Fig. 1. The radula-centric kinematic model. (A—D) The physical construction of the model. The model consists of two radular halves, a cylindrical radular stalk with a rounded ventral dome and two cylindrical I7 muscles. The model is constructed in a standard orientation such that the radular stalk is vertical. (A) Medio-lateral view with radular halves fully closed. Mid-sagittally, the radular halves are defined by an anterior ellipse quadrant a and a posterior parabolic segment b. The posterior tip of the radular halves is constrained to be level with the posterior edge of the radular stalk. The radular halves can rotate about this posterior tip point (pitch, _p). By convention, 0° is horizontal, anterior rotations are positive and posterior rotations are negative. The I7 muscles run between a point on the antero-ventral radular stalk and a defined point below the radular halves (corresponding to an anterior radular `skirt' whose surface is not explicitly represented, dotted line, ellipse segment c). I7 changes dimensions isovolumetrically as its anterior endpoint changes position. (B) Dorso-ventral view showing radular yaw (<sub>y</sub>). In this plane, the radular halves are defined by an anterior ellipse quadrant d and a posterior parabolic segment e. As in A, the posterior tip of the radula is constrained to be level with the posterior edge of the radular stalk. By convention, both radular halves are closed at 0°, and opening is a positive yaw. (C) Antero-posterior view showing radular roll (<sub>r</sub>). In this plane, the radular halves are defined by an ellipse quadrant f. Note that, as constructed, the dorsal endpoint of the I7 muscle (arrowhead) is fixed relative to the radular half and thus moves medially as the radular half rolls laterally. By convention, both radular halves are closed at 0°, and opening is a positive roll. (D) Method of odontophore volumetric database construction. All model components are represented as isosurfaces composed of triangles. A completed odontophore model is sliced in fixed steps along the antero-posterior axis, and ellipse quadrants are used to fill in `missing' unmodeled space (presumed to contain the I4 muscle and other structures) in the ventral half of each slice. The resulting volumetric database, as well as a smoothed outline from the mid-sagittal view, is used as input for the buccal mass model. (E—G) In-vivo-derived model parameter inputs. All timebases have been normalized to the mean t1, t2, t3 and t4 intervals (defined in Materials and methods) of the constituent data sets (data not shown), allowing data from multiple swallows to be combined. Each data point in E and F represents the mean of a normalized time interval (0.2s). Values are mean ± S.E.M.; N=4 for each time interval in E; N=2-9 (mean=4.7) for each time interval in F. E and F are from mid-sagittal magnetic resonance images of an adult; smoothed curves from these data were used as radula-centric model inputs. G represents a synthesis of all available video and image data, including biting and swallowing in large adults. (E) Radular stalk angle from four swallows. This is the angle formed by the long axis of the radular stalk and a line perpendicular to the buccal mass axis (the line from the jaws to the esophagus after external rotation of the entire buccal mass has been removed, buccal mass angle 0°). By convention, vertical is 0°, anterior rotations are positive and posterior rotations are negative. (F) Radular pitch angle from nine swallows. (G) Radular roll and yaw angles used as direct inputs to the model.

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