ASPs for Alamosaurus

January 4, 2010

A section of the cotyle of a presacral vertebra of Alamosaurus (Woodward and Lehman 2009:fig. 6A). The arrow will be explained in a future post!

Last year was good for sauropod pneumaticity. In the past few months we’ve had the publication of the first FEA of pneumatic sauropod vertebrae by Schwarz-Wings et al (2009), as well as a substantial section on pneumaticity in the big Alamosaurus histology paper by Woodward and Lehman (2009). I won’t repeat here everything that Woodward and Lehman have to say about pneumaticity, I just want to draw attention to a little piece of it. Their work is observant, up-to-date, and worth reading, so if you can get access to the paper, read it.

The major brake on the growth of our knowledge and understanding of pneumaticity is sample size. I harped on this in 2005 (Wedel 2005), and Mike just brought it up again in a comment on a previous post. In fact, what he had to say is so relevant that I’m going to just cut and paste it here:

How does degree of pneumatisation vary between individuals? Here are three more: how does it vary along the neck, how does it vary long the length of an individual vertebra, and how does it vary through ontogeny? Then of course there is variation between taxa across the tree. So what we have here is a five-and-half-dimensional space that we want to fill with observations so that we can start to deduce conclusions. Trouble is, there are, so far, 22 published observations (neatly summarised by Wedel 2005:table 7.2), which is not really enough to let us map out 5.5-space! That’s one reason why, at the moment, each observation is valuable — it adds 4% to the total knowledge in the world.

To be fair, there are a few more published observations. Schwarz and Fritsch (2006) published ASPs for cervicals of Giraffatitan and Dicraeosaurus, and I have a gnawing feeling that there are a couple here and there that I’ve seen but not remembered. I’ve got some more of my own data in the as-yet-unpublished fourth chapter of my diss, which I failed to get out as part of the Paleo Paper Challenge. And, getting back to the subject of the post, Woodward and Lehman (2009:819) have some tasty new data to report:

Digital images of sections of vertebrae and ribs were imported into ArcGIS 8.1 (Dangermond, 2001; for methods see Woodward, 2005). A unitless value for the total area of the image was calculated, using the outline of the bone as a perimeter. Subtracted from this was the area value taken up by bone, as determined by color differences (lighter areas are camellate cavities, darker areas are bone). Using this method, longitudinal sections of centra are estimated to be roughly 65% air filled. The amount of open space similarly calculated for the pneumatic proximal and medial rib sections is about 52%, whereas the cancellous spongiosa in distal rib transverse sections yields an average estimate of about 44% of their cross sectional area. Hence, the camellate cavities result in an appreciably lower bone volume compared to spongiosa.

The ASP of 0.65 for centra is right in line with the numbers I’ve gotten for neosauropods, and with the results of Schwarz and Fritsch (2006) for Giraffatitan (Dicraosaurus had a much lower ASP, around 0.2 IIRC). The stuff about the ribs is particularly interesting. Using densities of 0.95 for bone marrow, 1.8 for avian (and sauropod) compact bone, and 1.9 for mammalian compact bone we get the following:

  • Pneumatic Alamosaurus vertebrae – ASP of 0.65, density of 0.63 g/cm^3.
  • Pneumatic Alamosaurus ribs – ASP of 0.52, density of 0.86 g/cm^3.
  • Apneumatic Alamosaurus ribs – MSP (marrow space proportion) of 0.44, density of 1.43 g/cm^3.
  • Pneumatic bird long bones – ASP of 0.59, density of 0.74 g/cm^3.
  • Apneumatic bird long bones – MSP of 0.42, density of 1.44 g/cm^3.
  • Apneumatic mammal long bones – MSP of 0.28, density of 1.63 g/cm^3.

ASPs and MSPs of bird and mammal bones are calculated from K values reported by Cubo and Casinos (2000) for birds and Currey and Alexander (1985) for mammals. I don’t know what the in vivo density of sauropod compact bone was; changing it from the avian value of 1.8 to the mammalian value of 1.9 would have a negligible effect on the outcome.

At least with the data in hand, we can make the following generalizations:

  • The apneumatic bones of birds are thinner-walled than those of mammals, on average. (This has been known for a long time.)
  • The apneumatic ribs of Alamosaurus were more similar in density to apneumatic bird bones than to apneumatic mammal bones.
  • In both birds and Alamosaurus, pneumatization reduces the amount of bone tissue present by 15-30% in the same elements (long bones for birds, ribs for Alamosaurus). Pneumatic bones are light not just because the marrow is replaced by air, but because there is less bone tissue than in apneumatic bones, as bird people have been observing for ages.

