Characterizing intra‐axonal water diffusion with direction‐averaged triple diffusion encoding MRI

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Purpose To demonstrate how triple diffusion encoding (TDE) MRI can be applied to separately estimate the intra‐axonal and extra‐axonal diffusion tensors in white matter (WM). Methods Using a TDE pulse sequence with an axially symmetric b‐matrix, diffusion MRI data were acquired at 3T for 3 healthy adults with an axial b‐value of 4000 s/mm2, a radial b‐value of 307 s/mm2, and 64 diffusion encoding directions. This acquisition was then repeated with the radial b‐value set to 0. A previously proposed theory was applied to these data in order to estimate the intra‐axonal diffusivity and axonal water fraction for each WM voxel. Conventional single diffusion encoding data were also obtained with b‐values of 1000 and 2000 s/mm2, which provided additional information sufficient for determining both the intra‐axonal and extra‐axonal diffusion tensors. Results From the TDE data, the average intra‐axonal diffusivity in WM was found to be 2.24 ± 0.18 µm2/ms, and the average axonal water fraction was found to be 0.60 ± 0.11. From the 2 diffusion tensors, average WM values were estimated for several compartment‐specific diffusion parameters. In particular, the extra‐axonal mean diffusivity was 1.09 ± 0.19 µm2/ms, the intra‐axonal fractional anisotropy was 0.50 ± 0.14, and the extra‐axonal fractional anisotropy was 0.23 ± 0.13. Conclusion By using a simple TDE pulse sequence with an axially symmetric b‐matrix, the diffusion tensors for the intra‐axonal and extra‐axonal spaces can be separately estimated in adult WM. This allows one to determine compartment‐specific diffusion properties for these 2 water pools.

“…The validity of Equations and requires that b || be approximately ≥4000 s/mm 2 and that

b_{⊥} < < b_{| |}

. The different ordering of the radial and axial gradient pulses used here, in comparison to our previous work, does not affect the accuracy of these 2 equations.…”

Section: Methodsmentioning

confidence: 81%

“…This corresponds to

g_{| |} \approx g_{⊥} \approx

Section: Methodsmentioning

confidence: 99%

“…The intra‐axonal diffusivity in WM was then calculated from Equation :

D_{a} = \frac{1}{b_{⊥}} \ln (\frac{{\bar{S}}_{1}}{{\bar{S}}_{2}} \sqrt{\frac{b_{| |}}{b_{false| false|} - b_{⊥}}})

where

{\bar{S}}_{1}

is the direction‐averaged signal when

b_{⊥}

= 0 s/mm 2 and

{\bar{S}}_{2}

is the direction‐averaged signal when

b_{⊥}

= 307 s/mm 2 . We also calculated the axonal water fraction in each voxel from Equation :

f = 2 \sqrt{\frac{D_{a} b_{false| false|}}{π}} \cdot \frac{{\bar{S}}_{1}}{{\bar{S}}_{0}}

where

{\bar{S}}_{0}

is the average signal for the b0 images. The validity of Equations and requires that b || be approximately ≥4000 s/mm 2 and that

b_{⊥} < < b_{| |}

.…”

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Triple diffusion encoding MRI predicts intra‐axonal and extra‐axonal diffusion tensors in white matter

Ramanna

Moss

McKinnon

et al. 2019

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Measuring intra‐axonal T₂ in white matter with direction‐averaged diffusion MRI

McKinnon

Jensen

2018

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Purpose To demonstrate how the T2 relaxation time of intra‐axonal water (T2a) in white matter can be measured with direction‐averaged diffusion MRI. Methods For b‐values larger than about 4000 s/mm2, the direction‐averaged diffusion MRI signal from white matter is dominated by the contribution from water within axons, which enables T2a to be estimated by acquiring data for multiple TE values and fitting a mono‐exponential decay curve. If given a value of the intra‐axonal diffusivity, an extension of the method allows the extra‐axonal relaxation time (T2e) to be calculated also. This approach was applied to estimate T2a in white matter for 3 healthy subjects at 3 T, as well as T2e for a selected set of assumed intra‐axonal diffusivities. Results The estimated T2a values ranged from about 50 ms to 110 ms, with considerable variation among white matter regions. For white matter tracts with primarily collinear fibers, T2a was found to depend on the angle of the tract relative to the main magnetic field, which is consistent with T2a being affected by magnetic field inhomogeneities arising from spatial differences in magnetic susceptibility. The T2e values were significantly smaller than the T2a values across white matter regions for several plausible choices of the intra‐axonal diffusivity. Conclusion The relaxation time for intra‐axonal water in white matter can be determined in a straightforward manner by measuring the direction‐averaged diffusion MRI signal with a large b‐value for multiple TEs. In healthy brain, T2a is greater than T2e and varies considerably with anatomical region.

Direction‐averaged diffusion‐weighted MRI signal using different axisymmetric B‐tensor encoding schemes

Afzali

Aja‐Fernández

Jones

2020

Purpose: It has been shown, theoretically and in vivo, that using the Stejskal-Tanner pulsed-gradient, or linear tensor encoding (LTE), and in tissue exhibiting a "stick-like" diffusion geometry, the direction-averaged diffusion-weighted MRI signal at high b-values (7000 < b < 10000 s∕mm 2 ) follows a power-law, decaying as 1∕ √ b. It has also been shown, theoretically, that for planar tensor encoding (PTE), the directionaveraged diffusion-weighted MRI signal decays as 1/b. We aimed to confirm this theoretical prediction in vivo. We then considered the direction-averaged signal for arbitrary b-tensor shapes and different tissue substrates to look for other conditions under which a power-law exists. Methods: We considered the signal decay for high b-values for encoding geometries ranging from 2-dimensional PTE, through isotropic or spherical tensor encoding to LTE. When a power-law behavior was suggested, this was tested using in silico simulations and, when appropriate, in vivo using ultra-strong (300 mT/m) gradients. Results: Our in vivo results confirmed the predicted 1/b power law for PTE.Moreover, our analysis showed that using an axisymmetric b-tensor a power-law only exists under very specific conditions: (a) "stick-like" tissue geometry and purely LTE or purely PTE waveforms; and (b) "pancake-like" tissue geometry and a purely LTE waveform. Conclusions:A complete analysis of the power-law dependencies of the diffusionweighted signal at high b-values has been performed. Only three specific forms of encoding result in a power-law dependency, pure linear and pure PTE when the tissue geometry is "stick-like" and pure LTE when the tissue geometry is "pancake-like". The different exponents of these encodings could be used to provide independent validation of the presence of different tissue geometries in vivo. K E Y W O R D SB-tensor encoding, diffusion-weighted MRI, direction-averaged diffusion signal, high b-value, power-law 1580 | AFZALI et AL.