The Effect Of Interaction Between Coupling Delay And Strength On Brain Functional Connectivity

The coupling delay and the coupling strength in brain network structure connectivity have important influence on the brain functional connectivity.The neural signal passing through the signal path between nodes takes a certain transmission time and dynamical relaying,so there is a large coupling delay between the nodes of the mesoscopic scale brain network.However,there is a need to conduct deep and quantitative research on the influence rule of the coupling delay to brain network nodes phase synchronization.In order to explain the effect mechanism of coupling delay on functional connectivity in the feedback loop structure,we study the effect of motif with different feedback loops on phase synchronization.We analyze the frequency of the oscillation output signal at different coupling delay by constructing the feedback loop structure,and it provide an effective explanation for the periodicity of phase synchronization.Basing on the alpha frequency band neural mass model,we used phase coherence function to analyze the influence of interaction of coupling delay and coupling strength between nodes on phase synchronization.1?Firstly,we employed the alpha range neural mass model(NMM)to construct a mesoscopic brain network and simulated the structure connectivity to obtain alpha frequency range signal of all nodes.By computing the phase coherence between the neural oscillations of the NMMs in the brain network analysed the phase synchronization between signals.We analyzed the effect of coupling delay on the phase synchronization between nodes through the functional connectivity matrix,the phase-synchronization curve between the nodes with the coupling delay,and the effect of interaction of coupling delay and coupling strength(connection probability)on phase synchronization.The result showed that: I.The coupling delay has a periodic effect on the phase synchronization as a whole.II.The interaction of coupling delay and coupling strength(or connection probability)determine the specific form of the periodic influence law: When the coupling strength is low,the coupling delay exerts a “sine” form effect on the phase synchronization for the resting state brain function network;when the coupling strength is high,coupling delay results in a transition between the synchrinazation and asynchrinazation state.III.When the coupling strength is very high,the phase between nodes gradually tend to the synchronous state.2 ? To further explain the influence of coupling delay on the phase synchronization between nodes,in this section,we studied typical three-node mitif and classified them into three major categories: 1.Motifs do not contain a feedback loop;2.Motifs contain a single feedback loop;3.Motifs contain multiple feedback loops.The influence of the feedback loops in brain network on the phase synchronization was explained by studying motifs with different numbers of feedback loop.We studied the effect of coupling delay on phase synchronization between nodes by analyzing the trend of phase synchronization between nodes and the two-dimensional analysis chart under interaction of coupling delay and coupling strength.The result shows that: I.If the motif contains a feedback loop,the phases between the nodes are more likely to be in a synchronous state,and the more the feedback loops are,the more obvious the trend is.II.For motif without a feedback loop,the phase synchronization shows periodicity influence which is similar to “sine” form,but the phase does not tend to synchronize as the coupling delay increases.III.For the motif with feedback loop,the phase synchronization appears a periodic change with the increase of the coupling delay,and the phase gradually reaches the synchronization state with the increase of the coupling strength and remains unchanged.The number of feedback loops included in motif is used to explain the existence of feedback connections in the structure network and the influence of the feedback connections on the phase synchronization.3?In order to further explain the influence of the coupling delay on the phase synchronization between nodes,in this section,we analyzed node output oscillation frequency with different coupling delays through the feedback loop structure constructed by multiple neural mass models.The result showed that: the period of the frequency component contained in the output signal of the node is consistent with the phase synchronization period as the coupling delay increases.When the oscillation signal contains multiple frequency components,the phase synchronization between the nodes is small;when the oscillation frequency is uniform the phase synchronization between the nodes is large.