Heelstrike and the pathomechanics of osteoarthrosis: a simulation study

A simulation model and trajectory matching method were developed to investigate the differences between two swing phase gait patterns; one giving rise to a large impulse at heelstrike, the other giving a small impulse. Subtle changes in the kinematics of the swing leg dramatically reduced the vertical contact velocity of the ankle at the moment of heelstrike. Phasing of the hip flexor muscles at the start of swing was responsible for the level of impulse observed at heelstrike.     

A bipedal compliant walking model generates periodic gait cycles with realistic swing dynamics

A simple spring mechanics model can capture the dynamics of the center of mass (CoM) during human walking, which is coordinated by multiple joints. This simple spring model, however, only describes the CoM during the stance phase, and the mechanics involved in the bipedality of the human gait are limited. In this study, a bipedal spring walking model was proposed to demonstrate the dynamics of bipedal walking, including swing dynamics followed by the step-to-step transition. The model consists of two springs with different stiffnesses and rest lengths representing the stance leg and swing leg. One end of each spring has a foot mass, and the other end is attached to the body mass. To induce a forward swing that matches the gait phase, a torsional hip joint spring was introduced at each leg. To reflect the active knee flexion for foot clearance, the rest length of the swing leg was set shorter than that of the stance leg, generating a discrete elastic restoring force. The number of model parameters was reduced by introducing dependencies among stiffness parameters. The proposed model generates periodic gaits with dynamics-driven step-to-step transitions and realistic swing dynamics. While preserving the mimicry of the CoM and ground reaction force (GRF) data at various gait speeds, the proposed model emulated the kinematics of the swing leg. This result implies that the dynamics of human walking generated by the actuations of multiple body segments is describable by a simple spring mechanics.     

Kinematics of lower limbs during walking are emulated by springy walking model with a compliantly connected,off-centered curvy foot

The dynamics of the center of mass (CoM) during walking and running at various gait conditions are well described by the mechanics of a simple passive spring loaded inverted pendulum (SLIP). Due to its simplicity, however, the current form of the SLIP model is limited at providing any further information about multi-segmental lower limbs that generate oscillatory CoM behaviors and their corresponding ground reaction forces. Considering that the dynamics of the CoM are simply achieved by mass-spring mechanics, we wondered whether any of the multi-joint motions could be demonstrated by simple mechanics. In this study, we expand a SLIP model of human locomotion with an off-centered curvy foot connected to the leg by a springy segment that emulates the asymmetric kinematics and kinetics of the ankle joint. The passive dynamics of the proposed expansion of the SLIP model demonstrated the empirical data of ground reaction forces, center of mass trajectories, ankle joint kinematics and corresponding ankle joint torque at various gait speeds. From the mechanically simulated trajectories of the ankle joint and CoM, the motion of lower-limb segments, such as thigh and shank angles, could be estimated from inverse kinematics. The estimation of lower limb kinematics showed a qualitative match with empirical data of walking at various speeds. The representability of passive compliant mechanics for the kinetics of the CoM and ankle joint and lower limb joint kinematics implies that the coordination of multi-joint lower limbs during gait can be understood with a mechanical framework.     

The role of the heel pad and shank soft tissue during impacts: a further resolution of a paradox

The aim of this study was to test the hypothesis that the motion of the soft tissue of the lower leg contributes significantly to the attenuation of the forces during heel impacts. To examine this, a two-dimensional model of the shank and heel pad was developed using DADS. The model contained a heel pad element and a rigid skeleton to which was connected soft tissue which could move relative to the bone. Simulations permitted estimation of heel pad properties directly from heel pad deformations, and from the kinematics of an impacting pendulum. These two approaches paralleled those used in vitro and in vivo, respectively. Measurements from the pendulum indicated that heel pad properties changed from those found in vitro to those found in vivo as relative motion of the bone and soft tissue was allowed. This would indicate that pendulum measures of the in vivo heel pad properties are also measuring the properties of the whole lower leg. The ability of the wobbling mass of the shank to dissipate energy during an impact was found to be significant. These results demonstrate the important role of both the heel pad and soft tissue of the shank to the dissipation of mechanical energy during impacts. These results provide a further clarification of the paradox between the measurements of heel pad properties made in vivo and in vitro.     

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.     

