A Nonlinear Stochastic Differential Model of EEG Dynamics with Bayesian Change-Point Detection for Early Identification of Brain Abnormalities

Abstract

Electroencephalography (EEG) signals exhibit complex nonlinear and stochastic dynamics that fundamentally reflect underlying neural processes. Despite decades of clinical application, conventional EEG analysis remains constrained by linear assumptions or opaque black-box architectures that obscure mechanistic understanding. This study proposes a mathematically grounded nonlinear stochastic differential equation (SDE) framework integrated with Bayesian change-point detection for early, interpretable identification of abnormal brain states. The proposed methodology explicitly characterises nonlinear neural interactions and time-varying stochastic fluctuations through estimation of biophysically meaningful parameters. As a proof-of-concept, validation is performed on data from a single patient (Patient 1, CHB-MIT Scalp EEG Seizure Database) and a single EEG channel (Fp1-F7). Within-patient five-fold cross-validation demonstrates high temporal consistency, with mean sensitivity of 96.8 +/- 0.3% and specificity of 94.2 +/- 0.2%, substantially outperforming conventional linear autoregressive (87.3%, 1.82 s latency) and spectral power density methods (81.5%, 1.35 s). An ablation study confirms that the combined SDE-Bayesian framework yields the highest performance, demonstrating a synergistic gain of +12.4 percentage points in sensitivity over SDE-alone and +8.5 over Bayesian change-point alone. Detection latency of 0.47 s falls within the clinically critical 1-2 second intervention window. Parameter estimation accuracy, validated on simulated data, achieves errors below 2% for all model parameters. Unlike existing approaches, the framework provides physiologically interpretable parameters-neural damping, nonlinearity strength, and stochastic noise level-suitable for mechanistic understanding of pathological brain dynamics. These proof-of-concept results represent a meaningful first step toward clinical deployment; robust generalisation conclusions await future multi-patient and multi-channel validation.