Este trabalho apresenta a modelagem matemática e a simulação de potenciais de ação de unidades motoras de músculos de vertebrados visando a posterior simulação do eletromiograma. Para conseguir isso, inicialmente se fez uma compilação de dados existentes para a distribuição das fibras musculares (FBs) nas unidades motoras (MUs) de vários músculos, e as modelagens matemáticas descritos na literatura para o potencial de ação de uma FB (SFAP) e de uma MU (MUAP). Com base nos dados fisiológicos, primeiro se localizou as FBs em um músculo, por meio de uma aproximação de que as FBs estão rodeadas de outras seis no músculo. Para conseguir isto se construiram hexágonos concêntricos por MU, e posteriormente se localizou as FBs nas MUs, cobrindo uma faixa entre 75 e 2000 FBs, o que corresponde a músculos distais de mamíferos. Depois se fez uma aproximação para a distribuição de 170000 FBs nas 272 MUs da cabeça medial do músculo gastrocnêmio (MG) do gato, conseguindo numa primeira simulação localizar cerca de 70% das FBs para cada MU. Com esta localização das FBs no músculo baseados nos dados da literatura se aproximaram os retardos axonais por uma distribuição gaussiana, com média de 2 ms (gato) ou 10 ms (homem) e com desvio padrão de menos de 0,5 ms, desprezando o atraso axonal nas ramificações axonais, que foi estimado no máximo 29 vezes menor. Para a geração do SFAP trabalhou-se com dois modelos, um analítico, o qual resulta em simulações numéricas demoradas, e, outro numérico baseado na convolução da corrente com uma função peso. Para o modelo numérico dobrou-se imaginariamente o comprimento das FBs, para levar em conta o erro computacional de fim de fibra. O modelo numérico resultou em um tempo de simulação 30 vezes menor que o analítico. Adicionalmente, para simular a captação externa (i.e. na pele), fez-se uma aproximação para a função que modela os eletrodos de superfície de secção circular localizados a uma distância maior que 1,79 mm das FBs, mostrando um espectro similar ao reportado na literatura. Finalmente, os MUAPs obtidos resultavam com formas de onda e espectros similares ao descrito na literatura. Além disto, em certos casos, obtiveram-se MUAPs com indentações, seja localizando as junções neuromusculares em bandas da ordem de 1 mm de espessura, seja quando o tempo de atraso axonal foi considerado junto com a velocidade de condução da FB em função da raiz quadrada do diâmetro da FB. Foram feitas simulações para os MG e bíceps braquial do homem. Neste último caso, foram obtidos MUAPs similares aos captados para pessoas saludáveis, e foi observada a freqüência de disparos dos potenciais de ação do motoneurônio no espectro do MUAP. Quanto às formas dos agrupamentos das FBs em uma MU, não se obtiveram diferenças significativas para as FBs posicionadas homogênea e aleatoriamente, exceto uma ligeira variação nas amplitudes. No entanto, ocurreu uma mudança na faixa espectral, quando as FBs estavam concentradas. / This work presents the mathematical model and simulation of motor unit action potentials of vertebrate muscles aiming at after simulation of the electromyogram. To obtain this, initially, it was made a compilation of several data about the distribution of muscle fibers (FBs) in motor units (MUs) of many muscles, and the mathematical models of the action potential of a single FB (SFAP) and MU (MUAP), reported in previous works. On the basis of this physiological data, first, the FB was located in a muscle, using an approximation in which the FBs are encircled with other six FBs in the muscle. To reach this, concentric hexagons were constructed to build the surface of the MU, and later the FBs were situated in the MU, covering a range between 75 and 2000 FBs, corresponding to mammals extremity muscles. Later, a new approximation were was madein order to distribute the 170000 FBs in the 272 MUs of the medial head of muscle medialis gastrocnemius (MG) of the cat, reaching, in a first