A manipulability analysis of human walking

From the literature of biomechanics, it is now clear that humans use elevating, lowering and delayed-lowering strategies in order to maintain stability during perturbed walking. The main purpose of this study is to provide insights into the role of manipulability in selection of these strategies. A 37 degrees of freedom (DoFs) model of the human body is developed to evaluate the manipulability indices during walking. The model is considered as a tree-like structure and its forward kinematics equations and the Jacobian are derived based on the Denavit-Hartenberg (DH) convention. A hybrid genetic algorithm (HGA) is then employed to map the experimental kinematics of a human to the model. The kinematic and dynamic manipulability indices of the swing phase of walking are evaluated concentrating on early, mid and late swing phases. The results indicate that the manipulability indices can characterize well the selection of elevating, lowering and delayed-lowering strategies at different stages of the swing phase. The results kinematically describe the reason of selecting delayed-lowering strategy at mid-swing phase that was not obvious in previous studies. Moreover, the results show that at mid-swing phase of walking the kinematic maneuverability is lower than that of the early and late swing phases.     

Changes in knee function associated with treadmill ambulation

A comparison of level walking, on a walkway and on a treadmill, was performed using ten normal subjects. Motion about the knee was measured using a triaxial electrogoniometer, and foot-floor contact patterns were recorded by means of four foot switches attached to the sole of each shoe. On the walkway, the data were collected with the subject moving at a comfortable walking speed. The treadmill was then set at the average velocity obtained on the walkway. Knee joint rotation in the coronal and transverse planes did not change significantly between the walkway and the treadmill. In the sagittal plane, significant differences were found for total motion (p less than 0.01), swing phase motion (p less than 0.01), knee position at heel strike (p less than 0.05), and maximum swing phase extension (p less than 0.01). A comparison of the foot-floor contact patterns between walkway and treadmill ambulation revealed reduced heel contact time, with an increase in toe contact while on the treadmill. It was concluded that sagittal plane knee kinematics during level treadmill walking differ significantly from level overground walking.     

Stability of an underactuated bipedal gait

A self-excited biped walking mechanism consisting of two legs that are connected in series at the hip joint through a servomotor is studied as a cyclic system with collisions. A torque proportional to angle between the shank of the swinging leg and the vertical is seen to sustain a gait. Each leg has a thigh and a shank connected at a passive knee joint that has a knee stopper restricting hyperextension similar to the human knee. A mathematical model for the dynamics of the system including the impact equations is used to analyse the stability of the system through examination of phase plane plots. Attractor lines along which the system approaches stability have been identified. A leg length for optimal stability has been identified. The biological basis for the proposed system has been identified by comparison with human gait.     

Walking in Aretaon asperrimus

This article describes basic parameters characterizing walking of the stick insect Aretaon asperrimus to allow a comparative approach with other insects studied. As in many other animals, geometrical parameters such as step amplitude and leg extreme positions do not vary with walking velocity. However, the relation between swing duration and stance duration is quite constant, in contrast to most insects studied. Therefore, velocity profiles during swing vary with walking velocity whereas time course of leg trajectories and leg angle trajectories are independent of walking velocity. Nevertheless, A. asperrimus does not show a classical tripod gait, but performs a metachronal, or tetrapod, gait, showing phase values differing from 0.5 between ipsilateral neighbouring legs. As in Carausius morosus, the detailed shape of the swing trajectory may depend on the form of the substrate. Effects describing coordinating influences between legs have been found that prevent the start of a swing as long as the posterior leg performs a swing. Further, the treading on tarsus reflex can be observed in Aretaon. No hint to the existence of a targeting influence has been found. Control of rearward walking is easiest interpreted by maintaining the basic rules but an anterior-posterior reversal of the information flow.     

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.     

Assessment of intersegmental coordination of rats during walking at different speeds – Application of continuous relative phase

The present study investigated the feasibility and reliability of continuous relative phase (CRP) and deviation phase (DP) to assess intersegmental hind limb coordination pattern and coordination variability in rats during walking. Twenty-six adult rats walked at 8 m/min, 12 m/min and 16 m/min while two-dimensional kinematics were recorded. Segment angles and segment angular velocities of the paw, shank and thigh on the left hind-limb were extracted from 15 strides and CRP was calculated for the paw-shank and shank-thigh coupling. The effect of walking speed on the time point average curve of the CRP (ACRP) and DP and on the mean ACRP and mean DP was established by statistical parametric mapping (SPM) and a one-way ANOVA for repeated measures. Absolute and relative reliability were assessed by measurement error and intra-class correlation coefficient. The SPM analysis revealed time dependent differences in the effect of speed. Thus, the CRP of the paw-shank coupling decreased with increasing speed during most of the gait cycle while the CRP of the shank-thigh coupling was decreased during the swing phase. The session-to-session reliability was fair to good for the coordination measure and poor for the variability measure.     

