Impact of intra-axonal kurtosis on fiber orientation density functions estimated with fiber ball imaging

Abstract

Purpose: To determine the impact of an intra-axonal kurtosis on estimates of the fiber orientation density function (fODF) obtained with fiber ball imaging (FBI).

Theory and methods: Standard FBI assumes Gaussian diffusion within individual axons and estimates the fODF by applying an inverse generalized Funk transform to diffusion MRI data for b-values of 4000 s/mm² or higher. However, recent work based on numeric simulations shows that diffusion inside axons is non-Gaussian with an intra-axonal kurtosis of ∼ 0.4. Here, the theory underlying FBI is extended to incorporate an intra-axonal kurtosis. This is done to first order in the intra-axonal kurtosis without making assumptions about the details of the diffusion dynamics and to all orders for a specific model based on a gamma distribution of diffusivities. The first order approximation is used to assess the effect of an intra-axonal kurtosis on FBI estimates for the fODF and axonal water fraction. The gamma distribution model is used to test the validity of the approximation.

Results: The first order approximation indicates the estimated fODF is altered by a few percent for an intra-axonal kurtosis of 0.4 in comparison to predictions of standard FBI. If one neglects the intra-axonal kurtosis, the angular resolution of the point spread function for the fODF is changed by <1°, whereas the axonal water fraction is overestimated by ∼ 5%. The gamma distribution model shows that the first order approximation is accurate to within a few percent.

Conclusion: The intra-axonal kurtosis has a small impact on fODFs estimated with FBI.

Keywords: fiber ball imaging; fiber orientation density function; intra-axonal; kurtosis; non-Gaussian; white matter.