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Computing brain networks with complex dynamics

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Abstract

The interplay between neuronal network connectivity and neuron dynamics is known to drive global brain behavior; however, the exact relationship between network connectivity and node dynamics is complex and remains poorly understood. Previous theoretical and modeling work has shown that in small toy networks, when nodes are equipped with discrete quadratic dynamics, properties of the emergent behavior of the complex quadratic network (CQN) can give rise to features that relate to the underlying topology. Specifically, when the long-term behavior of CQNs is represented by asymptotic fractal sets, certain topological features of the fractal can be used to classify the network topology. However, the success of this approach has thus far not been tested on more complex real-world networks. Here, we apply a CQN modeling approach to capture individual differences in real-world brain networks derived from human connectome data. We show that CQNs are more sensitive than traditional graph theoretic measures at capturing individual differences in the topology of the human connectome, and that features of the associated equi-M sets can differentiate between male and female connectomes. This study, therefore, provides a basis upon which future work can build in order to better quantify individual differences in brain connectivity, and how these differences drive brain function and behavior.

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Data availability and materials

Data were provided [in part] by the Human Connectome Project, WU-Minn Consortium (Principal Investigators: David Van Essen and Kamil Ugurbil; 1U54MH091657) funded by the 16 NIH Institutes and Centers that support the NIH Blueprint for Neuroscience Research and by the McDonnell Center for Systems Neuroscience at Washington University.

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Funding

The project received support from the Simons Foundation (Rǎdulescu, #523763) and from the SUNY New Paltz Foundation and RSCA programs. Support was also provided by the Center for Computational Research at the University at Buffalo.

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Authors and Affiliations

  1. Mathematics Department, State University of New York at New Paltz, 1 Hawk Dr., New Paltz, 12561, New York, USA

    Anca Rǎdulescu

  2. School of Psychology, Georgia Institute of Technology, Atlanta, USA

    Johan Nakuci

  3. Department of Surgery, Dartmouth-Hitchcock Medical Center, Lebanon, USA

    Simone Evans

  4. Department of Molecular and Systems Biology, Geisel School of Medicine, Dartmouth College, Hanover, USA

    Simone Evans

  5. Mathematics Department, Institute for Artificial Intelligence and Data Sciences, and Neuroscience Program, University at Buffalo, SUNY, Buffalo, USA

    Sarah Muldoon

Authors
  1. Anca Rǎdulescu
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  2. Johan Nakuci
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  3. Simone Evans
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  4. Sarah Muldoon
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Contributions

All authors contributed to the study conception and design. The complex dynamics analysis was performed by Rǎdulescu and Evans. The tractography data processing was completed by Nakuci and Muldoon. The model analysis was performed by Rǎdulescu and Nakuci. All authors contributed to writing the first version of the manuscript. All authors read and approved the submission.

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Correspondence to Anca Rǎdulescu.

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Rǎdulescu, A., Nakuci, J., Evans, S. et al. Computing brain networks with complex dynamics. Neural Comput & Applic 35, 21115–21127 (2023). https://doi.org/10.1007/s00521-023-08903-4

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  • DOI: https://doi.org/10.1007/s00521-023-08903-4

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