simulation, the localization of almost 70% of the FBs at each MU. With the FBs lalready allocated in the muscle, and based in data of previous works, their axonal delay were approximated by a gaussian distribution, with mean of 2 ms (cat) or 10 ms (man) and standard deviation of less than 0,5 ms, discarding the axonal delay in the axonal branching, that were estimated to affectup to 29 times less. To SFAP generation, two models were used, the first analytical, resulting in delayed numerical simulations, and the other based on convolution of the second derivate of the current with a weight function, where the length of the FBs was imaginarily duplicated, in order to consider the end fiber effect. Using this, a simulation time 30 times lesser than the analytical one was obtained. Additionally, so as to simulate the external recording (i.e. in the skin), it was made an approximation to the function that models the circular shape surface electrodes located at distances greater than 1,79 mm of the FBs, showing a similar spectrum reported. Finally, the waves and spectrum of the simulated MUAPs resulted similar to the ones reported in the literature. Beyond this, in certain cases, MUAPs were simulated with some tuned, either locating the neuromuscular junctions with thickness bands of 1 mm, or, when the axonal delay and the FB muscle fiber conduction velocity were considered as a function of the square root fiber diameter. This was simulated for MUAPs of MG and biceps brachii muscles of human beings, in the last case it has reached the waveforms and tuned found in heath subjects, and it was visualized the mean frequency of firing rate at the spectrum. In order to know how much affects grouping for the FBs to waves a MU, they were not found significant differences with FBs located homogeneously and randomly, except a little variation in the amplitude of the MUAP. However, they presented a change in the spectral bandwidth when the FBs are more concentrated.

Este trabalho apresenta a modelagem matemática e a simulação de potenciais de ação de unidades motoras de músculos de vertebrados visando a posterior simulação do eletromiograma. Para conseguir isso, inicialmente se fez uma compilação de dados existentes para a distribuição das fibras musculares (FBs) nas unidades motoras (MUs) de vários músculos, e as modelagens matemáticas descritos na literatura para o potencial de ação de uma FB (SFAP) e de uma MU (MUAP). Com base nos dados fisiológicos, primeiro se localizou as FBs em um músculo, por meio de uma aproximação de que as FBs estão rodeadas de outras seis no músculo. Para conseguir isto se construiram hexágonos concêntricos por MU, e posteriormente se localizou as FBs nas MUs, cobrindo uma faixa entre 75 e 2000 FBs, o que corresponde a músculos distais de mamíferos. Depois se fez uma aproximação para a distribuição de 170000 FBs nas 272 MUs da cabeça medial do músculo gastrocnêmio (MG) do gato, conseguindo numa primeira simulação localizar cerca de 70% das FBs para cada MU. Com esta localização das FBs no músculo baseados nos dados da literatura se aproximaram os retardos axonais por uma distribuição gaussiana, com média de 2 ms (gato) ou 10 ms (homem) e com desvio padrão de menos de 0,5 ms, desprezando o atraso axonal nas ramificações axonais, que foi estimado no máximo 29 vezes menor. Para a geração do SFAP trabalhou-se com dois modelos, um analítico, o qual resulta em simulações numéricas demoradas, e, outro numérico baseado na convolução da corrente com uma função peso. Para o modelo numérico dobrou-se imaginariamente o comprimento das FBs, para levar em conta o erro computacional de fim de fibra. O modelo numérico resultou em um tempo de simulação 30 vezes menor que o analítico. Adicionalmente, para simular a captação externa (i.e. na pele), fez-se uma aproximação para a função que modela os eletrodos de superfície de secção circular localizados a uma distância maior que 1,79 mm das FBs, mostrando