How do you solve cable equations?
λ = r m r e + r i and τ = r m c m , where ri and re are the intracellular resistance (in Ω/cm) and extracellular resistance (in Ω/cm). The values rm and cm are the membrane resistance (in Ω/cm) and membrane capacitance (in F/cm), respectively.
What is wire theory?
Neuronal cable theory is a set of assumptions and results relating to the propagation and interaction of electrical signals in spatially extended nerve cells.
What is the purpose of cable theory?
Cable theory is concerned with how these inputs propagate to the soma or the axon initial segment, how these inputs interact with one another, and how the placement of an input on a dendritic tree affects its functional importance to the neuron.
What is cable theory of nerve conduction?
On the basis of this equivalent circuit model, the conduction of the nerve is often described by using a theory in which the conduction is regarded as an electric current on imaginary electric longitudinal leads running inside and outside the axon membrane, known as a cable theory (Koch, 1984).
What are cable properties?
– properties of the nerve; axon, cell body and dendrite that affect distance and speed of a membrane potential. – passive conduction properties are called cable because they are analogous to properties of long copper telecommunication cables (before satellites)
Who Discovered cable theory?
William Thompson (Lord Kelvin) developed cable theory in the 1850s as a way to model the decay of signals along underwater telegraph cables. Hodgkin and Rushton applied it to passive conduction along axons (Hodgkin and Rushton, 1946).
What is the function of wire?
Wires are used to bear mechanical loads or electricity and telecommunications signals. Wire is commonly formed by drawing the metal through a hole in a die or draw plate. Wire gauges come in various standard sizes, as expressed in terms of a gauge number.
What is cable constant?
Impedance – Cable constants calculation is an easy-to-use tool for positive and zero sequence impedance calculations. It uses the user-friendly graphical interface of the cable editor and the complete ETAP cable library.
What is cable type?
The following sections discuss the types of cables used in networks and other related topics. Unshielded Twisted Pair (UTP) Cable. Shielded Twisted Pair (STP) Cable. Coaxial Cable. Fiber Optic Cable.
What is the equation for neuronal cable theory?
The mathematical centerpiece of neuronal cable theory is the cable equation: ∂ V ∂ T = ∂ 2 V ∂ X 2 − V This differential equation describes the change in voltage along a cable in both time and space, where X and T are dimensionless variables ( X = x / λ and T = t / τ ).
How is the current calculated in cable theory?
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.
Where did the idea of cable theory come from?
History. Cable theory in computational neuroscience has roots leading back to the 1850s, when Professor William Thomson (later known as Lord Kelvin) began developing mathematical models of signal decay in submarine (underwater) telegraphic cables. The models resembled the partial differential equations used by Fourier to describe heat…
Which is the first version of a cable equation?
Combining equations ( 6) and ( 11) gives a first version of a cable equation: which is a second-order partial differential equation (PDE). . The following sections focus on these terms. (lambda), is a parameter that indicates how far a stationary current will influence the voltage along the cable.