Balance control during an arm raising movement in bipedal stance: which biomechanical factor is controlled?

In order to obtain new insight into the control of balance during arm raising movements in bipedal stance, we performed a biomechanical analysis of kinematics and dynamical aspects of arm raising movements by combining experimental work, large-scale models of the body, and techniques simulating human behavior. A comparison between experimental and simulated joint kinematics showed that the minimum torque change model yielded realistic trajectories. We then performed an analysis based on computer simulations. Since keeping the center of pressure (CoP) and the projection of the center of mass (CoM) inside the support area is essential for equilibrium, we modeled an arm raising movement where displacement of one or the other variable is limited. For this optimization model, the effects of adding equilibrium constraints on movement trajectories were investigated. The results show that: (a) the choice of the regulated variable influences the strategy adopted by the system and (b) the system was not able to regulate the CoM for very fast movements without compromising its balance. Consequently, we suggest that the system is able to maintain balance while raising the arm by only controlling the CoP. This may be done mainly by using hip mechanisms and controlling net ankle torque.     

Feed-forward control of a redundant motor system

We describe a model of feed-forward control of a redundant motor system and validate it using, as examples, tasks of multi-finger force production. The model assumes the existence of two input signals at an upper level of the control hierarchy, related and unrelated to a task variable. Knowledge of the Jacobian of the system is assumed at the level of generation of elemental variables (variables at the level of effectors). Variance at the level of elemental variables is considered as the sum of two components, related and unrelated to variability in the task variable. An index of stabilization of the task variable is similarly introduced as to how it was done in several studies using the framework of the uncontrolled manifold hypothesis. Several phenomena have been simulated including data point distributions corresponding to presence and absence of force-stabilizing synergies in two-finger tasks, changes in synergies with practice, and changes in synergy indices in preparation to a fast action. The model is discussed in comparison to other models of control of multi-element systems based on feedback processes. It shows that patterns of structured variability in the space of elemental variables can result from feed-forward processes. Relations of the model to the equilibrium-point hypothesis are also discussed.     

Improving elbow torque output of stroke patients with assistive torque controlled by EMG signals

This paper develops an assistive torque system which uses homogeneic surface electromyogram (EMG) signals to improve the elbow torque capability of stroke patients by applying an external time-varying assistive torque. In determining the magnitude of the torque to apply, the incorporated assistive torque algorithm considers the difference between the weighted biceps and triceps EMG signals such that the applied torque is proportional to the effort supplied voluntarily by the user. The overall stability of the assistive system is enhanced by the incorporation of a nonlinear damping element within the control algorithm which mimics the physiological damping of the elbow joint and the co-contraction between the biceps and triceps. Adaptive filtering of the control signal is employed to achieve a balance between the bandwidth and the system adaptability so as to ensure a smooth assistive torque output. The innovative control algorithm enables the provision of an assistive system whose operation is both natural to use and simple to learn. The effectiveness of the proposed assistive system in assisting elbow movement performance is investigated in a series of tests involving five stroke patients and five able-bodied individuals. The results confirm the ability of the system to assist all of the subjects in performing a number of reaching and tracking tasks with reduced effort and with no sacrifice in elbow movement performance.     

The relationship between joint strength and standing vertical jump performance

The effect of joint strengthening on standing vertical jump height is investigated by computer simulation. The human model consists of five rigid segments representing the feet, shanks, thighs, HT (head and trunk), and arms. Segments are connected by frictionless revolute joints and model movement is driven by joint torque actuators. Each joint torque is the product of maximum isometric torque and three variable functions of instantaneous joint angle, angular velocity, and activation level, respectively. Jumping movements starting from a balanced initial posture and ending at takeoff are simulated. A matching simulation reproducing the actual jumping movement is generated by optimizing joint activation level. Simulations with the goal of maximizing jump height are repeated for varying maximum isometric torque of one joint by up to +/-20% while keeping other joint strength values unchanged. Similar to previous studies, reoptimization of activation after joint strengthening is necessary for increasing jump height. The knee and ankle are the most effective joints in changing jump height (by as much as 2.4%, or 3 cm). For the same amount of percentage increase/decrease in strength, the shoulder is the least effective joint (which changes height by as much as 0.6%), but its influence should not be overlooked.     

