An approach to a muscle force model with force-pulse amplitude relationship of human quadriceps muscles

Electrically Elicited Force Response Characteristics of Forearm Extensor Muscles for Electrical Muscle Stimulation-Based Haptic Rendering

“…Table 4 lists the resulting parameters of the model for all subjects with the corresponding RMSE, NRMSE and values. The parameter values were estimated using the force response measured at the maximum amplitude [ 28 ]. The averaged of the estimation was 0.93, indicating that the force response model provides reliable estimation results similar to the results presented in literature [ 27 ].…”

“…Two objective functions were used to determine the optimal parameters of the force response model. The five parameters ( ) of the force response model expressed in Equations (2) and (3) were obtained by minimizing the following objective function [ 28 , 30 ] where is the number of samples in the force response, and and represent the simulated force response with the estimated parameter values and the measured force in the experiment at the sampling time , respectively. The trust-region-reflective algorithm was used to determine the optimal parameter values [ 29 ].…”

“…To avoid the local minima, the initial values of the parameters were set randomly in a predefined range, and the iterative optimization procedure was continued until the value of the objective function was less than . The parameters of ( were obtained by minimizing the following objective function [ 28 , 30 ]. where m is the number of the peak force samples acquired for each frequency, and represent the estimated and measured peak force, respectively, and is the index of the sample.…”

“…In the field of rehabilitation, EMS has been utilized to treat impaired muscle contraction caused by neuromuscular injuries. Various force response models [ 27 , 28 , 29 , 30 ] with sensors to measure level of muscle contraction, such as electromyography (EMG) [ 31 , 32 ], mechanomyography (MMG) [ 33 , 34 ], and piezoresistive sensors [ 35 , 36 , 37 , 38 , 39 ], have been proposed to precisely control the contraction of impaired muscles in EMS-based rehabilitation. Although these models can represent the nonlinear features of the force response with respect to the various parameters of an electrical stimulation, it remains difficult to apply these models to haptic applications because of the discrepancy of target muscles.…”

“…In addition, the complexity of the previous models makes it difficult to use them for haptic rendering. The previous models representing the force–amplitude relationship [ 28 ] and force–pulse width relationship [ 30 ] include 9 to 10 adjustable coefficients. Too many variables in the model can not only lead to an overfitting problem, but also decrease the computational efficiency, which is critical in real-time haptic applications.…”