The six determinants of gait and the inverted pendulum analogy: A dynamic walking perspective

We examine two prevailing, yet surprisingly contradictory, theories of human walking. The six determinants of gait are kinematic features of gait proposed to minimize the energetic cost of locomotion by reducing the vertical displacement of the body center of mass (COM). The inverted pendulum analogy proposes that it is beneficial for the stance leg to behave like a pendulum, prescribing a more circular arc, rather than a horizontal path, for the COM. Recent literature presents evidence against the six determinants theory, and a simple mathematical analysis shows that a flattened COM trajectory in fact increases muscle work and force requirements. A similar analysis shows that the inverted pendulum fares better, but paradoxically predicts no work or force requirements. The paradox may be resolved through the dynamic walking approach, which refers to periodic gaits produced almost entirely by the dynamics of the limbs alone. Demonstrations include passive dynamic walking machines that descend a gentle slope, and active dynamic walking robots that walk on level ground. Dynamic walking takes advantage of the inverted pendulum mechanism, but requires mechanical work to transition from one pendular stance leg to the next. We show how the step-to-step transition is an unavoidable energetic consequence of the inverted pendulum gait, and gives rise to predictions that are experimentally testable on humans and machines. The dynamic walking approach provides a new perspective, focusing on mechanical work rather than the kinematics or forces of gait. It is helpful for explaining human gait features in a constructive rather than interpretive manner.     

Visual control of locomotion: strategies for changing direction and for going over obstacles.

Dynamics of gait adjustments required to go over obstacles and to alter direction of locomotion when cued visually were assessed through the measurement of ground reaction forces, muscle activity, and kinematics. The time of appearance of obstacles of varying heights, their position within the step cycle, and cue lights for direction change were varied. Direction change must be planned in the previous step to reduce the acceleration of the body center of mass toward the landing foot to 0. The inability of steering within the step cycle is due to the incapacity of muscles to rotate the body and translate it along the mediolateral axes. For obstacle avoidance, Ss systematically manipulated the gait patterns as a function of obstacle height and position and the time available within the ongoing step. Greater supraspinal involvement in control of locomotion is found.     

Kinematic assessment of treadmill running using different body-weight support harnesses

10 male collegiate runners (M age = 21.4, SD = 1.5 yr.) ran on a treadmill with no body-weight support (BWS), 20% BWS, and 40% BWS conditions. In addition, they wore three different commercially available harnesses at the 20% and 40% BWS conditions. The aim was to run on the treadmill at a fast speed while maintaining an adequate step length. The purpose was to investigate how each harness changed running gait, and the differences in running gait between the harnesses with various body-weight support. Analysis of variance indicated significant restriction of upper body torso rotation between the harnesses at the 40% BWS conditions. Body-weight support resulted in a longer stride, decreased cadence, less vertical displacement of the center of mass, and diminished hip and ankle joint excursions. These changes indicated that increased body-weight support results in longer steps with the foot contacting the belt for a shorter period of time with less leg angular changes throughout the running cycling.     

Enhanced arm swing alters interlimb coordination during overground walking in individuals with traumatic brain injury

The current study investigated interlimb coordination in individuals with traumatic brain injury (TBI) during overground walking. The study involved 10 participants with coordination, balance, and gait abnormalities post-TBI, as well as 10 sex- and age-matched healthy control individuals. Participants walked 12 m under two experimental conditions: 1) at self-selected comfortable walking speeds; and 2) with instructions to increase the amplitude and out-of-phase coordination of arm swinging. The gait was assessed with a set of spatiotemporal and kinematic parameters including the gait velocity, step length and width, double support time, lateral displacement of the center of mass, the amplitude of horizontal trunk rotation, and angular motions at shoulder and hip joints in sagittal plane. Interlimb coordination (coupling) was analyzed as the relative phase angles between the left and right shoulders, hips, and contralateral shoulders and hips, with an ideal out-of-phase coupling of 180° and ideal in-phase coupling of 0°. The TBI group showed much less interlimb coupling of the above pairs of joint motions than the control group. When participants were required to increase and synchronize arm swinging, coupling between shoulder and hip motions was significantly improved in both groups. Enhanced arm swinging was associated with greater hip and shoulder motion amplitudes, and greater step length. No other significant changes in spatiotemporal or kinematic gait characteristics were found in either group. The results suggest that arm swinging may be a gait parameter that, if controlled properly, can improve interlimb coordination during overground walking in patients with TBI.     

