Abstracts

Rationale: Epilepsy affects about 1% of the world’s population. The disease is marked by recurrent and unprovoked seizures that often cause motor and cognitive impairments and occasionally death. The ability to reliably reconstruct and model brain signals without extensive recording is crucial for understanding epileptic networks, localization of seizure onset zones, and developing neuromodulation therapies. Dynamic linear time-invariant (LTI) state space models, x[t+1] = Ax[t], where x[t] is a vector of recorded intracranial EEG (iEEG) signals, can reliably reconstruct short-term brain activity given only initial state conditions. The classical method to estimate the model’s transition matrix A uses the ordinary least squares (OLS) approach. Unfortunately, this method is sensitive to outliers and initial conditions, and the signal reconstruction quality significantly degrades with time. We investigate the effectiveness of LTI models in characterizing the dynamic behavior of multichannel iEEG data, evaluate optimization strategies for robust modeling, and explore whether a weighted least squares (WLS) approach could reduce the effect of outliers and initial conditions on the reconstructed signal.

Methods: Data from 3 patients across 8 sets (30 windows in time) of recordings from the Fragility Multi-Center Study was used, and these data were sampled at 1000 Hz. We estimated A matrices to characterize the dynamics of the brain data in epilepsy patients using OLS and WLS methods in 0.5[s] or 1[s] long sliding time windows of iEEG data. To assess the effectiveness of each method in capturing the underlying dynamics, the state vector was reconstructed using the initial iEEG state conditions and the estimated A matrix. The reconstructed state vectors for the OLS and WLS models were computed, and the root mean square error (RMSE) between the original iEEG signal and each reconstruction was then calculated to compare the accuracy of the models. The weights were modified piecewise linearly to produce minimal error. Also, outliers were identified, and their weight was reduced. Statistical significance was determined by the t-test.

Results: We tested 3 different weighting profiles and found a systematic improvement in computed RMSE for the WLS method when compared to OLS. For 500-sample windows, WLS with linearly scaled weights mean±SD (RMSE=13K±3K) compared to OLS (RMSE=17K±7K) better reconstructed the signal, p< 0.001. This trend continued for window sizes of 1000 samples; WLS (RMSE=29.5K±10K) performed better than OLS (RMSE=36K±11K), p=0.022.


Conclusions: Using the WLS method to estimate dynamical brain signal models produced reliable reconstructions of brain signals for longer time windows. Optimization of weighting parameters may significantly reduce the effects of outliers and initial conditions on the model estimation.

Funding: AES Junior Investigator Award 1042632, CURE Epilepsy Foundation Taking Flight Award 1061181, and NIH UG3NS130202 Award.