Fast connectivity gradient approximation: maintaining spatially fine-grained connectivity gradients while reducing computational costs

Abstract

Brain connectome analysis suffers from the high dimensionality of connectivity data, often forcing a reduced representation of the brain at a lower spatial resolution or parcellation. This is particularly true for graph-based representations, which are increasingly used to characterize connectivity gradients, capturing patterns of systematic spatial variation in the functional connectivity structure. However, maintaining a high spatial resolution is crucial for enabling fine-grained topographical analysis and preserving subtle individual differences that might otherwise be lost. Here we introduce a computationally efficient approach to establish spatially fine-grained connectivity gradients. At its core, it leverages a set of landmarks to approximate the underlying connectivity structure at the full spatial resolution without requiring a full-scale vertex-by-vertex connectivity matrix. We show that this approach reduces computational time and memory usage while preserving informative individual features and demonstrate its application in improving brain-behavior predictions. Overall, its efficiency can remove computational barriers and enable the widespread application of connectivity gradients to capture spatial signatures of the connectome. Importantly, maintaining a spatially fine-grained resolution facilitates to characterize the spatial transitions inherent in the core concept of gradients of brain organization.

Fig. 1. Gradient approximation facilitates spatially fine-grained connectivity gradients while reducing computational costs.

a A schematic workflow of the proposed Fast Connectivity Gradient Approximation (FCGA) approach. b FCGA provides high fidelity to the full connectivity structure with only a fraction of landmarks. Thin line plots denote the spatial similarity of the first 25 gradients, and thick line plots denote the respective average. c FCGA facilitates a high spatial similarity with reduced computational time and memory requirements. d The core topography is similar across a different number of landmarks and sampling choices.

Fig. 2. Gradient approximation preserves informative individual features and improves brain-behavior predictions.

Intraclass correlation and discriminability analysis confirms the reliability, repeatability, and the preservation of individual features (a) within and (b) across sessions. Boxplots show intraclass correlation and discriminability for the first 25 gradients, and colored boxes indicate interquartile range (iqr) with whiskers spanning 1.5*iqr. Markers and line plots denote respective means. c Parcel-averaging of spatially fine-grained gradients outperforms gradient calculation on a parcel level for both age and FSIQ prediction. Fast connectivity gradient approximation (FCGA) with landmarks based on the group-average Schaefer parcellation (n = 1000) was used to establish vertex-level gradients before parcel averaging. The first five gradients were used as features. Boxplots show 100 runs of tenfold cross-validation, and colored boxes indicate interquartile range (iqr) with whiskers spanning 1.5*iqr. Predictions that are not significantly better than prediction with randomly shuffled labels are denoted as n.s.