INTERVERTEBRAL JOINT POLARITY IN SAUROPODS
and Wilson (2013). Therefore, the presence of cervical opisthocoely and caudal procoely in sauropods cannot be satisfactorily described as increasing the displacement per unit rotation of the neck and tail. The second advantage hypothesized by
Troxell (1925), and also independently suggested by Nopcsa (1930), concerns the distribution of compressive force on a concavo-convex joint. Troxell (1925) declared that the thrust generated by the crocodylian tail during swimming must act parallel to the distal, free element in any given intervertebral joint, in the process always passing through the COR of the joint (Fig. 4). In the author’swords (Troxell 1925: p. 607), “It must be clearly understood that the thrust through each vertebra is transmitted (lateralmuscular pull not considered) in the direction and along the line of the longer axis to the next vertebra in front.” In this scenario, the force acts at an angle to the proximal, fixed vertebra. When the centra are proximally concave, the force acts upon the condyle of the more proximal centrum, which offers a greater thickness of bone to resist the force (Fig. 4, s). When the centra are proximally convex, the force acts upon the thinner bone of the cotylar rim(Fig. 4, n), presenting a greater risk of breakage. Nopcsa (1930: p. 23) presented a similar argument, stating, “In the one case unilateral pressure is taken on the center of the spherical articular surface, but in the other case it is taken on the thin edge of the socket. Now, since in the first case, the same possibility ofmovement is connected with a much greater mechanical strength than in the second, the first construction is obviously better; at the same time, this is the
one in which the joint socket looks toward the fixed part” (translated from the German by J.A.F.). Both authors presented the hypothesis only on the basis of geometric considerations, without experimental modeling. Gosnold and Slaughter (1977) reportedan experiment inwhich alligator vertebrae were loaded in accordance with Troxell’s predictions using a hydraulic press andstressedtothe pointoffailure.Whenthe force was directed from the cotyle into the condyle, the force required to fracture the fixed centrum was three times greater than when it was directed into the cotylar rim; details of the experiment and quantitative results were not provided. Both Nopcsa (1930) and Gosnold and
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FIGURE 4. Resistance of centrum articular surfaces to stress when forces are directed parallel to the free element of a concavo-convex joint, as predicted by Troxell (1925). If compressional forces act parallel to the free element, proximally concave centra result in a greater resistance to stress. A proximally concave centrum (A) directs forces into the thicker condyle (s). A proximally convex centrum (B) directs forces into the thinner cotylar rim (n), increasing the risk of fracture. Arrows indicate the presumed direction of compression. White circles represent the center of rotation. The labeled black lines indicate the thickness of bone in the fixed element resisting the applied compressive force. Modified from Troxell (1925). n, nonsauropod-type joint polarity; s, sauropod-type joint polarity.
Slaughter (1977) recognized the applicability of this hypothesis to a variety of vertebrates, including sauropods, and Powell (2003) applied it specifically to procoelous caudal vertebrae in titanosaur sauropods. To date, the distribution of forces across a concavo-convex intervertebral joint has not been documented, so Troxell’s assertion that the proximally directed force acts parallel to the more mobile vertebra in a joint requires further assessment. Functional Hypotheses Evaluated in This Study.—
Two hypotheses for the functional advantage of proximally concave over proximally convex vertebrae are considered here: (1) proximally concave centra exert stresses against a greater thickness of bone, the condyle, instead of the thin cotylar rim, reducing the risk of fracture; and (2) proximally concave centra prevent the destabilizing rotation of the proximal end of the mobile centrum down and out of joint. The validity of each hypothesis is examined using
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