The use of inverse dynamics solutions in direct dynamics simulations

Muscle Synergies Facilitate Computational Prediction of Subject-Specific Walking Motions

Researchers have explored a variety of neurorehabilitation approaches to restore normal walking function following a stroke. However, there is currently no objective means for prescribing and implementing treatments that are likely to maximize recovery of walking function for any particular patient. As a first step toward optimizing neurorehabilitation effectiveness, this study develops and evaluates a patient-specific synergy-controlled neuromusculoskeletal simulation framework that can predict walking motions for an individual post-stroke. The main question we addressed was whether driving a subject-specific neuromusculoskeletal model with muscle synergy controls (5 per leg) facilitates generation of accurate walking predictions compared to a model driven by muscle activation controls (35 per leg) or joint torque controls (5 per leg). To explore this question, we developed a subject-specific neuromusculoskeletal model of a single high-functioning hemiparetic subject using instrumented treadmill walking data collected at the subject's self-selected speed of 0.5 m/s. The model included subject-specific representations of lower-body kinematic structure, foot-ground contact behavior, electromyography-driven muscle force generation, and neural control limitations and remaining capabilities. Using direct collocation optimal control and the subject-specific model, we evaluated the ability of the three control approaches to predict the subject's walking kinematics and kinetics at two speeds (0.5 and 0.8 m/s) for which experimental data were available from the subject. We also evaluated whether synergy controls could predict a physically realistic gait period at one speed (1.1 m/s) for which no experimental data were available. All three control approaches predicted the subject's walking kinematics and kinetics (including ground reaction forces) well for the model calibration speed of 0.5 m/s. However, only activation and synergy controls could predict the subject's walking kinematics and kinetics well for the faster non-calibration speed of 0.8 m/s, with synergy controls predicting the new gait period the most accurately. When used to predict how the subject would walk at 1.1 m/s, synergy controls predicted a gait period close to that estimated from the linear relationship between gait speed and stride length. These findings suggest that our neuromusculoskeletal simulation framework may be able to bridge the gap between patient-specific muscle synergy information and resulting functional capabilities and limitations.

Long-latency muscle activity reflects continuous, delayed sensorimotor feedback of task-level and not joint-level error

In both the upper and lower limbs, evidence suggests that short-latency electromyographic (EMG) responses to mechanical perturbations are modulated based on muscle stretch or joint motion, whereas long-latency responses are modulated based on attainment of task-level goals, e.g., desired direction of limb movement. We hypothesized that long-latency responses are modulated continuously by task-level error feedback. Previously, we identified an error-based sensorimotor feedback transformation that describes the time course of EMG responses to ramp-and-hold perturbations during standing balance (Safavynia and Ting 2013; Welch and Ting 2008, 2009). Here, our goals were 1) to test the robustness of the sensorimotor transformation over a richer set of perturbation conditions and postural states; and 2) to explicitly test whether the sensorimotor transformation is based on task-level vs. joint-level error. We developed novel perturbation trains of acceleration pulses such that perturbations were applied when the body deviated from the desired, upright state while recovering from preceding perturbations. The entire time course of EMG responses (∼4 s) in an antagonistic muscle pair was reconstructed using a weighted sum of center of mass (CoM) kinematics preceding EMGs at long-latency delays (∼100 ms). Furthermore, CoM and joint kinematic trajectories became decorrelated during perturbation trains, allowing us to explicitly compare task-level vs. joint feedback in the same experimental condition. Reconstruction of EMGs was poorer using joint kinematics compared with CoM kinematics and required unphysiologically short (∼10 ms) delays. Thus continuous, long-latency feedback of task-level variables may be a common mechanism regulating long-latency responses in the upper and lower limbs.

Sensorimotor feedback based on task-relevant error robustly predicts temporal recruitment and multidirectional tuning of muscle synergies

We hypothesized that motor outputs are hierarchically organized such that descending temporal commands based on desired task-level goals flexibly recruit muscle synergies that specify the spatial patterns of muscle coordination that allow the task to be achieved. According to this hypothesis, it should be possible to predict the patterns of muscle synergy recruitment based on task-level goals. We demonstrated that the temporal recruitment of muscle synergies during standing balance control was robustly predicted across multiple perturbation directions based on delayed sensorimotor feedback of center of mass (CoM) kinematics (displacement, velocity, and acceleration). The modulation of a muscle synergy's recruitment amplitude across perturbation directions was predicted by the projection of CoM kinematic variables along the preferred tuning direction(s), generating cosine tuning functions. Moreover, these findings were robust in biphasic perturbations that initially imposed a perturbation in the sagittal plane and then, before sagittal balance was recovered, perturbed the body in multiple directions. Therefore, biphasic perturbations caused the initial state of the CoM to differ from the desired state, and muscle synergy recruitment was predicted based on the error between the actual and desired upright state of the CoM. These results demonstrate that that temporal motor commands to muscle synergies reflect task-relevant error as opposed to sensory inflow. The proposed hierarchical framework may represent a common principle of motor control across motor tasks and levels of the nervous system, allowing motor intentions to be transformed into motor actions.

