**Diffusion MRI** (or **dMRI**) is a Magnetic Resonance Imaging (MRI) method which came into existence in the mid-1980s. It allows the mapping of the diffusion process of molecules, mainly water, in biological tissues, in vivo and non-invasively. Molecular diffusion in tissues is not free, but reflects interactions with many obstacles, such as macromolecules, fibers, membranes, etc. Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state. The first diffusion MRI images of the normal and diseased brain were made public in 1985. Since then, diffusion MRI has been extraordinarily successful. Its main clinical application has been in the study and treatment of neurological disorders, especially for the management of patients with acute stroke. It is rapidly becoming a standard for white matter disorders, as diffusion tensor imaging (DTI) can reveal abnormalities in white matter fiber structure and provide models of brain connectivity. The ability to visualize anatomical connections between different parts of the brain, non-invasively and on an individual basis, has emerged as a major breakthrough for neurosciences (so-called Human Brain Connectome project ). More recently, a new field has emerged, **diffusion functional MRI** (**DfMRI**) as it was suggested that with dMRI one could also get images of neuronal activation in the brain. Finally, the method of diffusion MRI has been shown to be also sensitive to perfusion, as the movement of water in blood vessels mimics a random process (IntraVoxel Incoherent Motion or IVIM model). IVIM dMRI is rapidly becoming a major method to obtain images of perfusion in the body, especially for cancer detection and monitoring. In **diffusion weighted imaging** (DWI), each image voxel (three dimensional pixel) has an image intensity that reflects a single best measurement of the rate of water diffusion at that location. This measurement is more sensitive to early changes after a stroke than more traditional MRI measurements such as T1 or T2 relaxation rates. A variant of diffusion weighted imaging, **diffusion spectrum imaging** (DSI) (Wedeen, 2005), was used in deriving the Connectome data sets; DSI is a variant of diffusion-weighted imaging that is sensitive to intra-voxel heterogeneities in diffusion directions caused by crossing fiber tracts and thus allows more accurate mapping of axonal trajectories than other diffusion imaging approaches (Wedeen, 2008).

DWI is most applicable when the tissue of interest is dominated by isotropic water movement e.g. grey matter in the cerebral cortex and major brain nuclei, or in the body—where the diffusion rate appears to be the same when measured along any axis. However, DWI also remains sensitive to T1 and T2 relaxation. To entangle diffusion and relaxation effects on image contrast, one may obtain quantitative images of the diffusion coefficient, or more exactly the Apparent Diffusion Coefficient (ADC). The ADC concept was introduced to take into account the fact that the diffusion process is complex in biological tissues and reflects several different mechanisms.

**Diffusion tensor imaging** (DTI) is important when a tissue—such as the neural axons of white matter in the brain or muscle fibers in the heart—has an internal fibrous structure analogous to the anisotropy of some crystals. Water will then diffuse more rapidly in the direction aligned with the internal structure, and more slowly as it moves perpendicular to the preferred direction. This also means that the measured rate of diffusion will differ depending on the direction from which an observer is looking.

Traditionally, in diffusion-weighted imaging (DWI), three gradient-directions are applied, sufficient to estimate the trace of the diffusion tensor or 'average diffusivity', a putative measure of edema. Clinically, trace-weighted images have proven to be very useful to diagnose vascular strokes in the brain, by early detection (within a couple of minutes) of the hypoxic edema.

More extended DTI scans derive neural tract directional information from the data using 3D or multidimensional vector algorithms based on six or more gradient directions, sufficient to compute the diffusion tensor. The diffusion model is a rather simple model of the diffusion process, assuming homogeneity and linearity of the diffusion within each image voxel. From the diffusion tensor, diffusion anisotropy measures such as the fractional anisotropy (FA), can be computed. Moreover, the principal direction of the diffusion tensor can be used to infer the white-matter connectivity of the brain (i.e. tractography; trying to see which part of the brain is connected to which other part).

Recently, more advanced models of the diffusion process have been proposed that aim to overcome the weaknesses of the diffusion tensor model. Amongst others, these include q-space imaging and generalized diffusion tensor imaging.

Read more about Diffusion MRI: Bloch–Torrey Equation, Diffusion Imaging, Diffusion Tensor Imaging, Mathematical Foundation—tensors, HARDI: High-angular-resolution Diffusion Imaging and Q-ball Vector Analysis