TOWARDS A BETTER UNDERSTANDING OF THE
GENETICS OF THE HUMAN CORTICAL FOLDING

Antoine Dufournet, Joël Chavas, Julien Laval, Denis Rivière, Vincent Frouin, Jean-François Mangin

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Antoine Dufournet, Joël Chavas, Julien Laval, Denis Rivière, Vincent Frouin, et al. TOWARDS A BETTER UNDERSTANDING OF THE GENETICS OF THE HUMAN CORTICAL FOLDING. 2025. hal-05060025

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# TOWARDS A BETTER UNDERSTANDING OF THE GENETICS OF THE HUMAN
CORTICAL FOLDING

Antoine Dufournet*, Joël Chavas*, Julien Laval*, Denis Rivière*, Vincent Frouin*, Jean-François Mangin*

* Université Paris-Saclay, CEA, NeuroSpin, Baobab, Saclay, France

## ABSTRACT

The folding of the human cerebral cortex, partly influenced by genetics, allows a large cortex surface area to fit efficiently within the limited skull space. Understanding folding shapes is limited given their wide variability, and identifying them is difficult. Here, we report the first genomic association study on a comprehensive representation of folding patterns. Via a multivariate statistical test applied to latent spaces generated by contrastive learning on 18,118 UKBioBank subjects (mean age, 62.5 years; 47.0% male), we identified in the orbitofrontal cortical region (OFC), respectively in the left and the right hemispheres, 15 and 11 loci ($p < 5 \times 10^{-8}$), 11 and 5 genes ($p < 2 \times 10^{-6}$) related to brain folding. Finally, we introduce a method for interpreting genetic associations in terms of folding shapes. These findings pave the way for future research to map cortical folding patterns to genetic factors.

**Index Terms—** Brain MRI, Deep learning, Barlow Twins, folding pattern, MOSTest, genetics

## I. INTRODUCTION

Like a fingerprint, each person's brain is unique. Its surface is folded, crossed by hills and valleys, respectively called gyri and sulci, as shown in Figure 1a. Gyri and sulci are not specific to individuals because a large proportion of the population shares common sulci, as highlighted in Figure 1b. However, when comparing two individuals, some valleys may appear longer, narrower, closer together, or more sinuous. By taking into account the variability of sulci shapes and the combinations they form, it is possible to characterize the morphology of the cerebral cortex via patterns. Accurate measurement of this diversity is essential to uncover the genetic factors that influence it.

While studies are underway to map the genes involved in human brain development based on cortical volumes, cortical thicknesses, and surfaces (Van der Meer et al. [1]), no research to date has mapped genes to a comprehensive representation of brain folds. Here, we used an unsupervised contrastive model—named Champollion V0—[2] to encode sulcal shapes in a low dimensional space to enable association studies with the multivariate omnibus statistical test

(MOSTest) [3] approach. We focused on the orbitofrontal region (OFC), already known to be associated with heritable behavioral disorders (schizophrenia, bipolar disorder, autism spectrum) [4, 5]. The proposed method is versatile and can be applied to any cortical region, allowing for broader investigations across the entire brain.

<figure><img src="image_2.png" /><figcaption>(a) Central sulcus highlighted in blue (left hemisphere).</figcaption></figure>

<figure><img src="image_3.png" /><figcaption>(b) Diversity among sulci (right hemisphere).</figcaption></figure>

**Fig. 1.** Examples of a 3D reconstruction of the white matter surface of the right and left hemisphere from 3T MRIs, with sulci highlighted in color according to their name. The central sulcus is blue on (a), and red on (b). See how straight or sinuous it can be by comparing the three examples.

## II. METHODS

### A. Dataset

The UKBioBank dataset is a large-scale biomedical dataset that has recruited 500,000 participants [6], with their genotyping data. As part of project #64984, 21,045 MRI images from two scanning sites were acquired and processed with the BrainVISA/Morphologist toolbox [7]. After quality control, we obtained sulcal data for 21,045 subjects, whose average age is $62.5 \pm 7.5$ years, comprising 47% male.
## B. Preprocessing

From T1 MRI, we extracted a three-dimensional mesh of the brain's white matter and generated a skeleton representing the folding patterns of the cortex (essentially a negative cast of the cortex), using BrainVISA/Morphologist, as shown in Figure 1. For this study, the skeleton has a resolution of 2 *mm* isotropic. The skeleton is then segmented into distinct sulcal regions using Deepfolding [8]. Figure 2 illustrates the OFC region, where the region of interest is highlighted in red against the blue skeleton. We generated masks for each sulcal region based on an external database where sulci were manually labeled. Using these masks, we cropped the cortical skeleton following the method described in [8] on all the 3D brain representations from the 21,045 subjects. This allows us to control the input to deep learning models to ensure they learn on specific sulci.