Neuromechanic: a computational platform for simulation and analysis of the neural control of movement

Neuromusculoskeletal models solve the basic problem of determining how the body moves under the influence of external and internal forces. Existing biomechanical modeling programs often emphasize dynamics with the goal of finding a feed-forward neural program to replicate experimental data or of estimating force contributions or individual muscles. The computation of rigid-body dynamics, muscle forces, and activation of the muscles are often performed separately. We have developed an intrinsically forward computational platform (Neuromechanic, www.neuromechanic.com) that explicitly represents the interdependencies among rigid body dynamics, frictional contact, muscle mechanics, and neural control modules. This formulation has significant advantages for optimization and forward simulation, particularly with application to neural controllers with feedback or regulatory features. Explicit inclusion of all state dependencies allows calculation of system derivatives with respect to kinematic states and muscle and neural control states, thus affording a wealth of analytical tools, including linearization, stability analyses and calculation of initial conditions for forward simulations. In this review, we describe our algorithm for generating state equations and explain how they may be used in integration, linearization, and stability analysis tools to provide structural insights into the neural control of movement.

During walking elders increase efforts at proximal joints and keep low kinetics at the ankle

BACKGROUND

Both ageing and speed definitely affect gait patterns. Since most of the comparisons between young and elderly people while walking have been carried out at different "self-selected" speeds, results might be biased by a lack of control of the effects of both the concomitant issues. Therefore, further investigations aimed at separating the influence of both the sources of variability are required.

METHODS

Nine young and eight elderly healthy subjects walked on a treadmill at five normalised speeds according to the Froude Number, from 0.5 to 1.3 m/s. Step parameters and peaks belonging to kinematic and kinetic patterns have been compared between the groups and over the five speeds by the two-factor (Group and Speed) ANOVA.

FINDINGS

After making walking speed comparable between the groups, in elders, hip and knee concentric powers during the stance phase were higher than in young subjects despite their decreased ankle plantarflexor kinetics. Kinematic differences occurred in conjunction with the modifications of the kinetic patterns.

INTERPRETATION

Since proximal and distal extensor muscles contribute to the same functional tasks during walking (e.g., stabilisation, forward acceleration of the trunk, body support against gravity), ageing would involve a different sharing of muscle efforts among leg joints, increasing the work load of the proximal extensor muscles. Moreover, gait analysis, when carried out at controlled and comparable speeds, can better pinpoint features of each group of subjects than the comparison at self-selected speed.

A novel two-stage framework for musculoskeletal dynamic modeling: an application to multifingered hand movement

In this paper, we present a new computational framework for biodynamic modeling of human movement. The framework decouples the conventional dynamic modeling process into two stages: in the first stage, two-component "agonist-antagonist" torque actuators under hypothesized and testable parametric control drive the forward dynamics, and parameters are identified by tracking both kinematics and kinetics; the second stage completes the mapping from the muscle-tendon forces to the predicted joint torques. An empirical test using multifinger grasping movement data was conducted to illustrate the application of the proposed framework and showed that the model reproduced the measurement accurately in both kinematics and kinetics. The torque components exhibited consistent spatial-temporal patterns across joints, digits, and subjects. The muscle-tendon forces computed based on the model-predicted kinematics and kinetics had the peak values within the same order of magnitude as in vivo data reported in the literature. The potential to predict was also demonstrated as we applied the control parameters of one subject to another and achieved close matches.

