Jens H Jensen1,2,3. 1. Center for Biomedical Imaging, Medical University of South Carolina, Charleston, South Carolina, USA. 2. Department of Neuroscience, Medical University of South Carolina, Charleston, South Carolina, USA. 3. Department of Radiology and Radiological Science, Medical University of South Carolina, Charleston, South Carolina, USA.
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.
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.
Authors: Sudhir Ramanna; Hunter G Moss; Emilie T McKinnon; Essa Yacoub; Joseph A Helpern; Jens H Jensen Journal: Magn Reson Med Date: 2019-11-25 Impact factor: 4.668
Authors: Lorna Bryant; Emilie T McKinnon; James A Taylor; Jens H Jensen; Leonardo Bonilha; Christophe de Bezenac; Barbara A K Kreilkamp; Guleed Adan; Udo C Wieshmann; Shubhabrata Biswas; Anthony G Marson; Simon S Keller Journal: Hum Brain Mapp Date: 2021-02-19 Impact factor: 5.038