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Chin. Phys. B, 2015, Vol. 24(3): 038701    DOI: 10.1088/1674-1056/24/3/038701
INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY Prev   Next  

Closed-loop control of epileptiform activities in a neural population model using a proportional-derivative controller

Wang Jun-Song (王俊松)a b, Wang Mei-Li (王美丽)a, Li Xiao-Li (李小俚)c, Ernst Nieburb
a School of Biomedical Engineering, Tianjin Medical University, Tianjin 300072, China;
b Zanvyl Krieger Mind/Brain Institute and Solomon Snyder Department of Neuroscience, Johns Hopkins University, Baltimore 21218, MD, USA;
c National Key Laboratory of Cognitive Neuroscience and Learning, Beijing Normal University, Beijing 100875, China
Abstract  

Epilepsy is believed to be caused by a lack of balance between excitation and inhibitation in the brain. A promising strategy for the control of the disease is closed-loop brain stimulation. How to determine the stimulation control parameters for effective and safe treatment protocols remains, however, an unsolved question. To constrain the complex dynamics of the biological brain, we use a neural population model (NPM). We propose that a proportional-derivative (PD) type closed-loop control can successfully suppress epileptiform activities. First, we determine the stability of root loci, which reveals that the dynamical mechanism underlying epilepsy in the NPM is the loss of homeostatic control caused by the lack of balance between excitation and inhibition. Then, we design a PD type closed-loop controller to stabilize the unstable NPM such that the homeostatic equilibriums are maintained; we show that epileptiform activities are successfully suppressed. A graphical approach is employed to determine the stabilizing region of the PD controller in the parameter space, providing a theoretical guideline for the selection of the PD control parameters. Furthermore, we establish the relationship between the control parameters and the model parameters in the form of stabilizing regions to help understand the mechanism of suppressing epileptiform activities in the NPM. Simulations show that the PD-type closed-loop control strategy can effectively suppress epileptiform activities in the NPM.

Keywords:  neural population model      epileptiform activities      proportional-derivative controller      stabilizing region  
Received:  31 October 2014      Revised:  21 November 2014      Accepted manuscript online: 
PACS:  87.19.lr (Control theory and feedback)  
  87.19.lw (Plasticity)  
  87.18.Sn (Neural networks and synaptic communication)  
Fund: 

Project supported by the National Natural Science Foundation of China (Grant Nos. 61473208, 61025019, and 91132722), ONR MURI N000141010278, and NIH grant R01EY016281.

Corresponding Authors:  Wang Jun-Song     E-mail:  wjsong2004@126.com

Cite this article: 

Wang Jun-Song (王俊松), Wang Mei-Li (王美丽), Li Xiao-Li (李小俚), Ernst Niebur Closed-loop control of epileptiform activities in a neural population model using a proportional-derivative controller 2015 Chin. Phys. B 24 038701

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