Estimation of tensors and tensor‐derived measures in diffusional kurtosis imaging

This article presents two related advancements to the diffusional kurtosis imaging estimation framework to increase its robustness to noise, motion, and imaging artifacts. The first advancement substantially improves the estimation of diffusion and kurtosis tensors parameterizing the diffusional kurtosis imaging model. Rather than utilizing conventional unconstrained least squares methods, the tensor estimation problem is formulated as linearly constrained linear least squares, where the constraints ensure physically and/or biologically plausible tensor estimates. The exact solution to the constrained problem is found via convex quadratic programming methods or, alternatively, an approximate solution is determined through a fast heuristic algorithm. The computationally more demanding quadratic programming‐based method is more flexible, allowing for an arbitrary number of diffusion weightings and different gradient sets for each diffusion weighting. The heuristic algorithm is suitable for real‐time settings such as on clinical scanners, where run time is crucial. The advantage offered by the proposed constrained algorithms is demonstrated using in vivo human brain images. The proposed constrained methods allow for shorter scan times and/or higher spatial resolution for a given fidelity of the diffusional kurtosis imaging parametric maps. The second advancement increases the efficiency and accuracy of the estimation of mean and radial kurtoses by applying exact closed‐form formulae. Magn Reson Med, 2011. © 2010 Wiley‐Liss, Inc.     

A simple isotropic phantom for diffusional kurtosis imaging

Dairy cream is shown to be a simple, inexpensive, isotropic phantom useful for testing diffusional kurtosis imaging data acquisition and postprocessing. The MR-visible protons of cream exhibit slow and fast diffusion components, attributed to the fat and water protons, respectively, which give rise to a diffusion coefficient of 1.1 μm(2)/ms and a diffusional kurtosis of 1.2. These parameter values are similar to those observed in vivo for human brain. Heating the cream is found to increase the T(2)-relaxation time of the fat protons, which facilitates the evaluation of typical diffusional kurtosis imaging protocols used in clinical settings. The diffusion coefficient and diffusional kurtosis can both be measured directly and predicted based on the corresponding diffusion parameters of the individual water and fat components, which are independently measurable due to chemical shift misregistration, thus providing an important consistency check. This phantom is proposed as a convenient calibration standard for multicenter diffusional kurtosis imaging studies.     

Regional values of diffusional kurtosis estimates in the healthy brain

Purpose:

To provide estimates of the diffusional kurtosis in the healthy brain in anatomically defined areas and list these along previously reported values in pathologies.

Materials and Methods:

Thirty‐six volunteers (mean age = 33.1 years; range, 19–64 years) underwent diffusional kurtosis imaging. Mean kurtosis (MK), radial kurtosis (RK), mean diffusivity (MD), radial diffusivity (RD), and fractional anisotropy (FA) were determined in 26 anatomical structures. Parameter estimates were assessed regarding age dependence.

Results:

MK varied from 1.38 in the splenium of the corpus callosum to 0.66 in the caudate head, MD varied from 0.68 to 0.62 μm²/ms and FA from 0.87 to 0.29. MK, and FA showed a strong positive correlation, RK and RD a strong negative correlation. Parameter estimates showed age correlation in some regions; also the average MK and RK for all WM and all GM areas, respectively, were negatively correlated with age.

Conclusion:

DKI parameter estimates MK and RK varied depending on the anatomical region and varied with age in pooled WM and GM data. MK estimates in the internal capsule, corpus callosum, and thalamus were consistent with previous studies. The range of values of MK and RK in healthy brain overlapped with that in pathologies. J. Magn. Reson. Imaging 2013;37:610–618. © 2012 Wiley Periodicals, Inc.     

Effect of cerebral spinal fluid suppression for diffusional kurtosis imaging

Purpose:

To evaluate the cerebral spinal fluid (CSF) partial volume effect on diffusional kurtosis imaging (DKI) metrics in white matter and cortical gray matter.

Materials and Methods:

Four healthy volunteers participated in this study. Standard DKI and fluid‐attenuated inversion recovery (FLAIR) DKI experiments were performed using a twice‐refocused‐spin‐echo diffusion sequence. The conventional diffusion tensor imaging (DTI) metrics of fractional anisotropy (FA), mean, axial, and radial diffusivity (MD, D_‖, D_?) together with DKI metrics of mean, axial, and radial kurtosis (MK, K_‖, K_?), were measured and compared. Single image slices located above the lateral ventricles, with similar anatomical features for each subject, were selected to minimize the effect of CSF from the ventricles.

