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First published online April 18, 2008
Journal of Experimental Biology 211, iv (2008)
Copyright © 2008 The Company of Biologists Limited
doi: 10.1242/jeb.011379
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CONSEQUENCES OF BULGING
University of Maryland
tytell{at}umd.edu
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Nicolaus Steno, famous today as the founder of modern geology, was better known in his own day as an anatomist. His public dissections attracted crowds across Europe in the 17th century. Undergraduates today still know his anatomical work – even if they may not know its source – because Steno provided a description of the structure and function of pennate muscles. Pennate muscles look a bit like feathers, or `pennae' in Latin; many short muscle fibers insert at an angle on a long central tendon, called an aponeurosis, like the vanes of a feather attach to the central shaft. Surrounding the feather-like structure is another tendonous aponeurosis.
Steno understood that this feather-like structure allowed more muscle fibers to be packed into a given volume of muscle – and more muscle fibers means more force. To analyze the function, he assumed that the aponeuroses stay the same distance apart at all times, which means that as the muscle fibers shorten they rotate. And because of the rotation, the velocity of the central aponeurosis can exceed the fibers' own shortening velocity. However, the fibers trade this increased shortening velocity for decreased force because they insert at an angle on the central aponeurosis. This tradeoff is called the architectural gear ratio.
However, Steno's analysis was two dimensional, and neglected one important constraint: muscles cannot change volume. As muscle fibers shorten, they also bulge out. To examine the consequences of bulging, Brown University researchers Emmanuel Azizi, Elizabeth Brainerd and Thomas Roberts constructed a three-dimensional mathematical model of a pennate muscle, essentially stacking multiple `feathers' on top of each other. Then they constrained how the fibers could bulge. According to the calculations, if the fibers bulge out perpendicular to the flat surface of the `feather', then the aponeuroses can stay the same distance apart or even get closer together. If they get closer, then the fibers don't need to rotate as far, which reduces the gear ratio, resulting in stronger but slower contractions. Alternatively, the fibers could bulge in the plane of the feather, which causes the aponeuroses to get further apart even as the fibers themselves get shorter, resulting in even larger angular changes and a higher gear ratio for fast but weak contractions.
To test how real pennate muscles change shape, the researchers examined the lateral gastrocnemius muscle from wild turkeys. They stimulated the muscle to contract and used a servomotor to vary the shortening velocity so that the force remained fixed at certain levels. Throughout the contraction, they measured the angle and length of the muscle fibers and the width and thickness of the whole muscle.
They found that the gear ratio changed automatically, depending on the total force. For high forces, the fibers tended to rotate relatively little, pulling the aponeuroses together and resulting in a slow whole-muscle contraction and a low gear ratio. For low forces, the fibers rotated much more, and the bulging fibers pushed the aponeuroses apart, causing a fast whole-muscle contraction and a high gear ratio. This automatic change in gear ratio with varying load expands the range of possible operating conditions for the muscle, increasing both the maximum force at low speeds and the maximum speed at low forces.
References
Azizi, E., Brainerd, E. L. and Roberts, T. J.
(2008). Variable gearing in pennate muscles. Proc.
Natl. Acad. Sci. USA 105,1745
-1750.
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