Figure P19

1.10. This problem simulates saltatory conduction on a section of myelinated nerve axon. The approach is to model the active nerve membrane at the nodes of Ranvier by a slightly modified set of HH equations (see Plonsey, 1969, Section 4.10). As was seen in Section 1.4, the original HH equations described the behavior of a 1-cm2 patch of (active) axon membrane. They were written and scaled so that time was in milliseconds, voltages were in millivolts, and current densities were in | amps/cm2. To obtain this curious scaling, the membrane capacitance is in mF/cm2, and all conduc-

tances are in mS/cm2. In addition, the depolarization voltage, v, used in the HH ODE goes negative for membrane depolarization and spiking (which it is accustomary to view as positive). From this viewpoint, the complete transmembrane voltage is given by Vm = (-v + Vmo). Vmo is the resting transmembrane potential, often taken as -70 mV. Between the nodes of Ranvier are 2-mm-long, myelin "beads," which respond passively to the voltages at the active nodes of Ranvier. This problem models the linear, distributed-parameter RCG transmission line formed by the myelin-covered axon by a five-internal-node, lumped-parameter RCG transmission line (TL) circuit, as shown in Figure P1.10A and B. Because the HH system operates with a millisecond timescale, the myelin transmission line sections must be given a similar timescale; thus, millifarads must be used for Cm. The Rs and Gs of the TL are not scaled to preserve millivolts everywhere in the linear circuit portions of the model.

Model parameters are taken from Plonsey (1969) and are based on measured data from Tasaki (1955, Am. J. Physiol. 181: 63). Beginning with the input HH (v0) node, one can use Kirchoffs current law to write the main HH ODE as

Myelin bead jhuzm

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