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Fig. 1. (A) Drawing of myomere architecture in king salmon (after Greene and Greene, 1913). (B) Schematic drawing of curved muscle trajectories in the anterior trunk muscles of a teleost [redrawn from Alexander (Alexander, 1969)]. (C) Helical muscle fibre-trajectories (red) run over cylindrical surfaces (green). The medial plane is straight in this reference configuration (shown in blue). The central muscle-fibre trajectory (1) runs over a cylinder with a radius of zero and therefore forms a straight line in the centre of the other two cylinders. Muscle trajectory 3 has a pitch angle of 32°8' as proposed in Alexander's model (Alexander, 1969). The geodesic trajectory follows the shortest path between the end points at the medial plane. The cylinder is not fully drawn because it is cut off by the medial plane. In the reference configuration, the strain in the trajectories is assumed to be zero. Trajectory 2 makes a full turn over a cylinder with a smaller radius that almost touches the medial plane [not considered by Alexander (Alexander, 1969)]. Halfway along its length, the trajectory is parallel to the medial plane. This would lead to very small strains at this location. (D) Similar to C, but with a curved medial plane. The largest cylinder of C is shown deformed into a torus with an identical volume (Alexander's case iii). The radius of curvature of the medial plane is 10 times the maximum distance between the most lateral location on the cylinder and the medial plane in the reference position (C). The computed average strain in the peripheral trajectory is –0.039 as computed from (s–s₀)/s₀, against –0.02 in the central trajectory, where s₀ is the trajectory length in the reference configuration and s is the length in the contracted situation.

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