Stochastic Modulation of Stimulation Signals to Counter Fatigue in Ambulation Via FES

Abstract

This paper proposes a possible design of stimulation signals for use in both transcutaneous and implanted FES systems where the inter-pulse interval is stochastically modulated around a best-selected interval (namely, around a desired mean pulse repetition frequency). The motivation for this proposed stochastic modulation of pulse intervals is based on physiological observations of intervals between action potentials and on theoretical results from vibrational control theory that concern the stabilizing effects of stochastic modulation in nonlinear systems Preliminary test results obtained in approximately 200 blind tests on a complete thoracic level paraplegic patient are reported. These results point to the possibility that adequate stochastic modulation of pulse intervals may meaningfully postpone the onset of muscle fatigue. Certainly, many more tests are still needed.

1. Introduction

It is well known in nonlinear control theory that stochastic modulation of control signals increases the range of stability (the limit cycle) of the system under control (cf. work on Vibrational Control and stabilizaability

of nonlinear systems,, by Richard Bellman, et al., 1986 [1], and more specifically, on stochastic modulation on the basis of stochastic calculus and of the Wong-Zakai equation (see: Meerkov, Runolfsson and Schuss, [2]).

Since neuromuscular control is certainly a nonlinear control problem, it makes sense to assume that the evolution of the neuromuscular control would attempt to maximize the stability of the neuromuscular system. Indeed, measurements of trains of action potentials in natural physiological single fibers (in cases of an intact spinal cord) indicate [3] that these trains of pulses are not exactly equally-spaced in time and that some stochastic modulation of the spacing between the action potentials exists (in the order of 5 to 15 percent around the mean, when measured visually in Figure 11 of page 24 of [3]). The probability distributions and the modulation rates (of a few percent) can be easily computed.

The above considerations led this author to study the effect of applying such stochastic modulation to FES stimulation signals [4] in the PARASTEP-I FES ambulation system that had been developed by him earlier (presently manufactured by Sigmedics Inc., Dayton, OH, USA), while keeping all average parameters of these signal exactly as in the FDA-approved PARASTEP-I system [5].

2. Method

The testing was done in about 200 hundred runs on one FES-trained volunteer who is a complete T-7 traumatic paraplegic. Time-to-fatigue was measured in doubly blind tests, for leg extension while the patient was seated, comparing unmodulated and stochastically modulated stimuli through switching of algorithms in the PARASTEP System. Stimuli levels were kept unchanged in all tests, as were signal (level-) means and all other FES parameters. Also, the seating position was kept unchanged from test to test and the same shoes were always worn by the patient (to avoid effects of varying shoe-weight). To measure rate of onset of muscle fatigue, the time was measured from the switching on of the stimulation (to a same constant level), to the time when the heel first touched the floor.

The tests were varied daily at random between three stochastic modulation menus that were never disclosed to the patient or to the tester who took the measurements. The modulation menus were:

(1). No stochastic modulation (0% modulation).

(2.) +/-5% random modulation.

(3) +/-10% random modulation.

(4) +/-20% random modulation.

The random modulation considered was taken from a uniformly-distributed white noise generator, and applied around a mean of 42 milliseconds inter-pulse interval throughout the tests.. The modulation was applied on a DSP chip that was incorporated with a standard PARASTEP-I stimulation system. A different DSP chip was programmed for each modulation rate and was changed (unknown and inaccessible to the patient and to the tester) on every day of testing, to avoid biasing of test results. Three tests were performed each day, starting at the same time of day and with a 15 minutes interval between these three tests.

3. Test Results

The results, that we present below are certainly only preliminary and must be considered as such, since they involved only one patient. These results, which we hope to repeat on further patients, indicated that time from stimulation onset to fatigue (to when the stimulated leg hit the floor) increased with stochastic modulation by an average of 36.63%, in a statistically significant manner, for the case of a +/-5% stochastic modulation, as compared with no modulation. At other modulation rates, the time-to-fatigue was consistently shorter, as shown in Table 1.

TABLE 1:

Leg-Extension Time versus Modulation Rate

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Menu: 42+/-0% 42+/-5% 42+/-10% 42+/-20%

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Av.

Extension 82.22 112.33 97.42 94.78

time(sec)

standard

deviation 11.43 18.06 16.8 13.2

(sec)

95%

confidence 8.8 11.45 10.7 10.2

rate (+/-sec)

4. Conclusions

Obviously, our results, though statistically significant for a single patient (as measured by the statistical t-test), must be taken as strictly preliminary. Still, this preliminary set of results and the control-theoretical and physiological observations motivations behind it, do call, in the author’s opinion, to further testing, not only for paraplegics with regards to ambulation, but for all other situations where functional electrical stimulation is employed and where muscle fatigue may be a factor.

If confirmed by further tests, stochastic modulation, even if at different modulation rates for different FES situations, may provide a simple way (algorithmic only) to reduce rate of muscle fatigue at the stimulation sites. We note that the mean rates need not be changed. Hence mean parameters, such as mean electric charge applied at a stimulation site are unchanged, as may be significant in case of approvals by FDA or by similar agencies.

References

[1]. Richard Bellman, Joseph Bentsman and Semyon M. Meerkov, “Vibrational Control of Nonlinear Systems: Vibrational Stabilizability”, IEEE Trans. Automatic Control, AC-31, 1986.

[2] S.M. Meerkov, T. Runolfsson and Z. Schuss, “Correlation Free Forms for Nonlinear Stochastic Systems”, J. Mathemat. Analysis and Appl., 139, pp. 483-493, 1989.

[3]. Eric Stalberg and Joze V,. Trontelj, Single Fiber Action Electromyography, Mirvalle Press, Old Woking, Surrey, U.K., 1979.

[4]. D. Graupe, P. Suliga, C. Prudian and K.H. Kohn, “Stochastically-Modulated Stimulation to Slow Down Muscle Fatigue at Stimulated Sites in Paraplegics Using Functional Electrical Stimulation for Leg Extension”, Neurological Research, 22, pp. 703-704, 2000.

[5]. Daniel Graupe and Kate H. Kohn, Functional Electrical Stimulation for Ambulation by Paraplegics, Krieger Publishing Co., Malabar, FL, 1994.