Abstract¾The focus of this paper is a new look at fatigue phenomena, and characterization of the relationship between the variation of the Evoked EMG (EEMG) and the variation of muscle force during prolonged electrical stimulation of paralyzed muscle using stimulation patterns corresponding to neural prosthesis operation. Experiments were conducted on paraplegic subjects with the lower limb vastus-lateralis muscle stimulated via percutaneous intramuscular electrodes under isometric conditions. An "artifact balancing" technique was used for recording the EEMG and overcoming the stimulus artifact. To characterize the changes of the muscle behavior during prolonged periodic ramp-hold stimulation, we fit hyperbolic functions to the EEMG and the torque. It is observed that functions' dead-zone regions increase with time, indicating decreasing excitability and contractibility. The changes in the dead-zone region of the torque responses closely track the changes in the corresponding EEMG responses with a delay. In addition, the time constant of the EEMG responses closely matches the changes in the torque responses. In this work, we also developed a calibration procedure that enables us to predict the torque from EEMG during prolonged ramp-hold stimulation with an average mean prediction error of about 6%.
Keywords: Functional Neuromuscular Stimulation, Muscle
Fatigue, Time-Frequency Representation.
1. Introduction
An understanding of fatigue phenomena in electrically stimulated muscle is still illusive and an important pre-requisite for the development of improved “neural prostheses” using Functional Neuromuscular Stimulation (FNS). Many investigators have attempted to quantify the muscle fatigue during voluntary and electrically elicited contraction [1]. Some have used the spectral and time-domain variables of EMG signal as indices of muscle fatigue [2-5]. Other researchers have modeled the decrease of force or torque over time by an exponential [6] or hyperbolic tangent [7], and used regression-based parameters as muscle fatigue indices. In spite of the body of work in the literature regarding fatigue phenomena during voluntary and electrically induced muscle contraction, the problem of fatigue detection in real-time has not been studied. The time-domain and spectral variables of the EEMG exhibit some variation during sustained electrical stimulation, but these variations are not repeatable. The relationships between changes in the variables of the EEMG and measured decrease of muscle force have not been adequately characterized.
In this work, we present new aspects of the fatigue process when the lower limb vastus-lateralis muscle in paraplegic subjects is stimulated via percutaneous intramuscular electrodes to provide selective stimulation. We will show that the EEMG signals contain substantial information about the fatigue condition of the muscle, if properly collected, processed and analyzed.
2. Experimental Procedure
Experiments were conducted on two complete-level-T7 spinal cord injury paraplegics. Percutaneous intramuscular electrodes were implanted near the motor points of the major lower limbs as described in [8] During the experiments reported here, only the lower limb vastus lateralis muscle was stimulated, by activating the corresponding intramuscular electrode. The muscle was stimulated using pulse-width modulation at a constant frequency (20 Hz) and constant amplitude (10 mA), under isometric conditions. The knee of the test leg was fixed securely in 30o of flexion (where full extension is 0o).
Isometric
knee torque was measured using a Cybex II dynamometer.
Measured values of the knee torque were low-pass filtered (cut-off frequency
100 Hz), and sampled at 1200 Hz. EEMG data were collected by a differential
amplifier with a common mode rejection ratio of 120 dB and bandwidth of 250 kHz
and then sampled at a rate of 1200 Hz.
3. Exponential Time-Frequency Distribution of EEMG During Prolonged Electrical Stimulation
Analysis using the Exponential Distribution (ED) of Choi and Williams [9] overcomes many of the limitations of the Short-Time Fourier Transform, providing high resolution in both time and frequency while reducing the cross component amplitudes [9]. The ED for a discrete-time signal is defined as follows [9]:
where 
represents the complex conjugate. The cross terms can be
controlled by the parameter 
. A small value of reduces the effects of
cross terms. On the other hand, the frequency resolution also depends on .
(a)
(b)
Fig. 1: Exponential time-frequency representation of the EEMG during sustained
electrical stimulation of paralyzed muscle where the value of has been set to 0.1
(a) and 1.0 (b).
