18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam 1996 5.7.2: EMG Pattern Analysis and Identification
Parametric modelling of EMG signals Dean KoroSec, Claude Martinezt, Damjan Zazula Faculty of Electrical Engineering and Computer Science, Smetanova 17, 2000 Maribor, Slovenia tLNGI - IUT OGP, La Chantrerie, CP 3003, 44087 Nantes cedex 03
[email protected],
[email protected],
[email protected] Parametric modeling of EMG signals W e propose a parametric description of electromyographic signals, based o n simplified lane source model f o r generation of single muscle fiber action potentials. Signals are assumed t o be a superposition of such components described with two parameters, called depth and delay. W e further describe a decomposition technique, in fact a parameter searching procedure which enables a compact presentation of needle as well as surface electromyograms. Presented model can be used f o r generation of synthetic signals o n which our decomposition was tested first, Results o n real needle and surface EMGs have shown that model is appropriate f o r both types of signals and decomposition technique has proven itself as a n efiecient tool in evaluation of such signals in a sense of a set model.
1 Introduction An electromyogram (Eh4G) is the signal obtained by measurement, of electrical activity of a muscle. Each muscle consists of muscle fibers organized in motor units (MUS) according to motoneurons which activate them. A recorded response of each single fiber is called action potential (AP), while summation of APs of fibers belonging to the same MU is a motor unit action potential (MUAP). Different types of electrodes can be used to obtain such recordings, mainly concentric needle EMG (CNEMG), single fiber (SF) and surface electrodes are used for different applications in analysis of a neuro-muscular system condition. EMGs are complex signals and therefore difficult to evaluate. Investigations are often done using different models where parametric description, physiological or other, is sought.
weight function representing the potential as recorded by thc electrode at a certain distance, when a unit current source travels along the muscle fiber. Parametric line source model Simplification and generalization of this model was possible through the work of Gygi [4] and Martinez [5] who showed that the sum of all influences to the shape of an action potential can be expressed and replaced by a single low-pass filter, depending on the distance between a muscle fiber and the active surface of the recording electrode itself. Comparing this idea to the mentioned line source model, one can see that this filter in fact replaces the weight function used there. As filtering effect of tissue has major impact on amplitudes of APs composing MUAPs, the main information for separating them can be found in the time component of each AP, that is in moments of appearances of their main peaks. This time component depends on several physiological facts, but we decided to use a time delay itself as a parameter instead of its causes like the position of the motoneuronal junction or conduction velocity. Model itself becomes very simplified with this but, on the other hand, it is this simplification that enables us to find an inverse solution by parameteric search at all.
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Decomposition procedure
The decomposition method developed represents a synthesis of known search approaches [l]. It could be described as iterative univariable search used in a typical multimodal case. Although the method is particulary suited for the applicat.ion involving the presented model, we believe that it is applicable t o other similar types of search problems, too. As a criterion function we used Euclidean distance be-
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Parametric line source model
As a basis for modelling of an AP we use previously described line source model [2, 31. Single extracellular AP is presented as a convolution of the transmembrane current approximated by an empirical expression and a
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tween the original signal and the model at each iteration step. The idea of finding a partial solution on each step comes from the wavy shape of the distance function which proposes a two-step univariable procedure. After the fit'of the model can no longer be improved, stopping rule is invoked to conclude the search.
18th Annual International Conference of the IEEE Engineering in Medicine and Biology Society, Amsterdam 1996 5.7.2: EMG Pattern Analysis and Identification
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Results
Results on synthetic signals. First, we have tested the procedure on segments of simulated random signals with 3-7 componentes with the random choicc of uniformly distributed depth-delay parameters. The average absolute error of the models found was 3.33 % (variance was 0.25 %) of the maximum amplitude of the original signal. The modelling procedure also misestimated the exact number of present components at 0.83 of AP. For noisy signals (20 d B noise-), the mean absolute error is 8.35 % and variance 0.43 %, but the mean error in the estimated number of components remains the same as in the tests without noise and is 0.82. Our conclusion is that we can ensure cxccllcnt fitting of the model even in the case of many present, components and very high level of additive noise. Modeling of needle electromyograms. Next, we took some extracted MUAP waveshapes and tried to characterize them as a summation of components used in our model as examplified in Figure 1. The main problem with the MUAPs observed is there baseline shift. The model cannot cope with it, the reconstructed amplitudes are not correct. Aberrance of the model is also a kind of a problem in case of different widths of peaks in MUAPs, that is their different frequency content. The model is unable to describe wide shapes with a small number of parameters, but approximation with larger number of components is, anyway, quite satisfactory. What is most important for the further exploatation of rcsults: there is still enough differences in the obtained model for classification of MUAPs to be made possible. A bit worse fit in the sense of the absolute error criteria does not mean that the algorithm cannot be used as an introductory step in standard problems of needle EMG decomposition and recognition of motor units firing statistics.
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ing to a lower frequency content of surface EMGs and the observed width of peaks present in such signals. The procedure was always able to build models very close to original signals, as for example depicted in Figure 2. Such succesfui modelling shows, that our action potential model coresponds well t o the components present in surface electromyograms, although physiological explanation can not be the same as in case of needle EMGs.
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Figure 2: Example of surface EMG segment modeling.
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Conclusion
We have presented a parametric description of electromyographic signals, based on simplified line source model. Tests has shown that the introduced decomposition technique is succesful, reliable, additive-noise resistant and appropriate for both types of EMGs, of course, with adaption to different time scales. The simplifications introduced are of such a nature that we have found the model a bit more appropriate for modelling of surface electromyograms. The parametric description obtianed is useful in applications like compression of signals, classification of MUAPs, or standard needle EMG decomposition.
References [1] J. M. Mendel, "A prelude to neural networks: Adap-
Figure 1: Example of MUAP modelling.
Modeling of surface electromyograms. Whole segments of surface EMGs have been used as an input signal for the decomposition procedure. We extended parameter space in the direction of delay to enable processing of longer signals, also action potentials were changed accord-
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tive and learning systems", Adaptive optimization procedures, Prentice-Hall, Englewood Cliffs, 1994, pp. 243-287. [2] S. Andreassen, A. Rosenfalck, "Relationship of intracellular and extracellular action potential of skeletal muscle fibre", Critical reviews in bioengineering, CRC Press Inc. 6, 1981, pp. 267-306 [3] S. Nandedkar, E. Stblberg, "Simulation of single muscle fibre action potentials", Medical & Biological Engineering & Computing 21, 1983, pp. 158-165 [4] A. Gygi, "Analyse des Nadel- und Oberflachen Elektromyogramms mittels Statistiken hoheren Ordnung", PhD Thesis, Eidgenossischen Technischen Hochshule Zurich, 1994 [5] C. Martinez, "Surface EMG Forward and Inverse Filter Models", Proceedings of the IV. Slovenian Electrotechnical Conf., 1995, Vol. B, pp. 385-389
