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Commentary by Zoltán Somogyvári and Péter Érdi

Forward and Backward Modeling: From Single Cells to Neural Population and Back

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Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields

Part of the book series: Studies in Systems, Decision and Control ((SSDC,volume 39))

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Abstract

Some aspects of forward and backward neural modeling are discussed, showing, that the neural mass models may provide a “golden midway” between the detailed conductance based neuron models and the oversimplified models, dealing with the input–output transformations only. Our analysis combines historical perspectives and recent developments concerning neural mass models as a third option for modeling large neural populations and inclusion of detailed anatomical data into them. The current source density analysis and the geometrical assumption behind the different methods, as an inverse modeling tool for determination of the sources of the local field potential is discussed, with special attention to the recent results about source localization on single neurons. These new applications may pave the way to the emergence of a new field of micro-electric imaging .

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References

  1. Amari S (1983) Field theory of self-organizing neural nets. IEEE Trans Syst Man Cybern SMC–13:741–748

    Article  MathSciNet  MATH  Google Scholar 

  2. Barna Gy, Grőbler T, Érdi P (1988) Statistical model of the Hippocampal CA3 region I. The single-cell module: bursting model of the pyramidal cell. Biol Cybern 79:301–308

    MATH  Google Scholar 

  3. Berényi A, Somogyvári Z, Nagy A, Roux L, Long J, Fujisawa S, Stark E, Leonardo A, Harris T, Buzski G (2014) Large-scale, high-density (up to 512 channels) recording of local circuits in behaving animals. J. Neurophysiol 111:1132–1149. doi:10.1152/jn.00785.2013BiolCybern,79:309-321

    Article  Google Scholar 

  4. Bergmann U, von der Malsburg C (2011) Self-organization of topographic bilinear networks for invariant recognition. Neural Comput 23:2770–2797

    Article  Google Scholar 

  5. Bower JM, Beeman D (1994) The book of GENESIS: exploring realistic neural models with the GEneral NEural SImulation System. TELOS, Springer, New York

    Google Scholar 

  6. Buzsáki G (2004) Large-scale recording of neuronal ensembles. Nat Neurosci 7(5):446–51

    Article  Google Scholar 

  7. Buzsáki G, Anastassiou CA, Koch C (2012) The origin of extracellular fields and currents–EEG, ECoG, LFP and spikes. Nat Rev Neurosci 13(6):407–420

    Article  Google Scholar 

  8. Érdi P (2000) Narrowing the gap between neural models and brain imaging data: a mesoscopic approach to neural population dynamics. The 2000 Neuroscan Workshop at Duke University. http://www.rmki.kfki.hu/biofiz/cneuro/tutorials/duke/index.html

  9. Érdi P (2007) Complexity explained. Springer, New York

    MATH  Google Scholar 

  10. Freeman WJ (1975) Mass action in the nervous system. Academic Press, Massachusetts

    Google Scholar 

  11. Freeman WJ (1980) A software lens for image reconstitution of the EEG. Prog Brain Res 54:123–127

    Article  Google Scholar 

  12. Freeman WJ (1980) Use of spatial deconvolution to compensate for distortion of EEG by volume conduction. IEEE Trans Biomed Eng 27(8):421–429

    Article  Google Scholar 

  13. Gerstner W, Kistler M, Naud R, Paninski (2014) Neuronal dynamics: from single neurons to networks and models of cognition. Cambridge University Press, Cambridge

    Google Scholar 

  14. Grech R, Cassar T, Muscat J, Camilleri KP, Fabri GS, Zervakis M, Xanthopoulos P, Sakkalis V, Vanrumste B (2008) Review on solving the inverse problem in EEG source analysis. J NeuroEng Rehabil 5(25):1–33

    Google Scholar 

  15. Griffith JA (1963) A field theory of neural nets. I. Derivation of field equations. Bull Math Biophys 25:111–120

    Article  MathSciNet  MATH  Google Scholar 

  16. Grőbler T, Barna Gy, Érdi P (1998) Statistical model of the Hippocampal CA3 region II. The population framework: model of rhythmic activity in the CA3 slice. Biol Cybern 79:309–321

    Article  MATH  Google Scholar 

  17. Hines M (1984) Efficient computation of branched nerve equations. J Biol-Med Comp 15:69–74

    Google Scholar 

  18. Hines M (1993) The NEURON simulation program. Neural network simulation environments. Kluwer Academic Publication, Norwell

    Google Scholar 

  19. Hodgkin A, Huxley A (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500–544

    Article  Google Scholar 

  20. Jirsa VK (2004) Connectivity and dynamics of neural information processing. Neuroinformatics 2:183204

    Article  Google Scholar 

  21. Jirsa V,K (2009) Neural field dynamics with local and global connectivity and time delay. Philos Trans R Soc A: Math Phys Eng Sci 367(1891):1131–1143

    Article  MathSciNet  MATH  Google Scholar 

  22. Kipke D, Shain W, Buzsáki G, Fetz E, Henderson J, Hetke J, Schalk G (2008) Advanced neurotechnologies for chronic neural interfaces: new horizons and clinical opportunities. J Neurosci 28(46):11830–11838

    Article  Google Scholar 

  23. Kiss T (2000) Az agykéreg normális és epileptikus működésének tanulmányozása statisztikus neurodinamikai modellel (in Hungarian). Master’s thesis, Eötvös Lorán Tudományegyetem. http://cneuro.rmki.kfki.hu/files/diploma.pdf

