Physics-based predictive simulations of human movement have the potential to support personalized medicine, but large computational costs and difficulties to model control strategies have limited their use. We have developed a computationally efficient optimal control framework to predict human gaits based on optimization of a performance criterion without relying on experimental data. The framework generates three-dimensional muscle-driven simulations in 36 min on average—more than 20 times faster than existing simulations—by using direct collocation, implicit differential equations and algorithmic differentiation. Using this framework, we identified a multi-objective performance criterion combining energy and effort considerations that produces physiologically realistic walking gaits. The same criterion also predicted the walk-to-run transition and clinical gait deficiencies caused by muscle weakness and prosthesis use, suggesting that diverse healthy and pathological gaits can emerge from the same control strategy. The ability to predict the mechanics and energetics of a broad range of gaits with complex three-dimensional musculoskeletal models will allow testing novel hypotheses about gait control and hasten the development of optimal treatments for neuro-musculoskeletal disorders.

Knowledge of human-exoskeleton interaction forces is crucial to assess user comfort and effectiveness of the interaction. The subject-exoskeleton collaborative movement and its interaction forces can be predicted in-silico using computational modelling techniques. We developed an optimal control framework that consisted of three phases. First, the foot-ground (Phase A) and the subject-exoskeleton (Phase B) contact models were calibrated using three experimental sit-to-stand trials. Then, the collaborative movement and the subject-exoskeleton interaction forces, of six different sit-to-stand trials were predicted (Phase C). The results show that the contact models were able to reproduce experimental kinematics of calibration trials (mean RMSD coordinates. 1.1 degrees, and velocities. 6.8 degrees/s), ground reaction forces (mean RMSD. 22.9 N), as well as the interaction forces at the pelvis, thigh and shank (mean RMSD. 5.4 N). Phase C could predict the collaborative movements of prediction trials (mean RMSD coordinates. 3.5 degrees, and velocities. 15.0 degrees/s), and their subject-exoskeleton interaction forces (mean RMSD. 13.1 N). In conclusion, this optimal control framework could be used while designing exoskeletons to have in silico knowledge of new optimal movements and their interaction forces.

Algorithmic differentiation (AD) is an alternative to finite differences (FD) for evaluating function derivatives. The primary aim of this study was to demonstrate the computational benefits of using AD instead of FD in OpenSim-based trajectory optimization of human movement. The secondary aim was to evaluate computational choices including different AD tools, different linear solvers, and the use of first- or second-order derivatives. First, we enabled the use of AD in OpenSim through a custom source code transformation tool and through the operator overloading tool ADOL-C. Second, we developed an interface between OpenSim and CasADi to solve trajectory optimization problems. Third, we evaluated computational choices through simulations of perturbed balance, two-dimensional predictive simulations of walking, and three-dimensional tracking simulations of walking. We performed all simulations using direct collocation and implicit differential equations. Using AD through our custom tool was between 1.8 ± 0.1 and 17.8 ± 4.9 times faster than using FD, and between 3.6 ± 0.3 and 12.3 ± 1.3 times faster than using AD through ADOL-C. The linear solver efficiency was problem-dependent and no solver was consistently more efficient. Using second-order derivatives was more efficient for balance simulations but less efficient for walking simulations. The walking simulations were physiologically realistic. These results highlight how the use of AD drastically decreases computational time of trajectory optimization problems as compared to more common FD. Overall, combining AD with direct collocation and implicit differential equations decreases the computational burden of trajectory optimization of human movement, which will facilitate their use for biomechanical applications requiring the use of detailed models of the musculoskeletal system.

