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UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model

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Abstract

A novel closed loop control framework is proposed to inhibit epileptiform wave in a neural mass model by external electric field, where the unscented Kalman filter method is used to reconstruct dynamics and estimate unmeasurable parameters of the model. Specifically speaking, the iterative learning control algorithm is introduced into the framework to optimize the control signal. In the proposed method, the control effect can be significantly improved based on the observation of the past attempts. Accordingly, the proposed method can effectively suppress the epileptiform wave as well as showing robustness to noises and uncertainties. Lastly, the simulation is carried out to illustrate the feasibility of the proposed method. Besides, this work shows potential value to design model-based feedback controllers for epilepsy treatment.

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References

  • Ahn HS, Chen YQ, Moore KL (2007) Iterative learning control: brief survey and categorization. IEEE Trans Syst Man Cybern Part C Appl Rev 37(6):1099–1121

    Article  Google Scholar 

  • Arimoto S, Naniwa T, Suzuki H (1990) Robustness of P-type learning control with a forgetting factor for robotic motions. In: Proceedings of the 29th IEEE conference on decision and control, IEEE, Honolulu, Hawaii, pp 2640–2645

  • Berényi A, Belluscio M, Mao D et al (2012) Closed-loop control of epilepsy by transcranial electrical stimulation. Science 337(6095):735–737

    Article  PubMed  Google Scholar 

  • Bhattacharya BS, Coyle D, Maguire LP (2011) A thalamo–cortico–thalamic neural mass model to study alpha rhythms in Alzheimer’s disease. Neural Netw 24(6):631–645

    Article  PubMed  Google Scholar 

  • Bristow DA, Tharayil M, Alleyne AG (2006) A survey of iterative learning control. IEEE Control Syst Mag 26(3):96–114

    Article  Google Scholar 

  • Chakravarthy N, Sabesan S, Tsakalis K et al (2009a) Controlling epileptic seizures in a neural mass model. J Comb Optim 17(1):98–116

    Article  Google Scholar 

  • Chakravarthy N, Tsakalis K, Sabesan S et al (2009b) Homeostasis of brain dynamics in epilepsy: a feedback control systems perspective of seizures. Ann Biomed Eng 37(3):565–585

    Article  PubMed Central  PubMed  Google Scholar 

  • Chien CJ, Liu JS (1996) A P-type iterative learning controller for robust output tracking of nonlinear time-varying systems. Int J Control 64(2):319–334

    Article  Google Scholar 

  • Chong M, Postoyan R, Nešić D et al (2012) Estimating the unmeasured membrane potential of neuronal populations from the EEG using a class of deterministic nonlinear filters. J Neural Eng 9(2):026001

    Article  PubMed  Google Scholar 

  • Cona F, Zavaglia M, Massimini M et al (2011) A neural mass model of interconnected regions simulates rhythm propagation observed via TMS-EEG. NeuroImage 57(3):1045–1058

    Article  CAS  PubMed  Google Scholar 

  • David O, Friston KJ (2003) A neural mass model for meg/eeg: coupling and neuronal dynamics. NeuroImage 20(3):1743–1755

    Article  PubMed  Google Scholar 

  • Eeckman FH, Freeman WJ (1991) Asymmetric sigmoid non-linearity in the rat olfactory system. Brain Res 557(1–2):13–21

    Article  CAS  PubMed  Google Scholar 

  • Fisher R, Salanova V, Witt T et al (2010) Electrical stimulation of the anterior nucleus of thalamus for treatment of refractory epilepsy. Epilepsia 51(5):899–908

    Article  PubMed  Google Scholar 

  • Freeman WJ (1977) Models of the dynamics of neural populations. Electroencephalogr Clin Neurophysiol Suppl 34:9–18

    Google Scholar 

  • Freeman WJ (1987) Simulation of chaotic EEG patterns with a dynamic model of the olfactory system. Biol Cybern 56(2–3):139–150

    Article  CAS  PubMed  Google Scholar 

  • Galka A, Ozaki T, Muhle H et al (2008) A data-driven model of the generation of human EEG based on a spatially distributed stochastic wave equation. Cogn Neurodyn 2(2):101–113

