Identification of Rare Cortical Folding Patterns using Unsupervised Deep Learning

TL;DR

This work tackles the challenge of identifying rare cortical folding patterns amid substantial inter-individual variability in MR images. It introduces an unsupervised framework based on a $\beta$-VAE to learn normal folding variability from distance-map representations of the central sulcus, and assesses rare-pattern detectability via both latent-space and reconstruction-error signals. Synthetic benchmarks (deletion and asymmetry) and a real rare pattern (interrupted central sulcus) are used to characterize detection power, while generalization is demonstrated on corpus callosum dysgenesis in a pediatric dataset. The study finds that latent and folding-space signals provide complementary information, enabling robust identification of diverse rare patterns and supporting potential extensions to whole-brain analysis with careful consideration of data size and domain shift.

Abstract

Like fingerprints, cortical folding patterns are unique to each brain even though they follow a general species-specific organization. Some folding patterns have been linked with neurodevelopmental disorders. However, due to the high inter-individual variability, the identification of rare folding patterns that could become biomarkers remains a very complex task. This paper proposes a novel unsupervised deep learning approach to identify rare folding patterns and assess the degree of deviations that can be detected. To this end, we preprocess the brain MR images to focus the learning on the folding morphology and train a beta-VAE to model the inter-individual variability of the folding. We compare the detection power of the latent space and of the reconstruction errors, using synthetic benchmarks and one actual rare configuration related to the central sulcus. Finally, we assess the generalization of our method on a developmental anomaly located in another region. Our results suggest that this method enables encoding relevant folding characteristics that can be enlightened and better interpreted based on the generative power of the beta-VAE. The latent space and the reconstruction errors bring complementary information and enable the identification of rare patterns of different nature. This method generalizes well to a different region on another dataset. Code is available at https://github.com/neurospin-projects/2022_lguillon_rare_folding_detection.

Figures (15)

• Figure 1: Central sulcus region variability. A. Localization of the studied region of interest (ROI) on a 3D view of one right hemisphere. The colored ribbons represent sulci, defined as a negative cast of the furrows. The central sulcus is red. B. Examples of non-interrupted central sulci. C. Examples of interrupted central sulci.
• Figure 2: Overview of the BrainVISA/Morphologist pipeline's main steps and of the folds representation.A. Main steps of BrainVISA/Morphologist pipeline. 1. Raw T1-w MRI, 2. Bias-corrected image, 3. Segmentation of the brain, 4. Segmentation of the hemispheres and of the grey and white matter, 5. Skeleton representation of the folding graph, representing a negative cast of the 4. 6. Mesh representation of the white matter of the right hemisphere, 7. Folding graph that represents the folds (in green) as the negative cast of the white matter of the right hemisphere (white mesh). B. Folds representation. 1. Example of a central sulcus, which is composed of several elementary entities called simple surfaces (SS). (Orientation: A: Anterior, P: Posterior, S: Superior, I: Inferior). 2. Corresponding schematic representation of the sulcus represented in 1, which is formed by four simple surfaces. Depth variation caused by the buried gyrus and the presence of two branches lead to the division into four different simple surfaces. 3. Corresponding folding graph.
• Figure 3: Pipeline. A mask of the central sulcus area is defined based on a distinct manually labeled dataset. HCP is processed with Morphologist to obtain folding graphs, which are used to obtain 3D images of skeletons (1). The Chamfer distance is applied to the skeletons to obtain geodesic distance maps (2). Distance maps are then downsampled and cropped according to the mask (3) and are fed as input to a $\beta-VAE$.
• Figure 4: Skeleton's description of the test set. Left: Stacked histogram representing the distribution of simple surfaces sizes for the test subjects for the three main sulci of our crop, the central sulcus (S.C._right), the precentral sulcus (S.Pe.C._right) and the postcentral sulcus (S.Po.C._right). (Note: The labeling used is automatic and therefore not entirely reliable, but these labels are sufficient to draw conclusions regarding the SS size distribution.) Right: Distribution of the number of skeletons' fold voxels for the test subjects when the mask is applied to the crops.
• Figure 5: Deletion benchmarks. Visualization of original sulcal pattern and its altered versions from the four deletion benchmarks showing patterns with increasing simple surface size deleted. Upper row: Mesh visualization. Middle and bottom rows: distance maps on axial view, visualization at depths 15 and 37.