The Passive Cable Equation Mat

The cable equation passive cable module implements a passive cable using a brian2 multicompartment model.

The passive cable equation mat.

The first model was a cylinder of finite length consisting of uniform passive nerve membrane rall 1962a. It can be verified that it is also equivalent to the total axial resistance for a cableoflength λ. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey. Dendrites and the passive cable equation.

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. Cable equations defined usual cable equation steady state cable equations augmented cable equations comment. In this section the cable equation is derived steady state cable properties are studied and total input resistance of a cell is defined. Lectures by walter lewin.

In chapter 3 section 2 the cable equation is derived and compartmental models are introduced. Information flows in the nervous system from the soma to the axon and then to the dendrites. Tosummarise theequations thatgovern theelectrical characteristics of acableare. Equivalent cylinder model and cable equation.

In most models the dendrites are regarded as being passive electrical cables. Nerve and muscle were begun in the 1840 s by mat teucci professor of physics at pisa and by du bois. The neuron soma lies at one end x 0 while the dendritic terminals lie at the other end x l. In this reduced model a dendritic tree was collapsed into a single cylinder.

To get started import the module and call the demo function. 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. 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. For the love of physics walter lewin may 16 2011 duration.

Tranchinaandnicholson 15 providedsteady statesolutions for the cable equation in which an extrinsic electric field was applied to a uniform passive cylindrical cable. The passive cable equation. 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. Cable versus wave equation.

Passive finite cables exposed to extracellular electric fields. By numerically solving the cable equation they showed that the rate of. Passive cable parameters of invertebrate axons. Of cable λ long.