INTERVERTEBRAL JOINT POLARITY IN SAUROPODS


silicone molding rubber. These molds were used to cast the models in EPO-TEK 301 epoxy, a two-component epoxy that cures at low temperature and exhibits photoelastic properties. To conserve material and enhance optical clarity, casts were poured to a thickness of 1 cm rather than the 3 cm width of the ABS plastic models. Batches of epoxy were limited to 25 g at a time; mixing greater amounts resulted in cloudiness and anomalous birefringence under cross-polarized light, likely due to excess heat generation during the reaction between the two component phases. After pouring, the epoxy models were allowed to cure for a minimum of 24 hours at room temperature. Measurements of the models taken with digital calipers showed a variation in width from 0.82cm to 1.07 cm, including a meniscus of not more than 0.10cm. To test each of the two hypotheses, the


models were first suspended in articulation loaded as cantilevers with a fixed proximal element and a free distal element that could be


rotated relative to it. This was accomplished by fixing one model to a wooden testing rig at its flat end by two 0.62cm (¼ inch) diameter


wooden dowels; these were received by corresponding holes, 0.66cm apart, drilled into the wooden frame and the flat end of the model. This modular setup allowed the proximal element to be switched out between the convex and concave elements to create either a proximally concave or proximally convex joint. To further stabilize the fixed element against rotation, a steel drawer handle with a clearance of 3.2cm was attached below it and lined with foam to prevent damage to the epoxy of the model. The free element was suspended from the rig by a tensile element (either a wire or a string; see below) originating proximally on a metal hook. The hook could be moved up and down to vary the angle of rotation of the free element and the insertion angle of the tensile element. To allow this, the hook was screwed into a separate wooden board bolted to the back of the wooden frame via a vertical slot. The board could be moved vertically when the bolts were loosened and, with the bolts tightened, stayed firmly in one position regardless of the load applied. This testing rig is shown in Supplementary Figure 2,


631


where it is configured for the rotational stability experiments. The hypothesis that proximally concave


centra distribute forces more evenly across the articular surface than do proximally convex centra was tested using photoelastic analysis. The principles and applications of photoelastic analysis are detailed by Post (1979) and are summarized only briefly here. Photoelastic materials are optically isotropic in anunstrained state, and therefore appear dark when viewed under cross-polarized light. The introduction of strain produces anisotropy in the index of refraction of the material, meaning that light travels through thematerial at a different speed depending on the direction in which the light vibrates. When viewed under cross-polarized light, rays passing through the material are out of phase and therefore interfere, resulting in birefringence. The greater the strain in the material is, the greater the difference in velocity between the rayswill be, and the light observed will have a progressively higher-order inter- ference color.Using this technique, the distribu- tion of strain in a material can be observed and the relative magnitude of stress assessed. The EPO-TEK 301 epoxy used to create the models described above is a photoelastic material with a typical index of refraction of 1.519 at 23°C (Epoxy Technology, Inc. 2012). The models, which were unstrained as a result of the molding and casting process, exhibited a slight biaxial anisotropy with first-order gray inter- ference colors. Strain-visualization experiments were


conducted using the wooden testing frame described above. The epoxy models were modified with the addition of a metal hook on the top and bottom surface, providing a strong attachment for the tensile element and heavy weights. In each model, a 1.1cm deep hole was drilled into the top and bottom surface, into which was placed a 1.6cm metal cup hook. The hole was placed 2cm from the flat end to prevent the strain associated with drilling the hole and applying forces to the hook from overprinting experimentally induced strain at the articular surface. The hooks were set into the holes with epoxy, rather than screwed in, creating a strong bond to the epoxy model without introducing additional strain. For each


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