Geometrical learning of brain surface data

Abstract

Neuronal cell bodies primarily reside in the cerebral cortex. The study of this thin and highly convoluted surface is essential for understanding how the brain works. However, the analysis of surface data is challenging due to the high variability of the cortical geometry. Ignoring this complex geometry poses an unsolved challenge in the statistical analysis of surface data. Most conventional methods rely on a heuristic multi-step process, such as geometrical simplifications and spherical inflations, requiring a considerable computational time. The main objective of this thesis is to develop geometrical frameworks to learn directly on cortical surfaces. Specifically, we first propose a spectral graph convolution network to perform surface analysis applied to cortical parcellation. Next, we present an adaptive pooling technique for surface classification and regression tasks to facilitate a hierarchical learning of multiple surface data. Finally, we illustrate a joint cortical surface reconstruction and segmentation approach to work directly from the MRI volume. This thesis has resulted in three journals and five peer-reviewed conference publications. The individual contributions of this thesis are presented below. In our first objective, we present a novel approach for learning and exploiting surface data directly across multiple surface domains. Direct learning of surface data via graph convolutions provide a new family of fast algorithms for processing brain surfaces. However, the current limitation of existing state-of-the-art approaches is their inability to compare surface data across different surface domains. Surface representations are indeed incompatible between brain geometries. We leverage the recent advances in spectral graph matching to transfer surface data across aligned spectral domains. This novel approach enables a direct learning of surface data across compatible surface bases. A spectral graph convolution network exploits spectral filters over intrinsic representations of surface neighborhoods. We illustrate the benefits of this approach with an application to brain parcellation. We validate the algorithm over 101 manually labeled brain surfaces. The improvements in parcellation reveal a 29% increase in accuracy with drastic speed gains over conventional methods. In the second objective, we propose a new learnable graph pooling method for processing multiple surface-valued data to output subject-based information. The presented method innovates by learning an intrinsic aggregation of graph nodes based on graph spectral embedding. We illustrate the advantages of our approach with in-depth experiments on two large-scale benchmark datasets. The ablation study in the chapter illustrates the impact of various factors affecting our learnable pooling method. The flexibility of the pooling strategy is evaluated on four different prediction tasks, namely, subject-sex classification, regression of cortical region sizes, classification of Alzheimer’s disease stages, and brain age regression. Our learnable pooling approach demonstrates improvements ranging from 7% to 11% compared to other pooling techniques for graph convolutional networks, with results improving the state-of-the-art in brain surface analysis. Our third objective presents an adversarial training strategy for unsupervised domain adaptation to learn surface data across inconsistent graph domains. This novel approach comprises of a segmentator that uses graph convolution layers to enable parcellation across brain surfaces of varying geometry and a discriminator that predicts the alignment-domain of surfaces from their segmentation. The adversarial training learns an alignment-invariant representation that yields consistent parcellations for differently aligned surfaces by fooling the discriminator. Using manually-labeled brain surface from MindBoggle, the largest publicly available dataset of this kind, we demonstrate a 2%–13% improvement in mean Dice over a non-adversarial training strategy for test brain surfaces with no alignment or aligned on a different reference than source examples. Our fourth final objective proposes SegRecon, an integrated end-to-end deep learning method to jointly reconstruct and segment cortical surfaces directly from an MRI volume in one single step. We train a volume-based neural network to predict, for each voxel, the signed distances to multiple nested surfaces and their corresponding spherical representation in atlas space. This is, for instance, useful for jointly reconstructing and segmenting the white-to-grey-matter interface and the grey-matter-to-CSF (pial) surface. We evaluate the performance of our surface reconstruction and segmentation method with a comprehensive set of experiments on the MindBoggle, ABIDE and OASIS datasets. Our reconstruction error is found to be less than 0.52mm and 0.97mm in terms of average Hausdorff distance to the FreeSurfer generated surfaces. Likewise, the parcellation results show over 4% improvements in average Dice with respect to FreeSurfer, in addition to an observed drastic speed-up from hours to seconds of computation on a standard desktop station. The work described in this thesis benefits neuroscience studies. Practically, the proposed algorithms will significantly assist clinicians in targeting any particular area of the brain for drug planning and in early prediction of cortical atrophy using the geometry of the complex folding of the cortex and isolate the discriminating geometry linked with the Alzheimer’s disease. Additionally, this thesis can help in fast and accurate surface extraction and parcellation from structural MRI volumes. This work will also reduce financial burdens on patients by providing algorithmic tools for therapeutic research to aid clinicians. In general, the work would be used to find new geometry-based biomarkers for the early detection of the Alzheimer’s disease and assist the understanding of other neurological disorders.

Date	2 Dec 2021
Original language	American English
Awarding Institution	École de technologie supérieure
Supervisor	Hervé Lombaert (Supervisor) & Christian Desrosiers (Co-supervisor)