title: Automatic control: the vertebral column of dogfish sharks behaves as a continuously variable transmission with smoothly shifting functions.
abstract: During swimming in dogfish sharks, Squalus acanthias, both the intervertebral joints and the vertebral centra undergo significant strain. To investigate this system, unique among vertebrates, we cyclically bent isolated segments of 10 vertebrae and nine joints. For the first time in the biomechanics of fish vertebral columns, we simultaneously characterized non-linear elasticity and viscosity throughout the bending oscillation, extending recently proposed techniques for large-amplitude oscillatory shear (LAOS) characterization to large-amplitude oscillatory bending (LAOB). The vertebral column segments behave as non-linear viscoelastic springs. Elastic properties dominate for all frequencies and curvatures tested, increasing as either variable increases. Non-linearities within a bending cycle are most in evidence at the highest frequency, 2.0 Hz, and curvature, 5 m-1Viscous bending properties are greatest at low frequencies and high curvatures, with non-linear effects occurring at all frequencies and curvatures. The range of mechanical behaviors includes that of springs and brakes, with smooth transitions between them that allow for continuously variable power transmission by the vertebral column to assist in the mechanics of undulatory propulsion.
authors.affiliation: Florida Atlantic University, Biological Sciences, 777 Glades Road, Boca Raton, FL 33431, USA me.porter@fau.edu.
authors.forename: Marianne E
authors.identifier: http://orcid.org/0000-0002-3622-7114
authors.initials: ME
authors.lastname: Porter
authors.affiliation: University of Illinois at Urbana-Champaign, Department of Mechanical Science and Engineering, 1206 W. Green Street, Urbana, IL 61801, USA.
authors.forename: Randy H
authors.initials: RH
authors.lastname: Ewoldt
authors.affiliation: Vassar College, Department of Biology, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA Vassar College, Department of Cognitive Science, 124 Raymond Avenue, Poughkeepsie, NY 12604, USA.
authors.forename: John H
authors.initials: JH
authors.lastname: Long
keywords: Elastic modulus; Intervertebral joint capsule; Mineralized cartilage; Stiffness; Viscoelastic; Viscous modulus