During volitional muscle activation, motor units often fire with varying discharge patterns that include brief, high-frequency bursts of activity. These variations in the activation rate allow the central nervous system to precisely control the forces produced by the muscle. The present study explores how varying the instantaneous frequency of stimulation pulses within a train affects nonisometric muscle performance. The peak excursion produced in response to each stimulation train was considered as the primary measure of muscle performance. The results showed that at each frequency tested between 10 and 50 Hz, variable-frequency trains that took advantage of the catchlike property of skeletal muscle produced greater excursions than constant-frequency trains. In addition, variable-frequency trains that could achieve targeted trajectories with fewer pulses than constant-frequency trains were identified. These findings suggest that similar to voluntary muscle activation patterns, varying the instantaneous frequency within a train of pulses can be used to improve muscle performance during functional electrical stimulation.
- nonisometric contractions
- mathematical modeling
functional electrical stimulation (FES) is the coordinated electrical excitation of paralyzed or weak muscles in patients with upper motoneuron injuries to produce purposeful movements (1, 18, 21, 25). Functional activities often demand precisely controlled contractions of the muscle being activated. Achieving such performance during FES applications is often limited by the nonlinear relationship between muscle output and stimulation train input (28), person to person variability in muscle contractile characteristics (18), and other factors such as muscle fatigue, voluntary or involuntary activation of the muscle, and coupling between limb segments (28).
During volitional activation of muscle, motor units often fire with varying discharge patterns that include brief, high-frequency bursts of activity [in humans (2, 22, 23, 32); in rats (16)]. These variations in the activation rate may allow the central nervous system (CNS) to take advantage of the catchlike property of skeletal muscle (7), which is the tension enhancement produced when a brief high-frequency burst of pulses (2–4 pulses) is used within a subtetanic constant-frequency train to activate the muscle (3–5, 7). More recent work on the catchlike property of skeletal muscle concluded that the force augmentation in nonfatigued mammalian muscle in response to variable-frequency trains depended on the characteristics of the initial high-frequency burst and the frequency of the subsequent portion of the stimulation train (5). Work done by Garland and Griffin (15) showed that doublets, or a closely spaced pair of stimulation pulses, occur naturally when the CNS activates skeletal muscle and may act to augment both the rate and amount of force production. These results show that the conventional constant-frequency stimulation used during FES may not be similar to voluntary muscle activation and so may not be optimal for activating skeletal muscle.
During FES, pulses are grouped together to form trains lasting from tenths of a second to several seconds. If the pulses within a train are separated by regular interpulse intervals, a particular pulse rate or frequency can be assigned to the train. Trains that contain only one frequency are constant-frequency trains (CFTs); trains with more than one instantaneous frequency within the train are variable-frequency trains (VFTs). Catchlike-inducing trains (CITs) are VFTs that begin with a high-frequency burst of two to four pulses to take advantage of the force augmentation due to the catchlike property of skeletal muscle. Another type of VFT is a doublet-frequency train (DFT), which contains doublets (2 pulses separated by <10 ms) separated by longer interpulse intervals (see Fig. 1).
Dynamic contractions are an important component of normal movement and often occur in response to FES. Few studies have investigated the relationship between activation frequency and the dynamic performance of human skeletal muscle in response to stimulation trains with different patterns (17, 19, 20, 30). These nonisometric studies investigated either constant velocity (isovelocity) or constant load (isotonic) constrained motions. The purpose of the first part of the present study was, therefore, to explore the effect of CFTs, CITs, and DFTs on unconstrained nonisometric contractions, where the limb is free to move in response to electrical stimulation. For this study we hypothesize that CITs and DFTs will produce greater excursion than CFTs for the same mean frequency. In addition, because Mela and colleagues (24) suggested that a reduction in the number of pulses could help decrease the energy expenditure both at the neuromuscular junction and during calcium cycling, the goal of the second part of the present study was to identify stimulation patterns that minimized the number of pulses needed to produce a targeted trajectory. For the second study, we hypothesize that the identified stimulation patterns will be VFTs that contain fewer pulses than the CFTs used to generate the targeted trajectories. Conclusions of the present study are particularly relevant in the design of FES systems used to control functional (unconstrained) movements, such as during the swing phase of gait.