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior-posterior and medial-lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were 相似文献   

Modelling 3D control of upright stance using an optimal control strategy

A 3D balance control model of quiet upright stance is presented, based on an optimal control strategy, and evaluated in terms of its ability to simulate postural sway in both the anterior–posterior and medial–lateral directions. The human body was represented as a two-segment inverted pendulum. Several assumptions were made to linearise body dynamics, for example, that there was no transverse rotation during upright stance. The neural controller was presumed to be an optimal controller that generates ankle control torque and hip control torque according to certain performance criteria. An optimisation procedure was used to determine the values of unspecified model parameters including random disturbance gains and sensory delay times. This model was used to simulate postural sway behaviours characterised by centre-of-pressure (COP)-based measures. Confidence intervals for all normalised COP-based measures contained unity, indicating no significant differences between any of the simulated COP-based measures and corresponding experimental references. In addition, mean normalised errors for the traditional measures were < 8%, and those for most statistical mechanics measures were ～3–66%. On the basis these results, the proposed 3D balance control model appears to have the ability to accurately simulate 3D postural sway behaviours.     

Postural control model interpretation of stabilogram diffusion analysis

Collins and De Luca [Collins JJ, De Luca CJ (1993) Exp Brain Res 95: 308–318] introduced a new method known as stabilogram diffusion analysis that provides a quantitative statistical measure of the apparently random variations of center-of-pressure (COP) trajectories recorded during quiet upright stance in humans. This analysis generates a stabilogram diffusion function (SDF) that summarizes the mean square COP displacement as a function of the time interval between COP comparisons. SDFs have a characteristic two-part form that suggests the presence of two different control regimes: a short-term open-loop control behavior and a longer-term closed-loop behavior. This paper demonstrates that a very simple closed-loop control model of upright stance can generate realistic SDFs. The model consists of an inverted pendulum body with torque applied at the ankle joint. This torque includes a random disturbance torque and a control torque. The control torque is a function of the deviation (error signal) between the desired upright body position and the actual body position, and is generated in proportion to the error signal, the derivative of the error signal, and the integral of the error signal [i.e. a proportional, integral and derivative (PID) neural controller]. The control torque is applied with a time delay representing conduction, processing, and muscle activation delays. Variations in the PID parameters and the time delay generate variations in SDFs that mimic real experimental SDFs. This model analysis allows one to interpret experimentally observed changes in SDFs in terms of variations in neural controller and time delay parameters rather than in terms of open-loop versus closed-loop behavior. Received: 13 August 1998 / Accepted in revised form: 12 November 1999     

Modeling of a simple motor task in man: intentional arrest of an ongoing movement

Normal subjects and cerebellar patients were instructed to arrest “as soon as possible” a ballistically initiated flexion movement of the forearm. The intentional actions consist essentially of a downward torque, the peak value of which has almost a constant latency (about 200 msec) from the beginning of the movement. A variable number of oscillations precede the arrest of the movement, the characteristics of which depend on the initial velocity of the flexion and on the mass with which the forearm is loaded. The motor commands responsible for the intentionally produced downward torque are controlled centrally as to leave the ratio between the peak values of the angular velocity which precede and follow the peak of the torque almost constant, under all conditions. To describe the oscillations a simple analytical model was proposed which includes the mechanical as well as the reflex factors, the latter under the form of a delayed velocity term. The satisfactory fitting of this model to the experimental findings permitted to establish the following points:

1. The oscillations are sustained by both a mechanical and a reflex stiffness. The contribution of the reflex loop is however quantitatively dominant since it accounts for about 75% of the inertial torque. It is fairly constant over the range of frequency of the oscillations considered.
2. Under the imposed experimental conditions angular velocity appears to be the parameter of the movement which is predominantly sensed and fed back by the reflex loop.