A large value of will leads to have a
sharp autoterm resolution. Thus, the parameter trades off autoterm resolution for cross-term suppression.
Fig.
1(a) shows the Exponential
time-frequency distribution (ED) of the EEMG during prolonged constant
electrical stimulation of paralyzed muscle. where a 120-point rectangular
window has been used and the value of has been set to 0.1.
The most interesting result is that the power of EEMG is concentrated in the
frequency of the stimulation signal and its first harmonic. In addition, as
muscle becomes more fatigued, frequency components appear which are not the
harmonics of stimulation frequency. Fig.
1(b) shows the same information as in Fig.
1(a) when the parameter has the value 1.0. It
is clearly observed that a peak component appears at 
due to interference of
the signal components with increasing values of . As expected, the distribution oscillates in the direction
of the time axis. The amplitude of oscillation depends on and the signal
structure.
4. Fatigue Estimation During Prolonged Electrical
Stimulation
Fig. 2(a) and (b) shows the measured EEMG and the knee torque during prolonged constant electrical stimulation of paralyzed muscle. We will associate excitation fatigue with changes in the envelope of the measured EEMG, and contraction fatigue with changes in the measured torque. The greatest discrepancy between the measured EEMG and measured torque is during potentiation. The measured EEMG changes track the knee torque reduction well during fatigued and maximally fatigued conditions. The variability of the EEMG is more than that of the torque, and that the contraction process behaves as low pass filtering of the EEMG.
In order to
extract the DC gain of the EEMG, and of the torque, and thus to observe the
relationship between excitation and contraction fatigue, we filter both
signals by a first order elliptic lowpass
filter [10] with a cutoff frequency of 
Hz, and then smooth
the filtered values by a moving average
filter with order 10. Fig. 2(b) shows the processed values of
EEMG and knee torque. Note that the variations of DC gain of the EEMG match the
torque.
The correlation coefficient was used to measure the linear correlation between the excitation fatigue (measured EEMG) and contraction fatigue (measured torque). It was found that the average of the correlation coefficient for different day experiments has the value 0.9610.
The results show that the processed EEMG would be able to track the muscle force with mean prediction error of 6%.
Fig 2. Torque prediction during prolonged constant
electrical stimulation of paralyzed muscle using the measured EEMG: measured
Evoked EMG (a), measured torque (b), predicted torque (c).
5. Prediction of Incipient Fatigue During Ramp-Hold Stimulation
Fig. 4(a) shows the measured knee torque and the lower envelope of EEMG during a typical periodic ramp-and-hold stimulation (period=10 s, ramp=4 s, hold=6 s). It is observed that that the EEMG does not track the long time variations of the torque during this ramp-hold stimulation pattern. In order to characterize changes of the muscle behavior during prolonged periodic ramp-hold electrical stimulation, we fit hyperbolic functions with four parameters to the EEMG and the knee torque which are measured during each period of ramp-hold stimulation.
where 
is the nth muscle response (EEMG or knee
torque) to the ramp-hold stimulation. The reciprocal of 
represents the time
constant, the product 
denotes the slope and
describes how fast the torque or EEMG increases. The 
represents the
dead-zone region and explains the level of excitability and contractibility.
Finally 
term is used to fit
any offset in the output. For estimating the parameters, we used the Levenberg-Marquard method [11].
Fig. 3(a)-(c) show the evolution of the dead-zone
region, time-constant, and slope, respectively. We observe that the increases with time,
indicating increasing the dead-zone regions, and therefore, decreasing the
excitability and contractibility. Changes in the dead-zone region of the torque
responses appear to closely track the changes in the EEMG, but with a delay. It
is observed that the time constant of the EEMG responses closely track the
changes in the measured torque.
(a)
(b)
(c)
Fig. 3. Parameters of the fitted curves to the measured EEMG (solid) and to the knee torque (dot): (a) time constant; (b) dead-zone; (c) slope.
The
slope of the ramp response does not change during prolonged ramp-hold
stimulation. These observations suggest that the torque decreases
proportionally to decreases in contractibility. To estimate the torque response
using the EEMG, we define the calibration factor
