Effects of the physiological parameters on the signal-to-noise ratio of single myoelectric channel
© Ma and Zhang; licensee BioMed Central Ltd. 2007
Received: 12 January 2006
Accepted: 08 August 2007
Published: 08 August 2007
An important measure of the performance of a myoelectric (ME) control system for powered artificial limbs is the signal-to-noise ratio (SNR) at the output of ME channel. However, few studies illustrated the neuron-muscular interactive effects on the SNR at ME control channel output. In order to obtain a comprehensive understanding on the relationship between the physiology of individual motor unit and the ME control performance, this study investigates the effects of physiological factors on the SNR of single ME channel by an analytical and simulation approach, where the SNR is defined as the ratio of the mean squared value estimation at the channel output and the variance of the estimation.
Mathematical models are formulated based on three fundamental elements: a motoneuron firing mechanism, motor unit action potential (MUAP) module, and signal processor. Myoelectric signals of a motor unit are synthesized with different physiological parameters, and the corresponding SNR of single ME channel is numerically calculated. Effects of physiological multi factors on the SNR are investigated, including properties of the motoneuron, MUAP waveform, recruitment order, and firing pattern, etc.
The results of the mathematical model, supported by simulation, indicate that the SNR of a single ME channel is associated with the voluntary contraction level. We showed that a model-based approach can provide insight into the key factors and bioprocess in ME control. The results of this modelling work can be potentially used in the improvement of ME control performance and for the training of amputees with powered prostheses.
The SNR of single ME channel is a force, neuronal and muscular property dependent parameter. The theoretical model provides possible guidance to enhance the SNR of ME channel by controlling physiological variables or conscious contraction level.
The surface myoelectric (ME) signal is an effective and important indicator of neuromuscular characteristics and inherent mechanisms underlying muscle activity. This accessible signal has been widely studied for diverse purposes, such as fundamental understanding of neuromuscular processes, diagnosis and therapy of neuromuscular diseases. Especially for amputee, features extracted from ME signals are adopted as parameters to control the powered prostheses, which is termed, ME control.
Proper measurement of ME control performance is crucial in determining feasible techniques for successful training for neuromuscular rehabilitation or multifunctional prostheses. Because the surface recorded ME signal is amplitude modulated corresponding to muscle contraction level, its amplitude is usually assumed as constant for nonfatiguing, constant-force and -angle contractions. However, estimate of ME signal amplitude is not constant due to its stochastic property. Variations around the mean value of the amplitude estimate are considered to be noise. It should be noticed that the "noise" used in this context is distinct from the interference residing in the ME signal measurement, such as the interferences arose from the recording electrodes and power line. In such a circumstance, signal-to-noise ratio (SNR), defined as the ratio of the amplitude of a desired signal to the amplitude of noise, can be used as a measure of the quality of an ME signal processor. Root-mean-square, mean-absolute-value (MAV), and mean-square-value (MSV) are generally used functions for the ME signal processor.
Most of the research on factors that influence the SNR in the ME control has focused on signal processors, such as the effects of the averaging filter [1, 2] and the nonlinearity of the processor [3, 4]. In recent studies, Zhang et al.  employed the SNR to study the MSV processor based on the linear model, where the ME signal is modelled as a temporal and spatial summation of motor unit action potentials. The results of their study showed that the SNR nonlinearly increased with the increment of the contraction level, and its theoretic asymptote was equal to that which would result if the ME signal were modelled as a Gaussian random process. Clancy and Hogan  used the SNR as the standard metric to compare the performance of ME signal processors, MAV and RMS. They found that if the electromyographic density is Laplacian, the MAV processing is optimal in terms of SNR. Due to the different SNR computation, it is difficult to directly compare the results from Clancy and Hogan with those from Zhang's study. However, the theoretical results of both groups could be repeated in experiments, validating the respective modelling methods.
By the linear model, an ME signal is the temporal and spatial summation of the signals generated by all activated motor units. One merit of this model is that it lends itself to study individual ME channels and their interrelationship. Based on such a modelling scheme, Zhang et al.  indicated that the SNR, defined as the ratio of the MSV estimation at the channel output and the variance of the estimation, is largely influenced by the statistics of ME signals , which are determined by the neuromuscular physiology. However, only a few studies have reported on the effects of the interaction between the neuron and muscle on the SNR at the ME control channel output. The purpose of this paper is to investigate the effects of neuromuscular physiology on the SNR at the single ME channel output, to obtain a better understanding of the relationship between muscle contraction and ME control performance. If there is no special description, the SNR in this study refers to the ratio of the MSV estimation at the channel output and the variance of the estimation, the same in Zhang's research. A theoretical model will be proposed and simulations will be performed accordingly.
