Application of complex network method to spatiotemporal patterns in a neuronal network

Spiral waves have been found to appear alternatively with plane waves in the brain cerebral cortex, which has a significant effect on neuron firing behaviors. In this paper, we propose a functional firing network based on the correlated firing behaviors among neuronal populations and use the complex network method to investigate the effects of spiral waves and plane waves on the structure and function of the network. We first analyze the correlation coefficient and the largest eigenvalue Of the functional firing network. We find a larger range distribution of correlation coefficients and greater largest eigenvalue of the functional firing network for spiral waves than those for plane waves, which indicates that spiral waves induce higher network synchronization. In addition, we explore the topological structure of the functional firing network using the complex network method. We find that the functional firing network for spiral waves has a larger degree and global efficiency and a lower modularity and characteristic path length than that for plane waves, revealing that spiral waves contribute to neural information transmission and strengthen the functional integration. Our work not only provides new insights for studying spatiotemporal patterns, but is also helpful for explaining the modulation of spiral waves on brain function