### Unbelievable

File this under "Dissertation-related nerdosity".

Sauropods have big pneumatic vertebrae and I have been curious for a long time about the ratio of bone tissue to air in the skeletons of sauropods and other vertebrates. I made a stab at quantifying this with the Air Space Proportion (ASP), which is the volume of air in an element divided by the total volume of the element. A bone with an ASP of 0.60 is 60% air, by volume. Actually measuring volumes is a bitch, and for my current purposes no great precision is necessary, so I've been happy to take the area of air vs. bone in a two-dimensional slice (or, ideally, a series of slices) as an approximation of the volume. You can get 2D slices of bones with a CT scanner, which I've done, but you can also get them by photographing broken bones. That's nice because the world has a lot more broken fossils than it does CT scanners.

One problem with computing ASPs for sauropod vertebrae is that the air spaces that are actually enclosed by bone are a very small part of the total. The largest air spaces lay alongside the vertebrae, so they are only constrained by bone on one side. We don't know whether those air spaces were big and fat like balloons, or whether they just formed a thin skin of air over the surface of the bone, or what. So ASP is nice, but it only gets you so far.

About two years after I came up with ASP, I realized that if you have a stack of 2D slices through a bone, and if you know the density of bony tissue, you can easily compute the mass of a bone. In retrospect, that's really obvious, but it didn't occur to me until seven years after I first CT scanned a sauropod vertebra. So I guess it pays to keep thinking about some things, because you never know when you're going to spot something obvious.

Anyway, just knowing the masses of the vertebrae might tell you different things than you would find out by looking at ASP alone. For one thing, once you know the volume of a bone or a neck or a whole vertebral column, you can plug in whatever density you like and see how the mass changes. If you want to know how much the cervical column of Brachiosaurus would weigh if Brachiosaurus was a big giraffe, just switch the densities. (As it happens, giraffe vertebrae are a bit more than twice as dense as Brachiosaurus vertebrae, so the hypothetical Giraffasaurus would be screwed.)

It turns out that the 8.5-meter cervical series of Brachiosaurus only massed about 600 kg. That's really surprisingly light. The bones of that 28-foot neck weighed about as much as a small cow. In fact, the humeri of Brachiosaurus, each 2 meters long, weighed about as much together as the cervical series. That's because they are really dense, with a density of 1.8 or 1.9 g/cm^3. By comparison, the cervical vertebrae were about 70% air by volume, which would give them a density of 0.6 g/cm^3.

All of that is simple junior high math. But it's still a surprising result. Hence the title of this post. I've been over the numbers and it all checks out, but it still blows my mind.

Here's a graphical representation, which is going into my SVP poster. Comments welcome.

Sauropods have big pneumatic vertebrae and I have been curious for a long time about the ratio of bone tissue to air in the skeletons of sauropods and other vertebrates. I made a stab at quantifying this with the Air Space Proportion (ASP), which is the volume of air in an element divided by the total volume of the element. A bone with an ASP of 0.60 is 60% air, by volume. Actually measuring volumes is a bitch, and for my current purposes no great precision is necessary, so I've been happy to take the area of air vs. bone in a two-dimensional slice (or, ideally, a series of slices) as an approximation of the volume. You can get 2D slices of bones with a CT scanner, which I've done, but you can also get them by photographing broken bones. That's nice because the world has a lot more broken fossils than it does CT scanners.

One problem with computing ASPs for sauropod vertebrae is that the air spaces that are actually enclosed by bone are a very small part of the total. The largest air spaces lay alongside the vertebrae, so they are only constrained by bone on one side. We don't know whether those air spaces were big and fat like balloons, or whether they just formed a thin skin of air over the surface of the bone, or what. So ASP is nice, but it only gets you so far.

About two years after I came up with ASP, I realized that if you have a stack of 2D slices through a bone, and if you know the density of bony tissue, you can easily compute the mass of a bone. In retrospect, that's really obvious, but it didn't occur to me until seven years after I first CT scanned a sauropod vertebra. So I guess it pays to keep thinking about some things, because you never know when you're going to spot something obvious.

Anyway, just knowing the masses of the vertebrae might tell you different things than you would find out by looking at ASP alone. For one thing, once you know the volume of a bone or a neck or a whole vertebral column, you can plug in whatever density you like and see how the mass changes. If you want to know how much the cervical column of Brachiosaurus would weigh if Brachiosaurus was a big giraffe, just switch the densities. (As it happens, giraffe vertebrae are a bit more than twice as dense as Brachiosaurus vertebrae, so the hypothetical Giraffasaurus would be screwed.)

It turns out that the 8.5-meter cervical series of Brachiosaurus only massed about 600 kg. That's really surprisingly light. The bones of that 28-foot neck weighed about as much as a small cow. In fact, the humeri of Brachiosaurus, each 2 meters long, weighed about as much together as the cervical series. That's because they are really dense, with a density of 1.8 or 1.9 g/cm^3. By comparison, the cervical vertebrae were about 70% air by volume, which would give them a density of 0.6 g/cm^3.

All of that is simple junior high math. But it's still a surprising result. Hence the title of this post. I've been over the numbers and it all checks out, but it still blows my mind.

Here's a graphical representation, which is going into my SVP poster. Comments welcome.

Labels: Dinosaurs, Nerdosity, Not Quite Science

## 2 Comments:

Was the skull really apneumatic?

Yep. Sorta.

"Yep" because the individual bones of the skull are all apneumatic. I don't know of any sauropodomorph that has skull bones that contain pneumatic cavities. Usually if anything in an archosaur skull is pneumatic it's the braincase, but all of the sauropod braincases I've scanned or know anything about are apneumatic.

"Sorta" because even though the bones don't contain pneumatic cavities themselves, the head still contained large air spaces in life. So the skull as a whole was very similar to the vertebrae, in that it is a collection of flat, plate-like bones that border or contain big air spaces. But I don't want to get hammered by pedants, so I'm leaving the skull black.

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