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Lecture

Cable equation: Passive Dendrites Stimulation

Description

This lecture covers the derivation of the cable equation for passive dendrites, explaining how dendritic stimulation affects neuronal dynamics. It discusses the space constant of a passive cable, the voltage distribution after current injection, and the impact of dendritic location on EPSP shape.

In MOOC

Neuronal Dynamics - Computational Neuroscience of Single Neurons

Official source

Related concepts (11)

Dendrite

A dendrite (from Greek δένδρον déndron, "tree") or dendron is a branched protoplasmic extension of a nerve cell that propagates the electrochemical stimulation received from other neural cells to the cell body, or soma, of the neuron from which the dendrites project. Electrical stimulation is transmitted onto dendrites by upstream neurons (usually via their axons) via synapses which are located at various points throughout the dendritic tree.

Telegrapher's equations

The telegrapher's equations (or just telegraph equations) are a set of two coupled, linear equations that predict the voltage and current distributions on a linear electrical transmission line. The equations are important because they allow transmission lines to be analyzed using circuit theory. The equations and their solutions are applicable from 0 Hz to frequencies at which the transmission line structure can support higher order non-TEM modes. The equations can be expressed in both the time domain and the frequency domain.

Coaxial cable

Coaxial cable, or coax (pronounced 'koʊ.æks), is a type of electrical cable consisting of an inner conductor surrounded by a concentric conducting shield, with the two separated by a dielectric (insulating material); many coaxial cables also have a protective outer sheath or jacket. The term coaxial refers to the inner conductor and the outer shield sharing a geometric axis. Coaxial cable is a type of transmission line, used to carry high-frequency electrical signals with low losses.

Transmission line

In electrical engineering, a transmission line is a specialized cable or other structure designed to conduct electromagnetic waves in a contained manner. The term applies when the conductors are long enough that the wave nature of the transmission must be taken into account. This applies especially to radio-frequency engineering because the short wavelengths mean that wave phenomena arise over very short distances (this can be as short as millimetres depending on frequency).

Characteristic impedance

The characteristic impedance or surge impedance (usually written Z0) of a uniform transmission line is the ratio of the amplitudes of voltage and current of a single wave propagating along the line; that is, a wave travelling in one direction in the absence of reflections in the other direction. Alternatively, and equivalently, it can be defined as the input impedance of a transmission line when its length is infinite. Characteristic impedance is determined by the geometry and materials of the transmission line and, for a uniform line, is not dependent on its length.

Related lectures (11)

Dendrite as a Cable MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Discusses dendrites as cables, covering the cable equation derivation and current conservation in coupled compartments.

Derivation of the Cable Equation MOOC: Neuronal Dynamics - Computational Neuroscience of Single Neurons

Explores the derivation of the cable equation for modeling dendrites in computational neuroscience.

Cable properties: Cellular Mechanisms of Brain Function MOOC: Cellular Mechanisms of Brain Function

Explores the dynamics of membrane potential in neurons and the cable equation at steady state.