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A sensor setup with a small number of sensors, i.e., a sparse sensor setup, could enable a comprehensive unobtrusive motion analysis using inertial motion capture (IMC) with little obtrusion to the user, which is critical for clinical and sports applications, such as assessing disease, providing biofeedback in rehabilitation, or enhancing performance in sports. When sparse sensor setups were used, the motion analysis was either not comprehensive or physical correctness was not considered. Furthermore, the relationship between sensor setup and the resulting accuracy of spatiotemporal, kinematic, or kinetic variables has not been investigated systematically. Therefore, we investigated the accuracy of biomechanical gait reconstructions from different sparse inertial sensor setups, in which the number of sensors is reduced by not placing sensors on all body segments of interest. We created biomechanical reconstructions by solving optimal control problems with a sagittal plane musculoskeletal model. The resulting simulations tracked raw accelerometer and gyroscope data while minimizing muscular effort. We applied this approach to six different sparse sensor setups to investigate the reconstruction quality of spatiotemporal, kinematic, and kinetic variables for each of these setups at three walking and three running speeds. We found that correlations between IMC and optical motion capture (OMC) were large for all sensor setups, but that those setups without a pelvis sensor led to a forward trunk lean that was too high, as well as unrealistic kinetics and kinematics. Spatiotemporal variable estimations generally also benefitted from a pelvis sensor, but not as much as the kinetic and kinematic estimations. We found that for setups including a pelvis sensor, there was no clear benefit for including additional sensors. While walking speed, step length, and joint kinematics generally benefited from using more sensors, the hip moment and knee moment did not. During running, the ankle moment and vertical ground reaction force were even estimated more accurately with smaller sensor setups. Therefore, we conclude that sagittal-plane reconstruction of walking and running kinetics and kinematics using sparse sensor setups can improve usability at the cost of only minor reductions in accuracy. When using a sparse sensor setup for gait reconstructions using optimal control, we advise to always include a pelvis sensor to achieve accurate results.

Muscular co-contraction of antagonistic muscle pairs is often observed in human movement, but it is considered inefficient and it can currently not be predicted in simulations where muscular effort or metabolic energy are minimized. Here, we investigated the relationship between minimizing effort and muscular co-contraction in systems with random uncertainty to see if muscular co-contraction can minimize effort in such system. We also investigated the effect of time delay in the muscle, by varying the time delay in the neural control as well as the activation time constant. We solved optimal control problems for a one-degree-of-freedom pendulum actuated by two identical antagonistic muscles, using forward shooting, to find controller parameters that minimized muscular effort while the pendulum remained upright in the presence of noise added to the moment at the base of the pendulum. We compared a controller with and without feedforward control. Task precision was defined by bounding the root mean square deviation from the upright position, while different perturbation levels defined task difficulty. We found that effort was minimized when the feedforward control was nonzero, even when feedforward control was not necessary to perform the task, which indicates that co-contraction can minimize effort in systems with uncertainty. We also found that the optimal level of co-contraction increased with time delay, both when the activation time constant was increased and when neural time delay was added. Furthermore, we found that for controllers with a neural time delay, a different trajectory was optimal for a controller with feedforward control than for one without, which indicates that simulation trajectories are dependent on the controller architecture. Future movement predictions should therefore account for uncertainty in dynamics and control, and carefully choose the controller architecture. The ability of models to predict co-contraction from effort or energy minimization has important clinical and sports applications. If co-contraction is undesirable, one should aim to remove the cause of co-contraction rather than the co-contraction itself.