A Dynamic Optimization Solution for Vertical Jumping in Three Dimensions

Sensitivity of model predictions of muscle function to changes in moment arms and muscle-tendon properties: a Monte-Carlo analysis

Hill-type muscle models are commonly used in musculoskeletal models to estimate muscle forces during human movement. However, the sensitivity of model predictions of muscle function to changes in muscle moment arms and muscle-tendon properties is not well understood. In the present study, a three-dimensional muscle-actuated model of the body was used to evaluate the sensitivity of the function of the major lower limb muscles in accelerating the whole-body center of mass during gait. Monte-Carlo analyses were used to quantify the effects of entire distributions of perturbations in the moment arms and architectural properties of muscles. In most cases, varying the moment arm and architectural properties of a muscle affected the torque generated by that muscle about the joint(s) it spanned as well as the torques generated by adjacent muscles. Muscle function was most sensitive to changes in tendon slack length and least sensitive to changes in muscle moment arm. However, the sensitivity of muscle function to changes in moment arms and architectural properties was highly muscle-specific; muscle function was most sensitive in the cases of gastrocnemius and rectus femoris and insensitive in the cases of hamstrings and the medial sub-region of gluteus maximus. The sensitivity of a muscle's function was influenced by the magnitude of the muscle's force as well as the operating region of the muscle on its force-length curve. These findings have implications for the development of subject-specific models of the human musculoskeletal system.

Trunk position modulates anterior cruciate ligament forces and strains during a single-leg squat

BACKGROUND

Although the squat exercise and its variations are commonly prescribed for anterior cruciate ligament rehabilitation, whether trunk position affects these ligament forces and strains during the squat is unclear. Our purpose was to evaluate the effects of trunk position on anterior cruciate ligament forces and strains during a single-leg squat.

METHODS

While instrumented for biomechanical analysis, twelve recreationally active subjects performed single-leg squats with minimal and moderate amounts of forward trunk lean. A combination of inverse dynamics, Hill-type muscle modeling, and mathematical computations estimated anterior cruciate ligament forces, strains and quadriceps, hamstrings, and gastrocnemius forces.

FINDINGS

The moderate forward trunk lean condition vs. minimal forward trunk lean condition had lower peak anterior cruciate ligament forces (↓24%), strains (↓16%), and average anterior cruciate ligament forces and strains during knee flexion ranges of motion of 25-55°(descent) and 35-55°(ascent). A moderate vs. minimal forward trunk lean also produced 35% higher hamstring forces throughout the majority of the squat, but lower quadriceps forces only at knee flexion angles greater than 65°.

INTERPRETATION

Single-leg squats performed with a moderate forward trunk lean (~40°) can minimize anterior cruciate ligament loads. Mechanistically, trunk lean reduced anterior cruciate ligament forces and strains through concomitant modulations in hip flexion angle and biarticular thigh muscle forces. These findings are clinically relevant for anterior cruciate ligament rehabilitation as a common goal is to minimize anterior cruciate ligament forces and strains through enhancing hamstring and quadriceps co-contractions.

Comparison of different methods for estimating muscle forces in human movement

The aim of this study was to compare muscle-force estimates derived for human locomotion using three different methods commonly reported in the literature: static optimisation (SO), computed muscle control (CMC) and neuromusculoskeletal tracking (NMT). In contrast with SO, CMC and NMT calculate muscle forces dynamically by including muscle activation dynamics. Furthermore, NMT utilises a time-dependent performance criterion, wherein a single optimisation problem is solved over the entire time interval of the task. Each of these methods was used in conjunction with musculoskeletal modelling and experimental gait data to determine lower-limb muscle forces for self-selected speeds of walking and running. Correlation analyses were performed for each muscle to quantify differences between the various muscle-force solutions. The patterns of muscle loading predicted by the three methods were similar for both walking and running. The correlation coefficient between any two sets of muscle-force solutions ranged from 0.46 to 0.99 ( p < 0.001 for all muscles). These results suggest that the robustness and efficiency of static optimisation make it the most attractive method for estimating muscle forces in human locomotion.

LEARNING AND RECOGNITION OF HUMAN ACTIONS USING OPTIMAL CONTROL PRIMITIVES

We propose a unified approach for recognition and learning of human actions, based on an optimal control model of human motion. In this model, the goals and preferences of the agent engaged in a particular action are encapsulated as a cost function or performance criterion, that is optimized to yield the details of the movement. The cost function is a compact, intuitive and flexible representation of the action. A parameterized form of the cost function is considered, wherein the structure reflects the goals of the actions, and the parameters determine the relative weighting of different terms. We show how the cost function parameters can be estimated from data by solving a nonlinear least squares problem. The parameter estimation method is tested on motion capture data for two different reaching actions and six different subjects. We show that the problem of action recognition in the context of this representation is similar to that of mode estimation in a hybrid system and can be solved using a particle filter if a receding horizon formulation of the optimal controller is adopted. We use the proposed approach to recognize different reaching actions from the 3D hand trajectory of subjects.

