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First published online June 15, 2007
Journal of Experimental Biology 210, 2390-2398 (2007)
Published by The Company of Biologists 2007
doi: 10.1242/jeb.02782

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Energetic cost of producing cyclic muscle force, rather than work, to swing the human leg

Jiro Doke and Arthur D. Kuo^*

Department of Mechanical Engineering, University of Michigan, Ann Arbor, MI 48109-2125, USA

View larger version (13K): [in this window] [in a new window]   Fig. 1. Experimental apparatus. Subject performed swinging of one leg while securely strapped to a rigid frame. Leg angle was measured using an optical encoder. Subjects attempted to swing at a target amplitude, displayed through visual feedback. The target amplitude was varied with frequency to maintain a constant average rate of positive mechanical work on the leg. A force plate measured ground reaction forces, which were used with to calculate the leg torque about the hip. Electromyographic (EMG) activity of the medial hamstring was also recorded to assess duration of muscle force production. Oxygen consumption was measured to provide indirect calorimetry of metabolic energy expenditure.

View larger version (18K): [in this window] [in a new window]   Fig. 2. Model predictions of metabolic energy expenditure as a function of frequency of leg swinging. A simple pendulum model shows that (A) setting target amplitudes to decrease with swing frequency (according to Eqn 1) will result in (B) a constant rate of positive work performed on the leg. (C) The work hypothesis predicts that a constant rate of work will result in a constant rate of metabolic energy expenditure (Eqn 6). (D) In contrast, the cyclic work hypothesis, where energy is expended to produce force for short durations, predicts that metabolic rate will increase with swing frequency (Eqn 7). Both hypotheses predict trends (rather than absolute metabolic rates) that are to be tested against experimental data with least-squares fits. The ability to predict energy expenditure may independently be tested at a different combination of swing frequency and amplitude (extrapolation point, denoted by open circles). The extrapolated model, fitted from the original data, may be compared against the extrapolation data. All predictions apply to swing frequencies at least as fast as the natural frequency, labeled in A, of the leg swinging freely under gravity, as computed from leg inertial properties.

View larger version (17K): [in this window] [in a new window]   Fig. 3. Mechanics of leg swinging as a function of frequency f, were modeled well by a forced pendulum. (A) Subjects performed leg swinging at decreasing amplitudes (filled symbols) with increasing frequency. Target swing amplitudes were selected (Eqn 1) to maintain a constant average rate of positive mechanical work. An additional trial (open symbols) was performed at smaller amplitude for 0.67 Hz, to provide an independent test of metabolic energy predictions. (B) Hip torque amplitude T0 increased with f0.5 (R2=0.97), as predicted by the pendulum model (Eqn 5). (C) The average rate of positive mechanical work, (+), remained nearly constant for frequencies between 0.75 Hz and 1.08 Hz. A linear fit to these data yielded a slope not significantly different from zero (P>0.05). These data demonstrate that the experimental conditions successfully produced leg swinging at a variety of frequencies but keeping rate of mechanical work constant, facilitating the isolation of the cyclic force cost. Data fits were performed using dimensionless variables (right-hand axis) with body mass, gravitational constant, and leg length serving as base units; conventional units are shown (left-hand axis) for convenience. Data values shown are means ± s.d. (N=6).

View larger version (17K): [in this window] [in a new window]   Fig. 4. Electromyography (EMG) data showed decreasing burst durations and increasing amplitudes as a function of swing frequency. (A) Medial hamstring (MH) and (B) rectus femoris (RF) average burst durations, , decreased in inverse proportion to swing frequency f (P<0.05; R2=0.72 and 0.94, respectively), as expected. Burst durations were determined from rectified EMG (as shown by inset diagram). Root-mean-square (RMS) amplitudes of (C) MH and (D) RF increased with leg swing frequency (R2=0.67 and 0.86, respectively), roughly similar to hip torque amplitude (Eqn 5). RMS amplitudes were determined from low-pass filtered, rectified EMG. Data shown (filled and unfilled circles) are means ± s.d. (N=6 for A-C; N=3 for D). Model fits were performed in accordance with predicted trends (f-1 and Eqn 5, respectively), with coefficients determined by least-squares fits.

View larger version (12K): [in this window] [in a new window]   Fig. 5. Metabolic rate was predicted well by the cyclic force hypothesis. (A) Metabolic rate, , increased (P<0.05), approximately with frequency f raised to the 2.5 power, as in Eqn 7 (R2=0.95). The same prediction, extrapolated to the low-amplitude trial performed at 0.67 Hz (broken line), also agrees reasonably well with the independently measured data (open symbol). (B) Metabolic rate also increased approximately linearly with the empirically measured rate of force/time as in Eqn 8 (R2=0.95).