The Peripheral Neuropathy Solution
A morphological adaptation of vertebrates that increases the spike propagation velocity on their axons is myelinization. An electron micrograph of the cross section of a myelinated axon is shown in Figure 1.2-5 (from a rat sciatic nerve, x 52,000). Where the axon is wrapped in the myelin "tape," two important changes occur in the cable parameters. Because of the insulation of multiple, close-packed layers of UM, gm decreases, perhaps by a factor of 1/64. Because of the effective thickening of the axon wall, Cm and cm decrease by a factor of about 1/20. Thus, the effective space constant of the covered axon increases by about eight-fold, and the passive velocity of propagation, which is proportional to (ri cm)-1, increases by about 20-fold. Once a spike has been initiated at the SGL, it propagates down the axon to the first myelin "bead." There it propagates electrotonically because the myelin blocks the high JNa and JK required for conventional regenerative propagation. Because of the increased space constant, there is little attenuation along the myelin bead, and the velocity of the electrotonic spread is higher than the conduction velocity on the unmyelinated axon. The nodes of Ranvier between the myelin beads on the axon allow the propagating spike to regenerate to its full height. At the nodes, conventional voltage-gated ion channels in the membrane can carry the normal ion currents required for the action potential. The process of fast electrotonic spread followed
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FIGURE 1.2-3 Plots of the axon transmembrane potential, Vm(t), the sodium ion conductance, gNa(t), and the transmembrane potassium conductance, gK(t), all measured at point xo on the axon. Note the rapid drop in gNa after Vm(t) reaches its peak. A plot of this type is easily obtained from a simulation of the HH (1952) model equations for a nerve action potential.
FIGURE 1.2-3 Plots of the axon transmembrane potential, Vm(t), the sodium ion conductance, gNa(t), and the transmembrane potassium conductance, gK(t), all measured at point xo on the axon. Note the rapid drop in gNa after Vm(t) reaches its peak. A plot of this type is easily obtained from a simulation of the HH (1952) model equations for a nerve action potential.
by regeneration at each node is called saltatory conduction. The term saltatory is used because early neurophysiologists visualized the velocity of propagation speeding up at the nodes of Ranvier, then slowing down along each myelin-covered stretch of axon. This view is misleading, because the nodes are only about 0.002 mm in length, and serve to regenerate the spike height to make up for the passive attenuation that occurs in the electrotonic phase of propagation under the 1 to 2 mm myelin beads. It appears that the spike velocity is essentially constant, and above the velocity of the same axon without myelin because of the greatly reduced cm. In 1949, Huxlely and Stampfli (reported in Plonsey, 1969) measured saltatory conduction times on a myelinated axon: They found the internodal propagation time to be 0.02 ms, and the propagation time along a myelin bead to be 0.1 ms. If one assumes the node is 0.002 mm wide, then the nodal velocity is 0.1 mm/ms and the electrotonic velocity is 1 mm/0.1 s = 10 mm/ms. Thus, their myelinated axon conducted at slightly over 10 m/s, and the ratio of electrotonic velocity to regenerative velocity is about 100:1. There is a huge survival advantage for myelinization.
A myelinated axon also has a metabolic advantage over a bare axon of the same diameter. Far less total Na+ enters and K+ leaves the axon at the nodes than would over the same length of bare axon conducting a spike. Thus, less metabolic energy in the form of ATP is required to drive the ion pumps that maintain the steady-state ion concentrations in the axon axoplasm.
The analytical differential equation model of Fitzhugh (1962) for saltatory conduction on a myelinated axon has been described by Plonsey (1969), sec. 4.10. Fitzhugh used the continuous partial differential equation derived from the lumped parameter, per unit length RC transmission line to model electrotonic conduction under the myelin beads, and he used the Hodgkin-Huxley, regenerative model for spike generation to simulate what happens to vm at the nodes of Ranvier. The electrotonic differential equation (DE) used was
FIGURE 1.2-5 Electron micrograph of the cross section of a myelinated nerve axon. A living glial (Schwann) cell wraps itself around a peripheral nerve axon much like one would wrap electrical tape around a bare wire. The myelin wrapping has two major effects: It speeds the conduction of the nerve action potential and it mechanically protects and insulates the axon. (From University of Delaware, Mammalian Histology B408 Web site www.udel.edu/Biology/Wags/histopage/histopage.htm.)
FIGURE 1.2-5 Electron micrograph of the cross section of a myelinated nerve axon. A living glial (Schwann) cell wraps itself around a peripheral nerve axon much like one would wrap electrical tape around a bare wire. The myelin wrapping has two major effects: It speeds the conduction of the nerve action potential and it mechanically protects and insulates the axon. (From University of Delaware, Mammalian Histology B408 Web site www.udel.edu/Biology/Wags/histopage/histopage.htm.)
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(See Section 1.4.1 for the Hodgkin-Huxley equations.) Some seven or eight nodes were modeled. The parameters used were cm (myelinated axon) = 1.6 pF/mm, ri = 15 x 106 ohm s/mm, gm = 3.45 x 10-9 S/mm, the area of the node was 0.003 mm2, the capacitance of the node was 1.5 pF. Figure 1.2-6 illustrates a three-dimensional plot of the calculated transmembrane potential distribution at various times along a myelinated axon having an area of 0.003 mm2, and nodes every 2 mm (at the vertical lines). A 10 |is, 30 mA pulse was given at t = 0, x = 0. Note that the peak of the traveling wave has reached x = 10 mm in 1.32 ms, giving an approximate conduction velocity of v = 7.58 m/s to the right.
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