## C. Contrastive learning and Champollion V0

Contrastive learning captures relationships within a latent space by bringing similar data points closer and pushing dissimilar ones farther apart. It is commonly used in tasks like clustering and dimensionality reduction. In our approach, we aim to construct a representation where people with similar sulcus shapes are positioned close to each other while those with different shapes are separated. To achieve this, we use a self-supervised learning (SSL) model called Champollion V0, inspired by the Barlow Twins framework [9], and which encodes the morphometric and geometric information of crops in a 256-dimension latent space. This model incorporates several incremental optimizations, particularly focusing on augmentations tailored to the sulci shape analysis task [10, 2].

The training process, conducted on the 21,045 subjects for maximum statistical power, is outlined as follows: two augmented views are generated for each image of sulci in a batch, forming a positive pair. A typical augmentation is to reduce the depth of each sulcus randomly. SSL losses aim to bring the representations of these positive pairs closer in the latent space, ensuring that the model is invariant to the applied augmentations and can learn semantically meaningful representations [2]. The loss of Barlow Twins further enhances this process by reducing redundancy, encouraging the model to decorrelate the latent space variables and capture unique information in each dimension.

## D. MOSTest

Our goal is to identify linear combinations of dimensions, representing directions within the latent space, that encode genetic information. The MOSTest approach was introduced by Van der Meer et al. [3] to find associations between single nucleotide polymorphisms (SNPs) and a set of phenotypes. By combining the summary statistics of independent Genome Wide Association Studies (GWASs) for each phenotype, it is

<figure><img src="image_4.png" /><figcaption>**Fig. 2.** From T1 MRI to a crop: example of the OFC region (right hemisphere). First, we process the MRI volume to construct the sulcal skeleton (represented in blue), then select the sulcal region of interest (in red) by applying a mask.</figcaption></figure>

possible to reveal variants that were missed by unique phenotypes. Instead of using cortical volumes, cortical thicknesses, and surfaces, a 256-dimension vector is used as input for each subject, as highlighted in Figure 3. This study focuses on people with white British ancestry (n=18,118). Only bir Allelic SNPs (those with two variants) with a Minor Allele Frequency (MAF) > 0.05 are considered. The following covariates are removed by pre-residualization: the ten principal genetic components, Age, Sex, Age×Sex, Age², Age²×Sex, and the acquisition site. Here, the threshold for SNPs association is 0.05/1 × 10⁶ = 5 × 10⁻⁸ (red dashed line in the Manhattan plot Figure 4), after a Bonferroni correction based on the number of SNPs (n = 1 × 10⁶). Then, input SNPs are mapped to 18,840 protein-coding genes; therefore, the threshold for genome-wide significance was defined at 0.05/18840 = 2 × 10⁻⁶. Plots are obtained from the Functional Mapping and Annotation of GWAS (FUMA) [11] and the Multi-marker Analysis of GenoMic Annotation (MAGMA) [12].

## E. Interpretation

We aim to interpret the 256-dimensional latent space by following Van der Meer's approach for MOSTest [3], where each SNP's test statistic is the sum of univariate associations (squared Z-scores after removing the correlation between Z-scores from permuted genotypes). For lead SNPs strongly associated with our cortical folding representations, we compute a linear combination of the latent space dimensions, with each dimension weighted by the sign of the Z-score multi-
<figure><img src="image_5.png" /><figcaption>**Fig. 3.** Overview of the proposed framework: from the initial crop extraction to SNP association analysis. The encoded crops are visualized here using Uniform Manifold Approximation and Projection (UMAP), reducing the 256-dimensional latent space into two dimensions for easier visualization, with each point retaining its original color from the input data. In the MOSTest approach, each dimension of the latent space is treated as an independent phenotype.</figcaption></figure>

plied by its squared Z-score from its univariate association with the phenotype. Then, we project the representation of each subject onto the direction of interest, sort them, and apply a moving average to identify which phenotype is encoded in the direction indicated by genetic associations. The moving average is calculated by grouping crops in packs of 200 subjects according to their increasing projection coordinate along the direction indicated by a given SNP. Therefore, we now have a proposed interpretation of the genetic associations within the latent space.

### III. RESULTS

15 loci (located on the chromosomes 1, 2, 3, 6, 7, 8, 12, 16, 17) and 11 genes (ZIC4, CENPW, CCDC91, C16orf95, NSF, KANSL1, MAPT, CRHR1, SPPL2C, ARL17B, LRRC37A) are strongly associated with the latent space corresponding to the left OFC region.

