This study presents a modelling framework in which information on muscle fiber direction and orientation during contraction is derived from diffusion tensor imaging (DTI) and incorporated in a computational model of the surface electromyographic (EMG) signal. The proposed model makes use of the principle of reciprocity to simultaneously calculate the electric potentials produced at the recording electrode by charges distributed along an arbitrary number of muscle fibers within the muscle, allowing for a computationally efficient evaluation of extracellular motor unit action potentials. The approach is applied to the complex architecture of the first dorsal interosseous (FDI) muscle of the hand to simulate EMG during index finger flexion and abduction. Using diffusion tensor imaging methods, the results show how muscle fiber orientation and curvature in this intrinsic hand muscle change during flexion and abduction. Incorporation of anatomically accurate muscle architecture and other hand tissue morphologies enables the model to capture variations in extracellular action potential waveform shape across the motor unit population and to predict experimentally observed differences in EMG signal features when switching from index finger abduction to flexion. The simulation results illustrate how structural and electrical properties of the tissues comprising the volume conductor, in combination with fiber direction and curvature, shape the detected action potentials. Using the model, the relative contribution of motor units of different sizes located throughout the muscle under both conditions is examined, yielding a prediction of the detection profile of the surface EMG electrode array over the muscle cross-section.

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The natural-element method (NEM) has proved to be able to provide more accurate and computationally efficient solutions than the finite-element method (FEM) for first-order consistency approximations. However, higher order approximations in the NEM framework are not obtained straightforwardly. This paper addresses a method of constructing higher order approximations out of the standard first-order NEM shape functions. This process is achieved through the de Boor algorithm. Accuracy of the scheme is compared with FEM. Results show that in second-order approximations context the NEM is still able to provide better accuracies for a given number of degrees of freedom.Index Terms-De Boor, finite-element method (FEM), natural-element method (NEM), second-order consistency, splines.