We develop an analytical framework that benefits from a set of information theory variables to study brain activity under different stimuli. fMRI signals from different brain regions are treated as time series, and information production as well as pattern redundancy are measured using entropy density, effective measure complexity, and informational distance estimated by Lempel-Ziv complexity. The estimators assume neither linearity nor stationarity, so both linear and non-linear dynamics contribute to the measures. The framework requires no generative model, no design matrix, and no parameters fitted to the data; the fixed choices are the binarization threshold, the neighborhood size of the activation criterion, and the distance threshold of the connectivity graphs.
The framework is applied to task-based fMRI data from the Human Connectome Project under motor, working memory, emotion recognition, and language tasks, as well as resting state. The complexity entropy map identifies regional engagement consistent with established task-relevant areas, providing a model-free indicator of activation. The Lempel-Ziv distance between region pairs is then used to construct distance matrices, dendrograms, and connectivity graphs that recover hierarchical and modular functional structure: active regions cluster by functional specialization, while non-active regions form a densely interconnected backbone shared across tasks.
Since the analytical framework neither depends on prior knowledge nor assumes linearity, it is well suited for exploratory research and for the study of brain connectivity, where non-linear interactions occur across multiple functional levels. CITMA is acknowledged for financial support under the project CARDENT, grant PN223LH010-053. Kárel García and Roberto Bernal Arencibia are acknowledged for valuable discussions.
The University of Havana and Max Planck Institute for the Physics of Complex Systems are acknowledged for their computer support and working environment. JS Armand Eyebe Fouda is acknowledged for valuable discussions, particularly regarding the creation of Figure 8. Max Planck Institute for the Physics of Complex Systems, Nonlinear Dynamics and Time Series Analysis, Dresden, 01187, Germany Physics and Mathematics Faculties, University of Havana, 10400, La Habana, Cuba Ania Mesa-Rodríguez & Ernesto Estevez-Rams The authors declare no competing interests.
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material.
If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/. Mesa-Rodríguez, A., Estevez-Rams, E. & Kantz, H.
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