A multisegment computer simulation of normal human gait

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods. Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Does joint impedance improve dynamic leg simulations with explicit and implicit solvers?

The nervous system predicts and executes complex motion of body segments actuated by the coordinated action of muscles. When a stroke or other traumatic injury disrupts neural processing, the impeded behavior has not only kinematic but also kinetic attributes that require interpretation. Biomechanical models could allow medical specialists to observe these dynamic variables and instantaneously diagnose mobility issues that may otherwise remain unnoticed. However, the real-time and subject-specific dynamic computations necessitate the optimization these simulations. In this study, we explored the effects of intrinsic viscoelasticity, choice of numerical integration method, and decrease in sampling frequency on the accuracy and stability of the simulation. The bipedal model with 17 rotational degrees of freedom (DOF)-describing hip, knee, ankle, and standing foot contact-was instrumented with viscoelastic elements with a resting length in the middle of the DOF range of motion. The accumulation of numerical errors was evaluated in dynamic simulations using swing-phase experimental kinematics. The relationship between viscoelasticity, sampling rates, and the integrator type was evaluated. The optimal selection of these three factors resulted in an accurate reconstruction of joint kinematics (err < 1%) and kinetics (err < 5%) with increased simulation time steps. Notably, joint viscoelasticity reduced the integration errors of explicit methods and had minimal to no additional benefit for implicit methods . Gained insights have the potential to improve diagnostic tools and accurize real-time feedback simulations used in the functional recovery of neuromuscular diseases and intuitive control of modern prosthetic solutions.

Joint kinetic response during unexpectedly reduced plantar flexor torque provided by a robotic ankle exoskeleton during walking

During human walking, plantar flexor activation in late stance helps to generate a stable and economical gait pattern. Because plantar flexor activation is highly mediated by proprioceptive feedback, the nervous system must modulate reflex pathways to meet the mechanical requirements of gait. The purpose of this study was to quantify ankle joint mechanical output of the plantar flexor stretch reflex response during a novel unexpected gait perturbation. We used a robotic ankle exoskeleton to mechanically amplify the ankle torque output resulting from soleus muscle activation. We recorded lower-body kinematics, ground reaction forces, and electromyography during steady-state walking and during randomly perturbed steps when the exoskeleton assistance was unexpectedly turned off. We also measured soleus Hoffmann- (H-) reflexes at late stance during the two conditions. Subjects reacted to the unexpectedly decreased exoskeleton assistance by greatly increasing soleus muscle activity about 60ms after ankle angle deviated from the control condition (p<0.001). There were large differences in ankle kinematic and electromyography patterns for the perturbed and control steps, but the total ankle moment was almost identical for the two conditions (p=0.13). The ratio of soleus H-reflex amplitude to background electromyography was not significantly different between the two conditions (p=0.4). This is the first study to show that the nervous system chooses reflex responses during human walking such that invariant ankle joint moment patterns are maintained during perturbations. Our findings are particularly useful for the development of neuromusculoskeletal computer simulations of human walking that need to adjust reflex gains appropriately for biomechanical analyses.

Human-like control strategy of a bipedal walking model

This paper presents a two-level control strategy for bipedal walking mechanism that accounts for implicit control of push-off on the between-step control level and tracking of imposed holonomic constraints on kinematic variables via feedback control on within-step control level. The proposed control strategy was tested in a biologically inspired model with minimal set of segments that allows evolution of human-like push-off and power absorption. We investigated controller's stability characteristics by using Poincaré return map analysis in eight simulation cases and further evaluated the performance of the biped walking model in terms of how variations in torso position and gait velocity relate to push-off and power absorption. The results show that the proposed control strategy, with the same set of controller's gains, enables stable walking in a variety of chosen gait parameters and can accommodate to various trunk inclinations and gait velocities in a similar way as seen in humans.

A model of cerebrocerebello-spinomuscular interaction in the sagittal control of human walking

A computationally developed model of human upright balance control (Jo and Massaquoi on Biol cybern 91:188-202, 2004) has been enhanced to describe biped walking in the sagittal plane. The model incorporates (a) non-linear muscle mechanics having activation level -dependent impedance, (b) scheduled cerebrocerebellar interaction for control of center of mass position and trunk pitch angle, (c) rectangular pulse-like feedforward commands from a brainstem/ spinal pattern generator, and (d) segmental reflex modulation of muscular synergies to refine inter-joint coordination. The model can stand when muscles around the ankle are coactivated. When trigger signals activate, the model transitions from standing still to walking at 1.5 m/s. Simulated natural walking displays none of seven pathological gait features. The model can simulate different walking speeds by tuning the amplitude and frequency in spinal pattern generator. The walking is stable against forward and backward pushes of up to 70 and 75 N, respectively, and with sudden changes in trunk mass of up to 18%. The sensitivity of the model to changes in neural parameters and the predicted behavioral results of simulated neural system lesions are examined. The deficit gait simulations may be useful to support the functional and anatomical correspondences of the model. The model demonstrates that basic human-like walking can be achieved by a hierarchical structure of stabilized-long loop feedback and synergy-mediated feedforward controls. In particular, internal models of body dynamics are not required.

