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TractLearn: a geodesic learning framework for quantitative dissection of brain bundles
Arnaud Attyé1,2, Felix Renard3, Monica Baciu2, Elise Roger2, Laurent Lamalle4, Patrick Dehail5, Hélène Cassoudesalle5, and Fernando Calamante6,7
1School of Biomedical Engineering, University of Sydney, Sydney, Australia, 2CNRS LPNC UMR 5105, University of Grenoble Alpes, Grenoble, France, 3Laboratoire d'informatique de Grenoble, Grenoble, France, 4University of Grenoble Alpes, Grenoble, France, 5Bordeaux Universitary Hospital, Bordeaux, France, 6Sydney Imaging Lab, University of Sydney, Sydney, Australia, 7School of Aerospace, Mechanical and Mechatronic Engineering, Sydney, Australia

Synopsis

Here we present a unified framework for brain fascicles quantitative analyses by geodesic learning (TractLearn) — as a data-driven unsupervised learning task. TractLearn allows a mapping between the image high-dimensional domain and the reduced latent space of brain fascicles. Besides providing a framework to test the reliability of various brain metrics with a global overview, it allows to identify subtle quantitative alteration in disease model with small subset of patients and/or data sparsity. With this regard, TractLearn is a ready-to-use algorithm for precision medicine.

Introduction

Streamlines from diffusion-weighted imaging (DWI) provide a wealth of information regarding brain structural connectivity. A deep-learning approach was recently proposed to generate major brain fascicles from fiber orientation distribution (FOD) function peaks [1]. The information contained in these local tractograms can be subsequently exploited to generate maps with different contrasts using the track-weighted imaging (TWI) framework [2]. However, statistical analyses on all quantitative values contained in each fascicle is difficult owing to the curse of dimensionality. In addition, classical voxel-based analysis doesn’t consider the global interaction between voxel modification in a dedicated bundle. Here, we propose a 3-step method to obtain a fast-quantitative analysis of all brain bundles, through their TWI contrast. Firstly, we will reduce the dimensionality of all voxels contained in each bundle, to have one point per bundle and individual in a manifold subspace. Secondly, we will learn the manifold [3,4] from our healthy controls first dataset and project onto the second retest dataset to check the reliability. Finally, we propose to mathematically detect abnormalities in a trauma model by applying Z-scores to the projection of a new subject onto the same manifold.

METHODS

20 healthy males (age=20.9±3.3) were scanned on a 3T Siemens Prisma scanner: high-angular resolution, multi-shell DWI acquired for each subject over two sessions (12 months apart). 5 patients referred with mild traumatic brain injury were also included with the same protocol.
Preprocessing included denoising [5], eddy current and motion correction [6], bias field and Gibbs artifacts’ corrections [7], and up-sampling to 1 mm3 [8]. FODs were computed using Spherical Deconvolution [9] in MRtrix3 (www.mrtrix.org). TractSeg (https://github.com/MIC-DKFZ/TractSeg) used pre-trained DWI data to reconstruct 72 discrete bundles [1]. For each bundle, we calculated the mean TW-FOD, which was computed using the FODs in the TWI framework [2]).
Modeling brain fascicles with TractLearn
We use the strategy developed in [4, 10] to localize an anomaly among TractSeg fascicles, which can be summarized as follow:
1/Dimensionality reduction to convert collection of voxels quantitative values from each bundle into a unique point in a manifold subspace. Here we have used U-map [11].
2/ We built an atlas based on healthy controls dataset: Y=f(x)+epsilon. Y being healthy control data in real space (ie. TWI values extracted from each bundle), x the corresponding point in the reduced space and epsilon the residuals. f will be the regression equation between the reduced space and the natural space. To ensure robustness, epsilon was estimated using a leave-one-out strategy.
3/ Any new subject (retest or mTBI patient) will be "projected" onto the learned manifold representing the normal controls. The projection f will correspond to the image closest to that of the tested subject, while belonging to the normal controls manifold.
We consider that the residual epsilon is representative of any abnormalities present in a new subject when it is greater than the model variability learned during the leave-one-out on controls. A bootstrap method was applied to estimate the uncertainty of the distance distribution, by randomly selecting inter and intra-individual distance in the manifold. We finally identified altered voxels in each fascicle by applying a Z-Score, with threshold corresponding to p<0.01 (Figure 1).

RESULTS

69 of 72 brain bundles were successfully-reconstructed in all subject using TractSeg. We have then extracted voxel values from 69 tract masks in all subject to project in the manifold subspace (Figure 2).
Using TractLearn, the distance in the geodesic space for one bundle was significantly shorter between the test and the retest procedure (same subject) than between two different subjects (p<0.001) (Figure 3). In the mTBI cohort, we have identified significantly altered Z-Score in 3 out of 5 subjects. Subjects 1 and 2 presented voxels alterations in Corpus Callosum sub-divisions 1 (CC1), CC2 and CC5 for the former (figure 4); CC2 and CC3 for the latter. Subject 5 presented alterations in left corticospinal tract (p<0.01).

DISCUSSION

TractLearn demonstrates high test-retest values, and allowed detecting white matter abnormalities in the corpus callosum of 2 mTBI subjects, and in the corticospinal tract of a further patient. The injuries location are compatible with the known pathophysiology of mTBI [12, 13].
In addition, we propose a new statistical test for the evaluation of a collection of biomarkers extracted from brain bundles, here employed to demonstrate the reliability of both TractSeg and the track-weighted contrast of each fascicle over time.
The demonstration relies on the vicinity of each manifold point (ie. Test and Retest points) using a bootstrap method. TWI has proved to be powerful in mapping fascicles alterations in neurodegenerative diseases [14, 15] or mild traumatic brain injury (mTBI) preclinical imaging [16] to cite a few. Yet other DWI markers could be also tested with the same framework as it only needs a collection of quantitative metrics as input.
U-map [11] has been developed to merge the visualization power of t-SNE algorithm [3] with more respect to the global structure, in our case the brain white matter bundle voxels. We also propose a generalization of the classical z-score where f(x) corresponds to the mean value. We have modeled the population by a regression function instead of a unique sample [4].

Acknowledgements

The Grenoble MRI facility IRMaGe was partly funded by the French program “Investissement d’Avenir” run by the “Agence nationale pour la recherche” (grant number: ANR-11-INBS-0006).

References

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Figures

Overview of the workflow put forward in this work

Dimensionality reduction pipeline (part A). Here is an example of the corpus callosum (third subdivision, as obtained from TractSeg (CC3)). A&B represent the test session, while C&D the retest session 12 months after. A&C are tracks directly obtained from TractSeg (3D tracts files) while B&D are images files after the track-weighted conversion using a contrast weighted by the fiber orientation distribution amplitude.

Dimensionality reduction pipeline (part B). Here is a representation of the manifold subspace of the 20 healthy volunteers’ (numbered from 0 to 19) corpus callosum (CC3). Blue dots represent the test procedure (Sess1) and orange dots represent the retest procedure (Sess2). For most of the subjects, blue and orange dots are in close vicinity in the manifold – being indistinguishable for some of them at this scale –.

Back projection of the manifold residual in the subject space. Here is the example of the first part of the corpus callosum with the track file (A), the track-weighted mask (B) and the back projection of the Z Score (C). The Z score has allowed to identify voxels with significantly modified TWI contrast (p<0.01 for red voxels), in comparison with the control group.

Proc. Intl. Soc. Mag. Reson. Med. 28 (2020)
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