A Gaussian Process Model of Muscle Synergy Functions for Estimating Unmeasured Muscle Excitations Using a Measured Subset

Estimation of muscle excitations from a reduced sensor array could greatly improve current techniques in remote patient monitoring. Such an approach could allow continuous monitoring of clinically relevant biomechanical variables that are ideal for personalizing rehabilitation. In this paper, we introduce the notion of a muscle synergy function which describes the synergistic relationship between a subset of muscles. We develop from first principles an approximation to their behavior using Gaussian process regression and demonstrate the utility of the technique for estimating the excitation time-series of leg muscles during normal walking for nine healthy subjects. Specifically, excitations for six muscles were estimated using surface electromyography (sEMG) data during a finite time interval (called the input window) from four different muscles (called the input muscles) with mean absolute error (MAE) less than 5.0% of the maximum voluntary contraction (MVC) and that accounts for 82-88% of the variance (VAF) in the true excitations. Further, these estimated excitations informed muscle activations with less than 4.0% MAE and 89-93% VAF. We also present a detailed analysis of a number of different modeling choices, including every possible combination of four-, three- and two-muscle input sets, the size and structure of the input window, and the stationarity of the Gaussian process covariance functions. Further, application specific modifications for future use are discussed. The proposed technique lays a foundation to explore the use of reduced wearable sensor arrays and muscle synergy functions for monitoring clinically relevant biomechanics during daily life.