for a given spatial and temporal resolution. In most cases, the acquisition data are concentrated on the low spatial frequency. However, dynamic image changes can occur at any view in k-space. Low spatial frequency views provide crucial position and contrast information, while high spatial frequency views provide edge and detail information. Also, for these methods, it is difficult to predict the accuracy of the image. We investigate the properties of the temporal power spectra of k-space views and present a new way to predict the minimum error of the dynamic imaging for the different sampling strategies. Furthermore, the temporal frequency power spectrum provides a possibility to predict the locations in k-space where the dynamic changes will occur, then the most effective sampling strategy can be determined. In this study, two dynamic sampling schemes, Keyhole and Full Sequential, are compared. Both simulation of a contrast-enhanced arterial bifurcation and experimental cardiac imaging study are presented.

Measurements of the dynamic transfer of a tracer into and out of regions of interest can provide a wealth of clinically relevant data. These 4D data can be considered as a collection of time-activity curves (one for each measured voxel). Here we focus on using only the temporal information from each voxel and neglect the spatial information present in the data. That is, given a set of time-activity curves, can we extract some few basis curves that contain maximal physiologic information and have optimal SNR? Two approaches are investigated: 1. Factor analysis-type where each curve is considered a linear combination of underlying basis curves, and 2. K-means type classification which examines distances between curves. In the latter method, several different curve metrics are explored, and a term has been added to accommodate some overlap in time signatures. Compartmental models are included in some of the formulations to regularize the solution. This work aims to eventually use both spatial and temporal information jointly to find optimal segmentations and physiologic basis curves for dynamic MRI, SPECT, and PET data sets.

Clinically, cardiac SPECT is performed with static imaging protocols and visually assessed for perfusion defects based upon the relative intensity of myocardial regions. Dynamic imaging, however, has the potential to provide quantitative measures of flow, possibly improving diagnosis. The objective of this study was to compare the information content of dynamic and static thallium SPECT imaging as measures of myocardial perfusion. To make this comparison, canine studies and patient studies were performed. The canine studies were done by occlusion of the left anterior descending coronary artery to evaluate contrast ratios between normal and hypoperfused regions. Microsphere-derived flow estimates were used as the gold standard. Dynamic SPECT imaging was performed at rest and under adenosine stress and subsets of the data were summed to provide corresponding static datasets for identical physiologic conditions. The dynamic data were fit to a two-compartment model, providing regional estimates of washin rate parameters. Occluded to normal ratios were also calculated for each study. Preliminary results show comparable results with regards to flow estimates. In addition, dynamic data provided higher defect contrasts which were significantly more accurate than the static occluded to normal ratios, using microsphere-derived flows as the standard.

In dynamic SPECT patient studies, region of interest (ROI) selection is of great importance. Time-activity curves and thus kinetic parameters are dependent on ROI selection. Although tedious and time-consuming, manual ROI selection is considered superior to automated approaches. The accuracy of manual ROI selection still depends on the user interface for region selection and on the expertise of the user. User expertise includes knowledge of the imaging system and processing methods so that optimal regions can be chosen. For example, a component of the background in the tissue region can lead to incorrect fits, while a component of the blood in the tissue may not compromise accuracy. An efficient manual method was investigated to choose ROIs from the short-axis slices of reconstructed dynamic Teboroxime SPECT images. Data were interpolated into polar coordinates to aid in selecting the ROIs. From the ROIs selected, time-activity curves (TAC) and kinetic parameters were obtained. In order to distinguish where the TAC and kinetic parameters came from, the ROIs were marked clearly in the short-axis slices. Also, an algorithm was developed to automatically choose the ROIs. Results from manual and automated ROI selection on three dynamic teboroxime patient studies were obtained and compared.

Important physiological information can often be obtained by tracking the change in concentration over time of a tracer or contrast agent in a region and fitting to a model. Typically, the model requires knowledge of a blood input function which can be difficult or impossible to obtain. Blind estimation methods are methods that only require measurement of Tissue Activity Curves for different regions of tissue and no measurements of blood input function are taken. Several blind estimation methods of reconstruction for washin( k1) and washout (k2) parameters of a one compartmental model were compared for accuracy in moderately noisy conditions. Uniqueness of the solution for those methods has been studied. In one compartmental model case the solution is unique. To estimate the accuracy of the method, k1 and k2 reconstructions were made for ten thousand noise realizations of Tissue Activity Curves (TACs) which were simulated for cardiac MRI case. Sufficient statistics allowed more knowledge about the accuracy of each method to be obtained. The methods considered were the Cross relations method , Iterative Quadratic Maximum likelihood (IQML) and IQML with various Linear Regularization terms. The results show better accuracy for IQML and that incorporating Linear Regularization in IQML does not give any improvement in accuracy. The same interface for estimation of accuracy will be used for other methods and for FDG two compartmental model where more than two coefficients are involved.

