Notes
In this doctoral dissertation, we are discussing tracking and prediction of impulse response changes in non-stationary convolutional mixtures of impulse sources and their influence on the success of the identification of impulse sources. In doing so, we derive from the properties of multichannel surface electromyograms (EMGs), in which impulse responses represent the motor unit action potentials (MUAPs) and the impulse sources carry information about the firing moments of individual motor units (MU). During dynamic or fatiguing contractions of skeletal muscles, the MUAPs continuously change over time. In the doctoral dissertation, we show that these changes are at least piecewise linear, i.e. the change in the MUAPs can be considered as a sequence of linear changes. Since MUAPs are an essential building block of MU filters, which are used to estimate MU pulse trains from multichannel surface EMGs, predicting changes in MUAPs allows us to decompose multichannel surface EMG signals into MU firing patterns.In the doctoral dissertation, the knowledge mentioned above is incorporated into a Kalman filter for predicting changes of MUAPs in the individual channel of multichannel surface EMG, and the results of the Kalman filter prediction of individual channels are combined into a comprehensive prediction of the MU filter at a given time. The mentioned solution is evaluated on synthetic and experimental multichannel surface EMGs, which are recorded from the biceps brachii (BB) and abductor pollicis brevis (APB) muscles. We carefully study the influence of Kalman filter parameters on the performance of MU filters and propose their optimal values. Since the dynamics of changes in MUAPs differ between individual muscles and experimental protocols, the optimal values of the Kalman filter also vary between individual experimental protocols.A statistical comparison with other existing methods for the decomposition of multichannel surface EMGs, especially with the previously published cyclostationary convolution kernel compensation (csCKC), shows that the described method of tracking and predicting the MUAPs gives statistically significantly better results than the existing methods. On synthetic dynamic multichannel surface EMGs of the BB muscle, the new method detects 9,9 ± 2,2 MUs with a sensitivity of 93,1 ± 7,8 % and a precision of 98,2 ± 2,6 %. In the same conditions, the csCKC method detects 3,8 ± 1,8 MUs with a sensitivity of 78,7 ± 15,1 % and a precision of 97,6 ± 3,4 %. In the synthetic multichannel surface EMGs of the APB muscle that are generated during extensive isometric muscle fatigue, the newly described method detects 10,4 ± 2,3 MUs, with a sensitivity of 89,3 ± 23,6 % and a precision of 90,0 ± 18,9 %. In the same conditions, the csCKC method detects 5,4 ± 1,1 MUs, with a sensitivity of 61,3 ± 41,2 % and a precision of 66,0 ± 36,9 %. The method is also evaluated on experimental signals with unknown MU firing patterns. In this case, we use the results of the csCKC method as reference values, which were additionally reviewed and edited by an expert. In the case of fatiguing contractions of APB muscle, the proposed method detects 10,6 ± 5,5 MUs, with a sensitivity of 91,8 ± 15,9 % and a precision of 92,7 ± 10,7 %. In the same conditions, the csCKC method detects 3,6 ± 3,0 MUs, with a sensitivity of 69,5 ± 30,2 % and a precision of 74,0 ± 26,0 %.The presented method significantly exceeds the efficiency of the state-of-the-art methods for the decomposition of non-stationary multichannel surface electromyograms developed so far and is also suitable for studying contractions in which the shapes of MUAPs do not repeat in cycles. Such cases include recordings of movements performed only once and recordings of skeletal muscle fatigue. With this, the proposed method significantly improves the previously published csCKC method, which builds precisely on the cyclostationarity of surface EMG during repeated non-fatiguing measurements.