Deep learning-based embedding of functional connectivity profiles for precision functional mapping

Abstract

Spatial similarity of functional connectivity profiles across matching anatomical locations in individuals is often calculated to delineate individual differences in functional networks. Likewise, spatial similarity is assessed across average functional connectivity profiles of groups to evaluate the maturity of functional networks during development. Despite its widespread use, spatial similarity is limited to comparing two samples at a time. In this study, we employed a variational autoencoder to embed functional connectivity profiles from various anatomical locations, individuals, and group averages for simultaneous comparison. We demonstrate that our variational autoencoder, with pre-trained weights, can project new functional connectivity profiles from the vertex space to a latent space with as few as two dimensions, yet still retain meaningful global and local structures in the data. Functional connectivity profiles from various functional networks occupy distinct compartments of the latent space. Moreover, the variability of functional connectivity profiles from the same anatomical location is readily captured in the latent space. We believe that this approach could be useful for visualization and exploratory analyses in precision functional mapping.

Keywords: functional connectivity; individual differences; latent space; resting-state fMRI.

Fig. 1.

Comparing seed-based FC profiles in the vertex space versus in the latent space. (A) Vertex space: FC profiles from individual seed locations can have the spatial correlation (R) to the FC profile of a network template, despite the subtle differences between themselves. (B) Latent space: FC profiles were approximate with two-dimensional latent embeddings whose relative positions were visualized as stars.

Fig. 2.

Geometric reformatting and the autoencoder model architecture. (A) Geometric reformatting. The cortical distribution of fMRI activity is converted into a spherical surface and then to an image by evenly resampling the spherical surface with respect to sin(e) and a, where e and a indicate elevation and azimuth, respectively. (B) Architecture of an autoencoder. An encoder network samples latent variables given an input image under the inference model, while a decoder network generates a genuine input image under the generative model. Both the encoder and decoder networks contain 5 convolutional layers. Adapted from Kim et al. (2021). Copyright 2021 by Elsevier Inc.

Fig. 3.

Reconstructed FC profiles obtained by traversing the latent space of the beta-VAE model. (A) One latent dimension varies in equal steps from one end to the other, while the other dimension is fixed at zero. (B) Grids representing different combinations of z₁ and z₂.

Fig. 4.

Separation of functional connectivity (FC) profiles by functional networks in the average of 94 HCP subjects. (A) Gordon network assignments for 286 area parcels (some networks were renamed from the original publication based on later discovery of domain functions). (B) The flattened FC profiles from each of the 286 area parcels. (C) The mean correlational distance between each pair of the FC profiles in B. (D) The mean silhouette index for each functional network based on the correlation distance in C. The dashed line shows the mean across all areas. (E) The FC profile latent embeddings with two dimensions in VAE. Each circle represents each area parcel’s mean functional connectivity profile across Rest1 sessions of 94 subjects. (F) The mean Euclidean distance between the latent embeddings of the average across 94 subjects. (G) The mean silhouette index for each functional network based on the Euclidean distance in F. The dashed line shows the mean across all areas. (H) A scatter plot of the Euclidean distance in the latent space (F) and correlational distance in the vertex space (C).

Fig. 5.

FC profile embeddings from the Rest1 session for areas within the 12 Gordon networks across all 94 HCP subjects. (A) All 12 networks. (B) Each individual network. The large circles demonstrate the average of each parcel across subjects, and the smaller dots represent individual parcels from individual subjects.

Fig. 6.

Sub-clusters within the DMN network in the latent space. (A) Clustering the DMN latent embeddings into two sub-clusters with the k-means algorithm. (B) The sub-cluster membership across parcels and subjects. (C) The probability of each parcel belonging to each cluster is calculated as a percentage of the population. (D) The sub-cluster membership in two example subjects. (E) The reconstructed FC profiles from the centroids of the two sub-clusters. The axes scales were the same as Figure 5.

Fig. 7.

Interindividual variability in each parcel’s FC embedding across 94 HCP subjects in the VAE latent representation in Rest1 and Rest2 sessions. (A) The FC embedding for example parcel 213. Each data point is a subject indicated by the numbers 1 to 94. The “Somatomotor_Hand” and “DorsalAttention” markers were from Lynch et al. 2024. The axes scales were the same as Figure 5. (B) The FC profiles from parcel 213 for example subjects 8 and 33 in Rest1 and Rest2 were visualized on standard brain surfaces. (C) Intersubject dispersion in the Rest1 sessions. (D) Dispersion signal-to-noise ratio (SNR) of each parcel’s FC calculated as the ratio of intersubject dispersion and intrasubject dispersion.

Fig. 8.

Fingerprinting accuracy and age prediction. (A) The lines show fingerprinting performances from increasing amounts of data in each session, and the isolated markers show the fingerprinting performance from the whole session in 94 HCP individuals. (B) Age prediction accuracy is measured as the Pearson’s correlation (r) between the actual and predicted age in years for 301 BCP sessions. Error bars show the mean and standard deviation across the 1000 samples. The horizontal line and shaded area show the performance (mean and standard deviation) using features in the parcel space.

Fig. 9.

Relating cognitive traits to FC latent embeddings. (A–C) Parcels with significant correlation with intelligence composite scores. (D–F) Scatter plot of the intelligence composite scores and the latent embedding values of dimension 1 or dimension 2 of an example parcel.

Fig. 10.

Distribution of functional connectivity profiles from different parcels in different cohorts. (A) FC profiles from 286 area parcels (group-average adult parcellation) in 94 subjects in the HCP dataset with 2 scan sessions each. The network legend for the colors was the same as Figure 4A. (C) FC profiles from 567 to 710 individual-level area parcels in 10 highly-sampled adult individuals with 10 scan sessions each. The area parcels displayed on the brain are from one example subject, with the area parcels and network legend for all subjects in the Supplementary Materials. (E) 326 area parcels (group-average toddler parcellation) in 301 mixed longitudinal and cross-sectional sessions from 178 infant/toddlers aged 8–60 months, with the network legend in the Supplementary Materials. (B, D, F) is the same as (A, C, E) but plotted as a probability density plot. (G) Difference in probability density between BCP and HCP. (H) Difference in probability density between BCP and HCP.