Peter G. Adamczyk

Dynamic arm swinging in human walking

Humans tend to swing their arms when they walk, a curious behaviour since the arms play no obvious role in bipedal gait. It might be costly to use muscles to swing the arms, and it is unclear whether potential benefits elsewhere in the body would justify such costs. To examine these costs and benefits, we developed a passive dynamic walking model with free-swinging arms. Even with no torques driving the arms or legs, the model produced walking gaits with arm swinging similar to humans. Passive gaits with arm phasing opposite to normal were also found, but these induced a much greater reaction moment from the ground, which could require muscular effort in humans. We therefore hypothesized that the reduction of this moment may explain the physiological benefit of arm swinging. Experimental measurements of humans (n = 10) showed that normal arm swinging required minimal shoulder torque, while volitionally holding the arms still required 12 per cent more metabolic energy. Among measures of gait mechanics, vertical ground reaction moment was most affected by arm swinging and increased by 63 per cent without it. Walking with opposite-to-normal arm phasing required minimal shoulder effort but magnified the ground reaction moment, causing metabolic rate to increase by 26 per cent. Passive dynamics appear to make arm swinging easy, while indirect benefits from reduced vertical moments make it worthwhile overall.

The advantages of a rolling foot in human walking.

SUMMARY The plantigrade human foot rolls over the ground during each walking step, roughly analogous to a wheel. The center of pressure progresses on the ground like a wheel of radius 0.3 L (leg length). We examined the effect of varying foot curvature on the mechanics and energetics of walking. We controlled curvature by attaching rigid arc shapes of various radii to the bottoms of rigid boots restricting ankle motion. We measured mechanical work performed on the center of mass (COM), and net metabolic rate, in human subjects (N=10) walking with seven arc radii from 0.02–0.40 m. Simple models of dynamic walking predict that redirection of COM velocity requires step-to-step transition work, decreasing quadratically with arc radius. Metabolic cost would be expected to change in proportion to mechanical work. We measured the average rate of negative work performed on the COM, and found that it followed the trend well (r2=0.95), with 2.37 times as much work for small radii as for large. Net metabolic rate (subtracting quiet standing) also decreased with increasing arc radius to a minimum at 0.3 L, with a slight increase thereafter. Maximum net metabolic rate was 6.25 W kg–1 (for small-radius arc feet), about 59% greater than the minimum rate of 3.93 W kg–1, which in turn was about 45% greater than the rate in normal walking. Metabolic rate was fit reasonably well (r2=0.86) by a quadratic curve, but exceeded that expected from COM work for extreme arc sizes. Other factors appear to increase metabolic cost for walking on very small and very large arc feet. These factors may include effort expended to stabilize the joints (especially the knee) or to maintain balance. Rolling feet with curvature 0.3 L appear energetically advantageous for plantigrade walking, partially due to decreased work for step-to-step transitions.

A simple method for calibrating force plates and force treadmills using an instrumented pole

We propose a new method for calibrating force plates to reduce errors in center of pressure locations, forces, and moments. These errors may be caused by imperfect mounting of force plates to the ground or by installation of a treadmill atop a force plate, which may introduce distorting loads. The method, termed the Post-Installation Least-Squares (PILS) calibration, combines features of several previous methods into a simple procedure. It requires a motion capture system and an instrumented pole for applying reference loads. Reference loads may be manually applied to the force plate in arbitrary locations and directions. The instrumented pole measures applied load magnitudes through a single-axis load cell, and load directions through motion capture markers. Reference data and imperfect force plate signals are then combined to form a linear calibration matrix that simultaneously minimizes mean square errors in all forces and moments. We applied the procedure to standard laboratory force plates, as well as a custom-built, split-belt force treadmill. We also collected an independent set of verification data for testing. The proposed calibration procedure was found to reduce force errors by over 20%, and moment errors by over 60%. Center of pressure errors were also reduced by 63% for standard force plates and 91% for the force treadmill. The instrumented pole is advantageous because it allows for fast and arbitrary load application without needing a precise fixture for aligning loads. The linear calibration matrix is simpler than nonlinear correction equations and more compatible with standard data acquisition software, yet it yields error reductions comparable to more complex methods.