um espectro similar ao reportado na literatura. Finalmente, os MUAPs obtidos resultavam com formas de onda e espectros similares ao descrito na literatura. Além disto, em certos casos, obtiveram-se MUAPs com indentações, seja localizando as junções neuromusculares em bandas da ordem de 1 mm de espessura, seja quando o tempo de atraso axonal foi considerado junto com a velocidade de condução da FB em função da raiz quadrada do diâmetro da FB. Foram feitas simulações para os MG e bíceps braquial do homem. Neste último caso, foram obtidos MUAPs similares aos captados para pessoas saludáveis, e foi observada a freqüência de disparos dos potenciais de ação do motoneurônio no espectro do MUAP. Quanto às formas dos agrupamentos das FBs em uma MU, não se obtiveram diferenças significativas para as FBs posicionadas homogênea e aleatoriamente, exceto uma ligeira variação nas amplitudes. No entanto, ocurreu uma mudança na faixa espectral, quando as FBs estavam concentradas. / This work presents the mathematical model and simulation of motor unit action potentials of vertebrate muscles aiming at after simulation of the electromyogram. To obtain this, initially, it was made a compilation of several data about the distribution of muscle fibers (FBs) in motor units (MUs) of many muscles, and the mathematical models of the action potential of a single FB (SFAP) and MU (MUAP), reported in previous works. On the basis of this physiological data, first, the FB was located in a muscle, using an approximation in which the FBs are encircled with other six FBs in the muscle. To reach this, concentric hexagons were constructed to build the surface of the MU, and later the FBs were situated in the MU, covering a range between 75 and 2000 FBs, corresponding to mammals extremity muscles. Later, a new approximation were was madein order to distribute the 170000 FBs in the 272 MUs of the medial head of muscle medialis gastrocnemius (MG) of the cat, reaching, in a first simulation, the localization of almost 70% of the FBs at each MU. With the FBs lalready allocated in the muscle, and based in data of previous works, their axonal delay were approximated by a gaussian distribution, with mean of 2 ms (cat) or 10 ms (man) and standard deviation of less than 0,5 ms, discarding the axonal delay in the axonal branching, that were estimated to affectup to 29 times less. To SFAP generation, two models were used, the first analytical, resulting in delayed numerical simulations, and the other based on convolution of the second derivate of the current with a weight function, where the length of the FBs was imaginarily duplicated, in order to consider the end fiber effect. Using this, a simulation time 30 times lesser than the analytical one was obtained. Additionally, so as to simulate the external recording (i.e. in the skin), it was made an approximation to the function that models the circular shape surface electrodes located at distances greater than 1,79 mm of the FBs, showing a similar spectrum reported. Finally, the waves and spectrum of the simulated MUAPs resulted similar to the ones reported in the literature. Beyond this, in certain cases, MUAPs were simulated with some tuned, either locating the neuromuscular junctions with thickness bands of 1 mm, or, when the axonal delay and the FB muscle fiber conduction velocity were considered as a function of the square root fiber diameter. This was simulated for MUAPs of MG and biceps brachii muscles of human beings, in the last case it has reached the waveforms and tuned found in heath subjects, and it was visualized the mean frequency of firing rate at the spectrum. In order to know how much affects grouping for the FBs to waves a MU, they were not found significant differences with FBs located homogeneously and randomly, except a little variation in the amplitude of the MUAP. However, they presented a change in the spectral bandwidth when the FBs are more concentrated.

