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First published online August 18, 2005
Journal of Experimental Biology 208, 3249-3261 (2005)
Published by The Company of Biologists 2005
doi: 10.1242/jeb.01770

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Muscle fiber angle, segment bulging and architectural gear ratio in segmented musculature

Elizabeth L. Brainerd^*, and Emanuel Azizi^*

Department of Biology and Program in Organismic and Evolutionary Biology, University of Massachusetts, Amherst, MA 01003, USA

View larger version (40K): [in a new window]   Fig. 1. The lateral hypaxial musculature (LHM) of an aquatic salamander, Siren lacertina, and an isovolumetric planar model of this segmented musculature. The skin and superficial layers of LHM have been progressively removed from cranial to caudal along the myoseptal boundaries. The positions of the sonomicrometry crystals used to test the segmented muscle model are shown, and the initial muscle fiber angle, , of the external oblique (EO) is indicated. (A) Lateral view of the EO, internal oblique (IO) and transverse abdominis (TA) layers of the LHM as well as the rectus abdominis (RA) and epaxial (EP) musculature (modified from Simons and Brainerd, 1999). (B) Isovolumetric planar model of a muscle segment in the relaxed and contracted states. Note that the muscle fiber angle increases from to ß and the segment bulges out in the y and z dimensions to maintain constant volume. Variables: and ß, muscle fiber angle before and after shortening; x1 and x2, length of segment before and after muscle fiber shortening; z1 and z2, depth of segment before and after shortening; y1 and y2, height of triangle defined by x1 and and x2 and ß; f, initial muscle fiber length; f, extension ratio of the muscle fiber; x, y and z, extension ratios of the three dimensions, x, y and z of the segment. Modified from Azizi et al. (2002).

View larger version (15K): [in a new window]   Fig. 2. Model simulations of the relationship between architectural gear ratio (AGR=x/f) and initial muscle fiber angle () for a fiber shortening of 10% (f=–0.1). The AGR is shown for the four bulging conditions defined in the text. These conditions are part of a continuum of bulging conditions. The AGR increases most rapidly when all of the bulging is in the y (dorsoventral) direction (z=1) and progressively less rapidly with less dorsoventral bulging.

View larger version (22K): [in a new window]   Fig. 3. Effect of the four segment bulging conditions on axial bending. Longitudinal strain and body curvature are drawn to scale. (A) Initial fiber angle of 25°. (B) If all of the bulging occurs in the dorsoventral direction such that z=1, then 10% muscle fiber shortening leads to 19.2% shortening of the right side of the body and the greatest axial bending. (C) If dorsoventral and mediolateral bulging are equal, y=z, then 10% muscle fiber shortening leads to 14.7% segment shortening. (D) If all the bulging occurs in the mediolateral direction, y=1, then 10% muscle fiber shortening leads to 12.4% segment shortening. (E) If the dorsoventral height of the segment decreases by the same proportion as the segment shortens, x=y, then 10% muscle fiber shortening leads to 10% segment shortening. Modified from Azizi et al. (2002).

View larger version (24K): [in a new window]   Fig. 4. Sonomicrometry traces from the external oblique (EO) muscle layer of Siren lacertina (=40.5° in this individual). (A) Proportional changes in the muscle fiber length (f; red), segment length (x; black) and segment height (f; blue) are shown over seven swimming tailbeats. Note that the amplitude of changes in longitudinal strain are larger than the changes in muscle fiber strain, indicating that the AGR is greater than one. (B) Comparison of measured y (solid blue line) with predicted y from two of the bulging condition models (broken lines). The empirical trace falls between these two bulging conditions, indicating that the EO shows some dorsoventral bulging but not as much dorsoventral bulging as mediolateral bulging.

View larger version (14K): [in a new window]   Fig. 5. Measured longitudinal segment strain versus predicted strain from the model. Inputs to the model are the empirically determined values of for each individual, and f and y from sonomicrometry for each swimming sequence. Least-squares regression yields the relationship y=0.95x+0.80, r2=0.66, P<0.0001. The three symbols represent three individuals, with the following number of swimming sequences per individual: solid circle, N=14; solid square, N=16; open circle, N=13.

View larger version (20K): [in a new window]   Fig. 6. Electromyograms of the external oblique (EO) and internal oblique (IO) during steady swimming in S. lacertina. Segment strain at the depth of the EO was recorded simultaneously on the same side of the body and in the same longitudinal position as the electromyograms.

View larger version (16K): [in a new window]   Fig. 7. Model calculations of absolute shortening distance and relative force of segmented muscle. (A) Absolute segment shortening (cm) versus when initial muscle fiber length is held constant (1 cm). Results are shown for 10% fiber strain (0.1 cm muscle fiber shortening). (B) Relationship between and the relative force produced in the longitudinal direction during 10% muscle fiber shortening (force normalized to the =0 condition). In Appendix 3, we use shortening distance and force to calculate segment work, and we find that work is independent of muscle fiber angle and bulging condition.