Redirection of center-of-mass velocity during the step-to-step transition of human walking

SUMMARY Simple dynamic walking models based on the inverted pendulum predict that the human bodys center of mass (COM) moves along an arc during each step, with substantial work performed to redirect the COM velocity in the step-to-step transition between arcs. But humans do not keep the stance leg perfectly straight and need not redirect their COM velocity precisely as predicted. We therefore tested a pendulum-based model against a wide range of human walking data. We examined COM velocity and work data from normal human subjects (N=10) walking at 24 combinations of speed (0.75 to 2.0 m s–1) and step length. These were compared against model predictions for the angular redirection of COM velocity and the work performed on the COM during redirection. We found that the COM is redirected through angular changes increasing approximately linearly with step length (R2=0.68), with COM work increasing with the squared product of walking speed and step length (R2=0.82), roughly in accordance with a simple dynamic walking model. This model cannot, however, predict the duration of COM redirection, which we quantified with two empirical measures, one based on angular COM redirection and the other on work. Both indicate that the step-to-step transition begins before and ends after double support and lasts about twice as long – approximately 20–27% of a stride. Although a rigid leg model can predict trends in COM velocity and work, the non-rigid human leg performs the step-to-step transition over a duration considerably exceeding that of double support.

The effect of prosthetic foot push-off on mechanical loading associated with knee osteoarthritis in lower extremity amputees.

Lower extremity amputation not only limits mobility, but also increases the risk of knee osteoarthritis of the intact limb. Dynamic walking models of non-amputees suggest that pushing-off from the trailing limb can reduce collision forces on the leading limb. These collision forces may determine the peak knee external adduction moment (EAM), which has been linked to the development of knee OA in the general population. We therefore hypothesized that greater prosthetic push-off would lead to reduced loading and knee EAM of the intact limb in unilateral transtibial amputees. Seven unilateral transtibial amputees were studied during gait under three prosthetic foot conditions that were intended to vary push-off. Prosthetic foot-ankle push-off work, intact limb knee EAM and ground reaction impulses for both limbs during step-to-step transition were measured. Overall, trailing limb prosthetic push-off work was negatively correlated with leading intact limb 1st peak knee EAM (slope=-.72±.22; p=.011). Prosthetic push-off work and 1st peak intact knee EAM varied significantly with foot type. The prosthetic foot condition with the least push-off demonstrated the largest knee EAM, which was reduced by 26% with the prosthetic foot producing the most push-off. Trailing prosthetic limb push-off impulse was negatively correlated with leading intact limb loading impulse (slope=-.34±.14; p=.001), which may help explain how prosthetic limb push-off can affect intact limb loading. Prosthetic feet that perform more prosthetic push-off appear to be associated with a reduction in 1st peak intact knee EAM, and their use could potentially reduce the risk and burden of knee osteoarthritis in this population.

Systematic Variation of Prosthetic Foot Spring Affects Center-of-Mass Mechanics and Metabolic Cost During Walking

Lower-limb amputees expend more energy to walk than non-amputees and have an elevated risk of secondary disabilities. Insufficient push-off by the prosthetic foot may be a contributing factor. We aimed to systematically study the effect of prosthetic foot mechanics on gait, to gain insight into fundamental prosthetic design principles. We varied a single parameter in isolation, the energy-storing spring in a prototype prosthetic foot, the controlled energy storage and return (CESR) foot, and observed the effect on gait. Subjects walked on the CESR foot with three different springs. We performed parallel studies on amputees and on non-amputees wearing prosthetic simulators. In both groups, spring characteristics similarly affected ankle and body center-of-mass (COM) mechanics and metabolic cost. Softer springs led to greater energy storage, energy return, and prosthetic limb COM push-off work. But metabolic energy expenditure was lowest with a spring of intermediate stiffness, suggesting biomechanical disadvantages to the softest spring despite its greater push-off. Disadvantages of the softest spring may include excessive heel displacements and COM collision losses. We also observed some differences in joint kinetics between amputees and non-amputees walking on the prototype foot. During prosthetic push-off, amputees exhibited reduced energy transfer from the prosthesis to the COM along with increased hip work, perhaps due to greater energy dissipation at the knee. Nevertheless, the results indicate that spring compliance can contribute to push-off, but with biomechanical trade-offs that limit the degree to which greater push-off might improve walking economy.

Measurement of foot placement and its variability with inertial sensors

Gait parameters such as stride length, width, and period, as well as their respective variabilities, are widely used as indicators of mobility and walking function. Foot placement and its variability have thus been applied in areas such as aging, fall risk, spinal cord injury, diabetic neuropathy, and neurological conditions. But a drawback is that these measures are presently best obtained with specialized laboratory equipment such as motion capture systems and instrumented walkways, which may not be available in many clinics and certainly not during daily activities. One alternative is to fix inertial measurement units (IMUs) to the feet or body to gather motion data. However, few existing methods measure foot placement directly, due to drift associated with inertial data. We developed a method to measure stride-to-stride foot placement in unconstrained environments, and tested whether it can accurately quantify gait parameters over long walking distances. The method uses ground contact conditions to correct for drift, and state estimation algorithms to improve estimation of angular orientation. We tested the method with healthy adults walking over-ground, averaging 93 steps per trial, using a mobile motion capture system to provide reference data. We found IMU estimates of mean stride length and duration within 1% of motion capture, and standard deviations of length and width within 4% of motion capture. Step width cannot be directly estimated by IMUs, although lateral stride variability can. Inertial sensors measure walks over arbitrary distances, yielding estimates with good statistical confidence. Gait can thus be measured in a variety of environments, and even applied to long-term monitoring of everyday walking.

