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J Theor Biol. 2012 Nov 21;313:68-78. doi: 10.1016/j.jtbi.2012.07.033. Epub 2012 Aug 8.

Elastic recoil can either amplify or attenuate muscle-tendon power, depending on inertial vs. fluid dynamic loading.

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  • 1The Rowland Institute at Harvard, Harvard University, Cambridge, MA 02142, USA.


Frog jumps exceed muscle power limits. To achieve this, a muscle may store elastic energy in tendon before it is released rapidly, producing 'power amplification' as tendon recoil assists the muscle to accelerate the load. Do the musculoskeletal modifications conferring power amplification help or hinder frog swimming? We used a Hill-type mathematical model of a muscle-tendon (MT) with contractile element (CE) and series elastic element (SEE) properties of frogs. We varied limb masses from 0.3 to 30 g, foot-fin areas from 0.005 to 50 cm(2) and effective mechanical advantage (EMA=in-lever/out-lever) from 0.025 to 0.1. 'Optimal' conditions produced power amplification of ~19% greater than the CE limit. Yet, other conditions caused ~80% reduction of MT power (power attenuation) due to SEE recoil absorbing power from (rather than adding to) the CE. The tendency for elastic recoil to cause power amplification vs. attenuation was load dependent: low fluid drag loads, high limb mass and EMA=0.1 caused power amplification whereas high drag, low mass and low EMA (=0.025) caused attenuation. Power amplification emerged when: (1) CE shortening velocity is 1/3V(max), (2) elastic energy storage is neither too high nor too low, and (3). peak inertial-drag force ratio ≥ ~1.5. Excessive elastic energy storage delayed the timing of recoil, causing power attenuation. Thus our model predicts that for fluid loads, the benefit from a compliant tendon is modest, and when the system is 'poorly tuned' (i.e., inappropriate EMA), MT power attenuation can be severe.

Copyright © 2012 Elsevier Ltd. All rights reserved.

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