Here’s my face.

I went to the dentists’ office recently for a regular checkup and cleaning, and when my dentist learned that I taught human anatomy, he volunteered to send me a high-res copy of my panoramic x-ray. I couldn’t think of any plausible scenario wherein someone could use it for evil, and it has lots of cool stuff in it besides teeth, so decided to post it so I could yakk about it.

First things first: my teeth are in pretty good shape. I had to have my wisdom teeth (3rd molars) pulled back in 2009, and my upper 1st molar on the left has a root canal and a porcelain crown, which stands out bright white on the radiograph. Everyone else is present and looking good. If it’s been a while since you’ve covered this, the full human dentition consists of 2 incisors, 1 canine, 2 premolars, and 3 molars on each side, top and bottom, for a total of 32 teeth. Because I’ve had all four 3rd molars removed, I’m down to 28.

I could go on and on about the cool stuff in this image. Here are 12 things that stand out:

  1. The mandibular condyle, which is the articular end of the mandible that fits into the mandibular fossa, a shallow socket on the inferior surface of the temporal bone, to form the temporomandibular joint (TMJ). There’s an articular disk made of fibrocartilage inside the joint, which separates it into two fluid-filled spaces, one against the condyle and one against the fossa. This allows us to do all kinds of wacky stuff with our lower jaws besides simply opening and closing them, such as slide the jaw fore and aft or side to side. This is a strong contrast to most carnivores, which bite down hard and therefore need a jaw joint that works as a pure hinge. See this post for pictures and discussion of the jaw joint in a bear skull.
  2. The coronoid process of the mandible, which is a muscle attachment site. A few fibers of the masseter and buccinator muscles can encroach onto the coronoid process, but mostly it is buried in the temporalis, one of the primary jaw-closing muscles. Put your fingers on the side of your head a little above and in front of your ear and bite down. That muscle you feel bulging outward is the temporalis. Back in the 1960s, Melvin Moss (1968) discovered that if he removed the temporalis muscles from newborn rats, the coronoid processes would fail to develop. Moss’s ambition was to discover the quanta of anatomy, which in his view were “functional matrices” – finite sets of soft tissues related by development and function, which might contain “skeletal units” that grew because of the morphogenetic demands of the functional matrices. His tagline was, “Functional matrices evolve, skeletal units respond”. Not all of Moss’s ideas have aged well in light of what we now know about the genetic underpinnings of skeletal development, but he wasn’t completely wrong, either, and functional matrix theory is still an interesting and frequently productive way to think about the interrelationships of bones and soft tissues. For more horrifying/enlightening Moss experiments on baby rats, see this post.
  3. The mandibular angle, which is another muscle attachment. The medial pterygoid muscle attaches to the medial surface, and the masseter attaches laterally. You can feel this, too, by putting your fingers over your mandibular angle and biting down – that’s the masseter you feel bulging outward. Note that the angle flares downward and outward on either side of my jaw. This flaring of the angle tends to be more pronounced in males than in females, and it is one of many features that forensic anthropologists (like the one I belong to) take into account when attempting to determine biological sex from human skeletal remains. Like most sexually dimorphic features of the skeleton, this is a tendency along a spectrum of variation rather than a binary yes/no thing. There are women with flared jaw angles (Courtney Thorne-Smith, probably) and men with slender mandibles, so you wouldn’t want to sex a skeleton by that feature alone.
  4. The mandibular canal, a tubular channel through the mandible that houses the inferior alveolar artery, vein, and nerve. This neurovascular bundle provides innervation and blood supply to the tooth-bearing part of the mandible and to the teeth themselves, and emerges through the mental foramen to provide sensory innervation and blood supply to the chin.
  5. The upper surface of the hard palate, formed by the palatine process of the maxilla anteriorly and by the palatine bones posteriorly. The palate is the roof of the mouth and the floor of the nasal airways.
  6. The median septum of the nasal cavity, formed by cartilage anteriorly, the perpendicular plate of the ethmoid bone superiorly, and the vomer posteriorly and inferiorly.
  7. The blue lines are the inferior margins of my maxillary sinuses – air-filled spaces created when pneumatic diverticula of the nasal cavity hollow out the maxillae. You have these, too, as well as air spaces in your frontal, ethmoid, sphenoid, and temporal bones. It looks like many of the roots of my upper molars stick up into my maxillary sinuses. This is not an illusion, as shown below.
  8. When I had the root canal on my left upper 2nd molar, the endodontist filled the pulp cavities of the tooth roots with gutta-percha, a rigid natural latex made from the sap of the tree Palaquium gutta. Gutta-percha is bioinert, so it makes a good filling material (it was also used to insulate transoceanic telegraph cables), and it’s radiopaque, which allows endodontists to confirm that the cavities have been filled completely. The other teeth show the typical structure of a dense enamel crown, less dense dentine forming the bulk of the tooth, and radiolucent pulp cavities containing blood vessels and nerves.
  9. This is the rubber bit I gripped with my incisors to keep my teeth apart and my head motionless while the CT machine rotated around me to make the scan. Not that cool in a science sense, but I figured it deserved a label.
  10. Note that the roots of the canines go farther into the jaws than those of the other teeth. This is true for all four canines, it’s just easiest to see with this one. This is a pretty standard mammalian thing, for taxa that still have canines – they tend to be big and mechanically important, so they have deep roots. Even though our canines are absolutely and proportionally much smaller than those in the other great apes, we can still see traces of their earlier importance, like these deep roots.
  11. In places you can see the trabecular internal structure of my mandible clearly. As someone who geeks out pretty much anytime I get a look inside a bone, this tickled me.
  12. The remains of an alveolus or tooth socket. I had my 3rd molars out almost a decade ago, and by now the sockets will have mostly filled in with new trabecular bone. But you can still see the ghostly outline of at least this one – a sort of morphogenetic trace fossil buried inside my mandible. I assume that in another decade or two this will have disappeared through regular bone remodeling.

