Belirsiz beyin korteks modelinin durum ve parametre kestirimi

Yıl 2018, Cilt: 24 Sayı: 8, 1425 - 1434, 29.12.2018

Meriç Çetin , Selami Beyhan

Öz

Beyin korteksinin yaklaşık modeli, günümüzde başta
epilepsi, Parkinson gibi hastalıklar olmak üzere birçok hastalığın tedavisinde
kullanılmaktadır. Korteks matematiksel modeli kesin olduğu kabul edilmektedir.
Fakat zamanla değişen parametreler, gürültü ve diğer bozucu etkilerden dolayı
bu model her zaman geçerli değildir. Ayrıca bazı durumların ölçülmesi zor ve
pahalı olmasından dolayı yazılım temelli yapılması hedeflenmiştir. Dolayısıyla,
bu çalışmada, belirsizlik içeren beyin korteks modelinin durum ve parametre
kestirimi farklı karakteristiklere sahip doğrusal-olmayan gözetleyiciler ile
beraber yapılmaktadır. Sadece durum kestirimi [1] çalışmasında yapılmıştır.
Doğrusal-olmayan gözetleyici genişletilmiş Kalman filtre (EKF), kayan kip
gözetleyici (SMO) ve ayrıklaştırma temelli gradyan gözetleyici (DBGO)
yaklaşımları tasarlanmıştır. Ölçülemeyen durum ve belirsizlik parametresi
kestirimleri normal çalışma ve epileptik durumları için yapılmaktadır. Çünkü
korteks model doğrusal-olmayan dinamiklere sahiptir fakat epilepsi esnasında
kaotik bir davranışa sahiptir. Bu yüzden önce normal durum çalışma sonra nöbet
durumu için tahminler yapılmaktadır. Sayısal benzetimlerde tasarlanan
gözetleyicilerin başarılı şekilde ölçülemeyen durum ve parametre tahminlerini
yaptığı gözlenmiştir. Tahmin sonuçları ve tahmin başarım performansları
tasarlanan gözetleyicileri gürültülü ve gürültüsüz durumlarda karşılaştırmak
için verilmiştir.

Anahtar Kelimeler

Korteks model, Doğrusal-olmayan gözetleyici, Durum ve parametre kestirimi, EKF, SMO, DBGO

State and parameter estimation of uncertain brain cortex model

Öz

Nowadays, an approximate mathematical model of the
brain cortex has been used for the treatment of the first epilepsy and
Parkinson, and several diseases. It is assumed that the mathematical model of
the cortex is an exact model. However, due to the time-varying parameters,
noise and other disturbances, this model is not always valid. Moreover, since
it is difficult and expensive to measure some states, software based solution
is aimed here.  Consequently, in this
paper, state and parameter estimation of the brain cortex model are jointly
achieved using nonlinear observers of different characteristics. The state
estimation of the model was merely performed in [1]. As the nonlinear
observers, extended-Kalman filter (EKF), sliding-mode observer (SMO) and
discretization based gradient observer (DBGO) approaches are designed. The
estimation of unmeasurable states and parameters are performed both for the
epileptic and normal state of the mathematical model since the cortex model has
normally nonlinear dynamics but it exhibits chaotic behavior in epileptic
state. Therefore, the estimations are provided for first normal state, then
epileptic state. In computational results, it is observed that the designed
nonlinear observers resulted successful estimations for unmearuable states and
parameters. The estimation results and estimation performances are given to compare
the nonlinear observers for noisy and noiseless cases.