Data were also presented on the performance of the motor task by patients who underwent surgical ablations of the cerebellar cortex. Comparison of these results with those of normal subjects strongly supports the hypothesis that cerebellar-related activities are instrumental in determining the sensitivity of the stretch reflex to angular velocity.     

Ankle intrinsic stiffness changes with postural sway

In standing, the human body is inherently unstable and its stabilization requires constant regulation of ankle torque, generated by a combination of ankle intrinsic properties, peripheral reflexes, and central contributions. Ankle intrinsic stiffness, which quantifies the joint intrinsic properties, has been usually assumed constant in standing; however, there is strong evidence that it is highly dependent on the joint torque, which changes significantly with sway in stance. In this study, we examined how ankle intrinsic stiffness changes with postural sway during standing. Ten subjects stood on a standing apparatus, while subjected to pulse perturbations of ankle position. The mean torque of a short period before the start of each pulse was used as a measure of background torque. Responses with similar background torques were grouped together and used to estimate the parameters of an intrinsic stiffness model. Stiffness estimates were normalized to the critical stiffness and the background torque was transformed to the center of pressure location. We found that in most subjects, the normalized stiffness increased linearly with the movement of center of pressure towards the toes, with an average slope of 2.11 ± 0.80 1/m·rad. This modulation of ankle intrinsic stiffness seems functionally appropriate, since the intrinsic stiffness increases quickly, as the center of pressure moves toward the toes and the limits of stability. These large changes of ankle intrinsic stiffness with postural sway must be incorporated in any model of stance control.     

Coping with perturbations to a layout somersault in tumbling

Tumbling is a dynamic movement requiring control of the linear and angular momenta generated during the approach and takeoff phases. Both of these phases are subject to some variability even when the gymnast is trying to perform a given movement repeatedly. This paper used a simulation model of tumbling takeoff to establish how well gymnasts can cope with perturbations of the approach and takeoff phases. A five segment planar simulation model with torque generators at each joint was developed to simulate tumbling takeoffs. The model was customised to an elite gymnast by determining subject specific inertia and torque parameters and a simulation was produced which closely matched a performance of a layout somersault by the gymnast. The performance of a layout somersault was found to be sensitive to the approach characteristics and the activation timings but relatively insensitive to the elasticity of the track and maximum muscle strength. Appropriate variation of the activation timings used during the takeoff phase was capable of coping with moderate perturbations of the approach characteristics. A model of aerial movement established that variation of body configuration in the flight phase was capable of adjusting for takeoff perturbations that would lead to rotation errors of up to 8%. Providing the errors in perceiving approach characteristics are less than 5% or 5 degrees and the errors in timing activations are less than 7ms, perturbations in the approach can be accommodated using adjustments during takeoff and flight.     

Estimating propulsive forces--sink or swim?

The purpose of this study was to investigate the validity of hydrodynamic force estimation in swimming as calculated by the quasi-static approach. To achieve this a full-scale mechanical arm was developed, built and tested. The mechanical arm, covered with a prosthetic shell and driven at the shoulder was used to simulate a single plane underwater rotation at four elbow configurations. A computer program controlled the shoulder movement to achieve a replicable angular velocity profile for each arm movement. A strain gauge system was used to directly measure the generated arm torque. Repeated trials were conducted at fixed elbow angles of 110 degrees, 135 degrees, 160 degrees and 180 degrees. All trials were filmed using a three-dimensional underwater set-up. Each trial was digitised at 25 Hz and the hydrodynamic drag force profile of the hand calculated using the quasi-static procedure. From these data, the estimated shoulder torque was calculated and compared to the direct measurement of shoulder torque from the mechanical arm. The results showed that the arm produced a repeatable movement through the water. The shoulder torque profiles using the direct measure (the arm) and the indirect measures (quasi-static approach) differed considerably. The quasi-static approach appears not to accurately reflect the hydrodynamic force profile generated by the arm movement in swimming. Furthermore, it seems that the swimmer's hand contribution is overstated in up to date studies. It is essential that the propulsive mechanisms in swimming be further investigated if factors underpinning an optimal technique are to be established.     

