Axial and radial axonal diffusivities and radii from single encoding strongly diffusion-weighted MRI

Mapping axon diameters and conduction velocity in the rat brain – different methods tell different stories of the structure-function relationship

“…Additionally, the presence of axons with diameters in the transition area may explain the variation we observed in the dMRI results when compared with shrinkage-corrected Epon-TEM. Studies have presented in vivo axon diameter estimations in the human brain 27,35,36,64 with robust rescan findings 65 . Due to the hardware and SNR, those dMRI studies also had a diameter lower bound on a scale of several micrometers 27,34 .…”

Bridging the 3D geometrical organisation of white matter pathways across anatomical length scales and species

“…We used data from four subjects of the Human Connectome Project (HCP) Adult Diffusion database to compute the eigenvalues and eigenvectors of the diffusion tensor ( 16 ) via a two-step weighted and iterated least-squares method ( 49 ) as implemented in MRtrix3 ( 23 ). Data were denoised as indicated in ( 50 ) using a Rician variance stabilisation transform ( 51 ) in combination with PCA optimal shrinkage ( 52 ), with subsequent application of Gibbs ringing removal ( 48 ) and eddy current distortion correction ( 53 ). For the estimation of the tensor, we selected only the b=0 and the 64 volume-directions corresponding to b=1000s/mm 2 .…”

Pore size estimation in axon‐mimicking microfibers with diffusion‐relaxation MRI

“…The spherical mean diffusion‐weighted signal $$$ {\overline{S}}_{\mathrm{Diff}}\left(b,r\right) $$$ from a cylinder with radius $$$ r $$$, in Eq. (), is modeled as $$$$ {\overline{S}}_{\mathrm{Diff}}\left(b,r\right)=\sqrt{\frac{\pi }{4}}\exp \left(-{D}_{\perp }(r)b\right)\frac{\operatorname{erf}\left(\sqrt{b\left({D}_{\parallel }-{D}_{\perp }(r)\right)}\right)}{\sqrt{b\left({D}_{\parallel }-{D}_{\perp }(r)\right)}}, $$$$ which is the spherical mean signal equation for an axis‐symmetric diffusion tensor, 2,13,36,37,40,41 where $$$ \operatorname{erf} $$$ denotes the error function, and the radial diffusivity $$$ {D}_{\perp } $$$ depends on $$$ r $$$ according to the van Gelderen model, 38 defined in Eq. () in .…”

“…which is the spherical mean signal equation for an axis-symmetric diffusion tensor, 2,13,36,37,40,41 where erf denotes the error function, and the radial diffusivity D ⊥ depends on r according to the van Gelderen model, 38 defined in Eq. (A1) in Appendix A.…”

“…Accurately measuring the diameter of axons in vivo has been a crucial goal in diffusion MRI (dMRI), [1][2][3][4][5][6][7][8][9][10][11][12][13] because the axon diameter modulates the speed of action potentials along the axon and may serve as a biomarker of axonal degeneration. [14][15][16][17] However, existing dMRI techniques are affected by a resolution limit, or diameter lower-bound, below which smaller axons cannot be detected.…”