Factor analysis of dynamic structures (FADS) is an established technique used for the analysis of dynamic sequences in medical imaging. The most common technique used for factor analysis is an algorithm that uses an orthogonal decomposition of the dynamic data and an oblique rotation with non-negativity constrains to determine the factors and factor coefficients. However, the results are not unique. In this work we propose a technique to solve the problem of non-uniqueness. Methods: In order to perform factor analysis an objective function is constructed for which a least squares minimization of such a function forces an agreement between the acquired data and the model. We refer to the algorithm as a Least Squares FADS (LS-FADS) technique. In our work, the objective function has two very important terms. One term ensures that the results are non-negative. The other term gives a solution that is unique. The non-uniqueness problems found in other algorithms are non-existent for our LS-FADS implementation. The method was applied to dynamic cardiac single photon emission computed tomography (SPECT) data acquired in canine and patient studies. Also, it was used for the removal of liver contamination in 99mTc-teboroxime cardiac imaging. LS-FADS was also used for the analysis of 99mTc-MAG3 renal data from patient studies. Results: The technique overcomes the problem of non-uniqueness and was successfully applied in all applications.

The objective of this research was to comparatively evaluate image quality for rotating slant-hole (RSH) versus parallel beam SPECT. RSH collimators provide a means for increasing SPECT sensitivity to a region of interest (ROI), e.g. the heart, but, RSH has an asymmetric geometric response function (GRF) and requires fully-3D reconstruction. A series of phantom simulations were used to study overall image quality in terms of contrast, resolution and noise. Cardiac phantom experiments, with and without background activity, were also performed to evaluate myocardial uniformity and to perform an overall assessment of the visual image quality. The results from the simulations demonstrated very similar contrast and resolution for RSH and parallel beam images when compensating for attenuation and detector response. For the same acquisition time, the normalized standard deviation of voxels in the ROI for a uniform phantom was found to be higher for parallel beam than for RSH. The cardiac phantoms were reconstructed and found to give comparable results. These results show that the increased detection efficiency and improved noise properties of RSH might make it a good choice for cardiac and breast imaging.

Although 70% of patients with epilepsy experience satisfactory control using medication only, as many as 30% become refractory to conservative medical management. These refractory patients become candidates for surgical therapy when drug therapy fails to control the seizures. Pre-operative MR imaging anatomical identification of an explanatory abnormality is critical to maximize the likelihood of a good or excellent surgical outcome, and may obviate the need for additional invasive monitoring, limit the area of surgical resection, and/or exclude an occult neoplasm. The area of cortical abnormality defined by MRI has been shown to be a more important predictor of successful surgical resection than the area identified by scalp EEG or invasive EEG monitoring. Choosing the appropriate area to study is difficult using conventional surface EEG or semiology. Compared to clinical localization or conventional MR imaging, use of a phase array surface coil substantially improves the detection rate of focal cortical lesions in medically refractory epilepsy patients. We investigated magnetoencephalography (MEG) as a tool to localize areas of abnormal epileptiform activity that could constrain the high resolution MRI and MR spectroscopy evaluation. To date eight patients with extratemporal epilepsy who have undergone MEG evaluation have been entered into the study. Using MEG localization of epileptiform activity, high resolution MR imaging including T1 3D SPGR and T2 FSE sequences was performed using a 4-channel phased-array surface coil placed over the area(s) of interest. The SPGR sequence was reformatted into 3 mm slices in the coronal, sagittal, and axial planes. Additional interactive multiplanar review was performed on a GE workstation to scrutinize the regions most suspected clinically. Single voxel MR spectroscopy was performed using a standard head coil, with voxels placed over both the suspected areas and the contralateral homologous "normal" regions. All imaging data was correlated with non-invasive and invasive clinical results. Data will be presented showing the utility of this multimodality epilepsy approach to these clinically difficult patients.