A nonlinear tracking method of computing net joint torques for human movement

Determining individual muscles forces from human performance has greatly depended on the quality of inverse dynamics solutions, as muscle force decomposition remains the only feasible approach for determining muscle forces non-invasively in human movement. However, legitimate questions about the accuracy of inverse dynamics arise, with resultant torques/forces failing to drive a forward model through the observations from which they were derived. While optimization of forward dynamics to match experimental data is considered more accurate, the simplicity and low computational costs of inverse methods are favored over the large computing requirements of optimization. In this paper, an evolution in the inverse methods for computing accurate and reliable torques is presented, whereby the relative speed of inverse dynamics is combined with the desired accuracy of forward dynamics. This method is based on developing a nonlinear tracker that determines the net muscle torques which accurately follow clinically observed kinematics and ground reaction forces. The results show that the method is robust and can produce accurate estimates of the joint torques during movement. The method outlined here is a necessary first step to solving the muscle force indeterminancy problem more efficiently.

Optimal sensorimotor transformations for balance

Here we have identified a sensorimotor transformation that is used by a mammalian nervous system to produce a multijoint motor behavior. Using a simple biomechanical model, a delayed-feedback rule based on an optimal tradeoff between postural error and neural effort explained patterns of muscle activation in response to a sudden loss of balance in cats. Following the loss of large sensory afferents, changes in these muscle-activation patterns reflected an optimal reweighting of sensory feedback gains to minimize postural instability. Specifically, a loss of center-of-mass-acceleration information, which allowed for a rapid initial rise in the muscle activity in intact animals, was absent after large-fiber sensory neuropathy. Our results demonstrate that a simple and flexible neural feedback control strategy coordinates multiple muscles over time via a small set of extrinsic, task-level variables during complex multijoint natural movements.

Optimal Combination of Minimum Degrees of Freedom to be Actuated in the Lower Limbs to Facilitate Arm-Free Paraplegic Standing

Arm-free paraplegic standing via functional electrical stimulation (FES) has drawn much attention in the biomechanical field as it might allow a paraplegic to stand and simultaneously use both arms to perform daily activities. However, current FES systems for standing require that the individual actively regulates balance using one or both arms, thus limiting the practical use of these systems. The purpose of the present study was to show that actuating only six out of 12 degrees of freedom (12-DOFs) in the lower limbs to allow paraplegics to stand freely is theoretically feasible with respect to multibody stability and physiological torque limitations of the lower limb DOF. Specifically, the goal was to determine the optimal combination of the minimum DOF that can be realistically actuated using FES while ensuring stability and able-bodied kinematics during perturbed arm-free standing. The human body was represented by a three-dimensional dynamics model with 12-DOFs in the lower limbs. Nakamura’s method (Nakamura, Y., and Ghodoussi, U., 1989, “Dynamics Computation of Closed-Link Robot Mechanisms With Nonredundant and Redundant Actuators,” IEEE Trans. Rob. Autom., 5(3), pp. 294–302) was applied to estimate the joint torques of the system using experimental motion data from four healthy subjects. The torques were estimated by applying our previous finding that only 6 (6-DOFs) out of 12-DOFs in the lower limbs need to be actuated to facilitate stable standing. Furthermore, it was shown that six cases of 6-DOFs exist, which facilitate stable standing. In order to characterize each of these cases in terms of the torque generation patterns and to identify a potential optimal 6-DOF combination, the joint torques during perturbations in eight different directions were estimated for all six cases of 6-DOFs. The results suggest that the actuation of both ankle flexion∕extension, both knee flexion∕extension, one hip flexion∕extension, and one hip abduction∕adduction DOF will result in the minimum torque requirements to regulate balance during perturbed standing. To facilitate unsupported FES-assisted standing, it is sufficient to actuate only 6-DOFs. An optimal combination of 6-DOFs exists, for which this system can generate able-bodied kinematics while requiring lower limb joint torques that are producible using contemporary FES technology. These findings suggest that FES-assisted arm-free standing of paraplegics is theoretically feasible, even when limited by the fact that muscles actuating specific DOFs are often denervated or difficult to access.

A neuromusculoskeletal tracking method for estimating individual muscle forces in human movement

A neuromusculoskeletal tracking (NMT) method was developed to estimate muscle forces from observed motion data. The NMT method combines skeletal motion tracking and optimal neuromuscular tracking to produce forward simulations of human movement quickly and accurately. The skeletal motion tracker calculates the joint torques needed to actuate a skeletal model and track observed segment angles and ground forces in a forward simulation of the motor task. The optimal neuromuscular tracker resolves the muscle redundancy problem dynamically and finds the muscle excitations (and muscle forces) needed to produce the joint torques calculated by the skeletal motion tracker. To evaluate the accuracy of the NMT method, kinematics and ground forces obtained from an optimal control (parameter optimization) solution for maximum-height jumping were contaminated with both random and systematic noise. These data served as input observations to the NMT method as well as an inverse dynamics analysis. The NMT solution was compared to the input observations, the original optimal solution, and a simulation driven by the inverse dynamics torques. The results show that, in contrast to inverse dynamics, the NMT method is able to produce an accurate forward simulation consistent with the optimal control solution. The NMT method also requires 3 orders-of-magnitude less CPU time than parameter optimization. The speed and accuracy of the NMT method make it a promising new tool for estimating muscle forces using experimentally obtained kinematics and ground force data.

