Neural Modeling: Electrical Signal Processing in the Nervous System

ISBN-13: 9781468421927 / Angielski / Miękka / 2013 / 414 str.

Ronald MacGregor

Opis

The purpose of this book is to introduce and survey the various quantitative methods which have been proposed for describing, simulating, embodying, or characterizing the processing of electrical signals in nervous systems. We believe that electrical signal processing is a vital determinant of the functional organization of the brain, and that in unraveling the inherent complexities of this processing it will be essential to utilize the methods of quantification and modeling which have led to crowning successes in the physical and engineering sciences. In comprehensive terms, we conceive neural modeling to be the attempt to relate, in nervous systems, function to structure on the basis of operation. Sufficient knowledge and appropriate tools are at hand to maintain a serious and thorough study in the area. However, work in the area has yet to be satisfactorily integrated within contemporary brain research. Moreover, there exists a good deal of inefficiency within the area resulting from an overall lack of direction, critical self-evaluation, and cohesion. Such theoretical and modeling studies as have appeared exist largely as fragmented islands in the literature or as sparsely attended sessions at neuroscience conferences. In writing this book, we were guided by three main immediate objectives. Our first objective is to introduce the area to the upcoming generation of students of both the hard sciences and psychological and biological sciences in the hope that they might eventually help bring about the contributions it promises.

Spis treści

I. Introduction.- 1 Signal Processing in Nervous Systems.- 1.1. Neurons.- 1.2. Modeling.- 2 The Idealized “Standard Neuron”.- 2.1. The Idealized “Standard Neuron”.- II. Neural Modeling: Models of Excitation And Conduction.- 3 Models of Passive Membrane.- 3.1. The Nernst-Planck Model.- 3.2. The Einstein Relation.- 3.3. The Nernst Equation and Ionic Reversal Potentials.- 3.4. Space-Charge Neutrality.- 3.5. Nernst-Planck Membranes with Space-Charge Neutrality and Obeying the Einstein Relation.- 3.6. Space-Charge Neutrality in a Homogeneous Nernst-Planck Membrane.- 3.7. Sources of Permanent Potential Differences across Membranes.- 3.8. Impedance to Ion Flow at Donnan Jumps.- 3.9. Ion-Concentration and Electrical Potential Profiles for Various Membrane Models.- 3.10. Summary: A Quantitative Model of Neuronal Membrane.- 4 Equivalent Circuits for Passive Membrane.- 4.1. The Basic Equivalent Circuit for a Patch of Membrane.- 4.2. Small-Signal Equivalent Circuits.- 4.3. Equivalent Circuits for Large Signals.- 4.4. The Frankenhaeuser-Hodgkin Space.- 4.5. Summary.- 5 Models of Signal Generation in Neural Elements.- 5.1. Some General Considerations.- 5.2. The Eccles Model of Chemical Synapse.- 5.3. Bullock’s Degrees of Freedom for a Chemical Synapse.- 5.4. The Quantum Model of Transmitter Release.- 5.5. Discrete Inputs to Other Receptors.- 5.6. Reliable Detection of Weak Signals in the Presence of Noise.- 5.7. The Fuortes-Hodgkin Model Ill.- 5.8. Spontaneous Activity in Neurons.- 6 Models of Distributed Passive Membrane.- 6.1. The Basic Model.- 6.2. Dipole Annihilation and Redistribution.- 6.3. Continuous Model for Response Spread over Neuronal Fibers.- 6.4. Continuous Analysis of the Uniform, Passively Conducting Fiber with Time-Invariant Parameters.- 6.5. Continuous Analysis of Branching Dendritic.- Trees: Rail’s Equivalent Cylinder Model.- 6.6. Spatially Discrete Analysis of Passively Conducting Fibers and Fiber Trees.- 6.7. Shapes of Passively Conducted Signals.- 6.8. Conduction of Signals to Very Remote Sites.- 7 Models of Spike Generation and Conduction.- 7.1. The Iron Wire (or Heathcote-Lillie) Model.- 7.2. Threshold and Accommodation (or the Hill-Rashevsky-Monnier Model).- 7.3. The Hodgkin-Huxley Model.- 7.4. Abstractions of the Hodgkin-Huxley Model.- 7.5. Conduction of Spikes.- 7.8. Concluding Remarks.- III. Neural Coding: Models of Electrical Signal Processing.- 8 Neuromimes.- 9 Stochastic Models of Neuron Activity.- 9.1. Gerstein’s Model.- 9.2. More General Models.- 10 Statistical Analysis of Neuronal Spike Trains.- 10.1. Statistical Measures for Single Trains.- 10.2. Statistical Measures for Simultaneously Recorded Trains.- 10.3. Applications of Neuronal Spike Train Analysis.- 11 Models of Neuron Pools.- 12 Models of Large Networks: Analytic Approaches.- 13 Models of Large Networks: Computer-Oriented Approaches.- 14 Models of Field Potentials, Slow Waves, and the EEG.- 14.1. Models of Field Potentials Resulting from Unit Activity.- 14.2. Models of the EEG.- 15 Models of Specific Neural Networks.- 15.1. Cerebral Cortex.- 15.2. Thalamus and Hippocampus: Brain Rhythms.- 15.3. Reticular Formation.- 15.4. The Retina and Lateral Inhibition.- IV. Conclusion.- 16 Neural Modeling: The State of the Art.- 16.1. The Stratification of Variables.- 16.2. Goals of Neural Network Modeling.- 16.3. Guidelines for Brain Modeling.- References.