Chantal M.W. Tax^{1}, Filip Szczepankiewicz ^{2,3}, Markus Nilsson^{2}, and Derek K Jones^{1}

The
accuracy of biophysical models requires that all relevant tissue compartments
are modelled. The so-called “dot compartment” is a conjectured compartment that
represents small cells with apparent diffusivity approaching zero. We establish
an upper limit of the “dot-fraction” across the whole brain in vivo, by using ultra-high
gradients and optimized gradient waveforms for spherical tensor encoding. We
report a notable signal above the noise floor in the cerebellar gray matter
even for an extremely high b-value of 15000 s/mm^{2}. For cerebral
tissue, the dot-fraction seems negligible, and we consider how exchange may
have affected this result.

The signal arising from each compartment represented by diffusion tensor $$$\mathbf{D}$$$ probed by b-tensor $$$\mathbf{B}$$$ can be described by $$$f\cdot\exp(\mathbf{B:D})$$$, which in the specific case of STE and two non-exchanging compartments (one dot-compartment) simplifies to

$$S(b)=f_{\text{dot}}\cdot\exp(−bD_{\text{dot}})+(1−f_{\text{dot}}){\cdot}\exp(−bD_{\text{iso}})=f_{\text{dot}}+(1−f_{\text{dot}}){\cdot}\exp(−bD_{\text{iso}}).$$

For infinite SNR, the $$$S(0)$$$-normalised signal at the plateau equals the dot signal fraction $$$(f_{\text{dot}}=S_{\text{plateau}}/S(0))$$$.
Fig.1 shows the simulated signal in the case of two non-exchanging
compartments with isotropic diffusivities of 1 and 0 µm^{2}/ms. In the absence of a plateau, the normalised signal at $$$b_{\text{max}}$$$ can serve as an upper limit of $$$f_{\text{dot}}$$$, because $$$f_{\text{dot}}≤S_{b_{\text{max}}}/S(0)$$$. The accuracy is limited by the presence of the noise floor but still
yields an upper-limit of $$$f_{\text{dot}}$$$, at
least in the absence of exchange.

Data: A healthy volunteer was
scanned on a 3T, 300mT/m Siemens Connectom using
a prototype spin-echo sequence that enables arbitrary b-tensor encoding. We
used b-values=[0,250,1500,3000,...,15000]s/mm^{2} repeated [1,6,9,12,...,36]
times, respectively. No in-plane
acceleration was used, voxel size=4.4×4.4×6 mm^{3}, matrix=64×64, 26
slices, TR/TE=5000/90ms, partial-Fourier=6/8,
bandwidth=1594Hz/pix. Maxwell-compensated waveforms^{11} were optimized
numerically^{12}, and yielded a diffusion time of approximately 20ms.
This approach renders superior encoding efficiency compared to standard 1-scan-trace imaging (requires
TE=270ms for b=15000s/mm^{2}). An MPRAGE was acquired for brain
segmentation.

Processing: To investigate whether a
potential plateau arising in the signal decay was not solely an effect of
the noise floor, the data was corrected for Rician bias^{13-15}.
Masks for different tissue types were created in Freesurfer based on the MPRAGE registered to the susceptibility-distortion corrected^{16} dMRI data,
and used to guide the definition four regions for further analysis: cerebral white
and gray matter (WM and GM), and cerebellar white and gray matter (cWM and cGM).

Fig.2 shows that the signal in most of the cerebral tissue was reduced to the noise
floor at $$$b$$$>9000 s/mm^{2}. However, cGM was observed to
have a remarkably high signal at high b-values, remaining well above the noise
floor even at b=15000 s/mm^{2},
unlike any other tissue.

Fig.3 shows that the signal-verus-b curve in cGM was markedly non-monoexponential,
with signal values above the noise floor for all sampled b-values. However, no
plateau is found at b=15000s/mm^{2}.
In the absence of exchange, the estimated upper-bound of $$$f_{\text{dot}}$$$ in
WM, GM, cWM and cGM is approximately 0.5%,0.5%,1% and 2%, respectively.

