nach oben

Neuroinformatics

Erschienen in:

18.03.2022 | Original Article

Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression

verfasst von: João Angelo Ferres Brogin, Jean Faber, Douglas D. Bueno

Erschienen in: Neuroinformatics | Ausgabe 4/2022

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

Epilepsy is one of the most common brain disorders worldwide, affecting millions of people every year. Given the partially successful existing treatments for epileptiform activity suppression, dynamic mathematical models have been proposed with the purpose of better understanding the factors that might trigger an epileptic seizure and how to mitigate it, among which Epileptor stands out, due to its relative simplicity and consistency with experimental observations. Recent studies using this model have provided evidence that establishing a feedback-based control approach is possible. However, for this strategy to work properly, Epileptor’s parameters, which describe the dynamic characteristics of a seizure, must be known beforehand. Therefore, this work proposes a methodology for estimating such parameters based on a successive optimization technique. The results show that it is feasible to approximate their values as they converge to reference values based on different initial conditions, which are modeled by an uncertainty factor or noise addition. Also, interictal (healthy) and ictal (ongoing seizure) conditions, as well as time resolution, must be taken into account for an appropriate estimation. At last, integrating such a parameter estimation approach with observers and controllers for purposes of seizure suppression is carried out, which might provide an interesting alternative for seizure suppression in practice in the future.

Vorheriger Artikel Real-time and Recursive Estimators for Functional MRI Quality Assessment

Nächster Artikel How Machine Learning is Powering Neuroimaging to Improve Brain Health

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Nur mit Berechtigung zugänglich

See, for instance, references Hodgkin and Huxley (1952); FitzHugh (1961); Morris and Lecar (1981); Hindmarsh and Rose (1984); Izhikevich (2003); Grimbert and Faugeras (2006); Jirsa et al. (2014); Chizhov et al. (2018).

In the context of system identification, this process is known as parameter estimation, which implies finding the parameters of a model that best describe the existing data Ljung (1998); Van den Bos (2007).

An interesting investigation on this topic is provided by Luersen and Le Riche (2004).

As stated by Ref. Luersen and Le Riche (2004), the number of analyses (in this case, optimizations) in real situations is usually restricted. Naturally, we take this fact into account by using a limited number of iterations and threshold, since computational applications are sometimes time-consuming and require a high processing. However, as seen in the next sections, our approach provides a good strategy for estimating the parameters of the system with a strong practical appeal.

This formulation, although applied to the notation developed in this work, is consistent with Gao and Han (2012).

A detailed formulation on how to obtain such an equivalence can be found in Tanaka and Wang (2004); Brogin et al. (2020, 2021) and Appendix A.

In practice, once the model and nonlinear functions are available, they are measured for a specific time interval of interest, so the model is exactly reconstructed for this period of time. Further details can be found in Brogin et al. (2020).

Further details about how to obtain these MFs can be found in Appendix A.

All the steps and derivatives for this formulation have been addressed elsewhere. For a detailed analysis, refer to Brogin et al. (2021).

Although II is considered as the best region for \(I_{\text{rest2}}\), note that there is not a clear visual distinction between II and IC, in terms of estimation.

The effect of progressive degradation caused by noise is commonly found in applications envolving brain signals, in which the source can be from eye movements, muscle artifacts or the environment, for example Agarwal et al. (2017); Hussein et al. (2018).

Abuhasel, K. A., Iliyasu, A. M., & Fatichah, C. (2015). A hybrid particle swarm optimization and neural network with fuzzy membership function technique for epileptic seizure classification. Journal of Advanced Computational Intelligence and Intelligent Informatics, 19(3), 447–455.CrossRef

Agarwal, S., Rani, A., Singh, V., & Mittal, A. P. (2017). EEG signal enhancement using cascaded S-Golay filter. Biomedical Signal Processing and Control, 36, 194–204.CrossRef

Altan, A. (2020). Performance of metaheuristic optimization algorithms based on swarm intelligence in attitude and altitude control of unmanned aerial vehicle for path following. In: 4th International Symposium on Multidisciplinary Studies and Innovative Technologies (ISMSIT) (pp. 1–6.) IEEE

Altan, A & Parlak, A. (2020). Adaptive control of a 3D printer using whale optimization algorithm for bio-printing of artificial tissues and organs. In: Innovations in Intelligent Systems and Applications Conference (ASYU) (pp. pp. 1–5). IEEE.

