A Push-Pull Network Mechanism Revealed by Describing Function Analysis for Alzheimer's Pathological Oscillations.

Abnormal theta band (4-8 Hz) cortical oscillations have been identified as a pathological hallmark in Alzheimer's disease (AD), which can be suppressed through high-frequency electrical stimulation (ES). However, their neural origins and mechanistic underpinnings remain poorly understood. In this work, we develop a mathematical model to characterize AD-related cortical theta oscillations. Through linear equivalent transformation of the physiological model and describing function analysis, we elucidate the network mechanism underlying these pathological oscillations. The results demonstrate that the reduced synaptic inhibition from fast inhibitory interneurons to pyramidal neuron populations drives the cortical network into a pathological low-frequency (theta band) oscillatory state. The oscillation frequency and amplitude can be directly determined from the intersection points between the Nyquist curve of the model's linear component and the negative inverse curve of the nonlinear element's describing function. Conversely, the separation between these curves driven by external stimulation visually represents how stimulation can shift the cortical network away from abnormal theta oscillations. The describing function analysis not only provides a mechanistic explanation for aberrant oscillations but also enables precise prediction of effective stimulation parameters for suppressing pathological theta activity. This work offers a novel framework to reveal the "push-pull" network effects of AD, providing an intuitive understanding of cortical stimulation mechanisms and a quantitative approach for optimizing neuromodulation strategies in AD.