The occurrence and risk of recurrence of brain related injuries and diseases are difficult to characterize due to various factors including inter-individual variability. A useful approach is to analyze the brain electroencephalogram (EEG) for differences in brain frequency bands in the signals obtained from potentially injured and healthy normal subjects. However, significant shortcomings include: (1) contrary to empirical evidence, current spectral signal analysis based methods often assume that the EEG signal is linear and stationary; (2) nonlinear time series analysis methods are mostly numerical and do not possess any predictive features. In this work, we develop models based on stochastic differential equations that can output signals with similar frequency and magnitude characteristics of the brain EEG. Initially, a coupled linear oscillator model with a large number of degrees of freedom is developed and shown to capture the characteristics of the EEG signal in the major brain frequency bands. Then, a nonlinear stochastic model based on the Duffing oscillator with far fewer degrees of freedom is developed and shown to produce outputs that can closely match the EEG signal. It is shown that such a compact nonlinear model can provide better insight into EEG dynamics through only few parameters, which is a step towards developing a framework with predictive capabilities for addressing brain injuries.
- Dynamic Systems and Control Division
Stochastic Dynamic Modeling of the Human Brain EEG Signal
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Ghorbanian, P, Ramakrishnan, S, Simon, AJ, & Ashrafiuon, H. "Stochastic Dynamic Modeling of the Human Brain EEG Signal." Proceedings of the ASME 2013 Dynamic Systems and Control Conference. Volume 2: Control, Monitoring, and Energy Harvesting of Vibratory Systems; Cooperative and Networked Control; Delay Systems; Dynamical Modeling and Diagnostics in Biomedical Systems; Estimation and Id of Energy Systems; Fault Detection; Flow and Thermal Systems; Haptics and Hand Motion; Human Assistive Systems and Wearable Robots; Instrumentation and Characterization in Bio-Systems; Intelligent Transportation Systems; Linear Systems and Robust Control; Marine Vehicles; Nonholonomic Systems. Palo Alto, California, USA. October 21–23, 2013. V002T22A003. ASME. https://doi.org/10.1115/DSCC2013-3881
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