Brain activity often involves complex patterns that can be difficult to capture with traditional tools. Topological data analysis (TDA) offers a way to study the shape of these patterns, revealing structures in brain signals that might otherwise be missed.
In my work, I use TDA to explore how brain dynamics change across different conditions, such as epilepsy in fish or altered states in humans. This approach helps highlight collective features of neural activity and offers new perspectives on how the brain organizes its activity over time.
References
Topological analysis of brain dynamical signals indicates signatures of seizure susceptibility
M. Lucas, D. Francois, C. Donato, A. Skupin, and D. Proverbio
Epilepsy is known to drastically alter brain dynamics during seizures (ictal periods), but its effects on background (non-ictal) brain dynamics remain poorly understood. To investigate this, we analyzed an in-house dataset of brain activity recordings from epileptic zebrafish, focusing on two controlled genetic conditions across two fishlines. After using machine learning to segment and label recordings, we applied time-delay embedding and Persistent Homology – a noise-robust method from Topological Data Analysis (TDA) – to uncover topological patterns in brain activity. We find that ictal and non-ictal periods can be distinguished based on the topology of their dynamics, independent of genetic condition or fishline, which validates our approach. Remarkably, within a single wild-type fishline, we identified topological differences in non-ictal periods between seizure-prone and seizure-free individuals. These findings suggest that epilepsy leaves detectable topological signatures in brain dynamics even outside of ictal periods. Overall, this study demonstrates the utility of TDA as a quantitative framework to screen for topological markers of epileptic susceptibility, with potential applications across species.
@unpublished{lucas2024topological,title={Topological analysis of brain dynamical signals indicates signatures of seizure susceptibility},author={Lucas, M. and Francois, D. and Donato, C. and Skupin, A. and Proverbio, D.},journal={arXiv:2412.01911},doi={10.48550/arXiv.2412.01911},year={2025},}
Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior
A. Santoro, F. Battiston, M. Lucas, G. Petri, and E. Amico
Traditional models of human brain activity often represent it as a network of pairwise interactions between brain regions. Going beyond this limitation, recent approaches have been proposed to infer higher-order interactions from temporal brain signals involving three or more regions. However, to this day it remains unclear whether methods based on inferred higher-order interactions outperform traditional pairwise ones for the analysis of fMRI data. To address this question, we conducted a comprehensive analysis using fMRI time series of 100 unrelated subjects from the Human Connectome Project. We show that higher-order approaches greatly enhance our ability to decode dynamically between various tasks, to improve the individual identification of unimodal and transmodal functional subsystems, and to strengthen significantly the associations between brain activity and behavior. Overall, our approach sheds new light on the higher-order organization of fMRI time series, improving the characterization of dynamic group dependencies in rest and tasks, and revealing a vast space of unexplored structures within human functional brain data, which may remain hidden when using traditional pairwise approaches.
@article{santoro2023higher,title={Higher-order connectomics of human brain function reveals local topological signatures of task decoding, individual identification, and behavior},author={Santoro, A. and Battiston, F. and Lucas, M. and Petri, G. and Amico, E.},journal={Nature Communications},volume={15},number={1},pages={10244},year={2024},doi={10.1038/s41467-024-54472-y}}