Evaluation of a method to scale muscle strength for gait simulations of children with cerebral palsy

Change the direction: 3D optimal control simulation by directly tracking marker and ground reaction force data

Optimal control simulations of musculoskeletal models can be used to reconstruct motions measured with optical motion capture to estimate joint and muscle kinematics and kinetics. These simulations are mutually and dynamically consistent, in contrast to traditional inverse methods. Commonly, optimal control simulations are generated by tracking generalized coordinates in combination with ground reaction forces. The generalized coordinates are estimated from marker positions using, for example, inverse kinematics. Hence, inaccuracies in the estimated coordinates are tracked in the simulation. We developed an approach to reconstruct arbitrary motions, such as change of direction motions, using optimal control simulations of 3D full-body musculoskeletal models by directly tracking marker and ground reaction force data. For evaluation, we recorded three trials each of straight running, curved running, and a v-cut for 10 participants. We reconstructed the recordings with marker tracking simulations, coordinate tracking simulations, and inverse kinematics and dynamics. First, we analyzed the convergence of the simulations and found that the wall time increased three to four times when using marker tracking compared to coordinate tracking. Then, we compared the marker trajectories, ground reaction forces, pelvis translations, joint angles, and joint moments between the three reconstruction methods. Root mean squared deviations between measured and estimated marker positions were smallest for inverse kinematics (e.g., 7.6 ± 5.1 mm for v-cut). However, measurement noise and soft tissue artifacts are likely also tracked in inverse kinematics, meaning that this approach does not reflect a gold standard. Marker tracking simulations resulted in slightly higher root mean squared marker deviations (e.g., 9.5 ± 6.2 mm for v-cut) than inverse kinematics. In contrast, coordinate tracking resulted in deviations that were nearly twice as high (e.g., 16.8 ± 10.5 mm for v-cut). Joint angles from coordinate tracking followed the estimated joint angles from inverse kinematics more closely than marker tracking (e.g., root mean squared deviation of 1.4 ± 1.8 deg vs. 3.5 ± 4.0 deg for v-cut). However, we did not have a gold standard measurement of the joint angles, so it is unknown if this larger deviation means the solution is less accurate. In conclusion, we showed that optimal control simulations of change of direction running motions can be created by tracking marker and ground reaction force data. Marker tracking considerably improved marker accuracy compared to coordinate tracking. Therefore, we recommend reconstructing movements by directly tracking marker data in the optimal control simulation when precise marker tracking is required.

The effect of musculoskeletal model scaling methods on ankle joint kinematics and muscle force prediction during gait for children with cerebral palsy and equinus gait

Clinical gait analysis incorporated with neuromusculoskeletal modelling could provide valuable information about joint movements and muscle functions during ambulation for children with cerebral palsy (CP). This study investigated how imposing pre-calculated joint angles during musculoskeletal model scaling influence the ankle joint angle and muscle force computation. Ten children with CP and equinus gait underwent clinical gait analysis. For each participant, a "default" (scaled without pre-calculated joint angles) and a "PJA" (scaled with pre-calculated ankle joint angles) model were generated to simulate their gait. Ankle joint angles were calculated with an inverse kinematic (IK) and direct kinematic (DK) approach. Triceps surae and tibialis anterior muscle forces were predicted by static optimisation and EMG-assisted modelling. We found that PJA-derived ankle angles showed a better agreement with what derived from the DK approach. The tibialis anterior muscle prediction was more likely to be affected by the scaling methods for the static optimisation approach and the gastrocnemius muscle force prediction was more likely to be influenced for the EMG-assisted modelling. This study recommends using the PJA model since the good consistency between IK and DK-derived joint angles facilitates communication among different research disciplines.

SENSITIVITY OF MODEL-PREDICTED MUSCLE FORCES OF PATIENTS WITH CEREBRAL PALSY TO VARIATIONS IN MUSCLE-TENDON PARAMETERS

Computational musculoskeletal modeling and simulation platforms are efficient tools to gain insight into the muscular coordination of patients with motor disabilities such as cerebral palsy (CP). Muscle force predictions from simulation programs are influenced by the architectural and contractile properties of muscle-tendon units. In this study, we aimed to evaluate the sensitivity of major lower limb muscle forces in patients with CP to changes in muscle-tendon parameters. Open-access datasets of children with CP ([Formula: see text]) and healthy children ([Formula: see text]) were considered. Monte Carlo analysis was executed to specify how sensitive the muscle forces to perturbations between [Formula: see text]% and [Formula: see text]% of the nominal value of the maximum isometric muscle force, optimal muscle fiber length, muscle pennation angle, tendon slack length, and maximum contraction velocity of muscle. The sensitivity analysis revealed that muscle forces of CP patients and healthy individuals were most sensitive to perturbations in the tendon slack length ([Formula: see text]), while forces of CP patients were more sensitive to tendon slack length when compared to the healthy group ([Formula: see text]). Muscle forces of patients and healthy individuals were insensitive to the other four parameters ([Formula: see text]), except for the gracilis and sartorius muscles in which the proportion of optimal muscle fiber length to tendon slack length is higher than 1; forces of these two muscles were also sensitive to the optimal muscle fiber length. The results of this study are expected to contribute to our understanding of which parameters should be personalized when conducting musculoskeletal modeling and simulation of patients with CP.

Muscle Synergy Constraints Do Not Improve Estimates of Muscle Activity From Static Optimization During Gait for Unimpaired Children or Children With Cerebral Palsy

Neuromusculoskeletal simulation provides a promising platform to inform the design of assistive devices or inform rehabilitation. For these applications, a simulation must be able to accurately represent the person of interest, such as an individual with a neurologic injury. If a simulation fails to predict how an individual recruits and coordinates their muscles during movement, it will have limited utility for informing design or rehabilitation. While inverse dynamic simulations have previously been used to evaluate anticipated responses from interventions, like orthopedic surgery or orthoses, they frequently struggle to accurately estimate muscle activations, even for tasks like walking. The simulated muscle activity often fails to represent experimentally measured muscle activity from electromyographic (EMG) recordings. Research has theorized that the nervous system may simplify the range of possible activations used during dynamic tasks, by constraining activations to weighted groups of muscles, referred to as muscle synergies. Synergies are altered after neurological injury, such as stroke or cerebral palsy (CP), and may provide a method for improving subject-specific models of neuromuscular control. The aim of this study was to test whether constraining simulation to synergies could improve estimated muscle activations compared to EMG data. We evaluated modeled muscle activations during gait for six typically developing (TD) children and six children with CP. Muscle activations were estimated with: (1) static optimization (SO), minimizing muscle activations squared, and (2) synergy SO (SynSO), minimizing synergy activations squared using the weights identified from EMG data for two to five synergies. While SynSO caused changes in estimated activations compared to SO, the correlation to EMG data was not higher in SynSO than SO for either TD or CP groups. The correlations to EMG were higher in CP than TD for both SO (CP: 0.48, TD: 0.36) and SynSO (CP: 0.46, TD: 0.26 for five synergies). Constraining activations to SynSO caused the simulated muscle stress to increase compared to SO for all individuals, causing a 157% increase with two synergies. These results suggest that constraining simulated activations in inverse dynamic simulations to subject-specific synergies alone may not improve estimation of muscle activations during gait for generic musculoskeletal models.