There’s loads more work to be done on this sort of thing, so I’m going to stop blogging now and get back to it. Stay tuned!

References

Advertisements

Weren’t we just discussing the problem of keeping up with all the good stuff on da intert00bz? The other day Rebecca Hunt-Foster, a.k.a. Dinochick, posted a “mystery photo” that is right up our alley here at SV-POW!, but, lazy sods that we are, we missed it until just now. Here’s the pic:

IMG_7857

I flipped it 90 degrees so that you can see more clearly what is going on. This is a cut and polished section of a pneumatic sauropod vertebra–the bottom half of the mid-centrum of a dorsal vertebra, to be precise. Cervicals usually have concave ventral surfaces, and sacrals are usually either wider and flatter or narrower and V-shaped in cross sections, so I am pretty confident that this slice is from a dorsal. Compare to the classic anchor cross-section in this Camarasaurus dorsal:

camarasaurus-internal-structure(You may remember this image from Xenoposeidon week–almost two years ago now!)

Naturally as soon as I saw ReBecca’s shard of excellence, I wondered about its ASP, so after a bit of GIMPing, voila:

IMG_7857 ASP

As usual, bone is black, air is white, and everything else is gray. And the ASP is:

461080 white pixels/(461080 white + 133049 black pixels) = 0.78

So, we know what this is, and we know the ASP of this bit of it, and we can even figure out the in vivo density of this bit. The density of cortical bone ranges from about 1.8  g/cm^3 for some birds to about 2.0 for most mammals. For the sake of this example–and so I can hurry back to writing my lecture about the arse–let’s call it 1.9. The density is then the fraction of bone multiplied by the density of bone, full stop. If it was an apneumatic bone, we’d have to add the fraction of marrow multiplied by the density of marrow, but the density of air is negligible so we can skip that step here. The answer is 0.22 x 1.9 = 0.42 g/cm^3, which is pretty darned light. Keep in mind, though, that some slices of Sauroposeidon (and ‘Angloposeidon’, as it turns out) have ASPs of 0.89, and thus had an in vivo density half that of the above slice (0.11 x 1.9 = 0.21 g/cm^3).

What’s that in real money? Well, your femora are roughly 60% bone and 40% marrow, with a density of ((0.6 x 2.0)+(0.4 x 0.93)) = 1.6 g/cm^3, four times as dense as the bit of vertebra shown above, and eight times as dense as some slices of Sauroposeidon and ‘Angloposeidon’. If that doesn’t make you self-conscious about your heavy thighs, I don’t know what will.

Yes, that was a lame joke, and yes, I’m going out on it.

Hat tip to Dinochick.

P.S. It’s the 40th anniversary of the first moon landing today. Hoist a brew for Neil and Buzz, wouldja?

Condrosteo_scan

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).

Condrosteo_ASP

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.

References

Matt is staying here at Taylor Towers for a couple of weeks while his wife spends some quality time with some leprous human remains in Bradford (yes, really). Since both Matt and I are big fans of sushi, I took a stab at making some at home on Sunday night:

Fig. 1. Sushi plate, poorly preserved due to predation

Fig. 1. Sushi plate, poorly preserved due to predation

We noticed that the spring onion in one of the rolls had held its shape sufficiently well to preserve an air-space running along the length of the roll:

av, avocado; cs, crab-stick; pf, pneumatic foramen; pr, prawn.

Fig. 2. Spring-onion california roll, cross-section in anterior view. A, photograph; B, interpretive drawing. Anatomical abbreviations: av, avocado; cs, crab-stick; pf, pneumatic foramen; pr, prawn.

Using the technique of Wedel (2005:212-213), we can calculate the air-space proportion of this roll (ASP) by dividing the area of the enclosed pneumatic space by total cross-section.

fig. 7.5)

The simplest way to do this is to reduce the image to simple black-and-white with a grey background and count the pixels:

Fig. 4. Spring-onion California roll depicted in figure 2, with solid material drawn in black and pneumatic space in white.

Fig. 4. Sushi roll depicted in figure 2, with solid material drawn in black and pneumatic space in white.

According to image-processing program, the full-sized version of this images has 21961 white pixels and 302993 black pixels, yielding an ASP of W/(W+B) = 21961/(21961+302993) = 0.067, or 6.7%. This is a very low value compared to most sauropod vertebrae: according to Wedel (2005:table 7.2), values are mostly in the range 50-70% — nearly ten times as pneumatic as this sushi roll — with Sauroposeidon reaching 89% in a cervical prezygapophyseal ramus.

References