INTERVERTEBRAL JOINT POLARITY IN SAUROPODS


applied at the proximal end of the free element will tend to rotate the entire vertebra ventrally, a movement that is opposed by the tensile element. As demonstrated in the experiments, it is possible for a sufficiently large force acting close to the joint to pull the cotyle away from the condyle, causing joint failure. However, the forces required to do this are typically much greater than those causing joint failure in an equivalent proximally convex joint. In a proximally convex joint (Fig. 8B), the free element rotates about a point within itself. Consistent with the observations of Fick (1890), any dorsiflexion of the distal end of the free element will have the consequence of rotating the condyle ventrally and distally; that is, out and away from the cotyle. Conversely, if a force acts to rotate the condyle out of joint, the distal end of the centrum will rotate dorsally, and the tension in the supporting tensile element will be reduced. It is possible to compensate for joint


instability with particular morphologies and orientations of the vertebrae and tensile elements. Three of the parameters examined in our experiments bore the same relationship to stability for both joint polarities. Proximal tensile element insertion sites, distal loading of the free vertebra, and deeper cotyles conferred greater stability. A configuration of these parameter states that provides stability to proximally convex joints would increase stability as much or more for proximally concave joints (Fig. 7). The first two variables also involve trade-offs between joint stability and mechanical advan- tage, as proximal insertion sites decrease the leverage with which the tensile element supports the increasing distal load. Deeper cotyles could decrease joint mobility due to impingement, although a previous study of Alligator did not find a relationship between intervertebral joint morphology and range of motion (J. A. Fronimos and J. A. Wilson unpublished). The angle of rotation of the free element


and the angle of insertion of the tensile element affect the two joint polarities differently, although the insertion angle has an inconsistent influence. The two polarities are generally comparable in stability when the vertebrae are oriented horizontally, but the


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sauropod-type joints become more stable at higher angles of rotation, whereas the opposite type become less stable. The sauropod-type joints therefore permit a greater mobility to be maintained without sacrificing stability. Some uncertainty surrounds the insertion angle of the supraspinal or nuchal ligament in sauropod cervical vertebrae (e.g., Tsuihiji 2004; Schwarz et al. 2007); high insertion angles are associated with an avian- or ungulate-type nuchal ligament that spans multiple segments (Tsuihiji 2004; see also Dimery et al. 1985). Insertion angles would be steepest in posterior cervical vertebrae, especially in taxa with anterior dorsal neural spines that are much taller than the cervical spines (e.g., Giraffatitan [Janensch 1950]). Osteological evidence led Tsuihiji (2004) to conclude that the sauropod nuchal ligament did not extend to the anterior cervical vertebrae; even if it did, the length of the neck would cause the insertion angles to be much lower than at the base of the neck. Proximally concave joints, which are generally more stable with lower insertion angles, would be most advantageous in longer necks. The zygapophyses, cervical ribs, articular


capsules, and epaxial musculature, which were notmodeled in this study, also have the potential to stabilize joints that are otherwise susceptible to joint failure. These structures provide stabilizing influences regardless of the polarity of a joint, but in proximally convex joints the absence of support provided by the centrum articulations results in greater stress on other intervertebral structures. Zygapophyses limit vertebral rotation, which, depending on zygapophyseal orientation, can prevent the condyle from rotating out of articulation. Zygapophyses have a smaller surface area than do articulations between vertebral centra, so the same applied force results in greater stress. Soft tissues between vertebrae, including the articular capsule between centra and the intercostal liga- ments joining cervical ribs, provide tensile forces resisting dislocation of centra. In each case, the sauropod-type polarity results in lower stress because the forces associated with joint stabilization are distributed across the greater surface area of the centrum articulation. A final mechanism for stabilizing proximally convex joints is active contraction of the epaxialmuscles,


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