### Abstract

The sections in this article are:

- 1 Introduction
- 1.1 Core Conductor Concept
- 1.2 Perspective
- 1.3 Comment
- 1.4 Reviews and Monographs

- 2 Brief Historical Notes
- 2.1 Early Electrophysiology
- 2.2 Electrotonus
- 2.3 Passive Membrane Electrotonus
- 2.4 Passive Versus Active Membrane
- 2.5 Cable Theory
- 2.6 Core Conductor Concept
- 2.7 Core Conductor Theory
- 2.8 Estimation of Membrane Capacitance
- 2.9 Resting Membrane Resistivitiy
- 2.10 Passive Cable Parameters of Invertebrate Axons
- 2.11 Importance of Single Axon Preparations
- 2.12 Estimation of Parameters for Myelinated Axons
- 2.13 Space and Voltage Clamp

- 3 Dendritic Aspects of Neurons
- 3.1 Axon‐Dendrite Contrast
- 3.2 Microelectrodes in Motoneurons
- 3.3 Theoretical Neuron Models and Parameters
- 3.4 Class of Trees Equivalent to Cylinders
- 3.5 Motoneuron Membrane Resistivity and Dendritic Dominance
- 3.6 Dendritic Electrotonic Length
- 3.7 Membrane Potential Transients and Time Constants
- 3.8 Spatiotemporal Effects with Dendritic Synapses
- 3.9 Excitatory Postsynaptic Potential Shape Index Loci
- 3.10 Comments on Extracellular Potentials
- 3.11 Additional Comments and References

- 4 Cable Equations Defined
- 4.1 Usual Cable Equation
- 4.2 Steady‐state Cable Equations
- 4.3 Augmented Cable Equations
- 4.4 Comment: Cable Versus Wave Equation
- 4.5 Modified Cable Equation for Tapering Core
- 4.6 General Solution of Steady‐state Cable Equation
- 4.7 Basic Transient Solutions of Cable Equation
- 4.8 Solutions Using Separation of Variables
- 4.9 Fundamental Solution for Instantaneous Point Charge

- 5 List of Symbols
- 6 Assumptions and Derivation of Cable Theory
- 6.1 One Dimensional in Space
- 6.2 Intracellular Core Resistance
- 6.3 Ohm's Law for Core Current
- 6.4 Conservation of Current
- 6.5 Relation of Membrane Current to Vi
- 6.6 Effect of Assuming Extracellular Isopotentiality
- 6.7 Passive Membrane Model
- 6.8 Resulting Cable Equation for Simple Case
- 6.9 Physical Meaning of Cable Equation Terms
- 6.10 Physical Meaning of τ
- 6.11 Physical Meaning of λ
- 6.12 Electrotonic Distance, Length, and Decrement
- 6.13 Effect of Placing Axon in Oil
- 6.14 Effect of Applied Current
- 6.15 Comment on Sign Conventions
- 6.16 Effect of Synaptic Membrane Conductance
- 6.17 Effect of Active Membrane Properties

- 7 Input Resistance and Steady Decrement with Distance
- 7.1 Note on Correspondence with Experiment
- 7.2 Cable of Semi‐infinite Length
- 7.3 Comments about R∞, G∞, Core Current, and Input Current
- 7.4 Doubly Infinite Length
- 7.5 Case of Voltage Clamps at X1 and X2
- 7.6 Relations Between Axon Parameters
- 7.7 Finite Length: Effect of Boundary Condition at X= X1
- 7.8 Sealed End at X= X1: Case of B1 = 0
- 7.9 Voltage Clamp(V1 = 0) at X = X1: Case of B1 = ∞
- 7.10 Semi‐infinite Extension at X = X1: Case of B1 = 1
- 7.11 Input Conductance for Finite Length General Case
- 7.12 Branches at X = X1
- 7.13 Comment on Branching Equivalent to a Cylinder
- 7.14 Comment on Membrane Injury at X = X1
- 7.15 Comment on Steady Synaptic Input at X= X1
- 7.16 Case of Input to One Branch of Dendritic Neuron Model

- 8 Passive Membrane Potential Transients and Time Constants
- 8.1 Passive Decay Transients
- 8.2 Time Constant Ratios and Electrotonic Length
- 8.3 Effect of Large L and Infinite L
- 8.4 Transient Response to Applied Current Step, for Finite Length
- 8.5 Applied Current Step with L Large or Infinite
- 8.6 Voltage Clamp at X = 0, with Infinite L
- 8.7 Voltage Clamp with Finite Length
- 8.8 Transient Response to Current Injected at One Branch of Model

- 9 Relations Between Neuron Model Parameters
- 9.1 Input Resistance and Membrane Resistivity
- 9.2 Dendritic Tree Input Resistance and Membrane Resistivity
- 9.3 Results for Trees Equivalent to Cylinders
- 9.4 Result for Neuron Equivalent to Cylinder
- 9.5 Estimation of Motoneuron Parameters