Topological brain connectomics for task decoding, brain fingerprinting, and behavioral association

1807 

Abstract Submission 

Andrea Santoro¹, Federico Battiston², Maxime Lucas³, Giovanni Petri⁴, Enrico Amico⁵

¹Ecole Polytechnique Fédérale de Lausanne, Geneva, Geneva, ²Central European University, Vienna, Vienna, ³CENTAI, Turin, Turin, ⁴Northeastern University London, London, London, ⁵Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland

Andrea Santoro  
Ecole Polytechnique Fédérale de Lausanne
Geneva, Geneva

Federico Battiston  
Central European University
Vienna, Vienna

Maxime Lucas  
CENTAI
Turin, Turin

Giovanni Petri  
Northeastern University London
London, London

Enrico Amico  
Ecole Polytechnique Federale de Lausanne
Lausanne, Switzerland

Traditional models depict human brain activity as a network of pairwise interactions, commonly utilizing functional connectivity (FC). Recent approaches challenge these models by inferring higher-order interactions (HOIs) involving three or more regions from temporal brain signals. This study evaluates whether methods based on inferred HOIs outperform traditional pairwise ones for fMRI data analysis, using a topological approach capable of reconstructing HOI structures in time [1].

Our method builds on prior work with edge-level signals and extends functional connectivity research beyond pairs [2, 3]. It leverages low-order signals to define higher-order ones in four key steps [1], illustrated in Fig. 1(a-d). (i) We standardize the N original fMRI signals through z-scoring; (ii) Compute all possible k-order time series as element-wise products of k + 1 of these z-scored time series, further z-scored for cross-k-order comparability. These k-order time series represent instantaneous co-fluctuation magnitudes of associated (k + 1)-node interactions, like edges and triangles. We assign a sign to the resulting k-order time series at each time based on a strict parity rule: positive for fully concordant group interactions, and negative for discordant interactions. (iii) For each time t, we encode all instantaneous k-order (co-fluctuation) time series into a weighted simplicial complex. Finally, at each time t, we apply computational topology tools to analyze weights of the simplicial complex and extract two local indicators. We aim to assess the performance of higher-order local indicators in different applications, relying on fMRI data of the 100 unrelated subjects from HCP [4].

We tested our approach on three brain applications: task decoding, functional brain fingerprinting, and brain-behavior association (two shown). This assessment ran parallel to traditional brain network techniques, including node [5] and edge functional connectivity [2], aiming to unveil the advantages of higher-order methods. For BOLD, edges, triangles, and scaffold signals, we constructed time-time correlation matrices, obtained when concatenating resting-state and seven task fMRI datasets, excluding rest blocks. We then binarized at the 95th percentile, and applied the Louvain algorithm [6] to identify communities. To assess community partitions' effectiveness in decoding task and rest timings, we used the element-centric similarity (ECS) measure [7]. ECS values between 0 and 1 indicate task decoding quality.
In Fig. 2, we present the results of computing local higher-order topological indicators on resting-state and task-related fMRI data of HCP [8]. Violating triangles and homological scaffolds time-time plots effectively decoded individual tasks and rest blocks. In particular, task differentiability increases as we transition from lower-order methods to higher-order ones, as evidenced by the decrease in ECS values (Fig. 2a-d).
We conducted Partial Least Square Correlation (PLSC) analyses to evaluate brain-behavior association when considering static connectivity values (FC, eFC, triangles, scaffold) and ten cognitive scores from HCP subjects. When considering whole-brain connections, all four methods performed similarly, explaining brain-behavior covariance within the 10%-20% range (Fig. 2e). By contrast, focusing on connections within specific resting-state functional subsystems (Fig. 2f), distinctions became noticeable. Transitioning from lower-order methods to higher-order ones, such as triangles or scaffolds, resulted in a sharp increase in brain-behavior associations, particularly for somatosensory areas, with triangles reaching approximately 80% of the covariance explained.

Overall, our analysis demonstrates that higher-order indicators, extracted from instantaneous topological descriptions of the data, outperform traditional node and edge-based methods[2, 3] in task decoding and provide a more robust association between brain activity and behavior.

fMRI Connectivity and Network Modeling ¹

Methods Development ²

Task-Independent and Resting-State Analysis

Other Methods

Computational Neuroscience

Data analysis

FUNCTIONAL MRI

Modeling

NORMAL HUMAN

Other - Higher-order interactions; Persistent Homology; Topology