Validation of net joint loads calculated by inverse dynamics in case of complex movements: Application to balance recovery movements

The joint forces and moments driving the motion of a human subject are classically computed by an inverse dynamic calculation. However, even if this process is theoretically simple, many sources of errors may lead to huge inaccuracies in the results. Moreover, a direct comparison with in vivo measured loads or with "gold standard" values from literature is only possible for very specific studies. Therefore, assessing the inaccuracy of inverse dynamic results is not a trivial problem and a simple method is still required. This paper presents a simple method to evaluate both: (1) the consistency of the results obtained by inverse dynamics; (2) the influence of possible modifications in the inverse dynamic hypotheses. This technique concerns recursive calculation performed on full kinematic chains, and consists in evaluating the loads obtained by two different recursive strategies. It has been applied to complex 3D whole body movements of balance recovery. A recursive Newton-Euler procedure was used to compute the net joint loads. Two models were used to represent the subject bodies, considering or not the upper body as a unique rigid segment. The inertial parameters of the body segments were estimated from two different sets of scaling equations [De Leva, P., 1996. Adjustments to Zatsiorsky-Suleyanov's segment inertia parameters. Journal of Biomechanics 29, 1223-1230; Dumas, R., Chèze, L., Verriest, J.-P., 2006b. Adjustments to McConville et al. and Young et al. Body Segment Inertial Parameters. Journal of Biomechanics, in press]. Using this comparison technique, it has been shown that, for the balance recovery motions investigated: (1) the use of the scaling equations proposed by Dumas et al., instead of those proposed by De Leva, improves the consistency of the results (average relative influence up to 30% for the transversal moment); (2) the arm motions dynamically influence the recovery motion in a non negligible way (average relative influence up to 15% and 30% for the longitudinal force and the transversal moment, respectively).

Dimensional reduction in sensorimotor systems: a framework for understanding muscle coordination of posture

The simple act of standing up is an important and essential motor behavior that most humans and animals achieve with ease. Yet, maintaining standing balance involves complex sensorimotor transformations that must continually integrate a large array of sensory inputs and coordinate multiple motor outputs to muscles throughout the body. Multiple, redundant local sensory signals are integrated to form an estimate of a few global, task-level variables important to postural control, such as body center of mass (CoM) position and body orientation with respect to Earth-vertical. Evidence suggests that a limited set of muscle synergies, reflecting preferential sets of muscle activation patterns, are used to move task-variables such as CoM position in a predictable direction following postural perturbations. We propose a hierarchical feedback control system that allows the nervous system the simplicity of performing goal-directed computations in task-variable space, while maintaining the robustness afforded by redundant sensory and motor systems. We predict that modulation of postural actions occurs in task-variable space, and in the associated transformations between the low-dimensional task-space and high-dimensional sensor and muscle spaces. Development of neuromechanical models that reflect these neural transformations between low- and high-dimensional representations will reveal the organizational principles and constraints underlying sensorimotor transformations for balance control, and perhaps motor tasks in general. This framework and accompanying computational models could be used to formulate specific hypotheses about how specific sensory inputs and motor outputs are generated and altered following neural injury, sensory loss, or rehabilitation.

Experimental/analytical analysis of human locomotion using bondgraphs

A new vectorial bondgraph approach for modeling and simulation of human locomotion is introduced. The vectorial bondgraph is applied to an eight-segment gait model to derive the equations of motion for studying ground reaction forces (GRFs) and centers of pressure (COPs) in single and double support phases of ground and treadmill walking. A phase detection technique and accompanying transition equation is proposed with which the GRFs and COPs may be calculated for the transitions from double-to-single and single-to-double support phases. Good agreement is found between model predictions and experimental data obtained from force plate measurements. The bondgraph modeling approach is shown to be both informative and adaptable, in the sense that the model resembles the human body structure, and that modeled body segments can be easily added or removed.