Here’s a closeup of my left upper 2nd premolar and first two (and only remaining) molars. The gutta-percha filling the pulp cavities of the three roots of the 1st molar is obvious. The disparity in root length is mostly illusory – this was an oblique shot and the two ‘short’ roots are foreshortened.

Here’s the same image with the roots of the 2nd molar traced in pink, and the inferior margin of the maxillary sinus traced in blue. It’s not that uncommon for upper molar roots to stick up into the maxillary sinuses. That was true of my 3rd molars as well, and when I had them taken out, the endodontist had to put stitches into my gums to close the holes. Otherwise I would have had open connections between my oral cavity and maxillary sinuses, which would have sucked and been dangerous. Nasal mucus in the maxillary sinuses could have drained into my mouth, and food I was chewing could have been forced up into the sinuses, where it would have decomposed and caused a truly vile sinus infection.

In a developmental sense, it’s not that the roots of the teeth grow upward into the sinuses, it’s that the sinuses grow downward, eroding the bone around the roots of the teeth. This happens well after the teeth are done forming – the sinuses continue to expand as long as the skull is growing, and they retain the potential to remodel the surrounding bone for as long as we live. Even in cases like mine where the roots of the molars stick up into the sinuses, the tooth roots are still covered by soft tissue, including branches of the superior alveolar artery, vein, and nerve that enter the pulp cavities of the tooth roots through foramina at their tips.

If you ask your dentist for copies of your own dental x-rays, you’ll probably get them. If you do, have fun exploring the weird territory inside your head.

Reference

  • Moss, M. L. (1968). A theoretical analysis of the functional matrix. Acta Biotheoretica, 18(1), 195-202.
jvp-fig-12

Fig. 14. Vertebrae of Pleurocoelus and other juvenile sauropods. in right lateral view. A-C. Cervical vertebrae. A. Pleurocoelus nanus (USNM 5678, redrawn fromLull1911b: pl. 15). B. Apatosaurus sp. (OMNH 1251, redrawn from Carpenter &McIntosh 1994: fig. 17.1). C. Camarasaurus sp. (CM 578, redrawn from Carpenter & McIntosh 1994: fig. 17.1). D-G. Dorsal vertebrae. D. Pleurocoelus nanus (USNM 4968, re- drawn from Lull 1911b: pl. 15). E. Eucamerotus foxi (BMNH R2524, redrawn from Blows 1995: fig. 2). F. Dorsal vertebra referred to Pleurocoelus sp. (UMNH VP900, redrawn from DeCourten 1991: fig. 6). G. Apatosaurus sp. (OMNH 1217, redrawn from Carpenter & McIntosh 1994: fig. 17.2). H-I. Sacral vertebrae. H. Pleurocoelus nanus (USNM 4946, redrawn from Lull 1911b: pl. 15). I. Camarasaurus sp. (CM 578, redrawn from Carpenter & McIntosh 1994: fig. 17.2). In general, vertebrae of juvenile sauropods are characterized by large pneumatic fossae, so this feature is not autapomorphic for Pleurocoelus and is not diagnostic at the genus, or even family, level. Scale bars are 10 cm. (Wedel et al. 2000b: fig. 14)

The question of whether sauropod cervicals got longer through ontogeny came up in the comment thread on Mike’s “How horrifying was the neck of Barosaurus?” post, and rather than bury this as a comment, I’m promoting it to a post of its own.

