نوع مقاله: مقاله کامل پژوهشی

نویسندگان

1 دانشجوی کارشناسی ارشد مهندسی برق، گروه مهندسی برق، دانشکده‌ی فنی و مهندسی، دانشگاه قم، قم، ایران

2 استادیار، گروه مهندسی برق، دانشکده‌ی فنی و مهندسی، دانشگاه قم، قم، ایران

3 دانشیار، گروه مهندسی برق، دانشکده‌ی فنی و مهندسی، دانشگاه قم، قم، ایران

چکیده

بیماری صرع یکی از مهم‌ترین اختلالات عصبی در جهان به شمار می­رود. برای مهار حمله‌های صرعی از الگوریتم­های کنترلی گوناگونی استفاده شده است. در کنترل حملات صرعی، زمان کنترل و کاهش حملات و مقاوم بودن کنترل کننده در برابر تغییرات پارامترهای پاتولوژیکی و نوسانات ناخواسته از اهمیت زیادی برخوردار است. برای فراهم ساختن این الزامات و از آن‌جا که یکی از روش­های سرکوب امواج صرعی، تغییر در میانگین پتانسیل الکتریکی نورون­های محرک است، در این مقاله یک کنترل کننده‌ی مد لغزشی انتگرالی فراپیچشی زمان معین به مدل ترکیبی قشر مغز و اپتوژنتیک اعمال شده است. ابتدا جریان یونی تولید شده در کانال­های یونی در روش اپتوژنتیک به متغیر حالت مربوط به میانگین پتانسیل الکتریکی نورون­های محرک در مدل قشر مغز اعمال شده و دو مدل اپتوژنتیک و قشر مغز با یک‌دیگر ترکیب شده تا ولتاژ کنترلی اعمال شده به سیستم از طریق مدل اپتوژنتیک به صورت فوتون­های نور به نورون­های ناحیه‌ی صرعی در مغز اعمال شود. سپس کنترل کننده‌ی مذکور با این هدف که مدل صرعی، مدل سالم را در مدت زمان معینی دنبال کند به این مدل ترکیبی اعمال شده است. در نهایت با استفاده از کنترل کننده‌ی مد لغزشی انتگرالی فراپیچشی زمان معین مشاهده می­شود که در مدت زمان معین، خطای هم‌گرایی وضعیت صرعی به وضعیت سالم کاملا صفر شده، دامنه‌ی سیگنال کنترل نسبت به حالت مد لغزشی کلاسیک کاهش یافته و هم‌چنین مشکلات تکینگی و نوسانات ناخواسته که از محدودیت­های کنترل کننده‌ی مد لغزشی کلاسیک می‌باشد، برطرف شده است.

کلیدواژه‌ها

عنوان مقاله [English]

Epilepsy Control in a Combination of the Cortical and Optogenetic Models using Fixed Time Integral Super Twisting Sliding Mode Controller

نویسندگان [English]

  • Samira Rezvani Ardakani 1
  • Sajad Mohammad-Ali-Nezhad 2
  • Reza Ghasemi 3

1 M.Sc. Student, Electrical & Electronics Engineering Department, Engineering Faculty, University of Qom, Qom, Iran

2 Assistant Professor, Electrical & Electronics Engineering Department, Engineering Faculty, University of Qom, Qom, Iran

3 Associate Professor, Electrical & Electronics Engineering Department, Engineering Faculty, University of Qom, Qom, Iran

چکیده [English]

Epilepsy is one of the most important neurological disorders in the world. In order to suppress epileptic seizures, various control algorithms have been used. Time to control and reduce attacks and robustness of the controller against variations of pathologic parameters and unwanted oscillations are important to control epileptic seizure. In order to consider these requirements and considering that one of the methods used to suppress epileptic waves is the change in mean soma (electric) potential of the excitatory neurons, this paper applies a fixed-time integral super twisting sliding mode controller to the combination of cortical and optogenetic models.  First, the ion current produced in ion channels in optogenetic method is applied to the state variable of the mean electric potential of the excitatory neurons of the cortical model and the cortical and optogenetic models are combined and the controlled voltage applied to the system is applied to neurons of the epileptic zone of the brain as optic photons via the optogenetic model. Then, the mentioned controller is applied to the hybrid model so that the healthy model is tracked by the epileptic model in a fixed time. Finally, using the fixed-time integral super twisting sliding mode controller, the convergence error of the epileptic state to the healthy state has become zero. The amplitude of the control signal is reduced compared to the classic sliding mode control and technical problems and unwanted oscillations which are the shortcomings of the classic sliding mode controller are resolved.   

