INTERVERTEBRAL JOINT POLARITY IN SAUROPODS


could be rotated to 35° with only a barely visible opening of the joint space. For config- urations using the less-stable shallow cotyle, an additional set of trials was conducted to determine whether the stabilizing effect of a distal load (e.g., an additional vertebra in series) would negate any stability difference between polarities. To do this, an additional 20g (the approximate mass of an epoxy model) was suspended from the distal end of the free element at the position of the farthest insertion site from the joint. For conducting each trial, the elements were


first placed in articulation, and it was observed whether the free element stayed in joint or whether it disarticulated under its own weight. If the configuration was stable, more weight was suspended from a loop of string affixed on the free element, for consistency of position, at the insertion site nearest the joint (Supplemen- tary Fig. 2). Gram calibration weights were added in 5 g increments until disarticulation occurred or until 250 g had been applied, and the weight at which disarticulation occurred was recorded. When a 20 g weight was suspended from the distal end of the free element, the maximum weight applied to the proximal end was 230 g. When all measure- ments had been taken, comparisons were made between the results for each polarity, and the influence of each additional variable was compared between polarities. To deter- mine whether a stability difference was significant (i.e., not attributable to model uncertainty), several trials were repeated at a later date; the weights recorded differed from the previous outcomes by up to 15 g. It was also noted that the convex model, bearing the additional weight of a condyle, weighed 11.8 g more than the lightest concave model. There- fore, a difference in stability between model configurations was considered significant only if the weight required for joint failure differed by more than 30 g.


Results Stress Resistance.—As revealed by the


photoelastic analysis, strain on the concavo- convex joints was consistently concentrated


633


in the cotylar rim, regardless of joint polarity (Fig. 6). The distribution and magnitude of strain was dependent on the insertion angle of the tensile element. With a horizontal tensile element, strain was concentrated in the ventral cotylar rim for joints between proximally convex centra (hereafter “proximally convex joints”;Fig.6A),aspredicted.For joints between proximally concave centra (hereafter “proximally concave joints”), strain was not evenly distributed across the articular surface; instead, it was concentrated in the dorsal cotylar rim (Fig. 6B). Within the sensitivity of the analysis, the magnitude of strain was consistent between the two polarities (Fig. 6, lower panels),with one exception. With the free element at a 25° angle of rotation, the strain magnitude was much greater in the proximally convex joint (lowthird-order interference colors) than the proximally concave joint (middle first- order colors). With a steeply angled tensile element (55° to the horizontal), no difference in strain magnitudewas detected between the two polarities. Joints with a shallow cotyle exhibited a strain distribution as described above, but the magnitude of strain was much lower, barely exceeding the first-order gray colors of unstrained epoxy. The strain distribution differed with a deeper cotyle, as the proximally concave joint exhibited strain in both the dorsal and the ventral cotylar rim, and the strain magnitude was nearer to that of joints with a horizontal insertion. Rotational Stability.—For any given


combination of parameter states, proximally concave centra always required more weight for joint failure to occur than did proximally convex centra, except when both polarities were stable at the greatest weight applied (Fig. 7, Supplementary Table 1). The stability difference between the two polarities was significant (i.e., it exceeded the model uncertainty) for greater than 80% of the parameter state combinations (Fig. 7). Proximally concave joints were always stable without applied weight, and an applied weight significantly greater than zero was required for joint failure in all but three of the 72 variable combinations (Supplementary Table 1). Proximally convex joints were stable in an unloaded state for most variable combinations,


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71  |  Page 72  |  Page 73  |  Page 74  |  Page 75  |  Page 76  |  Page 77  |  Page 78  |  Page 79  |  Page 80  |  Page 81  |  Page 82  |  Page 83  |  Page 84  |  Page 85  |  Page 86  |  Page 87  |  Page 88  |  Page 89  |  Page 90  |  Page 91  |  Page 92  |  Page 93  |  Page 94  |  Page 95  |  Page 96  |  Page 97  |  Page 98  |  Page 99  |  Page 100  |  Page 101  |  Page 102  |  Page 103  |  Page 104  |  Page 105  |  Page 106  |  Page 107  |  Page 108  |  Page 109  |  Page 110  |  Page 111  |  Page 112  |  Page 113  |  Page 114  |  Page 115  |  Page 116  |  Page 117  |  Page 118  |  Page 119  |  Page 120  |  Page 121  |  Page 122  |  Page 123  |  Page 124  |  Page 125  |  Page 126  |  Page 127  |  Page 128  |  Page 129  |  Page 130  |  Page 131  |  Page 132  |  Page 133  |  Page 134  |  Page 135  |  Page 136  |  Page 137  |  Page 138  |  Page 139  |  Page 140  |  Page 141  |  Page 142  |  Page 143  |  Page 144  |  Page 145  |  Page 146  |  Page 147  |  Page 148  |  Page 149  |  Page 150  |  Page 151  |  Page 152  |  Page 153  |  Page 154  |  Page 155  |  Page 156  |  Page 157  |  Page 158  |  Page 159  |  Page 160  |  Page 161  |  Page 162  |  Page 163  |  Page 164  |  Page 165  |  Page 166  |  Page 167  |  Page 168  |  Page 169  |  Page 170  |  Page 171  |  Page 172  |  Page 173  |  Page 174  |  Page 175  |  Page 176  |  Page 177  |  Page 178  |  Page 179  |  Page 180  |  Page 181  |  Page 182  |  Page 183  |  Page 184  |  Page 185  |  Page 186  |  Page 187  |  Page 188  |  Page 189  |  Page 190  |  Page 191  |  Page 192