A Generalized SMT-Based Framework for Diffusion MRI Microstructural Model Estimation
Diffusion Magnetic Resonance Imaging (DMRI) has been widely used to characterize the principal directions of white matter fibers, also known as fiber Orientation Distribution Function (fODF), and axonal density in brain tissues.
Recently, different multi-compartment models have been proposed allowing the joint estimation of both the fODF and axonal densities following different approaches. In this work, the problem has been cast in a unified framework using the Spherical Mean Technique (SMT), where the presence of multiple compartments is accounted for and the fODF is expressed in a parametric form allowing the estimation of the whole set of parameters. In this formulation, the fODF is expressed by its Spherical Harmonics (SH) representation and different multi-compartment models can be easily plugged in, enabling a structured and simple comparison of the respective performance.
Starting from a general multi-compartment formulation, four simplified two-parameters models are considered: Fiber ORientation Estimated using Continuous Axially Symmetric Tensors (FORECAST), Multi Compartment Microscopic Diffusion Imaging (MC-MDI), Neurite Orientation Dispersion and Density Imaging (NODDI), and Ball & Stick (BS). Their performances are compared against a synthetic ground truth evaluating the precision in the estimation of the intra-axonal volume fraction and the signal reconstruction error as well as the ability of the estimated fODF of capturing the fiber configuration. Results show that good parameter estimation can be reached with simplified two-parameters models, and highlight a different behavior for models where intra-axonal diffusivity is considered as a free parameter in terms of both axonal density and fODF estimation. This result suggests that although the intra-axonal volume fraction map estimated from human brain may be not completely accurate, it still mirrors the underlying tissue microstructure. The proposed formulation, relying on SMT and SH representation, allows unifying several microstructural models proposed in diffusion MRI literature under the same mathematical framework, providing the mean for easily comparing different models while highlighting their similarities and differences, and could be used as a reference for model selection on in vivo data.
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