Boyd, S., El Ghaoui, L., & Feron, E. (1994). & Balakrishnan (Vol. Linear). SIAM-Philadelphia, Pennsylvania: Matrix Inequalities in System and Control Theory.

Brogin, J. A. F., Faber, J., & Bueno, D. D. (2020). An efficient approach to define the input stimuli to suppress epileptic seizures described by the epileptor model. Journal of Neural Systems, 2050062.

Brogin, J. A. F., Faber, J., & Bueno, D. D. (2021). Burster reconstruction considering unmeasurable variables in the Epileptor model. Neural Computation, 33(12), 3288–3333.PubMedCrossRef

Browne, T. R., & Holmes, G. L. (2008). Handbook of epilepsy. Pennsylvania: Lippincott Williams & Wilkins-Philadelphia.

Chen, X., Liu, A., Chiang, J., Wang, Z. J., McKeown, M. J., & Ward, R. K. (2015). Removing muscle artifacts from EEG data: Multichannel or single-channel techniques? IEEE Sensors Journal, 16(7), 1986–1997.CrossRef

Chizhov, A. V., Zefirov, A. V., Amakhin, D. V., Smirnova, E. Y., & Zaitsev, A. V. (2018). Minimal model of interictal and ictal discharges epileptor-2. PLOS Computational Biology, 14(5), 1–25.CrossRef

Cota, V. R., de Castro Medeiros, D., da Páscoa Vilela, M. R. S., Doretto, M. C., & Moraes, M. F. D. (2009). Distinct patterns of electrical stimulation of the basolateral amygdala influence pentylenetetrazole seizure outcome. Epilepsy & Behavior, 14(1), 26–31.CrossRef

D’Andrea Meira, I., Romão, T. T., Pires do Prado, H. J., Krüger, L. T., Pires, M. E. P. & da Conceição, P. O. (2019). Ketogenic diet and epilepsy: what we know so far. Frontiers in Neuroscience-Switz, 13, 5.

Dollfuss, P., Hartmann, M. M., Skupch, A., Frbass, F., & Kluge, T. (2013). Automatic optimization of parameters for seizure detection systems. In: 5th Annual International Conference of the IEEE Engineering in Medicine and Biology Society (EMBC) (pp. 1976–1979). IEE,.

El Houssaini, K., Ivanov, A. I., Bernard, C., & Jirsa, V. K. (2015). Seizures, refractory status epilepticus, and depolarization block as endogenous brain activities. Physical Review E, 91, 010701.

Fisher, R. S., & Schachter, S. C. (2000). The postictal state: a neglected entity in the management of epilepsy. Epilepsy & Behavior, 1(1), 52–59.CrossRef

FitzHugh, R. (1961). Impulses and physiological states in theoretical models of nerve membrane. Biophysical Journal, 1(6), 445–466.PubMedPubMedCentralCrossRef

Gao, F., & Han, L. (2012). Implementing the Nelder-Mead simplex algorithm with adaptive parameters. Computational Optimization and Applications, 51(1), 259–277.CrossRef

Grimbert, F., & Faugeras, O. (2006). Bifurcation analysis of Jansen’s neural mass model. Neural Computation, 18(12), 3052–3068.PubMedCrossRef

Hamad, A., Houssein, E. H., Hassanien, A. E., & Fahmy, A. A. (2018). Hybrid grasshopper optimization algorithm and support vector machines for automatic seizure detection in EEG signals. In: International conference on advanced machine learning technologies and applications (pp. 82–91). Springer, Cham

Hardt, M., Schraknepper, D., & Bergs, T. (2021). Investigations on the application of the downhill-simplex-algorithm to the inverse determination of material model parameters for FE-machining simulations. Simulation Modelling Practice and Theory, 107, 102214.

