The Passive Cable Equation Mat

Nerve and muscle were begun in the 1840 s by mat teucci professor of physics at pisa and by du bois.

The passive cable equation mat.

Cable versus wave equation. Passive cable parameters of invertebrate axons. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey. To get started import the module and call the demo function.

Tosummarise theequations thatgovern theelectrical characteristics of acableare. 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. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey 7. Lectures by walter lewin.

Tranchinaandnicholson 15 providedsteady statesolutions for the cable equation in which an extrinsic electric field was applied to a uniform passive cylindrical cable. Information flows in the nervous system from the soma to the axon and then to the dendrites. 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. In this reduced model a dendritic tree was collapsed into a single cylinder.

For the love of physics walter lewin may 16 2011 duration. Equivalent cylinder model and cable equation. The passive cable equation. In most models the dendrites are regarded as being passive electrical cables.

The neuron soma lies at one end x 0 while the dendritic terminals lie at the other end x l. 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. The first model was a cylinder of finite length consisting of uniform passive nerve membrane rall 1962a. Passive finite cables exposed to extracellular electric fields.

In this section the cable equation is derived steady state cable properties are studied and total input resistance of a cell is defined. Cable equations defined usual cable equation steady state cable equations augmented cable equations comment. Dendrites and the passive cable equation. In chapter 3 section 2 the cable equation is derived and compartmental models are introduced.

Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances and resistances combined in parallel see fig. It can be verified that it is also equivalent to the total axial resistance for a cableoflength λ. Of cable λ long. The cable equation passive cable module implements a passive cable using a brian2 multicompartment model.