A comparison of the ability of different spatial filters to reduce the amount of crosstalk in a surface electromyography (sEMG) measurement was conducted. It focused on the influence of different properties of the muscle anatomy and detection system used on the amount of crosstalk present in the measurements. An analytical model was developed which enabled the simulation of single fibre action potentials (SFAPs). These fibres were grouped together in motor units (MUs). Each MU has characteristics which, along with the SFAPs, are used to obtain the motor unit action potential (MUAP). A summation of the MUAPs from all the MUs in a muscle leads to the electromyogram (EMG) signal generated by the muscle. This is the first model which simulates a complete muscle for crosstalk investigation. Previous studies were done for single fibres (Farina&Rainoldi 1999; Farina et al. 2002e; Farina et al. 2004a) or MUs (Dimitrova et al. 2002; Dimitrov et al. 2003; Winter et al. 1994). Lowery et al. simulated a complete muscle, but only investigated one spatial filter (Lowery et al. 2003a). This model is thus the first of its kind. EMG signals were generated for limbs with different anatomical properties and recorded with various detection systems. The parameters used for comparison of the recorded signals are the average rectified value (ARV) and mean frequency (MNF), which describe the amplitude and frequency components of an EMG signal, respectively. These parameters were computed for each EMG signal and interpreted to make recommendations on which detection system results in the best crosstalk rejection for a specific experimental set-up. The conclusion is that crosstalk selectivity in an sEMG measurement is decreased by increasing the thickness of the fat layer, increasing the skin conductivity, decreasing the fibre length, increasing the interelectrode distance of the detection system, placing the detection electrodes directly above the end-plate area or an increased state of muscle contraction. Varying the contraction force strength or placing the detection electrodes directly above the tendon area has no influence on the crosstalk selectivity. For most of the conditions investigated, the normal double differential (NDD) detection system results in the best crosstalk reduction. The only exceptions are a set-up with poor skin conductivity where NDD and double differential (DD) performed comparably, and the two simulations in which the muscle length is varied, where the DD filter performed best. Previous studies have found DD to be more selective for crosstalk rejection than NDD (Dimitrov et al. 2003; Farina et al. 2002a; Van Vlugt&Van Dijk 2000). Possible reasons for the contradictory results are the high value of skin conductivity currently used or influences of the muscle geometry. / Dissertation (MEng(Bio-Engineering))--University of Pretoria, 2007. / Electrical, Electronic and Computer Engineering / unrestricted

Surface electromyography records the motor unit action potential signals in the vicinity of the electrode to reveal information on muscle activation. Decomposition of sEMG signals for characterization of constituent motor unit action potentials in terms of amplitude and firing times is useful for clinical research as well as diagnosis of neurological disorders. Successful decomposition of sEMG signals would allow for pertinent motor unit action potential information to be acquired without discomfort to the subject or the need for a well-trained operator (compared with intramuscular EMG). To determine amplitudes and firing times for motor unit action potentials in an sEMG recording, Szlavik's perturbation based decomposition may be applied. The decomposition was initially applied to synthetic sEMG signals and then to experimental data collected from the biceps brachii. Szlavik's decomposition estimator yields satisfactory results for synthetic and experimental sEMG signals with reasonable complexity.

This thesis has evaluated the use of Independent Component Analysis (ICA) on Surface Electromyography (sEMG), focusing on the biosignal applications. This research has identified and addressed the following four issues related to the use of ICA for biosignals: • The iterative nature of ICA • The order and magnitude ambiguity problems of ICA • Estimation of number of sources based on dependency and independency nature of the signals • Source separation for non-quadratic ICA (undercomplete and overcomplete) This research first establishes the applicability of ICA for sEMG and also identifies the shortcomings related to order and magnitude ambiguity. It has then developed, a mitigation strategy for these issues by using a single unmixing matrix and neural network weight matrix corresponding to the specific user. The research reports experimental verification of the technique and also the investigation of the impact of inter-subject and inter-experimental variations. The results demonstrate that while using sEMG without separation gives only 60% accuracy, and sEMG separated using traditional ICA gives an accuracy of 65%, this approach gives an accuracy of 99% for the same experimental data. Besides the marked improvement in accuracy, the other advantages of such a system are that it is suitable for real time operations and is easy to train by a lay user. The second part of this thesis reports research conducted to evaluate the use of ICA for the separation of bioelectric signals when the number of active sources may not be known. The work proposes the use of value of the determinant of the Global matrix generated using sparse sub band ICA for identifying the number of active sources. The results indicate that the technique is successful in identifying the number of active muscles for complex hand gestures. The results support the applications such as human computer interface. This thesis has also developed a method of determining the number of independent sources in a given mixture and has also demonstrated that using this information, it is possible to separate the signals in an undercomplete situation and reduce the redundancy in the data using standard ICA methods. The experimental verification has demonstrated that the quality of separation using this method is better than other techniques such as Principal Component Analysis (PCA) and selective PCA. This has number of applications such as audio separation and sensor networks.