    Article  PubMed Central  PubMed  Google Scholar 

  • Halpern CH, Samadani U, Litt B et al (2008) Deep brain stimulation for epilepsy. Neurotherapeutics 5(1):59–67

    Article  PubMed Central  PubMed  Google Scholar 

  • Han CX, Wang J, Yi GS et al (2013) Investigation of EEG abnormalities in the early stage of Parkinson’s disease. Cogn Neurodyn 7(4):351–359

    Article  PubMed Central  PubMed  Google Scholar 

  • Hodaie M, Wennberg RA, Dostrovsky JO et al (2002) Chronic anterior thalamus stimulation for intractable epilepsy. Epilepsia 43(6):603–608

    Article  PubMed  Google Scholar 

  • Iasemidis LD, Sabesan S, Chakravarthy N et al (2009) Brain dynamics and modeling in epilepsy: prediction and control studies. In: Dana SK, Roy PK, Kurths J (eds) Complex dynamics of physiological systems: from heart to brain, part IV. Springer Science + Business Media B.V., Berlin, pp 185–214

    Chapter  Google Scholar 

  • Jansen BH, Zouridakis G, Brandt ME (1993) A neurophysiologically-based mathematical model of flash visual evoked potentials. Biol Cybern 68(3):275–283

    Article  CAS  PubMed  Google Scholar 

  • Jobst BC, Darcey TM, Thadani VM et al (2010) Brain stimulation for the treatment of epilepsy. Epilepsia 51(s3):88–92

    Article  PubMed  Google Scholar 

  • Julier S, Uhlmann J, Durrant-Whyte HF (2000) A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans Autom Control 45(3):477–482

    Article  Google Scholar 

  • Kerrigan JF, Litt B, Fisher RS et al (2004) Electrical stimulation of the anterior nucleus of the thalamus for the treatment of intractable epilepsy. Epilepsia 45(4):346–354

    Article  PubMed  Google Scholar 

  • Kiebel SJ, Garrido MI, Moran RJ et al (2008) Dynamic causal modelling for EEG and MEG. Cogn Neurodyn 2(2):121–136

    Article  PubMed Central  PubMed  Google Scholar 

  • Li Z, O’Doherty JE, Hanson TL et al (2009) Unscented Kalman filter for brain-machine interfaces. PLoS One 4(7):e6243

    Article  PubMed Central  PubMed  Google Scholar 

  • Little S, Brown P (2012) What brain signals are suitable for feedback control of deep brain stimulation in Parkinson’s disease? Ann N Y Acad Sci 1265(1):9–24

    Article  PubMed Central  PubMed  Google Scholar 

  • Liu X, Gao Q (2013) Parameter estimation and control for a neural mass model based on the unscented Kalman filter. Phys Rev E 88(4):042905

    Article  Google Scholar 

  • Lopes da Silva FH, Hoeks A, Smits H et al (1974) Model of brain rhythmic activity. Kybernetik 15(1):27–37

    Article  CAS  PubMed  Google Scholar 

  • Lopes da Silva FH, Van Rotterdam A, Barts P et al (1976) Models of neuronal populations: the basic mechanisms of rhythmicity. Prog Brain Res 45:281–308

    Article  CAS  PubMed  Google Scholar 

  • Ma Y, Wang Z, Zhao X et al (2010) A UKF algorithm based on the singular value decomposition of state covariance. In: Proceedings of the 8th World congress on intelligent control and automation, IEEE, Jinan, China, pp 5830–5835

  • Moore KL (2001) An observation about monotonic convergence in discrete-time, P-type iterative learning control. In: Proceedings of the 2001 IEEE international symposium on l, IEEE, Mexico, USA, pp 45–49

  • Moore KL, Dahleh M, Bhattacharyya SP (1992) Iterative learning control: a survey and new results. J Robot Syst 9(5):563–594

    Article  Google Scholar 

  • Morrell MJ (2011) Responsive cortical stimulation for the treatment of medically intractable partial epilepsy. Neurology 77(13):1295–1304

    Article  PubMed  Google Scholar 

  • Nevado-Holgado AJ, Marten F, Richardson MP et al (2012) Characterising the dynamics of EEG waveforms as the path through parameter space of a neural mass model: application to epilepsy seizure evolution. Neuroimage 59(3):2374–2392