کلیدواژه‌ها [English]

  • Epilepsy
  • cortical model
  • optogenetic
  • the fixed time integral super twisting sliding mode controller

[1]   م. خدابخشی، ا.ح. دوائی مرکزی، " تحلیل دینامیکی و دوشاخگی‌های مدل تودة نورونی جانسن-ریت و کاربرد آن در توصیف حملات صرعی،" فصلنامه علمی پژوهشی مهندسی پزشکی زیستی، دوره 11، شماره 1، صفحه 61-68، بهار 1396.

[2]   A.D. Bui, A. Alexander, L. Soltesz,” Seizing control: from current treatments to optogenetic interventions in epilepsy,” The Neuroscientist, vol. 23, no. 1, pp. 68-81, Feb, 2017.

[3]   V. Salanova, “Deep brain stimulation for epilepsy,” Epilepsy & Behavior, vol. 88, pp. 21-24, Jul, 2018.

[4]   P. Selvaraj et al, “Closed-loop feedback control and bifurcation analysis of epileptiform activity via optogenetic stimulation in a mathematical model of human cortex,” Physical Review E, vol. 93, no.1, Jan, 2016.

[5]   A. Mirzaei, S. Ozgoli, “Chaotic analysis of the human brain cortical model and robust control of epileptic seizures using sliding mode control,” Systems Science & Control Engineering, vol. 2, no.1, pp. 216-227, Dec, 2014.

[6]   A.L. Hodgkin, A.F Huxley. “A quantitative description of membrane current and its application to conduction and excitation in nerve,” The Journal of physiology, vol. 117, no.4, pp. 500-544, Aug, 1952.

[7]   P.F. Pinsky, J. Rinzel, ”Intrinsic and network rhythmogenesis in a reduced Traub model for CA3 neurons”. Journal of computational neuroscience,” vol. 1, no. 1-2, pp. 39-60, Jun, 1994.

[8]   B.H. Jansen, V.G. Rit, “Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns,” Biological cybernetics, vol. 73, no. 4, pp. 357-366, Sep, 1995.

[9]   D.T. Liley, P.J. Cadusch, J.J. Wright, “A continuum theory of electro-cortical activity,” Neurocomputing, vol. 26, pp. 795-800, Jun, 1999.

[10]H.R. Wilson, “Simplified dynamics of human and mammalian neocortical neurons,” Journal of theoretical biology. vol. 200, no. 4, pp. 375-388, Oct, 1999.

[11]P.A. Robinson et al., “Estimation of multiscale neurophysiologic parameters by electroencephalographic means”, Human brain mapping. vol. 23, no. 1, pp. 53-72, Sep, 2004.

[12]P. Suffczynski, S. Kalitzin, F.L. Da Silva, “Dynamics of non-convulsive epileptic phenomena modeled by a bistable neuronal network,” Neuroscience. vol. 26, no. 2, Jan, 2004.

[13]J.E. Rubin, D. Terman, “High frequency stimulation of the subthalamic nucleus eliminates pathological thalamic rhythmicity in a computational model,” Journal of computational neuroscience, vol. 16, no. 3, pp. 211-235, May, 2004.

[14]M. Chen et al., “Bidirectional control of absence seizures by the basal ganglia: a computational evidence,” PLoS computational biology. vol. 10, no.3, Mar, 2014.

[15]J. Wang, L. Chen, X. Fei, “Bifurcation control of the Hodgkin–Huxley equations,” Chaos, Solitons & Fractals, vol. 33, no.1, pp. 217- 224, Jul, 2007.

[16]M.A. Kramer et al., “Bifurcation control of a seizing human cortex,” Physical Review E, vol. 73, no. 4, Apr, 2006.

[17]N. Chakravarthy et al., “Controlling epileptic seizures in a neural mass model,” Journal of Combinatorial Optimization, vol. 17, no. 1, pp. 98-116, Jan, 2009.

[18]B.A. Lopour, A.J.  Szeri. “A model of feedback control for the charge-balanced suppression of epileptic seizures,” Journal of computational neuroscience. vol. 28, no. 3, pp. 375-387, Jun, 2010.

[19]B. Deng et al., “Dynamic control of seizure states with input-output linearization method based on the Pinsky-Rinzel model,” In 2014 7th International IEEE Conference on Biomedical Engineering and Informatics, pp. 425-430, Oct, 2014.

[20]P. Selvaraj et al., “Open loop optogenetic control of simulated cortical epileptiform activity,” Journal of computational neuroscience. vol. 36, no. 3, pp. 515-525, Jun, 2014.