Responses of the lower limb to load carrying in walking man

Muscle activity patterns of several lower limb muscles were examined in the left leg of normal human subjects walking at comfortable speed on a treadmill. In addition knee angular changes and the durations of the swing and stance phases of the step cycle were recorded. Data were collected during a period of normal control walking and when the subject carried a load, either in his right or left hand or on his back. Load (up to 20% of body weight) carried in either hand caused minimal changes in the kinematic parameters investigated but evoked significant prolongation of the normal ongoing electromyographic activity in the contralateral Gluteus medius and in the ipsilateral Gastrocnemius, Vastus lateralis and Semimembranosus. Load (up to 50% of body weight) carried on the back significantly shortened the swing phase and prolonged the ongoing electromyographic activity of the Vastus lateralis. These findings would seem to indicate that the activity of the leg musculature during walking is so tightly controlled that deviation from the normal kinematic pattern of the legs is largely prevented even when body posture and balance are disturbed by carrying substantial additional load.     

Resonant frequencies of arms and legs identify different walking patterns

The present study is aimed at investigating changes in the coordination of arm and leg movements in young healthy subjects. It was hypothesized that with changes in walking velocity there is a change in frequency and phase coupling between the arms and the legs. In addition, it was hypothesized that the preferred frequencies of the different coordination patterns can be predicted on the basis of the resonant frequencies of arms and legs with a simple pendulum model. The kinematics of arms and legs during treadmill walking in seven healthy subjects were recorded with accelerometers in the sagittal plane at a wide range of different velocities (i.e., 0.3-1. 3m/s). Power spectral analyses revealed a statistically significant change in the frequency relation between arms and legs, i.e., within the velocity range 0.3-0.7m/s arm movement frequencies were dominantly synchronized with the step frequency, whereas from 0.8m/s onwards arm frequencies were locked onto stride frequency. Significant effects of walking speed on mean relative phase between leg and arm movements were found. All limb pairs showed a significantly more stable coordination pattern from 0.8 to 1.0m/s onwards. Results from the pendulum modelling demonstrated that for most subjects at low-velocity preferred movement frequencies of the arms are predicted by the resonant frequencies of individual arms (about 0.98Hz), whereas at higher velocities these are predicted on the basis of the resonant frequencies of the individual legs (about 0.85Hz). The results support the above-mentioned hypotheses, and suggest that different patterns of coordination, as shown by changes in frequency coupling and phase relations, can exist within the human walking mode.     

Linear approximations for swing leg motion during gait

The applicability of a linear systems analysis of two-dimensional swing leg motion was investigated. Two different linear systems were developed. A linear time-varying system was developed by linearizing the nonlinear equations describing swing leg motion about a set of nominal system and control trajectories. Linear time invariant systems were developed by linearizing about three different fixed limb positions. Simulations of swing leg motion were performed with each of these linear systems. These simulations were compared to previously performed nonlinear simulations of two-dimensional swing leg motion and the actual subject motion. Additionally, a linear system analysis was used to gain some insight into the interdependency of the state variables and controls. It was shown that the linear time varying approximation yielded an accurate representation of limb motion for the thigh and shank but with diminished accuracy for the foot. In contrast, all the linear time invariant systems, if used to simulate more than a quarter of the swing phase, yielded generally inaccurate results for thigh shank and foot motion.     

Oscillation and Reaction Board Techniques for Estimating Inertial Properties of a Below-knee Prosthesis

The purpose of this study was two-fold: 1) demonstrate a technique that can be used to directly estimate the inertial properties of a below-knee prosthesis, and 2) contrast the effects of the proposed technique and that of using intact limb inertial properties on joint kinetic estimates during walking in unilateral, transtibial amputees. An oscillation and reaction board system was validated and shown to be reliable when measuring inertial properties of known geometrical solids. When direct measurements of inertial properties of the prosthesis were used in inverse dynamics modeling of the lower extremity compared with inertial estimates based on an intact shank and foot, joint kinetics at the hip and knee were significantly lower during the swing phase of walking. Differences in joint kinetics during stance, however, were smaller than those observed during swing. Therefore, researchers focusing on the swing phase of walking should consider the impact of prosthesis inertia property estimates on study outcomes. For stance, either one of the two inertial models investigated in our study would likely lead to similar outcomes with an inverse dynamics assessment.     