Model of Myoelectric (ME) Channel
where τ m = C m R m is the membrane time constant; I0 is the constant current stimulus to MN, V th refers to the threshold voltage for MN firing, t arp represents the absolute refractory period, and b is the shape factor of MUAP. The detailed mathematical derivation procedure can be found in the Appendix.
It should be noted that the SNR defined by Eq.7 considers the noise as the amplitude variation only caused by the stochastic characteristics of the ME signal itself. In reality, there could be other noise sources, such as motion artifact, which could be arisen by movement of the muscles other than the target or the recording electrodes. Due to the main purpose, this study only focuses on the physiological factor effect on the SNR regardless any additional noise. Related analysis for the effect of the additional noise on ME control have been extensively investigated by Zhang . Equation 7 clearly shows that the SNR of a single ME channel output is determined by the driving signal, I0, and the physiology of the motor unit.
Simulation of the ME channel
where n is the number of data points per MUAP train at an effective sampling rate of 104 samples per second.
It is accepted that muscles generate force under two mechanisms, motor unit recruitment and firing rate modulation, both of which are determined by voluntary contraction level and neuromuscular physiology. In this paper, the SNR of a single ME channel was first modelled at the cellular level including the MN firing mechanisms. It provided a tool to understand the ME control process and to investigate influential factors individually, which would be very difficult to achieve by experimental methods.
SNR sensitivity to the neural control signal
It is possible for the brain to judge the effort required and send suitable depolarizing signals to the MNs. Therefore, the stimulus intensity, which conveys the information of conscious contraction level, will determine the force generated by muscles. The recruitment of a motor unit depends on the neuronal firing threshold of its innervated MN. The one-to-one relationship between the occurrence of action potentials in a MN and in the muscle fibers it innervates infers that the CNS modulates the unit firing pattern by changing the input intensity of MN. When a larger force is required for the activated motor units, the firing rate will be increased. On one hand, the integral input of a MN can be equally modelled by an effective synaptic current [9, 11, 22], which is represented by a constant current, I0, in our model. On the other hand, indicated by Eqs.1 and 7, the SNR is largely sensitive to the mean firing rate of the motor unit among all the firing statistical characteristics. Therefore, the driving current of MN only influences the SNR at the ME channel output in terms of its mean value. Figure 5 clearly demonstrated that the SNR is enhanced with increased mean driving current.
SNR sensitivity to MUAP morphology
Equation 7 shows that the SNR at the ME channel output is insensitive to the amplitude of the MUAP but inversely related to the shape factor b. The impact of the shape factor b on the morphology of the MUAP is studied by simulation. Thirty three MUAPs are synthesized with different shape factors based on Eq.6. Two examples are shown in Fig. 8(a). The durations of synthesized MUAPs are within the physiological range, normally 5~20 ms for human skeleton muscle . It is observed that a larger b results in wider duration of the MUAP, as illustrated in Fig. 8.
SNR related to the muscle contraction level
rp (pps) (peak firing rate)
The modelling results indicate that large size motor units recruited at high contraction levels will enhance the SNR of the ME channels. Therefore, the SNR of a ME control channel is positively related to target force and will reach its peak value at the maximum contraction. A similar phenomenon was also reported in a previous experimental study .
According to above findings, ME control can be better understood and evaluated. For example, for small muscle with low contraction level task, SNR could be limited by the nature of the muscular physiologies, such as the driving current from the nerve, small size of the recruited motor units, etc. In the design of training strategies for amputee, muscles with large size of motor units should be chosen to achieve a high SNR of ME control.
As an important measure of the ME control, the SNR of a single ME channel has been modelled including the physiological characteristics of MN and muscle unit. The effects of different physiological parameters on the SNR of the ME channel were investigated individually. The modelling results provided better a understanding of the relationship between the SNR of the ME channel and the neuromuscular physiology during a contraction. The major findings include:
1. The SNR of a single ME channel is highly related to the stimulus intensity of the motoneuron, which carries the information of the voluntary contraction level for a force task. As a result, it is clear that the performance of ME control would be enhanced with the increasing force task.
2. The SNR of a single ME channel is sensitive to the MUAP duration, which is mainly determined by the depolarization process, the muscle fiber length, conduction velocity, and end-plate dispersion within the motor unit. This conclusion may provide guidance to improve the performance of powered prostheses by considering the physiological factors in the control strategy design and the choice of proper target muscle for ME control.
3. The SNR of a single ME channel is generally ranged from 0.004 to 0.2. Techniques based on multi-channels are needed to improve the SNR for ME control.
4. Large size motor units will have higher SNR in the ME channel. Therefore, proper selection of the target muscle in a ME control may improve performance in terms of SNR.
shape factor of action potential
central nerve system
mean square value
motor unit action potential
mean firing rate
squared myoelectric signal
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