Detection and modeling of non‐Gaussian apparent diffusion coefficient profiles in human brain data

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Abstract
This work details the observation of non-Gaussian apparent diffusion coefficient (ADC) profiles in multi-direction, diffusion-weighted MR data acquired with easily achievable imaging parameters (b approximately 1000 s/mm(2)). A technique is described for modeling the profile of the ADC over the sphere, which can capture non-Gaussian effects that can occur at, for example, intersections of different tissue types or white matter fiber tracts. When these effects are significant, the common diffusion tensor model is inappropriate, since it is based on the assumption of a simple underlying diffusion process, which can be described by a Gaussian probability density function. A sequence of models of increasing complexity is obtained by truncating the spherical harmonic (SH) expansion of the ADC measurements at several orders. Further, a method is described for selection of the most appropriate of these models, in order to describe the data adequately but without overfitting. The combined procedure is used to classify the profile at each voxel as isotropic, anisotropic Gaussian, or non-Gaussian, each with reference to the underlying probability density function of displacement of water molecules. We use it to show that non-Gaussian profiles arise consistently in various regions of the human brain where complex tissue structure is known to exist, and can be observed in data typical of clinical scanners. The performance of the procedure developed is characterized using synthetic data in order to demonstrate that the observed effects are genuine. This characterization validates the use of our method as an indicator of pathology that affects tissue structure, which will tend to reduce the complexity of the selected model.