Optimized rectification of fiber orientation density function with background threshold.

Purpose: To describe an optimized fiber orientation density function (fODF) rectification procedure that removes negative values and absorbs all features below a specified threshold into a constant background.

Theory And Methods: The fODF for a white matter imaging voxel describes the angular density of axons. Because of signal noise and Gibbs ringing, fODFs estimated with diffusion MRI may take on unphysical negative values in some directions and contain spurious peaks. In order to suppress such artifacts, an fODF rectification procedure is proposed that both eliminates all negative values and incorporates all features below a specified threshold, η, into a constant background while at the same time minimizing the mean square deviation from the original, unrectified fODF. Calculating this fODF is straightforward, and the directions and shapes of peaks not absorbed into the background are preserved. The rectification method is illustrated for an analytic fODF model and for experimental diffusion MRI data obtained in healthy human brain, with the original fODFs being obtained from fiber ball imaging.

Results: Examples of optimal rectified fODFs are given for three choices of the background threshold referred to as minimal rectification (η = 0), average-level rectification (η ≈ 0.08), and fractional-anisotropy-axonal-based rectification (η ≈ 0.1). As η is increased, artifacts and other small features are more strongly suppressed, but the major fODF peaks are largely unaffected for the range of η values illustrated by these three alternatives.

Conclusion: Artifactual features of fODFs estimated with diffusion MRI can be effectively suppressed by applying the proposed optimized rectification procedure. Since it minimizes fODF distortion in the mean square sense, it may be useful in the study of how fODF fine structure is affected by aging and disease.