NHM 46870 Strikes Back: ASP

July 18, 2009


By now you’ll recognize this as NHM 46870, a minor celebrity in the world of pneumatic sauropod vertebrae. Darren has covered the history of the specimen before, and in the last post he showed photographs of both this chunk and its other half. He also briefly discussed the Air Space Proportion (ASP) of the specimen, and I’ll expand on that now.

People have mentioned the weight-saving properties of sauropod vertebrae from the very earliest discoveries of sauropods. But as far as I know, no one tried to quantify just how light they might have been until 2003.

That fall I was starting my third year of PhD work at Berkeley, and I was trying to think of everything that could possibly be investigated about pneumaticity in sauropod vertebrae. I came up with a list of four things:

  • external traces of pneumaticity (foramina, fossae, tracks, laminae)
  • form and complexity of internal spaces (camerae, camellae, branching patterns)
  • ratio of bone to air space within a pneumatic element
  • distribution of postcranial skeletal pneumaticity (PSP) in the body

That list of four things formed the outline for my first dissertation chapter (Wedel 2005), and for my dissertation itself. In fact, all of my papers that have anything to do with pneumaticity can be classified into one or more of those four bins:

That list is not exhaustive. It’s every aspect of PSP that I was able to think of back in 2003, but there are lots more. For example, I’ve only ever dealt with the internal complexity of sauropod vertebrae in a qualitative fashion, but the interconnections among either chambers or bony septa could be quantified, as Andy Farke has done for the frontal sinuses of hartebeests (Farke 2007). External traces on vertebrae and the distribution of PSP in the body can also be quantified, and were shortly after I drew up the list–see Naish et al. (2004) for a simple, straightforward approach to quantifying the extent of external pneumatic fossae, and O’Connor (2004, 2009) for a quantitative approach to the extent of pneumaticity in the postcranial skeletons of birds. There are undoubtedly still more parameters waiting to be thought of and measured. All of these papers are first steps, at least as applied to pneumaticity, and our work here is really just beginning.

Also, it took me an embarrassingly long time to “discover” ASPs.  I’d had CT slices of sauropod vertebrae since January, 1998, and it took me almost six years to realize that I could use them to quantify the amount of air inside the bones. I later discovered that Currey and Alexander (1985) and Casinos and Cubo (2000) had done related but not identical work on quantifying the wall thickness of tubular bones, and I was able to translate their results into ASPs (and MSPs for marrow-filled bones).


The procedure is pretty simple, as Mike has shown here before. Open up the image of interest in Photoshop (or GIMP if you’re all open-sourcey, like we are), make the bone one color, the air space a second color, and the background a third color. Count pixels, plug ‘em into a simple formula, and you’ve got the ASP. I always colored the bone black, the air space white, and the background gray, so

ASP = (white pixels)/(black + white pixels)

For the image above, that’s 460442/657417 = 0.70.

Two quick technical points. First, most images are not just black, white, and one value of gray. Because of anti-aliasing, each black/white boundary is microscopically blurred by a fuzz of pixels of intermediate value. I could have used some kind of leveling threshold thing to bin those intermediate pixels into the bone/air/background columns, but I wanted to keep the process as fast and non-subjective as possible, so I didn’t. My spreadsheet has columns for black, white, gray, and everything else. The everything else typically runs 1-3%, which is not enough to make a difference at the coarse level of analysis I’m currently stuck with.

Second, I prefer transverse sections to longitudinal, because most of the internal chambers are longitudinally oriented. That means that longitudinal sections, whether sagittal or horizontal, are likely to cut through a chamber wall on its long axis, which makes the walls look unnaturally thick. For example, in the image above the median septum looks 5-10 times thicker than the outer walls of the bone, which would be a first–usually the outer walls are thicker than the internal septa, as you can see here. I don’t think the median septum really is that thick; I strongly suspect that a very thin plate of bone just happened to lie in the plane of the cut. It takes some work to get used to thinking about how a 2D slice can misrepresent 3D reality. When I first started CT scanning I was blown away by how thick the bone is below the pre- and postzygapophyses. I was thinking, “Wow, those centrozygapophyseal laminae must have been way more mechanically important than anyone thinks!” It took me a LONG time to figure out that if you take a transverse slice through a vertical plate of bone, it is going to look solid all the way up, even if that plate of bone is very thin.

Even apart from those considerations, there is still a list of caveats here as long as your arm. You may not get to choose your slice. That’s almost always true of broken or historically sectioned material, like NHM 46870. It’s even true in some cases for CT scans, because some areas don’t turn out very clearly, because of mineral inclusions, beam-hardening artifacts, or just poor preservation.

The slice you get, chosen or not, may not be representative of the ASP of the vertebra it’s from. Even if it is, other elements in the same animal may have different ASPs. Then there’s variation: intraspecific, ontogenetic, etc. So you have to treat the results with caution.

