We extract cytoarchitectural characteristics of brain gray matter from diffusion MRI signals including soma size, neurite signal fraction and water exchange. Our model improves on state-of-the-art in that 1) we extract an invertible system leading to stable parameters estimation, 2) our simulation-based inference approach allows to obtain the full posterior distribution of the parameters given a signal. Our solution is a two-step model. First, a new forward model relates summary statistics of the dMRI signal to different tissue parameters. Then, a likelihood-free inference-based algorithm is applied to invert the model, and returns a full posterior distribution over the parameter space.
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