Though walking impairments are prevalent in society, clinical treatments are often ineffective at restoring lost function. For this reason, researchers have begun to explore the use of patient-specific computational walking models to develop more effective treatments. However, the accuracy with which models can predict internal body forces in muscles and across joints depends on how well relevant model parameter values can be calibrated for the patient. This study investigated how knowledge of internal knee contact forces affects calibration of neuromusculoskeletal model parameter values and subsequent prediction of internal knee contact and leg muscle forces during walking. Model calibration was performed using a novel two-level optimization procedure applied to six normal walking trials from the Fourth Grand Challenge Competition to Predict In Vivo Knee Loads. The outer-level optimization adjusted time-invariant model parameter values to minimize passive muscle forces, reserve actuator moments, and model parameter value changes with (Approach A) and without (Approach B) tracking of experimental knee contact forces. Using the current guess for model parameter values but no knee contact force information, the inner-level optimization predicted time-varying muscle activations that were close to experimental muscle synergy patterns and consistent with the experimental inverse dynamic loads (both approaches). For all the six gait trials, Approach A predicted knee contact forces with high accuracy for both compartments (average correlation coefficient r = 0.99 and root mean square error (RMSE) = 52.6 N medial; average r = 0.95 and RMSE = 56.6 N lateral). In contrast, Approach B overpredicted contact force magnitude for both compartments (average RMSE = 323 N medial and 348 N lateral) and poorly matched contact force shape for the lateral compartment (average r = 0.90 medial and −0.10 lateral). Approach B had statistically higher lateral muscle forces and lateral optimal muscle fiber lengths but lower medial, central, and lateral normalized muscle fiber lengths compared to Approach A. These findings suggest that poorly calibrated model parameter values may be a major factor limiting the ability of neuromusculoskeletal models to predict knee contact and leg muscle forces accurately for walking.

Objectives: Opening wedge high tibial osteotomy (HTO) is an established surgical procedure for the treatment of early-stage knee arthritis. Other than infection, the majority of complications are related to mechanical factors – in particular, stimulation of healing at the osteotomy site. This study used finite element (FE) analysis to investigate the effect of plate design and bridging span on interfragmentary movement (IFM) and the influence of fracture healing on plate stress and potential failure. Materials and Methods: A 10° opening wedge HTO was created in a composite tibia. Imaging and strain gauge data were used to create and validate FE models. Models of an intact tibia and a tibia implanted with a custom HTO plate using two different bridging spans were validated against experimental data. Physiological muscle forces and different stages of osteotomy gap healing simulating up to six weeks postoperatively were then incorporated. Predictions of plate stress and IFM for the custom plate were compared against predictions for an industry standard plate (TomoFix). Results: For both plate types, long spans increased IFM but did not substantially alter peak plate stress. The custom plate increased axial and shear IFM values by up to 24% and 47%, respectively, compared with the TomoFix. In all cases, a callus stiffness of 528 MPa was required to reduce plate stress below the fatigue strength of titanium alloy. Conclusion: We demonstrate that larger bridging spans in opening wedge HTO increase IFM without substantially increasing plate stress. The results indicate, however, that callus healing is required to prevent fatigue failure. Cite this article: A. R. MacLeod, G. Serrancoli, B. J. Fregly, A. D. Toms, H. S. Gill. The effect of plate design, bridging span, and fracture healing on the performance of high tibial osteotomy plates: An experimental and finite element study. Bone Joint Res 2018;7:639–649. DOI: 10.1302/2046-3758.712.BJR-2018-0035.R1.

The knowledge of muscle activation patterns when doing a certain task in subjects with anterior cruciate ligament deficiency could help to improve their rehabilitation treatment. The goal of this study is to identify differences in such patterns between anterior cruciate ligament-deficient and healthy subjects during walking. Electromyographic data for eight muscles were measured in a sample of eighteen subjects with anterior cruciate ligament deficiency, in both injured (ipsilateral group) and non-injured (contralateral group) legs, and a sample of ten healthy subjects (control group). The analysis was carried out at two levels: activation-deactivation patterns and muscle synergies. Muscle synergy components were calculated using a non-negative matrix factorization algorithm. The results showed that there was a higher co-contraction in injured than in healthy subjects. Although all muscles were activated similarly since all subjects developed the same task (walking), some differences could be observed among the analyzed groups. The observed differences in the synergy components of injured subjects suggested that those individuals alter muscle activation patterns to stabilize the knee joint. This analysis could provide valuable information for the physiotherapist to identify alterations in muscle activation patterns during the follow-up of the subject's rehabilitation.