A mode hypothesis for finger interaction during multi-finger force-production tasks

 Finger forces are known to change involuntarily during multi-finger force-production tasks, even when a finger's involvement in a task is not consciously changed (the enslaving effect). Furthermore, during maximal force-production (MVC) tests, the force produced by a given finger in a multi-finger task is smaller than the force generated by this finger in its single-finger MVC test (the force-deficit effect). A set of hypothetical control variables – modes – is introduced. Modes can be estimated based on individual finger forces during single-finger MVC tests. We show that a simple formal model based on modes with only one free parameter accounts for finger forces during a variety of multi-finger MVC tests. The free parameter accounts for the force-deficit effect, and its value depends only on the number of explicitly involved fingers. This approach offers a simple framework for the analysis of finger interaction during multi-finger actions. Received: 7 December 2001 / Accepted in revised form: 17 April 2002 Correspondence to: F. Danion (e-mail: danion@laps.univ-mrs.fr, Tel.: +33-491-172265, Fax: +33-491-172252)     

Acceleration Workspace of Cooperating Multi-Finger Robot Systems

We present a mathematical method for acceleration workspace analysis of cooperating multi-finger robot systems using a model of point-contact with friction. A new unified formulation from dynamic equations of cooperating multi-finger robots is derived considering the force and acceleration relationships between the fingers and the object to be handled. From the dynamic equation, maximum translational and rotational acceleration bounds of an object are calculated under given constraints of contact conditions, configurations of fingers, and bounds on the torques of joint actuators for each finger. Here, the rotational acceleration bounds can be applied as an important manipulability index when the multi-finger robot grasps an object. To verify the proposed method, we used a set of case studies with a simple multi-finger mechanism system. The achievable acceleration boundary in task space can be obtained successfully with the proposed method and the acceleration boundary depends on the configurations of fingers.     

A surface electromyography based objective method to identify patients with nonspecific chronic low back pain,presenting a flexion related movement control impairment

Movement control impairments (MCI) are often present in patients with non-specific chronic low back pain (NS-CLBP). Therefore, movement control exercises are widely used to rehabilitate patients. However, the objective assessment remains difficult.The purpose of this study was to develop a statistical model, based on logistic regression analysis, to differentiate patients with NS-CLBP presenting a flexion-related MCI from healthy subjects. This model is based on trunk muscle activation patterns measured by surface electromyography (sEMG), during movement control exercises.Sixty-three healthy male subjects and 36 male patients with a flexion-related MCI participated in this study. Muscle activity of the internal obliques, the external obliques, the lumbar multifidus and the thoracic part of the iliocostalis was registered. Ratios of deep stabilizing to superficial torque producing muscle activity were calculated to examine trunk muscle recruitment patterns during 6 different exercises. Logistic regression analyses were performed (1) to define the ratios and exercises that were most discriminating between patients and non-patients, (2) to make a predictive model. K-Fold cross-validation was used to assess the performance of the predictive model.This study demonstrated that sEMG trunk muscle recruitment patterns during movement control tests, allows differentiating NSCLBP patients with a flexion-related MCI from healthy subjects.     

Comparative analysis of methods for estimating arm segment parameters and joint torques from inverse dynamics

