fODF

In diffusion MRI, the fiber orientation distribution function (fODF) is a function on the unit sphere that describes the distribution of fiber orientations within a voxel. It represents the probability density of fibers pointing in a given direction and is typically interpreted as fiber density along directions.

The fODF is estimated from high angular resolution diffusion imaging data using deconvolution or reconstruction techniques such as Q-ball imaging and constrained spherical deconvolution. These methods aim to recover the fODF from the measured diffusion signal, often by assuming a single-fiber response function and imposing constraints to enforce non-negativity and sparsity.

fODF-based analysis enables tractography to reconstruct multiple fiber compartments in a voxel, improving detection of crossing, kissing, or fanning fibers. It is widely used in studies of structural connectivity and white matter architecture.

Normalizations: the fODF is often constrained to integrate to one over the sphere, and its values can be interpreted as relative fiber density along directions. Multi-tissue variants extend the model to account for cerebrospinal fluid and gray matter contributions.

Limitations include sensitivity to noise, the need for high-quality diffusion data, and dependence on the assumed response function and regularization. Interpretations should consider partial-volume effects and calibration.