Molecular diffusion refers to the random translational motion of molecules moving with thermal velocities - Brownian motion. During their random motion, molecules probe tissue structure at a microscopic scale well beyond the usual image resolution. The dependence of the molecular displacement on the measurement duration is defined by the Einstein relationship: <r2> = 6Dt , where t is the observation (i.e. diffusion) time and <r2> is the mean squared displacement of an ensemble of spins in three dimensions and corresponds to the variance of the displacement distribution. The proportionality constant in this relationship is D, the diffusion coefficient. The Einstein relationship results from characterizing molecular displacement in 3 dimensions by a Gaussian probability of finding a given spin initially at point r1 between positions r2 and r2+dr2 after a time interval τD. The Gaussian nature of this distribution underlies the quantification of the diffusion coefficient with NMR. For a typical diffusion time of about 50 msec, roughly the time scale of MRI diffusion encoding, water molecules sample the brain tissue environment over distances of around 10 um. This is a considerable distance at cellular scale, allowing molecules to interact with various tissue components such as cell membranes, fibers, or macromolecules. Diffusion in tissue is seldom ‘free’ on such long time and distance scales, but either restricted or hindered. Several water compartments – possibly in exchange with each other – will be present. Moreover, there are a variety of ways in which water can be transported in biological systems. However, assuming a Gaussian propagator for diffusion – which is strictly correct only for free diffusion - allows one to greatly simplify modeling the attenuation of the NMR signal following its sensitization to diffusion by use of gradient pulses. The attenuation is usually described as S(b)=S0exp(-bD), where b is a factor depending on the concrete experimental details and D is the molecular self-diffusion coefficient for e.g. an isotropic liquid. In an unconfined liquid the diffusion coefficient would be determined by its viscosity and the molecular size as well as temperature (which governs Brownian motion). But in biological tissue the local diffusion reflects the complicated biophysical processes that dictate the movement of water, such that the measured signal changes will reflect a convoluted ‘apparent diffusion coefficient’ that can differ significantly from the diffusion coefficient of the free (unrestricted) liquid. Diffusion is truly a three-dimensional process and molecular mobility in tissues such as white matter in the brain is different for different directions. Diffusion is encoded in the MRI signal by using magnetic field gradient pulses and hence only molecular displacements that occur along the direction of the gradient are visible. The effect of diffusion anisotropy can then easily be detected by observing variations in the diffusion measurements when the direction of the gradient pulses is changed. Diffusion anisotropy in brain white matter originates from its specific organization in bundles of more or less myelinated axonal fibers running in parallel. Diffusion in the direction of the fibers is faster than in the perpendicular direction. This property was exploited very early on in diffusion-sensitised MRI to map the fibre orientation in the brain, assumed to be identical with the direction of fastest diffusion. Mapping fibre orientation with the sophistication achieved nowadays has started with the introduction of the diffusion tensor formalism by Basser et al. – DTI.

Several indices have been derived from the diffusion tensor; the most widely used parameter of DTI is fractional anisotropy, FA, representing the motional anisotropy of water molecules. FA is sensitive to the presence and integrity of white matter fibers. The possibility to track a fiber system opened the field of anatomical connectivity. Tractography is prone to error, some inherent in the DTI model, and since its advent, considerable effort has been devoted to validating its results.

This presentation will address in greater or lesser detail the following aspects:

- general properties of diffusion (free/restricted/hindered, temperature dependence)

- the diffusion tensor model and diffusion indices (ADC, FA, axial and radial diffusivity,…)

- correlations of these indices with other quantities reflecting tissue structure, either MRI-derived (myelin water, magnetization transfer) or based on histology (e.g. cellularity)

- acquisition strategies (single- and multi-shot acquisitions)

- data sampling strategies (directions, b-value) - validation strategies (histology, phantoms)

- applications: tractography in neurosurgery, brain connectivity in vivo, gray matter structure and connectivity in fixed tissue

- what does DTI leave out?