Determination of three-dimensional joint loading within the lower extremities in snowboarding

In the biomechanical literature only a few studies are available focusing on the determination of joint loading within the lower extremities in snowboarding. These studies are limited to analysis in a restricted capture volume due to the use of optical video-based systems. To overcome this restriction the aim of the present study was to develop a method to determine net joint moments within the lower extremities in snowboarding for complete measurement runs. An experienced snowboarder performed several runs equipped with two custom-made force plates as well as a full-body inertial measurement system. A rigid, multi-segment model was developed to describe the motion and loads within the lower extremities. This model is based on an existing lower-body model and designed to be run by the OpenSim software package. Measured kinetic and kinematic data were imported into the OpenSim program and inverse dynamic calculations were performed. The results illustrate the potential of the developed method for the determination of joint loadings within the lower extremities for complete measurement runs in a real snowboarding environment. The calculated net joint moments of force are reasonable in comparison to the data presented in the literature. A good reliability of the method seems to be indicated by the low data variation between different turns. Due to the unknown accuracy of this method the application for inter-individual studies as well as studies of injury mechanisms may be limited. For intra-individual studies comparing different snowboarding techniques as well as different snowboard equipment the method seems to be beneficial. The validity of the method needs to be studied further.

Hamstring musculotendon dynamics during stance and swing phases of high-speed running

INTRODUCTION

Hamstring strain injuries are common in sports that involve high-speed running. It remains uncertain whether the hamstrings are susceptible to injury during late swing phase, when the hamstrings are active and lengthening, or during stance, when contact loads are present. In this study, we used forward dynamic simulations to compare hamstring musculotendon stretch, loading, and work done during stance and swing phases of high-speed running.

METHODS

Whole-body kinematics, EMG activities, and ground reactions were collected as 12 subjects ran on an instrumented treadmill at speeds ranging from 80% to 100% of maximum (avg max speed = 7.8 m·s(-1)). Subject-specific simulations were then created using a whole-body musculoskeletal model that included 52 Hill-type musculotendon units acting about the hip and the knee. A computed muscle control algorithm was used to determine muscle excitation patterns that drove the limb to track measured hip and knee sagittal plane kinematics, with measured ground reactions applied to the limb.

RESULTS

The hamstrings lengthened under load from 50% to 90% of the gait cycle (swing) and then shortened under load from late swing through stance. Although peak hamstring stretch was invariant with speed, lateral hamstring (biceps femoris) loading increased significantly with speed and was greater during swing than stance at the fastest speed. The biarticular hamstrings performed negative work on the system only during swing phase, with the amount of negative work increased significantly with speed.

CONCLUSION

We concluded that the large inertial loads during high-speed running appear to make the hamstrings most susceptible to injury during swing phase. This information is relevant for scientifically establishing muscle injury prevention and rehabilitation programs.

An optimal feedback control framework for grasping objects with position uncertainty

As we move, the relative location between our hands and objects changes in uncertain ways due to noisy motor commands and imprecise and ambiguous sensory information. The impressive capabilities humans display for interacting and manipulating objects with position uncertainty suggest that our brain maintains representations of location uncertainty and builds compensation for uncertainty into its motor control strategies. Our previous work demonstrated that specific control strategies are used to compensate for location uncertainty. However, it is an open question whether compensation for position uncertainty in grasping is consistent with the stochastic optimal feedback control, mainly due to the difficulty of modeling natural tasks within this framework. In this study, we develop a stochastic optimal feedback control model to evaluate the optimality of human grasping strategies. We investigate the properties of the model through a series of simulation experiments and show that it explains key aspects of previously observed compensation strategies. It also provides a basis for individual differences in terms of differential control costs-the controller compensates only to the extent that performance benefits in terms of making stable grasps outweigh the additional control costs of compensation. These results suggest that stochastic optimal feedback control can be used to understand uncertainty compensation in complex natural tasks like grasping.

Effects of step rate manipulation on joint mechanics during running

PURPOSE

the objective of this study was to characterize the biomechanical effects of step rate modification during running on the hip, knee, and ankle joints so as to evaluate a potential strategy to reduce lower extremity loading and risk for injury.

METHODS

three-dimensional kinematics and kinetics were recorded from 45 healthy recreational runners during treadmill running at constant speed under various step rate conditions (preferred, ± 5%, and ± 10%). We tested our primary hypothesis that a reduction in energy absorption by the lower extremity joints during the loading response would occur, primarily at the knee, when step rate was increased.

RESULTS

less mechanical energy was absorbed at the knee (P < 0.01) during the +5% and +10% step rate conditions, whereas the hip (P < 0.01) absorbed less energy during the +10% condition only. All joints displayed substantially (P < 0.01) more energy absorption when preferred step rate was reduced by 10%. Step length (P < 0.01), center of mass vertical excursion (P < 0.01), braking impulse (P < 0.01), and peak knee flexion angle (P < 0.01) were observed to decrease with increasing step rate. When step rate was increased 10% above preferred, peak hip adduction angle (P < 0.01) and peak hip adduction (P < 0.01) and internal rotation (P < 0.01) moments were found to decrease.

CONCLUSION

we conclude that subtle increases in step rate can substantially reduce the loading to the hip and knee joints during running and may prove beneficial in the prevention and treatment of common running-related injuries.