Results:

In white matter, differences of less than 10% were observed between diffusion metrics measured with standard DKI and FLAIR‐DKI sequences, suggesting minimal CSF contamination. For gray matter, conventional DTI metrics differed by 19% to 52%, reflecting significant CSF partial volume effects. Kurtosis metrics, however, changed by 11% or less, indicating greater robustness with respect to CSF contamination.

Conclusion:

Kurtosis metrics are less sensitive to CSF partial voluming in cortical gray matter than conventional diffusion metrics. The kurtosis metrics may then be more specific indicators of changes in tissue microstructure, provided the effect sizes for the changes are comparable. J. Magn. Reson. Imaging 2013;37:365–371. © 2012 Wiley Periodicals, Inc.

     

Spatial normalization of the fiber orientation distribution based on high angular resolution diffusion imaging data

Comparison of high angular resolution diffusion imaging (HARDI) measurements between subjects or between timepoints for the same subject are facilitated by spatial normalization. In this work an algorithm was developed to transform the fiber orientation distribution (FOD) function, based on HARDI data, taking into account not only translation, but also rotation, scaling, and shearing effects of the spatial transformation. The algorithm was tested using simulated data and intrasubject and intersubject normalization of in vivo human data. All cases demonstrated reliable transformation of the FOD. This technique makes it possible to compare the intravoxel fiber distribution between subjects, between groups, or between timepoints for a single subject, which will be helpful in HARDI studies of white matter disease. Magn Reson Med, 2009. © 2009 Wiley‐Liss, Inc.     

Accelerated diffusion spectrum imaging in the human brain using compressed sensing

We developed a novel method to accelerate diffusion spectrum imaging using compressed sensing. The method can be applied to either reduce acquisition time of diffusion spectrum imaging acquisition without losing critical information or to improve the resolution in diffusion space without increasing scan time. Unlike parallel imaging, compressed sensing can be applied to reconstruct a sub-Nyquist sampled dataset in domains other than the spatial one. Simulations of fiber crossings in 2D and 3D were performed to systematically evaluate the effect of compressed sensing reconstruction with different types of undersampling patterns (random, gaussian, Poisson disk) and different acceleration factors on radial and axial diffusion information. Experiments in brains of healthy volunteers were performed, where diffusion space was undersampled with different sampling patterns and reconstructed using compressed sensing. Essential information on diffusion properties, such as orientation distribution function, diffusion coefficient, and kurtosis is preserved up to an acceleration factor of R = 4.     

Diffusional kurtosis imaging: the quantification of non-gaussian water diffusion by means of magnetic resonance imaging.

A magnetic resonance imaging method is presented for quantifying the degree to which water diffusion in biologic tissues is non-Gaussian. Since tissue structure is responsible for the deviation of water diffusion from the Gaussian behavior typically observed in homogeneous solutions, this method provides a specific measure of tissue structure, such as cellular compartments and membranes. The method is an extension of conventional diffusion-weighted imaging that requires the use of somewhat higher b values and a modified image postprocessing procedure. In addition to the diffusion coefficient, the method provides an estimate for the excess kurtosis of the diffusion displacement probability distribution, which is a dimensionless metric of the departure from a Gaussian form. From the study of six healthy adult subjects, the excess diffusional kurtosis is found to be significantly higher in white matter than in gray matter, reflecting the structural differences between these two types of cerebral tissues. Diffusional kurtosis imaging is related to q-space imaging methods, but is less demanding in terms of imaging time, hardware requirements, and postprocessing effort. It may be useful for assessing tissue structure abnormalities associated with a variety of neuropathologies.     

Reorientation of fiber orientation distributions using apodized point spread functions

Using high angular resolution diffusion-weighted images, spherical deconvolution enables multiple white matter fiber populations to be resolved within a single voxel by computing the fiber orientation distribution (FOD). Higher order information provided by FODs could improve several methods for investigating population differences in white matter, including image registration, voxel-based analysis, atlas-based segmentation and labeling, and group average fiber tractography. All of these methods require spatial normalization of FODs. In this article, a novel method to reorient the FOD is presented, which is an important step required for FOD spatial normalization. The proposed method was assessed using both qualitative and quantitative experiments, with numerical simulations and in vivo human data. Results demonstrate that the proposed method improves FOD reorientation accuracy, removes undesired artefacts, and decreases computation time compared to a previous approach. The utility of the proposed method is illustrated by nonlinear FOD spatial normalization of 10 human subjects. Accurate reorientation and normalization of FODs is a critical step toward investigating white matter tissue in the context of multiple fiber orientations.