Analysis of optimal control problem formulations in skeletal movement predictions

Postprint (published version

Increased use of stepping strategy in response to medio-lateral perturbations in the elderly relates to altered reactive tibialis anterior activity

Background The influence of aging on reactive control of balance during walking has been mainly investigated in the sagittal plane, whereas balance control in response to frontal plane perturbations is largely unexplored in the elderly. This is remarkable, given that walking mainly requires active control in the frontal plane. An extensive gait perturbation protocol was used to test whether reactive control of walking balance changes with aging and whether these changes are more pronounced in the frontal than in the sagittal plane. Research question Do alterations in reactive muscle activity cause an age-related shift in stepping strategy in response to perturbations in the frontal and sagittal planes during walking? Method A treadmill-based perturbation protocol imposed frontal and sagittal plane perturbations of different magnitudes during different phases of the gait cycle. Motion capture and electromyography measured the response to the different perturbations in a group of eighteen young and ten older adults. Results Only for a small subset of the perturbations, reactive muscle activity and kinematic strategies differed between young and older subjects. When perturbation magnitude increased, the older adults relied more on a stepping strategy for inward directed frontal plane perturbations and for sagittal plane perturbation just before heelstrike. Tibialis anterior activity increased less in the older compared to the young subjects. Using simulations, we related tibialis anterior activity to backward and outward movement of the center of pressure in the stance foot and confirmed its contribution to the ankle strategy. We concluded that deficient tibialis anterior activity predisposes elderly to use stepping rather than lateral ankle strategies to control balance. Significance Rehabilitation targets for fall prevention in elderly need to also focus on ankle muscle reactivit

Evaluation of Different Optimal Control Problem Formulations for Solving the Muscle Redundancy Problem

This study evaluates several possible optimal control problem formulations for solving the muscle redundancy problem with the goal of identifying the most efficient and robust formulation. One novel formulation involves the introduction of additional controls that equal the time derivative of the states, resulting in very simple dynamic equations. The nonlinear equations describing muscle dynamics are then imposed as algebraic constraints in their implicit form, simplifying their evaluation. By comparing different problem formulations for computing muscle controls that can reproduce inverse dynamic joint torques during gait, we demonstrate the efficiency and robustness of the proposed novel formulation

Insights into muscle metabolic energetics: Modelling muscle-tendon mechanics and metabolic rates during walking across speeds

Prior studies have produced models to predict metabolic rates based on experimental observations of isolated muscle contraction from various species. Such models can provide reliable predictions of metabolic rates in humans if muscle properties and control are accurately modeled. This study aimed to examine how muscle-tendon model calibration and metabolic energy models influenced estimation of muscle-tendon states and time-series metabolic rates, to evaluate the agreement with empirical data, and to provide predictions of the metabolic rate of muscle groups and gait phases across walking speeds. Three-dimensional musculoskeletal simulations with prescribed kinematics and dynamics were performed. An optimal control formulation was used to compute muscle-tendon states with four levels of individualization, ranging from a scaled generic model and muscle controls based on minimal activations, to calibration of passive muscle forces, personalization of Achilles and quadriceps tendon stiffnesses, to finally informing muscle controls with electromyography. We computed metabolic rates based on existing models. Simulations with calibrated passive forces and personalized tendon stiffness most accurately estimate muscle excitations and fiber lengths. Interestingly, the inclusion of electromyography did not improve our estimates. The whole-body average metabolic cost was better estimated using Bhargava et al. 2004 and Umberger 2010 models. We estimated metabolic rate peaks near early stance, pre-swing, and initial swing at all walking speeds. Plantarflexors accounted for the highest cost among muscle groups at the preferred speed and was similar to the cost of hip adductors and abductors combined. Also, the swing phase accounted for slightly more than one-quarter of the total cost in a gait cycle, and its relative cost decreased with walking speed.Comment: 33 pages, 7 figure

Algorithmic differentiation improves the computational efficiency of OpenSim-based trajectory optimization of human movement

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.Postprint (published version

The formulation of the foot-ground contact model influences the computation time of biomechanical optimal control problems

Postprint (published version

Modulation of gluteus medius activity reflects the potential of the muscle to meet the mechanical demands during perturbed walking

Mediolateral stability during walking can be controlled by adjustment of foot placement. Reactive activity of gluteus medius (GM) is modulated during the gait cycle. However, the mechanisms behind the modulation are yet unclear. We measured reactive GM activity and kinematics in response to a mediolateral platform translation during different phases of the gait cycle. Forward simulations of perturbed walking were used to evaluate the isolated effect of the perturbation and the GM response on gait stability. We showed that the potential of GM to adjust lateral foot placement and prevent collisions during swing varies during the gait cycle and explains the observed modulation. The observed increase in stance, swing or combined GM activity causes an outward foot placement and therefore compensates for the loss of stability caused by a perturbation early in the gait cycle. GM activity of the swing leg in response to a platform translation late in the gait cycle counteracts foot placement, but prevents collision of the swing foot with the stance leg. This study provides insights in the neuromechanics of reactive control of gait stability and proposes a novel method to distinguish between the effect of perturbation force and reactive muscle activity on gait stability

Rapid predictive simulations with complex musculoskeletal models suggest that diverse healthy and pathological human gaits can emerge from similar control strategies

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.Postprint (published version

Subject-exoskeleton contact model calibration leads to accurate interaction force predictions

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 modeling 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 root mean square differences - RMSD - coordinates = 1.1° and velocities = 6.8°/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° and velocities = 15.0°/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.Postprint (author's final draft