Polynomial regression is the most common method to estimate the relationship between muscle signals and torque during muscle contraction, but it is not capable of characterizing important transient patterns in the signal–torque relationship that only exist during short bursts of torque but may convey detailed information of muscle behavior. In this study, we proposed an integrated data analysis approach based on local polynomial regression (LPR) to identify transient patterns in the signal–torque relationship. For each subject, the LPR method can represent electromyography (EMG), mechanomyography (MMG) and ultrasonography (US) features as nonlinear functions of torque and can further estimate the derivatives of these signal–torque nonlinear functions. Further, a number of break points can be detected from the derivatives of the signal–torque relationships at the group level, and they can segment the signal–torque relationships into several stages, where multimodal features change with torque in different dynamic manners. Eight subjects performed isometric ramp contraction of knee up to 90% of the maximal voluntary contraction (MVC). EMG, MMG and US were simultaneously recorded from the rectus femoris muscle. Results showed that, for each feature, the whole torque range were clearly segmented into several distinct stages by the proposed method and the feature–torque relationship could be approximately described by a piecewise linear function with different slopes at different stages. A critical break-point of 20% MVC was detected during the isometric contraction for all muscle signals. As compared with the conventional regression methods, the proposed LPR-based data analysis approach can effectively identify stage-dependent transient patterns in the feature–torque relationships, providing deeper insights into the motor unit activation strategy. 
Identifying transient patterns of in vivo muscle behaviors during isometric contraction by local polynomial regression