Speed influences on the scaling behavior of gait cycle fluctuations during treadmill running

The current study examined the temporal structure of gait cycle fluctuations in running. Participants ran at 80%, 90%, 100%, 110% and 120% of preferred running speed for 8min trials. Kinematic and kinetic gait cycle variables were generated from ground reaction force data. Mean, SD and CV of the kinematic and kinetic variables changed linearly with speed, whereas U-shaped functions were found for the scaling exponent alpha in 5 of the 8 variables investigated. Our findings reveal that long range correlations are present in both kinetic and kinematic variables of the gait cycle. The dependent structure of the stride interval is reduced at preferred running speed and this is hypothesized to be related to the enhanced stability and flexibility of this gait speed.     

Comparison of kinematic and kinetic methods for computing the vertical motion of the body center of mass during walking

The vertical excursion of the body center of mass (BCOM) was calculated using three different techniques commonly used by motion analysis laboratories. The sacral marker method involved estimating vertical BCOM motion by tracking the position of a reflective marker that was placed on the sacrum of subjects as they walked. The body segmental analysis technique determined the vertical motion of the BCOM from a weighted average of the vertical positions of the centers of mass of individual body segments for each frame of kinematic data acquired during the data trial. Anthropomorphic data from standard tables were used to determine the mass fractions and the locations of the centers of mass of each body segment. The third technique involved calculating BCOM vertical motion through double integration of force platform data. Data was acquired from 10 able-bodied, adult research subjects--5 males and 5 females--walking at speeds of 0.8, 1.2, 1.6, and 2.0 m/s. A repeated measures ANOVA indicated that at the slowest walking speed the vertical excursions calculated by all three techniques were similar, but at faster speeds the sacral marker significantly (p < 0.001) overestimated the vertical excursion of the BCOM compared with the other two methods. The body segmental analysis and force platform techniques were in agreement at all walking speeds. Discrepancies between the sacral marker method and the other two techniques were explained using a simple model; the reciprocal configuration of the legs during double support phase significantly raises the position of the BCOM within the trunk at longer step lengths, corresponding to faster walking speeds. The sacral marker method may provide a reasonable approximation of vertical BCOM motion at slow and freely selected speeds of able-bodied walking. However, the body segmental analysis or force platform techniques will probably yield better estimates at faster walking speeds or in persons with gait pathologies.     

Control of Gait Initiation

The initiation of gait from a standing posture by 6 subjects, who took controlled-length steps, was analyzed. Using an inverted-pendulum model, we found that the duration of gait initiation was independent of gait velocity. This finding suggests that subjects' biomechanical constants are the determining factors for initiating movement. Both the instantaneous velocity of the center of gravity at the end of the first step (resulting in the propulsive forces measured on the ground) and the steady-state velocity (resulting in the step length and frequency) varied with step length, whereas step frequency did not. But step frequency and progression velocity were linked, for step frequency always increased in parallel with increased progression velocity. We interpret the correlation between velocity and frequency variations to be a peripheral expression of the posturodynamic control of the step parameters by the progression forces.     

Whole Body Coordination and Knee Movement Control During Five Rehabilitation Exercises

Knee rehabilitation exercises to improve motor control, target movement fluency, and displacement variability. Although knee movement in the frontal plane during exercise is routinely assessed in clinical practice, optimal knee control remains poorly understood. In this study, 29 healthy participants (height: 1.73 ± 0.11 m, mass: 73.5 ± 16.4 kg, age: 28.0 ± 6.9 years) performed 4 repetitions of 5 rehabilitation exercises while motion data were collected using the VICON PlugInGait full-body marker set. Fluency and displacement variability were calculated for multiple landmarks, including center of mass (CoM) and knee joint centers. Fluency was calculated as the inverse of the average number of times a landmark velocity in the frontal plane crossed zero. Variability was defined as the standard deviation of the frontal plane movement trajectories. CoM fluency and displacement variability were significantly different between tasks (p < .001). CoM displacement variability was consistently smallest compared to the constituent landmarks (p < .005). This was interpreted as a whole body strategy of compensatory variability constraining CoM frontal plane movement. Ipsilateral knee fluency (p < .01) and displacement variability (p < .001) differed substantially between tasks. The role of the weight-bearing knee seemed dependent on task constraints of the overall movement and balance, as well as constraints specific for knee joint stability.     

