Design and simulation of closed-loop electrical stimulation orthoses for restoration of quiet standing in paraplegia

Simulation models of quiet standing have been developed to study the potential use of closed-loop stimulation orthoses in mid-thoracic spinal cord injury. The first model (static) consists of a multi-link inverted pendulum. The second model (dynamic) consists of a single-link inverted pendulum, with electrically stimulated muscles providing balancing activation at the ankle joint and stabilization of the knee and hip joints. The initial simulations have shown that it may be possible to restore quiet standing in paraplegic individuals within certain limits subject to biomechanical constraints and to the available torque produced by the stimulated muscle.     

All leg joints contribute to quiet human stance: A mechanical analysis

According to the state of the art model (single inverted pendulum) the regulation of quiet human stance seems to be dominated by ankle joint actions. Recent findings substantiated both in-phase and anti-phase fluctuations of ankle and hip joint kinematics can be identified in quiet human stance. Thus, we explored in an experimental study to what extent all three leg joints actually contribute to the balancing problem of quiet human stance. We also aimed at distinguishing kinematic from torque contributions. Thereto, we directly measured ankle, knee, and hip joint kinematics with high spatial resolution and ground reaction forces. Then, we calculated the six respective joint torques and, additionally, the centre of mass kinematics. We searched for high cross-correlations between all these mechanical variables. Beyond confirming correlated anti-phase kinematics of ankle and hip, the main results are: (i) ankle and knee joint fluctuate tightly (torque) coupled and (ii) the bi-articular muscles of the leg are well suited to fulfil the requirements of fluctuations around static equilibrium. Additionally, we (iii) identified high-frequency oscillations of the shank between about 4 and 8 Hz and (iv) discriminated potentially passive and active joint torque contributions. These results demonstrate that all leg joints contribute actively and concertedly to quiet human stance, even in the undisturbed case. Moreover, they substantiate the single inverted pendulum paradigm to be an invalid model for quiet human stance.     

Postural dynamics in the standing human

The purpose of this study was to develop a mathematical model of the linkage dynamics in upright standing, and to use this model to study output principles for postural control. The standing human was modelled in the sagittal plane as a three-segment linkage. Mechanical disturbances were simulated as forces which could be applied at various points in this linkage. An iterative approach was used to find joint torque combinations which would restore balance within 80 ms of these mechanical disturbances. The model predicted that a specific proportional relationship was necessary between the hip, knee and ankle torques in order for balance to be restored. This proportional relationship was shown to be a function of the model structure, but independent of the location, direction and amplitude of the disturbance. These predictions were tested experimentally. A disturbance apparatus was designed to apply an impulsive force to the subjects. The joint torque responses of the subjects were in quantitative agreement with the predictions of the model. The results suggest that a fixed relationship between joint torques may be required to restore balance, and this fixed relationship may make the task of postural control simpler for the nervous system.     

Effect of landing height on frontal plane kinematics, kinetics and energy dissipation at lower extremity joints

Lack of the necessary magnitude of energy dissipation by lower extremity joint muscles may be implicated in elevated impact stresses present during landing from greater heights. These increased stresses are experienced by supporting tissues like cartilage, ligaments and bones, thus aggravating injury risk. This study sought to investigate frontal plane kinematics, kinetics and energetics of lower extremity joints during landing from different heights. Eighteen male recreational athletes were instructed to perform drop-landing tasks from 0.3- to 0.6-m heights. Force plates and motion-capture system were used to capture ground reaction force and kinematics data, respectively. Joint moment was calculated using inverse dynamics. Joint power was computed as a product of joint moment and angular velocity. Work was defined as joint power integrated over time. Hip and knee joints delivered significantly greater joint power and eccentric work (p<0.05) than the ankle joint at both landing heights. Substantial increase (p<0.05) in eccentric work was noted at the hip joint in response to increasing landing height. Knee and hip joints acted as key contributors to total energy dissipation in the frontal plane with increase in peak ground reaction force (GRF). The hip joint was the top contributor to energy absorption, which indicated a hip-dominant strategy in the frontal plane in response to peak GRF during landing. Future studies should investigate joint motions that can maximize energy dissipation or reduce the need for energy dissipation in the frontal plane at the various joints, and to evaluate their effects on the attenuation of lower extremity injury risk during landing.     