In general, the clinical need for transmission attenuation correction in FDG imaging remains controversial. The purpose of this study was to evaluate the feasibility of using a transmission source of Ba-133 for attenuation correction in myocardial viability imaging with F-18 FDG. Methods: F-18 FDG clinical phantom studies and patient studies were investigated. Pre-injection transmission scans were performed with sources of 10 mCi Ba-133 as transmission scanning point sources. Transmission scans were performed over 360 degrees in 4 to 12 minutes and were reconstructed using an OSEM algorithm. Emission coincidence list mode data were rebinned into projection images and reconstructed using OSEM and employed the reconstructed transmission map data for attenuation compensation. Results: Transmission scans gave an acceptable transmission correction map, even when the total scan time was as short as 4 min. Attenuation corrected images were compared with non-corrected images. Myocardial visualization in both phantoms and patient studies were improved with Ba-133 attenuation correction. In myocardial F-18 FDG phantom and patient studies with pre-injection transmission scans, attenuation corrected images demonstrated a significant improvement in visualization of the heart. Conclusion: Ba-133 transmission scans for attenuation compensation provide profoundly improved attenuation corrected images of the myocardium as compared to no correction. Ba-133 provides accurate attenuation maps for correcting F-18 images.

Magnetic source imaging (MSI) is a non-invasive method combining functional data obtained by magnetoencephalography (MEG) and structural information obtained by MRI. Despite ongoing efforts to improve for source models and volume conductor models at the present, this method provides clinically useful information using very simple algorithms. MSI is a valid, and cost-effective clinical tool in functional mapping for patients with brain lesions like tumors or AVMs. Mapping of sensorimotor function, auditory and visual mapping and language lateralization are valid clinical applications. Lateralization of memory function is still experimental. The characterization of epileptiform activity in temporal lobe epilepsies without lesions and all extratemporal lobe epilepsies helps support neurosurgical decision-making relative to the extent of invasive monitoring. Especially in extratemporal lobe epilepsies MSI enhances the identification of previously unknown small structural brain abnormalities. In patients suffering from Landau-Kleffner-Syndrome and autism spectrum disorders (ASD) MSI identifies the regions of abnormal (epileptogenic) brain activity and is important for optimizing treatment strategies. At the present MSI/MEG is a useful research tool but not a medical indication for stroke and other ischemic diseases, headtrauma, dementia, general psychiatric conditions including schizophrenia, depression, and bipolar disorder.

Dual X-ray absorptiometry (DXA) and computed tomography approaches are extremely useful to assess skeletal mass and structure in the human or live experimental animals. These technologies are used in humans, for example, for the diagnosis of osteoporosis and monitoring the longer-term effects of therapies. In experimental studies, these technologies allow the non-invasive determinations of skeletal mass and structure and body composition. The "Densitometry and Imaging Center" in the Radiobiology laboratory is equipped with the following instruments (all for animal research): Single photon absorptiometer (Norland), whole body DXA (Hologic), peripheral DXA (pDXA, Norland), and a peripheral quantitative computed tomography (pQcT, Stratec). Additionally, there is a very sensitive whole-body gamma counter (for animals) that is used in metabolic and metabolism studies. The pDXA machine will also measure lean and fat body mass. Examples of the data derived from these machines and the use of these data in experimental studies will be presented. Additionally, how these in vivo data are used relative to other skeletal structural and functional relationships will be briefly presented. Some of the current research activities that utilize these technologies include: 1) Skeletal metabolism during pregnancy and lactation. 2) Effects of skeletal loading and underloading on skeletal structure, mass, dynamics and gene expression. 3) Evaluation of novel drugs for the treatment of osteoporosis. 4) Effects of phytoestrogens as alternatives to hormone replacement therapy after menopause. 5) Effects of burn injuries on longer term skeletal growth and metabolism. 6) Osteopenias associated with diabetes. 7) Bone loss during space flight. 8) Evaluation of novel drugs that reduce toxic radionuclides and metals.

