EEG Signal Processing and Machine Learning. Saeid Sanei
examples of these models are as follows. The electronic neuron model developed by [62] is realized with integrated circuit technology. The circuit includes one neuron with eight synapses. The chip area of the integrated circuit is 4.5 × 5 mm2. The array contains about 200 NPN and 100 PNP transistors, and about 200 of them are used. In 1991, Mahowald and Douglas [63] published an integrated circuit realization of electronic neuron model. The model was realized with complementary metal oxide semiconductor (CMOS) circuits using very large‐scale integrated (VLSI) technology. Their model accurately simulates the spikes of a neocortical neuron. The power dissipation of the circuit is 60 μW, and it occupies less than 0.1 mm2. It is estimated that 100–200 such neurons could be fabricated on a 1 cm × 1 cm die.
3.6 Dynamic Modelling of Neuron Action Potential Threshold
Neuron threshold is the transmembrane voltage level at which any further depolarization will activate a sufficient number of sodium channels to enter a self‐generative positive feedback phase [64]. This threshold is often considered constant. Any alteration to the threshold influences the neuron spike train temporal transformation. There are however evidences that the threshold is nonlinearly affected by the AP firing history [65–67]. In [64] a method for dynamically varying the threshold for intercellular activity has been proposed. The method is suitable for systems with spikes in both their inputs and outputs.
3.7 Summary
Most of the models generated mathematically are very primitive representations of EEG generators. More complicated models will be necessary to represent the brain EPs and the abnormal EEGs recorded under various brain diseases and disorders. The model based on phase coupling explained here introduces the WCOs which can be used to model the interactions between the neurons. Hodgkin and Huxley model conversely provides a detailed and accurate model for generation of active potentials. Linear and nonlinear prediction filers can be used in modelling the neuro generators. Gaussian mixtures are capable in modelling the EEG particularly event‐related, evoked, and movement‐related potentials. Finally, circuit models have been introduced to combine the excitatory and inhibitory post‐synaptic potentials for generation of an EEG signal. The synaptic currents have also been modelled using electronic circuits. These circuits can be expanded to have very accurate model of either a single neuron or a membrane. They can also be used to model a large number of neurons for generation of particular brain waveforms. The electronic models have potential to be used in brain morphing technology.
References
1 1 van Vreeswijk, C., Abbott, L.F., and Ermentrout, G.B. (1994). When inhibition not excitation synchronizes neural firing. Journal of Computational Neuroscience 1: 313–321.
2 2 Penny, W.D., Litvak, V., Fuentemilla, L. et al. (2009). Dynamic causal models for phase coupling. Journal of Neuroscience Methods 183 (1): 19–30.
3 3 Ward, L. (2003). Synchronous neural oscillations and cognitive processes. Trends in Cognitive Sciences 7 (12): 553–559.
4 4 von Stein, A., Rappelsberger, P., Sarnthein, J., and Petsche, H. (1999). Synchronization between temporal and parietal cortex during multimodal object processing in man. Cerebral Cortex 9 (2): 137–150.
5 5 Jones, M. and Wilson, M. (2005). Theta rhythms coordinate hippocampal–prefrontal interactions in a spatial memory task. PLoS Biology 3 (12): e402.
6 6 Penny, W.D., Stephan, K.E., Mechelli, A., and Friston, K.J. (2004). Comparing dynamic causal models. NeuroImage 22 (3): 1157–1172.
7 7 Hoppensteadt, F. and Izhikevich, E. (1997). Weakly Connected Neural Networks. New York, USA: Springer‐Verlag.
8 8 Benedek, G. and Villars, F. (2000). Physics, with Illustrative Examples from Medicine and Biology. New York: Springer‐Verlag.
9 9 Hille, B. (1992). Ionic Channels of Excitable Membranes. Sunderland, MA: Sinauer.
10 10 Hodgkin, A. and Huxley, A. (1952). A quantitative description of membrane current and its application to conduction and excitation in nerve. Journal of Physiology (London) 117: 500–544.