11 loci (located on the chromosomes 1, 2, 5, 6, 7, 12, 16) and 5 genes (WARS2, ZIC4, CENPW, SHFM1, C16orf95) (Figure 4) are strongly associated with the latent space corresponding to the right OFC region.

We identified five loci common to the OFC for both hemispheres. These loci are on: (i) 2p24.2 (start=18,699,768,

length=23 kb) with its strongest association related to the lead SNP rs11675029 ($p = 7 \times 10^{-9}$); (ii) 2p14 (start=65,937,041, length=70kb) with its strongest association related to the lead SNP rs7576487 ($p = 3 \times 10^{-21}$); (iii) 6q22.32 (start=126,657,472, length=423 kb) with its strongest association related to the lead SNP rs1120786 ($p = 6 \times 10^{-9}$); (iv) 7p21.1 (start=19,528,238, length=126 kb) with its strongest association related to the lead SNP rs4329170 ($p = 9 \times 10^{-23}$); (v) 16q24.2 (start=87,220,694, length=44 kb) with its strongest association related to the lead SNP rs9308343 ($p = 3 \times 10^{-13}$).

By analyzing the shape changes over the direction indicated by rs2109873 on 7p21.1 ($p = 1 \times 10^{-21}$), the length of the transverse orbital sulcus seems to discriminate patterns in the OFC region. This observation may provide an alternative description to that proposed by Troiani et al. [13] (Figure 5).

### IV. DISCUSSION

To our knowledge, it is the first time that an exhaustive representation of the full geometry and morphometry of the sulci is associated with genetics.

We observed associations at genetic loci consistently implicated in prior genetic studies of neuroimaging phenotypes,
<figure><img src="image_6.png" /><figcaption>**Fig. 4.** Manhattan plot showing significance of each variant's association with the right OFC region. Each dot represents a SNP, with SNPs ordered on the x-axis according to their genomic position. The y-axis represents the strength of their association measured as -log₁₀ transformed p values. The red line marks the SNP significance threshold of *p* < 5 × 10⁻⁸. A significant peak highlights a potentially important genomic region for further investigation.</figcaption></figure>

<figure><img src="image_7.png" /><figcaption>**Fig. 5.** The two extreme averages (in orange at the top panels), calculated on 200 crops each, corresponding to the 200 most extreme subjects on either end of the projection direction indicated by rs2109873, for the left OFC region. The panels on the bottom row represent examples of subjects (in blue) with the corresponding pattern found above, displayed together with the white matter mesh (in grey).</figcaption></figure>

such as the heterozygous deletion of ZIC1 and ZIC4, which is associated with a congenital cerebellar malformation [14]. CRHR1 is found by Hibar et al. [15] for subcortical brain region volumes. CENPW and KANSL1 by Warrier et al. [16] for cortical organization and development. Focusing on loci, eight are common with the studies done by Van der Meer et al. [17] in mapping the genetic to cortical volumes, thicknesses, and surfaces.

Despite the promising nature of these initial results, certain limitations must be acknowledged. The database used to train the deep model for sulcal shape analysis is the same as that employed for genetic testing. While over-fitting is unlikely since the model does not receive any genetic information during training, validation with MOSTest using a dataset

not seen by Champollion V0 is required to confirm the generalizability of these findings.

The full validation of the results will be achieved in three steps: first, we will perform the genetic tests on 20,000 other UKBioBank subjects not seen by Champollion V0 (they will be available and preprocessed soon). Second, we will conduct an independent validation test on UKB subjects with non-white British ancestry to confirm the robustness of the results. Last, when new UKBioBank subjects are available, we will increase the sample size to improve the statistics of these tests.

By combining results from all brain regions using this method, we could gain a comprehensive understanding of the genetic basis of brain folding, potentially revealing new links between brain structure, behavior, and neurological disorders.

## V. COMPLIANCE WITH ETHICAL STANDARDS

This research study was conducted retrospectively using human subject data made available in open access by UK Biobank Limited. Ethical approval was not required as confirmed by the license attached with the open access data.

## VI. ACKNOWLEDGMENTS

This project has been funded by ANR via FOLDDICO (ANR-20-CHIA-0027), BHT (ANR-22-PESN-0012) and StratifyAging (ANR-22-PESN-0010), RHU-PsyCARE (ANR-18-RHUS-0014), and by European Union's Horizon 2020 for R-LINK (H2020-SC1-2017, 754907), and EBRAINS2 (HORIZON-INFRA-2022-SERV-B-01).
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