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.

Quantification of non-Gaussianity for water diffusion in brain by means of diffusional kurtosis imaging (DKI) is reviewed. Diffusional non-Gaussianity is a consequence of tissue structure that creates diffusion barriers and compartments. The degree of non-Gaussianity is conveniently quantified by the diffusional kurtosis and derivative metrics, such as the mean, axial, and radial kurtoses. DKI is a diffusion-weighted MRI technique that allows the diffusional kurtosis to be estimated with clinical scanners using standard diffusion-weighted pulse sequences and relatively modest acquisition times. DKI is an extension of the widely used diffusion tensor imaging method, but requires the use of at least 3 b-values and 15 diffusion directions. This review discusses the underlying theory of DKI as well as practical considerations related to data acquisition and post-processing. It is argued that the diffusional kurtosis is sensitive to diffusional heterogeneity and suggested that DKI may be useful for investigating ischemic stroke and neuropathologies, such as Alzheimer’s disease and schizophrenia.

Diffusional kurtosis imaging (DKI) is a clinically feasible extension of diffusion tensor imaging that probes restricted water diffusion in biological tissues using magnetic resonance imaging. Here we provide a physically meaningful interpretation of DKI metrics in white matter regions consisting of more or less parallel aligned fiber bundles by modeling the tissue as two non-exchanging compartments, the intra-axonal space and extra-axonal space. For the b-values typically used in DKI, the diffusion in each compartment is assumed to be anisotropic Gaussian and characterized by a diffusion tensor. The principal parameters of interest for the model include the intra- and extra-axonal diffusion tensors, the axonal water fraction and the tortuosity of the extra-axonal space. A key feature is that these can be determined directly from the diffusion metrics conventionally obtained with DKI. For three healthy young adults, the model parameters are estimated from the DKI metrics and shown to be consistent with literature values. In addition, as a partial validation of this DKI-based approach, we demonstrate good agreement between the DKI-derived axonal water fraction and the slow diffusion water fraction obtained from standard biexponential fitting to high b-value diffusion data. Combining the proposed WM model with DKI provides a convenient method for the clinical assessment of white matter in health and disease and could potentially provide important information on neurodegenerative disorders.

Measuring molecular diffusion is widely used for characterizing materials and living organisms noninvasively. This characterization relies on relations between macroscopic diffusion metrics and structure at the mesoscopic scale commensurate with the diffusion length. Establishing such relations remains a fundamental challenge, hindering progress in materials science, porous media, and biomedical imaging. Here we show that the dynamical exponent in the time dependence of the diffusion coefficient distinguishes between the universality classes of the mesoscopic structural complexity. Our approach enables the interpretation of diffusion measurements by objectively selecting and modeling the most relevant structural features. As an example, the specific values of the dynamical exponent allow us to identify the relevant mesoscopic structure affecting MRI-measured water diffusion in muscles and in brain, and to elucidate the structural changes behind the decrease of diffusion coefficient in ischemic stroke.A macroscopically uniform sample of a biological tissue, porous rock, or composite material appears incredibly complex at the mesoscopic scale. This scale, typically of the order ∼ 0:1 to 10 μm, is intermediate between the microscopic scale of molecular dimensions, where material properties such as the local diffusion coefficient originate, and the macroscopic sample dimensions or imaging resolution. Quantifying the mesoscopic complexity noninvasively is important in the physical sciences for characterizing artificial and natural samples, and in the life sciences for diagnosing diseases, such as stroke and Alzheimer's, that manifest themselves at a cellular level.Measuring molecular diffusion, e.g., of water, in such media has emerged as a universal noninvasive structural probe (1-8). Obtained with techniques ranging from single-molecule tracking (3) to diffusion-weighted MRI (dMRI) (4), macroscopic diffusion metrics are sensitive to the nominally invisible micronlevel sample architecture, thanks to the diffusion length, i.e., the rms molecular displacement LðtÞ = hδx 2 ðtÞi 1=2 , providing the mesoscopic length scale. However, a challenging ill-posed problem (1, 2, 9) has long been to quantitatively interpret a bulk diffusion measurement, i.e., to convert this manifestly sensitive metric into specific mesoscopic structural parameters, such as geometric properties of pores or biophysical parameters of cells.Characterizing structure below a nominally achievable imaging resolution requires a structural model that predicts the result of the bulk measurement; by comparing the measurement to the prediction, the model parameters may be quantified. At the most basic level, a model is a rough sketch which captures the most essential parts of the structural complexity while neglecting the rest. Given the inherently irregular, or disordered nature of most specimens, a key challenge is to adequately and parsimoniously represent structural disorder.Here we advocate that there are only a handful of qualitatively distinct ways to...

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 realtime 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 65:823-836, 2011. V C 2010 Wiley-Liss, Inc.