Stephen L. Keeling

Diffusion tensor imaging using single-shot SENSE-EPI.

SENSitivity Encoding (SENSE) greatly enhances the quality of diffusion‐weighted echo‐planar imaging (EPI) by reducing blurring and off‐resonance artifacts. Such improvement would also be desirable for diffusion tensor imaging (DTI), but measures derived from the diffusion tensor can be extremely sensitive to any kind of image distortion. Whether DTI is feasible in combination with SENSE has not yet been explored, and is the focus of this study. Using a SENSE‐reduction factor of 2, DTI scans in eight healthy volunteers were carried out with regular‐ and high‐resolution acquisition matrices. To further improve the stability of the SENSE reconstruction, a new coil‐sensitivity estimation technique based on variational calculus and the principles of matrix regularization was applied. With SENSE, maps of the trace of the diffusion tensor and of fractional anisotropy (FA) had improved spatial resolution and less geometric distortion. Overall, the geometric distortions were substantially removed and a significant resolution enhancement was achieved with almost the same scan time as regular EPI. DTI was even possible without the use of quadrature body coil (QBC) reference scans. Geometry‐factor‐related noise enhancement was only discernible in maps generated with higher‐resolution matrices. Error boundaries for residual fluctuations in SENSE reconstructions are discussed. Our results suggest that SENSE can be combined with DTI and may present an important adjunct for future neuroimaging applications of this technique. Magn Reson Med 48:128–136, 2002.

Improved diffusion-weighted single-shot echo-planar imaging (EPI) in stroke using sensitivity encoding (SENSE)

Diffusion‐weighted single‐shot EPI (sshEPI) is one of the most important tools for the diagnostic assessment of stroke patients, but it suffers from well known artifacts. Therefore, sshEPI was combined with SENSitivity Encoding (SENSE) to further increase EPIs potential for stroke imaging. Eight healthy volunteers and a consecutive series of patients (N = 8) with suspected stroke were examined with diffusion‐weighted SENSE‐sshEPI using different reduction factors (1.0 ≤ R ≤ 3.0). Additionally, a high‐resolution diffusion‐weighted SENSE‐sshEPI scan was included. All examinations were diagnostic and of better quality than conventional sshEPI. No ghostings or aliasing artifacts were discernible, and EPI‐related image distortions were markedly diminished. Chemical shift artifacts and eddy current‐induced image warping were still present, although to a markedly smaller extent. Measured direction‐dependent diffusion‐coefficients and isotropic diffusion values were comparable to previous findings but showed less fluctuation. We have demonstrated the technical feasibility and clinical applicability of diffusion‐weighted SENSE‐sshEPI in patients with subacute stroke. Because of the faster k‐space traversal, this novel technique is able to reduce typical EPI artifacts and increase spatial resolution while simultaneously remaining insensitive to bulk motion. Magn Reson Med 46:548–554, 2001.

Three-Dimensional Models of Individual Cardiac Histoanatomy: Tools and Challenges

Abstract:  There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high‐resolution cardiac structure–function models. The current article presents a step in this general direction: it illustrates how whole‐heart noninvasive imaging can be combined with whole‐heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 × 26.4 × 24.4 μm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.

Total variation based convex filters for medical imaging

Several variational based diffusion filters are applied to measured magnetic resonance images, and on this basis are evaluated for their suitability to medical imaging. In particular, a specific total variation based filter with a convex variational penalty function is introduced here for the enhancement of edge, flat, and grey image scales. In general, results reveal that convex total variation based filters can be implemented to perform very well to enhance the visual clarity of medical images. As a result, further support is provided to establish such methods for medical applications.

Nonlinear anisotropic diffusion filtering for multiscale edge enhancement

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinear evolution partial differential equations which seeks to improve images qualitatively by removing noise while preserving details and even enhancing edges. However, well known implementations are sensitive to parameters which are necessarily tuned to sharpen a narrow range of edge slopes; otherwise, edges are either blurred or staircased. In this work, nonlinear anisotropic diffusion filters have been developed which sharpen edges over a wide range of slope scales and which reduce noise conservatively with dissipation purely along feature boundaries. Specifically, the range of sharpened edge slopes is widened as backward diffusion normal to level sets is balanced with forward diffusion tangent to level sets. Also, noise is reduced by selectively altering the balance toward diminishing normal backward diffusion and particularly toward total variation filtering. The theoretical motivation for the proposed filters is presented together with computational results comparing them with other nonlinear anisotropic diffusion filters on both synthetic images and magnetic resonance images.