In
the cerebrum, we did not find evidence of a large dot-fraction. In the
cerebellum, however, the non-negligible signal at very high b-values points to
the existence of a dot-like compartment. The absence of a signal plateau
could be caused by compartments with low but non-zero isotropic
diffusivity, or a true dot-compartment with zero diffusivity but non-negligible
exchange. The effect of exchange^{17,18} is simulated in Fig.4, and can
result in an underestimation of $$$f_{\text{dot}}$$$.

Regardless
of model assumptions, the high signal retention at high b-values in the
cerebellum demonstrates that its microstructure is remarkably different
compared to the cerebrum. We speculate that this may
originate from granule and/or Purkinje cells, that have a morphology consistent with this finding (Fig.5). If so, STE at extremely
high b-values can become a very specific biomarker for better understanding of
diseases such as autism spectrum disorders^{19}, spinocerebellar ataxia^{20},
and Alzheimer disease^{21,22}, where such cells are affected.

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[8] Lasič, S., Szczepankiewicz, F., Eriksson, S., Nilsson, M. & Topgaard, D. 2014. Microanisotropy imaging: quantification of microscopic diffusion anisotropy and orientational order parameter by diffusion MRI with magic-angle spinning of the q-vector. Frontiers in Physics, 2, 11.

[9] Westin, C. F., Knutsson, H., Pasternak, O., Szczepankiewicz, F., Özarslan, E., Van Westen, D., Mattisson, C., Bogren, M., O'donnell, L. J., Kubicki, M., Topgaard, D. & Nilsson, M. 2016. Q-space trajectory imaging for multidimensional diffusion MRI of the human brain. Neuroimage, 135, 345-62.

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Fig. 1: Simulations of two non-exchanging compartments
with diffusivities of $$$D_{\text{iso}}$$$ = 1 and $$$D_{\text{dot}}$$$ = 0 µm^{2}/ms
for different SNR, and different signal fractions $$$f_{\text{dot}}$$$ (represented
by the different colours). At low SNR, the rectified noise floor inflates the
estimated upper limit of $$$f_{\text{dot}}$$$. As SNR increases, smaller signal
fractions can be resolved, where the relative signal approaches $$$f_{\text{dot}}$$$.

Fig. 2: Magnitude DWIs at
central (top row) and inferior (bottom row) slice-positions at variable b
values. Coloured outlines represent tissue types (red = white matter, yellow = gray
matter, green = cerebellar white matter, blue = cerebellar gray matter), and
were generated from the intersection of the mask-isosurface of each type with
the slice.

Fig. 3: shows the sample
median and 1-99th percentile of the S(0) normalised measured signals
(a) and Rician-bias corrected signals (b) across voxels in each ROI (location
visualised in figure a, right). The horizontal line in (a) represents the
estimated mean noise floor across voxels. Of the
regions investigated, cGM and wGM show the most significant signal above the
noise floor, indicating that the tissue is not comprised of a compartments with
a single isotropic diffusivity.

Fig. 4: Simulated signal at
variable SNR, $$$f_{\text{dot}}$$$ and exchange times assuming a two compartment
Kärger-model^{17,18}. Here,
diffusivities were set to 1 and 0 µm^{2}/ms. At infinite exchange times,
the relative signal approaches the true signal fraction of the dot compartment,
as in Fig. 1. However, at exchange times as long as 500 ms there is a relevant
loss of signal at high b-values caused by exchanging particles. This suggests
that the estimated upper limit of $$$f_{\text{dot}}$$$ is negatively biased in the
presence of exchange.

Fig. 5: Coronal DWI that
covers the cerebrum and cerebellum at b = 15 000 s/mm^{2} (left), nissl
stained coronal slice (right) showing presence of cells in a rhesus monkey
brain (http://www.brain-map.org/, access date: 2017-11-07). The figure showcases the agreement between
signal retention and high cell density that is expected in the cerebellum.