Control of gait initiation

The initiation of gait from a standing posture by 6 subjects, who took controlled-length steps, was analyzed. Using an inverted pendulum model, we found that the duration of gait initiation was independent of gait velocity. This finding suggests that subjects' biomechanical constants are the determining factors for initiating movement. Both the instantaneous velocity of the center of gravity at the end of the first step (resulting in the propulsive forces measured on the ground) and the steady-state velocity (resulting in the step length and frequency) varied with step length, whereas step frequency did not. But step frequency and progression velocity were linked, for step frequency always increased in parallel with increased progression velocity. We interpret the correlation between velocity and frequency variations to be a peripheral expression of the posturodynamic control of the step parameters by the progression forces.     

Early stage of walking: development of control in mediolateral and anteroposterior directions

The authors examined the changes in bipedal gait of toddlers in the anteroposterior (AP) and mediolateral (ML) directions, as a set, at the onset of independent gait and 1 month after onset. Two groups with distinctly different dynamic resources were studied: 8 toddlers with typical development (TD) and 8 toddlers with Down syndrome (DS). Three-dimensional kinematic data were collected, and gait parameters, such as walking speed, stride length, and stride frequency, as well as the ratio of exchange between potential energy and kinetic energy of the center of mass (COM), were calculated. Displacement of the COM in the AP and ML directions were also analyzed. For some gait variables, toddlers with DS seemed to show more mature values at walking onset than their peers with TD. Those group differences reversed and increased by Visit 2. When the authors considered the motion of the COM of the system, it became clear that the qualitative differences between those groups were characterized primarily by constraints in the ML direction. The authors propose that establishment of coupling between AP and ML oscillations is a key component for the emergence of independent bipedal walking for both populations.     

Tibialis posterior muscle pain effects on hip,knee and ankle gait mechanics

BackgroundTibialis posterior (TP) dysfunction is a common painful complication in patients with rheumatoid arthritis (RA), which can lead to the collapse of the medial longitudinal arch. Different theories have been developed to explain the causality of tibialis posterior dysfunction. In all these theories, pain is a central factor, and yet, it is uncertain to what extent pain causes the observed biomechanical alterations in the patients. The aim of this study was to investigate the effect of experimental tibialis posterior muscle pain on gait mechanics in healthy subjects.MethodsTwelve healthy subjects were recruited for this randomized crossover study. Experimental pain was induced by ultrasound-guided injection of 1 mL hypertonic saline into the upper part of the right tibialis posterior muscle with the use of isotonic saline as non-pain-inducing control. Subsequently, kinematic data during three self-paced over ground walking for each condition were collected. Ground reaction forces and external moments were measured from force plates installed in the floor. Painful areas were evaluated using body charts and pain intensity scoring via a verbal numerical rating scale.FindingsDecreased hip internal rotation was observed during the pain condition at the end of the stance phase. There were no changes in gait velocity and duration of stand phase between the pain and no pain conditions. Reduced external joint moment was found for external knee rotation and for external hip rotation.InterpretationThe study has demonstrated that induced pain in the TP muscle evokes kinematic alteration in the hip and the knee joints, but not in the ankle, which suggest an underlying early stage joint compensatory mechanism. These findings suggest the need to include those joints in current physical evaluations of tibialis posterior dysfunction.     