Still, there are some regularities in the data. From my own work, the mean of all ASP measurements for all sauropods is about 0.60. That was true when I had only crunched my first six images, late on the evening of October 9, 2003. It was true of the 22 measurements I had for Wedel (2005), and now that I have over a hundred measurements, it’s still true. More data is not shifting that number at all. And Woodward (2005) and Schwartz and Fritsch (2006) got very similar numbers, using different specimens.

This is cool for several reasons. It’s always nice when results are replicated–it decreases the likelihood that they’re a fluke, and in this case it suggests that although the limitations listed above are certainly real, they are not deal-killers for answering broad questions (we are at this point seeing the forest more clearly than the trees, though).

More importantly, the mean 0.60 ASP for all sauropod vertebrae is very similar to the numbers that you get from the data of Currey and Alexander (1985) and Cubo and Casinos (2000): 0.64 and 0.59, respectively. So sauropod vertebrae were about as lightly built as the pneumatic long bones of birds, on average.

Naturally, there are some deviations from average. Although I didn’t have enough data to show it in 2005, brachiosaurids tend to have higher ASPs than non-brachiosaurids. And Early Cretaceous brachiosaurids from the US and England are especially pneumatic–the mean for all of them, including Sauroposeidon, ‘Angloposeidon’, some shards of excellence from the Isle of Wight, and assorted odds and ends, is something like 0.75-0.80, higher even than Brachiosaurus. So there’s probably a combined phylogenetic/functional story in there about the highly pneumatic, hyper-long-necked brachiosaurids of the Early Cretaceous of Laurasia. Another paper waiting to be written.

Chondrosteosaurus broken face

Here’s another shard of excellence, referred to Chondrosteosaurus, NHM R96. As Mike had discussed here before, there’s no good reason to believe that it actually is Chondrosteosaurus, and the internal structure looks considerably more subdivided than in NHM 46870. This is an anterior view, and normally you’d be seeing a nice hemispherical condyle, but all of the cortical bone is gone and the internal structure is revealed. The little black traces are bone and the brownish stuff is rock matrix filling the pneumatic cavities.

Chondrosteosaurus broken face ASP

A few years ago, Mike asked me to look at that photo and guess the ASP, and then run the numbers and see how close I got. I guessed about 78%, then did the calculation, and lo and behold, the answer was 78%. So I’m pretty good at guessing ASPs.

Except I’m not, because as any of you armed with photo software can tell, that picture has 24520 black pixels and 128152 white ones, so the ASP is actually 128152/(128152+24520) = 0.84. The moral of the story is check your homework, kids! Especially if you seem to be an unnaturally good estimator.

ASP-ESP aside, I think ASP is cool and has some interesting potential at the intersection of phylogeny and biomechanics. But the method is severely limited by sample size, which is severely limited by how much of a pain in the butt preparing the images is. In most cases you can’t just play with levels or curves to get a black and white image that faithfully represents the morphology, or use the magic wand, or any of the other myriad shortcuts that modern imaging programs offer. Believe me, I’ve tried. Hard. But inevitably you get some matrix with the bone, or some bone with the matrix, and you end up spending an impossible amount of time fixing those problems (note that this is not a problem if you use perfect bones from extant animals, which is sadly not an option for sauropod workers). So almost all of my ASP images were traced by hand, which is really time-consuming. I could pile up a lot more data if I just sat around for a few weeks processing images, but every time I’ve gotten a few free weeks there has been something more important demanding my attention, and that may always be the case. Fortunately I’m not the only one doing this stuff now, and hopefully in the next few years we’ll get beyond these first few tottering steps.

Side Note: Does NHM 46870 represent a juvenile, or a dwarf?

This came up amongst the SV-POW!sketeers and we decided it should be addressed here. Darren noted that the vert at top is pretty darned small, ~23 cm for the preserved part and probably only a foot and a half long when it was complete, which is big for an animal but small for a sauropod and dinky for a brachiosaurid (if that’s what it is). Mike made the counter-observation that the internal structure is pretty complex, citing Wedel (2003b:fig. 12) and surrounding text, and suggested that it might be an adult of a small or even dwarfed taxon. And I responded:

I’m not at all certain that it is dwarfed. It matters a lot whether the complex internal structure is polycamerate or camellate. I was agnostic for a long time about how different those two conditions are, but there is an important difference that is relevant in this case: the two internal structures develop differently. Polycamerate verts really do get progressively more complex through development, as illustrated–there are at least two great series that show this, that I need to publish one of these days. But I think camellate vertebrae may be natively complex right from the get-go; i.e., instead of a big simple diverticulum pushing in from the side and making a big camera first, a bunch of smaller diverticula may remodel the small marrow spaces into small air spaces with no prior big cavities. At least, that’s how birds seem to do it. This needs more testing from sauropods–a good ontogenetic sequence from Brachiosaurus would be clutch here–but it’s my working hypothesis. In which case NHM 46870 may be a juvenile of a camellate taxon, rather than an adult of a polycamerate taxon.

