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Surface Electromyography and Muscle Fatigue
The objective of this experiment was to confirm that the frequency spectrum of an electromyography (EMG) signal shifts to lower frequencies as a muscle, under voluntary contraction, fatigues. The primary motivation for the experiment, however, was to gain engineering experience through the design and construction of the actual apparatus used to measure the EMG signal. Over the course of a two-minute experiment recording the mean EMG frequency from my right bicep, I observed the predicted downward shift in frequency as fatigue occurred. Introduction: Surface Electromyography is a non-invasive technique for detecting electrical signals given off during muscle contraction. These signals, on the order of hundreds of mV, are generated by the quasi-random activation of the individual fibers that make up a skeletal muscle. The EMG signal is actually a superposition of the many smaller signals that come from each fiber. The nature of the signal is quasi-random because, for a muscle under voluntary contraction, only some of the large number of fibers that make up the muscle are active at any given time. As the individual fibers fatigue, more and more of those signals vanish, resulting in a net shift to lower frequencies. Observing that shift was the objective of this experiment. The presence of a shift in the mean EMG frequency is an important phenomenon in biomechanics because it provides a way to assess the fatigue of muscles early on. In the past, the only way of assessing fatigue was to observe failure, the point at which muscle contraction could no longer be maintained. This approach has little use in applications where fatigue needs to be remedied before failure occurs. One example of such an application is the use of a biomechanical prosthetic. If the device could detect muscle fatigue before failure, it could take action to compensate. Using the mean EMG frequency as a fatigue index is one way that could be accomplished. Theory: As mentioned above, the EMG signal is on the order of hundreds of mV. It is also coming from a high impedance source, the human body. These two facts make detecting the signal a non-trivial task. Several different sources of noise can obscure the EMG signal. The first source to consider is Johnson noise, or thermal noise. It is present in all electronic devices, but can be minimized by careful circuit design. The second source is ambient noise. Ubiquitous 60Hz power line noise is one example, as are the many electrical signals that travel through the human body. Differential amplification, shielding the circuit, and careful electrode design are the primary ways that ambient noise can be minimized. The last source of noise is due to the quasi-random nature of the EMG signal, which means that only certain parts of the signal are useful. Specifically, the usable spectrum of the EMG signal is that in the range of 20-450Hz. Frequencies outside this range need to be filtered out. Once an EMG signal is obtained, one needs to consider what to do with it. After the signal has been transformed to the frequency domain, calculating the mean frequency is a rather trivial task. Given some distribution of frequencies from fmin to fmax, each with amplitude A(f) and a frequency f, the mean frequency is,
Equation 1 Since that distribution is being sampled with finite resolution, the integrals are replaced with summations, and we are left with,
Equation 2 EMG Apparatus: The apparatus I built is shown in Picture 1 .
Picture 1 It consisted of the basic components shown in Figure 1.
Figure 1 The band-pass filter and variable gain amplifier were housed in the shielded aluminum box along with a power conditioning circuit. They are shown in Picture 2.
Picture 2 The instrumentation amplifier was built into the electrode, which is shown in Picture 3.
Picture 3 The electrode was connected to the main circuit with a 3ft CAT5e twisted pair Ethernet cable that carried positive and negative supply voltages, pseudo ground, as well as the actual signal. The contacts were 99.9% silver wire with a diameter of 1mm. They were spaced 10mm apart. The reference electrode was a simple anti-static wristband, shown in picture 4.
