The Passive Cable Equation Mat

A detailed derivation of the passive cable equation.

The passive cable equation mat.

In its analytical form the cable equation can only be applied to passive dendrites with current sources i e no synaptic or voltage gated conductances. Information flows in the nervous system from the soma to the axon and then to the dendrites. Cable equations defined usual cable equation steady state cable equations augmented cable equations comment. Tranchina and nicholson provided steady state solutions for the cable equation in which an extrinsic electric field was applied to a uniform passive cylindrical cable.

Tranchinaandnicholson 15 providedsteady statesolutions for the cable equation in which an extrinsic electric field was applied to a uniform passive cylindrical cable. By numerically solving the cable equation they showed that the rate of. The first model was a cylinder of finite length consisting of uniform passive nerve membrane rall 1962a. Cable versus wave equation.

The passive cable equation. To get started import the module and call the demo function. The cable equation passive cable module implements a passive cable using a brian2 multicompartment model. For the love of physics walter lewin may 16 2011 duration.

Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances and resistances combined in parallel see fig. Nerve and muscle were begun in the 1840 s by mat teucci professor of physics at pisa and by du bois. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey 7. Tosummarise theequations thatgovern theelectrical characteristics of acableare.

Dendrites and the passive cable equation. In this section the cable equation is derived steady state cable properties are studied and total input resistance of a cell is defined. The neuron soma lies at one end x 0 while the dendritic terminals lie at the other end x l. It can be verified that it is also equivalent to the total axial resistance for a cableoflength λ.

In chapter 3 section 2 the cable equation is derived and compartmental models are introduced. Of cable λ long. Passive cable parameters of invertebrate axons. Classical cable theory uses mathematical models to calculate the electric current and accompanying voltage along passive neurites particularly the dendrites that receive synaptic inputs at different sites and times.

Rall realized however that dendrites were not likely to function as purely passive cables so he also applied the cable equation to numerical simulations in order to facilitate simulation. In most models the dendrites are regarded as being passive electrical cables. Equivalent cylinder model and cable equation. Passive finite cables exposed to extracellular electric fields.