Rafael Neto Henriques^{1} and Marta Morgado Correia^{1}

Previous studies have shown that measures of non-Gaussian diffusion from diffusion kurtosis images (DKI) provide unique information on age-related tissue changes. In this study, a novel non-Gaussian diffusion index invariant to the distribution of fibres is proposed and applied to 650 datasets from the Cam-CAN ageing project. The results show that the proposed biomarker is not only applicable to any tissue configuration but also less sensitive to noise and artefacts when compared to traditional DKI measures. Moreover, for white matter regions, age-related changes measured by this index seem to reflect axonal alterations likely related to axonal loss mechanisms.

Estimating
the mean signal kurtosis: the mean signal attenuation $$$\left\langle E(b)\right\rangle$$$ along
$$$N_g$$$ diffusion-weighted
gradient directions, $$$n_j$$$, can
be represented as a sum of $$$N_s$$$ signal
contributions each characterized by an individual diffusion coefficient $$$D_i$$$ and volume fraction $$$f_i$$$. In analogy to DKI, this equation can
be approximated to the cumulant expansion’s fourth order moments^{8}:

$$$\left\langle E(b)\right\rangle=\frac{1}{N_g}\sum_{j=1}^{N_g}\sum_{i=1}^{N_s}f_i\exp[-bD_{i}(n_j)]\approx \exp[-b\left\langle d\right\rangle+\frac{1}{6}b^2\left\langle d\right\rangle^2\left\langle k\right\rangle]$$$ (Eq.1)

From Eq.1, the mean diffusion-kurtosis index $$$\left\langle k\right\rangle$$$ (or MDKI) can be estimated from $$$\left\langle E(b)\right\rangle$$$ samples which are known to be
invariant to the fibre orientation distribution^{9}– thus, $$$\left\langle k\right\rangle$$$ is independent of fibre
configuration. In this study, Eq.1 is fitted using a weighted linear least squares
approach (weights=$$$N_g(b)\times\left\langle E(b)\right\rangle$$$).
This technique is evaluated using previously proposed multi-compartmental
simulations^{3}.

MRI
experiments: DW datasets were acquired for 650 subjects (318 males) aged between 18 and 89 years on a 3T Trio Scanner (32channel
coil) using a TRSE sequence to suppress eddy-current
artefacts (30 directions for bvalues=1000,2000s.mm^{2} and three repetitions for b-value=0)^{7}.

Data
processing:
To avoid partial volume effects from Gaussian smoothing, MRI noise is suppressed using a recently proposed PCA
denoising technique^{10}, while Gibbs artefacts are removed using local
subvoxels-shifts^{11}. Correction of volume misalignments due to
motion and exclusion of datasets highly corrupted by intra-volume motion artefacts
was performed following previous Cam-CAN studies^{12}. The estimates
obtained for MDKI, DKI’s mean kurtosis (MK), DTI’s fraction anisotropy(FA), and
WMTI are evaluated on JHU white matter ROIs^{13}.

This work was funded by Fundação para a Ciência e Tecnologia FCT/MCE (PIDDAC) under grant SFRH/BD/89114/2012.

In vivo data were provided by the Cambridge Center for ageing and Neuroscience (Cam-CAN) project funded by the Biotechnology and Biological Sciences Research Council under grant BB/H008217/1.

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[8] Kiselev VG. The Cumulant Expansion: An Overarching Mathematical Framework For Understanding diffusion NMR. In: Diffusion MRI: Theory, Methods and Applications, ed. Jones DK. Oxford University Press 2011, ISBN: 9780195396779.

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[14] Fieremans E, Jensen JH, Helpern JA, et al. Diffusion distinguishes between axonal loss and demyelination in brain white matter. Proceedings of the 20th Annual Meeting of the International Society for Magnetic Resonance Medicine; Melbourne, Australia. May 5–11, 2012.

Fig.1 – Median
and percentile ranges of DKI’s mean kurtosis (MK) and mean signal kurtosis (MDKI)
estimates as a function of the intersection angle of two synthetic crossing
fibres for different levels of per axon axonal water fraction (AWF). This
figure was obtained from 10000 repetitions of the multi-compartment simulations
proposed by [3] using Cam-CAN’s acquisition parameters and synthetic
rician noise (SNR=25).

Fig.2 -
Mean kurtosis (MK) and mean signal kurtosis (MDKI) maps obtained from diffusion-weighted data of a representative subject pre-processed
using a PCA denoising technique and gibbs artifact correction algorithm (panels A and B). For comparison proposes, the
maps are also computed from the data pre-processed with a Gaussian smoothing
filter with FWHM of 2.5mm (panels C and D).

Fig. 3 –
In-vivo measures of mean kurtosis (MK), mean signal kurtosis (MDKI) and
fractional anisotropy (FA) as a function of subject’s age. Upper panels were computed from the
mean of the voxels of all white matter ROIs while the lower panels were computed from the mean of
the well aligned voxels (corpus callosum).

Fig. 4 - In-vivo axonal water fraction (AWF) and
tortuosity (T) measures as a function of subject age computed from the mean of
the voxels of well aligned voxel (corpus callosum) are shown in panels A and B.
The correlation between these measures and the mean signal kurtosis (MSK) for these
voxels are shown in panels C and D.