    Article  PubMed  Google Scholar 

  • Nguyen DP, Wilson MA, Brown EN et al (2009) Measuring instantaneous frequency of local field potential oscillations using the Kalman smoother. J Neurosci Methods 184(2):365–374

    Article  PubMed Central  PubMed  Google Scholar 

  • Rummel C, Abela E, Hauf M et al (2013) Ordinal patterns in epileptic brains: analysis of intracranial EEG and simultaneous EEG-fMRI. Eur Phys J Spec Top 222(2):569–585

    Article  Google Scholar 

  • Saab SS (1994) On the P-type learning control. IEEE Trans Autom Control 39(11):2298–2302

    Article  Google Scholar 

  • Santaniello S, Fiengo G, Glielmo L et al (2011) Closed-loop control of deep brain stimulation: a simulation study. IEEE Trans Neural Syst Rehabil Eng 19(1):15–24

    Article  PubMed  Google Scholar 

  • Schiff SJ (2012) Neural control engineering: the emerging intersection between control theory and neuroscience. MIT Press, Cambrige

    Google Scholar 

  • Schiff SJ, Sauer T (2008) Kalman filter control of a model of spatiotemporal cortical dynamics. BMC Neurosci 9(Suppl 1):O1

    Article  Google Scholar 

  • Schütt M, Claussen JC (2012) Desynchronizing effect of high-frequency stimulation in a generic cortical network model. Cogn Neurodyn 6(4):343–351

    Article  PubMed Central  PubMed  Google Scholar 

  • Tan Y, Dai HH, Huang D et al (2012) Unified iterative learning control schemes for nonlinear dynamic systems with nonlinear input uncertainties. Automatica 48(12):3173–3182

    Article  Google Scholar 

  • Touboul J, Wendling F, Chauvel P et al (2011) Neural mass activity, bifurcations, and epilepsy. Neural Comput 23(12):3232–3286

    Article  PubMed  Google Scholar 

  • Ullah G, Schiff SJ (2009) Tracking and control of neuronal Hodgkin–Huxley dynamics. Phys Rev E 79(4):040901

    Article  Google Scholar 

  • Ullah G, Schiff SJ (2010) Assimilating seizure dynamics. PLoS Comput Biol 6(5):e1000776

    Article  PubMed Central  PubMed  Google Scholar 

  • Van Rotterdam A, Lopes da Silva FH, Van den Ende J et al (1982) A model of the spatial–temporal characteristics of the alpha rhythm. Bull Math Biol 44(2):283–305

    Article  PubMed  Google Scholar 

  • Voss HU, Timmer J, Kurths J (2004) Nonlinear dynamical system identification from uncertain and indirect measurements. Int J Bifurc Chaos 14(06):1905–1933

    Article  Google Scholar 

  • Wang C, Zou J, Zhang J et al (2010) Feature extraction and recognition of epileptiform activity in EEG by combining PCA with ApEn. Cogn Neurodyn 4(3):233–240

    Article  PubMed Central  PubMed  Google Scholar 

  • Wendling F, Bellanger JJ, Bartolomei F et al (2000) Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals. Biol Cybern 83(4):367–378

    Article  CAS  PubMed  Google Scholar 

  • Wendling F, Bartolomei F, Bellanger JJ et al (2002) Epileptic fast activity can be explained by a model of impaired GABAergic dendritic inhibition. Eur J Neurosci 15(9):1499–1508

    Article  CAS  PubMed  Google Scholar 

  • Xiong K, Zhang HY, Chan CW (2006) Performance evaluation of UKF-based nonlinear filtering. Automatica 42(2):261–270

    Article  Google Scholar 

Download references

Acknowledgments

This work is supported by National Natural Science Foundation of China (Grant Nos. 61374182 and 61172009).

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Correspondence to Bin Deng.

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Shan, B., Wang, J., Deng, B. et al. UKF-based closed loop iterative learning control of epileptiform wave in a neural mass model. Cogn Neurodyn 9, 31–40 (2015). https://doi.org/10.1007/s11571-014-9306-0

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  • DOI: https://doi.org/10.1007/s11571-014-9306-0

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