Homological Landscape of Human Brain Functional Sub-Circuits

Duy Duong-Tran, Ralph Kaufmann, Jiong Chen, Xuan Wang, Sumita Garai, Frederick H. Xu, Jingxuan Bao, Enrico Amico, Alan D. Kaplan, Giovanni Petri, Joaquin Goni, Yize Zhao and Li Shen ()
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Duy Duong-Tran: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Ralph Kaufmann: Department of Mathematics, Purdue University, West Lafayette, IN 47907, USA
Jiong Chen: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Xuan Wang: Department of Electrical and Computer Engineering, George Mason University, Fairfax, VA 22030, USA
Sumita Garai: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Frederick H. Xu: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Jingxuan Bao: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA
Enrico Amico: Neuro-X Institute, Swiss Federal Institute of Technology Lausanne, 1015 Geneva, Switzerland
Alan D. Kaplan: Computational Engineering Division, Lawrence Livermore National Laboratory, Livermore, CA 94550, USA
Giovanni Petri: CENTAI Institute, 10138 Torino, Italy
Joaquin Goni: Purdue Institute for Integrative Neuroscience, Purdue University, West Lafayette, IN 47907, USA
Yize Zhao: School of Public Health, Yale University, New Heaven, CT 06520, USA
Li Shen: Department of Biostatistics, Epidemiology and Informatics, Perelman School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, USA

Mathematics, 2024, vol. 12, issue 3, 1-25

Abstract: Human whole-brain functional connectivity networks have been shown to exhibit both local/quasilocal (e.g., a set of functional sub-circuits induced by node or edge attributes) and non-local (e.g., higher-order functional coordination patterns) properties. Nonetheless, the non-local properties of topological strata induced by local/quasilocal functional sub-circuits have yet to be addressed. To that end, we proposed a homological formalism that enables the quantification of higher-order characteristics of human brain functional sub-circuits. Our results indicate that each homological order uniquely unravels diverse, complementary properties of human brain functional sub-circuits. Noticeably, the H 1 homological distance between rest and motor task was observed at both the whole-brain and sub-circuit consolidated levels, which suggested the self-similarity property of human brain functional connectivity unraveled by a homological kernel. Furthermore, at the whole-brain level, the rest–task differentiation was found to be most prominent between rest and different tasks at different homological orders: (i) Emotion task ( H 0 ), (ii) Motor task ( H 1 ), and (iii) Working memory task ( H 2 ). At the functional sub-circuit level, the rest–task functional dichotomy of the default mode network is found to be mostly prominent at the first and second homological scaffolds. Also at such scale, we found that the limbic network plays a significant role in homological reconfiguration across both the task and subject domains, which paves the way for subsequent investigations on the complex neuro-physiological role of such network. From a wider perspective, our formalism can be applied, beyond brain connectomics, to study the non-localized coordination patterns of localized structures stretching across complex network fibers.

Keywords: functional sub-circuit; functional networks; homological kernel; topological data analysis (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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