Effects of the Number of Diffusion Directions in Diffusion Kurtosis Imaging: a Structural Connectivity Study using in vivo data
Ricardo Loução1, Karolina Elsner1, Rita G. Nunes1, Rafael Neto-Henriques2, Marta Correia2, André Ribeiro3, and Hugo Ferreira1

1Instituto de Biofísica e Engenharia Biomédica, Lisbon, Portugal, 2Cognition and Brain Science Unit, MRC, Cambridge, United Kingdom, 3Centre for Neuropsychopharmacology, London, United Kingdom


Diffusion Kurtosis Imaging Tractography Reconstructions (DKI-TR) are often performed using high quality data. In clinical practice, that is often not possible, as only a lower number of b-values and diffusion gradient directions can be acquired. This study assessed the performance of DKI-TR for the two algorithms currently proposed for DKI-TR using variable amounts of data, and looked at their respective structural connectivity metrics. A 64 gradient direction data set was acquired in six healthy subjects, and down-sampled to 21 and 32 directions. Differences were found between gradient sets and also between algorithms, regarding the reconstructions and the connectivity metrics.


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=256x256mm2, slice thickness of 1mm and voxel size of 1x1x1mm3.

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 2x2x2mm3, 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 5x106 possible arrangements.

For anatomical parcellation and registration, the all-in-one MIBCA toolbox3 was used. To fit both diffusion and kurtosis tensors, extract the metrics and perform tract reconstructions, uDKI4 was used. Tract reconstructions were based on the ODF- and KT-based algorithms1,2. To inspect the tractography results and obtain tractography related statistics, TrackVis5 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 Freesurfer6) and also the comparison of the global network metrics: Characteristic Path Length (Lambda), Transitivity, Global Efficiency, and Small-Worldness, computed using the Brain Connectivity Toolbox7.

Results and Discussion

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 sensitivity2. 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.


Overall, the ODF algorithm seems more robust to the downsampling of gradient directions than the KT algorithm in tractography reconstruction. This may be helpful in clinical practice and pre-surgical planning, where the amount of data acquired is often limited due to time constraints. In the future it would be interesting to quantify the cone of uncertainty associated to the estimated directions for both models and apply validation methods such as those of Tractometer8.


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)