A finite element (FE) model for the generation of single fiber action potentials (SFAPs) in a muscle undergoing various degrees of fiber shortening has been developed. The muscle is assumed to be fusiform with muscle fibers following a curvilinear path described by a Gaussian function. Different degrees of fiber shortening are simulated by changing the parameters of the fiber path and maintaining the volume of the muscle constant. The conductivity tensor is adapted to the muscle fiber orientation. At each point of the volume conductor, the conductivity of the muscle tissue in the direction of the fiber is larger than that in the transversal direction. Thus, the conductivity tensor changes point-by-point with fiber shortening, adapting to the fiber paths. An analytical derivation of the conductivity tensor is provided. The volume conductor is then studied with an FE approach using the analytically derived conductivity tensor (Mesin, Joubert, Hanekom, Merletti&Farina 2006). Representative simulations of SFAPs with the muscle at different degrees of shortening are presented. It is shown that the geometrical changes in the muscle, which imply changes in the conductivity tensor, determine important variations in action potential shape, thus affecting its amplitude and frequency content. The model is expanded to include the simulation of motor unit action potentials (MUAPs). Expanding the model was done by assigning each single fiber (SF) in the motor unit (MU) a random starting position chosen from a normal distribution. For the model 300 SFs are included in an MU, with an innervation zone spread of 12 mm. Only spatial distribution was implemented. Conduction velocity (CV) was the same for all fibers of the MU. Representative simulations for the MUAPs with the muscle at different degrees of shortening are presented. The influence of interelectrode distance and angular displacement are also investigated as well as the influence of the inclusion of the conductivity tensor. It has been found that the interpretation of surface electromyography during movement or joint angle change is complicated owing to geometrical artefacts i.e. the shift of the electrodes relative to the muscle fibers and also because of the changes in the conductive properties of the tissue separating the electrode from the muscle fibers. Detection systems and electrode placement should be chosen with care. The model provides a new tool for interpreting surface electromyography (sEMG) signal features with changes in muscle geometry, as happens during dynamic contractions. / Dissertation (MEng (Bio-Engineering))--University of Pretoria, 2008. / Electrical, Electronic and Computer Engineering / MEng (Bio-Engineering) / unrestricted

This study proposes an approach to analyze EMG signals using wavelets transformed as a method of signal features extraction. The adopted methodology is based on the study of the aggregated power envelope and the aggregate power spectrum envelope, which are obtained from the distribution of energy of a certain signal, based on the potency of wavelet coefficients, showed like wavelets spectrograms or from a wavelet scalegram. EMG signals were captured in the surface of the human skin and came from the right leg rectus femoris muscle in a static condition (isometric), also from the flexor muscle form the right hand in dynamic contraction (isotonic) and also form a train of motor unit action potential (MUAP) form the First Dorsal Interosseous muscle during dynamic contraction. Having those signals, there were taken two research phases: extraction of the feature based on the analytical wavelet transformed (AWT) in muscles during contraction (isometric and isotonic) and the phase of detection of MUAPs. In the AWT phase, considering the calculation of the envelopes in the timefrequency chart (spectrogram), the results shoed that the wavelet transformed can be applied for extraction of spectral content of the signal and also showed the possibility of verifying the potency signal spectrum and the energy of such signal intimae. Those variables were according to the expected features for EMG signal, reported by literature. In the second phase, MUAP detection, it was used the calculation of the envelopes based on the scalegram, having as a main wavelet the Daubechies of 4 (db4), Coiflet of 4 (coif4) and Symlet of 5 (sym5) . The result showed that the method allowed to locate in time of MUAPs and showed that it is sensible enough to detect signals form motor units, far from the sensor, which contribute to formation of the EMG signal. The use of the wavelet Db4 showed to be better to detect the muscle activity on the beginning of it ( set-on ), because the Db4 is similar to a MUAP. This work proposes that future studies can be based on the research of families of wavelets, using of the method of the aggregated power envelope to control proteases for arms, or hands for example. It is also proposed studies