Effects of plantar cutaneo-muscular and tendon vibration on posture and balance during quiet and perturbed stance

Modulation of lower limb somatosensory information by tendon or plantar vibration produces directionally specific, vibration-induced falling reactions that depend on the tendon or the region of the sole that is vibrated. This study characterized the effects of different patterns of plantar cutaneo-muscular vibration and bilateral Achilles tendon vibration (ATV) on the postural strategies observed during quiet and perturbed stance. Twelve healthy young participants stood barefooted, with their vision blocked, on two sets of plantar vibrators placed on two AMTI force plates embedded in a moveable support surface. Two other vibrators were positioned over the Achilles tendons. Participants were randomly exposed to different patterns of plantar cutaneo-muscular and ATV. Tilts of the support surface in the toes-up (TU) and toes-down (TD) directions were given 5-8 s after the beginning of vibration. Body kinematics in 3D and ground reaction forces were recorded. Bilateral ATV applied with or without rearfoot vibration (RFV) during quiet stance resulted in a whole-body backward leaning accompanied by an increase in trunk extension and hip and knee flexion. RFV alone produced a forward whole-body tilt with increased flexion in trunk, hip, and ankle. When stance was perturbed by TU tilts, the center of mass (CoM) and center of pressure (CoP) displacements were larger in the presence of RFV or ATV and associated with increased peak trunk flexion. TD tilts with or without ATV resulted in no significant difference in CoM and CoP displacements, while larger trunk extension and smaller distal angular displacements were observed during ATV. RFV altered the magnitude of the balance reactions, as observed by an increase in CoP displacements and variable response in trunk displacement. Significant interactions between ATV and RFV were obtained for the peak angular excursions for both directions of perturbations, where ATV either enhanced (for TU tilts) or attenuated (for TD tilts) the influence of RFV. Manipulating somatosensory information from the plantar cutaneo-muscular and muscle spindle Ia afferents thus results in altered and widespread postural responses, as shown by profound changes in body kinematics and CoM and CoP displacements. This suggests that the CNS uses plantar cutaneo-muscular and ankle spindle afferent inputs to build an appropriate reference of verticality that influences the control of equilibrium during quiet and perturbed stance.     

An Energetic Comparison of Symmetrical and Asymmetrical Human Gait

This article contrasts the mechanical energy profiles of asymmetrical galloping with those of symmetrical running in adult humans. Seven female subjects were filmed while performing overground running and galloping at their preferred velocities. A previous study (Whitall & Caldwell, 1992) showed that kinematic differences between these gait modes included higher preferred velocity for running than galloping, with distinct differences in interlimb coordination but surprisingly similar intralimb patterns. Energetically, in the present study the whole body center of mass during galloping was found to behave much as it does in walking; kinetic and potential energy profiles were out of phase, as compared with running, which exhibited in-phase fluctuations of kinetic and potential energies. The primary reason for these center of mass differences was found in the energetics of the back leg of galloping, which demonstrated alterations in timing of its energy fluctuations and less energy generation than the front leg. Analysis of the power sources underlying the segmental energies during swing phase showed that the back leg's energy changes were accomplished mainly through reduced use of the hip muscles and less interlimb energy transfer. The back leg's energetics during swing also displayed a shift toward greater reliance on nonmuscular energy sources. A pattern of energy inflow during early swing and energy outflow during late swing was common to both running and galloping, although the galloping legs both demonstrated more abrupt transitions between these phases. The possibility is raised that the 67/33 interlimb phasing ratio used in galloping is selected to reduce mechanical energy variations of the total body center of mass. These data suggest that models of asymmetric gait in humans must account for more than merely phase alteration.     

The effects of unilateral grab rail assistance on the sit-to-stand performance of older aged adults

This study investigated the effects of unilateral grab rail assistance during the sit-to-stand transfer to develop an understanding of lower limb joint mechanics and whole body movement patterns. External reaction forces at the grab rail and floor interfaces were also investigated to understand the nature of the assistance provided by the introduction of unilateral upper body assistance. While 12 older aged adults performed the sit-to-stand, three-dimensional body segment kinematics were recorded to determine lower body joint motion and whole body centre of mass motion. Grab rail reaction forces and bilateral ground reaction forces were recorded to determine external reaction forces and lower body joint kinetics. Grab rail assisted conditions were compared with unassisted transfers. During grab rail assistance, a systematic asymmetry was introduced to lower limb joint kinetics, without noticeable alterations to peak lower body joint motion and whole body movement patterns. Ipsilateral net joint moments and powers decreased in the ankle and hip and increased in the knee, while the contralateral net joint moments and powers increased in the hip and decreased in the knee. Joint kinetic and kinematic responses suggest a motor control strategy that maintains symmetric sit-to-stand movement patterns by adjusting bilateral muscle control when a unilateral external reaction force is provided. Understanding the mechanical assistance that is generated during the sit-to-stand will facilitate optimal design of grab rails for older aged adults and may contribute to design for specific pathologies. Such design implementation will influence the ability of older aged adults to remain independent in the community.     