Spinal Mechanisms May Provide a Combination of Intermittent and Continuous Control of Human Posture: Predictions from a Biologically Based Neuromusculoskeletal Model

Several models have been employed to study human postural control during upright quiet stance. Most have adopted an inverted pendulum approximation to the standing human and theoretical models to account for the neural feedback necessary to keep balance. The present study adds to the previous efforts in focusing more closely on modelling the physiological mechanisms of important elements associated with the control of human posture. This paper studies neuromuscular mechanisms behind upright stance control by means of a biologically based large-scale neuromusculoskeletal (NMS) model. It encompasses: i) conductance-based spinal neuron models (motor neurons and interneurons); ii) muscle proprioceptor models (spindle and Golgi tendon organ) providing sensory afferent feedback; iii) Hill-type muscle models of the leg plantar and dorsiflexors; and iv) an inverted pendulum model for the body biomechanics during upright stance. The motor neuron pools are driven by stochastic spike trains. Simulation results showed that the neuromechanical outputs generated by the NMS model resemble experimental data from subjects standing on a stable surface. Interesting findings were that: i) an intermittent pattern of muscle activation emerged from this posture control model for two of the leg muscles (Medial and Lateral Gastrocnemius); and ii) the Soleus muscle was mostly activated in a continuous manner. These results suggest that the spinal cord anatomy and neurophysiology (e.g., motor unit types, synaptic connectivities, ordered recruitment), along with the modulation of afferent activity, may account for the mixture of intermittent and continuous control that has been a subject of debate in recent studies on postural control. Another finding was the occurrence of the so-called “paradoxical” behaviour of muscle fibre lengths as a function of postural sway. The simulations confirmed previous conjectures that reciprocal inhibition is possibly contributing to this effect, but on the other hand showed that this effect may arise without any anticipatory neural control mechanism.     

Simple and complex models for studying muscle function in walking

While simple models can be helpful in identifying basic features of muscle function, more complex models are needed to discern the functional roles of specific muscles in movement. In this paper, two very different models of walking, one simple and one complex, are used to study how muscle forces, gravitational forces and centrifugal forces (i.e. forces arising from motion of the joints) combine to produce the pattern of force exerted on the ground. Both the simple model and the complex one predict that muscles contribute significantly to the ground force pattern generated in walking; indeed, both models show that muscle action is responsible for the appearance of the two peaks in the vertical force. The simple model, an inverted double pendulum, suggests further that the first and second peaks are due to net extensor muscle moments exerted about the knee and ankle, respectively. Analyses based on a much more complex, muscle-actuated simulation of walking are in general agreement with these results; however, the more detailed model also reveals that both the hip extensor and hip abductor muscles contribute significantly to vertical motion of the centre of mass, and therefore to the appearance of the first peak in the vertical ground force, in early single-leg stance. This discrepancy in the model predictions is most probably explained by the difference in model complexity. First, movements of the upper body in the sagittal plane are not represented properly in the double-pendulum model, which may explain the anomalous result obtained for the contribution of a hip-extensor torque to the vertical ground force. Second, the double-pendulum model incorporates only three of the six major elements of walking, whereas the complex model is fully 3D and incorporates all six gait determinants. In particular, pelvic list occurs primarily in the frontal plane, so there is the potential for this mechanism to contribute significantly to the vertical ground force, especially during early single-leg stance when the hip abductors are activated with considerable force.     

Segment and joint angles of hind limb during bipedal and quadrupedal walking of the bonobo (Pan paniscus)

We describe segment angles (trunk, thigh, shank, and foot) and joint angles (hip, knee, and ankle) for the hind limbs of bonobos walking bipedally ("bent-hip bent-knee walking," 17 sequences) and quadrupedally (33 sequences). Data were based on video recordings (50 Hz) of nine subjects in a lateral view, walking at voluntary speed. The major differences between bipedal and quadrupedal walking are found in the trunk, thigh, and hip angles. During bipedal walking, the trunk is approximately 33-41 degrees more erect than during quadrupedal locomotion, although it is considerably more bent forward than in normal human locomotion. Moreover, during bipedal walking, the hip has a smaller range of motion (by 12 degrees ) and is more extended (by 20-35 degrees ) than during quadrupedal walking. In general, angle profiles in bonobos are much more variable than in humans. Intralimb phase relationships of subsequent joint angles show that hip-knee coordination is similar for bipedal and quadrupedal walking, and resembles the human pattern. The coordination between knee and ankle differs much more from the human pattern. Based on joint angles observed throughout stance phase and on the estimation of functional leg length, an efficient inverted pendulum mechanism is not expected in bonobos.     