The effects of single-leg landing technique on ACL loading

Anterior Cruciate Ligament (ACL) injury is one of the most serious and costly injuries of the lower extremity, occurring more frequently in females than males. Injury prevention training programs have reported the ability to reduce non-contact ACL injury occurrence. These programs have also been shown to alter an athletes' lower extremity position at initial contact with the ground and throughout the deceleration phase of landing. The purpose of this study was to determine the influence of single-leg landing technique on ACL loading in recreationally active females. Participants were asked to perform "soft" and "stiff" drop landings. A series of musculoskeletal models were then used to estimate muscle, joint, and ACL forces. Dependent t-tests were conducted to investigate differences between the two landing techniques (p<0.05). Instructing participants to land 'softly' resulted in a significant decrease in peak ACL force (p=0.05), and a significant increase in hip and knee flexion both at initial contact (IC) and the time of peak ACL force (F(PACL)). These findings suggest that altering landing technique using simple verbal instruction may result in lower extremity alignment that decreases the resultant load on the ACL. Along with supporting the findings of reduced ACL force with alterations in sagittal plane landing mechanics in the current literature, the results of this study suggest that simple verbal instruction may reduce the ACL force experienced by athletes when landing.

Analytical and numerical analysis of inverse optimization problems: conditions of uniqueness and computational methods

One of the key problems of motor control is the redundancy problem, in particular how the central nervous system (CNS) chooses an action out of infinitely many possible. A promising way to address this question is to assume that the choice is made based on optimization of a certain cost function. A number of cost functions have been proposed in the literature to explain performance in different motor tasks: from force sharing in grasping to path planning in walking. However, the problem of uniqueness of the cost function(s) was not addressed until recently. In this article, we analyze two methods of finding additive cost functions in inverse optimization problems with linear constraints, so-called linear-additive inverse optimization problems. These methods are based on the Uniqueness Theorem for inverse optimization problems that we proved recently (Terekhov et al., J Math Biol 61(3):423-453, 2010). Using synthetic data, we show that both methods allow for determining the cost function. We analyze the influence of noise on the both methods. Finally, we show how a violation of the conditions of the Uniqueness Theorem may lead to incorrect solutions of the inverse optimization problem.

Effect of posterior tibial slope on knee biomechanics during functional activity

Treatment of medial compartment knee osteoarthritis with high tibial osteotomy can produce an unintended change in the slope of the tibial plateau in the sagittal plane. The effect of changing posterior tibial slope (PTS) on cruciate ligament forces has not been quantified for knee loading in activities of daily living. The purpose of this study was to determine how changes in PTS affect tibial shear force, anterior tibial translation (ATT), and knee-ligament loading during daily physical activity. We hypothesized that tibial shear force, ATT, and ACL force all increase as PTS increases. A previously validated computer model was used to calculate ATT, tibial shear force, and cruciate-ligament forces for the normal knee during three common load-bearing tasks: standing, squatting, and walking. The model calculations were repeated with PTS altered in 1° increments up to a maximum change in tibial slope of 10°. Tibial shear force and ATT increased as PTS was increased. For standing and walking, ACL force increased as tibial slope was increased; for squatting, PCL force decreased as tibial slope was increased. The effect of changing PTS on ACL force was greatest for walking. The true effect of changing tibial slope on knee-joint biomechanics may only be evident under physiologic loading conditions which include muscle forces.

OpenSim: a musculoskeletal modeling and simulation framework for in silico investigations and exchange

Movement science is driven by observation, but observation alone cannot elucidate principles of human and animal movement. Biomechanical modeling and computer simulation complement observations and inform experimental design. Biological models are complex and specialized software is required for building, validating, and studying them. Furthermore, common access is needed so that investigators can contribute models to a broader community and leverage past work. We are developing OpenSim, a freely available musculoskeletal modeling and simulation application and libraries specialized for these purposes, by providing: musculoskeletal modeling elements, such as biomechanical joints, muscle actuators, ligament forces, compliant contact, and controllers; and tools for fitting generic models to subject-specific data, performing inverse kinematics and forward dynamic simulations. OpenSim performs an array of physics-based analyses to delve into the behavior of musculoskeletal models by employing Simbody, an efficient and accurate multibody system dynamics code. Models are publicly available and are often reused for multiple investigations because they provide a rich set of behaviors that enables different lines of inquiry. This report will discuss one model developed to study walking and applied to gain deeper insights into muscle function in pathological gait and during running. We then illustrate how simulations can test fundamental hypotheses and focus the aims of in vivo experiments, with a postural stability platform and human model that provide a research environment for performing human posture experiments in silico. We encourage wide adoption of OpenSim for community exchange of biomechanical models and methods and welcome new contributors.

Muscle contributions to propulsion and support during running

Muscles actuate running by developing forces that propel the body forward while supporting the body's weight. To understand how muscles contribute to propulsion (i.e., forward acceleration of the mass center) and support (i.e., upward acceleration of the mass center) during running we developed a three-dimensional muscle-actuated simulation of the running gait cycle. The simulation is driven by 92 musculotendon actuators of the lower extremities and torso and includes the dynamics of arm motion. We analyzed the simulation to determine how each muscle contributed to the acceleration of the body mass center. During the early part of the stance phase, the quadriceps muscle group was the largest contributor to braking (i.e., backward acceleration of the mass center) and support. During the second half of the stance phase, the soleus and gastrocnemius muscles were the greatest contributors to propulsion and support. The arms did not contribute substantially to either propulsion or support, generating less than 1% of the peak mass center acceleration. However, the arms effectively counterbalanced the vertical angular momentum of the lower extremities. Our analysis reveals that the quadriceps and plantarflexors are the major contributors to acceleration of the body mass center during running.

