Diffusion MRI: A Tool for White Matter Anatomy Inference
The general term “diffusion MRI” is used for various sets of MR imaging techniques based on the diffusion-weighted imaging (DWI). DWI is the most fundamental technique of dMRI and has been used clinically since the mid-1980s . A pair of DWI with identical direction of motion probing gradients (MPG), often called also as diffusion-sensitizing gradients, enables acquisition of map of diffusion coefficient in the direction. In the late 1990s, faster imaging techniques such as echo planar imaging (EPI) enabled multidirectional acquisition of DWI , which revealed the anisotropic characteristics of water diffusion around the fiber tracts. Such diffusion anisotropy is caused by restriction of water diffusion by the fiber structures . To determine the fiber orientation, the diffusion tensor imaging (DTI) technique was developed, which is a simple approximation of the anisotropic diffusion coefficient by a second-order tensor. The eigenvector corresponding to the maximal eigenvalue of the diffusion tensor is a good estimate of fiber orientation. DTI combined with streamline visualization techniques  including fiber tracking is called diffusion tensor tractography (DTT) and provides a three-dimensional display of fiber tract structures [32, 59, 196].
DTT is a powerful tool for navigation during minimally invasive brain neurosurgery as it provides information for localizing fiber tracts that must be avoided, such as the corticospinal tract. For diagnostic purposes, tract-specific analysis (TSA) is used to differentiate between various diseases by comparing diffusion tensor parameters within the tract volume. One critical drawback of DTT is the well-known problem of fiber crossing . The single tensor model of the anisotropic diffusion coefficient is not applicable to regions of fiber crossing where complex diffusion profiles are observed.
The most straightforward solution to overcome the fiber crossing problem involves DWI acquisition from many MPG directions to increase angular resolution of diffusion measurement. Following acquisition, non-tensor-based analysis of the orientation profile of the diffusion coefficient is conducted. Alternatively, diffusion spectrum imaging (DSI)  and q-ball imaging (QBI)  can estimate the orientation distribution function (ODF) of fibers at each location, which represents the likelihoods of fiber existence in each orientation. The DSI technique obtains the probability density function (PDF) of diffused water molecules before estimating ODF. The QBI directly estimates ODF from the profile of diffusion coefficient based on a simple approximation using the Funk-Radon transform . In ODF-based tractography, fiber tracking is performed by following the local maxima of the ODF profile instead of using the orientation of the maximum eigenvalue in DTT.
Furthermore, the non-Gaussianity of diffusion prompts the characterization of tissues including pathological structures . Basically, such non-Gaussianity is available by PDF analysis and can be described simply by a parameter kurtosis, which is obtained by diffusion kurtosis imaging (DKI). The dMRI techniques can be regarded as imaging techniques and models for understanding the signal values for the multiple directions and magnitudes of the MPG field. These signal models provide useful information for various purposes, which makes dMRI an indispensable tool for visualization and analysis of brain white matter fiber structures.