Biomedical subjects
Publications and source records attributed to J Maxwell Donelan.
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.
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 (R(2)=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).
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.
In the single stance phase of walking, center of mass motion resembles that of an inverted pendulum. Theoretically, mechanical work is not necessary for producing the pendular motion, but work is needed to redirect the center of mass velocity from one pendular arc to the next during the transition between steps. A collision model predicts a rate of negative work proportional to the fourth power of step length. Positive work is required to restore the energy lost, potentially exacting a proportional metabolic cost. We tested these predictions with humans (N=9) walking over a range of step lengths (0.4-1.1 m) while keeping step frequency fixed at 1.8 Hz. We measured individual limb external mechanical work using force plates, and metabolic rate using indirect calorimetry. As predicted, average negative and positive external mechanical work rates increased with the fourth power of step length (from 1 W to 38 W; r(2)=0.96). Metabolic rate also increased with the fourth power of step length (from 7 W to 379 W; r(2)=0.95), and linearly with mechanical work rate. Mechanical work for step-to-step transitions, rather than pendular motion itself, appears to be a major determinant of the metabolic cost of walking.
Numerous investigations over the past 15 years have demonstrated that sensory feedback plays a critical role in establishing the timing and magnitude of muscle activity during walking. Here we review recent studies reporting that sensory feedback makes a substantial contribution to the activation of extensor motoneurons during the stance phase. Quantitative analysis of the effects of loading and unloading ankle extensor muscles during walking on a horizontal surface has shown that sensory feedback can increase the activity of ankle extensor muscles by up to 60%. There is currently some uncertainty about which sensory receptors are responsible for this enhancement of extensor activity, but likely candidates are the secondary spindle endings in the ankle extensors of humans and the Golgi tendon organs in the ankle extensors of humans and cats. Two important issues arise from the finding that sensory feedback from the leg regulates the magnitude of extensor activity. The first is the extent to which differences in the magnitude of activity in extensor muscles during different locomotor tasks can be directly attributed to changes in the magnitude of sensory signals, and the second is whether the enhancement of extensor activity is determined primarily by feedback from a specific group of receptors or from numerous groups of receptors distributed throughout the leg. Limitations of current experimental strategies prevent a straightforward empirical resolution of these issues. A potentially fruitful approach in the immediate future is to develop models of the known and hypothesized neuronal networks controlling motoneuronal activity, and use these simulations to control forward dynamic models of the musculo-skeletal system. These simulations would help understand how sensory signals are modified with a change in locomotor task and, in conjunction with physiological experiments, establish the extent to which these modifications can account for changes in the magnitude of motoneuronal activity.