Jordan A. Chad1,2, Ofer Pasternak3, and J. Jean Chen1,2
1Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, 2Rotman Research Institute, Baycrest Health Sciences, Toronto, ON, Canada, 3Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States
1Department of Medical Biophysics, University of Toronto, Toronto, ON, Canada, 2Rotman Research Institute, Baycrest Health Sciences, Toronto, ON, Canada, 3Brigham and Women's Hospital, Harvard Medical School, Boston, MA, United States
A constant tissue-trace constraint on the two-compartment free-water model allots all variation in isotropic diffusivity to the free water compartment, which is found to be more linearly aligned with quadratic variations in diffusivity.
Figure 1. Reproduction of the “tissue compartment” results of a single-shell free-water study of aging white matter, simulated using the constant tissue-trace constraint. Metrics derived from the tissue compartment, as per Eq. 6, represent variation in the shape of the tissue tensor while the size remains constant, since all isotropic variations are allotted to the free water compartment. For a biological interpretation of these results, see ref. 6.
Figure 2. Reproduction of the “free water compartment” results of a single-shell free-water study of aging white matter, simulated using the constant tissue-trace constraint. The constant tissue-trace relationship between f and MD (Eq. 3) is nonlinear, so the linear correlation coefficients exhibited by f and MD differ. If MD better follows a quadratic distribution, as is thought to be the case in aging, f follows a distribution that can be better approximated by a line.