Effects of the Number of Diffusion Directions in Diffusion Kurtosis Imaging: a Structural Connectivity Study using in vivo data

Ricardo Loução^{1}, Karolina Elsner^{1}, Rita G. Nunes^{1}, Rafael Neto-Henriques^{2}, Marta Correia^{2}, André Ribeiro^{3}, and Hugo Ferreira^{1}

Diffusion Kurtosis
Imaging (DKI) can take into account the presence of crossing fibers when
performing tractography to reconstruct the brain’s white matter. The increased
sensitivity compared to Diffusion Tensor Imaging may lead to more accurate
representations of structural connectivity. At present, there are only two deterministic
streamline algorithms for DKI-based tractography: an ODF-based algorithm,
proposed by Lazar et al.^{1} and a KT-based algorithm, proposed by
Neto-Henriques et al.^{2}. Studies using these algorithms have always
used large amounts of data (high number of diffusion directions and sometimes
also more than the minimum of 3 b-values required). However, no study had yet
been performed to assess the algorithms’ robustness when using the minimum data
requirements. In this study we sought to explore the performance of the
DKI-based algorithms when performing whole-brain tractography using different
numbers of diffusion directions. We also looked at the variation in
connectivity metrics calculated for the structural networks obtained from the
different reconstructions.

Six healthy subjects were scanned (3 females) with mean±standard deviation age of 30±5 years.

A 3T Siemens Trio scanner was used for the acquisition, equipped with a 32-channel head coil.

The anatomical MRI scan included a
T1-weighted MPRAGE sequence, with TR=2250ms, TE=2.98ms, TI=900ms,
FOV=256x256mm^{2}, slice thickness of 1mm and voxel size of 1x1x1mm^{3}.

The
diffusion MRI acquisition sequence used was a Twice Refocused Spin Echo,
Echo-Planar Imaging, with TR=9400ms, TE=104ms, acquisition matrix=94x94, voxel
size of 2x2x2mm^{3}, and 64 equally spaced gradient directions per shell, at
b-values of 0, 1000 or 2000s.mm^{-2}.
Datasets
of 21 and 32 gradient directions were extracted from the original data, using
subsets of 21 and 32 directions of the original 64. The criterion used to
select each subset was having the lowest electrostatic repulsion amongst the
chosen directions, out of 5x10^{6} possible arrangements.

For
anatomical parcellation and registration, the all-in-one MIBCA toolbox^{3} was
used. To fit both diffusion and kurtosis tensors, extract the metrics and
perform tract reconstructions, uDKI^{4} was used. Tract reconstructions were based on the ODF- and KT-based algorithms^{1,2}.
To inspect the tractography results and obtain tractography related statistics,
TrackVis^{5} was used. Whole-brain network studies were
accomplished with MIBCA and encompassed the computation and comparison of adjacency matrices for 78 brain regions based on
the Destrieux brain atlas (provided by Freesurfer^{6}) and also the
comparison of the global network metrics: Characteristic Path Length (Lambda),
Transitivity, Global Efficiency, and Small-Worldness, computed using the Brain
Connectivity Toolbox^{7}.

Figure 1 shows the number of tracts reconstructed per algorithm and per number of directions considered. For every set of directions, the KT algorithm shows a reduced number of computed tracts, when compared to the ODF algorithm. This difference decreases when the number of acquired gradient directions increases.

Figures 2 and 3 show the mean adjacency matrices of the computed networks based on the tractography reconstructions. In Table 1, the Dice coefficients for all of the pairs of matrices are displayed.

The adjacency matrices revealed that the KT algorithm reconstructs lesser and weaker connections for 21 directions, when faced against the ODF algorithm. With the increase in considered directions, the difference becomes smaller, suggesting that the results obtained by both algorithms tend to overlay at higher numbers of gradient directions. This is also supported by the Dice coefficients: both reconstructions based on 64 directions show high degree of overlap. Additionally, the highest overlap was observed between 21 directions and 32 directions ODF reconstructions, and the lowest between 21 and 64 directions KT reconstructions.

The observed difference may be due to the
fact that the KT algorithm has an increased angular sensitivity^{2}. When sampling a lower number of directions, the uncertainty in the eigenvectors for each
voxel tends to increase, and thus the uncertainty cone widens, leading to
weaker reconstructions using streamline algorithms, which do not consider these
variations.

The global connectivity metrics obtained from all of the computed networks are displayed in Table 2. These are mean±standard deviation values across the 6 subjects considered.

Once again, the ODF algorithm showed better consistency in results than the KT algorithm. Nevertheless, the metrics seem to converge to a common value for both algorithms.

Research supported by Fundação para a Ciência e Tecnologia (FCT) and Ministério da Ciência e Educação (MCE) Portugal (PIDDAC) under grants UID/BIO/00645/2013, PTDC/SAU-ENB/120718/2010, and FCT Investigator Program, grant IF/00364/2013.

MRI scanning was funded by the Medical Research Council (MRC), UK

1. Lazar, M., Jensen, J. H., Xuan, L., Helpern, J. A. Estimation of the orientation distribution function from diffusional kurtosis imaging. Magn Reson Med. 2008, 60, 774-81.

2. Neto-Henriques, R., Correia, M., Nunes, R. G., Ferreira, H. A. (2015) Exploring the 3D geometry of the diffusion kurtosis tensor—Impact on the development of robust tractography procedures and novel biomarkers, NeuroImage, 111, 85-99

3. Ribeiro AS, Lacerda LM, Ferreira HA. (2015) Multimodal Imaging Brain Connectivity Analysis (MIBCA) toolbox. PeerJ 3:e1078

4. Neto Henriques, R., Ferreira, H.A., Correia, M.M., 2015. United Diffusion Kurtosis Imaging (UDKI) toolbox. MAGMA 28 (S1): 511-512

5. Ruopeng Wang, Van J. Wedeen, TrackVis.org, Martinos Center for Biomedical Imaging, Massachusetts General Hospital

6. Fischl, B. (2012). FreeSurfer. Neuroimage, 62(2), 774-781.

7. Rubinov, M., & Sporns, O. (2010). Complex network measures of brain connectivity: uses and interpretations. Neuroimage, 52(3), 1059-1069.

8. Côté, M.A., Girard, G., Boré, A., Garyfallidis, E., Houde, J.C., Descoteaux, M. Tractometer: Towards validation of tractography pipelines, Medical Image Analysis, 17(7) ,844 - 857

Figure 1 - Average number of computed tracts for each algorithm per set of directions. The red bars represent the ODF algorithm results, while the red bars represent the KT algorithm results.
The black lines indicate the standard deviation over subjects of the
number of tracts reconstructed for each algorithm.

Figure 2 -
Mean adjacency matrices of the structural connectivity networks (over
the 6 subjects). The upper nine matrices correspond to KT
based reconstructions and the lower to ODF reconstructions. Panels A)-C)
and J)-L) are the weighted undirected matrices, D)-F) and M)-O) are the respective
binary matrices, using a threshold of 80% of the maximum number of connections
in the network, and G)-I) and P)-R) are the difference matrices from the
previous row.

Figure 3 - Side-by-side
comparison of the mean adjacency matrices obtained from KT and ODF based
reconstructions from 21 [A) and B)], 32 [D) and E)] and 64 [G) and H)]
directions. The matrices on the right column are difference matrices from their
respective row, after applying a threshold of 80% to the maximum number of connections in the network.

Table 1 - Dice coefficients measuring overlap between the adjacency matrices.

Table 2 -
Global connectivity metrics obtained from all of the computed networks. These
values are mean +/- standard deviation values across the 6 subjects considered.

Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)

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