11 11 Doi, S., Inoue, J., Pan, Z., and Tsumoto, K. (2010). Computational Electrophysiology. Springer.
12 12 Simulator for Neural Networks and Action Potentials (SNNAP) (2003). Tutorial, The University of Texas‐Houston Medical School. https://med.uth.edu/nba/wp‐content/uploads/sites/29/2019/09/snnap_8_tutorial_v2019.pdf (accessed 19 August 2021).
13 13 Ziv, I., Baxter, D.A., and Byrne, J.H. (1994). Simulator for neural networks and action potentials: description and application. Journal of Neurophysiology 71: 294–308.
14 14 Gerstner, W. and Kistler, W.M. (2002). Spiking Neuron Models, 1e. Cambridge University Press.
15 15 Lagerlund, T.D., Sharbrough, F.W., and Busacker, N.E. (1997). Spatial filtering of multichannel electroencephalographic recordings through principal component analysis by singular value decomposition. Journal of Clinical Neurophysiology 14 (1): 73–82.
16 16 Da Silva, F.H., Hoeks, A., Smits, H., and Zetterberg, L.H. (1974). Model of brain rhythmic activity: the alpha‐rhythm of the thalamus. Kybernetic 15: 27–37.
17 17 da Silva, F.H.L., van Rotterdam, A., Barts, P. et al. (1976). Models of neuronal populations: the basic mechanisms of rhythmicity. In: Perspective of Brain Research, Prog. Brain Res, vol. 45 (eds. M.A. Corner and D.F. Swaab), 281–308.
18 18 Wilson, H.R. and Cowan, J.D. (1972). Excitatory and inhibitory interaction in localized populations of model neurons. Biophysical Journal 12: 1–23.
19 19 Zetterberg, L.H. (1973). Stochastic activity in a population of neurons – a system analysis approach. Report No. 2.3.153/1, 23, Issue no. 197418, p. 32. Utrecht: Institute of Medical Physics TNO, Utrecht.
20 20 Jansen, B.H. and Rit, V.G. (1995). Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns. Biological Cybernetics 73: 357–366.
21 21 Jansen, B.H., Zouridakis, G., and Brandt, M.E. (1993). A neurophysiologically based mathematical model of flash visual evoked potentials. Biological Cybernetics 68: 275–283.
22 22 Akaike, H. (1974). A new look at statistical model order identification. IEEE Transactions on Automatic Control 19: 716–723.
23 23 Kay, S.M. (1988). Modern Spectral Estimation: Theory and Application. Prentice Hall.
24 24 Guegen, C. and Scharf, L. (1980). Exact maximum likelihood identification of ARMA models: a signal processing perspective. In: Signal Processing Theory Applications (eds. M. Kunt and F. de Coulon), 759–769. Amsterdam: North Holland Publishing Co.
25 25 Akay, M. (2001). Biomedical Signal Processing. Academic Press.
26 26 Cavanaugh, J.E. and Neath, A.A. (2019). The Akaike information criterion: background, derivation, properties, application, interpretation, and refinements. WIREs Computational Statistics 11 (3): e1460.
27 27 Durbin, J. (1959). Efficient estimation of parameters in moving average models. Biometrika 46: 306–316.
28 28 Trench, W.F. (1964). An algorithm for the inversion of finite Toelpitz matrices. Journal of the Society for Industrial and Applied Mathematics 12: 515–522.
29 29 Morf, M., Vieria, A., Lee, D., and Kailath, T. (1978). Recursive multichannel maximum entropy spectral estimation. IEEE Transactions on Geoscience Electronics 16: 85–94.
30 30 Spreckelesen, M. and Bromm, B. (1988). Estimation of single‐evoked cerebral potentials by means of parametric modelling and Kalman filtering. IEEE Transactions on Biomedical Engineering 33: 691–700.
31 31 Demiralp, T. and Ademoğlu, A. (1992). Modeling of evoked potentials as decaying sinusoidal oscillations by PRONY‐method. 1992 14th Annual International Conference of the IEEE Engineering in Medicine and Biology