Medical Image Registration and Interpolation by Optical Flow with Maximal Rigidity

In this paper a variational method for registering or mapping like points in medical images is proposed and analyzed. The proposed variational principle penalizes a departure from rigidity and thereby provides a natural generalization of strictly rigid registration techniques used widely in medical contexts. Difficulties with finite displacements are elucidated, and alternative infinitesimal displacements are developed for an optical flow formulation which also permits image interpolation. The variational penalty against non-rigid flows provides sufficient regularization for a well-posed minimization and yet does not rule out irregular registrations corresponding to an object excision. Image similarity is measured by penalizing the variation of intensity along optical flow trajectories. The approach proposed here is also independent of the order in which images are taken. For computations, a lumped finite element Eulerian discretization is used to solve for the optical flow. Also, a Lagrangian integration of the intensity along optical flow trajectories has the advantage of prohibiting diffusion among trajectories which would otherwise blur interpolated images. The subtle aspects of the methods developed are illustrated in terms of simple examples, and the approach is finally applied to the registration of magnetic resonance images.

Nonlinear anisotropic diffusion filters for wide range edge sharpening

Nonlinear anisotropic diffusion filtering is a procedure based on nonlinear evolution partial differential equations which seeks to improve images qualitatively by removing noise while preserving details and even enhancing edges. However, well known implementations are sensitive to parameters which are necessarily tuned to sharpen a narrow range of edge slopes; otherwise, edges are either blurred or staircased. In this work, nonlinear anisotropic diffusion filters have been developed which sharpen edges over a wide range of slopes and which reduce noise conservatively with dissipation purely along feature boundaries. Specifically, the range of sharpened edge slopes is widened as backward diffusion normal to level sets is balanced with forward diffusion tangent to level sets. Also, noise is reduced by selectively altering the balance toward diminishing normal backward diffusion and particularly toward total variation filtering. The theoretical motivation for the proposed filters is presented together with computational results comparing them with other nonlinear anisotropic diffusion filters on both phantom images and magnetic resonance images.

A variational approach to magnetic resonance coil sensitivity estimation

A variational method for estimating a magnetic resonance coil sensitivity from its corresponding non-uniform illumination of magnetic resonance images is proposed and analyzed. The estimated sensitivity can then be used to correct non-uniformities and indeed to facilitate high-speed parallel image acquisition. The data available for estimation include two images of the same field of view but obtained with and without a uniform coil sensitivity. The non-uniformly illuminated image is ideally the product of the uniformly illuminated image with the coil sensitivity. Thus, the desired sensitivity is estimated roughly from a quotient of the two given images over the effective data support. However, the measurements are corrupted by noise, the data are discontinuous at tissue boundaries, and yet the coil sensitivity is very smooth. In the selected estimation procedure, the sum of a residual and a high order penalty is minimized. In this form, the problem is related to the surface estimation problem of early vision. In the present context, higher coil sensitivity decay rates are captured non-parametrically by higher order penalties together with natural boundary conditions. The role of alternative penalties and boundary conditions is investigated both analytically and numerically. Although high order operators are often approximated numerically with a product of low order factors, such factorizations are shown here to lead to conspicuously spurious boundary conditions for surface estimation with sparse data support. Furthermore, while finite elements present a natural numerical approach for solving the optimality system, it is demonstrated here that lumping is required to avoid aberrant consequences in the limit of vanishing regularization corresponding to an ever improving signal-to-noise ratio. Finally, with a proper analytical and numerical formulation, the estimation procedure is demonstrated for a magnetic resonance imaging application involving parallel image acquisition.

Galerkin/Runge-Kutta discretizations for semilinear parabolic equations

A new class of fully discrete Galerkin/Runge–Kutta methods is constructed and analyzed for semilinear parabolic initial boundary value problems. Unlike any classical counterpart, this class offers arbitrarily high-order convergence without suffering from what has been called order reduction. In support of this claim, error estimates are proved, and computational results are presented. Furthermore, it is noted that special Runge–Kutta methods allow computations to be performed in parallel so that the final execution time can be reduced to that of a low-order method.

Deconvolution for DCE-MRI using an exponential approximation basis

A deconvolution approach for dynamic contrast enhanced magnetic resonance imaging using an approximation basis of exponential functions constrained to be non-negative and non-increasing is developed and compared with widely used methods. Monotonicity in an exponential basis is implemented in terms of a newly derived condition which is a considerable generalization over a previous condition that implies complete monotonicity. Since the constraints imply a bound on the total variation, a well known staircasing effect may result with other approximation bases, but an exponential basis is shown to resist staircasing. In addition to the choice of approximation basis, further regularization is implemented in terms of the number of basis functions and the distribution of their parameters. The exponential approach is applied to dynamic contrast enhanced magnetic resonance imaging data to determine physiological parameters pixelwise to visualize a cerebral tumor, and the results are compared favorably with those of the standard truncated singular value decomposition approach. In particular, kernels estimated with constrained exponentials are free of oscillations and staircasing, and the images of estimated kernel parameters are sharper than those obtained by truncated singular value decomposition.