Optimized rectification of fiber orientation density function

Abstract

Purpose: To demonstrate an optimized rectification strategy for fiber orientation density functions (fODFs).

Theory and methods: In white matter, fODFs can be estimated with diffusion MRI. However, because of signal noise, imaging artifacts and other factors, experimentally determined fODFs may take on unphysical negative values in some directions. Here, we show how to rectify such fODFs to eliminate all negative values while minimizing the mean square difference between the original and rectified fODFs. The method is demonstrated for a mathematical model and for fODFs estimated from experimental human data using both constrained spherical deconvolution and fiber ball imaging. Comparison with an alternative nonoptimized rectification approach is also provided.

Results: For the mathematical model, it is found that the optimized rectification procedure removes negative fODF values while at the same time reducing the mean square error. Relative to the alternative rectification approach, the optimized fODFs are substantially more accurate. For the experimental data, the optimized fODFs have a lower average fractional anisotropy axonal and often fewer small peaks than the original, unrectified fODFs. The calculation of optimized fODFs is straightforward where the main step is the finding of the root to an equation in one variable, as may be efficiently accomplished with the bisection method.

Conclusion: Unphysical negative fODF values can be easily eliminated in a manner that minimizes the mean square difference between the original and rectified fODFs. Optimized fODF rectification may be useful in applications for which negative values are problematic.

Keywords: axon; constrained spherical deconvolution; fiber ball imaging; fiber orientation density function; rectification; white matter.