The short answer is, yeah, in most sauropods, and maybe all, the cervical vertebrae did lengthen over ontogeny. This is obvious from looking at the vertebrae of very young (dog-sized) sauropods and comparing them to those of adults. If you want it quantified for two well-known taxa, fortunately that work was published 16 years ago – I ran the numbers for Apatosaurus and Camarasaurus to see if it was plausible for Sauroposeidon to be synonymous with Pleurocoelus, which was a real concern back in the late ’90s (the answer is a resounding ‘no’). From Wedel et al. (2000b: pp. 368-369):

Despite the inadequacies of the type material of Pleurocoelus, and the uncertainties involved with referred material, the genus can be distinguished from Brachiosaurus and Sauroposeidon, even considering ontogenetic variation. The cervical vertebrae of Pleurocoelus are uniformly short, with a maximum EI of only 2.4 in all of the Arundel material (Table 4). For a juvenile cervical of these proportions to develop into an elongate cervical comparable to those of Sauroposeidon, the length of the centrum would have to increase by more than 100% relative to its diameter. Comparisons to taxa whose ontogenetic development can be estimated suggest much more modest increases in length.

Carpenter & McIntosh (1994) described cervical vertebrae from juvenile individuals of Apatosaurus and Camarasaurus. Measurements and proportions of cervical vertebrae from adults and juveniles of each genus are given in Table 4. The vertebrae from juvenile specimens of Apatosaurus have an average EI 2.0. Vertebrae from adult specimens of Apatosaurus excelsus and A. louisae show an average EI of 2.7, with an upper limit of 3.3. If the juvenile vertebrae are typical for Apatosaurus, they suggest that Apatosaurus vertebrae lengthened by 35 to 65% relative to centrum diameter in the course of development.

The vertebrae from juvenile specimens of Camarasaurus have an average EI of 1.8 and a maximum of 2.3. The relatively long-necked Camarasaurus lewisi is represented by a single skeleton, whereas the shorter-necked C. grandis, C. lentus, and C. supremus are each represented by several specimens (McIntosh, Miller, et al. 1996), and it is likely that the juvenile individuals of Camarasaurus belong to one of the latter species. In AMNH 5761, referred to C. supremus, the average EI of the cervical vertebrae is 2.4, with a maximum of 3.5. These ratios represent an increase in length relative to diameter of 30 to 50% over the juvenile Camarasaurus.

If the ontogenetic changes in EI observed in Apatosaurus and Camarasaurus are typical for sauropods, then it is very unlikely that Pleurocoelus could have achieved the distinctive vertebral proportions of either Brachiosaurus or Sauroposeidon.

apatosaurus-cm-555-c6-centrum-and-arch-united

C6 of Apatosaurus CM 555 – despite having an unfused neural arch and cervical ribs, the centrum proportions are about the same as in an adult.

A few things about this:

  1. From what I’ve seen, the elongation of the individual vertebrae over ontogeny seems to be complete by the time sauropods are 1/2 to 2/3 of adult size. I get this from looking at mid-sized subadults like CM 555 and the hordes of similar individuals at BYU, the Museum of Western Colorado, and other places. So to get to the question posed in the comment thread on Mike’s giant Baro post – from what I’ve seen (anecdata), a giant, Supersaurus-class Barosaurus would not necessarily have a proportionally longer neck than AMNH 6341. It might have a proportionally longer neck, I just haven’t seen anything yet that strongly suggests that. More work needed.
  2. Juvenile sauropod cervicals are not only shorter than those of adults, they also have less complex pneumatic morphology. That was the point of the figure at the top of the post. But that very simple generalization is about all we know so far – this is an area that could use a LOT more work.
  3. I’ve complained before about papers mostly being remember for one thing, even if they say many things. This is the canonical example – no-one ever seems to remember the vertebrae-elongating-over-ontogeny stuff from Wedel et al. (2000b). Maybe that’s an argument for breaking up long, kitchen-sink papers into two or more separate publications?