Determining finger segmental centers of rotation in flexion-extension based on surface marker measurement

This paper describes the development of a novel algorithm for deriving finger segmental center of rotation (COR) locations during flexion-extension from measured surface marker motions in vivo. The algorithm employs an optimization routine minimizing the time-variance of the internal link lengths, and incorporates an empirically quantifiable relationship between the local movement of a surface marker around a joint (termed "surface marker excursion") and the joint flexion-extension. The latter relationship constrains and simplifies the optimization routine to make it computationally tractable. To empirically investigate this relationship and test the proposed algorithm, an experiment was conducted, in which hand cylinder-grasping movements were performed by 24 subjects (12 males and 12 females). Spherical retro-reflective markers were placed at various surface landmarks on the dorsal aspect of each subject's right (grasping) hand, and were measured during the movements by an opto-electronic system. Analysis of experimental data revealed a highly linear relationship between the "surface marker excursion" and the marker-defined flexion-extension angle: the average R(2) in linear regression ranged from 0.89 to 0.97. The algorithm successfully determined the CORs of the distal interphalangeal, proximal interphalangeal, and metacarpophalangeal joints of digits 2-5 during measured motions. The derived CORs appeared plausible as examined in terms of the physical locations relative to surface marker trajectories and the congruency across different joints and individuals.

An EMG-based, muscle driven forward simulation of single support phase of gait

This paper describes the process used to generate lower limb kinematics during single limb stance phase of gait, using musculoskeletal modelling, muscle driven forward simulation and gradient based optimisation techniques (including design of experiment techniques). Initial inputs to the forward simulation process were the normalised quantified muscle activation patterns of 22 muscles, and the initial segmental configuration (both angles and angular velocity) derived from Winter (The biomechanics and motor control of human gait, 1987, University of Waterloo Press, pp. 1-72). Two distinct musculoskeletal models (one including 6 DOF, the other 7 DOF) were defined and a muscle driven forward simulation was implemented.A series of optimisation sequences then were executed to modify the muscle activation patterns and initial segmental configuration, until the system output of the forward simulation approximated the angle data reported by. The accuracy and effectiveness of the analysis sequence proposed and the model response obtained using two distinct musculoskeletal models were verified and analysed with respect to the kinesiology of normal walking.

Minimum measured-input models for the assessment of motor ability

The problem of assessing the physical functional limitation of a given individual and establishing the relationship between impairment/s and disability using a biomechanical approach is addressed. This endeavour was pursued with reference to the locomotor system and in order to address the following specific clinical issues: prognosis, eligibility for health services, measure of the outcome of a therapy, and therapeutic programming. A thorough biomechanical analysis of selected motor tasks would be effective but awkward to apply for subject-specific evaluation in clinical practice by reason of the complexity of both instrumentation and experimental protocols. In addition, as illustrated in the paper, the adequacy of the accuracy with which this type of analysis provides relevant information may be argued. Therefore, different methods were devised in the attempt to join objectivity with field applicability. These entailed the measurement of a minimum number of biomechanical variables during the execution of the selected motor task and these quantities were acquired using a low cost experimental apparatus least perceivable to the test subject, that is a dynamometric plate. However, since data thus obtained do not necessarily lend themselves to straightforward interpretation in terms of function assessment, models of the musculo-skeletal system that embodied the invariant aspects of both the modelled system and the specific motor task were devised. Using such "minimum measured-input models", physiology-related, and thus easier to interpret, information was obtained. Two different sets of mathematical models are presented: one deals with the lowest level of detail and normally aims at assessing a global physical performance score, the other discloses joint function and segmental mechanics and therefore contributes to establishing a relationship between impairment and disability. The validation of these models, carried out in the laboratory, has shown that they possess a potential for application in clinical practice.

Modeling and inverse simulation of somersaults on the trampoline

This paper describes a biomechanical model for numerical simulation of front and back somersaults, without twist, performed on the trampoline. The developed mathematical formulation is used to solve an inverse dynamics problem, in which the moments of muscle forces at the joints that result in a given (measured) motion are determined. The nature of the stunts and the way the human body is maneuvered and controlled can be studied. The calculated torques can then be used as control signals for a dynamic simulation. This provides a way to check the inverse dynamics procedures, and influence of typical control errors on somersault performance can be studied. To achieve these goals, the nonlinear dynamical model of the trampolinist and the interacting trampoline bed has been identified, and a methodology for recording the actual somersault performances was proposed. Some results of numerical simulations are reported.