Samuel St-Jean1, Max Viergever1, Geert Jan Biessels2, and Alexander Leemans1
1Image Sciences Institute, University Medical Center Utrecht, Utrecht, Netherlands, 2Department of Neurology, Rudolf Magnus Institute of Neuroscience, University Medical Center Utrecht, Utrecht, Netherlands
Synopsis
For diffusion MRI studies relying on statistics computed along fiber trajectories, the extracted values might not be optimally aligned between subjects in the metric space, which could lead to subsequent erroneous statistical analysis. We thus propose a 1D fast Fourier transform based correction algorithm for a fast realignment (< 1 second) directly in the metric space. Our experiments with a) synthetic signals and b) FA values along the uncinate fasciculus from real data show that our fiber-tract realignment algorithm improves the overlap of extracted metrics. This could help researchers uncover relationships of interest which were hidden by residual misalignment at first.Target Audience
Researchers computing along-tract spatial statistics derived from diffusion MRI tractography.
Introduction
While it is acknowledged that diffusion MRI datasets should be corrected for artifacts in population studies [1], the same is also recommended for fiber bundle group analyses. As shown by [2], along-tract based statistics offer a more realistic estimation than using a single averaged value from the entire studied fiber bundle. [3, 4] have previously proposed bundle-based registration algorithms, but most statistical analysis are done at the single tract level, as for example by extracting the mean representative pathway [5, 6]. In this context, the mean fiber may not be optimally aligned between various subjects as opposed to the bundles themselves, which may lead to an increased bias in the subsequent statistical analysis. To alleviate this caveat, we propose a fast and straightforward 1D rigid registration algorithm for metrics extracted along tracts based on the fast Fourier transform (FFT) and the cross-correlation theorem [7]. The algorithm works directly in the metric space by considering the extracted values as a 1D signal, thus making it perfectly suited for usage in population studies using any metric of interest.
Theory
The cross-correlation of two signals x and y can be computed with the FFT using $$\mathcal{F}^{-1} \left(\mathcal{F} (x) \odot \mathcal{F}^*(y)\right)$$where $$$\mathcal{F}$$$ is the Fourier transform, $$$\mathcal{F}^*$$$ is the complex conjugated Fourier transform and $$$\odot$$$ is the pointwise product. The cross-correlation theorem thus provides a computationally cheap way to find the maximum overlap between two 1D signals as shown in
Figure 1. Using this idea, extracted fiber bundles metrics from different subject can be viewed as a 1D signal, which can then be realigned directly in the metric space by finding the maximum value of the FFT based cross-correlation.
Datasets
10 subjects underwent a diffusion weighted scan of 45 diffusion encoding directions at b = 1200 s/mm² and 3 b = 0 s/mm² images on a 3T Intera Philips scanner at a spatial resolution of 1.7 x 1.7 x 2.5 mm³ with TR/TE = 6638 ms / 73 ms. The data was then corrected for subject motion and eddy current distortions with ExploreDTI [8]. Whole-brain deterministic fiber tracking was performed with FA > 0.2, with one seed point per voxel distributed on a 2 x 2 x 2 mm³ grid, maximum angle deviation of 30 degrees and a step size of 1 mm. Finally, the right UF was segmented for the 10 subjects and the FA values were collected along the mean fiber of the UF for each subject as shown in
Figure 2.
Results & Discussion
The 10 FA profiles of each subject were co-registered with our algorithm (which took less than 1 second to execute) and only the values in the region of full overlap were kept to prevent spurious effects near the endpoints. As shown in
Figure 3, our algorithm can realign the FA values extracted along the right UF from two different subjects by maximising their cross-correlation. The maximal cross-correlation is given by a shift of 1 mm to the right, which is also the position of the maximal Pearson’s correlation coefficient.