[21]P. Selvaraj et al., “Optogenetic induced epileptiform activity in a model human cortex,” SpringerPlus. vol. 4, no. 1, p. 155, Dec, 2015.

[22]B.J. Zhang, M. Chamanzar, M.R. Alam, “Suppression of epileptic seizures via Anderson localization,” Journal of The Royal Society Interface, vol. 14, no. 127, Feb, 2017.

[23]A. Farhoud, A. Erfanian, “Fully automatic control of paraplegic FES pedaling using higher-order sliding mode and fuzzy logic control,” IEEE Transactions on Neural Systems and Rehabilitation Engineering, vol. 22, no.3,  pp. 533-542, Jan, 2014.

[24]R. Ghasemi, M.B. Menhaj, A. Afshar. “A new decentralized fuzzy model reference adaptive controller for a class of large-scale nonaffine nonlinear systems”, European Journal of Control, vol.15, no. 5, p.534, Sep, 2009.

[25]F. Abdollahi, H.A. Talebi, R.V. Patel. “A stable neural network-based observer with application to flexible-joint manipulators”. IEEE Transactions on Neural Networks, vol. 17, no. 1, pp.118-129, Feb, 2006.

[26]ح. حیدری نژاد، ه. دلاوری، "تنظیم گلوکز خون با استفاده از کنترل مدلغزشی مرتبه کسری تطبیقی در بیماران دیابتی نوع 1،" فصلنامه علمی پژوهشی مهندسی پزشکی زیستی، دوره 9، شماره 4، صفحه 327-339، زمستان 1394.

[27]M.T. Wilson MT et al., “The K-complex and slow oscillation in terms of a mean-field cortical model,” Journal of Computational Neuroscience, vol. 21, no. 3, pp. 243-257, Dec, 2006.

[28]B.A. Lopour et al., “A continuous mapping of sleep states through association of EEG with a mesoscale cortical model,” Journal of computational neuroscience, vol. 30, no. 2, pp. 471-487, Apr, 2011.

[29]M.L. Steyn-Ross, D.A Steyn-Ross, J.W. Sleigh. “Modelling general anaesthesia as a first-order phase transition in the cortex,” Progress in biophysics and molecular biology, vol. 85, no. 23. pp. 360-385, Jun, 2004.

[30]X.J. Wang, “Neurophysiological and computational principles of cortical rhythms in cognition”, Physiological reviews, vol. 3, no. 90, pp.1195-1268, 2010.

[31]F. Crick, “The impact of molecular biology on neuroscience,” Philosophical Transactions of the Royal Society of London. Series B: Biological Sciences, vol. 29, no. 354, pp. 2021-2025, Dec, 1999.

[32]G. Nagel et al., “Channelrhodopsin-2, a directly light-gated cation-selective membrane channel,” Proceedings of the National Academy of Sciences, vol. 100, no. 24, pp. 13940-13945, Nov, 2003.

[33]N. Grossman et al., “Modeling study of the light stimulation of a neuron cell with channelrhodopsin-2 mutants,” IEEE Transactions on Biomedical Engineering, vol. 58, no. 6,  pp. 1742-1751, Jun, 2011.

[34]J.C. Williams et al.,  “Computational optogenetics: empirically-derived voltage-and light-sensitive channelrhodopsin-2 model,” PLoS computational biology, vol. 9, no. 9, Sep, 2013.

[35]M.P. Dafilis, D.T. Liley, P.J. Cadusch, “Robust chaos in a model of the electroencephalogram: Implications for brain dynamics,” Chaos: An Interdisciplinary Journal of Nonlinear Science, vol. 11, no. 1, pp. 474-478, Sep, 2001.

[36]M.P. Dafilis et al., “Visualising chaos in a model of brain electrical activity,” Computers & Graphics, vol. 26, no. 6, pp. 971-976, Dec, 2002.

[37]J.B. Wang et al., “Fixed time integral sliding mode controller and its application to the suppression of chaotic oscillation in power system”, Chinese Physics B, vol. 27, no. 7, Jul, 2018.

[38]J. Rivera et al., “Super-twisting sliding mode in motion control systems,” Sliding mode control, Rijeka, Croatia, pp. 273-254, 2011.

[39]H. Li H, Y. Cai, “On SFTSM control with fixed-time convergence”, IET Control Theory & Applications, vol. 11, no. 6, pp. 766-773, Jan, 2017.

[40]Z. Zuo, “Non-singular fixed-time terminal sliding mode control of non-linear systems”, IET control theory & applications, vol. 9, no. 4, Dec, 2014.