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PURPOSE: To develop a statistical model for the tridimensional diffusion MRI signal at each voxel that describes the signal arising from each tissue compartment in each voxel. THEORY AND METHODS: In prior work, a statistical model of the apparent diffusion coefficient was shown to well-characterize the diffusivity and heterogeneity of the mono-directional diffusion MRI signal. However, this model was unable to characterize the three-dimensional anisotropic diffusion observed in the brain. We introduce a new model that extends the statistical distribution representation to be fully tridimensional, in which apparent diffusion coefficients are extended to be diffusion tensors. The set of compartments present at a voxel is modeled by a finite sum of unimodal continuous distributions of diffusion tensors. Each distribution provides measures of each compartment microstructural diffusivity and heterogeneity. RESULTS: The ability to estimate the tridimensional diffusivity and heterogeneity of multiple fascicles and of free diffusion is demonstrated. CONCLUSION: Our novel tissue model allows for the characterization of the intra-voxel orientational heterogeneity, a prerequisite for accurate tractography while also characterizing the overall tridimensional diffusivity and heterogeneity of each tissue compartment. The model parameters can be estimated from short duration acquisitions. The diffusivity and heterogeneity microstructural parameters may provide novel indicator of the presence of disease or injury. Magn Reson Med 76:963-977, 2016. © 2015 Wiley Periodicals, Inc.

Original publication




Journal article


Magn Reson Med

Publication Date





963 - 977


diffusion compartment imaging, diffusion-weighted MRI, non-monoexponential decay, statistical distribution model, tissue microstructure, Animals, Anisotropy, Brain, Computer Simulation, Diffusion Magnetic Resonance Imaging, Humans, Image Interpretation, Computer-Assisted, Imaging, Three-Dimensional, Models, Neurological, Models, Statistical, Reproducibility of Results, Sensitivity and Specificity