Lower limb kinematic variability in dancers performing drop landings onto floor surfaces with varied mechanical properties

Elite dancers perform highly skilled and consistent movements. These movements require effective regulation of the intrinsic and extrinsic forces acting within and on the body. Customized, compliant floors typically used in dance are assumed to enhance dance performance and reduce injury risk by dampening ground reaction forces during tasks such as landings. As floor compliance can affect the extrinsic forces applied to the body, secondary effects of floor properties may be observed in the movement consistency or kinematic variability exhibited during dance performance. The aim of this study was to investigate the effects of floor mechanical properties on lower extremity kinematic variability in dancers performing landing tasks. A vector coding technique was used to analyze sagittal plane knee and ankle joint kinematic variability, in a cohort of 12 pre-professional dancers, through discrete phases of drop landings from a height of 0.2 m. No effect on kinematic variability was observed between floors, indicating that dancers could accommodate the changing extrinsic floor conditions. Future research may consider repeat analysis under more dynamic task constraints with a less experienced cohort. However, knee/ankle joint kinematic variability was observed to increase late in the landing phase which was predominantly comprised of knee flexion coupled with the terminal range of ankle dorsiflexion. These findings may be the result of greater neural input late in the landing phase as opposed to the suggested passive mechanical interaction of the foot and ankle complex at initial contact with a floor. Analysis of joint coordination in discrete movement phases may be of benefit in identifying intrinsic sources of variability in dynamic tasks that involve multiple movement phases.     

Biofeedback augmenting lower limb loading alters the underlying temporal structure of gait following anterior cruciate ligament reconstruction

Biofeedback has recently been explored to target deviant lower extremity loading mechanics following anterior cruciate ligament reconstruction (ACLR) to mitigate the development of post traumatic osteoarthritis. The impact this feedback has on the structure of the stride interval dynamics—a barometer of gait system health—however, have yet to be examined. This study was designed to assess how feedback, used to alter lower-extremity loading during gait, affects the structure of stride interval variability by examining long-range stride-to-stride correlations during gait in those with unilateral ACLR. Twelve participants walked under three separate loading conditions: (1) control (i.e., no cue) (2) high loading, and (3) low loading. Baseline vertical ground reaction force (vGRF) data was used to calculate a target 5% change in vGRF for the appropriate loading condition (i.e., high loading was +5% vGRF, low loading was −5% vGRF). The target for the load condition was displayed on a screen along with real-time vGRF values, prescribing changes in stride-to-stride peak vertical ground reaction forces of each limb. From time-series of stride intervals (i.e., duration), we analyzed the mean and standard deviation of stride-to-stride variability and, via detrended fluctuation analysis (i.e., DFA α), temporal persistence for each feedback condition. Both the high and low loading conditions exhibited a change toward more temporally persistent stride intervals (high loading: α =0.92, low loading: α = 0.98) than walking under the control condition (α = 0.78; high vs. control: p = .026, low vs. control: p = .001). Overall, these results indicate that altering lower extremity load changes the temporal persistence of the stride internal dynamics in ACLR individuals, demonstrating the implications of the design of gait training interventions and the influence feedback has on movement strategies.     

