User:Jadrian Miles/Diffusion MRI techniques

Note to author: check out [1] for a pretty good explanation. Please add references.

The Orientation Density Function

Imagine that we wanted to measure the diffusion characteristics in a tissue at only one point. Further imagine that we had a perfect scanner that gave us precise measurements with no noise, and that we had infinite time to perform as many scans as we wanted. Let's use this infinite time to perform a measurement at every point in Q space. By plotting all the values that we measured, we would get a scalar-valued function over Q space — the complete diffusion imaging signal profile. Thi

Actual acquisitions give us only a collection of point samples of the profile in Q space. If we had perfect knowledge of the tissue microstructure at a particular point, we could reconstruct the profile from this information. Modeling tissue microstructure given samples of the profile is the basic voxel-level problem of diffusion MRI processing.

 This is called an orientation density function (ODF).

DTI

Various simple representations of the ODF have been developed. The most popular is a six-degree-of-freedom diffusion tensor, which represents the ODF as a single ellipsoid. Diffusion tensor imaging (DTI) is a technique in which many DWIs are collected and then the measurements in each voxel are summarized as a diffusion tensor, to form a single image called a diffusion tensor image (which, confusingly, also has the initialism DTI).

Other ODF Models

The diffusion tensor model is not the only representation of diffusion ODFs that has been developed. Others include spherical harmonics, generalized diffusion tensors, and local tract models based on probability maximization, deconvolution, and regularization with nearby voxels (e.g. the spin-glass model).

Voxelwise Measurements

Various measurements of diffusion tensors have been