Poisson Flow of Cortical Folding in Juvenile Myoclonic Epilepsy

The human brain folds in utero, primarily during late gestation. Shortly after birth, cortical folding patterns are established and remain stable thereafter, making them promising early neurodevelopmental markers. Yet it is unclear whether the representations given by current neuroimaging foundation models capture cortical folding variability. Here, we introduce Champollion, a self-supervised learning framework that learns interpretable local representations of cortical folding from structural MRI. Optimized on representative folding-related tasks, Champollion accurately captures known folding patterns across cortical regions and external datasets. In a comprehensive benchmark, it consistently outperforms neuroimaging and general-purpose foundation models. Furthermore, Champollion reveals richer genetic associations than conventional morphometric descriptors and identifies localized folding signatures associated with incomplete hippocampal inversion, prematurity, and maternal smoking. These results establish cortical folding as a rich and largely untapped source of neurodevelopmental information, and Champollion provides a unified framework for discovering, localizing and interpreting long lasting cortical folding signatures.

Deep learning on cortical surfaces faces a dilemma: capturing the complex topology of over 60 nomenclature-dependent sulci per hemisphere requires high-capacity models, yet the extreme scarcity of expert annotations ($N=62$ subjects) inevitably causes overfitting. Standard supervised approaches fail to generalize in this data-scarce regime, particularly for variable and small sulci where topological ambiguity is high. To overcome this limitation, we introduce a Geometric-to-Semantic Spherical Transfer Learning framework. First, we leverage massive unlabeled data (UK Biobank, $\approx$30,000 subjects) to pre-train a spherical encoder using a locally-optimized strategy. By relying solely on continuous surface features (curvature and depth), the relevance of this pre-training is confirmed by the model's ability to detect localized and rare topological traits, such as sulcal interruptions. The downstream labeling task, however, introduces extracted sulcal fundi (lines) as an explicit semantic input. To bridge this dimensional domain gap (from purely geometric to semantic) without causing catastrophic forgetting, these anatomical lines are integrated into the pre-trained backbone via a soft-initialized Topological Prior Injector. Our experiments demonstrate that this approach outperforms fully supervised baselines trained from scratch, achieving a mean Dice of 0.77. Crucially, a local analysis reveals that the self-supervised geometric priors yield the largest performance gains on variable and tertiary sulci (up to 14.8%), confirming that learning the cortex shape is highly beneficial for identifying its rarest parts.

We present a unified computational approach to tensor-based morphometry in detecting the brain surface shape differences between two clinical groups based on magnetic resonance images. Our approach is novel in a sense that we combined surface modeling, surface data smoothing and statistical analysis in a coherent unified mathematical framework. The cerebral cortex has the topology of a 2D highly convoluted sheet. Between two different clinical groups, the local surface area and curvature of the cortex may differ. It is highly likely that such surface shape differences are not uniform over the whole cortex. By computing how such surface metrics differ, the regions of the most rapid structural differences can be localized. To increase the signal to noise ratio, diffusion smoothing based on the explicit estimation of Laplace-Beltrami operator has been developed and applied to the surface metrics. As an illustration, we demonstrate how this new tensor-based surface morphometry can be applied in localizing the cortical regions of the gray matter tissue growth and loss in the brain images longitudinally collected in the group of children.