J. Maxwell Donelan

Energetic consequences of walking like an inverted pendulum: step-to-step transitions

Walking like an inverted pendulum reduces muscle-force and work demands during single support, but it also unavoidably requires mechanical work to redirect the body’s center of mass in the transition between steps, when one pendular motion is substituted by the next. Production of this work exacts a proportional metabolic cost that is a major determinant of the overall cost of walking.

Simultaneous positive and negative external mechanical work in human walking

In human walking, the center of mass motion is similar to an inverted pendulum. Viewing double support as a transition from one inverted pendulum to the next, we hypothesized that the leading leg performs negative work to redirect the center of mass velocity, while simultaneously, the trailing leg performs positive work to replace the lost energy. To test this hypothesis, we developed a method to quantify the external mechanical work performed by each limb (individual limbs method). Traditional measures of external mechanical work use the sum of the ground reaction forces acting on the limbs (combined limbs method) allowing for the mathematical cancellation of simultaneous positive and negative work during multiple support periods. We expected to find that the traditional combined limbs method underestimates external mechanical work by a substantial amount. We used both methods to measure the external mechanical work performed by humans walking over a range of speeds. We found that during double support, the legs perform a substantial amount of positive and negative external work simultaneously. The combined limbs measures of positive and negative external work were approximately 33% less than those calculated using the individual limbs method. At all speeds, the trailing leg performs greater than 97% of the double support positive work while the leading leg performs greater than 94% of the double support negative work.

Mechanics and energetics of swinging the human leg

SUMMARY We measured how much metabolic energy is expended to swing a human leg. A previous dynamical model of walking predicted that increasing metabolic costs for walking with step length and step frequency trade-off against each other to determine the optimum step combination at a given speed. Simple pendulum dynamics indicate that the cost of walking at high step frequencies could be associated with driving the legs back and forth relative to the body, at a rate increasing approximately with the fourth power of frequency, possibly due to the low economy of producing muscle force for short durations. A similar cost would be expected for isolated swinging of a leg at faster than its natural frequency. We constructed an apparatus to measure work performed on the leg, and measured metabolic cost as human subjects (N=12) swung one leg at frequencies 0.5-1.1 Hz and fixed amplitude. Rate of mechanical work ranged from 0.02-0.27 W kg-1 over these frequencies. Net metabolic rate for leg swinging (subtracting that for quiet standing) increased from 0.41-2.10 W kg-1, approximately with the fourth power of frequency (R2=0.92) and in proportion to a hypothesized cost of force production for short durations. The costs of producing force and work could account for the increase. In a crude comparison, moving the legs back and forth at a typical stride frequency of 0.9 Hz, might consume about one-third of the net energy (2.8±0.8 W kg-1) needed for walking at 1.3 m s-1.

Dynamic Principles of Gait and Their Clinical Implications

A healthy gait pattern depends on an array of biomechanical features, orchestrated by the central nervous system for economy and stability. Injuries and other pathologies can alter these features and result in substantial gait deficits, often with detrimental consequences for energy expenditure and balance. An understanding of the role of biomechanics in the generation of healthy gait, therefore, can provide insight into these deficits. This article examines the basic principles of gait from the standpoint of dynamic walking, an approach that combines an inverted pendulum model of the stance leg with a pendulum model of the swing leg and its impact with the ground. The heel-strike at the end of each step has dynamic effects that can contribute to a periodic gait and its passive stability. Biomechanics, therefore, can account for much of the gait pattern, with additional motor inputs that are important for improving economy and stability. The dynamic walking approach can predict the consequences of disruptions to normal biomechanics, and the associated observations can help explain some aspects of impaired gait. This article reviews the basic principles of dynamic walking and the associated experimental evidence for healthy gait and then considers how the principles may be applied to clinical gait pathologies.

Humans Can Continuously Optimize Energetic Cost during Walking

People prefer to move in ways that minimize their energetic cost. For example, people tend to walk at a speed that minimizes energy use per unit distance and, for that speed, they select a step frequency that makes walking less costly. Although aspects of this preference appear to be established over both evolutionary and developmental timescales, it remains unclear whether people can also optimize energetic cost in real time. Here we show that during walking, people readily adapt established motor programs to minimize energy use. To accomplish this, we used robotic exoskeletons to shift peoples energetically optimal step frequency to frequencies higher and lower than normally preferred. In response, we found that subjects adapted their step frequency to converge on the new energetic optima within minutes and in response to relatively small savings in cost (<5%). When transiently perturbed from their new optimal gait, subjects relied on an updated prediction to rapidly re-converge within seconds. Our collective findings indicate that energetic cost is not just an outcome of movement, but also plays a central role in continuously shaping it.

Development of a biomechanical energy harvester

BackgroundBiomechanical energy harvesting–generating electricity from people during daily activities–is a promising alternative to batteries for powering increasingly sophisticated portable devices. We recently developed a wearable knee-mounted energy harvesting device that generated electricity during human walking. In this methods-focused paper, we explain the physiological principles that guided our design process and present a detailed description of our device design with an emphasis on new analyses.MethodsEffectively harvesting energy from walking requires a small lightweight device that efficiently converts intermittent, bi-directional, low speed and high torque mechanical power to electricity, and selectively engages power generation to assist muscles in performing negative mechanical work. To achieve this, our device used a one-way clutch to transmit only knee extension motions, a spur gear transmission to amplify the angular speed, a brushless DC rotary magnetic generator to convert the mechanical power into electrical power, a control system to determine when to open and close the power generation circuit based on measurements of knee angle, and a customized orthopaedic knee brace to distribute the device reaction torque over a large leg surface area.ResultsThe device selectively engaged power generation towards the end of swing extension, assisting knee flexor muscles by producing substantial flexion torque (6.4 Nm), and efficiently converted the input mechanical power into electricity (54.6%). Consequently, six subjects walking at 1.5 m/s generated 4.8 ± 0.8 W of electrical power with only a 5.0 ± 21 W increase in metabolic cost.ConclusionBiomechanical energy harvesting is capable of generating substantial amounts of electrical power from walking with little additional user effort making future versions of this technology particularly promising for charging portable medical devices.

