Architectural gear ratio

Figure 1 Anatomical gear ratio. The line aw represents a muscle fiber of length m with its origin at w and insertion into an aponeurosis (TT') at a. The fiber shortens to length m' and moves its insertion the distance d to point b. Note that the shortening muscle fiber does not pull the aponeurosis along the line of action of the fiber but rather rotates around its origin. This is because the 3-dimensional structure of the muscle resists inward movement of the aponeurosis so that the distance between the fiber origin and the aponeurosis remains constant. For a very small shortening of the muscle, the distance ac represents the shortening of the muscle and is equal to ab*cosΦ where Φ is the instantaneous pennation angle. For a pennate muscle, cosΦ is always less than 1, meaning that the distance ac is always shorter than the distance ab, thus the muscle fiber shortening is 'amplified' by a factor of 1/cosΦ.

Architectural gear ratio, also called anatomical gear ratio (AGR) is a feature of pennate muscle defined by the ratio between the longitudinal strain of the muscle and muscle fiber strain. It is sometimes also defined as the ratio between muscle-shortening velocity and fiber-shortening velocity.[1]

AGR = εx/εf

where εx = longitudinal strain (or muscle-shortening velocity) and εf is fiber strain (or fiber-shortening velocity) In fusiform muscle, the fibers are longitudinal, so longitudinal strain is equal to fiber strain, and AGR is always 1.

As the pennate muscle is activated, the fibers rotate as they shorten and pull at an angle. In pennate muscles, fibers are oriented at an angle to the muscle's line of action and rotate as they shorten, becoming more oblique such that the fraction of force directed along the muscle's line of action decreases throughout a contraction. Force output is dependent upon the angle of fiber rotation, so changes in muscle thickness and the vector of change in thickness vary; based upon the force being produced. Due to the rotational motion; pennate muscles operate at low velocities (low shortening distance). The shortening velocity of the pennate muscle as a whole is greater than that of the individual fibers. This gives rise to the property of AGR. Fiber rotation decreases a muscle's output force but increases output velocity by allowing the muscle to function at a higher gear ratio (muscle velocity/fiber velocity). Azizi and Brainerd demonstrated that the gear ratio of pennate muscle can vary; dependent on external load.[2]

Segmented musculature, like pennate muscle, has fibers aligned at an angle and due to this feature of design, when muscle fibers increase in angle with respect to the medial axis, along with the direction and amount of muscle bulging, the Architectural gear ratio increases.[1][3] A variable gear ratio, based upon different anatomical position, loading and movement conditions, has since been dubbed spatially varying gear ratio. The occurrence of spatially varying gear ratio gives rise to a new insight of muscle biology; “inhomogenous muscle mechanics.[4]”

One feature of the ratio is that there is an optimal gear ratio for each muscle; as the length-tension and force-velocity relationships describe. Length-tension refers to the max tension that can be created over the muscle fiber strain range and force-velocity refers to the power that is possible of the fiber compared to the shortening velocity. These two features of musculature help to define an optimal AGR for a muscle.[1]

  1. ^ a b c Azizi, E.; Brainerd, E.L. (2007). "Architectural Gear Ratio and Muscle Fiber Strain Homogeneity in Segmented Musculature". Journal of Experimental Zoology. 307A (3): 145–155. doi:10.1002/jez.a.358. PMID 17397068.
  2. ^ Azizi, E; Brainerd, EL; Roberts, TJ (February 2008). "Variable gearing in pennate muscles". Proceedings of the National Academy of Sciences. 105 (5): 1745–1750. Bibcode:2008PNAS..105.1745A. doi:10.1073/pnas.0709212105. PMC 2234215. PMID 18230734.
  3. ^ Brainerd, E.L.; Azizi, E. (2005). "Muscle fiber angle, segment bulging and architectural gear ratio in segmented musculature". Journal of Experimental Biology. 208 (17): 3249–3261. doi:10.1242/jeb.01770. PMID 16109887.
  4. ^ Shin, David D.; Hodgson, John A.; Edgerton, V. Reggie; Shina, Shantanu (2009). "In vivo intramuscular fascile-aponeuroses dynamics of the human medial gastrocnemius during plantarflexion and dorsiflexion of the foot". Journal of Applied Physiology. 107 (4): 1276–1284. doi:10.1152/japplphysiol.91598.2008. PMC 2763833. PMID 19608924.