The Passive Cable Equation Mat

Cable equations defined usual cable equation steady state cable equations augmented cable equations comment.

The passive cable equation mat. By numerically solving the cable equation they showed that the rate of. Passive cable parameters of invertebrate axons. 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. Dendrites and the passive cable equation.

In chapter 3 section 2 the cable equation is derived and compartmental models are introduced. 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. Information flows in the nervous system from the soma to the axon and then to the dendrites. In this reduced model a dendritic tree was collapsed into a single cylinder.

Cable versus wave equation. The cable equation passive cable module implements a passive cable using a brian2 multicompartment model. 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. Tranchinaandnicholson 15 providedsteady statesolutions for the cable equation in which an extrinsic electric field was applied to a uniform passive cylindrical cable.

Passive finite cables exposed to extracellular electric fields. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey 7. The first model was a cylinder of finite length consisting of uniform passive nerve membrane rall 1962a. For the love of physics walter lewin may 16 2011 duration.

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. The passive cable equation. To get started import the module and call the demo function. The neuron soma lies at one end x 0 while the dendritic terminals lie at the other end x l.

Nerve and muscle were begun in the 1840 s by mat teucci professor of physics at pisa and by du bois. It can be verified that it is also equivalent to the total axial resistance for a cableoflength λ. Estimates are made by modeling dendrites and axons as cylinders composed of segments with capacitances and resistances combined in parallel see fig. Of cable λ long.

Equivalent cylinder model and 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. A detailed derivation of the passive cable equation. The transient response of passive cables to extracellular stimulation was studied by cartee and plonsey.