Diffusion Spectrum Imaging

Diffusion spectrum imaging may be described as the reference standard of diffusion imaging because it is the practical implementation of the principles derived earlier and is the diffusion imaging technique that has a sound basis in physical theory (12). Suitable for in vivo application, it provides a sufficiently dense q-space signal sample from which to derive a displacement distribution with the use of the Fourier transform. The technique was first described by Wedeen et al (13).

If established practice is followed, 515 diffusion-weighted images are acquired successively, each corresponding to a different q vector, that are placed on a cubic lattice within a sphere with a radius of five lattice units. The lattice units correspond to different b (or q) values, from b = 0 (which corresponds to the centerpoint of the sphere) to, typically, b = 12,000 sec/mm2 (which is a very high b value). The Fourier transform is computed over the q-space data. If the imaging matrix size is 128 × 128 × 30, the same number of Fourier transform operations will be necessary as the diffusion probability density function is computed for every brain location.

Traditionally, 515 images were considered necessary to obtain data of good quality, although the acquisition of that number of images is very time consuming. With improvements in MR imaging hardware and techniques in recent years, and in view of additional very recent experience, fewer sampling points seem to be necessary; the probability density function can be reconstructed with approximately 257 or even 129 images by sampling only one hemisphere in q-space. Of course, the signal-to-noise ratio and angular resolution may change accordingly. The time for imaging of both brain hemispheres thus can be reduced from approximately 45–60 minutes to as little as 10–20 minutes, an acquisition time that makes the technique feasible in a clinical setting (14).

With the application of the Fourier transform over q-space in every brain position, a 6D image of both position and displacement is obtained. Diffusion at each position is described by the displacement distribution or the probability density function, which provides a detailed description of diffusion and excellent resolution of the highly complex fiber organization, including fiber crossings. Since diffusion spectrum imaging is mostly used for fiber tractography, in which only directional information is needed, the probability density function is normally reduced to an orientation distribution function by summing the probabilities of diffusion in each direction

Diagram shows how an orientation distribution function (ODF) is computed and represented. Left: Image of a section through a schematized 3D displacement distribution. The value of the orientation distribution function was computed along two axes (yellow lines). Center: Histograms represent the displacement distribution along the two axes. The value of the orientation distribution function along those axes equals the area under the curve for each axis. In this example, the two areas under the curve are respectively small and large, indicating that there is much less diffusion in the one direction than in the other. Right: The sum of the areas under the curve is represented by a deformed sphere in which the lengths of the two radii (yellow lines) are short and long, corresponding to little diffusion and much diffusion, respectively. To compute the orientation distribution function, the area under the curve is computed for every direction.