A parameter estimation method for neural mass model based on the improved chimp optimization algorithm and Riemannian geometry

Neural mass model (NMM) serves as an effective tool for understanding and exploring the complex dynamics of brain systems. Accurately estimating the model parameters of NMM is highly important for building brain models driven by observed electroencephalogram (EEG) data. However, existing methods for comparing model output with observed data primarily focus on one-dimensional linear comparisons, overlooking the high-dimensional nonlinear dynamics and Riemannian geometry characteristics of EEG data. To address this issue, we propose a novel parameter estimation method for NMM based on the improved chimp optimization algorithm (ChOA) and Riemannian geometry. First, ChOA is improved by incorporating the Aquila optimizer (AOChOA) is used to improve the convergence efficiency and accuracy of the nonlinear optimization problem. Then, a novel loss function based on the Riemannian geometry of symmetric positive definite matrices (LRSPD) is constructed to capture the high-dimensional nonlinear dynamics of EEG signals. Finally, we validate the effectiveness of the proposed method by using the model output with fixed model parameters and real EEG signals as observed data, respectively. When using the model output with fixed model parameters, the loss function LRSPD yielded more accurate parameter estimation results compared to others, with the fitted model closely matching the dynamics of the observed data. When using real EEG data, the proposed method successfully recovered differences in EEG dynamics for subjects at different consciousness levels. Additionally, our study reveals the neural mechanisms of decreased consciousness level in patients with disorders of consciousness (DOC), characterized by increased inhibitory neural activity of the brain.