Reference

Wedel, M.J., Cifelli, R.L., and Sanders, R.K. 2000b. Osteology, paleobiology, and relationships of the sauropod dinosaur Sauroposeidon. Acta Palaeontologica Polonica 45:343-388.

Wedel 2005 Morrison sauropod cervicals 1 - Diplodocus

When I was back in Oklahoma in March, I met with Anne Weil to see some of the new Apatosaurus material she’s getting out of her Homestead Quarry. It’s nice material, but that’s a post for another day. Anne said something that really resonated with me, which was, “I love it when you guys post about vertebral morphology, because it helps me learn this stuff.” Okay, Anne, message received. This will begin to make things right.

Wedel 2005 Morrison sauropod cervicals 2 - Barosaurus and centra shapes

I spent a week at BYU back in 2005, collecting data for my dissertation. One of the first things I had to do was teach myself how to identify the vertebrae of different sauropods, because BYU has just about all of the common Morrison taxa. These are the notes I made back then.

Wedel 2005 Morrison sauropod cervicals 3 - Brachiosaurus and Apatosaurus

I always planned to do something with them – clean them up, get them into a more usable form. There are a lot of scribbly asides that are probably hard for others to read, and it would be more useful if I put the easily confused taxa next to each other – Barosaurus next to Brachiosaurus, for example. And I didn’t go into serial changes at all.

Wedel 2005 Morrison sauropod cervicals 4 - Camarasaurus and Haplocanthosaurus

Still, hopefully someone will find these useful. If there are things I missed or got wrong, the comment thread is open. And if you want all four spreads in one convenient package, here’s a PDF: Wedel 2005 notes on Morrison sauropod cervicals

Mike and I leave for the Sauropocalypse tomorrow. I’m hoping to post at least a few pretty pictures from the road, as I did for the Mid-Mesozoic Field Conference two years ago. Stand by…

Back in 2013, when we were in the last stages of preparing our paper Caudal pneumaticity and pneumatic hiatuses in the sauropod dinosaurs Giraffatitan and Apatosaurus (Wedel and Taylor 2013b), I noticed that, purely by chance, all ten of the illustrations shared much the same limited colour palette: pale brows and blues (and of course black and white). I’ve always found this strangely appealing. Here’s a composite:

wedel-taylor-2013b-all-figures

I’m really happy with this coincidence. In fact I think I might get it printed up as a poster for my office.

(Thought: if I did, would anyone else be interested in buying it?)

Update (a couple of hours later)

At Matt’s suggestion, I switched the order of figures 7 and 8 (the last two on the third row) to get the following version of the image. It breaks the canonical order of the figures, but it’s visually more pleasing.

wedel-taylor-2013b-all-figures-v2

Now we should write an updated version of the paper that reverses the order in which we refer to figures 7 and 8 :-)

References

  • Wedel, Mathew J., and Michael P. Taylor. 2013. Caudal pneumaticity and pneumatic hiatuses in the sauropod dinosaurs Giraffatitan and Apatosaurus. PLOS ONE 8(10):e78213. 14 pages. doi:10.1371/journal.pone.0078213

photo1

I was at the Natural History Museum of Los Angeles County yesterday to do some research in the ornithology collection. After lunch I was working on this pelican skeleton and I thought, “Geez, there is just no way to do this thing justice with still photos. I should make a video.” Here it is. You’ll want to see it full-screen–this being my first time out making a video, I didn’t realize that I was holding the phone the wrong way for efficient viewing on other devices.

The specimen is LACM Ornithology 86262. I’m posting this video with the knowledge and kind permission of the ornithology collection staff.

For previous things in this vein, please see:

If you like it that stuff like this exists, please support your local natural history museum, especially the LACM, which has some really fantastic education and outreach programs.

This came out two months ago, and I should have blogged about it then, but as usual I am behind. I’m blogging about it now because it deals with a question that has been on my mind for about 10 years now. If you want to skip my blatherations and get on to the good stuff, here’s the paper (Martin and Palmer 2014).

An Unsolved Problem

Back in 2004 I realized that if one had CTs or other cross-sections of a pneumatic bone, it was possible to quantify how much of the cross-sectional space was bone, and how much was air, a ratio I called the Air Space Proportion (ASP). That was the subject of my 2004 SVP talk, and a big part–arguably the most important part–of my chapter in The Sauropods in 2005. Of course the same calculation works for marrow-filled bones as well, where you would refer to it as an MSP rather than an ASP. If you can quantify the areas of bone, air, and marrow, you can figure out how dense the element was. One-stop shopping for all the relevant (simple) math is in this post.

