Finite Element Analysis of sauropod vertebrae

October 27, 2009

Figure 3 from Schwarz-Wings et al. 2009. A is Diplodocus, B-D are Giraffatitan.

Figure 3 from Schwarz-Wings et al. 2009. A is Diplodocus, B-D are Giraffatitan.

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.

CT cross sections of BYU 12866, a mid-cervical of Brachiosaurus sp.

CT cross sections of BYU 12866, a mid-cervical of Brachiosaurus sp.

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 [1901] 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.

(Incidentally, this makes the perforate laminae in Giraffatitan all the weirder.)

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.


11 Responses to “Finite Element Analysis of sauropod vertebrae”

  1. William Miller Says:


    Do those subcutaneous pneumatocoels that occasionally happen in humans have any harmful effects on the person?

    How would the idea that the median septa were loaded under unusual conditions be tested? Could mating have something to do with it – presumably the female sauropod’s back had to support more weight than usual?

  2. qilong Says:

    Note also that the stressed, when present, appear from the dorsal and ventral extremities, and seldom in the anterior or posterior portions of the vertebrae. Continuing existence of laminae (instead of total resorption and hollowing of the epiphyses entirely, not even just the centrum) appear to also mitigate stresses on twisting of the bone. I need to check the paper to see if they modelled twisting and direction of loading relative to the orientation of the bone, given the contradicting hypotheses for neck positions (and therefore requiring a model that loads different positions of vertebrae differently).

  3. Nathan Myers Says:

    Three cheers for Daniela Schwarz-Wings (et al.)!

    For those of us without access to the paper, does it explore what mix of forces would result in evenly-distributed stress throughout a cervical vertebra? Since the bone itself adjusts to stresses, this should give a snapshot of the vertebra’s environment at its point of maximum typical stress. While that is far from the same as revealing habitual posture, it’s a start.

    An inability to resist stress in tension would put to bed the notion of pneumatic compressive support for the neck.

  4. David Marjanović Says:

    What about Nigersaurus? Hasn’t it got tubular vertebrae?

  5. Matt Wedel Says:

    What about Nigersaurus? Hasn’t it got tubular vertebrae?

    I’m sorry, I may not be understanding your question, but if you’re asking if Nigersaurus vertebrate have median septa, the answer is yes.

  6. Graham King Says:

    William Miller Says:

    October 27, 2009 at 5:28 am
    …Could mating have something to do with it – presumably the female sauropod’s back had to support more weight than usual?

    My contrary theory: I suggest that at least some dinosaurs mated not by mounting, but coupled side-by-side, while facing in opposite directions. In the case of stegosaurs and finbacks the practical advantages are obvious. A somewhat dexterous (or sinistrous) penis would be required; also, accurate longitudinal positioning: for which each could line the head up with the partner’s tail (maybe holding tail, or tail adornments, in mouth). Elaborate caudal adornments thus can be seen as secondary sexual characters, attracting attention there and so aiding in this head-to-tail pairing alignment.

    The long tails of sauropods in this theory were necessitated by their having long necks!
    I suspect that stiff flat tails of duckbills and others (now known to be held up, not dragging on ground), served as advertising billboards, perhaps with variation of colour thereon to signal mating season; perhaps even with a bulls-eye spot or band for precision alignment (partner’s eye alongside).

    These details would be complicated by likely range of sizes in sexually-mature males and females.

    If I find time, I may play around with some models and take photos.

    Ok, I know how that sounds..

  7. William Miller Says:

    Interesting ideas…

    The line-head-up-with-partner’s-tail method of alignment would only work if both sexes were of comparable length; more sexually dimorphic species would have to find another way.

    Could a sauropod roll onto its back? It seems that a hypothetical inverted sauropod would find it rather difficult to stand up again, but I’m not sure.

  8. […] are only rarely perforated (but it does happen), for possible (read: arm-wavy) reasons discussed in the recent FEA post. And maybe the amount of extra bone involved in making embossed laminae versus smooth ones was […]

  9. Jeff Waters Says:

    This is the coolest use of FEA I’ve seen in years. Great job!

  10. […] mechanical support and are aligned along lines of stress (for more on this subject see the piece on finite element analysis). An assortment of _Amphiuma_ cervical, dorsal and caudal vertebrae, from Gardner (2003). The […]

  11. […] Emma Schachner (not on pneumaticity per se, but too closely related [and too awesome] to ignore), Daniela Schwarz, and Jeff Wilson (and his students), plus important singleton papers like Woodward and Lehman […]

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