Picture 4 Figure 2 Experimental Technique: The actual experiment was very straightforward. The subject of the experiment held a weight so that the elbow was at a right angle, and the forearm was parallel to the ground. The weight was such that the bicep was fatigued after two minutes. That data acquisition system sampled 240 half-second epochs, transformed them to the frequency domain, and calculated the mean frequency for each epoch of data using an algorithm based on equation 2. The sampling rate was 4096Hz, yielding 2048 data points for each epoch. After transforming the data to the frequency domain, the number of data points was reduced to 1024. Since the sampling rate was well above the Nyquist frequency (900Hz), aliasing was not considered. Many things that I did not account for would need to have been considered in a more sophisticated experiment. Had I been concerned with the amplitude of the EMG signal, I would have needed to calibrate the gain of the circuit and be very careful with the position and orientation of the electrode. Since the only thing I was concerned with was observing a shift in the mean frequency over time, however, I only needed to compare the circuit with a signal of known frequency. To that effect, I generated a 100Hz sinusoidal signal and fed it into the EMG apparatus. The smallest signal I could achieve with the function generator I was using was 100mV. Since this was much too large to see with the apparatus, I attenuated it by a factor of 10000. I accomplished this by building a simple voltage divider using one 1MΩ resistor and one 100Ω resistor, both of which were accurate to within 5%. This resulted in a signal on the order of 10mV. As an aside, I believe the resolution of the circuit was on the order of 1mV-5mV. This is comparable to the commercially available EMG systems produced by Delsys, which generally state that the system noise is less than 1.2mV. Although I never actually tested the resolution of my apparatus, the 10mV sine wave was clearly visible without averaging or any other signal processing. Results: Figure 3 is a graph of the mean EMG frequency for my right bicep from flexure to fatigue. Notice the baseline 100Hz sine wave and the quasi-random nature of the EMG signal. Also notice that 38 of the 240 data points were deleted where the signal was lost (these were clearly visible as the mean frequency jumped to very high values with respect to the EMG signal at those points)
Figure 3 The mean EMG frequency, as shown above, is clearly decreasing. Applying a linear least-squares fit to the data yields a definitively negative slope of -0.15 ± .01 Hz/s. This is shown in figure 4 and is discussed in detail in the data analysis section. The chart in figure 4 is the same as figure 3, except that the error bars and the linear fit are plotted.
Figure 4 Figure 5 and Figure 6 are samples of different EMG signals. The first is the time domain and the second is the frequency domain. As discussed above, the actual amplitudes of the signals are unknown (and inconsequential), although they do correspond to each other. These signals are unrelated to the data shown in Figure 3 and Figure 4 .
Figure 5
Figure 6 Data Analysis: The claim that a decrease in mean EMG frequency was observed relies heavily on the fact that a fit line yielded a negative slope. As stated above, the slope was –0.15 ± .01 Hz/s. The uncertainty in that calculation is the crucial factor in determining whether the slope was actually decreasing, and that uncertainty relies heavily on the error in each measurement. In order to determine that error, I simply used Excel’s goal finder function. Since each of the measurements had to have the same error, I simply set the error as a parameter and had Excel find the value that made the reduced Chi^2 = 1. That value turned out to be ±6.79Hz. I could have calculated the error analytically, but since there were two numerical integrations involved in the calculation of the mean frequency, it would have been a tedious task. I deemed it unnecessary since the method I described above seemed valid. Figure 7 shows a graph of the individual deviations of each data point. Notice that they seem both random and evenly distributed about the fit (although this can be debated). The fit seems to indicate a linear relationship, if only in the fatigue regime in which this experiment took place.
Figure 7 Acknowledgements: I would like to thank my advisor, Professor William Durfee, who provided the idea for the experiment, the schematic for the apparatus, lots of advice, and who also taught me how to build the robot shown above. I would also like to thank Kurt Wick, who spent several hours helping me debug my circuit. Finally, I would like to thank Professor Paul Crowell, who teaches the most worthwhile course I have ever attended. Without his instruction, I would have been woefully unqualified to even attempt this experiment. Even though, thanks largely to his course, my junior year was miserable, I am grateful for the experience. References: (1) Surface Electromyography: Detection and Recording DelSys Incorporated http://www.delsys.com/library/papers/SEMGintro.pdf (2) The Use of Surface Electromyography in Biomechanics Carlo J. De Luca Neuro-Muscular Research Center, Boston University, Boston, Massachusetts 02215 |
