Sensitivity advantage of a two- over one-compartment diffusion model for studying aging: An analytic demonstration
Jordan A. Chad1,2, Nir Sochen3,4, J. Jean Chen1,2, and Ofer Pasternak5,6
1Rotman Research Institute, Baycrest Health Sciences, Toronto, ON, Canada, 2Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, 3School of Mathematical Sciences, Tel Aviv University, Tel Aviv, Israel, 4School of Neuroscience, Tel Aviv University, Tel Aviv, Israel, 5Department of Radiology, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States, 6Department of Psychiatry, Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States
Recent diffusion modeling studies aim to distinguish age-related degenerative processes specific to white matter fibers, such as axonal myelination and dispersion, from age-related elevated isotropic diffusivity, resulting from, e.g., enlargement of the extracellular space. Here we analytically investigate the relationship between two single-shell approaches for distinguishing these effects, respectively based on a one- and two-compartment model. We derive a nonlinear relationship between the models that renders a sensitivity advantage to the two-compartment model, and find that a linear elevation of an isotropic compartment with age explains the well-documented phenomenon of accelerated MD elevations (faster radially than axially) in aging.
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