(From Wedel 2005)

(From Wedel 2005)

Sometimes in science you end up with data that you don’t know what to do with, and that was my situation in 2004. Since I had CTs and other cross-sectional images of sauropod vertebrae, I could calculate ASPs for them, but I didn’t know what those results meant, because I didn’t have anything to compare them to. But I knew where to get I could get comparative data: from limb bone cross-sections. John Currey and R. McNeill Alexander had published a paper in 1985 titled, “The thickness of the walls of tubular bones”. I knew about that paper because I’d become something of an R. McNeill Alexander junkie after reading his book, Dynamics of Dinosaurs and Other Extinct Giants (Alexander 1989). And I knew that it had data on the cross-sectional properties of the limb bones in a host of animals, including crocs, birds, mammals, and–prophetically–pterosaurs.

If you know the inner and outer radii of a tubular bone, it is trivial to convert that to an ASP. So I could take the data from Currey and Alexander (1985) and calculate ASPs for the pneumatic bird and pterosaur bones in their study. Cubo and Casinos (2000) had a much larger sample of bird limb bones, and those got fed into my 2005 paper as well.

I was alert to the possibility that a mid-shaft cross-section might not be representative of the whole bone, and I hedged a bit in describing the bird ASPs (Wedel 2005: p. 212):

For the avian long bones described above, data were only presented for a single cross sec- tion located at midshaft. Therefore, the ASP values I am about to discuss may not be representative of the entire bones, but they probably approximate the volumes (total and air) of the diaphyses. For tubular bones, ASP may be determined by squaring K (if r is the inner diameter and R the outer, then K is r/R, ASP is πr^2/πR^2 or simply r^2/R^2, and ASP = K^2). For the K of pneumatic bones, Currey and Alexander (1985) report lower and upper bounds of 0.69 and 0.86, and I calculate a mean of 0.80 from the data presented in their table 1. Using a larger sample size, Cubo and Casinos (2000) found a slightly lower mean K of 0.77. The equivalent values of ASP are 0.48 and 0.74, with a mean of 0.64, or 0.59 for the mean of Cubo and Casinos (2000). This means that, on average, the diaphysis of a pneumatic avian long bone is 59%–64% air, by volume.

Now, even though I hedged and talked about diaphyses (shafts of long bones) rather than whole bones, I honestly expected that the ASP of any given slice would not change much along the length of a bone. Long bones tend to be tubular near the middle, with a thick bony cortex surrounding the marrow or air space, and honeycombed near the ends, with much thinner cortices and lots of bony septa or trabeculae (for marrow-filled bones, this is called spongy or trabecular bone, and for air-filled bones it is best referred to as camellate pneumatic bone). I figured that the decrease in cortical bone thickness near the ends of the bone would be offset by the increase in internal bony septa, and that the bone-to-air ratio through the whole element would be under some kind of holistic control that would keep it about even between the middle of the bone and the ends.

It is fair to ask why I didn’t just go check. The answer is that research is to some extent a zero-sum game, in that every project you take on means another that gets left waiting in the wings or abandoned completely. I was mainly interested in what ASP had to say about sauropods, not birds, and I had other fish to fry.

So that’s me from 2004-2012: aware that mid-shaft cross-sections of bird and pterosaur long bones might not be representative of whole elements, but not sufficiently motivated to go check. Then at SVPCA in Oxford that fall, Liz Martin rocked my world.

journal.pone.0097159.g001

Figure 1. CT scan images from two different regions of pterosaur first wing phalanx. A and B show the unmodified CT scans from A) the distal end of UP WP1 and B) the mid-shaft of UP WP1, while C and D show the modified and corrected images used in the calculation. Air space proportion (ASP) is calculated by determining the cross-sectional area of the internal, air filled cavity (the black centre of D) and dividing that by the total cross-sectional area, including the white cortical tissue and the black cavity. In areas with trabeculae, like C, the calculation of the air space includes the air found in individual trabeculae around the edges. Scale = 10 mm. doi:10.1371/journal.pone.0097159.g001 (From Martin and Palmer 2014)

A Paper in the Can

At SVPCA 2012, Liz Martin gave a talk titled, “A novel approach to estimating pterosaur bone mass using CT scans”, the result of her MS research with Colin Palmer at the University of Bristol. In that talk–the paper for which has been submitted to JVP–Liz and Colin were interested in using CT scans of pterosaur bones to quantify the volume of bone, in order to refine pterosaur mass estimates. I was fully on board, since estimating the masses of extinct animals is a minor obsession of mine. But what really caught my attention is that Liz and Colin had full stacks of slices spanning the length of each element–and therefore everything they needed to see how or if ASPs of pterosaur wing bones changed along their lengths.