Minimal formulation of joint motion for biomechanisms

Biomechanical systems share many properties with mechanically engineered systems, and researchers have successfully employed mechanical engineering simulation software to investigate the mechanical behavior of diverse biological mechanisms, ranging from biomolecules to human joints. Unlike their man-made counterparts, however, biomechanisms rarely exhibit the simple, uncoupled, pure-axial motion that is engineered into mechanical joints such as sliders, pins, and ball-and-socket joints. Current mechanical modeling software based on internal-coordinate multibody dynamics can formulate engineered joints directly in minimal coordinates, but requires additional coordinates restricted by constraints to model more complex motions. This approach can be inefficient, inaccurate, and difficult for biomechanists to customize. Since complex motion is the rule rather than the exception in biomechanisms, the benefits of minimal coordinate modeling are not fully realized in biomedical research. Here we introduce a practical implementation for empirically-defined internal-coordinate joints, which we call "mobilizers." A mobilizer encapsulates the observations, measurement frame, and modeling requirements into a hinge specification of the permissible-motion manifold for a minimal set of internal coordinates. Mobilizers support nonlinear mappings that are mathematically equivalent to constraint manifolds but have the advantages of fewer coordinates, no constraints, and exact representation of the biomechanical motion-space-the benefits long enjoyed for internal-coordinate models of mechanical joints. Hinge matrices within the mobilizer are easily specified by user-supplied functions, and provide a direct means of mapping permissible motion derived from empirical data. We present computational results showing substantial performance and accuracy gains for mobilizers versus equivalent joints implemented with constraints. Examples of mobilizers for joints from human biomechanics and molecular dynamics are given. All methods and examples were implemented in Simbody™-an open source multibody-dynamics solver available at https://Simtk.org.

An optimization approach to inverse dynamics provides insight as to the function of the biarticular muscles during vertical jumping

Traditional inverse dynamics approaches to calculating the inter-segmental moments are limited in their ability to accurately reflect the function of the biarticular muscles. In particular they are based on the assumption that the net inter-segmental moment is zero and that total joint moments are independent of muscular activity. Traditional approaches to calculating muscular forces from the inter-segmental moments are based on a consideration of joint moments which do not encapsulate the potential moment asymmetry between segments. In addition, traditional approaches may artificially constrain the activity of the biarticular muscles. In this study, an optimization approach to the simultaneous inverse determination of inter-segmental moments and muscle forces (the 1-step method) based on a consideration of segmental rotations was employed to study vertical jumping and contrasted with the more traditional 2-step approach of determining inter-segmental moments from an inverse dynamics analysis then muscle forces using optimization techniques. The 1-step method resulted in significantly greater activation of both the monoarticular and biarticular musculature which was then translated into significantly greater joint contact forces, muscle powers, and inter-segmental moments. The results of this study suggest that traditional conceptions of inter-segmental moments do not completely encapsulate the function of the biarticular muscles and that joint function can be better understood by recognizing the asymmetry in inter-segmental moments.

Adaptive Attitude Control of Redundant Time-Varying Complex Model of Human Body in the Nursing Activity

With the development of human society, there are more and more elderly people need to be taken care of. However, there is not enough labor force to take the nursing jobs. Nowadays robots play more and more important roles in our daily life, especially in nursing activities. In this paper, we illustrate a new attitude control approach to lift human regardless of the individual differences, such as height, weight, and so on. In detail, considering our daily experience that only very few joints are critical for accomplishing the lifting up task, we treats the human body as a redundant system. We use robust adaptive control to eliminate the effects from the “uninterested joints” and identify the human parameters in real time. In addition, the convergence analysis, including tracking time and track error, is also given. The approach is simulated by lifting a human skeleton with two robot arms, which verifies the efficiency and effectiveness of our strategy.

Effect of lumbar lordotic angle on lumbosacral joint during isokinetic exercise: a simulation study

BACKGROUND

It is important to consider lumbar lordotic angle for setup of training program in field of sports and rehabilitation to prevent unexpected posture deviation and back pain. The purpose of this study was to to analyze the biomechanical impact of the level of lumbar lordosis angle during isokinetic exercise through dynamic analysis using a 3-dimensional musculoskeletal model.

METHODS

Gait analysis and isokinetic exercise for the healthy adults (n=10) were performed to design a 3-dimensional musculoskeletal model and then we made each model for normal lordosis, excessive lordosis, lumbar kyphosis, and hypo-lordosis according to lordotic angle and inputted experimental data as initial values to perform inverse dynamic analysis to quantify muscle joint torque, joint forces of each joint, system energy, and estimated muscle forces at lumbosacral joint.

FINDINGS

Comparing the joint torques, the largest torque of excessive lordosis was 16.6% larger than that of normal lordosis, and lumbar kyphosis was 11.7% less than normal lordosis. There existed no significant difference in the compressive intervertebral forces of each lumbar joint (P>0.05), but statistically significant difference in the anterioposterior shear force (lumbar kyphosis>hypo-lordosis>excessive lordosis>normal lordosis, P<0.05). Lastly, lumbar kyphosis required the least and most energy during flexion and extension respectively.

INTERPRETATION

During the rehabilitation process, more efficient training will be possible by taking into consideration not simply weight and height but biomechanical effects on the skeletal muscle system according to lumbar lordortic angles.

