Four-bar linkage modelling in teleost pharyngeal jaws: computer simulations of bite kinetics

Abstract

The pharyngeal arches of the red drum (Sciaenops ocellatus) possess large toothplates and a complex musculoskeletal design for biting and crushing hard prey. The morphology of the pharyngeal apparatus is described from dissections of six specimens, with a focus on the geometric conformation of contractile and rotational elements. Four major muscles operate the rotational 4th epibranchial (EB4) and 3rd pharyngobranchial (PB3) elements to create pharyngeal bite force, including the levator posterior (LP), levator externus 3/4 (LE), obliquus posterior (OP) and 3rd obliquus dorsalis (OD). A biomechanical model of upper pharyngeal jaw biting is developed using lever mechanics and four-bar linkage theory from mechanical engineering. A pharyngeal four-bar linkage is proposed that involves the posterior skull as the fixed link, the LP muscle as input link, the epibranchial bone as coupler link and the toothed pharyngobranchial as output link. We used a computer model to simulate contraction of the four major muscles, with the LP as the dominant muscle, the length of which determined the position of the linkage. When modelling lever mechanics, we found that the effective mechanical advantages of the pharyngeal elements were low, resulting in little resultant bite force. By contrast, the force advantage of the four-bar linkage was relatively high, transmitting approximately 50% of the total muscle force to the bite between the toothplates. Pharyngeal linkage modelling enables quantitative functional morphometry of a key component of the fish feeding system, and the model is now available for ontogenetic and comparative analyses of fishes with pharyngeal linkage mechanisms.

Fig. 1

Parasagittal dissection of the branchial arches of S. ocellatus illustrating the multiple bone elements and extensive branchial musculature controlling pharyngognathy set deep within the gill chamber. Abbreviations: Lp (levator posterior), Le (levator externus 3/4), Od (obliquus dorsalis), Eb (epibranchial), Cb (ceratobranchial).

Fig. 2

Skeletal elements of the pharyngeal jaws of S. ocellatus. Dorsal view of the pharyngeal jaws looking down from the neurocranium (A). Lateral right side view of the 4th branchial arch upper jaw elements with lower toothplate, CB5 (B). Abbreviations: Eb (epibranchial), Cb (ceratobranchial), Pb (pharyngobranchial), Li (inlever), Lo (outlever).

Fig. 3

Upper pharyngeal jaw dissection showing close-up lateral view of digital landmarks of anatomical elements used to generate model simulations (A). Overlay depicting the morphometry of digital landmarks making up the links of the proposed four-bar linkage in the upper jaw mechanism (B). Blue lines/shapes depict bone links. Circles depict joint articulations and rotation points. Purple lines depict muscular links and input. Abbreviations: Lp (levator posterior), Le (levator externus 3/4), Od (obliquus dorsalis), Op (obliquus posterior), Eb (epibranchial), Cb (ceratobranchial), Pb (pharyngobranchial), Li3 (3rd levator internus), Pci (pharyngocleithralis internus), Pce (pharyngocleithralis externus), Nc (neurocranium).

Fig. 4

PharyngoModel 2.0 application screen showing application control features, linkage morphometric data calculated from input coordinates, simulation results and a drawing of the linkage positions under the current simulation parameters. Simulation results can be viewed onscreen for inspection and error checking, or extended results may be written to output files.

Fig. 5

Vector diagrams of the lever and linkage mechanisms in the pharyngeal jaws of Sciaenops ocellatus, showing the force vectors of (A) the levator posterior (LP) muscle (levator externus has a similar mechanism), (B) the obliquus posterior (OP) and (C) the obliquus dorsalis 3 (OD). Initial muscle force (Fm) can be decomposed into vectors (V1, V2) that are perpendicular to an inlever (Li) or provide a moment that swings the four-bar linkage medially. Input forces create torque (Tq) around a lever fulcrum (f) determined by the magnitude of V1, the angle of muscle insertion (α), and the length of the outlever (Lo). Forces from both lever (Flev) and linkage (Flink) are transmitted to the pharyngobranchial to exert bite force (Fbite).

Fig. 6

Kinematics of the pharyngeal bite of Sciaenops ocellatus as a function of LP contraction up to 10% of resting length. (A) Gape distance between pharyngobranchial tooth plate and lower pharyngeal jaw. (B) Distance travelled by the pharyngeal tooth plate toward the prey item. (C) Vector angle of travel of the pharyngeal toothplate relative to the y-axis (straight down) with positive angles indicating mediad translation of the toothplate. Error bars are standard deviations of the mean of six individuals.

Fig. 7

Kinematics of the pharyngeal bite of Sciaenops ocellatus as a function of LP contraction up to 10% of resting length. (A) Rotation of epibranchial 4 (EB4). (B) Rotation of pharyngobranchial 3 (PB3). (C) Kinematic transmission coefficient of the pharyngeal four-bar linkage, calculated as PB3 rotation divided by EB4 rotation. Error bars are standard deviations of the mean of six individuals.

Fig. 8

Relative bite force potential of the pharyngeal apparatus simulated by the model, expressed as total force assuming a constant 1.0-N input force from each muscle (4 N total for the four muscles) during a 10% shortening of the LP. (A) Force potential of the pharyngeal levers. (B) Force potential of the pharyngeal four-bar linkage. (C) Total bite force potential. Error bars are standard deviations of the mean of six individuals.

Fig. 9

Simulated torque and force profiles for each of the four major muscles of the pharyngeal apparatus, assuming a constant 1.0-N input force from each muscle during a 10% shortening of the LP. (A) Torque exerted by each muscle for its primary lever fulcrum (Fig. 5). (B) Lever output force for each muscle. (C) Force output of the pharyngeal four-bar linkage. Error bars are standard deviations of the mean of six individuals.