The kinematic consequences of invariant dynamics in children 6-18 years of age

The effect of limb dynamics on trajectory formation is unclear. The natural frequency of a limb is the major factor in its dynamics. It has previously been shown with an indirect measurement method that the natural frequency of body segments is invariant during human growth from the age of 6 to 18. The aim of our study was to determine, using a direct measurement method, whether human growth affects: (1) lower limb dynamics (i.e. the natural frequency of the lower leg) and (2) the maximum velocities of the knee during selected motor tasks. In 20 non-disabled children, 6-18 years of age, measurements were taken of the natural frequency of the lower leg (including the foot), and the maximum velocities of knee flexion and extension during voluntary movement (MVV) and at initial and terminal swing phases of self-paced walking (WAL). The velocities were also estimated using a dynamic model and the results were compared to the measured velocities with a paired t-test. Correlations among the frequencies, velocities, and body height (an indicator of growth) were calculated. The natural frequency of the lower leg (mean+/-standard deviation, omega(0)=6.58+/-0.54s(-1)), maximum velocities of knee extension and flexion during voluntary movement (MVV(e)=10.1+/-1.8rads(-1) and MVV(f)=7.8+/-1.3rads(-1), respectively), and maximum velocities of knee flexion and extension during the swing phase of walking (WAL(f)=5.4+/-0.6rads(-1) and WAL(e)=6.3+/-0.87rads(-1), respectively) were each found to be independent of body height. The MVV measured velocities were 22% larger and WAL(f) measured velocities were 25% smaller than the velocities predicted from the dynamic model (p<0.05). The study found that a segment's dynamic properties, as well as selected kinematics, may be considered invariant with human growth.     

How locomotion sub-functions can control walking at different speeds?

Inspired from template models explaining biological locomotory systems and Raibert׳s pioneering legged robots, locomotion can be realized by basic sub-functions: elastic axial leg function, leg swinging and balancing. Combinations of these three can generate different gaits with diverse properties. In this paper we investigate how locomotion sub-functions contribute to stabilize walking at different speeds. Based on this trilogy, we introduce a conceptual model to quantify human locomotion sub-functions in walking. This model can produce stable walking and also predict human locomotion sub-function control during swing phase of walking. Analyzing experimental data based on this modeling shows different control strategies which are employed to increase speed from slow to moderate and moderate to fast gaits.     

Multijoint Control Strategies Transfer Between Tasks

In this paper, the hypothesis that multijoint control strategies are transferred between similar tasks was tested. To test this hypothesis, we studied the take-off phase of two types of backward somersault dives: one while translating backwards (Back), the other while translating forward (Reverse). An experimentally based dynamic model of the musculoskeletal system was employed to simulate the measured kinematics and reaction force data and to study the sensitivity of take-off performance to initial kinematic conditions. It was found that the horizontal velocity of the total body center of mass (CM) was most sensitive to modifications in the initial shank conditions. Consequently, the initial shank kinematics of the Back dive was modified in the optimization procedure while maintaining the joint coordination of the Back in order to generate the CM trajectory and reaction forces of a Reverse. Similarly, the initial shank kinematics of the Reverse dive was modified to simulate the CM trajectory and reaction force of the Back. It was found that small modifications in the initial shank kinematics led to change in direction of horizontal CM velocity at take-off; resulting in a switch from Back to Reverse and vice versa. In both cases, the simulated momentum conditions at departure and the bimodal shape of the reaction force-time curve were consistent with those experimentally observed. The results of this study support the hypothesis that transfer of control strategies between similar tasks is a viable option in multijoint control. This transfer of control strategy is explained using a hierarchical model of the motion control system.     

Biomechanics of overground vs. treadmill walking in healthy individuals.

The goal of this study was to compare treadmill walking with overground walking in healthy subjects with no known gait disorders. Nineteen subjects were tested, where each subject walked on a split-belt instrumented treadmill as well as over a smooth, flat surface. Comparisons between walking conditions were made for temporal gait parameters such as step length and cadence, leg kinematics, joint moments and powers, and muscle activity. Overall, very few differences were found in temporal gait parameters or leg kinematics between treadmill and overground walking. Conversely, sagittal plane joint moments were found to be quite different, where during treadmill walking trials, subjects demonstrated less dorsiflexor moments, less knee extensor moments, and greater hip extensor moments. Joint powers in the sagittal plane were found to be similar at the ankle but quite different at the knee and hip joints. Differences in muscle activity were observed between the two walking modalities, particularly in the tibialis anterior throughout stance, and in the hamstrings, vastus medialis and adductor longus during swing. While differences were observed in muscle activation patterns, joint moments and joint powers between the two walking modalities, the overall patterns in these behaviors were quite similar. From a therapeutic perspective, this suggests that training individuals with neurological injuries on a treadmill appears to be justified.