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For accurate estimation of the ensemble average diffusion propagator (EAP), traditional multi-shell diffusion imaging (MSDI) approaches require acquisition of diffusion signals for a range of b-values. However, this makes the acquisition time too long for several types of patients, making it difficult to use in a clinical setting. In this work, we propose a new method for the reconstruction of diffusion signals in the entire q-space from highly undersampled sets of MSDI data, thus reducing the scan time significantly. In particular, to sparsely represent the diffusion signal over multiple q-shells, we propose a novel extension to the framework of spherical ridgelets by accurately modeling the monotonically decreasing radial component of the diffusion signal. Further, we enforce the reconstructed signal to have smooth spatial regularity in the brain, by minimizing the total variation (TV) norm. We combine these requirements into a novel cost function and derive an optimal solution using the Alternating Directions Method of Multipliers (ADMM) algorithm. We use a physical phantom data set with known fiber crossing angle of 45° to determine the optimal number of measurements (gradient directions and b-values) needed for accurate signal recovery. We compare our technique with a state-of-the-art sparse reconstruction method (i.e., the SHORE method of Cheng et al. (2010)) in terms of angular error in estimating the crossing angle, incorrect number of peaks detected, normalized mean squared error in signal recovery as well as error in estimating the return-to-origin probability (RTOP). Finally, we also demonstrate the behavior of the proposed technique on human in vivo data sets. Based on these experiments, we conclude that using the proposed algorithm, at least 60 measurements (spread over three b-value shells) are needed for proper recovery of MSDI data in the entire q-space., (Copyright © 2014 Elsevier B.V. All rights reserved.)

Diffusion magnetic resonance imaging (dMRI) is an important tool that allows non-invasive investigation of neural architecture of the brain. The data obtained from these in-vivo scans provides important information about the integrity and connectivity of neural fiber bundles in the brain. A multi-shell imaging (MSI) scan can be of great value in the study of several psychiatric and neurological disorders, yet its usability has been limited due to the long acquisition times required. A typical MSI scan involves acquiring a large number of gradient directions for the 2 (or more) spherical shells (several b-values), making the acquisition time significantly long for clinical application. In this work, we propose to use results from the theory of compressive sampling and determine the minimum number of gradient directions required to attain signal reconstruction similar to a traditional MSI scan. In particular, we propose a generalization of the single shell spherical ridgelets basis for sparse representation of multi shell signals. We demonstrate its efficacy on several synthetic and in-vivo data sets and perform quantitative comparisons with solid spherical harmonics based representation. Our preliminary results show that around 20-24 directions per shell are enough for robustly recovering the diffusion propagator.

New medical imaging modalities offering multi-valued data, such as phase contrast MRA and diffusion tensor MRI, require general representations for the development of automated algorithms. In this paper we propose a unified framework for the registration of medical volumetric multi-valued data using local matching. The paper extends the usual concept of similarity between two pieces of data to be matched, commonly used with scalar (intensity) data, to the general tensor case. Our approach to registration is based on a multiresolution scheme, where the deformation field estimated in a coarser level is propagated to provide an initial deformation in the next finer one. In each level, local matching of areas with a high degree of local structure and subsequent interpolation are performed. Consequently, we provide an algorithm to assess the amount of structure in generic multi-valued data by means of gradient and correlation computations. The interpolation step is carried out by means of the Kriging estimator, which provides a novel framework for the interpolation of sparse vector fields in medical applications. The feasibility of the approach is illustrated by results on synthetic and clinical data.

This paper presents processing and visualization techniques for Diffusion Tensor Magnetic Resonance Imaging (DT-MRI). In DT-MRI, each voxel is assigned a tensor that describes local water diffusion. The geometric nature of diffusion tensors enables us to quantitatively characterize the local structure in tissues such as bone, muscle, and white matter of the brain. This makes DT-MRI an interesting modality for image analysis. In this paper we present a novel analytical solution to the Stejskal-Tanner diffusion equation system whereby a dual tensor basis, derived from the diffusion sensitizing gradient configuration, eliminates the need to solve this equation for each voxel. We further describe decomposition of the diffusion tensor based on its symmetrical properties, which in turn describe the geometry of the diffusion ellipsoid. A simple anisotropy measure follows naturally from this analysis. We describe how the geometry or shape of the tensor can be visualized using a coloring scheme based on the derived shape measures. In addition, we demonstrate that human brain tensor data when filtered can effectively describe macrostructural diffusion, which is important in the assessment of fiber-tract organization. We also describe how white matter pathways can be monitored with the methods introduced in this paper. DT-MRI tractography is useful for demonstrating neural connectivity (in vivo) in healthy and diseased brain tissue.

