## Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and Dendritic StructureThe human brain contains billions of nerve cells whose activity plays a critical role in the way we behave, feel, perceive, and think. This two-volume set explains the basic properties of a neuron--an electrically active nerve cell--and develops mathematical theories for the way neurons respond to the various stimuli they receive. Volume 1 contains descriptions and analyses of the principle mathematical models that have been developed for neurons in the past thirty years. It provides a brief review of the basic neuroanatomical and neurophysiological facts that will form the focus of the mathematical treatment. Tuckwell discusses the mathematical theories, beginning with the theory of membrane potentials. He then goes on to treat the Lapicque model, linear cable theory, and time-dependent solutions of the cable equations. He concludes with a description of Rall's model nerve cell. Because the level of mathematics increases steadily upward from Chapter Two some familiarity with differential equations and linear algebra is desirable. |

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### Contents

the properties of motoneurons | 1 |

2 The classical theory of membrane potentials | 33 |

3 The Lapicque model of the nerve cell | 85 |

steadystate solutions | 124 |

5 Timedependent cable theory for nerve cylinders and dendritic trees | 180 |

6 Rails model neuron | 234 |

283 | |

290 | |

### Other editions - View all

Introduction to Theoretical Neurobiology: Volume 1, Linear Cable Theory and ... Henry C. Tuckwell No preview available - 2006 |

### Common terms and phrases

action potential anion applied current assumed boundary conditions branch points cable equation cable theory cat spinal motoneuron cation cell body chapter characteristic length coefficients concentration constant current constant-field cosh current density current injection curve daughter cylinders delta function dendritic terminals dendritic tree depolarization diameter differential equation dimensionless electrical potential EPSP equivalent cylinder example excitatory frequency given Goldman formula Green’s function Hence inhibitory initial input current integration intracellular ion species IPSP killed end Lapicque model Laplace transform linear lumped soma method muscle muscle spindles myelin nerve cell nerve cylinder neuron obtain order of branching origin parameters permeability phase locking Physiological Society postsynaptic potentials potassium Renshaw cells resistance response resting potential reversal potential satisfies sealed end sealed-end condition Section segment semiinfinite shown in Figure sinh sodium solve soma spike squid axon subthreshold synaptic input tanh Theorem threshold time-dependent tion variables various voltage zero