Vascular disease in the head and neck can occur in many forms such as dissections, aneurysms, arterial venous malformations, congenital abnormalities, and atherosclerotic plaque. The purpose of this work is to develop the necessary hardware for efficient screening of these diseases. Current screening protocols require a low-resolution scan of the head and neck, using a neurovascular (NV) array coil. Subsequent scans are then performed on suspect regions of interest using high-resolution coils for the specific anatomy. Because atherosclerotic plaques are the most frequently occurring diseases, imaging the carotid bifurcation is a major focus of this work. Carotid coils for this purpose already exist and work well with precise placement over the bifurcation, however, they are difficult to place effectively and have minimal longitudinal sensitivity. Our first objective is to verify the importance of the carotid coils in plaque imaging using signal to noise measurements from a modified Z-buffer algorithm. Next, the carotid and NV array coils will be integrated such that either coil can be selected without repositioning the patient. This allows the NV array to be used for the low-resolution scan and the carotid array for the high-resolution scan. Finally, a new ladder coil design will be presented. The ladder design allows for improved coverage and coil placement while maintaining the high sensitivity of the current carotid array. In theory, the ladder concept could be extended to obtain high-resolution images of any local vasculature in the head and neck.

The phase dispersion among the spins in a voxel is the main source of the signal loss in a MR Angiogram, caused by the various flow phenomena such as vorticing, turbulence, or flow separation. The phase dispersion is usually due to high moments of motion: acceleration, jerk or unstable flow, while the spins with constant velocity during TE may be refocused by the flow-compensating gradient lobes and contribute to the signal. This phase dispersion can be reduced with a shorter TE. In MR angiography, the minimum TE is always desirable, but the flow-compensating gradients greatly increase the echo-times. To reduce the time of the flow-compensation gradients and TE, the duration of the flow-compensation gradients needs to be minimized with the amplitude maximized. In this study, multiple TEs are used with the shortest TE at the central segments of ky and kz, where the area of flow-compensation gradients are small. The ky-kz space was segmented with several partitions with different TEs, such that echo-time increases linearly from central to outer ky-kz segments. Since the signal intensity is the greatest at the center of k-space, the Signal-to-Noise ratio of this method would be expected to be larger than that with the conventional sequence.

Longitudinal Magnetic Resonance Angiography (MRA) studies function to monitor changes in the blood vessels. When images are taken at two different times the patient position can be quite different, making a comparison of the blood vessels difficult. The hypothesis is that by using computer algorithms these images can be aligned to give a clear picture of any changes in plaques, aneurysms, and vascular anomalies. The images are processed using the Z-buffer segmentation algorithm. By keeping track of the offset as one of the subregions is registered with a corresponding slice from another exam series, two images from different times can be overlayed. The goal is to register the images and display them simultaneously so that the changes in blood vessels can be measured and the accuracy of these measurements can be determined.

X-ray Angiography remains the gold standard imaging test for the diagnosis of carotid artery disease (CAD). It is a very risky procedure with a potential of morbidity from (0.1 to 3%). It is costly in both dollars and lost work time, as patients must endure a full day of hospitalization. The significance of these disadvantages is compounded by the fact that most patients with carotid ischemic symptoms do not have carotid stenosis. MRA techniques, which are non-invasive and have no known side effects, have addressed the need for an alternative imaging method to diagnose and follow the progression of CAD. We will discuss the use of high-resolution MRI to serially monitor medical / surgical patients diagnosed with CAD.

The diffusion and other transport mechanisms of water in the brain are very complex. Currently, the most widely applied model for diffusion in brain MRI studies is the diffusion tensor. While the diffusion tensor is a simple, yet eloquent model for diffusion behavior, it is inadequate to describe complex diffusion behavior associated with multiple diffusion compartments, restricted diffusion and microcirculation. By utilizing the full imaging gradient strength that is now available on many MRI scanners (40 mT/m), we modified a single-shot diffusion-weighted EPI pulse sequence to obtain Fourier displacement measurements for measuring the 3D displacement profiles in brain tissues. The technique obtains a set of single-shot EPI images at discrete values of q (the reciprocal space variable; q ~ gd, where g and d are the amplitude and duration of the diffusion-weighting gradients). Images are obtained on a 3D q-space grid. Thus for each voxel in the image, a 3D q-space is measured. A 3D Fourier transform of the q-space data is performed to estimate the 3D displacement profile for each voxel. The displacement profile can be used to infer complex microstructural information (membrane spacings, permeabilities, diffusion rates, etc.) within single image voxels. The resolution and range of the measured displacements are inversely related to the maximum q value and the q spacing. To test the technique, a 3-slice study on a normal volunteer was performed with the q-space technique (single shot EPI, and diffusion weighting) to cover the 3D q-space (equal q intervals in qx, qy, qz). The largest q corresponded to a b-factor of 8400 sec/mm2. The q-space matrix was 9x9x9 and zero-filled to 18x18x18. Other imaging parameters were TR = 2 sec, 128x128 matrix, 20 cm FOV, 5 mm slice thickness. The resultant 3D displacement images appear to be consistent with known brain structures.