Muscle contributions to support and progression during single-limb stance in crouch gait

Pathological movement patterns like crouch gait are characterized by abnormal kinematics and muscle activations that alter how muscles support the body weight during walking. Individual muscles are often the target of interventions to improve crouch gait, yet the roles of individual muscles during crouch gait remain unknown. The goal of this study was to examine how muscles contribute to mass center accelerations and joint angular accelerations during single-limb stance in crouch gait, and compare these contributions to unimpaired gait. Subject-specific dynamic simulations were created for ten children who walked in a mild crouch gait and had no previous surgeries. The simulations were analyzed to determine the acceleration of the mass center and angular accelerations of the hip, knee, and ankle generated by individual muscles. The results of this analysis indicate that children walking in crouch gait have less passive skeletal support of body weight and utilize substantially higher muscle forces to walk than unimpaired individuals. Crouch gait relies on the same muscles as unimpaired gait to accelerate the mass center upward, including the soleus, vasti, gastrocnemius, gluteus medius, rectus femoris, and gluteus maximus. However, during crouch gait, these muscles are active throughout single-limb stance, in contrast to the modulation of muscle forces seen during single-limb stance in an unimpaired gait. Subjects walking in crouch gait rely more on proximal muscles, including the gluteus medius and hamstrings, to accelerate the mass center forward during single-limb stance than subjects with an unimpaired gait.

Hamstring muscle forces prior to and immediately following an acute sprinting-related muscle strain injury

A thorough understanding of the biomechanics of the hamstrings during sprinting is required to optimise injury rehabilitation and prevention strategies. The main aims of this study were to compare hamstrings load across different modes of locomotion as well as before and after an acute sprinting-related muscle strain injury. Bilateral kinematic and ground reaction force data were captured from a single subject whilst walking, jogging and sprinting prior to and immediately following a significant injury involving the right semitendinosis and biceps femoris long head muscles. Experimental data were input into a three-dimensional musculoskeletal model of the body and used, together with optimisation theory, to determine lower-limb muscle forces for each locomotor task. Hamstrings load was found to be greatest during terminal swing for sprinting. The hamstrings contributed the majority of the terminal swing hip extension and knee flexion torques, whilst gluteus maximus contributed most of the stance phase hip extension torque. Gastrocnemius contributed little to the terminal swing knee flexion torque. Peak hamstrings force was also substantially greater during terminal swing compared to stance for sprinting, but not for walking and jogging. Immediately following the muscle strain injury, the hamstrings demonstrated an intolerance to perform an eccentric-type contraction. Whilst peak hamstrings force during terminal swing did not decrease post-injury, both peak hamstrings length and negative work during terminal swing were considerably reduced. These results lend support to the paradigm that the hamstrings are most susceptible to muscle strain injury during the terminal swing phase of sprinting when they are contracting eccentrically.

Lower-extremity musculoskeletal geometry affects the calculation of patellofemoral forces in vertical jumping and weightlifting

The calculation of the patellofemoral joint contact force using three-dimensional (3D) modelling techniques requires a description of the musculoskeletal geometry of the lower limb. In this study, the influence of the complexity of the muscle model was studied by considering two different muscle models, the Delp and Horsman models. Both models were used to calculate the patellofemoral force during standing, vertical jumping, and Olympic-style weightlifting. The patellofemoral forces predicted by the Horsman model were markedly lower than those predicted by the Delp model in all activities and represented more realistic values when compared with previous work. This was found to be a result of a lower level of redundancy in the Delp model, which forced a higher level of muscular activation in order to allow a viable solution. The higher level of complexity in the Horsman model resulted in a greater degree of redundancy and consequently lower activation and patellofemoral forces. The results of this work demonstrate that a well-posed muscle model must have an adequate degree of complexity to create a sufficient independence, variability, and number of moment arms in order to ensure adequate redundancy of the force-sharing problem such that muscle forces are not overstated.

Optimal handgrip height of four-wheeled walker on various road conditions to reduce muscular load for elderly users with steady walking

A four-wheeled walker is a valuable tool for assisting elderly persons with walking. The handgrip height is one of the most important factor determining the usefulness of the walker. However, the optimal handgrip height for elderly users has not been considered from a biomechanical viewpoint. In this study, the handgrip height was optimized by a two-dimensional mechanical model to reduce muscular loads in the lower body as well as in the upper body with various road conditions during steady walking. A critical height of the handgrip existed at 48% of the body height for the user regardless of gender and body dimension. A lower handgrip relieved muscular load for stooping users with a lower standing height. The stooping user pushed the handgrip strongly in the perpendicular direction by leaning the upper body on the walker. However, upright users with a higher standing height should use a four-wheeled walker with a higher handgrip for maintaining his or her upright posture. For downhill movement, the optimal handgrip height depended on the slope angle and the friction coefficient between the road and the wheels of the walker. On a low-friction downhill such as asphalt with a steeper slope angle, the user was required to maintain an erect trunk with a higher handgrip and to press on the handgrip strongly in the perpendicular direction. Movement on a low-friction road was easier for users on a flat road and an uphill road, but it compelled distinct effort from users when moving downhill.