Comparative studies on the wide frequency band electrocardiogram and vectorcardiogram in pigeon and mouse

Wide frequency band ECG and vectorcardiogram in anesthetized pigeon and mouse were studied from the standpoint of comparison. The key results were as follows: in pigeon, the direction of the main QRS was inverted in leads II, III and aVF, and upright in lead aVR, which was contrary to that in mouse. The T wave was upright in leads II, III and aVF, but inverted in lead aVR in pigeon, which was the same as that in mouse. In pigeon, there was a large notch on the upstroke of the S wave in lead II without exception, but there was no such notch in the corresponding lead in mouse. The QRS vector loop in the frontal plane lay between -90 and -180 degrees in pigeon, while that of mouse lay between 0 and 90 degrees. The relative power of high frequency range (80-1000 Hz) of the QRS in lead II was approximately 15% in pigeon, but 55% in mouse. The direction of the main QRS was contrary in pigeon and mouse because the subepicardial muscles were depolarized before the subendocardial muscles in pigeon, but the latter were depolarized before the former in mouse. The direction of the T waves was the same in both pigeon and mouse because subepicardial muscles were all repolarized before subendocardial muscles.     

An induced acceleration index for examining joint couplings

A muscle produces moments at the joints it crosses, but these moments can also cause accelerations at joints not crossed by the muscle. This phenomenon, the acceleration of a joint caused by a muscle not crossing the joint, is referred to as induced acceleration. For a system of rigid bodies this study examines how system configuration, and segmental inertial properties dictate the potential of one joint to cause the acceleration of other joints in the system. From the equations of motion for a series of rigid bodies, an induced acceleration index (IAI) was developed. The IAI permits quantification of the relative potential of moments produced at joints in the kinematic chain to accelerate other joints in the kinematic chain. The IAI is a function of system orientation, segment lengths, and inertial properties. The IAI was used to examine the roles of the ankle and hip joints in quiet standing. The ankle joint had over 12 times the ability to accelerate the hip joint, than the hip had to accelerate the ankle joint. These results in part explain the relative merits of the two strategies predominantly used to maintain upright stance: the ankle and hip strategies. This index permits an understanding of how the induced accelerations are dependent on system configuration and inertial properties. The IAI is also useful in situations where the inertial properties of the system under investigation changes, for example due to the fitting of a new prostheses to a trans-tibial amputee.     

The mechanical consequences of dynamic frontal plane limb alignment for non-contact ACL injury

This study investigated the mechanical consequences of differences in dynamic frontal plane alignment of the support limb and the influence of anticipatory muscle activation at the hip and ankle on reducing the potential for non-contact ACL injury during single-limb landing. A frontal plane, three-link passive dynamic model was used to estimate an ACL non-contact injury threshold. This threshold was defined as the maximum axial force that the knee could sustain before the joint opened 8 degrees either medially or laterally, which was deemed sufficient to cause injury. The limb alignment and hip and ankle muscle contractions were varied to determine their effects on the ACL injury threshold. Valgus or varus alignment reduced the injury threshold compared to neutral alignment, but increasing the anticipatory contraction of hip abduction and adduction muscle groups increased the injury threshold. Increasing anticipatory ankle inversion/eversion muscle contraction had no effect. This study provides a mechanical rationale for the conclusion that a neutral limb alignment (compared to valgus or varus) during landing and increasing hip muscle contraction (abductors/adductors) prior to landing can reduce the possibility of ACL rupture through a valgus or varus opening mechanism.     

Somatosensory graviception inhibits the soleus H-reflexin standing man - an underwater experiment-

H-reflexes were elicited in the soleus muscle in subjects standing on a force platform in a water tank, under different loading conditions at the ankle joint. The joint loading was altered by changing the combination of buoys and weights attached to lower limb segments, while the total body mass was kept the same. The results revealed that as the joint load was reduced the H-reflex was significantly enhanced as compared to that under the control condition, while it decreased as the joint load was increased, despite the same background EMG activity level. It was demonstrated that the augmented load information from the lower limb joints has an inhibitory effect on the soleus H-reflex, suggesting that this might be one of underlying neural mechanisms responsible for the suppression of H-reflex during human upright standing.     

Effect of hip and ankle muscle fatigue on unipedal postural control

Fatigue and deficits in postural control may predispose musculoskeletal injury. The purpose of this study was to examine the effects of fatigue at the hip and ankle during frontal plane movements on postural control during single-leg stance. Thirteen healthy volunteers completed two testing sessions 1 week apart consisting of isokinetic fatigue of the frontal plane movers of either the ankle or hip with measures of static unipedal postural control taken before and after fatigue. Postural control was assessed during three 30-s trials of unilateral stance with eyes open before and after the fatigue protocol at each testing session. Mean center of pressure (COP) excursion velocity in the sagittal and frontal planes was compared between pre- and post-fatigue across the two joints. Fatigue of the hip musculature led to postural control impairments in the frontal and sagittal planes, while fatigue of the ankle musculature did not significantly impair postural control in either plane. Our results suggest that there is a greater effect of localized fatigue of the frontal plane movers of the hip compared to the ankle on maintenance of a postural control in single-leg stance.     