Tissue Water Spin Self-Diffusion Tensor Imaging (DTI) is achieved by acquiring a minimum of seven encoded diffusion weighted images along at least six noncolinear directions. The cartesian diffusion tensor is represented by a 3x3 Hermitian matrix that has six independent components. The matrix diagonalization captures the local orientation and magnitude of the diffusion along each of the local axes. There are three rotational invariants of the tensor that can be calculated directly from the decoded diffusion measurements. An accurate analytical noniterative approach to diagonalize the MRI diffusion tensor has been derived. The direct algebraic diagonalization gives the three-eigenvalues and the three corresponding mutuallay orthogonal eigenvectors which are needed to construct useful scalar and vector field maps. The approach uses standard math functions and requires no sorting. The noise in the NMR-DTI measured data rules out some esoteric cases where the algorithm behavior is pathological. This approach has a simple geometric interpretation in the Mobius-Plucker Trilinear coordinate system. This algebraic approach may be used to: 1. Formulate the eigenvalue-dependent anisotropy measures and eigenvector field attributes directly in terms of the three invariants. 2. Perform error propagation analysis. By combining this approach with the tensor Measurement Model used to encode the diffusivities, and the Bootstrap we have an analytical means to predict how small variations in the measured data propagate into the metrics of interest. 3. Accelerate the computation of all Eigenvector-Eigenvalue metric maps. These maps have diagnostic applications and may be considered as "stains" of local tissue anisotropy, connectivity, similarity, and fiber-tracks. The approach has accelerated the Bootstrap resampling technique and Monte Carlo simulations. This development provided us with a method to study the interplay between anisotropy and fiber track angular dispersion, signal-to-noise versus fiber orientation and encoding scheme bias.

Tensor tomography is being investigated as a technique for reconstruction of in vivo tensor fields in developing more accurate models of the properties of biological tissue. This paper presents backprojection filtering algorithms for reconstructing vector and second order tensor fields in 2D and 3D. The weighted backprojection of a complete set of directional projection measurements gives simple straightforward results that are fairly simple extensions of the usual scalar reconstruction methods. Although it is not immediately obvious, it is shown that shift invariant filters can also be derived for the unweighted backprojection of a complete set of directional measurements. In 3D backprojection filtering algorithms are developed for the reconstruction of both X-ray and Radon projections. It is shown that the solenoidal component of the vector or tensor field can be reconstructed from a single set of directional measurements. For the X-ray transform, this means that we only need to measure the scalar product of the tensor with the unit vector along the projection ray. For the 3D Radon transform, this corresponds to measuring plane integrals of the scalar product with the vector orthogonal to the plane. Results of computer simulations that demonstrate the validity of the mathematical formulations will be presented.

The aim of this research project is to determine theoretical limits of tomographic capability for any cone-beam system. We assume a finite number of vertex positions (finite number of projections, which would arise for example, from a finite number of positions of an x-ray source) and an effectively infinite resolution for the two-dimensional detector. We are only trying to analyze tomographic capability in a theoretically ideal sense; we are assuming no noise or other sources of error in the data. For our current phase of the research we assume that the projections are not truncated although the ultimate goal of the project is to admit truncated projections also. To characterize tomographic capability we propose the concept of local directional resolution which we will try to define, for each position x in the field-of-view and for each direction q , using a single number R(x,q ). The idea is that at location x, the resolution in the q direction can be no better than R(x,q ) no matter what reconstruction algorithm is applied. Given a cone-beam system, in this case characterized by a set of vertex locations, we can calculate our candidate function R(x,q ) easily. We are still developing these ideas. Some computer-simulated examples will be shown in the presentation including reconstructions of a small test-object phantom to illustrate the concept.

