A spatio-temporal approach to brain dynamics


A spatio-temporal response model of brain activity is presented in this paper. The model is a non-autonomous reaction-diffusion model, i.e., a non-autonomous parabolic partial differential equation. The model is deduced as a spatial generalization of the time response model presented in other works. The analytical solution of the model is obtained for an idealized brain geometry given by a parallelepiped. The boundary conditions provide the quantization of the brain frequencies and the initial conditions are needed to obtain the coefficients of a Fourier series that take part of the model solution. The ways of validation are discussed, particularly those related with the brain resting state, and those related with getting the theoretical values of the so-called brain wave frequencies and comparing them with the experimental values. Some generalization hypotheses are commented to the model becomes more realistic and useful in a future investigation.

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