Neurodynamics: An Exploration in Mesoscopic Brain Dynamics

by Walter Freeman

Overview

Cortical evoked potentials are of interest primarily as tests of changing neuronal excitabilities accompanying normal brain function. The first three steps in the analysis of these complex waveforms are proper placement of electrodes for recording, the proper choice of electrical or sensory stimulus parameters, and the establish­ ment of behavioral control. The fourth is development of techniques for reliable measurement. Measurement consists of comparison of an unknown entity with a set of standard scales or dimensions having numerical attributes in preassigned degree. A physical object can be described by the dimensions of size, mass, density, etc. In addition there are dimensions such as location, velocity, weight, hardness, etc. Some of these dimensions can be complex (e. g. size depends on three or more subsidiary coordi­ nates), and some can be interdependent or nonorthogonal (e. g. specification of size and mass may determine density). In each dimension the unit is defined with refer­ ence to a standard physical entity, e. g. a unit of mass or length, and the result of measurement is expressed as an equivalence between the unknown and the sum of a specified number of units of that entity. The dimensions of a complex waveform are elementary waveforms from which that waveform can be built by simple addition. Any finite single-valued function of time is admissible. They are called basis functions (lO, 15), and they can be expressed in numeric as well as geometric form.

Product Details

ISBN-13:	9781852336165
Publisher:	Springer London
Publication date:	03/30/2000
Series:	Perspectives in Neural Computing
Edition description:	1st Edition.
Pages:	398
Product dimensions:	6.10(w) x 9.25(h) x 0.03(d)

Table of Contents

Prologue.- Prologue.- I The dynamics of neural interaction and transmission.- 1. Spatial mapping of evoked brain potentials and EEGs to 27 define population state variables.- 2. Linear models of impulse inputs and linear basis functions for measuring impulse responses.- 3. Rational approximations in the complex plane for Laplace transforms of transcendental linear operators.- 4. Root locus analysis of piecewise linearized models with multiple feedback loops and unilateral or bilateral saturation.- 5. Opening feedback loops with surgery and anesthesia; closing them with noise.- 6. Three degrees of freedom in neural populations: Arousal, learning, and bistability.- 7. Analog computation to model responses based on linear integration, modifiable synapses, and nonlinear trigger zones.- 8. Stability analysis to derive and regulate homeostatic set points for negative feedback loops.- II Designation of contents as meaning, not information.- 9. Multichannel recording to reveal the “code” of the cortex: spatial patterns of amplitude modulation (AM) of mesoscopic carrier waves.- 10. Relations between microscopic and mesoscopic levels shown by calculating pulse probability conditional on EEG amplitude, giving the asymmetric sigmoid function.- 11. Euclidean distance in 64-space and the use of behavioral correlates to optimize filters for gamma AM pattern classification.- 12. Simulating gamma waveforms, AM patterns and 1/f? spectra by means of mesoscopic chaotic neurodynamics.- 13. Tuning curves to optimize temporal segmentation and parameter evaluation of adaptive filters for neocortical EEG.- 14. Shastic differential equations and random number generators minimize numerical instabilities in digital simulations.- Epilogue: Problems for further development in mesoscopicbrain dynamics.- Epilogue: Problems for further development in mesoscopic brain dynamics.- References.- Author Index.