Reflection of muscle exertion level and fatigue in force tremor patterns
Authors:   , Sarver Joseph J. , Seliktar Rahamim 
Published: July 2024

Despite the broad range of possible clinical, industrial and commercial applications, the complex nature of muscular fatigue has made its non-invasive detection somewhat elusive. A neuromuscular model which incorporates the intricate complexities of fatigue could provide a useful tool in terms of its understanding, and therefore predict possible non-invasive measures that could be used for its detection. As a first step toward this goal, a preliminary neuromuscular model was developed with the specific aim of investigating how known fatigue related changes in certain physiological parameters would affect the non-invasive measurement of isometric force-tremor (IFT). The neuromuscular model was based on several motor units working in parallel, where each unit consisted of one motor neuron and a group of muscle fibers, and whose output forces were summed together at the tendon to produce the muscle's output force. Each unit's fibers were modeled as cascading neural/calcium and calcium/force dynamics, whose twitch contraction times and tetanic forces were taken from distributions found in the literature. The model's motor neurons were recruited in order of strength, and increased their firing frequencies logarithmically with increased target force. Fatigue was modeled as a point process, where fiber dynamics and motor neuron recruitment were modified in accordance with changes found in the literature. The modeled predicted: (1) a decrease in IFT after fatigue, (2) different changes in muscle's force-frequency relationship dependent upon the severity of fatigue, (3) an underlying relationship between motor unit recruitment and IFT and finally (4) an increase in IFT with motor unit synchronization. To validate the model, IFT, as well as vibromyography (VMG) and electromyography (EMG) were collected from adult volunteer subjects performing isometric tests before and after exhaustive exercise of the elbow. All signals were analyzed in the time and frequency domains using both wavelet (Morlet) and root-mean-square (RMS) analyses. The separation between fresh and exhausted (fatigued) data were compared using receiver-operating-characteristic (ROC) statistics. On average subjects IFT wavelet power (WP) and RMS values were found to decrease significantly after exercise. Furthermore these decreases were larger than changes in either VMG or EMG under the same conditions. VMG was also found to decrease significantly after exercise, in accordance with the literature. Finally, EMG measured at both the biceps-brachii and brachioradialis increased significantly in RMS after exercise, again in agreement with the literature. In conclusion, the fatigue-related changes in IFT predicted by the neuromuscular model matched well with changes observed in the experimental data. Specifically, both the simulated and experimental results indicated that, for the conditions tested, IFT could provide a simple non-invasive means for detecting muscular fatigue. The model's validity could be enhanced by comparing predicted and experimental results from other muscles. Furthermore, by expanding fatigue into a continuous rather than a point process, the model could provide a useful tool in muscular fatigue research.