The effects of a controlled energy storage and return prototype prosthetic foot on transtibial amputee ambulation

The lack of functional ankle musculature in lower limb amputees contributes to the reduced prosthetic ankle push-off, compensations at other joints and more energetically costly gait commonly observed in comparison to non-amputees. A variety of energy storing and return prosthetic feet have been developed to address these issues but have not been shown to sufficiently improve amputee biomechanics and energetic cost, perhaps because the timing and magnitude of energy return is not controlled. The goal of this study was to examine how a prototype microprocessor-controlled prosthetic foot designed to store some of the energy during loading and return it during push-off affects amputee gait. Unilateral transtibial amputees wore the Controlled Energy Storage and Return prosthetic foot (CESR), a conventional foot (CONV), and their previously prescribed foot (PRES) in random order. Three-dimensional gait analysis and net oxygen consumption were collected as participants walked at constant speed. The CESR foot demonstrated increased energy storage during early stance, increased prosthetic foot peak push-off power and work, increased prosthetic limb center of mass (COM) push-off work and decreased intact limb COM collision work compared to CONV and PRES. The biological contribution of the positive COM work for CESR was reduced compared to CONV and PRES. However, the net metabolic cost for CESR did not change compared to CONV and increased compared to PRES, which may partially reflect the greater weight, lack of individualized size and stiffness and relatively less familiarity for CESR and CONV. Controlled energy storage and return enhanced prosthetic push-off, but requires further design modifications to improve amputee walking economy.

Mechanisms of Gait Asymmetry Due to Push-Off Deficiency in Unilateral Amputees

Unilateral lower-limb amputees exhibit asymmetry in many gait features, such as ground force, step time, step length, and joint mechanics. Although these asymmetries result from weak prosthetic-side push-off, there is no proven mechanistic explanation of how that impairment propagates to the rest of the body. We used a simple dynamic walking model to explore possible consequences of a unilateral impairment similar to that of a transtibial amputee. The model compensates for reduced push-off work from one leg by performing more work elsewhere, for example during the middle of stance by either or both legs. The model predicts several gait abnormalities, including slower forward velocity of the body center-of-mass during intact-side stance, greater energy dissipation in the intact side, and more positive work overall. We tested these predictions with data from unilateral transtibial amputees (N = 11) and nonamputee control subjects (N = 10) walking on an instrumented treadmill. We observed several predicted asymmetries, including forward velocity during stance phases and energy dissipation from the two limbs, as well as greater work overall. Secondary adaptations, such as to reduce discomfort, may exacerbate asymmetry, but these simple principles suggest that some asymmetry may be unavoidable in cases of unilateral limb loss.

The role of series ankle elasticity in bipedal walking

The elastic stretch-shortening cycle of the Achilles tendon during walking can reduce the active work demands on the plantarflexor muscles in series. However, this does not explain why or when this ankle work, whether by muscle or tendon, needs to be performed during gait. We therefore employ a simple bipedal walking model to investigate how ankle work and series elasticity impact economical locomotion. Our model shows that ankle elasticity can use passive dynamics to aid push-off late in single support, redirecting the bodys center-of-mass (COM) motion upward. An appropriately timed, elastic push-off helps to reduce dissipative collision losses at contralateral heelstrike, and therefore the positive work needed to offset those losses and power steady walking. Thus, the model demonstrates how elastic ankle work can reduce the total energetic demands of walking, including work required from more proximal knee and hip muscles. We found that the key requirement for using ankle elasticity to achieve economical gait is the proper ratio of ankle stiffness to foot length. Optimal combination of these parameters ensures proper timing of elastic energy release prior to contralateral heelstrike, and sufficient energy storage to redirect the COM velocity. In fact, there exist parameter combinations that theoretically yield collision-free walking, thus requiring zero active work, albeit with relatively high ankle torques. Ankle elasticity also allows the hip to power economical walking by contributing indirectly to push-off. Whether walking is powered by the ankle or hip, ankle elasticity may aid walking economy by reducing collision losses.