Water molecule diffusion patterns can therefore reveal microscopic details about tissue architecture, either normal or in a diseased state.

A special kind of DWI, diffusion tensor imaging (DTI), has been used extensively to map white matter tractography in the brain.

Because the mobility of water is driven by thermal agitation and highly dependent on its cellular environment, the hypothesis behind DWI is that findings may indicate (early) pathologic change.

It is also used more and more in the staging of non-small-cell lung cancer, where it is a serious candidate to replace positron emission tomography as the 'gold standard' for this type of disease.

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.

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.

[6] 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.

[7] DBSI has been shown to differentiate some types of brain tumors and multiple sclerosis with higher specificity and sensitivity than conventional DTI.

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.

Regular MRI acquisition utilizes the behavior of protons in water to generate contrast between clinically relevant features of a particular subject.

The versatile nature of MRI is due to this capability of producing contrast related to the structure of tissues at the microscopic level.

The refocusing will not be perfect for protons that have moved during the time interval between the pulses, and the signal measured by the MRI machine is reduced.

The equation set by Stejskal and Tanner then becomes inaccurate and the signal attenuation must be calculated, either analytically or numerically, integrating all gradient pulses present in the MRI sequence and their interactions.

The result quickly becomes very complex given the many pulses present in the MRI sequence, and as a simplification, Le Bihan suggested gathering all the gradient terms in a "b factor" (which depends only on the acquisition parameters) so that the signal attenuation simply becomes:[1] Also, the diffusion coefficient,

, to indicate that the diffusion process is not free in tissues, but hindered and modulated by many mechanisms (restriction in closed spaces, tortuosity around obstacles, etc.)

and that other sources of IntraVoxel Incoherent Motion (IVIM) such as blood flow in small vessels or cerebrospinal fluid in ventricles also contribute to the signal attenuation.

, of the b factor according to: Although this ADC concept has been extremely successful, especially for clinical applications, it has been challenged recently, as new, more comprehensive models of diffusion in biological tissues have been introduced.

[22] Torrey modified Bloch's original description of transverse magnetization to include diffusion terms and the application of a spatially varying gradient.

In some methods, hundreds of measurements—each making up a complete image—are made to generate a single resulting calculated image data set.

In addition the directional information can be exploited at a higher level of structure to select and follow neural tracts through the brain—a process called tractography.

The relationship between the properties of driving force that generate diffusion of the water molecules and the resulting pattern of their movement in the tissue can be described by a tensor.

The collection of molecular displacements of this physical property can be described with nine components—each one associated with a pair of axes xx, yy, zz, xy, yx, xz, zx, yz, zy.

In 1848, Henri Hureau de Sénarmont[31] applied a heated point to a polished crystal surface that had been coated with wax.

Measurement of an ellipsoid tensor further permits a retrospective analysis, to gather information about the process of diffusion in each voxel of the tissue.

The architecture of the axons in parallel bundles, and their myelin sheaths, facilitate the diffusion of the water molecules preferentially along their main direction.

This vector can be color-coded, yielding a cartography of the tracts' position and direction (red for left-right, blue for superior-inferior, and green for anterior-posterior).

In the classic diffusion ellipsoid tensor model, the information from the crossing tract appears as noise or unexplained decreased anisotropy in a given voxel.

We use "n-tuple" tessellations to add more evenly spaced apices to the original icosahedron (20 faces)—an idea that also had its precedents in paleomagnetism research several decades earlier.

Several in-vivo studies have shown that the choice of software and functions applied (directed at correcting artefacts arising from e.g. motion and eddy-currents) have a meaningful impact on the DTI parameter estimates from tissue.

In some cases, the full set of tensor properties is of interest, but for tractography it is usually necessary to know only the magnitude and orientation of the primary axis or vector.