Source-linked AI summary
Multilayer motif analysis of brain networks
Federico Battiston, Vincenzo Nicosia, Mario Chavez, Vito Latora
TL;DR
Brain network studies have usually treated anatomical and functional connectivity separately, leaving their correspondence difficult to characterize. This paper generalizes motif analysis to multiplex networks, applies it to structural and functional brain layers, and finds that positive functional correlations with physical connections are overrepresented. The results further indicate non-trivial dependence between functional connectivity and the anatomical network.
Problem
Brain network analysis has largely treated anatomical and functional connectivity as separate entities, while their correspondence remains difficult to characterize.
Method
The paper generalizes motif analysis to multiplex networks and applies it to two-layer brain networks derived from diffusion MRI and resting-state functional MRI.
Results
Positive functional correlations coexisting with direct structural connections are significantly overrepresented, while negative functional links with structural connections are as likely as in the random model.
Takeaways & Limitations
The findings support using multilayer motifs to study joint anatomical–functional organization and indicate that functional connectivity is non-trivially constrained by anatomical connectivity.
Takeaways & Limitations
The analyzed brain connectivity matrices are symmetrical because DW-MRI fiber estimation cannot distinguish afferent from efferent projections.
Abstract
from arXiv · showhide
In the last decade, network science has shed new light both on the structural (anatomical) and on the functional (correlations in the activity) connectivity among the different areas of the human brain. The analysis of brain networks has made possible to detect the central areas of a neural system, and to identify its building blocks by looking at overabundant small subgraphs, known as motifs. However, network analysis of the brain has so far mainly focused on anatomical and functional networks as separate entities. The recently developed mathematical framework of multi-layer networks allows to perform an analysis of the human brain where the structural and functional layers are considered together. In this work we describe how to classify the subgraphs of a multiplex network, and we extend motif analysis to networks with an arbitrary number of layers. We then extract multi-layer motifs in brain networks of healthy subjects by considering networks with two layers, anatomical and functional, respectively obtained from diffusion and functional magnetic resonance imaging. Results indicate that subgraphs in which the presence of a physical connection between brain areas (links at the structural layer) coexists with a non-trivial positive correlation in their activities are statistically overabundant. Finally, we investigate the existence of a reinforcement mechanism between the two layers by looking at how the probability to find a link in one layer depends on the intensity of the connection in the other one. Showing that functional connectivity is non-trivially constrained by the underlying anatomical network, our work contributes to a better understanding of the interplay between structure and function in the human brain.
I. INTRODUCTION
Brain connectivity can be studied anatomically or functionally, but their correspondence remains difficult to characterize. The paper addresses this gap by extending motif analysis to multiplex networks combining both modalities.
- Anatomical networks represent physical connections among brain regions, whereas functional networks represent interactions between their activities.
- Although anatomical connections may influence brain dynamics, how they support or facilitate functional-network properties remains unclear.
- This correspondence matters for understanding normal neural processes and identifying or predicting connectivity alterations in brain diseases.
- The paper uses motif analysis, which identifies small subgraphs statistically overrepresented relative to a null model, to study structure–function relations.
- It generalizes motif analysis to multiplex networks and applies the framework to two-layer brain networks built from structural and functional measurements.
II. MULTILAYER MOTIF ANALYSIS
The paper develops a framework for classifying motifs in multiplex networks while preserving how connections are distributed across layers. It applies this framework to increasingly complex multilayer subgraphs, including structural and signed functional brain connections.
- Multi-layer motifs with n = 2 nodes: For M = 3 layers, there are c = 7 possible two-node multi-links when each layer has one edge type.
- Motifs in multi-layer networks: A multiplex network is represented by one adjacency matrix per interaction layer, while aggregation collapses layer-specific links into a single network.
- Motifs in multi-layer networks: Single-layer motif analysis can lose layered organization because one aggregated subgraph may arise from multiple cross-layer edge configurations.
- Motifs in multi-layer networks: Multilayer subgraphs are classified by node count, their aggregated subgraph, and the exact connection pattern across layers.
- Multi-layer motifs with n > 3 nodes: Larger multilayer motifs require accounting for symmetries and can be decomposed into combinations of multi-links, pairs, and triples.
III. DATA
The study analyzes multiplex brain networks with structural and functional layers derived from multimodal imaging of 19 healthy subjects. Structural edges represent axonal connections, while functional edges represent significant correlations between regional activity time series.