A common problem in the analyses of upper limb unfettered reaching movements is the estimation of joint torques using inverse dynamics. The inaccuracy in the estimation of joint torques can be caused by the inaccuracy in the acquisition of kinematic variables, body segment parameters (BSPs), and approximation in the biomechanical models. The effect of uncertainty in the estimation of body segment parameters can be especially important in the analysis of movements with high acceleration. A sensitivity analysis was performed to assess the relevance of different sources of inaccuracy in inverse dynamics analysis of a planar arm movement. Eight regression models and one water immersion method for the estimation of BSPs were used to quantify the influence of inertial models on the calculation of joint torques during numerical analysis of unfettered forward arm reaching movements. Thirteen subjects performed 72 forward planar reaches between two targets located on the horizontal plane and aligned with the median plane. Using a planar, double link model for the arm with a floating shoulder, we calculated the normalized joint torque peak and a normalized root mean square (rms) of torque at the shoulder and elbow joints. Statistical analyses quantified the influence of different BSP models on the kinetic variable variance for given uncertainty on the estimation of joint kinematics and biomechanical modeling errors. Our analysis revealed that the choice of BSP estimation method had a particular influence on the normalized rms of joint torques. Moreover, the normalization of kinetic variables to BSPs for a comparison among subjects showed that the interaction between the BSP estimation method and the subject specific somatotype and movement kinematics was a significant source of variance in the kinetic variables. The normalized joint torque peak and the normalized root mean square of joint torque represented valuable parameters to compare the effect of BSP estimation methods on the variance in the population of kinetic variables calculated across a group of subjects with different body types. We found that the variance of the arm segment parameter estimation had more influence on the calculated joint torques than the variance of the kinematics variables. This is due to the low moments of inertia of the upper limb, especially when compared with the leg. Therefore, the results of the inverse dynamics of arm movements are influenced by the choice of BSP estimation method to a greater extent than the results of gait analysis.     

Chimpanzee thumb muscle cross sections, moment arms and potential torques, and comparisons with humans.

This study investigates the morphological basis of differences between humans and chimpanzees in the kinematical and dynamical parameters of the musculature of the thumb. It is partly intended to test an hypothesis that human thumb muscles can exert significantly greater torques, due to larger muscle cross-sectional areas or to longer tendon moment arms or to both. We focus on the estimation of the potentials of thumb muscles to exert torques about joint axes in a sample of eight chimpanzee cadaver hands. The potential torque of a muscle is estimated by taking the product of a muscle's physiological cross-sectional area (an estimator of force) with its dynamical moment arm (derived from the slope of tendon excursion versus joint angular displacement, obtained during passive movements of cadaver thumb joints). Comparison of our results with similar data obtained for humans at the same Mayo Clinic laboratory shows significant differences between humans and chimpanzees in potential torque of most thumb muscles, those of humans generally exhibiting larger values. The primary reason for the larger torques in humans is that their average moment arms are significantly longer, permitting greater torque for a given muscle size. An additional finding is that chimpanzees and humans differ in the direction of secondary thumb metacarpal movements elicited by contraction of some muscles, as shown by differences in moment arm signs for a given movement in the same muscle. The differences appear to be related to differences in the musculo-skeletal structures of the trapeziometacarpal joint.     

Maximising forward somersault rotation in springboard diving

Performance in the flight phase of springboard diving is limited by the amounts of linear and angular momentum generated during the takeoff phase. A planar 8-segment torque-driven simulation model combined with a springboard model was used to investigate optimum takeoff technique for maximising rotation in forward dives from the one metre springboard. Optimisations were run by varying the torque activation parameters to maximise forward rotation potential (angular momentum × flight time) while allowing for movement constraints, anatomical constraints, and execution variability. With a constraint to ensure realistic board clearance and anatomical constraints to prevent joint hyperextension, the optimised simulation produced 24% more rotation potential than a simulation matching a 2½ somersault piked dive. When 2 ms perturbations to the torque onset timings were included for the ankle, knee and hip torques within the optimisation process, the model was only able to produce 87% of the rotation potential achieved in the matching simulation. This implies that a pre-planned technique cannot produce a sufficiently good takeoff and that adjustments must be made during takeoff. When the initial onset timings of the torque generators were unperturbed and 10 ms perturbations were introduced into the torque onset timings in the board recoil phase, the optimisation produced 8% more rotation potential than the matching simulation. The optimised simulation had more hip flexion and less shoulder extension at takeoff than the matching simulation. This study illustrates the difficulty of including movement variability within performance optimisation when the movement duration is sufficiently long to allow feedback corrections.     