  24. Kiss T, Érdi P (2002) Mesoscopic Neurodynamics. BioSystems, Michael Conrad’s special issue 64(1–3):119–126

    Google Scholar 

  25. Kozma R, Freeman WJ (2003) Basic principles of the KIV model and its application to the navigation problem. J Integr Neurosci 2(1):125–145

    Article  Google Scholar 

  26. Kozma R, Freeman WJ, Érdi P (2003) The KIV model—nonlinear spatio-temporal dynamics of the primordial vertberate forebrain. Neurocomputing 52–54:819–826

    Article  Google Scholar 

  27. Kozma R, Freeman WJ, Wong D, Érdi P (2004) Learning environmental clues in the KIV model of the Cortico-Hippocampal formation. Neurocomputing 58–60(2004):721–728

    Article  Google Scholar 

  28. Leski S, Wajcik DK, Tereszczuk J, Awiejkowski DA, Kublik E, Wrabel A (2007) Inverse Current-Source Density in three dimensions. Neuroinformatics 5:207

    Article  Google Scholar 

  29. Leski S, Pettersen KH, Tunstall B, Einevoll GT, Gigg J, Wajcik DK (2011) Inverse Current Source Density method in two dimensions: inferring neural activation from multielectrode recordings. Neuroinformatics 9:401–425

    Article  Google Scholar 

  30. Mitzdorf U (1985) Current source-density method and application in cat cerebral cortex: investigation of ecoked potentials and EEG phenomena. Physiol Rev 65:37–100

    Google Scholar 

  31. Nicholson C, Freeman JA (1975) Theory of current source-density analysis and determination of conductivity tensor for anuran cerebellum. J Neurophysiol 38:356–368

    Google Scholar 

  32. Pettersen KH, Devor A, Ulbert I, Dale AM, Einevoll GT (2006) Current-source density estimation based on inversion of electrostatic forward solution: effect of finite extent of neuronal activity and conductivity discontinuites. J Neurosci Methods 154(1–2):116–133

    Article  Google Scholar 

  33. Potworowski J, Jakuczun W, ȩski S, Wjcik DK (2012) Kernel current source density method. Neural Comput 24:541–575

    Article  MathSciNet  Google Scholar 

  34. Rall W (1962) Electrophysiology of a dendritic neuron model. Biophys J 2:145–167

    Article  Google Scholar 

  35. Rall W (1977) Core conductor theory ad cable properties of neurons. Handbook of physiology. The nervous system. William and Wilkins, Baltimore, pp 39–98

    Google Scholar 

  36. Scannell JW, Blakemore C, Young MP (1995) J Neurosci 15:1463–1483

    Google Scholar 

  37. Seelen W (1968) Informationsverarbeitung in homogenen netzen von neuronenmodellen. Kybernetik 5:181–194

    Article  MATH  Google Scholar 

  38. Somogyvári Z, Zalányi L, Ulbert I, Érdi P (2005) Model-based source localization of extracellular action potentials. J Neurosci Methods 147:126–137

    Article  Google Scholar 

  39. Somogyvári Z, Cserpán D, Ulbert I, Érdi P (2012) Localization of single-cell current sources based on extracellular potential patterns: the spike CSD method. Eur J Neurosci 36(10):3299–313

    Article  Google Scholar 

  40. Sporns O (2010) Networks of the brain. MIT Press, Cambridge

    MATH  Google Scholar 

  41. Ventriglia F (1974) Kinetic approach to neural systems. Bull Math Biol 36:534–544

    Article  MATH  Google Scholar 

  42. Ventriglia F (1982) Kinetic theory of neural systems: memory effects. In: Trappl R (ed) Proceedings of the Sixth European Meeting on Cybernetics and Systems Research. Austrian Society for Cybernetic Studies, North-Holland Publishing Company, Amsterdam, pp 271–276

    Google Scholar 

  43. Ventriglia F (1990) Activity in cortical-like neural systems: short-range effects and attention phenomena. Bull Math Biol 52:397–429

    Article  MATH  Google Scholar 

  44. Ventriglia F (1994) Towards a kinetic theory of cortical-like neural fields. Neural modeling and neural networks. Pergamon Press, Oxford, pp 217–249

    Chapter  Google Scholar 

  45. The Virtual Brain Project. http://www.thevirtualbrain.org/tvb/zwei

  46. Wilson HR, Cowan J (1973) A mathematical theory of the functional dynamics of cortical and thalamic neurons tissue. Kybernetik 13:55–80

    Article  MATH  Google Scholar 

  47. Willshaw DJ, von der Malsburg C (1976) How patterned neural connections can be set up by self-organization. Proc R Soc Lond B194:431–445

    Google Scholar 

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Acknowledgments

ZS was supported by grant OTKA K 113147. PE thanks to the Henry Luce Foundation to let him to be a Henry R Luce Professor.

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Somogyvári, Z., Érdi, P. (2016). Commentary by Zoltán Somogyvári and Péter Érdi. In: Cognitive Phase Transitions in the Cerebral Cortex - Enhancing the Neuron Doctrine by Modeling Neural Fields. Studies in Systems, Decision and Control, vol 39. Springer, Cham. https://doi.org/10.1007/978-3-319-24406-8_13

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  • DOI: https://doi.org/10.1007/978-3-319-24406-8_13

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