- Data sources: The dataset contains multiplex brain networks from 19 control subjects, with structural and functional layers inferred from diffusion MRI and fMRI, respectively.The functional recordings consisted of six-minute segments from the same subjects.
- Data sources: Both connectivity layers use 264 putative brain regions, enabling matched structural and functional representations across subjects.The functional data were normalized, corrected, filtered, and subsampled to the anatomical regions.
- Layer construction: Structural edge weights indicate axonal connection presence and strength, whereas functional weights are proportional to correlations in regional hemodynamic activity.Functional correlations were variance-stabilized with Fisher’s Z-transform before constructing connectivity matrices.
- Layer construction: The functional graph was thresholded at p < 0.05, corrected for multiple comparisons, retaining significant positive and negative links while setting nonsignificant links to zero.Structural connectivity remained sparse, whereas functional connectivity was thresholded from an initially fully connected graph.
- Layer construction: The multiplex representation distinguishes positive, negative, or absent functional links from existing or absent structural edges.This encodes the two interaction types jointly for each pair of brain regions.
IV. MOTIFS IN MULTI-LAYER BRAIN NETWORKS
The paper extends motif analysis to multiplex brain networks by comparing multi-layer subgraph abundances with hemisphere-preserving randomized null models. Significant motifs show coordinated structural and functional organization, especially positive functional correlations alongside physical connections.
- Elementary motifs: For two binary layers, the analysis identifies five elementary two-node motifs: +Y, -Y, 0Y, +N, and -N.The functional layer is signed, while the structural layer records whether a connection exists.
- Null model and significance: Motif significance is assessed by comparing real subgraph abundance with the mean and standard deviation from randomized networks; high positive Z-scores indicate recurrent motifs.The null model preserves each node’s total degree and its within- and between-hemisphere connection counts.
- Two-node motifs: The +Y motif is significantly overrepresented, while +N is markedly underrepresented, linking positive functional correlations with direct structural connections.The -Y motif is as likely in real data as in the randomized model, indicating no corresponding negative-functional association.
- Higher-order motifs: The analysis extends to n = 3, yielding t = 15 multi-layer triads and T = 35 multi-layer triangles evaluated against randomized ensembles.The triad analysis uses Z-scores computed from real-data abundances relative to randomized-network means and standard deviations.
- Higher-order motifs: Triangles 1, 4, 18, 22, 25, and 34 are statistically validated recurrent motifs, reflecting structural clustering or signed balance in functional correlations.The cited motifs include triangles with three positive functional links and triangles with one positive and two negative links.
V. NETWORK REINFORCEMENT MECHANISMS
The paper tests whether connection strength in one brain-network layer predicts link presence in the other. Real data show positive, non-monotonic cross-layer relationships that are absent from the corresponding null models.
- Cross-layer probabilities: The analysis measures positive-functional-link probability as a function of structural weight and structural-link probability as a function of functional correlation strength.These are dual conditional-probability analyses of the two connectivity layers.
- Cross-layer reinforcement: Stronger physical connectivity is typically associated with a higher probability of significant positive functional activity between the same regions.This positive trend is not observed in the corresponding null model.
- Cross-layer reinforcement: The probability of a structural link also increases positively, though non-monotonically, with the strength of functional correlation.The corresponding null model randomizes the binary structural layer while preserving the weighted positive functional structure.
- Interpretation: The observed cross-layer trends support anatomical connectivity as a predictor of functional interactions across most brain areas, with weaker predictive evidence in the reverse direction.The authors relate these findings to earlier work on correspondence between structural and functional networks.
VI. CONCLUSIONS
This study addresses multimodal brain-network analysis by examining anatomical and functional connectivity jointly through multilayer motifs. It identifies joint anatomofunctional motifs and reports that structural connectivity constrains functional coupling, while noting limits of the analyzed connectivity matrices.
- The study addresses the organization of brain motifs across anatomical and functional connectivity in multimodal brain networks.
- Multi-layer analysis identifies nonrandom joint anatomofunctional motifs that differ from motifs found in single structural networks.
- Positive functional correlations are found between brain areas connected by direct physical links, although spatial proximity may explain some cases.
- The analyzed connectivity matrices are symmetrical because DW-MRI fiber estimation cannot distinguish afferent from efferent projections.