Multiple Degrees of Freedom in the Fish Skull and Their Relation to Hydraulic Transport of Prey in Channel Catfish

Teleost fishes (subsequently referred to as “fishes”) can exert exquisite control over the flow of fluid and the motion of particles suspended in fluid into and within their mouths for behaviors such as filter feeding, mouthbrooding, suction feeding, and prey processing (Sibbing et al. 1986; Sanderson et al. 2001; Van Wassenbergh et al. 2016; Weller et al. 2017). Remarkably, fishes accomplish these complex manipulation tasks without hands or flexible muscular tongues (Dean et al. 2005), relying instead on the over 20 movable skeletal elements in their highly kinetic skulls including the mandibular and hyoid arches, the branchial apparatus that supports the gills, the shoulder girdle, and in some fishes the pharyngeal jaws. While some of these behaviors include direct manipulation of food particles through contact with the jaws and other skeletal elements, all of these behaviors depend to some extent on indirect manipulation achieved by controlling the unidirectional or bidirectional flow of fluid suspending these particles, termed “hydraulic transport” (Bemis and Lauder 1986). Effective object manipulation depends on the ability to control all the degrees of freedom (DoFs) of an object (the total parameters needed to characterize its position and orientation). This implies that the mobility (total DoFs) of a motor system must be equal to or greater than the mobility requirement of the motor tasks that the system performs. This correspondence between task-required mobility and minimum internal mobility is apparent across robotic manipulation systems. For example, robotic arms that grasp, translate, and rotate objects in 3D space, a task requiring seven DoFs, have at least seven DoFs (Koch et al. 2018). And flow-based particle trapping systems that use fluid stream interactions to control the 2D translation of particles, a two-DoF task, have two valves (i.e., DoFs) for flow control (Tanyeri and Schroeder 2013). Based on this principle, fish skulls must have a minimum internal mobility of three DoFs to control 3D translation (changes in position along three axes) or six DoFs to control translation and rotation. This raises not only the question of how many DoFs a fish skull has but also the possibility that fish skulls may be a source of inspiration in improving the design of human-engineered flow-based manipulation systems. The mobility of the fish skull remains unresolved because while several models have been tested, these models have not assumed consistent mobilities. A classic approach has been to represent the skeletal elements, ligaments, and muscles of the skull as a series of connected rigid links or bars, most commonly as one or more planar, one-DoF four-bar linkages (Westneat 1990). In spite of many simplifying assumptions (that all links remain rigid, that all joints are one-DoF hinge joints, and that the entire system has just a single DoF), planar four-bar models have been found to accurately replicate in vivo motion, however only when measured against 2D motion data and for certain skeletal elements (Westneat 1990; Van Wassenbergh et al. 2005). For example, a 3D four-bar with at least three DoFs is needed to accurately represent the 3D in vivo motion of a linkage that depresses the mandible in largemouth bass (Olsen et al. 2017), suggesting that planar four-bar models underestimate the mobility of the fish skull. In contrast to planar four-bar linkage models, hydrodynamic models that simulate the fluid flow patterns created by the skull suggest greater mobility. Expanding cone models (formed by one to three truncated cones) use two to four DoFs to control the rate of expansion along a hollow tube open at one end (Van Wassenbergh et al. 2006). And a computational fluid dynamics simulation that matches the prey velocities observed in vivo represents the head as a five-DoF deformable mesh (Van Wassenbergh 2015). The greater DoFs of these hydrodynamic models allow them to replicate the well-known rostrocaudal (RC) wave observed during suction feeding in fishes, a front-to-back sequential expansion that draws water into and through the mouth (Gibb and Ferry-Graham 2005; Bishop et al. 2008). Although the RC wave could be generated by passive coupling, our recent finding of a significant shift in the correlations among intracranial motions during suction feeding versus swallowing in channel catfish imply independent control, consistent with the fish skull acting as a high-DoF manipulation system (Olsen et al. 2019). In this study, we propose a new 3D linkage model for the mandibular arch, hyoid arch, and shoulder girdle of fishes that combines the fidelity to anatomical structure and connectivity of mechanical linkage models with the capacity for serially independent motions of hydrodynamic models. We used 3D in vivo motion data collected during feeding in channel catfish (Ictalurus punctatus; Fig. 1A; Olsen et al. 2019) to validate this model, to quantify the DoFs in the fish skull, and to test whether these cranial elements act as a prey manipulation system. If these elements function as a manipulation system then the in vivo motion of these elements should move with at least three DoFs for full translational control and at least six DoFs for full translational and rotational control. In addition, if these elements manipulate prey then motions of these elements should be associated with consistent patterns of prey motion. Open in a separate window Fig. 1 Anatomy of the channel catfish (I. punctatus) skull and its corresponding mechanism model. Unlike many other fishes, channel catfish have a relatively wide (dorsoventrally flattened) skull and mouth opening and long barbels that are used to detect food items (A). But similar to other fishes, channel catfish have kinetic skulls, with at least 11 mobile skeletal elements comprising the mandibular and hyoid arches and the shoulder (shown relative to the rostral body outline in (B) and labeled in (C)). Using four joint types (D), these elements can be represented as a five-loop parallel mechanism (shown as a linkage schematic in (E) and as a joint-and-loop graph in (F)). In (C) and (E), large renderings are shown in lateral view and smaller renderings in the upper right corner are shown in superolateral oblique view, with coordinate system arrows indicating anatomical axes and with corresponding colors and abbreviations. The four joint types (C) range from one to three DoFs (corresponding abbreviations in the upper right corner). In (F), lines correspond to links and boxes correspond to joints (angled, parallel lines indicate the fixed link, here, the neurocranium). Colors and link abbreviations in (F) correspond to those in (C) and (E), with subscripts “L” and “R” indicating left and right, respectively; roman numerals enumerate the five loops. Illustration in (A) by Aaron Olsen.