Hashemi, M., Vattikonda, A. N., Sip, V., Guye, M., Bartolomei, F., Woodman, M. M., & Jirsa, V. K. (2020). The Bayesian Virtual Epileptic Patient: A probabilistic framework designed to infer the spatial map of epileptogenicity in a personalized large-scale brain model of epilepsy spread. NeuroImage, 217, 116839.

Hawkins, D. M. (2004). The problem of overfitting. Journal of chemical information and computer sciences, 44(1), 1–12.PubMedCrossRef

Hindmarsh, J. L., & Rose, R. M. (1984). A model of neuronal bursting using three coupled first order differential equations. Proceedings of the Royal Society B: Biological Sciences, 221(1222), 87–102.

Hodgkin, A. L. & Huxley, A. F. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. The Journal of Physiology London, 117(4), 500–544.

Hussein, R., Elgendi, M., Wang, Z. J., & Ward, R. K. (2018). Robust detection of epileptic seizures based on L1-penalized robust regression of EEG signals. Expert Systems with Applications, 104, 153–167.CrossRef

Iasemidis, L. D. (2003). Epileptic seizure prediction and control. IEEE Transactions on Biomedical Engineering, 50(5), 549–558.PubMedCrossRef

Ichalal, D., Arioui, H. & Mammar, S. (2011). Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables. In: 2011 19th Mediterranean Conference on Control & Automation (MED) (pp. 934–939). IEEE.

Islam, M. K., Rastegarnia, A., & Yang, Z. (2015). A wavelet-based artifact reduction from scalp EEG for epileptic seizure detection. IEEE Journal of Biomedical and Health Informatics, 20(5), 1321–1332.PubMedCrossRef

Izhikevich, E. M. (2003). Simple model of spiking neurons. IEEE Transactions on Neural Networks and Learning Systems, 14(6), 1569–1572.CrossRef

Jirsa, V. K., Proix, T., Perdikis, D., Woodman, M. M., Wang, H., Gonzalez-Martinez, J., et al. (2017). The virtual epileptic patient: individualized whole-brain models of epilepsy spread. NeuroImage, 145, 377–388.PubMedCrossRef

Jirsa, V. K., Stacey, W. C., Quilichini, P. P., Ivanov, A. I., & Bernard, C. (2014). On the nature of seizure dynamics. Brain, 137(8), 2210–2230.PubMedPubMedCentralCrossRef

Luersen, M. A., & Le Riche, R. (2004). Globalized Nelder-Mead method for engineering optimization. Computers & Structures, 82(23–26), 2251–2260.CrossRef

Kim, H., Bernhardt, B. C., Kulaga-Yoskovitz, J., Caldairou, B., Bernasconi, A., & Bernasconi, N. (2014). Multivariate hippocampal subfield analysis of local MRI intensity and volume: application to temporal lobe epilepsy. In: International Conference on Medical Image Computing and Computer-Assisted Intervention (pp. 170–178). Springer, Cham.

Li, Y., Wang, X. D., Luo, M. L., Li, K., Yang, X. F., & Guo, Q. (2017). Epileptic seizure classification of EEGs using time-frequency analysis based multiscale radial basis functions. IEEE Journal of Biomedical and Health Informatics, 22(2), 386–397.PubMedCrossRef

Liu, W., & Lin, W. (2006). Additive white Gaussian noise level estimation in SVD domain for images. IEEE Transactions on Image Processing., 22(3), 872–883.CrossRef

Ljung, L. (1998). System identification: theory for the user. New Jersey: Prentice Hall.

Lofberg, J. (2011). YALMIP: A toolbox for modeling and optimization in MATLAB. In: 2004 IEEE international conference on robotics and automation (pp. 284–289). IEEE.

