Biomedical Engineering Reference
In-Depth Information
10.3.2 CableTheory
As discussed in Chapter 3, the excitable membranes of certain cells have ion chan-
nels whose gating is typically voltage-dependent. The dynamic interactions between
these ionic channels play a dominant role in the function of the cell. To under-
stand the transmission of signals and changes in membrane potentials, a model
describing the electrical properties of the tissue is required. Compartmental models
of neurons furnish a means for simulating both the steady-state and the transient
electrical activity of a neuron. In the compartmental approach (Figure 10.9), the
neuron's volume is partitioned into a finite number of contiguous regions. There
could be separate compartments for the cell body, the axon hillock, and several
compartments for the axon and each of the dendrites. The membrane is assumed
to be a cylinder of uniform radius along its length, although this assumption is not
required if resistivities are used while developing the model. A cable model, similar
to electrical cables, is used to describe the transmission of signals. A cable is an
extended structure consisting of a conducting core bounded by a thin insulating
layer or membrane. A neuron is thought of as a cable with particular electrical char-
acteristics. It is often visualized as cylindrical, but the form of the cross section is not
(a)
(b)
(c)
Figure 10.9
Cable theory: (a) portion of an axon of a neuron, (b) portion of the axon devided into three
compartments, and (c) electrical equivalent circuit for each compartment.
