With diffusion tensor imaging, the diffusion of water molecules through brain structures is quantified by parameters, which are estimated assuming monoexponential diffusion-weighted signal attenuation. The estimated diffusion parameters, however, depend on the diffusion weighting strength, the b-value, which hampers the interpretation and comparison of various diffusion tensor imaging studies. In this study, a likelihood ratio test is used to show that the diffusion kurtosis imaging model provides a more accurate parameterization of both the Gaussian and non-Gaussian diffusion component compared with diffusion tensor imaging. As a result, the diffusion kurtosis imaging model provides a b-value-independent estimation of the widely used diffusion tensor parameters as demonstrated with diffusionweighted rat data, which was acquired with eight different b-values, uniformly distributed in a range of [0,2800 sec/mm 2 ]. In addition, the diffusion parameter values are significantly increased in comparison to the values estimated with the diffusion tensor imaging model in all major rat brain structures. As incorrectly assuming additive Gaussian noise on the diffusionweighted data will result in an overestimated degree of nonGaussian diffusion and a b-value-dependent underestimation of diffusivity measures, a Rician noise model was used in this study. Diffusion tensor magnetic resonance imaging (DTI) is an important medical imaging modality in neuroscience research, because it allows the study of the complex network of myelinated axons, in vivo and noninvasively (1,2). In DTI, the diffusion of water molecules through brain structures is mathematically described by a second order 3D diffusion tensor (DT). It is generally accepted that the first eigenvector of the tensor, corresponding to the direction of maximal diffusion, is aligned with the underlying fiber structures. Furthermore, the diffusion is often quantified with diffusion parameters (i.e., fractional anisotropy (FA) and mean (MD), radial (D ⊥ ) and axial (D ) diffusivity), which provide insight in the organization, structural integrity, and development of white matter (WM) structures of the normal and pathological brain (3-9).In DTI, the diffusion of water molecules along a certain gradient direction is assumed to occur in an unrestricted environment. Consequently, the molecules' probability of diffusing from one location to another in a given time is described by a Gaussian distribution of which the standard deviation relates to the apparent diffusion coefficient (ADC). As a result, the normalized diffusion-weighted signal that is measured along a certain axis can be described by a monoexponential function; the exponent equals the ADC, weighted by the diffusion weighting strength that is given by the b-value. Several DTI studies, however, reported that the estimation of diffusion parameters depends on the b-value that is used during data acquisition. Therefore, the comparison and interpretation of various DTI studies are hampered. Jones and Basser (10) and Ande...

Diffusion kurtosis imaging (DKI) is a new magnetic resonance imaging (MRI) model that describes the non-Gaussian diffusion behavior in tissues. It has recently been shown that DKI parameters, such as the radial or axial kurtosis, are more sensitive to brain physiology changes than the well-known diffusion tensor imaging (DTI) parameters in several white and gray matter structures. In order to estimate either DTI or DKI parameters with maximum precision, the diffusion weighting gradient settings that are applied during the acquisition need to be optimized. Indeed, it has been shown previously that optimizing the set of diffusion weighting gradient settings can have a significant effect on the precision with which DTI parameters can be estimated. In this paper, we focus on the optimization of DKI gradients settings. Commonly, DKI data are acquired using a standard set of diffusion weighting gradients with fixed directions and with regularly spaced gradient strengths. In this paper, we show that such gradient settings are suboptimal with respect to the precision with which DKI parameters can be estimated. Furthermore, the gradient directions and the strengths of the diffusion-weighted MR images are optimized by minimizing the Cramér-Rao lower bound of DKI parameters. The impact of the optimized gradient settings is evaluated, both on simulated as well as experimentally recorded datasets. It is shown that the precision with which the kurtosis parameters can be estimated, increases substantially by optimizing the gradient settings.

Improving the resolution in magnetic resonance imaging comes at the cost of either lower signal-to-noise ratio, longer acquisition time or both. This study investigates whether so-called super-resolution reconstruction methods can increase the resolution in the slice selection direction and, as such, are a viable alternative to direct high-resolution acquisition in terms of the signal-to-noise ratio and acquisition time trade-offs. The performance of six super-resolution reconstruction methods and direct high-resolution acquisitions was compared with respect to these trade-offs. The methods are based on iterative back-projection, algebraic reconstruction, and regularized least squares. The algorithms were applied to low-resolution data sets within which the images were rotated relative to each other. Quantitative experiments involved a computational phantom and a physical phantom containing structures of known dimensions. To visually validate the quantitative evaluations, qualitative experiments were performed, in which images of three different subjects (a phantom, an ex vivo rat knee, and a postmortem mouse) were acquired with different magnetic resonance imaging scanners. The results show that super-resolution reconstruction can indeed improve the resolution, signal-to-noise ratio and acquisition time trade-offs compared with direct high-resolution acquisition.

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Estimation of the noise variance of a magnetic resonance (MR) image is important for various post-processing tasks. In the literature, various methods for noise variance estimation from MR images are available, most of which however require user interaction and/or multiple (perfectly aligned) images. In this paper, we focus on automatic histogram-based noise variance estimation techniques. Previously described methods are reviewed and a new method based on the maximum likelihood (ML) principle is presented. Using Monte Carlo simulation experiments as well as experimental MR data sets, the noise variance estimation methods are compared in terms of the root mean squared error (RMSE). The results show that the newly proposed method is superior in terms of the RMSE.

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Abstract-There is an ongoing debate on how to model diffusivity in fiber crossings. We propose an optimization framework for the selection of a dual tensor model and the set of diffusion weighting parameters b, such that both the diffusion shape and orientation parameters can be precisely as well as accurately estimated. For that, we have adopted the Cramér-Rao lower bound (CRLB) on the variance of the model parameters, and performed Monte Carlo simulations. We have found that the axial diffusion needs to be constrained, while an isotropic fraction can be modeled by a single parameter iso . Under these circumstances, the Fractional Anisotropy (FA) of both tensors can theoretically be independently estimated with a precision of 9% (at SNR = 25).

Diffusion weighted magnetic resonance images are often acquired with single shot multislice imaging sequences, because of their short scanning times and robustness to motion. To minimize noise and acquisition time, images are generally acquired with either anisotropic or isotropic low resolution voxels, which impedes subsequent posterior image processing and visualization. In this article, we propose a super-resolution method for diffusion weighted imaging that combines anisotropic multislice images to enhance the spatial resolution of diffusion tensor data. Each diffusion weighted image is reconstructed from a set of arbitrarily oriented images with a low through-plane resolution. The quality of the reconstructed diffusion weighted images was evaluated by diffusion tensor metrics and tractography. Experiments with simulated data, a hardware DTI phantom, as well as in vivo human brain data were conducted. Our results show a significant increase in spatial resolution of the diffusion tensor data while preserving high signal to noise ratio.