The Rowland Institute at Harvard, Harvard University, Cambridge, MA 02142, USA.
J Theor Biol. 2012 Nov 21;313:68-78. doi: 10.1016/j.jtbi.2012.07.033. Epub 2012 Aug 8.
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.
青蛙跳跃超过肌肉力量极限。为了实现这一点，肌肉可能会在肌腱中储存弹性能量，然后迅速释放，从而产生“功率放大”，因为肌腱的回弹会协助肌肉加速负载。赋予功率放大的肌肉骨骼修改是有助于还是阻碍青蛙游泳？我们使用了一种具有青蛙收缩元件（CE）和串联弹性元件（SEE）特性的肌肉肌腱（MT）的 Hill 型数学模型。我们将肢体质量从 0.3 克变化到 30 克，脚蹼面积从 0.005 平方厘米变化到 50 平方厘米，有效机械优势（EMA=内杠杆/外杠杆）从 0.025 变化到 0.1。“最佳”条件下产生的功率放大比 CE 极限高约 19%。然而，其他条件导致 MT 功率降低约 80%（功率衰减），因为 SEE 回弹从 CE 吸收功率（而不是增加）。弹性回弹引起功率放大与衰减的趋势取决于负载：低流体阻力负载、高肢体质量和 EMA=0.1 会引起功率放大，而高阻力、低质量和低 EMA（=0.025）会引起衰减。当出现以下情况时，会出现功率放大：（1）CE 缩短速度为 V(max)的 1/3；（2）弹性储能既不过高也不过低；（3）.峰值惯性-阻力比≥~1.5。过多的弹性储能会延迟回弹的时间，导致功率衰减。因此，我们的模型预测，对于流体负载，顺应性肌腱带来的好处是适度的，并且当系统“调谐不当”（即，EMA 不合适）时，MT 功率衰减可能会很严重。
