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Derivation of a mathematical equation for the EEG and the general solution within the brain and in space

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Abstract

A mathematical model for the EEG is presented here based on physical and anatomical characteristics of the brain. The important finding is that the system is characterised by a diffusion equation whose general solution represents a Fourier series expansion for the EEG at any point of the zone under consideration.

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Abbreviations

E :

The electric field

σ :

The conductivity of the medium

ε :

The permittivity of the medium

D :

The electrical displacement

ρ :

The charge density

C :

The capacitivity of the passive elements of the medium

J :

The current density

ø :

The potential

References

  • Abramowitz, M. and Stegun, I. A. (1964).Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. National Bureau of Standards, Applied Mathematical Series 55.

  • Bateman, H. (1959).Partial Differential Equations of Mathematical Physics. Cambridge University Press.

  • Cohen, D. (1972). Magnetoencephalography: Detection of the brain's electrical activity with a superconducting magnetometer.Science 175, 4022, 664.

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  • Ranck, J. B. (1963). Specific impedance of rabbit cerebral cortex.Experimental Neurology 7, 144.

    Google Scholar 

  • Walter, D. O. (1972). Computer program of the Data Processing Laboratory, UCLA.

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Author information

Author notes

  1. P. A. Anninos

    Present address: Department of Physics, Concordia University, Montreal, P.Q.

  2. S. Raman

    Present address: Department of Epidemiology and Community Medicine, University of Ottawa, Ottawa, Ontario

Authors and Affiliations

  1. Departments of Biomathematics and Anatomy and Mental Retardation Program of Neuropsychiatric Institute, University of California, 90024, Los Angeles

    P. A. Anninos & S. Raman

Authors
  1. P. A. Anninos
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  2. S. Raman
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Anninos, P.A., Raman, S. Derivation of a mathematical equation for the EEG and the general solution within the brain and in space. Int J Theor Phys 12, 1–9 (1975). https://doi.org/10.1007/BF01884105

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  • DOI: https://doi.org/10.1007/BF01884105

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