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The biomechanical model of the human elbow joint is extensively studied. In the model, the surface electromyography (sEMG) is used as the input signal, whereas the muscle force or muscle torque is commonly considered as the output signal. The estimation of the actual muscle force or torque is important to effectively modulate the tremor suppression. However, the measurement of the muscle force or torque in vivo is difficult. In this paper, a new angle-to-EMG biomechanical model of the elbow joint was developed and evaluated by comparing the measured sEMG with the calculated sEMG. Three sources of the sEMG signal, namely, the central nervous system (CNS), the Golgi tendon and the muscle spindle were considered in this model. Furthermore, a local PID algorithm was proposed to describe the impact of the CNS on the motor neuron and the Golgi tendon model was used to transform muscle forces to stimulus signals. The model was calibrated by an improved search procedure combining the Powell search and the direct search to determine optimal model parameters. In the experiment, an sEMG signal acquisition system was established to measure the sEMG signal and the elbow joint angle. The experimental results, the predicted sEMG signal well following the measured sEMG, demonstrated that the calibrated model could be used to estimate in vivo sEMG signals and is beneficial to explore the peripheral neural system and the pathogenesis of tremor.

Abstract.Tremor usually occurs in a patient's upper limb with a roughly sinusoidal profile. Understanding the inner mechanism of the involuntary movement is fundamental to improving tremor suppression treatments. Therefore, the musculoskeletal model of the elbow joint was developed in this study. Initially, healthy subjects were selected to simulate tremor and the tremulous data was collected with the purpose of sparing patients from fatigue. With the recorded joint angle and surface EMG (sEMG), the model was calibrated to subjects by optimization approach. The activation derived from the electric pulse was employed to drive the tuned model and the model's output was compared with the angle predicted by the EMG-driven musculoskeletal model. The results demonstrated that the performance of the calibrated model was improved by a smaller normalized root mean square error and a higher coefficient of determination compared with the no-tuned model. There was no significant difference between the angles estimated by the tuned model activated by the electric pulse and muscle excitation. It indicates that neural activation could be replaced by the electric pulse to excite the limbs for desired angle. Therefore, the study presents a good way to evaluate the feasibility of Functional Electric Stimulation to suppress tremor.

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Through the establishment of the elbow biomechanical model, it can provide theoretical guide for rehabilitation therapy on the upper limb of the human body. A biomechanical model of the elbow joint can be built by the connection of muscle force model and elbow dynamics. But there are many undetermined coefficients in the model like the optimal joint angle and optimal muscle force which are usually specified as the experimental parameters of other workers. Because of the individual differences, there is a certain deviation of the final result. To this end, the RMS value of the deviation between the actual angle and calculated angle is considered. A set of coefficients which lead to the minimum RMS value will be chosen to be the optimal parameters. The direct search method and the conjugacy search method are used to get the optimal parameters, thus the model can be more accurate and mode adaptability.