Biomechanics and muscle coordination of human walking: part II: lessons from dynamical simulations and clinical implications

Principles of muscle coordination in gait have been based largely on analyses of body motion, ground reaction force and EMG measurements. However, data from dynamical simulations provide a cause-effect framework for analyzing these measurements; for example, Part I (Gait Posture, in press) of this two-part review described how force generation in a muscle affects the acceleration and energy flow among the segments. This Part II reviews the mechanical and coordination concepts arising from analyses of simulations of walking. Simple models have elucidated the basic multisegmented ballistic and passive mechanics of walking. Dynamical models driven by net joint moments have provided clues about coordination in healthy and pathological gait. Simulations driven by muscle excitations have highlighted the partial stability afforded by muscles with their viscoelastic-like properties and the predictability of walking performance when minimization of metabolic energy per unit distance is assumed. When combined with neural control models for exciting motoneuronal pools, simulations have shown how the integrative properties of the neuro-musculo-skeletal systems maintain a stable gait. Other analyses of walking simulations have revealed how individual muscles contribute to trunk support and progression. Finally, we discuss how biomechanical models and simulations may enhance our understanding of the mechanics and muscle function of walking in individuals with gait impairments.

Computer modeling and simulation of human movement

Recent interest in using modeling and simulation to study movement is driven by the belief that this approach can provide insight into how the nervous system and muscles interact to produce coordinated motion of the body parts. With the computational resources available today, large-scale models of the body can be used to produce realistic simulations of movement that are an order of magnitude more complex than those produced just 10 years ago. This chapter reviews how the structure of the neuromusculoskeletal system is commonly represented in a multijoint model of movement, how modeling may be combined with optimization theory to simulate the dynamics of a motor task, and how model output can be analyzed to describe and explain muscle function. Some results obtained from simulations of jumping, pedaling, and walking are also reviewed to illustrate the approach.

A Method for Numerical Simulation of Single Limb Ground Contact Events: Application to Heel-Toe Running

The objective of this work was to develop a method to simulate single-limb ground contact events, which may be applied to study musculoskeletal injuries associated with such movements. To achieve this objective, a three-dimensional musculoskeletal model was developed consisting of the equations of motion for the musculoskeletal system, and models for the muscle force generation and ground contact elements. An optimization framework and a weighted least-squares objective function were presented that generated muscle stimulation patterns that optimally reproduced subject-specific movement data. Experimental data were collected from a single subject to provide initial conditions for the simulation and tracking data for the optimization. As an example application, a simulation of the stance phase of running was generated. The results showed that the average difference between the simulation and subject's ground reaction force and joint angle data was less than two inter-trial standard deviations. Further, there was good agreement between the model's muscle excitation patterns and experimentally collected electromyography data. These results give confidence in the model to examine musculoskeletal loading during a variety of landing movements and to study the effects of various factors associated with injury. Limitations were examined and areas of improvement for the model were presented.

The swing phase of human walking is not a passive movement

Many studies have assumed that the swing phase of human walking at preferred velocity is largely passive and thus highly analogous to the swing of an unforced pendulum. In other words, while swing-phase joint moments are generally nonzero during swing, it was assumed that they were either zero or at least negligibly small compared to gravity. While neglect of joint moments does not invalidate a study by default, it remains that the limitations of such an assumption have not been explored thoroughly. This paper makes five arguments that the swing phase cannot be passive, using both original data and the literature: (1) Computer simulations of the swing phase require muscular control to be accurate. (2) Swing-phase joint moments, while smaller than those during stance, are still greater than those due to gravity. (3) Gravity accounts for a minority of the total kinetics of a swing phase. (4) The kinetics due to gravity do not have the pattern needed to develop a normal swing phase. (5) There is no correlation between pendular swing times and human walking periods in overground walking. The conclusion of this paper is that the swing phase must be an actively controlled process, and should be assumed to be passive only when a study does not require a quantitative result. This conclusion has significant implications for many areas of gait research, including clinical study, control theory, and mechanical modeling.

Energy-conserving impact algorithm for the heel-strike phase of gait

Significant ground reaction forces exceeding body weight occur during the heel-strike phase of gait. The standard methods of analytical dynamics used to solve the impact problem do not accommodate well the heel-strike collision due to the persistent contact at the front foot and presence of contact at the back foot. These methods can cause a non-physical energy gain on the order of the total kinetic energy of the system at impact. Additionally, these standard techniques do not quantify the contact force, but the impulse over the impact. We present an energy-conserving impact algorithm based on the penalty method to solve for the ground reaction forces during gait. The rigid body assumptions are relaxed and the bodies are allowed to penetrate one another to a small degree. Associated with the deformation is a potential, from which the contact forces are derived. The empirical coefficient-of-restitution used in the standard approaches is replaced by two parameters to characterize the stiffness and the damping of the materials. We solve two simple heel-strike models to illustrate the shortcomings of a standard approach and the suitability of the proposed method for use with gait.