Realistic Thermodynamic and Statistical-Mechanical Measures for Neural Synchronization

Synchronized brain rhythms, associated with diverse cognitive functions, have been observed in electrical recordings of brain activity. Neural synchronization may be well described by using the population-averaged global potential $V_G$ in computational neuroscience. The time-averaged fluctuation of $V_G$ plays the role of a "thermodynamic" order parameter $\cal {O}$ used for describing the synchrony-asynchrony transition in neural systems. Population spike synchronization may be well visualized in the raster plot of neural spikes. The degree of neural synchronization seen in the raster plot is well measured in terms of a "statistical-mechanical" spike-based measure $M_s$ introduced by considering the occupation and the pacing patterns of spikes. The global potential $V_G$ is also used to give a reference global cycle for the calculation of $M_s$. Hence, $V_G$ becomes an important collective quantity because it is associated with calculation of both $\cal {O}$ and $M_s$. However, it is practically difficult to directly get $V_G$ in real experiments. To overcome this difficulty, instead of $V_G$, we employ the instantaneous population spike rate (IPSR) which can be obtained in experiments, and develop realistic thermodynamic and statistical-mechanical measures, based on IPSR, to make practical characterization of the neural synchronization in both computational and experimental neuroscience. Particularly, more accurate characterization of weak sparse spike synchronization can be achieved in terms of realistic statistical-mechanical IPSR-based measure, in comparison with the conventional measure based on $V_G$.