“Posture first”: Interaction between posture and locomotion in people with low back pain during unexpectedly cued modification of gait initiation motor command

The ability to adapt anticipatory postural adjustments (APAs) in response to perturbations during single-joint movements is altered in people with chronic low back pain (LBP), but a comprehensive analysis during functional motor tasks is still missing. This study aimed to compare APAs and stepping characteristics during gait initiation between people with LBP and healthy controls, both in normal (without cue occurrence) condition and when an unexpected visual cue required to switch the stepping limb. Fourteen individuals with LPB and 10 healthy controls performed gait initiation in normal and switch conditions. The postural responses were evaluated through the analysis of center of pressure, propulsive ground reaction forces, trunk and whole-body kinematics, and activation onsets of leg and back muscles. During normal gait initiation, participants with LBP exhibited similar APAs and stepping characteristics to healthy controls. In the switch condition, individuals with LBP were characterized by greater mediolateral postural stability but decreased forward body motion and propulsion before stepping. The thorax motion was associated with forward propulsion parameters in both task conditions in people with LBP but not healthy controls. No between-group differences were found in muscle activation onsets. The results suggest that postural stability is prioritized over forward locomotion in individuals with LBP. Furthermore, the condition-invariant coupling between thorax and whole-body forward propulsion in LBP suggests an adaptation in the functional use of the thorax within the postural strategy, even in poor balance conditions.     

Challenging horizontal movement of the body during sit-to-stand: impact on stability in the young and elderly

There are 3 significant challenges to sit-to-stand: (a) bringing the center of mass forward, (b) vertically raising the center of mass from the sitting to standing position, and (c) transition from a relatively large and stable base of support in sitting to a considerably smaller base of support when standing. The authors explored the challenges to stability control following sit-to-stand when the requirement for horizontal movement of the center of mass was influenced by foot position and their potential effect on the preceding phases of sit-to-stand. Eleven healthy young and 11 healthy elderly individuals performed the sit-to-stand with their feet further away and closer to the chair. Kinetic and kinematic data were recorded. Regardless of foot position, challenges in stability were greater in elderly participants than young participants despite their similar movement time and shear forces. The greater instability in elderly participants, despite their comparable movement characteristics, emphasizes the importance of stability control following sit-to-stand performance. For both young and elderly participants, the sit-to-stand duration and the shear forces were greater in the far condition. However, foot position did not affect the stability measures (i.e., duration of the stabilization phase and the total center of pressure path during the 1st second of the stabilization phase).     

Soft tissue contributions to impact forces simulated using a four-segment wobbling mass model of forefoot-heel landings

The purpose of this investigation was to develop and evaluate a wobbling mass model of a female performing a drop landing and to examine the influence of soft tissue properties on the impact loads experienced. A planar model comprising a foot, shank, thigh and upper body segment was developed. Spring-damper systems coupled the foot to the ground and the wobbling masses to the rigid masses. Unlike traditional wobbling mass models of landing, the model included a foot segment, which allowed replication of forefoot-heel landing techniques and also used subject and movement-specific properties to simulate the landings. Kinematics and force data collected for three drop landings (height 0.46 m) performed by a female were separately used to drive and evaluate the model. The wobbling mass model successfully reproduced the measured force profiles to 9% (RMS differences) of the measured range and replicated the measured peak vertical ground reaction forces to 6%. The accuracies of the wobbling mass model and a corresponding rigid mass model were compared. The inclusion of soft tissue properties in the model contributed up to an 8.6 bodyweights reduction in peak impact loading and produced a 52% more accurate replication of the measured force profiles. The prominent role soft tissues have in load attenuation and the benefits of modelling soft tissue in simulations of landings were therefore highlighted. The success of the wobbling mass model in replicating the kinetics of actual landing performances suggests the model may be used in the future to gain a realistic insight into load attenuation strategies used by females.     

Strength Training Effects on Muscle Forces and Contributions to Whole-Body Movement in Cerebral Palsy

Strength training is often prescribed for children with cerebral palsy (CP); however, links between strength gains and mobility are unclear. Nine children (age 14?±?3?years; GMFCS I-III) with spastic CP completed a 6-week strength-training program. Musculoskeletal gait simulations were generated for four children to assess training effects on muscle forces and function. There were increases in isometric joint strength, but no statistical changes in fast-as-possible walking speed or endurance after training. The walking simulations revealed changes in muscle forces and contributions to body center of mass acceleration, with greater forces from the hip muscles during walking most commonly observed. A progressive strength-training program can result in isometric and dynamic strength gains in children with CP, associated with variable mobility outcomes.