Morris, C., & Lecar, H. (1981). Voltage oscillations in the barnacle giant muscle fiber. Biophysical Journal, 35(1), 193–213.PubMedPubMedCentralCrossRef

Nagaraj, V., Lamperski, A. & Netoff, T. I. (2017). Seizure control in a computational model using a reinforcement learning stimulation paradigm. International Journal of Neural Systems, 27(07).

Nelder, J. A., & Mead, R. (1965). A simplex method for function minimization. The Computer Journal, 7(4), 308–313.CrossRef

Neto L. A., Erasme D., Genay N, Chanclou P., Deniel Q., Traore F., Anfray T., Hmadou R. & Aupetit-Berthelemot C. (2012). Simple estimation of fiber dispersion and laser chirp parameters using the downhill simplex fitting algorithm. Journal of Lightwave Technology, 31(2), 334–342.

Pinheiro, D. J., Oliveira, L. F., Souza, I. N., Brogin, J. A. F., Bueno, D. D., Miranda, I. A., et al. (2020). Modulation in phase and frequency of neural oscillations during epileptiform activity induced by neonatal Zika virus infection in mice. Scientific Reports, 10(1), 1–14.CrossRef

Poli, R., Kennedy, J., & Blackwell, T. (2007). Particle swarm optimization. Swarm Intelligence, 1(1), 33–57.CrossRef

Powell, T. D. (2002). Automated tuning of an extended Kalman filter using the downhill simplex algorithm. Journal of Guidance, Control, and Dynamics, 25(5), 901–908.CrossRef

Proix, T., Bartolomei, F., Guye, M., & Jirsa, V. K. (2017). Individual brain structure and modeling predict seizure propagation. Brain, 140(3), 641–654.PubMedPubMedCentralCrossRef

Proix, T., Bartolomei, F., Chauvel, P., Bernard, C., & Jirsa, V. K. (2014). Permittivity coupling across brain regions determines seizure recruitment in partial epilepsy. Journal of Neuroscience, 34(45), 15009–15021.PubMedCrossRef

Proix, T., Jirsa, V. K., Bartolomei, F., Guye, M., & Truccolo, W. (2018). Predicting the spatiotemporal diversity of seizure propagation and termination in human focal epilepsy. Nature Communications, 9(1), 1–15.CrossRef

Saggio, M. L., Crisp, D., Scott, J. M., Karoly, P., Kuhlmann, L., Nakatani, M., Murai, T., Dmpelmann, M., Schulze-Bonhage, A., Ikeda, A., Cook, M., Gliske, S. V., Lin, J., Bernard, C., Jirsa, V. & Stacey, W. C. (2020). A taxonomy of seizure dynamotypes. Elife, 9, e55632.

Sip, V., Guye, M., Bartolomei, F., & Jirsa, V. (2021). Computational modeling of seizure spread on a cortical surface. Journal of Computational Neuroscience, 1–15.

Subasi, A., Kevric, J., & Canbaz, M. (2019). Epileptic seizure detection using hybrid machine learning methods. Neural Computing and Applications, 31(1), 317–325.CrossRef

Ogata, K. (2010). Modern control engineering. Prentice Hall.

Oppenheim, A. V., Willsky, A. S., & Nawab, H. (1997). S. Prentice Hall-New Jersey: Signals and Systems.

Reyhanoglu, M., van der Schaft, A., McClamroch, N. H., & Kolmanovsky, I. (1999). Dynamics and control of a class of underactuated mechanical systems. IEEE Transactions on Automatic Control, 44(9), 1663–1671.CrossRef

Rizzone, M., Lanotte, M., Bergamasco, B., Tavella, A., Torre, E., Faccani, G., et al. (2001). Deep brain stimulation of the subthalamic nucleus in Parkinson’s disease: effects of variation in stimulation parameters. Journal of Neurology, Neurosurgery & Psychiatry, 71(2), 215–219.CrossRef

Sagnol, G. (2012). Picos documentation. A Python interface to conic optimization solvers.

