Online Learning Koopman Operator for Closed-Loop Electrical Neurostimulation in Epilepsy

Zhichao Liang; Zixiang Luo; Keyin Liu; Jingwei Qiu; Quanying Liu

2022

10.1109/JBHI.2022.3210303

IEEE Journal of Biomedical and Health Informatics   Impact Factor & Quartile

2168-2208

2168-2208

Electrical neuromodulation as a palliative treatment has been increasingly used in the control of epilepsy. However, current neuromodulations commonly implement predetermined actuation strategies and lack the capability of self-adaptively adjusting stimulation inputs. In this work, rooted in optimal control theory, we propose a Koopman-MPC framework for real-time closed-loop electrical neuromodulation in epilepsy, which integrates i) a deep Koopman operator based dynamical model to predict the temporal evolution of epileptic electroencephalogram (EEG) with an approximate finite-dimensional linear dynamics and ii) a model predictive control (MPC) module to design optimal seizure suppression strategies. The Koopman operator based linear dynamical model is embedded in the latent state space of the autoencoder neural network, in which we can approximate and update the Koopman operator online. The linear dynamical property of the Koopman operator ensures the convexity of the optimization problem for subsequent MPC control. The proposed deep Koopman operator model shows greater predictive capability than the baseline models (e.g., vector autoregressive model, kernel based method and recurrent neural network (RNN)) in both synthetic and real epileptic EEG data. Moreover, compared with the RNN-MPC framework, our Koopman-MPC framework can suppress seizure dynamics with better computational efficiency in both the Jansen-Rit model and the Epileptor model. Koopman-MPC framework opens a new window for model-based closed-loop neuromodulation and sheds light on nonlinear neurodynamics and feedback control policies.

Electrical Neuromodulation Closed-loop Neuromodulation Deep Koopman operator Model Predictive Control Online Learning

SCI

English

First

National Key Research and Development Program of China[2021YFF1200804] ; National Natural Science Foundation of China[62001205] ; Guangdong Natural Science Foundation[2019A1515111038] ; Shenzhen Science and Technology Innovation Committee["20200925155957004","KCXFZ2020122117340001"] ; Shenzhen-Hong Kong-Macao Science and Technology Innovation Project[SGDX2020110309280100] ; Shenzhen Key Laboratory of Smart Healthcare Engineering[ZDSYS20200811144003009]

Computer Science ; Mathematical & Computational Biology ; Medical Informatics

Computer Science, Information Systems ; Computer Science, Interdisciplinary Applications ; Mathematical & Computational Biology ; Medical Informatics

WOS:000927904300049

IEEE-INST ELECTRICAL ELECTRONICS ENGINEERS INC

IEEE

Shenzhen Key Laboratory of Smart Healthcare Engineering, Department of Biomedical Engineering, Southern University of Science and Technology, Shenzhen, P. R. China

Zhichao Liang,Zixiang Luo,Keyin Liu,et al. Online Learning Koopman Operator for Closed-Loop Electrical Neurostimulation in Epilepsy[J]. IEEE Journal of Biomedical and Health Informatics,2022,PP(99):1-12.

Zhichao Liang,Zixiang Luo,Keyin Liu,Jingwei Qiu,&Quanying Liu.(2022).Online Learning Koopman Operator for Closed-Loop Electrical Neurostimulation in Epilepsy.IEEE Journal of Biomedical and Health Informatics,PP(99),1-12.

Zhichao Liang,et al."Online Learning Koopman Operator for Closed-Loop Electrical Neurostimulation in Epilepsy".IEEE Journal of Biomedical and Health Informatics PP.99(2022):1-12.