The contribution of structural connectivity to dynamic and often highly variable brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure--function issue . We treat a system of Jansen--Rit neural-mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Direct simulations are used to determine the similarity of functional (inferred from correlated activity between brain areas ) and structural connectivity matrices as a function of the parameters controlling dynamics of a single node , highlighting a non-trivial structure--function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly determine the network instabilities that give rise to oscillations, and the set of false bifurcationsthat occur beyond this onset. In particular, we highlight that functional connectivity (FC) is inherited most robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, structure only weakly influences function . Secondly, we develop a weakly coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of the FC matrix can be predicted using a linear stability analysis. This study thereby emphasises  that local dynamics can have a substantial role in shaping large-scale functional brain states.
The contribution of structural connectivity to functional brain states remains poorly understood. We present a mathematical and computational study suited to assess the structure--function issue , treating a system of Jansen--Rit neural-mass nodes with heterogeneous structural connections estimated from diffusion MRI data provided by the Human Connectome Project. Via direct simulations we determine the similarity of functional (inferred from correlated activity between nodes ) and structural connectivity matrices under variation of the parameters controlling single-node dynamics , highlighting a non-trivial structure--function relationship in regimes that support limit cycle oscillations. To determine their relationship, we firstly calculate network instabilities giving rise to oscillations, and the so-called `false bifurcations' (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring beyond this onset. We highlight that functional connectivity (FC) is inherited robustly from structure when node dynamics are poised near a Hopf bifurcation, whilst near false bifurcations, structure only weakly influences FC . Secondly, we develop a weakly-coupled oscillator description to analyse oscillatory phase-locked states and, furthermore, show how the modular structure of FC matrices can be predicted via linear stability analysis. This study thereby emphasises the substantial role that local dynamics can have in shaping large-scale functional brain states.
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dynamic and often highly variable
functional
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. We treat
, treating
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Direct simulations are used to
Via direct simulations we
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brain areas
nodes
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as a function
under variation
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dynamics of a single node
single-node dynamics
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determine the network instabilities that give
calculate network instabilities giving
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set of false bifurcationsthat occur
so-called `false bifurcations' (for which a significant qualitative change in the orbit is observed, without a change of stability) occurring
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In particular, we
We
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most
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function
FC
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weakly coupled
weakly-coupled
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the FC matrix
FC matrices
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using a
via
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the substantial role
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a substantial role