Anahtar Kelimeler

Cortex model, Nonlinear observer, State and parameter estimation, EKF, SMO, DBGO

Kaynakça

• Çetin M, Beyhan S. "Gözetleyici Temelli Beyin Korteks Model Durum Tahmini". Otomatik Kontrol Türk Milli Komitesi, İstanbul, Türkiye, 21-23 Eylül 2017.
• Traub, RD, Contreras D, Cunningham MO, Murray H, LeBeau FE, Roopun A, Whittington MA. “Single-column thalamocortical network model exhibiting gamma oscillations, sleep spindles, and epileptogenic bursts”. Journal of Neurophysiology, 93(4), 2194-2232, 2005.
• Kramer MA, Szeri AL, Sleigh JW, Kirsch HE. “Mechanisms of seizure propagation in a cortical model”. Journal of Computational Neuroscience, 22(1), 63–80, 2007.
• Giridharan RS, Cheung CC, Rubchinsky LL. “Effects of electrical and optogenetic deep brain stimulation on synchronized oscillatory activity in parkinsonian basal ganglia”. IEEE Transactions on Neural Systems and Rahabilitation Engineering, 25(11), 2188-2195, 2017.
• Tsakalis K, Chakravarthy N, Sabesan S, Iasemidis LD, Pardalos PM. “A feedback control systems view of epileptic seizures”. Cybernetics and Systems Analysis, 42(4), 483-495, 2006.
• Chakravarthy N, Tsakalis K, Sabesan S, Iasemidis L. “Homeostasis of brain dynamics in epilepsy: A feedback control systems perspective of seizures”. Annals of Biomedical Engineering, 37(3), 565-585, 2009.
• Lopour B, Szeri AJ. “A model of feedback control for the charge-balanced suppression of epileptic seizures”. Journal of Computational Neuroscience, 28(3), 375-387, 2010.
• Mirzaei A, Ozgoli S, Jajarm AE. “Chaotic analysis of the human brain cortical model and robust control of epileptic seizures using sliding mode control”. Systems Science & Control Engineering, 2(1), 216–227, 2014.
• Selvaraj P, Sleigh JW, Kirsch HE, Szeri AJ. “Closed-loop feedback control and bifurcation analysis of epileptiform activity via optogenetic stimulation in a mathematical model of human cortex”. Physical Review E, 93(1), 012416, 2016.
• Wang J, Niebur E, Hu J, Li X. “Suppressing epileptic activity in a neural mass model using a closed-loop proportional-integral controller”. Scientific Reports, 6, 2016.
• Lopez-Cuevas A, Castillo-Toledo B, Medina-Ceja L, Ventura-Mejia C. “State and parameter estimation of a neural mass model from electrophysiological signals during the status epilepticus”. NeuroImage, 113, 374-386, 2015.
• Escuain-Poole L, Garcia-Ojalvo J, Pons AJ. “Extracranial estimation of neural mass model parameters using the unscented Kalman filter”. arXiv: 1708.05282, 2017.
• Simani S, Fantuzzi C, Patton RJ. “Model-based fault diagnosis techniques”. Model-based Fault Diagnosis in Dynamic Systems Using Identification Techniques, 19-60, 2003.
• Luenberger D. “Observers for multivariable systems”. IEEE Transactions on Automatic Control, 11(2), 190-197, 1966.
• Thau EE. “Observing the state of nonlinear systems”. International Journal of Control, 17, 471-479, 1973.
• Birk J, Zeitz M. “Extended-Luenberger observer for non-linear multivariable systems”. International Journal of Control, 47(6), 1823-1836, 1988.
• Cox H. “On the estimation of state variables and parameters for noisy dynamic systems”. IEEE Transactions on Automatic Control, 9(1), 5-12, 1964.
• Drakunov SV. “An adaptive quasioptimal filter with discontinuous parameters”. Automatic Remote Control, 44(9), 1167-1175, 1983.
• Slotine JJ, Hedrick JK, Misawa EA. “On sliding observers for nonlinear systems”. Journal of Dynamic Systems, Measurement and Control, 109, 245-252, 1987.
• Gauthier JP, Hammouri H, Othman S. “A simple observer for nonlinear systems applications to bioreactors”. IEEE Transactions on Automatic Control, 37(6), 875–880, 1992.
• İplikci S. “Runge-Kutta model-based adaptive predictive control mechanism for non-linear processes”. Transactions of the Institute of Measurement and Control, 35(2), 166–180, 2013.
• Beyhan S. “Runge-Kutta model-based nonlinear observer for synchronization and control of chaotic systems”. ISA Transactions, 52(4), 501–509, 2013.
• Cetin M, Beyhan S, İplikci S. “Soft sensor applications of RK-based nonlinear observers and experimental comparisons”. Intelligent Automation & Soft Computing, 23(1), 109–116, 2017.
• Simon D. Optimal State Estimation: Kalman, H-Infinity, and Nonlinear Approaches, John Wiley & Sons, 2006.
• Kalman RE. “A new approach to linear filtering and prediction problems”. Journal of Basic Engineering, 82(1), 35–45, 1960.
• Çetin M, Beyhan S. "Adaptive Stabilization of Uncertain Cortex Dynamics under Joint Estimates and Input Constraints”, IEEE Transactions on Circuits and Systems II: Express Briefs, doi: 10.1109/TCSII.2018.2855450, 2018.
• Spurgeon SK. “Sliding mode observers: a survey”. International Journal of Systems Science, 39(8), 751-764, 2008.
• Al-Hosani K, Utkin VI. “Parameters estimation using sliding mode observer with shift operator”. Journal of the Franklin Institute, 349(4), 1509–1525, 2012.
• Nunez PL, Srinivasan R. “Electric fields of the brain: the neurophysics of EEG”. Oxford University Press, USA, 2006.
• Wilson HR, Cowan JD. “A mathematical theory of the functional dynamics of cortical and thalamic nervous tissue”. Kybernetik, 13(2), 55-80,1973.
• Freeman WJ. “Mass action in the nervous system”, 1975.
• Yao Y, Freeman WJ. “Model of biological pattern recognition with spatially chaotic Dynamics”. Neural networks, 3(2), 153-170, 1990.
• Jirsa VK, Haken H. “Field theory of electromagnetic brain activity”. Physical Review Letters, 77(5), 960, 1996.
• Robinson PA, Rennie CJ, Wright JJ. “Propagation and stability of waves of electrical activity in the cerebral cortex”. Physical Review E, 56(1), 826, 1997.
• Liley DT, Cadusch PJ, Wright JJ. “A continuum theory of electro-cortical activity”. Neurocomputing, 26, 795–800, 1999.