Quantitative Electrophysiology

Transcription

1 ECE 795: Quantitative Electrophysiology Notes for Lecture #10 Wednesday, November 22, 2006

2 14. FUNDAMENTALS OF FUNCTIONAL ELECTRICAL STIMULATION (FES) We will look at: Design issues for FES Subthreshold response to extracellular stimulation Suprathreshold response to extracellular stimulation Nerve excitation Recruitment 2

3 Design of functional electrical stimulation: In functional electrical stimulation (FES), nerve stimulation is achieved by passing current between two or more electrodes implanted in the body. In order for this system to produce functional nerve activation, the appropriate spatial and temporal patterns of stimulation must be determined for the desired stimulus response. This requires an understanding of both the stimulus properties and the resulting nerve response properties. 3

4 Design of FES (cont.): Stimulus design considerations include electrode properties such as: number and positions of electrodes, material, size, shape, and stimulating current properties such as: strength, and waveform. 4

5 Design of FES (cont.): A crucial point in understanding FES is the difference between intracellular and extracellular stimulation. (Rattay, Neurosci. 1999) 5

6 Subthreshold response to an external point current stimulus: Consider the source-fiber geometry shown to the right. 6

7 Subthreshold response to an external point current stimulus (cont.): The resulting extracellular field is: where I 0 is the current strength, σ e is the conductivity of the extracellular medium, and r is the distance from the source to an arbitrary field point. Note that the effect of the fiber on the field is typically ignored. 7

8 Subthreshold response to an external point current stimulus (cont.): Reformulating Eqn. (6.25) gives: where z now defines the axial (longitudinal) coordinate. The transmembrane current i m must also equal the intrinsic ionic plus capacitive current of the membrane. 8

9 Subthreshold response to an external point current stimulus (cont.): Replacing φ i by v m + φ e and i m by i ion + c m v m / t in Eqn. (7.71) gives: At rest, v m = 0 for all z 2 v m / z 2 = 0 and i ion = v m /r m = 0. Consequently, when the stimulus is first applied: 9

10 Subthreshold response to an external point current stimulus (cont.): Thus, the region where excitation is possible is where 2 φ e / z 2 is positive, because this will make v m / t initially positive. Conversely, regions where 2 φ e / z 2 is negative will hyperpolarize, because this will make v m / t initially negative. Consequently, the function 2 φ e / z 2 has been named the activating function. 10

11 Subthreshold response to an external point current stimulus (cont.): 11

12 Suprathreshold response to an external point stimulus: A space-clamped patch of membrane subjected to an external point stimulus has a threshold potential that is relatively independent of the stimulus duration. In contrast, a fiber has higher threshold potentials for shorter stimuli, an effect that is strongest when the source is very close to the fiber and grows weaker as the source is moved away from the fiber. 12

13 Suprathreshold response to an external point stimulus (cont.): 13

14 Suprathreshold response to an external point stimulus (cont.): 14

15 Suprathreshold response to an external point stimulus (cont.): 15

16 Suprathreshold response to an external point stimulus (cont.): The effect of stimulus duration and distance from the fiber on the threshold potential results from the hyperpolarized regions that flank the depolarized region. The membrane potential decay is accelerated by the flow of current from the depolarized region into the surrounding hyperpolarized regions. As the source is moved away from the fiber, the hyperpolarized regions move away from the depolarized region, diminishing the effect. 16

17 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). 17

18 Nerve excitation (cont.): Consider the linear-core-conductor model of a myelinated fiber being stimulated by a bipolar electrode pair (i.e., delivering equal and opposite current). 18

19 Nerve excitation (cont.): 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. 19

20 Nerve excitation (cont.): 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: Note that we wish to minimize the total charge delivered in order to avoid electrochemical reactions at the electrode-electrolyte interface. 20

21 Nerve excitation (cont.): Thus, short pulse durations are highly desirable based on this criterion. 21

22 Nerve excitation (cont.): Example stimulus waveform shapes: monophasic, biphasic, chopped, triphasic, and asymmetric, and parameters: pulse amplitude, pulse width, interphase gap, and pulse rate. (From Shepherd & Javel, Hear. Res. 1999) 22

23 Nerve excitation (cont.): The injected primary current pulse is designed to achieve nerve activation. The secondary pulse in a biphasic current waveform is introduced to mitigate a build up of charge at the electrode-tissue 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. 23

24 Nerve excitation (cont.): The effect of inter-phase delay on action potential generation is illustrated below. 24

25 Nerve excitation (cont.): Another important factor is the electrodefiber geometry. Consider stimulation of the peripheral nerve via a cuff electrode as shown below. 25

26 Nerve excitation (cont.): Modelling cuff-electrode stimulation using the equivalent circuit illustrated below gives rise to the activation pattern shown on the next slide. 26

27 Nerve excitation (cont.): 27

28 Nerve excitation (cont.): Stimulation using a surface electrode produces the activation pattern shown on the next slide if the neuron is normal to the surface. 28

29 Nerve excitation (cont.): 29

30 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. 30

31 Nerve excitation (cont.): 31

32 Nerve excitation (cont.): 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. 32

33 Nerve excitation (cont.): However, if the electrode is more distant from the fiber, or close to the soma or dendrites, then more complicated excitation patterns can result. (Rattay, IEEE Trans. Biomed. Eng. 1998) 33

34 Nerve excitation (cont.): (Rattay, IEEE Trans. Biomed. Eng. 1998) 34

35 Recruitment: Control of both the pulse width and the pulse rate can be utilized to affect which fibers are recruited. 35

36 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. 36

37 Recruitment (cont.): I th versus fiber diameter and electrode-fiber distance. 37

38 Recruitment (cont.): I th versus fiber diameter and pulse duration. 38

39 Recruitment (cont.): I th versus pulse duration for nerve and muscle. 39

40 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. 40

41 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. 41