Dynamic System Modeling for Reconstruction of Intracranial EEG Signals in Epilepsy Using Weighted Least Squares

Epilepsy affects approximately 1% of the global population and is marked by seizures that can lead to severe motor and cognitive impairments or death. Models are needed for brain mapping and robust identification of epileptogenic regions. Dynamic linear time invariant state-space models reliably reconstruct short-term intracranial EEG (iEEG) activity and help with mapping. However, these models estimated using Ordinary Least Squares (OLS) are vulnerable to outliers. We investigated an alternative approach, Weighted Least Squares (WLS), that down-weights outliers and emphasizes longer-term prediction for more robust signal modeling. Five patient datasets (2,300 windows total) sampled at 1000 Hz were used. In each 0.5 sec window, we estimated model via OLS and WLS with forced stability and compared their signal reconstruction ability. We also introduced outliers in synthetic signals to test outlier susceptibility. Model performance was evaluated using root mean square error (RMSE) and paired t-tests. In synthetic data, WLS maintained low RMSE despite increasing outlier magnitudes, whereas OLS errors escalated (p < 0.0001). In human iEEG recordings, WLS showed lower RMSE (0.698 mV, IQR 0.566-0.798) than OLS (0.788 mV, IQR 0.657-0.926) with p<0.0001 for window size of 500 samples, and better preserved short- and long-term signal structure. WLS provides a robust framework for iEEG signal reconstruction, effectively mitigating outliers and stabilizing long-term estimates. This approach may enhance clinical applications, including seizure localization and neuromodulation therapy design.Clinical Relevance- Currently, clinicians visually inspect iEEG signals from each electrode to identify abnormal activity, a process that can be time-consuming and subjective. The proposed models could serve as a predictive aid in localizing the epileptogenic zones. By augmenting standard clinical workflows with these data-driven dynamical model approaches, clinicians may achieve more accurate seizure localization and better-informed decisions regarding surgical intervention and neuromodulatory treatments.