In order to enhance 3D image data from magnetic resonance angiography (MRA), a novel method based on the theory of multidimensional adaptive filtering has been developed. The purpose of the technique is to suppress image noise while enhancing important structures. The method is based on local structure estimation using six 3D orientation selective filters, followed by an adaptive filtering step controlled by the local structure information. The complete filtering procedure requires approximately 3 minutes of computational time on a standard workstation for a 256 x 256 x 64 data set. The method has been evaluated using a mathematical vessel model and in vivo MRA data (both phase contrast and time of flight (TOF)). 3D adaptive filtering results in a better delineation of small blood vessels and efficiently reduces the high-frequency noise. Depending on the data acquisition and the original data type, contrast-to-noise ratio (CNR) improvements of up to 179% (8.9 dB) were observed. 3D adaptive filtering may provide an alternative to prolonging the scan time or using contrast agents in MRA when the CNR is low., (Copyright 2001 Wiley-Liss, Inc.)

Objective: A major shortcoming of image-guided navigational systems is the use of preoperatively acquired image data, which does not account for intraoperative changes in brain morphology. The occurrence of these surgically induced volumetric deformations ("brain shift") has been well established. Maximal measurements for surface and midline shifts have been reported. There has been no detailed analysis, however, of the changes that occur during surgery. The use of intraoperative magnetic resonance imaging provides a unique opportunity to obtain serial image data and characterize the time course of brain deformations during surgery., Methods: The vertically open intraoperative magnetic resonance imaging system (SignaSP, 0.5 T; GE Medical Systems, Milwaukee, WI) permits access to the surgical field and allows multiple intraoperative image updates without the need to move the patient. We developed volumetric display software (the 3D Slicer) that allows quantitative analysis of the degree and direction of brain shift. For 25 patients, four or more intraoperative volumetric image acquisitions were extensively evaluated., Results: Serial acquisitions allow comprehensive sequential descriptions of the direction and magnitude of intraoperative deformations. Brain shift occurs at various surgical stages and in different regions. Surface shift occurs throughout surgery and is mainly attributable to gravity. Subsurface shift occurs during resection and involves collapse of the resection cavity and intraparenchymal changes that are difficult to model., Conclusion: Brain shift is a continuous dynamic process that evolves differently in distinct brain regions. Therefore, only serial imaging or continuous data acquisition can provide consistently accurate image guidance. Furthermore, only serial intraoperative magnetic resonance imaging provides an accurate basis for the computational analysis of brain deformations, which might lead to an understanding and eventual simulation of brain shift for intraoperative guidance.

A new parallel imaging technique was implemented which can result in reduced image acquisition times in MRI. MR data is acquired in parallel using an array of receiver coils and then reconstructed simultaneously with multiple processors. The method requires the initial estimation of the 2D sensitivity profile of each coil used in the receiver array. These sensitivity profiles are then used to partially encode the images of interest. A fraction of the total number of k-space lines is consequently acquired and used in a parallel reconstruction scheme, allowing for a substantial reduction in scanning and display times. This technique is in the family of parallel acquisition schemes such as simultaneous acquisition of spatial harmonics (SMASH) and sensitivity encoding (SENSE). It extends the use of the SMASH method to allow the placement of the receiver coil array around the object of interest, enabling imaging of any plane within the volume of interest. In addition, this technique permits the arbitrary choice of the set of k-space lines used in the reconstruction and lends itself to parallel reconstruction, hence allowing for real-time rendering. Simulated results with a 16-fold increase in temporal resolution are shown, as are experimental results with a 4-fold increase in temporal resolution. Magn Reson Med 44:301-308, 2000., (Copyright 2000 Wiley-Liss, Inc.)