MATERIALS AND METHODS
The materials and methods and results sections are divided into two parts. Part 1 explores the effects of stimulation pattern on the dynamic performance-stimulation frequency relationship. Part 2 identifies stimulation patterns that minimize the number of pulses required to produce a targeted trajectory.
Eleven healthy subjects (3 women, 8 men) ranging in age from 18 to 35 yr voluntarily participated in this study. All subjects signed informed consent forms approved by the Human Subjects Review Board of University of Delaware.
Part 1: Exploring the Effects of Stimulation Pattern on the Dynamic Performance—Stimulation Frequency Relationship
Apparatus and setup.
Ten subjects each participated in one testing session for this portion of the study. Subjects were seated on a computer-controlled dynamometer (KinCom II 500-11, Chattecx, Chattanooga, TN) with hips flexed to ∼85°. Two self-adhesive electrodes (Versa-Stim, 76 mm × 127 mm, CONMED) were used to stimulate the muscle. The anode was placed proximally over the motor point of the rectus femoris (quadriceps femoris muscle). The cathode was placed distally over the vastus medialis motor point with the knee at 15° of flexion to compensate for skin movement during knee extension. A Grass S8800 stimulator with a SIU8T stimulus isolation unit was used for stimulation (Grass Instruments, West Warwick, RI). The stimulator was driven by a personal computer that controlled the timing parameters of each stimulation protocol. Force and angle data were digitized at 200 Hz and stored for subsequent analysis.
The testing session consisted of an isometric component and a nonisometric component. The isometric testing involved the determination of the stimulation amplitude for the study. The subsequent nonisometric testing involved the collection of data relevant to the relationships investigated in this study.
For the isometric component, the dynamometer axis was aligned with the knee joint axis. The force transducer pad was positioned anteriorly against the tibia ∼4 cm proximal to the lateral malleolus. The subjects then performed a maximum voluntary isometric contraction (MVIC) of the quadriceps femoris muscle group with the knee positioned at 90° of flexion. The burst-superimposition technique was used to ensure that a maximal contraction (i.e., ≥95% of the electrically elicited force) was being performed (31). Next, with the knee at 90° of flexion, the stimulation amplitude was set to activate ∼20% of the muscles' MVIC using a 300-ms-long 100-Hz stimulation train. A 20% force level was used because this force level was well tolerated by all the subjects, the forces produced at this level were easily measurable, and this force level was well within the range of commonly used daily activities (12). Once the amplitude was set, it was held constant for the remainder of the session. The pulse duration was fixed at 600 μs throughout this study.
After the stimulation intensity was set, nonisometric data were collected. The dynamometer arm was replaced by a custom-built arm that provided minimal resistance to movement and measured the knee joint angle in response to electrical stimulation. A load of 4.54 kg was wrapped just above the subjects' ankle joint (27). A load of 4.54 kg was selected because a previous study from our laboratory (27) showed that this load allowed measurable excursions (i.e., 0°> and <90°) to be produced by all subjects tested. Eleven trains (770-ms train duration, 14-Hz frequency) were delivered with a 5-s rest time between trains to potentiate the muscle (11). Next, the muscle was stimulated with 300-ms trains with frequencies ranging from 10 to 133 Hz to describe the excursion-frequency relationship for each of the patterns tested (CFT, CIT, and DFT). Each CIT tested began with a pair of pulses (doublet) with an interpulse interval of 5 ms; the DFTs contained doublets (IPI of 5 ms) that were equally spaced throughout the train (Fig. 1). A train duration of 300 ms was chosen because it was similar to the activation pattern of the quadriceps femoris muscle during normal walking (26). As the train duration was strictly controlled (300 ms), the mean frequencies used for plotting the excursion-frequency relationships for each pattern were not the same. In all, 25 trains were tested as part of the present study (Table 1). The choice of which train characteristics to test was based on minimizing the total number of trains to avoid fatigue while still adequately representing a wide range of frequencies and patterns. The trains were delivered in a random sequence and then repeated in reverse order with only one train being delivered every 10 s to minimize muscle fatigue. We believe that the data collected in response to each stimulation train were due to direct electrical activation of the motor nerve to the muscles and not due to reflex or voluntary responses because all subjects were able-bodied and were trained to relax; all contractions were shortening and therefore should not have elicited a stretch reflex; and the modeling results, which did not account for reflex responses, predicted the measured data accurately. However, a small portion of the force responses may have been caused by the reflex activation of the motoneurons due to the recruitment of IA sensory fibers during the stimulation (8).
