First published online July 25, 2005
Journal of Experimental Biology 208, 2845-2853 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01710
Effects of series elasticity and activation conditions on muscle power output and efficiency
G. A. Lichtwark1 and
A. M. Wilson1,2,*
1 Structure and Motion Laboratory, Institute of Orthopaedics and
Musculoskeletal Sciences, University College London, Royal National Orthopedic
Hospital, Brockley Hill, Stanmore, Middlesex, HA7 4LP, UK
2 Structure and Motion Laboratory, The Royal Veterinary College, Hawkshead
Lane, North Mymms, Hatfield, Hertfordshire, AL9 7TA, UK
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Fig. 1. (A) Force–length relationship used to scale the maximum force output
(adapted from Gordon et al.,
1966 ) by scaling the number of possible crossbridges that can
attach. (B) Scaling of activation to represent 30%, 50% and 100% of activation
levels.
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Fig. 2. (A) Contour plot showing the range of duty cycles and phases of activation
that can achieve 99%, 80%, 60% and 40% of maximum power output (solid lines)
and efficiency (broken lines). The colour bar represents the absolute values
for power output (PoLo) and
efficiency. The values for achieving optimum power (x) and efficiency (o) are
also shown. The frequency of oscillation was 1.25 Hz. (B) Work loops (force
vs length) for optimal power output (Bi) and optimal efficiency
(Bii). The work loops of the contractile element (CE, green), the series
elastic element (SEE, red) and the muscle tendon unit (MTU, blue) are shown.
Positive length changes indicate stretch and the force is the same in the SEE,
CE and MTU at any point in time. The duty cycle and phase for optimal power
were found to be 0.368 and –5.11, respectively, compared to 0.098 and
5.91 for optimal efficiency. The thick lines indicate the duration of
activation.
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Fig. 3. Contour plot showing the range of duty cycles and phases of activation that
can achieve 99%, 80%, 60% and 40% of maximum power output (A,B) and efficiency
(C,D) for a compliant relative stiffness (solid lines) and a stiff relative
stiffness (broken lines) at two different amplitudes of oscillation
±0.0335Lo (A,C) and
±0.2Lo (B,D). The colour bars represent the
absolute values for power (A,B) and efficiency (C,D). Compliant relative
stiffness=3–4Po/Lo; stiff
relative stiffness=16–22Po/Lo
(lower stiffness value for forces less than 0.15Po; see
Lichtwark and Wilson,
2005).
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Fig. 4. (A) Maximum power output (solid lines) and efficiency (broken lines) with
changes in the amplitude of stretch/shortening at a low stiffness (blue) and
high stiffness (red). (B) Maximum power output and efficiency and the duty
cycle, phase of activation and amplitude of stretch/shortening that achieve
that power output with varying relative stiffness. Solid lines represent the
values obtained for maximum power output and broken lines those obtained for
maximum efficiency.
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Fig. 5. Surface plot of variation in power output (A) and efficiency (B) with duty
cycle and phase of activation at three different amplitudes of activation
levels. Activation levels were scaled to 30%, 50% and 100% of activation.
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© The Company of Biologists Ltd 2005