Inter-joint coupling effects on muscle contributions to endpoint force and acceleration in a musculoskeletal model of the cat hindlimb

The biomechanical principles underlying the organization of muscle activation patterns during standing balance are poorly understood. The goal of this study was to understand the influence of biomechanical inter-joint coupling on endpoint forces and accelerations induced by the activation of individual muscles during postural tasks. We calculated induced endpoint forces and accelerations of 31 muscles in a 7 degree-of-freedom, three-dimensional model of the cat hindlimb. To test the effects of inter-joint coupling, we systematically immobilized the joints (excluded kinematic degrees of freedom) and evaluated how the endpoint force and acceleration directions changed for each muscle in 7 different conditions. We hypothesized that altered inter-joint coupling due to joint immobilization of remote joints would substantially change the induced directions of endpoint force and acceleration of individual muscles. Our results show that for most muscles crossing the knee or the hip, joint immobilization altered the endpoint force or acceleration direction by more than 90° in the dorsal and sagittal planes. Induced endpoint forces were typically consistent with behaviorally observed forces only when the ankle was immobilized. We then activated a proximal muscle simultaneous with an ankle torque of varying magnitude, which demonstrated that the resulting endpoint force or acceleration direction is modulated by the magnitude of the ankle torque. We argue that this simple manipulation can lend insight into the functional effects of co-activating muscles. We conclude that inter-joint coupling may be an essential biomechanical principle underlying the coordination of proximal and distal muscles to produce functional endpoint actions during motor tasks.     

Biomechanical analysis of movement strategies in human forward trunk bending. I. Modeling

 Two behavioral goals are achieved simultaneously during forward trunk bending in humans: the bending movement per se and equilibrium maintenance. The objective of the present study was to understand how the two goals are achieved by using a biomechanical model of this task. Since keeping the center of pressure inside the support area is a crucial condition for equilibrium maintenance during the movement, we decided to model an extreme case, called “optimal bending”, in which the movement is performed without any center of pressure displacement at all, as if standing on an extremely narrow support. The “optimal bending” is used as a reference in the analysis of experimental data in a companion paper. The study is based on a three-joint (ankle, knee, and hip) model of the human body and is performed in terms of “eigenmovements”, i.e., the movements along eigenvectors of the motion equation. They are termed “ankle”, “hip”, and “knee” eigenmovements according to the dominant joint that provides the largest contribution to the corresponding eigenmovement. The advantage of the eigenmovement approach is the presentation of the coupled system of dynamic equations in the form of three independent motion equations. Each of these equations is equivalent to the motion equation for an inverted pendulum. Optimal bending is constructed as a superposition of two (hip and ankle) eigenmovements. The hip eigenmovement contributes the most to the movement kinematics, whereas the contributions of both eigenmovements into the movement dynamics are comparable. The ankle eigenmovement moves the center of gravity forward and compensates for the backward center of gravity shift that is provoked by trunk bending as a result of dynamic interactions between body segments. An important characteristic of the optimal bending is the timing of the onset of each eigenmovement: the ankle eigenmovement onset precedes that of the hip eigenmovement. Without an earlier onset of the ankle eigenmovement, forward bending on the extremely narrow support results in falling backward. This modeling approach suggests that during trunk bending, two motion units – the hip and ankle eigenmovements – are responsible for the movement and for equilibrium maintenance, respectively. Received: 1 July 1999 / Accepted in revised form: 23 October 2000     

Postural reactions of humans in upright stance: Dependence on different visual conditions and the level of stiffness in the ankle joints