The peak excursion produced in response to each stimulation train was employed as the muscle performance measure. The excursion-frequency relationship for 300-ms CFTs, CITs, and DFTs for all frequencies tested were plotted for each subject. The individual excursion-frequency relationships for each pattern tested were curve fit with a two-parameter exponential equation of the form: (1) where E is the measured peak excursion (degrees), Ep is a scaling factor (degrees), f is the stimulation frequency (Hz), and fp is characteristic frequency over which the excursion changes in response to frequency changes (Hz). R2 values were calculated to determine how well Eq. 1 fit the individual excursion-frequency relationship data. Because the trains tested were 300 ms in duration, the frequencies used to test the DFTs were not the same as those used to test the CFTs and CITs. Equation 1 represented the excursion-frequency relationships with average R2 values of 0.98, 0.96, and 0.94 for CFTs, CITs, and DFTs, respectively. We used Eq. 1 to interpolate the excursion produced by the DFTs for frequencies from 20 to 100 Hz at which the CFTs and CITs had been tested for each subject (see results). One-way repeated measures ANOVAs were used to determine the effect of stimulation pattern (CFTs, CITs, and DFTs) on the excursion produced at each of these frequencies (20–100 Hz). Statistical significance was set at P ≤ 0.05.
Part 2: Identification of Stimulation Patterns that Minimize the Number of Pulses Required to Produce a Targeted Trajectory
Because the stimulation pattern was shown to affect dynamic muscle performance (see results for Part 1), we attempted to identify pulse patterns that minimized the number of pulses needed to produce specific movement trajectories. A force and motion (F-M) mathematical model recently developed in our laboratory was used to assist in this identification (27). Specifically, we used our F-M model to predict stimulation patterns that used the fewest number of pulses to produce trajectories identical to those produced by 10-, 14-, 20-, and 50-Hz CFTs.
Three subjects were tested in this part of the study to identify the examples of pulse patterns that may be used to minimize the number of pulses needed to produce a specific motion trajectory. The experimental arrangements were similar to that described previously (27). For each subject, the data were collected over two testing sessions. The first session consisted of two phases. In the first phase, testing was done to calculate the values of the model parameters. Testing was first performed isometrically at angles of 15, 40, 65, and 90°. Then, isovelocity testing was performed while the dynamometer arm moved the leg at a shortening speed of 200°/s. The leg motion was initiated at 110° of knee flexion and stimulation began when the leg reached 90° of knee flexion and was terminated at 15° of knee flexion. Finally, nonisometric tests were performed with a weight of 4.54 kg wrapped just above the ankle joint (27). Only two trains (1-s-long 50-Hz CFT and a 20-Hz DFT) were tested at each condition to parameterize the model. For the isometric and isovelocity contractions, the force, velocity, and angle data were collected using a computer-controlled dynamometer. For the nonisometric data, the dynamometer arm was replaced by a low-friction, custom-built arm that measured knee joint angle and allowed the leg to move with minimal resistance.
In the second phase of the first testing session, targeted knee extension trajectories were obtained that could then be fit by the F-M model to generate optimized stimulation patterns that could achieve the targeted trajectories. These targeted trajectories were obtained in response to 10-, 14-, 20-, and 50-Hz CFTs. The 10-Hz train had 11 pulses, whereas the remaining trains had 15 pulses each. Fittings were done using a global sampling optimization algorithm called DIRECT (DIviding RECTangles), which was a modification of the Lipschitz optimization (13). The DIRECT algorithm was modified to allow integer optimization of the IPIs in steps of 5 ms up to a maximum IPI of 100 ms. The targeted trajectories were fit with a range of number of pulses. The stimulation pattern with the fewest pulses that gave a root mean square angular error (RMSE) of <2° was chosen as the predicted pattern.