At the next available break I dashed up to Liz, opened up my notebook, and started scribbling and gesticulating and in general carrying on like a crazy person. It’s a wonder she didn’t flee in terror. The substance of my raving was that (1) there was this outstanding problem in the nascent field of ASP research, and (2) she had everything she needed to address it, all that was required was a little math using the data she already had (I say this as if running the analyses and writing the paper were trivial tasks–they weren’t). Fortunately Liz and Colin were sufficiently interested to pursue it. Their paper on ASPs of pterosaur wing bones was submitted to PLOS ONE this February, and published on May 9 (while their earlier paper continues to grind its way through JVP).

And I’m blogging about it because the results were not what I expected.

Pterosaur wing bone ASPs - Martin and Palmer 2014

Figure 2. Plot of air space proportion over the length in six pterosaur wing bones. These plots show a polynomial line fit for each bone to show the general shape distribution. Exact measurements can be seen in Table S1. (From Martin and Palmer 2014).

Here’s the graph that tells the tale. Each line traces the ASP per slice along the length of a single pterosaur wing bone. A few things jump out:

  • Almost all of the lines drop near the left end. This is expected–if you’re cutting slices of a bone and measuring the not-bone space inside, then as you approach the end of the bone, you’re cutting through progressively more bone and less space. A few of the lines also drop near the right. I’m puzzled by that–if my explanation is correct, the ASP should plunge about equally at both ends. And the humerus USNM 11925 doesn’t follow the same pattern as the rest. As Martin and Palmer write, “It is unknown if this is a general feature of humeri, or this single taxon and more investigation is needed.”
  • Almost all of the bones have MUCH lower ASPs at mid-shaft than near the ends, on the order of 10% or more. So mid-shaft cross-sections of pterosaur wing bones tend to significantly underestimate how pneumatic they were. It would be interesting to know if the same holds true for bird long bones, or for the vertebrae of pterosaurs, birds, and sauropods. As Martin and Palmer point out, more work is needed.
  • The variation in ASP along the length of a single bone is in some cases greater than the variation between elements and individuals. That’s pretty cool. On the happy side, it means that getting into the nitty-gritty of ASP is not just stamp-collecting; you really need to know what is going on along the length of a bone before you can say anything intelligent about ASP or the density of the element. On the less happy side, that’s going to be a righteous pain in the butt for sauropod workers, because vertebrae are tough to get good scans of, assuming they will fit through a CT scanner at all (most don’t).
  • Finally, pterosaurs turn out to be even more pneumatic than you would think from looking at the already-freakishly-thin-walled shafts of their long bones. That’s pretty awesome, and it dovetails nicely with the emerging picture that pneumaticity in ornithodirans was more prevalent and more interesting than even I had suspected–it’s in prosauropods (Yates et al. 2012) and brachiosaur tails (Wedel and Taylor 2013) and rebbachisaur hips (Fanti et al. 2013) and saltasaur shoulders (Cerda et al. 2012) and, er, a couple of places that I can’t mention just yet. So life is good.

A few last odds and ends:

You can read more of this story at Liz Martin’s blog, scattered over several recent posts.

If you have CTs of bones and you want to follow in the footsteps of Martin and Palmer, you can do a lot of the work, and maybe all of it, in BoneJ, a free plug-in for ImageJ, which is also free.

A final note: this is Liz Martin’s first published paper, so congratulations are in order. Well done, Liz!

Almost Immediate Update: As soon as I posted this, I sent the link to Liz to see if I’d missed anything important. She writes, “It may be worth mentioning that it’s a question that I am actively following up on in my PhD, and looking into it with birds too hopefully. And it is indeed all possible using ImageJ, as that’s how I did the whole thing!”

References

OLYMPUS DIGITAL CAMERA

Now considered a junior synonym of Supersaurus, on very solid grounds.

Incidentally, unlike the neural spines of most non-titanosaurian sauropods, the neural spine of this vertebra is not simply a set of intersecting plates of bone. It is hollow and has a central chamber, presumably pneumatic. Evidence:

OLYMPUS DIGITAL CAMERA