Beam theory predicts muscle deformation and vertebral curvature during feeding in rainbow trout (Oncorhynchus mykiss)

Muscle shortening underpins most skeletal motion and ultimately animal performance. Most animal muscle generates its greatest mechanical output over a small, homogeneous range of shortening magnitudes and speeds. However, homogeneous muscle shortening is difficult to achieve for swimming fish because the whole body deforms like a bending beam: as the vertebral column flexes laterally, longitudinal muscle strain increases along a medio-lateral gradient. Similar dorsoventral strain gradients have been identified as the vertebral column flexes dorsally during feeding in at least one body location in one fish. If fish bodies also deform like beams during dorsoventral feeding motions, this would suggest the dorsal body (epaxial) muscles must homogenize both dorsoventral and mediolateral strain gradients. We tested this hypothesis by measuring curvature of the anterior vertebral column with XROMM and muscle shortening in 14 epaxial subregions with fluoromicrometry during feeding in rainbow trout (Oncorhynchus mykiss). We compared measured strain with the predicted strain based on beam theory's curvature–strain relationship. Trout flexed the vertebrae dorsally and laterally during feeding strikes, yet when flexion in both planes was included, the strain predicted by beam theory was strongly and significantly correlated with measured strain (P<0.01, R(2)=0.60). Beam theory accurately predicted strain (slope=1.15, compared with ideal slope=1) across most muscle subregions, confirming that epaxial muscles experience dorsoventral and mediolateral gradients in longitudinal strain. Establishing this deformation–curvature relationship is a crucial step to understanding how these muscles overcome orthogonal strain gradients to produce powerful feeding and swimming behaviours.