Power-law scaling of the diffusion signal in gray matter and the influence of exchange
Jonas L. Olesen1,2, Noam Shemesh3, and Sune N. Jespersen1,2
1Center of Functionally Integrative Neuroscience (CFIN) and MINDLab, Aarhus University, Aarhus, Denmark, 2Department of Physics and Astronomy, Aarhus University, Aarhus, Denmark, 3Champalimaud Research, Champalimaud Centre for the Unknown, Lisbon, Portugal
We report the first observation of a b-1/2
power-law in grey matter at very large b-values, which is obscured by the soma
signal contribution at smaller b-values. The effects of significant water
exchange are observed by varying the diffusion time.
Figure 1. a) ROI’s used for computing cortex and
corpus callosum voxel-averaged signals. The ROI’s are depicted on an estimate
of the b=0 signal (left) and the fractional anisotropy (right), both from a DKI
fit to the data fulfilling b≤3ms/µm2 for acquisition 1. Equivalent ROI’s were used for
acquisition 2. b) The
powder averaged signals as a function of $$$1/\sqrt{b}$$$ for acquisition 1. The black lines show linear
fits to data in the interval [0.1; 0.2].
Figure 2. Cortex signal (markers) as a function
of $$$1/\sqrt{b}$$$ for acquisition 1. Fits of SANDI (left panel)
and the Kärger SM (right panel) are shown by black lines. The dashed lines
depict the signal prediction at half the pulse separation using the estimated
parameters from the fits. SANDI estimates are: extra-cellular fec = 59%, Dec = 0.63µm2/ms, neurite fin = 49%, Din = 2.32µm2/ms, soma R = 5.6µm, offset < 1%. Kärger
SM estimates are: extra-cellular fec = 51%, Dec = 0.57µm2/ms, neurite Din = 1.73µm2/ms, mean intra-neurite residence time τin = 7.9ms, offset = 1%.