Cellular Bioelectricity

Transcription

1 ELEC ENG 3BB3: Cellular Bioelectricity Notes for Lecture #30 Thursday, March 30, 2006

2 Nerve excitation: To evaluate the pattern of nerve activation that is produced by a particular electrode configuration, we must consider: the geometry of the electrode(s) and nerve fibers, the conductivities of the medium in which the electrode(s) and nerve fibers lie, and the properties of the nerve fiber membrane, either subthreshold (i.e., linear) or suprathreshold (i.e., nonlinear). 2

3 Consider the linear-core-conductor model of a myelinated fiber being stimulated by a bipolar electrode pair (i.e., delivering equal and opposite current). 3

4 For this configuration, excitation will occur below the cathode if the stimulating current is large enough. The strength-duration behaviour can be described as: where I R is the rheobase current and K is an experimentally-determined constant that depends on the electrode geometry, medium conductivities, etc., as well as the membrane properties. 4

5 A result of this strength-duration behaviour is that charge is wasted in stimulating a nerve fiber if the duration of the pulse is much larger than the chronaxie, which is defined in this case as: Recall that we wish to minimize the total charge delivered in order to avoid electrochemical reactions at the electrode-electrolyte interface. 5

6 Thus, short pulse durations are highly desirable based on this criterion. 6

7 The injected primary current pulse is designed to achieve nerve activation. The secondary pulse in a biphasic current waveform is introduced solely to achieve reversibility in the electrode-electrolyte interface. However, this secondary pulse will be hyperpolarizing, and consequently it may suppress action potential generation. Adding an inter-phase delay can avoid this problem. 7

8 The effect of inter-phase delay on action potential generation is illustrated below. 8

9 When modelling the response of myelinated fibers, it may be sufficient to just included active (nonlinear) membrane properties in the node closest to the electrode. 9

10 Another important factor is the electrodefiber geometry. Consider stimulation of the peripheral nerve via a cuff electrode as shown below. 10

11 Modelling cuff-electrode stimulation using the equivalent circuit illustrated below gives rise to the activation pattern shown on the next slide. 11

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13 Stimulation using a surface electrode produces the activation pattern shown on the next slide if the neuron is normal to the surface. 13

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15 Nerve excitation (cont.): In contrast, the activation pattern is quite different if the electrode is adjacent to the fiber. In this case, the flanking hyperpolarized regions may block action potential generation. 15

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17 Recruitment: Control of both the pulse width and the pulse rate can be utilized to affect which fibers are recruited. 17

18 Recruitment (cont.): In myelinated nerve, the fiber diameter d can have a strong effect on the threshold current I th. The diameter has a direct effect through the axoplasmic resistance per unit length r i. An indirect effect of the diameter results from the fact that the internodal segment length (i.e., the distance between nodes of Ranvier) is proportional to the fiber diameter. 18

19 Recruitment (cont.): I th versus fiber diameter and electrode-fiber distance. 19

20 Recruitment (cont.): I th versus fiber diameter and pulse duration. 20

21 Recruitment (cont.): I th versus pulse duration for nerve and muscle. 21

22 Recruitment (cont.): Considering the results of the simulations and experimental data shown in the previous three slides, large diameter fibers tend to be recruited before small diameter fibers. However, under physiological conditions for motor units, small diameter fibers innervating slow oxidative (SO) muscle fibers tend to be recruited before larger diameter fibers innervating fast glycolytic (FG) muscle fibers. Thus, the natural order of recruitment is reversed in FES. 22

23 Recruitment (cont.): One approach to combat this recruitment-order problem is to utilize two electrodes. The first electrode supplies a large depolarizing current that excites fibers with a large range of diameters. The second electrode supplies a small hyperpolarizing current that prevents action potential propagation on the large diameter fibers excited by the first electrode. The hyperpolarizing pulse must be designed with a ramp that prevents anode-break excitation. 23