Quantifying pneumaticity

A few months ago I started talking about skeletal pneumaticity in pterosaurs and planned on following it up with this post on quantifying pneumaticity, but a few things got in the way, so here it is.

How do you quantify pneumaticity?

Most often in bones, and especially in the fossil record, pneumaticity is discussed on the basis of presence or absence, and documenting the location of pneumatic foramina. This is primarily done for taxonomic purposes, as the location of these foramina can be characteristic of the taxonomic group the pterosaur belongs in. Pat O'Connor started to look at quantifying pneumaticity in one way using what he called the Pneumaticity Index (PI), which was a way of comparing the number of pneumatic elements in different birds [1]. A PI of 1.00 indicates all potentially pneumatic elements of the bird's post cranial skeleton are pneumatised, and smaller numbers indicate fewer pneumatic elements. This allows for comparison of the number of pneumatised elements between taxa, but not the degree of pneumaticity between bones.

Air Space Proportion

Matt Wedel, a sauropod palaeontologist, does a lot of work on the pneumaticity in sauropod vertebrae and realised that there was no way of quantifying pneumaticity within a single bone. He proposed using the Air Space Proportion (ASP), a ratio of the cross-sectional area of the air-filled section compared to the total cross-sectional area [2]. From 0-1, an ASP closer to 1 indicates a bone that is mainly full of air, vs. closer to 0, which is mainly bone. He started doing this on sauropod vertebrae and comparing the ASP between different sauropods and different vertebrae. While Matt came up with the idea of ASP, several people in the past of used the K value (the ratio of the internal to outer diameter) to compare the bone thickness of different bird and pterosaur bones. In a tubular bone, ASP is roughly equal to K^2.

In 2012, Matt approached me after seeing a talk I gave on my MSc research on pterosaur bone mass and suggested that I look at ASP in pterosaurs using my CT scans. He had always been curious as to if it would change throughout the bone and if the cross-section of the bone would significantly change the ASP. I thought this was a good idea, and that it would also allow me to look at ASP in pterosaurs and see how it related to other animals.

Looking at CT scan slices at set intervals throughout several pterosaur bones, we found some interesting results. It turns out that ASP actually varies quite a lot throughout a bone, at least it does in pterosaur wing bones [3]. In fact, all pterosaur wing phalanges had high ASP values  at the ends of the bone (e.g. approximately 0.85 in NHMUK PV OR39411) and lower values in the shaft (e.g. approximately 0.71).

From Martin and Palmer [3]

This was not initially expected. Pterosaur bones are full of spongy trabecular bone in the ends, while the shafts are almost completely hollow with just cortical bone along the outsides, so at first glance you would expect less air in the ends. However, the ends are also expanded in diameter, the cortical thickness is extremely low and trabeculae are very small in thickness, while the shaft has higher cortical thickness, but a smaller diameter. The result of this is an increase in both air and bone at the ends, but proportionally more air. As most long bones in the fossil record are found broken in the shaft, it means that any estimates of pneumaticity of long bones using a shaft cross-section may be underestimating the values. It also means that single cross-sections of bones may not be accurately showing how pneumatic the bones are.

How do pterosaurs compare to other animals?

First of all, it's important to remember exactly what these numbers mean. If an ASP is 0.9, that means it 90% air, vs. an ASP of 0.1, or 10% air. Of the bones we looked at, they had average ASP values of 0.68-0.83, but the complete range was 0.56-0.88.

ASP values of pterosaur wing bones from Martin and Palmer [3]

This is significantly higher than the same bone and most others in a juvenile azhdarchid, similar to Pteranodon (calculated from K), and much higher than an unknown bone from a dsungaripteroid (from K). It's also higher than most birds, although these are all calculated from K values rather than ASPs. Finally, they are generally higher than sauropod vertebrae ASP, but there are some sauropods that have higher ASP values. This means that pterosaurs are among, if not THE, most pneumatic animals in the world.

ASP values of pterosaurs, birds, and sauropods from the literature in Martin and Palmer [2]

There is still a lot of work to be done on this. First of all, more bones need to be looked at as our study only included wing bones, and mostly wing phalanges. Next, more pterosaur taxa need to be studied. This is already underway and is showing some interesting results, so stay tuned! Finally, more groups need to be looked at, particularly birds. Do birds show the same patterns? Again, something that I am looking at! This work will be continued in my PhD in more detail, so more will come.

If you're interested, you can read more about this paper over at SVPOW where Matt Wedel summarised it. Also, the paper is published open access in Plos One, and can be read here.

Thanks to everyone who helped me along the way, especially Matt Wedel and Colin Palmer, and also Davide Foffa, Lorna Steel, Lauren Howard, Dave Martill, the staff at Muvis, Mike Habib, the Smithsonian staff, and Gareth Dyke. And of course to my other half Josh Silverstone :) 

References:
[1] O'connor 2004. Pulmonary pneumaticity in the postcranial skeleton of extant Aves: a case study examining Anseriformes. Journal of Morphology 261: 141-161.
[2] Wedel MJ (2005) Postcranial skeletal pneumaticity in sauropods and its implications for mass estimates. In: Curry Rogers K, Wilson J, editors. The sauropods: evolution and paleobiology. Berkeley: University of California Press. 201–228
[3] Martin EG, Palmer C (2014) Air space proportion in pterosaur limb bones using computed tomography and its implications for previous estimates for pneumaticity. Plos One 9: e97159.