Multi-scale dynamics modeling of spike and field potential activity via biologically realistic neural ordinary differential equations

To date, the investigation of neural population dynamics is mostly limited by single-scale analysis. Although in neuropsychiatric conditions, neural circuit-wide pathological activity impacts dynamics at multiple scales, either directly or indirectly, there is no broadly accepted multi-scale dynamical model for the collective activity of neuronal populations. Traditionally, the analysis has proceeded mainly without formal neurobiological models of the underlying multi-scale neuronal activity. Whereas cross-correlation or coherence have been employed to measure the coupling of activities at different scales (e.g., spiking and local field potential (LFP) for neuronal synchronization), they only capture patterns of statistical dependence. Instead, dynamical modeling, which is seldom explored at the multi-scale level, infers the causal interactions among brain regions or sources and potentially yields a mechanistic understanding of brain computations. Here we developed a neurobiological model-driven deep learning method, termed neural ordinary differential equation-based multi-scale dynamics modeling (msDyNODE), to uncover multi-scale brain communications governing cognitive behaviors. We showed the msDyNODE successfully captured multi-scale neural data and dynamics in both simulation and real experiments.