Although Essential Tremor (ET) is the most common type of tremor, many patients are left without satisfactory treatment options. One potential alternative treatment to medication or surgery is a wearable tremor-suppressing device. However, optimizing the effectiveness of such a device requires knowledge of which muscles/joints are most responsible for tremor. To answer this question, current efforts simulate tremor propagation using a model of the neuromusculoskeletal dynamics of the upper limb. To guide efforts to identify realistic model parameters and use the model to determine the mechanical origin of tremor, we performed preliminary parameter estimation work and a thorough sensitivity analysis of this tremor propagation model. The tremor propagation model included muscle activation inputs to the 15 major superficial muscles and joint displacement outputs in the 7 main degrees of freedom (DOF) from the shoulder to the wrist, resulting in 105 input-output relationships. We calculated the mean normalized sensitivities of all outputs to all 107 model parameters over the tremor band (4 to 8 Hz), resulting in approximately 12,000 sensitivities. We found that sensitivities were relatively constant in the tremor band, except for shoulder adduction-abduction, which exhibited a large peak in sensitivity between 4 and 5 Hz. Averaged across the tremor band, the system was most sensitive to select elements of inertia, muscle force, muscle moment arm, damping, muscle time constants, and stiffness (in that order). The 19 highest all-input-excitation sensitivities were between 1.2 and 4.57, meaning a 100% change in parameter value produces 120-457% change in tremor. Conversely, the model includes many parameters to which the outputs are relatively insensitive. For example, the sensitivities to almost one third of the 107 parameters are below 0.1, meaning a 100% change in parameter value produces only a 10% change in tremor. To gain additional insight, we compared the sensitivities of the full model to those of a simpler model including only two inputs and two outputs. Analyzing the two-input two-output model revealed patterns in sensitivity which persist in the full model. The sensitivities of the full model were further compared to past studies that performed rudimentary sensitivity analyses and were found to match while adding significantly more parameter-specific sensitivity information. Future work will extend this sensitivity analysis to tremor at the hand, where it matters most.



College and Department

Mechanical Engineering



Date Submitted


Document Type





sensitivity, tremor, propagation, model, parameter, estimation



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Engineering Commons