We checked on the supposition that the magnitude of postural reactions to an unexpected postural disturbance in upright stance in humans can be determined to a considerable extent by the level of background stiffness in the ankle joints. For this purpose, we estimated changes in the joint stiffness under different conditions of visual control; these values were estimated within the period of background body oscillations (i.e., before the beginning of a compensatory motor reaction) and compared with those in the course of postural reactions evoked by vibrational stimulation of the ankle (shin) muscles. Experiments were carried where the subjects stood with open and closed eyes (OE and CE, respectively) and while standing wearing spectacles with frosted glass passing only diffuse light (DL). In the course of the tests, the subjects stood in the usual comfortable vertical position (hereafter, standard stance) or in the same position but with the possibility to lightly touch an immobile object by a finger (stance with additional support). Such technique was used to weaken the effects of CE and DL on background sways of the body and to lead these sways close to the level typical of OE conditions. The joint stiffness was estimated using an approach based on frequency filtration of oscillations of the center of pressure of the feet (CPF) that allowed us to select signals proportional to displacements of the total center of gravity (CG) of the body and to calculate the difference between oscillations of the CPF and CG (a CPF-CG variable). The CPF-CG variable is proportional to the horizontal acceleration of the CG and, therefore, can be used for estimation of the changes in stiffness in the ankle joints. Under conditions of standard stance, the usual conditions rather similarly influenced both variables (CG and CPF-CG) in the course of both background body oscillations and a postural response. The examined variables were the greatest under CE conditions, decreased under conditions of perception of DL, and became smallest with OE. At standing with additional support, the dependence of the examined variables on visual conditions disappeared within the period of background body oscillations (before the beginning of postural reactions). In this case, the magnitude of oscillations of the CPF-CG variable under CE and DL conditions decreased to the level observed at standing under OE conditions. The magnitude of CG displacements induced by vibrational stimulations of the muscles remained, nevertheless, clearly dependent on visual conditions (the same regularities were observed as in the case of standing with no additional support). Thus, our findings demonstrate that the correlation between the characteristics of postural reactions in the upright stance and the level of ankle joint stiffness is not single-valued. Neirofiziologiya/Neurophysiology, Vol. 39, No. 2, pp. 146–153, March–April, 2007.     

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.     

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   

Alignment of the human body in standing

Alignment of the body in typical symmetrical standing was studied by photographing fifteen subjects in profile on a reaction board. Two aspects of alignment were studied: (1) the anteroposterior position of the body landmarks of knee joint, hip joint, shoulder joint, and ear, compared to the ankle joint; and (2) the positions of the partial centers of gravity above the knee and hip, as a measure of how the body is balanced above these joints. The knee, hip, shoulder, and ear were forward of the ankle in all subjects. On average, the knee was 3.8 (+/- 2.0), the hip 6.2 (+/- 1.3) the shoulder 3.8 (+/- 1.9), and the ear 5.9 (+/- 1.6) cm (+/-S.D.) anterior to the ankle. The positions of landmarks were positively correlated with one another but not highly. The position of the center of gravity could be predicted well from the positions of the landmarks within individual subjects' data, but not across subjects. The centers of gravity above the knee and hip were calculated by subtracting the mass and position of the segments below the joint from the whole-body center of gravity. The center of gravity above the knee was located on average 1.4 (+/- 1.1) cm in front of the joint, and that of the hip 1.0 (+/- 1.6) cm behind the trochanter. Thus, at both knee and hip in typical standing, there exist slight gravitational torques tending to extend the joints.     

Simulating mechanical consequences of voluntary movement upon whole-body equilibrium: the arm-raising paradigm revisited

Voluntary arm-raising movement performed during the upright human stance position imposes a perturbation to an already unstable bipedal posture characterised by a high body centre of mass (CoM). Inertial forces due to arm acceleration and displacement of the CoM of the arm which alters the CoM position of the whole body represent the two sources of disequilibrium. A current model of postural control explains equilibrium maintenance through the action of anticipatory postural adjustments (APAs) that would offset any destabilising effect of the voluntary movement. The purpose of this paper was to quantify, using computer simulation, the postural perturbation due to arm raising movement. The model incorporated four links, with shoulder, hip, knee and ankle joints constrained by linear viscoelastic elements. The input of the model was a torque applied at the shoulder joint. The simulation described mechanical consequences of the arm-raising movement for different initial conditions. The variables tested were arm inertia, the presence or not of gravity field, the initial standing position and arm movement direction. Simulations showed that the mechanical effect of arm-raising movement was mainly local, that is to say at the level of trunk and lower limbs and produced a slight forward displacement of the CoM (1.5 mm). Backward arm-raising movement had the same effect on the CoM displacement as the forward arm-raising movement. When the mass of the arm was increased, trunk rotation increased producing a CoM displacement in the opposite direction when compared to arm movement performed without load. Postural disturbance was minimised for an initial standing posture with the CoM vertical projection corresponding to the ankle joint axis of rotation. When the model was reduced to two degrees of freedom (ankle and shoulder joints only) the postural perturbation due to arm-raising movement increased compared to the four-joints model. On the basis of these results the classical assumption that APAs stabilise the CoM is challenged.