for detection of MUAPs as an important tool for muscles evaluation, in diagnosis of miopathologies and neuro-muscle disjunctions, envelope features extraction process for other biomedical signals, such as EEG and ECG. / Este trabalho propõe uma abordagem para a análise de sinais EMG utilizando as transformadas wavelet como método de extração de características do sinal. A metodologia aplicada utiliza o estudo da envoltória de potência agregada e da envoltória do espectro de potência agregada, que são extraídas a partir da distribuição de energia de um sinal, baseada na potência dos coeficientes wavelets exibidos sob a forma de espectrograma wavelet ou de escalograma wavelet. Os sinais EMG foram captados na superfície da pele e são oriundos, do músculo reto da coxa direita em contração estática (isométrica), do músculo flexor de punho direito em contração dinâmica (isotônica) e de um trem de potenciais de ação de unidade motora (MUAPs) do músculo primeiro dorsal interósseo em contrações dinâmicas. Com estes sinais, duas fases de investigação foram abordadas, as quais são: a fase de extração de característica baseada na transformada wavelet analítica nos músculos em contração (isométrica e isotônica) e a fase de detecção de MUAPs. Na fase baseada na transformada wavelet analítica (AWT), através dos cálculos das envoltórias na localização do plano tempo-freqüência (espectrograma), o resultado obtido foi que a transformada wavelet pode ser aplicada para extração do conteúdo espectral do sinal, e foi possível verificar que o espectro de potência do sinal e a energia deste sinal ao logo do tempo se mostraram dentro das características esperadas para o sinal EMG reportadas pela literatura. Na fase de detecção de MUAPs, utilizando o cálculo das envoltórias baseado no escalograma (diagrama tempo-escala), tendo como wavelet-mãe a Daubechies de ordem 4 (db4), Coiflet de ordem 4 (coif4) e Symlet de ordem 5 (sym5) , o resultado mostrou que o método permitiu a localização no tempo dos MUAPs e demonstrou que é sensível o suficiente para detectar sinais de unidades motoras distantes do sensor, os quais, contribuem para a formação do sinal EMG. O uso da wavelet Db4 mostrou-se melhor na detecção do início da atividade muscular ( set-on ) pois a Db4 se a semelha a uma MUAP. Este trabalho sugere que trabalhos futuros poderão ser baseados na investigação de famílias wavelets para análise de sinais EMG, bem como a utilização do método de envoltória de potência agregada para controle de próteses de membros superiores, a utilização de wavelets para detecção de MUAPs como uma importante ferramenta na avaliação muscular, no diagnóstico de miopatologias e disfunções neuromusculares e também a extração de características por envoltória para outros sinais biomédicos, como por exemplo, o EEG, o ECG etc. / Mestre em Ciências

<p>Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered.</p><p>First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units.</p><p>Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG.</p><p>Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.</p>

Signal processing within the neurophysiological field is challenging and requires short processing time and reliable results. In this thesis, three main problems are considered. First, a modified line source model for simulation of muscle action potentials (APs) is presented. It is formulated in continuous-time as a convolution of a muscle-fiber dependent transmembrane current and an electrode dependent weighting (impedance) function. In the discretization of the model, the Nyquist criterion is addressed. By applying anti-aliasing filtering, it is possible to decrease the discretization frequency while retaining the accuracy. Finite length muscle fibers are incorporated in the model through a simple transformation of the weighting function. The presented model is suitable for modeling large motor units. Second, the possibility of discerning the individual AP components of the concentric needle electromyogram (EMG) is explored. Simulated motor unit APs (MUAPs) are prefiltered using Wiener filtering. The mean fiber concentration (MFC) and jitter are estimated from the prefiltered MUAPs. The results indicate that the assessment of the MFC may well benefit from the presented approach and that the jitter may be estimated from the concentric needle EMG with an accuracy comparable with traditional single fiber EMG. Third, automatic, rather than manual, detection and discrimination of recorded C-fiber APs is addressed. The algorithm, detects the Aps reliably using a matched filter. Then, the detected APs are discriminated using multiple hypothesis tracking combined with Kalman filtering which identifies the APs originating from the same C-fiber. To improve the performance, an amplitude estimate is incorporated into the tracking algorithm. Several years of use show that the performance of the algorithm is excellent with minimal need for audit.