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Neural mass models can produce electroencephalography (EEG) like signals corresponding to interical, pre-ictal and ictal activities. In this paper, a novel closed-loop feedback control strategy based on algebraic estimation is proposed to eliminate epileptiform spikes in neural mass models. Algebraic estimation plays a role in observing the states of the model in order to construct the controller. For a network of coupled neural populations, the characteristics regarding the closed-loop feedback control strategy, including the relationship between the type of controlled populations and the ability of eliminating epileptiform spikes, the relationship between the number of controlled populations and control energy, the relationship between the model parameters and control energy, are determined by numerical simulations. The purpose is to establish the rules for the proper control of eliminating epileptiform spikes with as less control energy as possible. Moreover, the proposed control-loop control strategy is compared with a direct proportional feedback control strategy by numerical simulations. It is shown that the use of algebraic estimation makes a reduction of control energy.
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Keywords:
- neural mass model /
- epileptiform spike /
- feedback control /
- algebraic estimation
[1] Meng Q F, Zhou W D, Chen Y H, Peng Y H 2010 Acta Phys. Sin. 59 123 (in Chinese) [孟庆芳, 周卫东, 陈月辉, 彭玉华 2010 59 123]
[2] Lee U, Kim S, Jung K Y 2006 Phys. Rev. E 73 041920
[3] Wang C, Zhang C, Zou J, Zhang J 2012 Phys. A 391 1602
[4] Serge F T, Oleg Y P, Yuriy S P, Sergey A D, Alexander Y K 2012 Phys. A 391 1179
[5] Ma Q L, Bian C H, Wang J 2010 Acta Phys. Sin. 59 4480 (in Chinese) [马千里, 卞春华, 王俊 2010 59 4480]
[6] Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[7] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 61 020503]
[8] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 59 5319]
[9] Gu H G, Hui L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 61 080504]
[10] Jansen B H, Rit V G 1995 Biol. Cybern. 73 357
[11] Lopes S F H, Hoeks A, Smits H, Zetterberg L H 1974 Kybernetik 15 27
[12] David O, Friston K J 2003 NeuroImage 20 1743
[13] Ursino M, Cona F, Zavaglia M 2010 NeuroImage 52 1080
[14] Spiegler A, Kiebel S J, Atay F M, KnÄosche T R 2010 NeuroImage 52 1041
[15] Huang G, Zhang D, Meng J, Zhu X 2011 Neurocomputing 74 1026
[16] Hao D M, Ruan X G 2005 Acta Biophys. Sin. 21 39 (in Chinese) [郝冬梅, 阮晓刚 2005 生物 21 39]
[17] Wendling F, Bellanger J J, Bartolomei F, Chauvel P 2000 Biol. Cybern. 83 367
[18] Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[19] Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 2644
[20] Sunderam S, Gluckman B, Reato D, Bikson M 2010 Epilepsy and Behavior 17 6
[21] Doyle C D, Francis B A, Tannenbaum A R 1992 Feedback Control Theory (1st Ed.) (London: Macmillan) p31
[22] Sauer T D, Schiff J S 2009 Phys. Rev. E 79 051909
[23] Ullah G, Schiff J S 2009 Phys. Rev. E 79 040901
[24] Zehetner J, Reger J, Horn M 2007 16th IEEE International Conference on Control Applications Singapore, Republic of Singapore October 1-3, 2007 p331
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[1] Meng Q F, Zhou W D, Chen Y H, Peng Y H 2010 Acta Phys. Sin. 59 123 (in Chinese) [孟庆芳, 周卫东, 陈月辉, 彭玉华 2010 59 123]
[2] Lee U, Kim S, Jung K Y 2006 Phys. Rev. E 73 041920
[3] Wang C, Zhang C, Zou J, Zhang J 2012 Phys. A 391 1602
[4] Serge F T, Oleg Y P, Yuriy S P, Sergey A D, Alexander Y K 2012 Phys. A 391 1179
[5] Ma Q L, Bian C H, Wang J 2010 Acta Phys. Sin. 59 4480 (in Chinese) [马千里, 卞春华, 王俊 2010 59 4480]
[6] Hashemi M, Valizadeh A, Azizi Y 2012 Phys. Rev. E 85 021917
[7] Liu S B, Wu Y, Hao Z W, Li Y J, Jia N 2012 Acta Phys. Sin. 61 020503 (in Chinese) [刘少宝, 吴莹, 郝忠文, 李银军, 贾宁 2012 61 020503]
[8] Yang Z Q 2010 Acta Phys. Sin. 59 5319 (in Chinese) [杨卓琴 2010 59 5319]
[9] Gu H G, Hui L, Jia B 2012 Acta Phys. Sin. 61 080504 (in Chinese) [古华光, 惠磊, 贾冰 2012 61 080504]
[10] Jansen B H, Rit V G 1995 Biol. Cybern. 73 357
[11] Lopes S F H, Hoeks A, Smits H, Zetterberg L H 1974 Kybernetik 15 27
[12] David O, Friston K J 2003 NeuroImage 20 1743
[13] Ursino M, Cona F, Zavaglia M 2010 NeuroImage 52 1080
[14] Spiegler A, Kiebel S J, Atay F M, KnÄosche T R 2010 NeuroImage 52 1041
[15] Huang G, Zhang D, Meng J, Zhu X 2011 Neurocomputing 74 1026
[16] Hao D M, Ruan X G 2005 Acta Biophys. Sin. 21 39 (in Chinese) [郝冬梅, 阮晓刚 2005 生物 21 39]
[17] Wendling F, Bellanger J J, Bartolomei F, Chauvel P 2000 Biol. Cybern. 83 367
[18] Goodfellow M, Schindler K, Baier G 2011 NeuroImage 55 920
[19] Goodfellow M, Schindler K, Baier G 2012 NeuroImage 59 2644
[20] Sunderam S, Gluckman B, Reato D, Bikson M 2010 Epilepsy and Behavior 17 6
[21] Doyle C D, Francis B A, Tannenbaum A R 1992 Feedback Control Theory (1st Ed.) (London: Macmillan) p31
[22] Sauer T D, Schiff J S 2009 Phys. Rev. E 79 051909
[23] Ullah G, Schiff J S 2009 Phys. Rev. E 79 040901
[24] Zehetner J, Reger J, Horn M 2007 16th IEEE International Conference on Control Applications Singapore, Republic of Singapore October 1-3, 2007 p331
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