The impact of a systematic reduction in shoe-floor friction on heel contact walking kinematics-- A gait simulation approach

Falls initiated by slips and trips are a serious health hazard to older adults. Experimental studies have provided important descriptions of postural responses to slipping, but it is difficult to determine why some slips result in falls from experiments alone. Computational modeling and simulation techniques can complement experimental approaches by identifying causes of failed recovery attempts. The purpose of this study was to develop a method to determine the impact of a systematic reduction in the foot-floor friction coefficient (mu) on the kinematics of walking shortly after heel contact (approximately 200 s). A walking model that included foot-floor interactions was utilized to find the set of moments that best tracked the joint angles and measured ground reaction forces obtained from a non-slipping (dry) trial. A "passive" slip was simulated by driving the model with the joint-moments from the dry simulation and by reducing mu. Slip simulations with values of mu greater than the subject-specific peak required coefficient of friction (RCOF), an experimental measure of slip-resistant gait, resulted in only minor deviations in gait kinematics from the dry condition. In contrast, slip simulations run in environments characterized by mu<peak RCOF resulted in body kinematics that were substantially different from normal/dry gait patterns, more specifically greater knee extension and hip flexion angles were observed in the slip simulations. These findings imply the need for early and appropriate active corrective responses to prevent a fall in environments with mu values less than the peak RCOF.

An analytical approach to the problem of inverse optimization with additive objective functions: an application to human prehension

We consider the problem of what is being optimized in human actions with respect to various aspects of human movements and different motor tasks. From the mathematical point of view this problem consists of finding an unknown objective function given the values at which it reaches its minimum. This problem is called the inverse optimization problem. Until now the main approach to this problems has been the cut-and-try method, which consists of introducing an objective function and checking how it reflects the experimental data. Using this approach, different objective functions have been proposed for the same motor action. In the current paper we focus on inverse optimization problems with additive objective functions and linear constraints. Such problems are typical in human movement science. The problem of muscle (or finger) force sharing is an example. For such problems we obtain sufficient conditions for uniqueness and propose a method for determining the objective functions. To illustrate our method we analyze the problem of force sharing among the fingers in a grasping task. We estimate the objective function from the experimental data and show that it can predict the force-sharing pattern for a vast range of external forces and torques applied to the grasped object. The resulting objective function is quadratic with essentially non-zero linear terms.

Evaluation of predicted knee-joint muscle forces during gait using an instrumented knee implant

Musculoskeletal modeling and optimization theory are often used to determine muscle forces in vivo. However, convincing quantitative evaluation of these predictions has been limited to date. The present study evaluated model predictions of knee muscle forces during walking using in vivo measurements of joint contact loading acquired from an instrumented implant. Joint motion, ground reaction force, and tibial contact force data were recorded simultaneously from a single subject walking at slow, normal, and fast speeds. The body was modeled as an 8-segment, 21-degree-of-freedom articulated linkage, actuated by 58 muscles. Joint moments obtained from inverse dynamics were decomposed into leg-muscle forces by solving an optimization problem that minimized the sum of the squares of the muscle activations. The predicted knee muscle forces were input into a 3D knee implant contact model to calculate tibial contact forces. Calculated and measured tibial contact forces were in good agreement for all three walking speeds. The average RMS errors for the medial, lateral, and total contact forces over the entire gait cycle and across all trials were 140 +/- 40 N, 115 +/- 32 N, and 183 +/- 45 N, respectively. Muscle coordination predicted by the model was also consistent with EMG measurements reported for normal walking. The combined experimental and modeling approach used in this study provides a quantitative framework for evaluating model predictions of muscle forces in human movement.

Muscle-driven forward dynamics simulation for the study of differences in muscle function during stair ascent and descent

The main scope of this study is to analyse muscle-driven forward dynamics simulation of stair locomotion to understand the functional differences of individual muscles during the movement. A static optimization was employed to minimize a performance criterion based on the muscle energy consumption to resolve muscle redundancy during forward dynamics simulation. The proposed method was employed to simulate a musculoskeletal system with ten degrees of freedom in the sagittal plane and containing 18 Hill-type musculotendon actuators per leg. Simulation results illustrated that simulated joint kinematics closely tracked experimental quantities with root-mean-squared errors less than 1°. In addition, estimated muscle activations have a good agreement with the salient features of the electromyographic recordings of the major muscles of the lower extremity. Distribution of mechanical power for individual muscles was estimated to elucidate the muscle's contribution to body support and forward progression during stair locomotion. The accuracy and relatively high computational performance of the proposed method make it suitable to generate subject-specific simulations of various activities for individuals with movement disorders in clinical studies.

Feedback control of the neuromusculoskeletal system in a forward dynamics simulation of stair locomotion

The aim of this study is to employ feedback control loops to provide a stable forward dynamics simulation of human movement under repeated position constraint conditions in the environment, particularly during stair climbing. A ten-degrees-of-freedom skeletal model containing 18 Hill-type musculotendon actuators per leg was employed to simulate the model in the sagittal plane. The postural tracking and obstacle avoidance were provided by the proportional—integral—derivative controller according to the modulation of the time rate change of the joint kinematics. The stability of the model was maintained by controlling the velocity of the body's centre of mass according to the desired centre of pressure during locomotion. The parameters of the proposed controller were determined by employing the iterative feedback tuning approach to minimize tracking errors during forward dynamics simulation. Simultaneously, an inverse-dynamics-based optimization was employed to compute a set of desired musculotendon forces in the closed-loop simulation to resolve muscle redundancy. Quantitative comparisons of the simulation results with the experimental measurements and the reference muscles' activities illustrate the accuracy and efficiency of the proposed method during the stable ascending simulation.