The second testing session was conducted ∼2 h after the first session. The subjects were stimulated with the patterns that had the fewest pulses, as predicted by the F-M model. In addition, subjects were stimulated with each of the CFTs from the first session to note the variability in the muscles' response to the same train. The accuracy of the motions generated by the predicted trains were determined by calculating the angular RMSE between the measured trajectories in response to the CFTs tested in session I, the CFTs tested in session II, and the predicted patterns.
Part 1: Exploring the Effects of Stimulation Pattern on the Dynamic Performance—Stimulation Frequency Relationship
The knee joint trajectories produced in response to 300-ms CFTs, CITs, and DFTs for all frequencies tested for a representative subject are shown in Fig. 2. For each pattern tested, the peak excursion produced rose sharply between 10 and 40 Hz. For frequencies from 40 to 60 Hz, there were smaller increases in peak excursion. There were only small increases in the excursions produced at stimulation frequencies ≥60 Hz (Fig. 2). At stimulation frequencies ≤50 Hz, the DFTs produced greater excursions than either CITs or CFTs, and the CITs performed better than CFTs. At the higher frequencies, the performance of each pattern tested was comparable. The peak and total power relationships with frequency were qualitatively similar to the excursion-frequency relationship for CFTs, CITs, and DFTs (see Fig. 2).
The excursion-frequency relationships for CFTs, CITs, and DFTs for each subject were curve fit using Eq. 1. The R2 values of the fits for each pattern for each subject tested are shown in Table 2. The averaged values of Ep and fp for CFTs were 73 ± 14° and 20 ± 3 Hz, for CITs were 71 ± 13° and 16 ± 2 Hz, and for DFTs were 73 ± 16° and 13 ± 1 Hz.
A one-way repeated measures ANOVA to determine the effect of stimulation pattern (CFT, CIT, and DFT) on the excursion showed that for frequencies of 20, 30, and 50 Hz, the excursions produced for each pattern were significantly different (see Fig. 3). At 40, 59, and 100 Hz, there were differences only between the CFT vs. DFT and the CIT vs. DFT. At 83 Hz, no effect of pattern on the excursion produced was observed.
Part 2: Identification of Stimulation Patterns that Minimize the Number of Pulses Required to Produce a Targeted Trajectory
Angular RMSE of <6° between the measured angle trajectories in response to the stimulation train identified by the model and the four CFTs (10, 14, 20, and 50 Hz) for each of the three subjects tested showed that the model accurately identified the stimulation patterns that were able to produce the targeted trajectories generated in response to the each of the CFTs (Table 3 and Fig. 4). Table 3 shows the minimum number of pulses and mean frequency required to produce each targeted trajectory for the three subjects tested. For all three subjects, the predicted patterns needed 20–33% fewer pulses to produce the same excursions as the 14-, 20-, and 50-Hz CFTs. For these optimized trains, the occurrence of doublets (pair of stimulation pulses less than ∼10 ms apart) was common (see Fig. 4, A and B). For the 10-Hz trains, there was no reduction in the number of pulses needed (see Table 3). Figure 5 shows the stimulation patterns generated by our F-M model by fitting the measured responses to a 50-Hz CFT for each subject. The predicted patterns have irregular interpulse intervals and also contain at least one doublet. The number of pulses required to achieve the targeted trajectory for each subject was 10 compared with the 15 pulses required to generate the targeted trajectory for the 50-Hz CFT (Fig. 5).
The mean angular RMSEs for the three subjects varied from 3.5 to 6.7° for the four CFTs (10, 14, 20, and 50 Hz) tested during session I vs. session II (Fig. 6). Interestingly, these mean angular RMSEs were of a similar magnitude when comparing measured responses to the CFTs in session I vs. the corresponding predicted trains. Finally, the mean RMSEs between the measured responses to the CFTs tested in session II vs. the corresponding predicted trains varied from 2.7 to 4.2°.
