Multi-origins of pathological theta oscillation from neuron to network inferred by a combined data and model study with cubature Kalman filter

Abstract

The brain rhythm is strongly associated with the brain function. Alzheimer's disease (AD) is characterized reflected by the brain rhythm switching from the alpha band (9–12 Hz) to the theta band (4–8 Hz), accompanied with the loss of brain function. However, extracting the implicating intrinsic characteristic variations of the brain network by utilizing the Electroencephalogram (EEG) information is challenging. Kaman observer, serving as an effective Bayesian technique, can provide a visualization service for probing the intrinsic characteristics underlying the pathological theta oscillations. This work first establishes an excitation-inhibitory neural network model and explores the role of the fraction of the inhibitory neurons and inhibitory synapses in the pathological theta oscillation. The results indicate that the reduced inhibitory neuronal proportion and attenuated inhibitory synaptic weight are the main neural bases of the frequency reduction of neural oscillation. Then, we further explore the intrinsic spiking characteristic by considering spike frequency adaptation (SFA) to the inhibitory neurons. The results show that the SFA reduces the firing rate of neurons, which facilitates the theta rhythm. The enhancement of SFA current by increasing the time constant of its gating variable can further decrease the theta frequency from 7 Hz to 4 Hz. Furthermore, for this high-dimensional nonlinear excitation-inhibitory neural network model, cubature Kalman filter (CKF) is employed to estimate the above potential variations from the EEG data. The observation results show that the attenuated trends of the inhibitory neuronal proportion and the decreased inhibitory SFA current result in the descending brain rhythm. Finally, the theoretical simulation is deduced by utilizing the mean field theory for simplifying high-dimensional model to verify the simulation results. The theoretical variations of inhibitory parameters and adaptation gating variable are consistent with the simulation results. In summary, we investigate the multi-origin factors related to inhibitory neuronal intrinsic characteristics from forward model simulation and inverse EEG estimation process. And we further verify the simulation and data-driven results by theoretical derivation. This work enhances the understanding of the systematic function of inhibitory intrinsic characteristics on pathological theta oscillation and provides an effective method to decode the dynamics underlying neural activities.