Third Order Mathematical Model of the Brain Validated via Cerebral Evoked Potentials
51 Pages Posted: 8 Jan 2020 Last revised: 10 Jan 2020
Date Written: December 16, 2019
This paper presents the vital role mathematical modeling plays in the analysis of evoked potentials obtained from auditory, somatosensory, visual, and cognitive stimuli.
Analysis of this data was performed by using the concepts of Closed Loop Methodology (CLM) to create specific mathematical modes representative of the signals that were being analyzed. As a result of this effort, a Forensic Simulator was design and built to signal process the EEG's provided by patients of the Craig Hospital Neuroscience Laboratory located in Englewood, Colorado.
The Forensic Simulator provides a modern system analysis tool for neuroscience research. This device provides a user friendly environmental from which the electrical activity of the brain can be quantified. By using an adaptive processor to null out the error generate by comparing measured evoked potentials to those produce by a mathematical model, the neurophysiology of the central nervous system may be evaluated. Nulling of this error is achieved by defining the neurological classification set. Members of the set are defined to be: the uncertainty of the neuron firing, the neuronal staee characteristics, the characteristic brain parameters, estimates of the neuronal states, variances associated with the neuronal state estimates, and the variances attributable toe measurement error.
Members of the classification set are obtained by solving the modeling problem via solution to the subproblems of estimation, identification, and control. Algorithms solving the the estimation problem provide numerical time varying values for the states of the system. This ability is assured once the SID (System IDentification) has been solved. This solution yields the quantification of the uncertainties associated with the state estimates as well as the uncertainties associated with the evoked potential measurements.
Keywords: CLM, system, feedback, neuroscience, brain, bio-feedback, EEG, somasentsory, variance, quantification, estimation, system identification, variance, uncertainty
JEL Classification: l19, l19, l20, C02, C13, C30, C32, C52, C67
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