The primary finding of this study was that the pattern of a stimulation train had a significant effect on the relationship between mean stimulation frequency and dynamic muscle performance. The results showed that for clinically relevant frequencies (<59 Hz), the stimulation trains that consisted of varying instantaneous frequencies (CITs and DFTs) produced a significantly greater excursion than the CFTs. In addition, for the 300 ms CFTs, CITs, and DFTs, the excursion-frequency relationships were exponential. The greatest excursions were produced at frequencies >60 Hz for CFTs, CITs, and DFTs. The results also showed that for frequencies ≤50 Hz, the DFTs produced greater excursions than either CITs or CFTs and the CITs performed better than CFTs. Conversely, Binder-Macleod and colleagues (6) showed that for isometric contractions of nonfatigued human quadriceps muscle, the shape of the isometric force-frequency relationships for the CFTs and CITs tested were not exponential and there was no particular advantage to using six-pulse CITs compared with six-pulse CFTs (6). The authors also showed that the greatest peak isometric forces were produced by CFTs with frequencies ranging from 25 to 50 Hz and by CITs with frequencies ranging from 20 to 50 Hz. Lee and Binder-Macleod (20) found that the excursion-activation frequency relationship in response to six-pulse trains indicated a reduced performance by both the CFTs and CITs at the higher frequencies during isotonic contractions of human quadriceps femoris muscles (see Fig. 5 from Ref. 20). Their study showed that CITs performed better than CFTs only for frequencies from 10 to 14 Hz. In addition, their study showed that the peak excursion occurred for CFTs at 20 Hz and in response to CITs at ∼16 Hz. The reason for the differences in results between the previous work and the present study was that our study controlled for the duration of the trains tested (300 ms) and the previous studies controlled for the number of pulses (6 pulses). All of the above studies show that the number of pulses or the duration of a stimulation train markedly affects the shape of the muscle output-frequency relationship.
The present study showed that the excursion produced could be increased by either changing the stimulation pattern or the stimulation frequency (Fig. 7). The average data for the subjects tested were fit with Eq. 1, and a line indicating a randomly chosen desired excursion (55°) was plotted. The points at which this line intersected the curves gave us the train characteristics required to generate the desired excursion. These characteristics were calculated by dropping a line down to the x-axis and obtaining the mean frequency of the train and then, because the duration for all the trains tested were 300-ms, we could calculate the number of pulses in the train. In the case illustrated, it was possible to achieve a predicted targeted excursion of 55° with either a 28-Hz, 8-pulse DFT or a 37-Hz, 11-pulse CFT. The former would result in possibly lesser fatigue as both the frequency and number of pulses in the stimulation train were reduced (14). However, understanding of the effect of activation pattern on muscle fatigue requires further work and is beyond the scope of the present study.
Our results were the first to show that CFTs can be replaced by VFTs, with fewer pulses, to produce identical motion trajectories as that produced in response to the CFTs. In addition, our modeling results showed that for the three subjects tested the stimulation pattern that replaced a particular CFT was different for each subject (see Fig. 5). We believe the reason for this variability is due to differences in each subject's force-length and force-velocity relationships, the contractile characteristics of each muscle, and the biomechanical characteristics of the knee joint for each subject. The above differences in muscles and joints were captured in our F-M model (27) and allowed our model to predict a unique stimulation pattern for each subject to achieve the desired trajectory. Our F-M model also predicted the presence of doublets in the stimulation patterns optimized to match the excursions produced by the 20- and 50-Hz CFTs (Fig. 4, A and B). Our findings are similar to the findings of Christie and Kamen (9) who showed the presence of doublet firings in ∼45% (young adults) and ∼30% (older adults) of the motor units at different levels of maximal voluntary contraction. The findings of the present study suggest that similar to voluntary muscle activation, during electrical stimulation it may be necessary to vary the instantaneous frequency throughout the train to reduce the number of stimulation pulses and optimize muscle performance.
In conclusion, the results of the present study showed that the stimulation pattern has a significant effect on dynamic muscle performance. The modeling work in this study showed that by varying the pattern of the stimulation train it was possible to reduce the number of pulses and the mean frequency required to achieve a targeted trajectory. These findings suggest that similar to voluntary muscle activation patterns, varying the instantaneous frequency within a train of pulses can be used to improve dynamic muscle performance.
This work was supported by National Institutes of Health Grants HD-36797 and HD-38582.
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