Suction power output and the inertial cost of rotating the neurocranium to generate suction in fish
Introduction
Many aquatic vertebrates rely on generating a flow of water from the external environment into the mouth to capture prey (e.g., Lauder and Schaffen, 1993). Conservation of mass and the incompressibility of water dictate that any expansion of the buccopharyngeal cavity will generate a flow of water. During this process, which is typically referred to as suction feeding, prey items situated in the flow field in front of the mouth will experience hydrodynamic forces (Holzman et al., 2012a, Holzman et al., 2007, Skorczewski et al., 2010, Wainwright and Day, 2007). These forces are associated with highly unsteady water flows: adult suction feeders generally manage to accelerate water and prey from standstill to over 1 m s−1 in less than 0.05 s (Higham et al., 2006a, van Leeuwen, 1984, Van Wassenbergh et al., 2007a). In order to maximize suction feeding success on prey adhering to the substrate or trying to escape, the sudden increase in flow velocity in front of the mouth must be maximized. In other words, suction feeders must transfer as much kinetic energy to the water in the shortest possible amount of time. Consequently, to maximise prey capture performance, suction feeders must maximise instantaneous power.
To generate this power, fish mainly rely on contraction of the voluminous post-cranial musculature (Aerts, 1991, Camp and Brainerd, 2014, Carroll and Wainwright, 2006, Coughlin and Carroll, 2006, Muller, 1987, Thys, 1997, Van Wassenbergh et al., 2007b). This musculature consists of hypaxial (ventral to the vertebral column) and epaxial (dorsal to the vertebral column) components (Fig. 1A). Contraction of the hypaxial musles rotates the pectoral girdle posteriorly, while contraction of the epaxial muscles induce a dorsal rotation of the neurocranium (Fig. 1B). Despite rotating different skeletal elements, the role of hypaxial and epaxial muscle contractions in suction generation is identical: they both increase the angle between the pectoral girdle and the neurocranium, which in turn causes a displacement of the “roof” and the “floor” of the mouth cavity away from each other. This separation increases the buccopharyngeal volume. The increased angle between pectoral girdle and neurocranium results in an additional complex sequence of coupled motions of the hyoid arch and lower jaw which push on the ventral side of the mouth cavity tissues, and which via the hyoid also enforce widening of the head by suspensorium abduction (Aerts, 1991, De Visser and Barel, 1996, Muller, 1989). Although relatively small cranial muscles such as the sternohyoideus, protractor hyoideus, levator arcus palatini, and levator operculi probably assist in powering suction (e.g., Osse, 1968), their cumulative mass, and thus potential contribution to power generation, is small compared to the hypaxials and/or epaxials (Carroll and Wainwright, 2009).
Not all power produced by the feeding musculature will result in water acceleration: an unknown amount of the muscle’s power output will be lost due to the musculoskeletal mechanics underlying suction generation. Examples are joint friction, stretching of skin, resistive stress in the adductor muscles (e.g. adductor mandibulae during mouth opening), hydrodynamic resistance at the external head surfaces, and the inertia of the elements involved in expanding the buccopharygeal cavity. A study on suction feeding of the catfish Clarias gariepinus estimated that inertial force (integral over the entire buccopharyngeal cavity of acceleration multiplied by mass of the displaced tissues) is about 10% of the pressure force on the buccopharyngeal cavity surfaces (Van Wassenbergh et al., 2005). However, as C. gariepinus relies almost entirely on ventral depressions of the floor of the mouth cavity to generate suction, C. gariepinus is atypical compared to many other suction feeders (Gibb and Ferry-Graham, 2005) in showing (on average) no rotation of the neurocranium.
Dorsorotation of a large neurocranial mass for generating buccopharyngeal expansion may require an important fraction of the power budget of suction feeding. Of the potential sources of power loss identified above, it is the most conspicuous candidate as it is both massive and experiences large accelerations. In adult fishes, the functional unit referred to here as “neurocranium” typically includes a strongly ossified protective braincase and the brain, the eyes surrounded by the circumorbital bones, and anterior bony elements such as the rostrum, ethmoid, and vomer. During suction feeding, the neurocranium is rotated along with the suspensoria, upper oral and pharyngeal jaws attached to it. Measurements of Micropterus salmoides (largemouth bass), for example, show that the mass of this functional unit equals approximately 60% of the total cranium (including sternohyoideus and cleithrum).
Given the importance of feeding success for survival, a considerable inertial cost to rotate the neurocranium would imply a significant selective pressure on the shape and size of the neurocranium (or more specifically on the pitching moment of inertia about the instantaneous center of neurocranial rotation). Alternatively, recruitment of only the relatively light-weight, ventro-lateral series of skeletal elements by the hypaxial muscles for generating suction power would probably be favoured in case evolution has resulted in a neurocranium that is too heavy to retain a reasonable power efficiency (e.g. inertial losses divided by hydrodynamic power output). Unfortunately, the relative importance of the inertial cost of neurocranial elevation is currently unknown. Yet, this mechanical insight seems essential to better understand the functional morphology and kinematics of suction feeding fish.
To determine to what extent inertial costs of rotating the neurocranium affect suction performance, we address the following aims: (1) formulate an inverse dynamic model for estimating the instantaneous power requirement for rotating the neurocranium as observed on lateral-view high-speed videos, (2) establish a theoretical framework and mathematical models for calculating the total hydrodynamic power of suction feeding from different sources of experimental data and model simulations, (3) evaluate the results of these models for suction feeding in a species with a generalized percomorph trophic habit (M. salmoides).
Section snippets
Inverse dynamic model of neurocranial rotation
To calculate the inertial power required to rotate the neurocranium, the following mathematical model is used. The shape of the neurocranium is modeled as a quarter of an ellipsoid. This shape is chosen since elliptical cross-sections have proven to fit the external contours of fish relatively accurately (Drost and van den Boogaart, 1986), and ellipsoids can capture the anterior narrowing of a streamlined head. By setting l (length), h (height) and w (width) as the dimensions of the
Model geometry
The measurements of three M. salmoides individuals (head length (l)=48±10 mm; mean±s.d.) show a mean head width of 0.53±0.07l. The calculated height to achieve a balance between the measured neurocranium mass and that of the quarter ellipsoid model is 0.34±0.07l (Fig. 4). Using cubic spline interpolation with the data in Table 1, Table 2 reveals a drag moment coefficient of −0.0018 and an added mass coefficient of 0.0081, respectively. The selected alignment of the quarter ellipsoid with respect
Discussion and conclusion
We found that the inertial costs of rotating the neurocranium have a negligible impact on suction performance in largemouth bass, a generalized percomorph suction feeder. We estimated the loss not to exceed 4.0% of the generated suction power throughout the feeding sequence. In the worst case scenario for the bass, when focussing on the time at which this cost was maximal and performing the simulations with the lowest possible pressure magnitudes, the loss in power was 11% of the generated
Acknowledgements
This work was conducted as a part of the Suction Feeding Biomechanics Working Group at the National Institute for Mathematical and Biological Synthesis, sponsored by the National Science Foundation through NSF Award #DBI-1300426, with additional support from The University of Tennessee, Knoxville. CFD software and hardware was funded by grants from the Fund for Scientific Research Flanders (FWO Grant 1.5.160.08.N.00) and the University of Antwerp (BOF/KP 24346). Further support was provided by
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