BRAINERD, E.L.*; AZIZI, E.; Univ. of Massachusetts, Amherst: Muscle fiber angle and strain amplification in segmented musculature

Segmented axial musculature is a defining characteristic of vertebrates and their close relatives. We have developed a mathematical model of segmented muscle in which the relationships between muscle fiber angle, muscle fiber strain, segment strain and segment force are determined. Unlike a previous model of segmented musculature and most models of pinnate muscles, our model allows the relative changes in segment height and depth to vary within the isovolumetric constraint. Results from the model indicate that changes in height (H) of the segment have a strong influence on the relationship between initial muscle fiber angle (&alpha), muscle fiber strain, and segment strain. If H decreases with segment shortening, then muscle fiber strain and segment strain are equal for all initial muscle fiber angles. If H remains constant, segment strain is greater than muscle fiber strain (when &alpha is greater than zero). If H increases, then the �strain amplification� effect of angled muscle fibers is even greater. In both the H constant and H increases cases, strain amplification increases with increasing muscle fiber angle. Increased fiber angle is also associated with decreased segment force, but force does not decrease in direct proportion to strain amplification as would be the case in mechanical gear or lever systems. The trade-off is more favorable, with the increase in segment shortening velocity exceeding the decrease in force. Changes in the height and depth of segments may be constrained by myosepta and other axial connective tissues; therefore our model provides an explicit, quantitative framework for studying the effects of connective tissue geometry and material properties on strain amplification and segment force production. Supported by NSF 9875245.