Adaptive surrogate modeling for efficient coupling of musculoskeletal control and tissue deformation models

Finite element (FE) modeling and multibody dynamics have traditionally been applied separately to the domains of tissue mechanics and musculoskeletal movements, respectively. Simultaneous simulation of both domains is needed when interactions between tissue and movement are of interest, but this has remained largely impractical due to the high computational cost. Here we present a method for the concurrent simulation of tissue and movement, in which state of the art methods are used in each domain, and communication occurs via a surrogate modeling system based on locally weighted regression. The surrogate model only performs FE simulations when regression from previous results is not within a user-specified tolerance. For proof of concept and to illustrate feasibility, the methods were demonstrated on an optimization of jumping movement using a planar musculoskeletal model coupled to a FE model of the foot. To test the relative accuracy of the surrogate model outputs against those of the FE model, a single forward dynamics simulation was performed with FE calls at every integration step and compared with a corresponding simulation with the surrogate model included. Neural excitations obtained from the jump height optimization were used for this purpose and root mean square (RMS) difference between surrogate and FE model outputs (ankle force and moment, peak contact pressure and peak von Mises stress) were calculated. Optimization of the jump height required 1800 iterations of the movement simulation, each requiring thousands of time steps. The surrogate modeling system only used the FE model in 5% of time steps, i.e., a 95% reduction in computation time. Errors introduced by the surrogate model were less than 1 mm in jump height and RMS errors of less than 2 N in ground reaction force, 0.25 Nm in ankle moment, and 10 kPa in peak tissue stress. Adaptive surrogate modeling based on local regression allows efficient concurrent simulations of tissue mechanics and musculoskeletal movement.

Mechanisms of improved knee flexion after rectus femoris transfer surgery

Rectus femoris transfer is frequently performed to treat stiff-knee gait in subjects with cerebral palsy. In this surgery, the distal tendon is released from the patella and re-attached to one of several sites, such as the sartorius or the iliotibial band. Surgical outcomes vary, and the mechanisms by which the surgery improves knee motion are unclear. The purpose of this study was to clarify the mechanism by which the transferred muscle improves knee flexion by examining three types of transfers. Muscle-actuated dynamic simulations were created of ten children diagnosed with cerebral palsy and stiff-knee gait. These simulations were altered to represent surgical transfers of the rectus femoris to the sartorius and the iliotibial band. Rectus femoris transfers in which the muscle remained attached to the underlying vasti through scar tissue were also simulated by reducing but not eliminating the muscle's knee extension moment. Simulated transfer to the sartorius, which converted the rectus femoris' knee extension moment to a flexion moment, produced 32+/-8 degrees improvement in peak knee flexion on average. Simulated transfer to the iliotibial band, which completely eliminated the muscle's knee extension moment, predicted only slightly less improvement in peak knee flexion (28+/-8 degrees ). Scarred transfer simulations, which reduced the muscle's knee extension moment, predicted significantly less (p<0.001) improvement in peak knee flexion (14+/-5 degrees ). Simulations revealed that improved knee flexion following rectus femoris transfer is achieved primarily by reduction of the muscle's knee extension moment. Reduction of scarring of the rectus femoris to underlying muscles has the potential to enhance knee flexion.

A three-dimensional biomechanical evaluation of quadriceps and hamstrings function using electrical stimulation

Neurological disorders such as stroke impair locomotor control and result in abnormal 3-D gait kinematics. Establishment of effective rehabilitation strategies requires an understanding of how individual muscles contribute to pathological movement. Forward dynamic simulations account for complexities of interjoint coupling and can be used to predict dynamic muscle function. However to date, limited experimental validations of dynamic models have been performed. Our objective was to measure 3-D movement induced by the biceps femoris (BF), rectus femoris (RF), and vastus lateralis (VL) in limb configurations corresponding to the swing phase of gait, and to assess the biomechanical factors that affect dynamic function. Subjects were positioned in a robotic gait orthosis that included a compliant interface. Electrical stimulation was introduced into individual muscles while induced hip and knee joint movements were recorded. Measured hip to knee sagittal plane acceleration ratios were consistent with dynamic musculoskeletal model simulations. However RF and VL induced substantially larger frontal plane hip movements than model-based predictions. Sensitivity analyses on musculoskeletal model parameters revealed that muscle function depends primarily on moment arm assumptions. Though generic musculoskeletal models are suitable for predicting sagittal plane muscle function, improvements in moment arm accuracy are essential for investigation of 3-D pathological gait.

Estimation of anterior cruciate ligament tension from inverse dynamics data and electromyography in females during drop landing

BACKGROUND

Recent human performance studies have shown that various kinematic and kinetic parameters may be implicated in non-contact anterior cruciate ligament (ACL) injury during landing and cutting. In this paper, a phenomenological sagittal plane model was used to estimate the ACL tension during drop landing from the net knee moments and forces, obtained from inverse dynamics and electromyography.

METHODS

Model parameters were determined with data from anatomical and ACL loading studies of cadaveric specimens. The model was used to process averaged data from 60 cm drop landing trials of sixteen healthy females.

FINDINGS

ACL loading during drop landing occurred during the between toe and heel impact with a peak tension of 0.15 body weight. The factors that contributed to ACL tension were the patellar tendon force and the tibial slope in combination with the joint axial loads. Factors responsible for reducing ACL tension were hamstring and ground reaction forces.

INTERPRETATION

Sagittal plane results largely confirmed a previous forward dynamics study of landing. The knee appeared to be largely stabilized against abduction moments due to the large axial loads present during drop landing for typical landing trials. Rotational moments were small in drop landing and contributed little to ACL tension. Estimates from this model can be used in human performance studies to determine the relative amount of ACL tension produced in different landing scenarios.