MLEM and related algorithms are rapidly becoming the standard for ECT reconstruction, but such algorithms require arbitrary stopping criteria, have severe noise artifacts, and require accelerated implementations that may not work well for all imaging situations. We propose a new algorithm with a likelihood-based objective function that addresses these issues. The statistically regulated EM (StatREM) algorithm is closely related to OSEM with the following exceptions. It applies spatially-adaptive regularization, and uses statistically-adaptive subsets to accelerate convergence in a controlled manner. Projection data are processed sequentially and internal statistically-adaptive subsets are formed. When accumulated statistical power merits an update, as determined by paired sample t-test, then spatially-adaptive updates are applied and the corresponding test statistics and subsets accumulations are reset. Reconstruction continues iteratively until no further statistically-significant errors remain. The following properties were observed for clinical, phantom, and simulated data: (i) user-defined test levels provide statistically-based stopping criteria; (ii) StatREM accelerates recovery of spatial resolution in high-count regions while regulating low-count regions to suppress noise artifacts; (iii) notable acceleration is achieved for large, sparse datasets (such as fully-3D PET); and (iv) image quality is superior to conventional OSEM. Statistically regulated EM may potentially provide a new archetype for PET and SPECT reconstruction.

The aim of this research is to analyze the feasibility of achieving exact and stable reconstruction in SPECT imaging with 180-degree acquisition. In this study, SPECT data are described using the line-integral model of the exponential Radon transform, assuming that the attenuation is constant in the activity region. Deviations from that model, due to physical effects, such as Poisson statistics, scattering, or detector response, are viewed as sources of data noise. We investigate the theoretical problem of inverting the exponential Radon transform with projections limited to a range of 180 degrees. This problem has important implications in practice: by reducing the data acquisition from 360 to 180 degrees, better signal-to-noise ratio, and thus better image quality, can be achieved, for a same imaging time. Experimentally, one can show that iterative methods, such as the ML-EM algorithm, can provide accurate reconstruction from 180-degree data. But no theoretical results ensure convergence. On another hand, the literature on analytic inversion formulas is very meager. Currently, no results have been published on the inversion of the exponential Radon transform with projections on 180 degrees. At most, the FBP algorithm of Tretiak and metz is known to fail in handling 180-degree data. At this stage of our research, we have succeeded in deriving an inversion formula suitable for exact and stable reconstruction when the attenuation factor does not exceed some bound, which depends on the object diameter. It is still unclear whether this bound is required. The presentation will cover these early results including reconstructions of a test phantom.

This paper investigates the iterative reconstruction of a segment of a long object using cone-beam projections acquired with a practical-size detector. This reconstruction problem is commonly called the cone-beam long object problem. The cone-beam focal-point trajectory under our investigation is a helix or a helix with planar arcs. We assume that the long object is confined in a tall supporting cylinder, and the cone-beam detector is wide enough that the projections are not truncated transversely. If the detector is not wide enough, we use two asymmetric cone-beam detectors, each covering at least half the field of view in the transverse direction. The detector in the axial direction is not large enough to cover the segment. The detector size is used to determine the maximal helical pitch. A data sufficiency condition is established to design a focal-point trajectory. The trajectory defines a convex hull. Projection rays that touch the region outside the convex hull and inside the supporting cylinder are discarded in the iterative algorithm. Computer simulations verify that the proposed data acquisition and discarding strategy provides accurate segment reconstruction. Experimental data are also used to study some practical problems.

Projection reconstruction (PR) techniques are experiencing renewed interest in magnetic resonance. PR regained popularity for several reasons: (1) can use a short echo time (TE), (2) oversamples the region around the center of k-space. Short TE allows for rapid acquisition, imaging short T2 species, reduced motion and flow artifact. Oversampling the region near the origin is advantageous because this area contains most of the energy in the k-space. This oversampling can be exploited by angular undersampling by a factor of up to eight times (in 2D), resulting in significantly reduced scan time, and some tolerable spoke artifacts (MRM 2000 43:170-6). Angular undersampling decreases the radius of the alias-free FOV that may be reconstructed, but does not decrease spatial resolution. Through simulation, the point spread function for 3D Radon PR is demonstrated for various levels of undersampling. The reconstructed image quality versus level of undersampling is explored at various resolutions. After generating a phantom image, a constellation of radial sampling directions is chosen using an icosahedron-based pixelization of the sphere (ApJ Letters 470:L81 or http://www.sns.ias.edu/~max/icosahedron.html). A set of projections is generated from the phantom using these sampling directions. Finally, the projections are used to reconstruct the final image, using filtered backprojection or regridding.