Modeling Functional Connectivity on Empirical and Randomized Structural Brain Networks

Seyma Bayrak, Philipp Hövel (Corresponding Author), Vesna Vuksanovic

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This study combines modeling of neuronal activity and networks derived from neuroimaging data in order to investigate how the structural organization of the human brain affects the temporal dynamics of interacting brain areas. The dynamics of the neuronal activity is modeled with FitzHugh–Nagumo oscillators and the blood-oxygen-level-dependent (BOLD) time series is inferred via the Balloon–Windkessel hemodynamic model. The simulations are based on anatomical probability maps between considered brain regions of interest. These maps were derived from diffusion-weighted magnetic resonance imaging measurements. In addition, the length of the fiber tracks allows for inference of coupling delays due to finite signal propagation velocities. We aim to investigate (i) graph-theoretical properties of the network topology derived from neuroimaging data and (ii) how randomization of structural connections influences the dynamics of neuronal activity. The network characteristics of the structural connectivity data are compared to density-matched Erdős–Rényi random graphs. Furthermore, the neuronal and BOLD activity are modeled on both empirical and random (Erdős–Rényi type) graphs. The simulated temporal dynamics on both graphs are compared statistically to capture whether the spatial organization of these network affects the modeled time series. Results support previous findings that key topological network properties such as small-worldness of our neuroimaging data are distinguishable from random networks. We also show that simulated BOLD activity is affected by the underlying network topology and the strength of connections between the network nodes. The difference of the modeled temporal dynamics of brain networks from the dynamics on randomized graphs suggests that anatomical connections in the human brain together with dynamical self-organization are crucial for the temporal evolution of the resting-state activity.
Original languageEnglish
Pages (from-to)1-17
Number of pages17
JournalDifferential Equations and Dynamical Systems
Early online date11 Mar 2017
Publication statusPublished - 2017

Bibliographical note

This study was assisted by BMBF (Grant No. 01Q1001B) in the framework of BCCN Berlin (Project B7). We would like to thank Yasser Iturria-Medina for sharing the DW-MRI data used in this work. Şeyma Bayrak acknowledges additionally the support by Jochen Braun.


  • Brain networks
  • Functional and anatomical connectivity
  • Hemodynamic model
  • Resting state
  • Time-delayed oscillations


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