Distinct fast and slow processes contribute to the selection of preferred step frequency during human walking

Humans spontaneously select a step frequency that minimizes the energy expenditure of walking. This selection might be embedded within the neural circuits that generate gait so that the optimum is pre-programmed for a given walking speed. Or perhaps step frequency is directly optimized, based on sensed feedback of energy expenditure. Direct optimization is expected to be slow due to the compounded effect of delays and iteration, whereas a pre-programmed mechanism presumably allows for faster step frequency selection, albeit dependent on prior experience. To test for both pre-programmed selection and direct optimization, we applied perturbations to treadmill walking to elicit transient changes in step frequency. We found that human step frequency adjustments (n = 7) occurred with two components, the first dominating the response (66 ± 10% of total amplitude change; mean ± SD) and occurring quite quickly (1.44 ± 1.14 s to complete 95% of total change). The other component was of smaller amplitude (35 ± 10% of total change) and took tens of seconds (27.56 ± 16.18 s for 95% completion). The fast process appeared to be too fast for direct optimization and more indicative of a pre-programmed response. It also persisted even with unusual closed-loop perturbations that conflicted with prior experience and rendered the response energetically suboptimal. The slow process was more consistent with the timing expected for direct optimization. Our interpretation of these results is that humans may rely heavily on pre-programmed gaits to rapidly select their preferred step frequency and then gradually fine-tune that selection with direct optimization.

Scaling of sensorimotor control in terrestrial mammals

Sensorimotor control is greatly affected by two factors—the time it takes for an animal to sense and respond to stimuli (responsiveness), and the ability of an animal to distinguish between sensory stimuli and generate graded muscle forces (resolution). Here, we demonstrate that anatomical limitations force a necessary trade-off between responsiveness and resolution with increases in animal size. To determine whether responsiveness is prioritized over resolution, or resolution over responsiveness, we studied how size influences the physiological mechanisms underlying sensorimotor control. Using both new electrophysiological experiments and existing data, we determined the maximum axonal conduction velocity (CV) in animals ranging in size from shrews to elephants. Over the 100-fold increase in leg length, CV was nearly constant, increasing proportionally with mass to the 0.04 power. As a consequence, larger animals are burdened with relatively long physiological delays, which may have broad implications for their behaviour, ecology and evolution, including constraining agility and requiring prediction to help control movements.

Fast visual prediction and slow optimization of preferred walking speed

People prefer walking speeds that minimize energetic cost. This may be accomplished by directly sensing metabolic rate and adapting gait to minimize it, but only slowly due to the compounded effects of sensing delays and iterative convergence. Visual and other sensory information is available more rapidly and could help predict which gait changes reduce energetic cost, but only approximately because it relies on prior experience and an indirect means to achieve economy. We used virtual reality to manipulate visually presented speed while 10 healthy subjects freely walked on a self-paced treadmill to test whether the nervous system beneficially combines these two mechanisms. Rather than manipulating the speed of visual flow directly, we coupled it to the walking speed selected by the subject and then manipulated the ratio between these two speeds. We then quantified the dynamics of walking speed adjustments in response to perturbations of the visual speed. For step changes in visual speed, subjects responded with rapid speed adjustments (lasting <2 s) and in a direction opposite to the perturbation and consistent with returning the visually presented speed toward their preferred walking speed, when visual speed was suddenly twice (one-half) the walking speed, subjects decreased (increased) their speed. Subjects did not maintain the new speed but instead gradually returned toward the speed preferred before the perturbation (lasting >300 s). The timing and direction of these responses strongly indicate that a rapid predictive process informed by visual feedback helps select preferred speed, perhaps to complement a slower optimization process that seeks to minimize energetic cost.

A semi-automated method for identifying and measuring myelinated nerve fibers in scanning electron microscope images

Diagnosing illnesses, developing and comparing treatment methods, and conducting research on the organization of the peripheral nervous system often require the analysis of peripheral nerve images to quantify the number, myelination, and size of axons in a nerve. Current methods that require manually labeling each axon can be extremely time-consuming as a single nerve can contain thousands of axons. To improve efficiency, we developed a computer-assisted axon identification and analysis method that is capable of analyzing and measuring sub-images covering the nerve cross-section, acquired using a scanning electron microscope. This algorithm performs three main procedures - it first uses cross-correlation to combine the acquired sub-images into a large image showing the entire nerve cross-section, then identifies and individually labels axons using a series of image intensity and shape criteria, and finally identifies and labels the myelin sheath of each axon using a region growing algorithm with the geometric centers of axons as seeds. To ensure accurate analysis of the image, we incorporated manual supervision to remove mislabeled axons and add missed axons. The typical user-assisted processing time for a two-megapixel image containing over 2000 axons was less than 1h. This speed was almost eight times faster than the time required to manually process the same image. Our method has proven to be well suited for identifying axons and their characteristics, and represents a significant time savings over traditional manual methods.