Stochastic modelling of muscle recruitment during activity

Abstract

Muscle forces can be selected from a space of muscle recruitment strategies that produce stable motion and variable muscle and joint forces. However, current optimization methods provide only a single muscle recruitment strategy. We modelled the spectrum of muscle recruitment strategies while walking. The equilibrium equations at the joints, muscle constraints, static optimization solutions and 15-channel electromyography (EMG) recordings for seven walking cycles were taken from earlier studies. The spectrum of muscle forces was calculated using Bayesian statistics and Markov chain Monte Carlo (MCMC) methods, whereas EMG-driven muscle forces were calculated using EMG-driven modelling. We calculated the differences between the spectrum and EMG-driven muscle force for 1-15 input EMGs, and we identified the muscle strategy that best matched the recorded EMG pattern. The best-fit strategy, static optimization solution and EMG-driven force data were compared using correlation analysis. Possible and plausible muscle forces were defined as within physiological boundaries and within EMG boundaries. Possible muscle and joint forces were calculated by constraining the muscle forces between zero and the peak muscle force. Plausible muscle forces were constrained within six selected EMG boundaries. The spectrum to EMG-driven force difference increased from 40 to 108 N for 1-15 EMG inputs. The best-fit muscle strategy better described the EMG-driven pattern (R (2) = 0.94; RMSE = 19 N) than the static optimization solution (R (2) = 0.38; RMSE = 61 N). Possible forces for 27 of 34 muscles varied between zero and the peak muscle force, inducing a peak hip force of 11.3 body-weights. Plausible muscle forces closely matched the selected EMG patterns; no effect of the EMG constraint was observed on the remaining muscle force ranges. The model can be used to study alternative muscle recruitment strategies in both physiological and pathophysiological neuromotor conditions.

Keywords: electromyography; human locomotion; muscle synergy; neuromusculoskeletal modelling; statistic EMG-driven muscle force; stochastic muscle recruitment.

Figure 1.

The musculoskeletal model (a), the motion capture scheme (b) and the model during an intermediate frame of walking (c). (Online version in colour.)

Figure 2.

Comparison between the calculated joint torque (solid black line) at the hip, the knee and the ankle and the joint torque bands (grey bands) reported by Benedetti et al. [45] for healthy subjects.

Figure 3.

Distance between EMG-driven muscle forces and the solution space of the muscle load-sharing problem for an increasing number of EMGs input to the model. Diamonds, the muscle distance averaged over gait and muscles. Circles, the muscle-by-muscle distance averaged over gait. (Online version in colour.)

Figure 4.

Force patterns for the EMG-driven, the static optimization and the best-fit muscle synergy extracted from the solution space of the muscle recruitment problem.

Figure 5.

Linear regression analysis between the EMG-driven muscle forces, the static optimization solution (a) and the best-fit muscle synergy (b).

Figure 6.

Physiologically possible muscle forces. The dashed-black line represents the peak muscle force. The solid-red and solid-blue lines represent the upper and the lower muscle force boundary (low-band-pass filtered at 6 Hz, zero-pole design, sixth-order Butterworth filter). Each level represents an admissible muscle co-contraction of 0.2, 0.4, 0.6, 0.8 and 1. (Online version in colour.)

Figure 7.

Physiologically possible hip, knee and ankle contact forces. The shaded grey area represents possible joint forces calculated from constraining muscle forces between zero and the peak muscle force. The solid black lines represent the joint contact force boundary for an admissible muscle co-contraction of 0.2, 0.4, 0.6, 0.8 and 1 (low-band-pass filtered at 6 Hz, zero-pole design, sixth-order Butterworth filter).

Figure 8.

The 15-channel EMG signals for the seven gait trials. The shaded areas represent the 0.68 quantile (i.e. mean ± s.d.) of the EMG distribution. The EMG subset used to calculate the spectrum of physiologically plausible muscle forces is shaded in red. (Online version in colour.)

Figure 9.

Physiologically plausible muscle forces. The selected muscle force spectrums constrained between EMG-driven force boundaries are shaded in red whereas the remaining muscle force spectrums are shaded in grey. For the latter, the dashed-black line represents the peak muscle force. (Online version in colour.)