Investigation, modelling and quantification of the brain response to external stimuli

Abstract

No adequate mathematical model of the brain activity exists until today. This is due to the fact that the brain is an extremely complex non-linear system. This research work presents a novel mathematical model of the human brain response to external stimuli. Using the basic laws of physics: the conservation of energy principle, the second law of thermodynamics and the least action principle, a phase-lagging diffusion model of a single neuron action potential has been proposed with validation. This model overcomes the paradox of instantaneous propagation in the classical diffusion equation by introducing a time lag. Applying the external stimuli, simulated as a series of Gaussian energy pulses, to this model has generated fractal time series similar to EEG.Various functions describing concepts of the importance of information, relevance of information and information gain have been introduced. Measures like the Hurst exponent and the Jeffreys measure have been proposed to quantify the stimulus and its effects. Software has been developed to analyse the captured EEG signals from subjects and compute fractal measures of the signals. Analysis of the effects of different auditory, visual and olfactory stimuli on different subjects is performed and results have been provided with applications to real life.