Finite Element Analysis of sauropod vertebrae
October 27, 2009
Earlier this month Daniela Schwarz-Wings and colleagues published the first finite element analysis (FEA) of sauropod vertebrae (Schwarz-Wings et al. 2009). Above is one of the figures showing some of their results. Following standard convention, stresses are shown on a gradient with cooler colors indicating lower stresses and hotter colors indicating higher stresses. I’m not going to dwell on the on the nuts-n-bolts of FEA in general or of this study in particular. Instead, I want to talk about how sauropod vertebrae are built.
In cross-section, sauropod vertebrae often have thick bone at the outer edges of the laminae and in the walls and especially the floor of the centrum, as shown in this Brachiosaurus cervical. The bone everywhere else is pretty thin. If you hit one of these vertebrae with some magical forumula that would dissolve away all the bone thinner than, say, 1 cm, all that would be left would be the various apophyses, the outer margins of the laminae connecting them, and probably the bottom half of the centrum. It would be like the outline of a vertebra constructed from tent poles, or tinkertoys.
This is weird because most pneumatic sauropod vertebrae have at least something approaching an I-beam shape in cross-section. You might think that the median septum would be mechanically important, but it’s usually very thin, sometimes perforated (see Hatcher’s  Diplodocus cervicals, for example), and often asymmetrically deviated to one side or the other. Not what you would expect for a piece of bone that was doing any work.
And indeed, Schwarz-Wings et al. (2009) found that:
Comparative stresses are distributed evenly around the vertebrae and mainly on the bone cortex. Peak stresses occur only at points where the tendons and muscles are inserting because the insertion areas used were small resulting in extreme localized stresses. The interior of both vertebrae is nearly stress free. Almost no stresses occur around the cavities and in their bony walls (figure 3).
This reminds me not of I-beams but of the long bones of the limbs of terrestrial vertebrates. There’s a reason why you’ve got a big honkin’ marrow cavity running through the middle of your femur: the stresses are being borne by the walls of the bone. It makes sense that vertebrae would function similarly, especially sauropod cervicals which sometimes approximate limb bones in their proportions.
So how about that median septum? Why aren’t sauropod vertebrae just hollow tubes? My guess–and it is a guess–is that they got as close to being hollow tubes as their evolutionary and developmental origins allowed. The pneumatic diverticula invaded the centra from either side and pushed in lateral-to-medial, and I think the median septum is just the wimpy little bit of bone left in between the two sets of diverticula when they almost meet up in the middle.
Even if that’s correct, there’s another mystery: why don’t the diverticula just go ahead and erode away the median septum? I can think of two possible reasons. One is that, for reasons I don’t know and I’m not sure if anyone else does either, pneumatic diverticula are good at getting into bones but pretty lousy at getting back out. There are comparatively few cases of diverticula inside bones making foramina to get out into the surrounding tissue. It does happen–in humans, the mastoid air cells sometimes bust out and make subcutaneous pneumatocoels, basically bubbles of air under the skin (Anorbe et al. 2000)–but it seems to be rare. Maybe median septa fall under the same inscrutable rule.
Another, more mundane possibility is that the median septa (and other oddly thin bits of bone) are not never loaded, just infrequently loaded. Not enough to make them straight, thick, or normal-lookin’, but enough to make sure they don’t get resorbed entirely.
Sauropod vertebrae are just loaded with these growth-and-form-related mysteries. Kudos to Schwarz-Wings et al. for pushing us a little farther down the road toward solving them.
- Anorbe, E., Aisa, P. and Saenz de Ormijana, J. 2000. Spontaneous pneumatocele and pneumocephalus associated with mastoid hyperpneumatization. European Journal of Radiology 36:158–160. [abstract only for free]
- Hatcher, J.B. 1901. Diplodocus (Marsh): its osteology, taxonomy and probable habits, with a restoration of the skeleton. Memoirs of the Carnegie Museum 1: 1-63 and plates I-XIII.
- Schwarz-Wings, D., Meyer, C.A., Frey, E., Manz-Steiner, H.-R., and Schumacher, R. 2009. Mechanical implications of pneumatic neck vertebrae in sauropod dinosaurs. Proceedings of the Royal Society B. doi: 10.1098/rspb.2009.1275