Figure 4 shows the mean and standard deviation of the FA profiles for the 10 subjects. While correcting for along-tract metric misalignment produces different estimated mean FA values than the original, misaligned metrics, the standard deviation is also lower near the left endpoint of the UF but somewhat larger for the right endpoint. The bottom graph shows that the percentage difference of the mean FA between the unaligned and realigned metrics can be as large as 14%, where percentage difference = $$100 \times \frac{\left\lvert FA_{unaligned} - FA_{realigned} \right\rvert}{\left(FA_{unaligned} + FA_{realigned}\right)\big/2}. $$ While we only explored translation of at least 1 mm (which is the step size used in the tracking), our algorithm could also be modified for optimal sub-millimeter realignment to yield even more accurate inter-tract correspondence for large cohorts of subjects. This can potentially reduce the standard deviation of the mean FA in group studies for increased accuracy when estimating confidence intervals. In the same way, this could also help researchers uncover relationships of interest which might have been hidden by misalignment at first, but appear as statistically significant after realigning the diffusion metrics.
Acknowledgements
This research is supported by VIDI Grant 639.072.411 from the Netherlands Organisation for Scientific Research (NWO). Samuel St-Jean was also supported by the Fond de recherche du Québec - Nature et technologies (FRQNT). The authors would like to thank the members of the Utrecht Vascular Cognitive Impairment Study Group for providing the diffusion MRI data : University Medical Center Utrecht, The Netherlands, Department of Neurology: E. van den Berg, G.J. Biessels, M. Brundel, W.H. Bouvy, S.M. Heringa, L.J. Kappelle, Y.D. Reijmer; Department of Radiology/Image Sciences Institute: J. de Bresser, H.J. Kuijf, A. Leemans, P.R. Luijten, W.P.Th.M. Mali, M.A. Viergever, K.L. Vincken, J.J.M. Zwanenburg; Department of Geriatrics: H.L. Koek, J.E. de Wit; and Hospital Diakonessenhuis Zeist, The Netherlands: M. Hamaker, R. Faaij, M. Pleizier, E. Vriens.
References
[1] Derek K. Jones, Thomas R. Knösche, Robert Turner, White matter integrity, fiber count, and other fallacies: The do's and don'ts of diffusion MRI, NeuroImage, Volume 73, June 2013, Pages 239-254
[2] John B. Colby, Lindsay Soderberg, Catherine Lebel, Ivo D. Dinov, Paul M. Thompson, Elizabeth R. Sowell, Along-tract statistics allow for enhanced tractography analysis, NeuroImage, Volume 59, Issue 4, 15 February 2012
[3] Leemans, A., Sijbers, J., De Backer, S., Vandervliet, E., & Parizel, P. (2006). Multiscale white matter fiber tract coregistration: A new feature-based approach to align diffusion tensor data. Magnetic Resonance in Medicine, 55(6), 1414–1423.
[4] Eleftherios Garyfallidis, Omar Ocegueda, Demian Wassermann, Maxime Descoteaux, Robust and efficient linear registration of white-matter fascicles in the space of streamlines, NeuroImage, Volume 117, 15 August 2015, Pages 124-140
[5] S.M. Smith, M. Jenkinson, H. Johansen-Berg, D. Rueckert, T.E. Nichols, C.E. Mackay, K.E. Watkins, O. Ciccarelli, M.Z. Cader, P.M. Matthews, and T.E.J. Behrens. Tract-based spatial statistics: Voxelwise analysis of multi-subject diffusion data. NeuroImage, 31:1487-1505, 2006.
[6] Zimmerman-Moreno, G., Ben Bashat, D., Artzi, M., Nefussy, B., Drory, V., Aizenstein, O. and Greenspan, H. (2015), Whole brain fiber-based comparison (FBC)—A tool for diffusion tensor imaging-based cohort studies. Hum. Brain Mapp
[7] Lewis, J. P. (1995). Fast normalized cross-correlation. Vision Interface, 10(1), 120–123.
[8] Leemans A, Jeurissen B, Sijbers J, and Jones DK. ExploreDTI: a graphical toolbox for processing, analyzing, and visualizing diffusion MR data. In: 17th Annual Meeting of Intl Soc Mag Reson Med, p. 3537, Hawaii, USA, 2009