Slotine, J. J. E. (1991). & Li. Prentice hall-Englewood Cliffs, New Jersey: W. Applied Nonlinear Control.

Spong, M. W. (1998). Underactuated mechanical systems. In Control problems in robotics and automation (pp. 135-150). Springer, Berlin, Heidelberg.

Soong, T. T. (2004). Fundamentals of probability and statistics for engineers. John Wiley & Sons.

Tanaka, K., & Wang, H. O. (2004). Fuzzy control systems design and analysis: a linear matrix inequality approach. New York: Wiley-New York.

Taniguchi, T., Tanaka, K., Ohtake, H., & Wang, H. O. (2001). Model construction, rule reduction, and robust compensation for generalized form of Takagi-Sugeno fuzzy systems. IEEE Transactions on Fuzzy Systems, 9(4), 525–538.CrossRef

Tellez-Zenteno, J. F., McLachlan, R. S., Parrent, A., Kubu, C. S., & Wiebe, S. (2006). Hippocampal electrical stimulation in mesial temporal lobe epilepsy. Neurology, 66(10), 1490–1494.PubMedCrossRef

Van den Bos, A. (2007). Parameter estimation for scientists and engineers. New Jersey: John Wiley & Sons.

Velasco, F., Velasco, M., Velasco, A. L., Menez, D., & Rocha, L. (2001). Electrical stimulation for epilepsy: stimulation of hippocampal foci. Stereotactic & Functional Neurosurgery, 77(1–4), 223–227.CrossRef

Velasco, A. L., Velasco, F., Velasco, M., Trejo, D., Castro, G., & Carrillo-Ruiz, J. D. (2007). Electrical stimulation of the hippocampal epileptic foci for seizure control: a double-blind, long-term follow-up study. Epilepsia, 48(10), 1895–1903.PubMedCrossRef

Vezzani, A., French, J., Bartfai, T., & Baram, T. Z. (2011). The role of inflammation in epilepsy. Nature Reviews Neurology, 7(1), 31.PubMedCrossRef

Walker, J. E., & Kozlowski, G. P. (2005). Neurofeedback treatment of epilepsy. Child and Adolescent Psychiatric Clinics, 14(1), 163–176.CrossRef

Wendling, F., Benquet, P., Bartolomei, F., & Jirsa, V. (2015). Computational models of epileptiform activity. Journal of Neuroscience Methods, 260, 233–251.PubMedCrossRef

Zhang, H., & Xiao, P. (2018). Seizure dynamics of coupled oscillators with epileptor field model. International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 28(03), 1850041.

Zhu, D., Bieger, J., Molina, G. G. & Aarts, R. M. (2010). A survey of stimulation methods used in SSVEP-based BCIs, Computational Intelligence and Neuroscience, 1–13.

Titel: Estimating the Parameters of the Epileptor Model for Epileptic Seizure Suppression
verfasst von: João Angelo Ferres Brogin
Jean Faber
Douglas D. Bueno
Publikationsdatum: 18.03.2022
Verlag: Springer US
Erschienen in: Neuroinformatics / Ausgabe 4/2022
Print ISSN: 1539-2791
Elektronische ISSN: 1559-0089
DOI: https://doi.org/10.1007/s12021-022-09583-6

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Technik"

Springer Professional "Wirtschaft"

Weitere Artikel der Ausgabe 4/2022

Three-Dimensional Spatial Analyses of Cholinergic Neuronal Distributions Across The Mouse Septum, Nucleus Basalis, Globus Pallidus, Nucleus Accumbens, and Caudate-Putamen

How Machine Learning is Powering Neuroimaging to Improve Brain Health

Fast Streamline Search: An Exact Technique for Diffusion MRI Tractography

Cortical Representation of Touch in Silico

A Computational Neural Model for Mapping Degenerate Neural Architectures

RS-FetMRI: a MATLAB-SPM Based Tool for Pre-processing Fetal Resting-State fMRI Data

Premium Partner