Limitations of parallel global optimization for large-scale human movement problems

Global optimization algorithms (e.g., simulated annealing, genetic, and particle swarm) have been gaining popularity in biomechanics research, in part due to advances in parallel computing. To date, such algorithms have only been applied to small- or medium-scale optimization problems (<100 design variables). This study evaluates the applicability of a parallel particle swarm global optimization algorithm to large-scale human movement problems. The evaluation was performed using two large-scale (660 design variables) optimization problems that utilized a dynamic, 27 degree-of-freedom, full-body gait model to predict new gait motions from a nominal gait motion. Both cost functions minimized a quantity that reduced the external knee adduction torque. The first one minimized footpath errors corresponding to an increased toe out angle of 15 degrees, while the second one minimized the knee adduction torque directly without changing the footpath. Constraints on allowable changes in trunk orientation, joint angles, joint torques, centers of pressure, and ground reactions were handled using a penalty method. For both problems, a single run with a gradient-based nonlinear least squares algorithm found a significantly better solution than did 10 runs with the global particle swarm algorithm. Due to the penalty terms, the physically realistic gradient-based solutions were located within a narrow "channel" in design space that was difficult to enter without gradient information. Researchers should exercise caution when extrapolating the performance of parallel global optimizers to human movement problems with hundreds of design variables, especially when penalty terms are included in the cost function.

Importance of preswing rectus femoris activity in stiff-knee gait

Stiff-knee gait is characterized by diminished and delayed knee flexion during swing. Rectus femoris transfer surgery, a common treatment for stiff-knee gait, is often recommended when a patient exhibits prolonged activity of the rectus femoris muscle during swing. Treatment outcomes are inconsistent, in part, due to limited understanding of the biomechanical factors contributing to stiff-knee gait. This study used a combination of gait analysis and dynamic simulation to examine how activity of the rectus femoris during swing, and prior to swing, contribute to knee flexion. A group of muscle-actuated dynamic simulations was created that accurately reproduced the gait dynamics of ten subjects with stiff-knee gait. These simulations were used to examine the effects of rectus femoris activity on knee motion by eliminating rectus femoris activity during preswing and separately during early swing. The increase in peak knee flexion by eliminating rectus femoris activity during preswing (7.5+/-3.1 degrees ) was significantly greater on average (paired t-test, p=0.035) than during early swing (4.7+/-3.6 degrees ). These results suggest that preswing rectus femoris activity is at least as influential as early swing activity in limiting the knee flexion of persons with stiff-knee gait. In evaluating rectus femoris activity for treatment of stiff-knee gait, preswing as well as early swing activity should be examined.

Predicted threshold against backward balance loss following a slip in gait

The purpose of this study was to use a 7-link, moment-actuated human model to predict, at liftoff of the trailing foot in gait, the threshold of the center of mass (COM) velocity relative to the base of support (BOS) required to prevent backward balance loss during single stance recovery from a slip. Five dynamic optimization problems were solved to find the minimum COM velocities that would allow the simulation to terminate with the COM above the BOS when the COM started 0.25, 0.5, 0.75, 1.0, and 1.25 foot lengths behind the heel of the stance foot (i.e., behind the BOS). The initial joint angles of the model were based on averaged data from experimental trials. Foot-ground contact was modeled using 16 visco-elastic springs distributed under the stance foot. Slipping was modeled by setting the sliding coefficient of friction of these springs to 0.02. The forward velocity of the COM necessary to avoid a backward balance loss is nearly two times larger under slip conditions under non-slip conditions. The predicted threshold for backward balance loss following a slip agreed well with experimental data collected from 99 young adults in response to 927 slips during walking. In all trials in which a subject's COM had a velocity below the predicted threshold, the subject's recovery foot landed posterior to the slipping foot as predicted. Finally, combining experimental data with optimization, we verified that the 7-link model could more accurately predict gait stability than a 2-link model.

Design of patient-specific gait modifications for knee osteoarthritis rehabilitation

Abstract-Gait modification is a nonsurgical approach for reducing the external knee adduction torque in patients with knee osteoarthritis (OA). The magnitude of the first adduction torque peak in particular is strongly associated with knee OA progression. While toeing out has been shown to reduce the second peak, no clinically realistic gait modifications have been identified that effectively reduce both peaks simultaneously. This study predicts novel patient-specific gait modifications that achieve this goal without changing the foot path. The modified gait motion was designed for a single patient with knee OA using dynamic optimization of a patient-specific, full-body gait model. The cost function minimized the knee adduction torque subject to constraints limiting how much the new gait motion could deviate from the patient's normal gait motion. The optimizations predicted a "medial-thrust" gait pattern that reduced the first adduction torque peak between 32% and 54% and the second peak between 34% and 56%. The new motion involved three synergistic kinematic changes: slightly decreased pelvis obliquity, slightly increased leg flexion, and slightly increased pelvis axial rotation. After gait retraining, the patient achieved adduction torque reductions of 39% to 50% in the first peak and 37% to 55% in the second one. These reductions are comparable to those reported after high tibial osteotomy surgery. The associated kinematic changes were consistent with the predictions except for pelvis obliquity, which showed little change. This study demonstrates that it is feasible to design novel patient-specific gait modifications with potential clinical benefit using dynamic optimization of patient-specific, full-body gait models. Further investigation is needed to assess the extent to which similar gait modifications may be effective for other patients with knee OA.

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.