Multiscale effective connectivity analysis of brain activity using neural ordinary differential equations

Neural mechanisms and underlying directionality of signaling among brain regions depend on neural dynamics spanning multiple spatiotemporal scales of population activity. Despite recent advances in multimodal measurements of brain activity, there is no broadly accepted multiscale dynamical models for the collective activity represented in neural signals. Here we introduce a neurobiological-driven deep learning model, termed multiscale neural dynamics neural ordinary differential equation (msDyNODE), to describe multiscale brain communications governing cognition and behavior. We demonstrate that msDyNODE successfully captures multiscale activity using both simulations and electrophysiological experiments. The msDyNODE-derived causal interactions between recording locations and scales not only aligned well with the abstraction of the hierarchical neuroanatomy of the mammalian central nervous system but also exhibited behavioral dependences. This work offers a new approach for mechanistic multiscale studies of neural processes. Author Summary Multi-modal measurements have become an emerging trend in recent years due to the capability of studying brain dynamics at disparate scales. However, an integrative framework to systematically capture the multi-scale nonlinear dynamics in brain networks is lacking. A major challenge for creating a cohesive model is a mismatch in the timescale and subsequent sampling rate of the dynamics for disparate modalities. In this work, we introduce a deep learning-based approach to characterize brain communications between regions and scales. By modeling the continuous dynamics of hidden states using the neural network-based ordinary differential equations, the requirement of downsampling the faster sampling signals is discarded, thus preventing from losing dynamics information. Another advantageous feature of the proposed method is flexibility. An adaptable framework to bridge the gap between scales is necessary. Depending on the neural recording modalities utilized in the experiment, any suitable pair of well-established models can be plugged into the proposed multi-scale modeling framework. Thus, this method can provide insight into the brain computations of multi-scale brain activity. ### Competing Interest Statement The authors have declared no competing interest.