Modelling, simulation and optimisation of a human vertical jump.

This paper describes an efficient biomechanical model of the human lower limb with the aim of simulating a real human jump movement consisting of an upword propulsion, a flying and a landing phase. A multiphase optimal control technique is used to solve the muscle force sharing problem. To understand how intermuscular control coordinates limb muscle excitations, the human body is reduced to a single lower limb consisting of three rigid bodies. The biomechanical system is activated by nine muscle-tendon actuators representing the basic properties of muscles during force generation. For the calculation of the minimal muscle excitations of the jump movement, the trajectory of the hip joint is given as a rheonomic constraint and the contact forces (ground reaction forces) are determined by force plates. Based on the designed musculoskeletal model and on the differential equations of the multibody system, muscle excitations and muscle forces necessary for a vertical jump movement are calculated. The validity of the system is assessed comparing the calculated muscle excitations with the registered surface electromyogramm (EMG) of the muscles. The achieved results indicate a close relationship between the predicted and the measured parameters.     

Evaluation of a subject-specific female gymnast model and simulation of an uneven parallel bar swing

A gymnast model and forward dynamics simulation of a dismount preparation swing on the uneven parallel bars were evaluated by comparing experimental and predicted joint positions throughout the maneuver. The bar model was a linearly elastic spring with a frictional bar/hand interface, and the gymnast model consisted of torso/head, arm and two leg segments. The hips were frictionless balls and sockets, and shoulder movement was planar with passive compliant structures approximated by a parallel spring and damper. Subject-specific body segment moments of inertia, and shoulder compliance were estimated. Muscles crossing the shoulder and hip were represented as torque generators, and experiments quantified maximum instantaneous torques as functions of joint angle and angular velocity. Maximum torques were scaled by joint torque activations as functions of time to produce realistic motions. The downhill simplex method optimized activations and simulation initial conditions to minimize the difference between experimental and predicted bar-center, shoulder, hip, and ankle positions. Comparing experimental and simulated performances allowed evaluation of bar, shoulder compliance, joint torque, and gymnast models. Errors in all except the gymnast model are random, zero mean, and uncorrelated, verifying that all essential system features are represented. Although the swing simulation using the gymnast model matched experimental joint positions with a 2.15cm root-mean-squared error, errors are correlated. Correlated errors indicate that the gymnast model is not complex enough to exactly reproduce the experimental motion. Possible model improvements including a nonlinear shoulder model with active translational control and a two-segment torso would not have been identified if the objective function did not evaluate the entire system configuration throughout the motion. The model and parameters presented in this study can be effectively used to understand and improve an uneven parallel bar swing, although in the future there may be circumstances where a more complex model is needed.     

The mechanisms that enable arm motion to enhance vertical jump performance-a simulation study

The reasons why using the arms can increase standing vertical jump height are investigated by computer simulations. The human models consist of four/five segments connected by frictionless joints. The head-trunk-arms act as a fourth segment in the first model while the arms become a fifth segment in the second model. Planar model movement is actuated by joint torque generators. Each joint torque is the product of three variable functions of activation level, angular velocity dependence, and maximum isometric torque varying with joint angle. Simulations start from a balanced initial posture and end at jump takeoff. Jump height is maximized by finding the optimal combination of joint activation timings. Arm motion enhances jumping performance by increasing mass center height and vertical takeoff velocity. The former and latter contribute about 1/3 and 2/3 to the increased height, respectively. Durations in hip torque generation and ground contact period are lengthened by swinging the arms. Theories explaining the performance enhancement caused by arms are examined. The force transmission theory is questionable because shoulder joint force due to arm motion does not precisely reflect the change in vertical ground reaction force. The joint torque/work augmentation theory is acceptable only at the hips but not at the knees and ankles because only hip joint work is considerably increased. The pull/impart energy theory is also acceptable because shoulder joint work is responsible for about half of the additional energy created by arm swings.