Samo Lasic1,2, Filip Szczepankiewicz3, Markus Nilsson3, Tim B. Dyrby1,4, and Henrik Lundell1
1Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Copenhagen, Denmark, 2Random Walk Imaging, Lund, Sweden, 3Clinical Sciences, Lund University, Lund, Sweden, 4Department of Applied Mathematics and Computer Science, Technical University of Denmark, Copenhagen, Denmark
1Danish Research Centre for Magnetic Resonance, Centre for Functional and Diagnostic Imaging and Research, Copenhagen University Hospital Hvidovre, Copenhagen, Denmark, 2Random Walk Imaging, Lund, Sweden, 3Clinical Sciences, Lund University, Lund, Sweden, 4Department of Applied Mathematics and Computer Science, Technical University of Denmark, Copenhagen, Denmark
Considering time-dependent diffusion and spectral anisotropy of tensor-valued encoding suggests a novel way of inferring microstructure. Rotational dependence of spherical encoding in fixed monkey brain on a preclinical scanner indicates that diffusion is restricted in all directions.
Figure 2: Spectral content for the STE from Fig. 1 color coded based on 3 frequency bands with equal encoding power determined from $$$s(\omega)$$$ and its cumulative sum (inset). Projections 1-3 along the SPAS (dotted lines), relative to the laboratory frame (XYZ), have the most (along $$$\bf{u}_\mathrm{LF}$$$) to the least power in the low frequency band. The orange lines illustrate an ODF and its main direction $$$\boldsymbol{\mu}$$$ for which the angle $$$\sigma$$$ can be calculated.
Figure 3: STP differentiates sticks from cylinders. Noiseless calculations for Watson ODF with varying OP (columns) of axisymmetric restrictions with varying $$$D_\Delta$$$: sticks ($$$d = 5\mathrm{\mu m}, D_\Delta = 1$$$), prolate ellipsoids ($$$R_3/R_1 = 5\mathrm{\mu m}/1\mathrm{\mu m}, D_\Delta = 0.99$$$), cylinders ($$$R = 5\mathrm{\mu m}, D_\Delta = 0.38$$$), oblate ellipsoids ($$$R_3/R_1 = 1\mathrm{\mu m}/5\mathrm{\mu m}, D_\Delta = -0.5$$$). In all cases, $$$D_0 = 2\times 10^{-9} m^2/s$$$. Compare the marked examples (dotted) with experimental results (Fig. 4)