The whole camerate-vs-camellate problem deserves a post of its own, and this post is already too long, so we’ll save that for another day.


About these ads

17 Responses to “NHM 46870 Strikes Back: ASP”

  1. Mike Taylor Says:

    First, most images are not just black, white, and one value of gray. Because of anti-aliasing, each black/white boundary is microscopically blurred by a fuzz of pixels of intermediate value. I could have used some kind of leveling threshold thing to bin those intermediate pixels into the bone/air/background columns, but I wanted to keep the process as fast and non-subjective as possible, so I didn’t.

    If you ask GIMP to convert your greyscale image into a one-bit deep bitmap image, it’ll do the necessary dithering in an objective way that requires no judgement on your part.

  2. Matt Wedel Says:

    Thanks. I guess we should have had this conversation six years ago. Psssh! Where were you on that one, “buddy”?

  3. 220mya Says:

    Matt said in the post: “I could pile up a lot more data if I just sat around for a few weeks processing images”

    Isn’t that what undergraduate students are for?

  4. Andy Says:

    Re: the thresholding issue, the approach most seem to settle on is the full-width half-max approach advocated by Spoor et al. in 1993 (“Linear measurements of cortical bone and dental enamel by computed tomography”). Mark Coleman and Matt Colbert published a paper extending the method (with validation study) to 3 dimensions.

  5. Andy Says:

    And just to add a little more, I completely recognize that this isn’t necessarily straight-forward for cases where the CT values max out due to high density, or cases of extremely heterogeneous matrix, or any other number of problems.

  6. Nathan Myers Says:

    220mya: No, that’s what graduate students are for. Undergraduates are for when you want fabricated data.

  7. Matt Wedel Says:

    Matt said in the post: “I could pile up a lot more data if I just sat around for a few weeks processing images”

    Isn’t that what undergraduate students are for?

    Are you suggesting that I get a bunch of undergrads, cut them up, and measure their ASPs? Because I’m totally cool with that, but I don’t think it will be any faster.

  8. Tor Bertin Says:

    Distantly related question–

    I’m in the early stages of conducting a study that compares sauropod bone morphologies and the skull and tooth shape/body size of local theropod dinosaurs in search of correlations (specifically, I’m checking to see if sauropods grow morphologically different if there are no or few predators around capable of actively hunting them–‘do they re-design their body plans to further assist eating?’ etc.).

    Do you guys have any idea what the general policy is on measurements made in other papers? Are you allowed to use them with citation, or is the permission of the authors themselves needed?

    I have ample access to pretty much anything in the Morrison formation (Diplodocus, etc.); but some of the more exotic groups are nowhere near, so using other published measurements would be way helpful.

    Really neat post!

  9. 220mya Says:

    Matt – although a study of undergraduate ASPs would be awesome, I’m not sure what the Animal Care and Use Committee would think of it.

    Nathan – Many of my colleagues (and myself) have found that most undergrad students are just as good if not better than grad students at acurrately and efficiently collecting data, etc. You just have to do a decent job training the students and getting them excited about the research project.

  10. Nathan Myers Says:

    220mya: Maybe you just have less need for fabricated data than some. But maybe this joke has gone too far already.

  11. Matt Wedel Says:

    Do you guys have any idea what the general policy is on measurements made in other papers? Are you allowed to use them with citation, or is the permission of the authors themselves needed?

    The former. Give credit, for sure, but if they’re published, they’re out there.

  12. Nathan Myers Says:

    I wonder if you have any 3D MRI scans.

    I wonder, too, if brachiosauroid cervicals, particularly, have proximal ASPs lower than in distals, suggesting a more vertical neck.

  13. Tor, I know I am repeating Matt, but it’s just as well to be completely clear on this: any number that is published is out there for the world to use. That’s pretty much what “published” means. So go nuts — use what you like, the more the better, so long as you cite your sources (which you’d want to do anyway to make it easier for people to trust your database). By the way, your project sounds very interesting, I’m looking forward to seeing the results (even if they turn out to be “there is no correlation”).

    Nathan, why would lower proximal ASPs indicate a more vertical neck?

  14. Nathan Myers Says:

    Mike: I was imagining verts stacked on verts, and a lower ASP means a higher proportion of bone, so stronger. But just bigger is also stronger, and anyway a horizontal, cantilevered neck would also need stronger proximals. So I’m probably just wrong.

  15. [...] as soon as I saw ReBecca’s shard of excellence, I wondered about its ASP, so after a bit of GIMPing, [...]

  16. [...] is the mate of NHM 46870, a specimen that we have already given way too much coverage, and which has sometimes been considered the cotype along with 46869.  Unlike its mate, [...]

  17. […] just use ASP for air-filled bones and MSP for marrow-filled bones. See Tutorial 6 and these posts: one, two, […]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s


Get every new post delivered to your Inbox.

Join 377 other followers

%d bloggers like this: