Western University of Health Sciences

Matt Wedel

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.

Free papers you should read: Martin and Palmer (2014) on ASPs of pterosaur wing bones

This post pulls together information on basic parameters of tubular bones from Currey &amp; Alexander (1985), on ASP from Wedel (2005), and on calculating the densities of bones from Wedel (2009: Appendix). It’s all stuff we’ve covered at one point or another, I just wanted to have it all in one convenient place.

::: {#attachment_8142 .wp-caption .aligncenter shortcode="caption" style="width: 490px"}
[![Currey Alexander 1985 fig
1](https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=480&h=332){.size-full
.wp-image-8142 aria-describedby="caption-attachment-8142" loading="lazy"
attachment-id="8142"
permalink="http://svpow.com/2013/06/05/tutorial-24-variables-for-tubular-bones-asp-msp-and-bone-density/currey-alexander-1985-fig-1/"
orig-file="https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg"
orig-size="956,662" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="Currey Alexander 1985 fig 1" image-description=""
image-caption=""
medium-file="https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=300"
large-file="https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=956"
width="480" height="332"
srcset="https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=480&h=332 480w, https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=150&h=104 150w, https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=300&h=208 300w, https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg?w=768&h=532 768w, https://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg 956w"
sizes="(max-width: 480px) 100vw, 480px"}](http://svpow.files.wordpress.com/2013/03/currey-alexander-1985-fig-1.jpg)

Figure 1 from Currey and Alexander (1985)
:::

This post pulls together information on basic parameters of tubular
bones from Currey & Alexander (1985), on ASP from Wedel (2005), and on
calculating the densities of bones from Wedel (2009: Appendix). It's all
stuff we've covered at one point or another, I just wanted to have it
all in one convenient place.

Definitions:

- R = outer radius = r + t
- r = inner radius = R -- t
- t = bone wall thickness = R -- r

Cross-sectional properties of tubular bones are commonly expressed in
R/t or K (so that r = KR). K is defined as the inner radius divided by
the outer radius (r/R). For bones with elliptical or irregular
cross-sections, it's best to measure two radii at right angles to each
other, or use a different measure of cross-sectional geometry (like
second moment of area, which I'm not getting into here).

R/t and K can be converted like so:

- R/t = 1/(1-K)
- K = 1 -- (1/(R/t))

ASP (air space proportion) and MSP (marrow space proportion) measure the
cross-sectional area of an element not taken up by bone tissue. ASP and
MSP are the same measurement--the amount of non-bone space in a bony
element divided by the total--we just use ASP for air-filled bones and
MSP for marrow-filled bones. See [Tutorial
6](http://svpow.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/)
and these posts:
[one](http://svpow.com/2009/07/18/nh-46870-strikes-back/),
[two](http://svpow.com/2009/07/20/asp-target-of-opportunity/),
[three](http://svpow.com/2010/01/04/asps-for-alamosaurus/).

For tubular bones, ASP (or MSP) can be calculated from K:

- ASP = πr\^2/πR\^2 = r\^2/R\^2 = (r/R)\^2 = K\^2

Obviously R/t and K don't work for bones like vertebrae that depart
significantly from a tubular shape. But if you had a vertebra or other
irregular bone with a given ASP and you wanted to see what the
equivalent tubular bone would look like, you could take the square root
of ASP to get K and then use that to draw out the cross-section of that
hypothetical tubular bone.

To estimate the density of an element (at least near the point of a
given cross-section), multiply the proportional areas of bone and air,
or bone and marrow, by the specific gravities of those materials.
According to Currey and Alexader (1985: 455), the specific gravities of
fatty marrow and bone tissue are 0.93 and 2.1, respectively.

For a marrow-filled bone, the density of the element (or at least of the
part of the shaft the section goes through) is:

- 0.93MSP + 2.1(1-MSP)

Air is matter and therefore has mass and density, but it is so light
(0.0012-0.0013 g/mL) that we can effectively ignore it in these
calculations. So the density of a pneumatic element is: 2.1(1-ASP) For
the three examples in the figure at the top of the post, the ASP/MSP
values and densities are:

- \(b\) alligator femur (marrow-filled), K = 0.35, MSP = K\^2 = 0.12,
  density = (0.93 x 0.12) + (2.1 x 0.88) = 1.96 g/mL
- \(c\) camel tibia (marrow-filled), K = 0.57, MSP = K\^2 = 0.32,
  density = (0.93 x 0.32) + (2.1 x 0.68) = 1.73 g/mL
- \(d\) *Pteranodon* first phalanx (air-filled), K = 0.91, ASP = K\^2 =
  0.83, density = (2.1 x 0.17) = 0.36 g/mL

What if we switched things up, and imagined that the alligator and camel
bones were pneumatic and the *Pteranodon* phalanx was marrow-filled? The
results would then be:

- \(b\) alligator femur (hypothetical air-filled), K = 0.35, ASP = K\^2
  = 0.12, density = (2.1 x 0.88) = 1.85 g/mL
- \(c\) camel tibia (hypothetical air-filled), K = 0.57, ASP = K\^2 =
  0.32, density = (2.1 x 0.68) = 1.43 g/mL
- (d) *Pteranodon* first phalanx (hypothetical marrow-filled), K = 0.91,
  MSP = K\^2 = 0.83, density = (0.93 x 0.83) + (2.1 x 0.17) = 1.13 g/mL

In the alligator femur, the amount of non-bone space is so small that it
does much matter whether that space is filled by air or
marrow--replacing the marrow with air only lowers the density of the
element by 5-6%. The *Pteranodon* phalanx is a lot less dense than the
alligator femur for two reasons. First, there is much less bony
tissue--the hypothetical marrow-filled phalanx is 42% less dense as the
alligator femur. Second, the marrow is replaced by air, which reduces
the density by an additional 40% relative to the alligator.

Next time: how to write punchier endings for tutorial posts.

**References**

- Currey, J. D., and Alexander, R. McN. 1985. The thickness of the walls
  of tubular bones. Journal of Zoology 206:453--468.
- [Wedel, M.J. 2005. Postcranial skeletal pneumaticity in sauropods and
  its implications for mass estimates; pp. 201-228 in Wilson, J.A., and
  Curry-Rogers, K. (eds.), *The Sauropods: Evolution and Paleobiology*.
  University of California Press,
  Berkeley.](http://sauroposeidon.files.wordpress.com/2010/04/wedel-2005-mass-estimates.pdf)


Figure 1 from Currey and Alexander (1985)  This post pulls together information on basic parameters of tubular bones from Currey &amp; Alexander (1985), on ASP from Wedel (2005), and on calculating the densities of bones from Wedel (2009: Appendix). It’s all stuff we’ve covered at one point or another, I just wanted to have it all in one convenient place.

Tutorial 24: variables for tubular bones, ASP, MSP, and bone density

Last year was good for sauropod pneumaticity.

::: {#attachment_2368 .wp-caption .aligncenter shortcode="caption" style="width: 490px"}
[![](https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=480&h=436 "Alamosaurus cotyle section"){.size-full
.wp-image-2368 aria-describedby="caption-attachment-2368" loading="lazy"
attachment-id="2368"
permalink="http://svpow.com/2010/01/04/asps-for-alamosaurus/alamosaurus-cotyle-section/"
orig-file="https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg"
orig-size="616,560" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="Alamosaurus cotyle section" image-description=""
image-caption=""
medium-file="https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=300"
large-file="https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=616"
width="480" height="436"
srcset="https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=480&h=436 480w, https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=150&h=136 150w, https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg?w=300&h=273 300w, https://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg 616w"
sizes="(max-width: 480px) 100vw, 480px"}](http://svpow.files.wordpress.com/2009/12/alamosaurus-cotyle-section.jpg)

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](http://svpow.wordpress.com/2009/10/27/finite-element-analysis-of-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](http://svpow.wordpress.com/2009/11/18/ct-scanning-the-archbishop/#comment-5335)
on [a previous
post](http://svpow.wordpress.com/2009/11/18/ct-scanning-the-archbishop/).
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](http://openpaleo.blogspot.com/search/label/Paleo%20Paper%20Challenge).
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**

- Cubo, J., and Casinos, A. 2000. Incidence and mechanical significance
  of pneumatization in the long bones of birds. Zoological Journal of
  the Linnean Society 130: 499--510.
- Currey, J. D., and Alexander, R. McN. 1985. The thickness of the walls
  of tubular bones. Journal of Zoology 206:453--468.
- Schwarz D, and Fritsch G. 2006. Pneumatic structures in the cervical
  vertebrae of the Late Jurassic Tendaguru sauropods *Brachiosaurus*
  *brancai* and *Dicraeosaurus*. Eclogae Geologicae Helvetiae 99:65--78.
- Schwarz-Wings, D., Meyer, C.A., Frey, E., Manz-Steiner, H.-R., and
  Schumacher, R. 2009. Mechanical implications of pneumatic neck
  vertebrae in sauropod dinosaurs. Proceedings of the Royal Society B.
  doi: 10.1098/rspb.2009.1275
- [Wedel, Mathew J.  2005.  Postcranial skeletal pneumaticity in
  sauropods and its implications for mass estimates.  pp. 201-228 in
  Wilson, J. A., and Curry-Rogers, K. (eds.), The Sauropods: Evolution
  and Paleobiology.  University of California Press,
  Berkeley.](http://sauroposeidon.files.wordpress.com/2010/04/wedel-2005-mass-estimates.pdf)
- Woodward, H.N.,  and Lehman, T.M. 2009. Bone histology and
  microanatomy of *Alamosaurus sanjuanensis* (Sauropoda: Titanosauria)
  from the Maastrichtian of Big Bend National Park, Texas. Journal of
  Vertebrate Paleontology 29(3):807-821.


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).

ASPs for Alamosaurus

Weren't we [just
discussing](http://svpow.wordpress.com/2009/06/16/yet-more-uninformed-noodling-on-the-future-of-scientific-publishing-and-that-kind-of-thing/#comment-3206)
the problem of keeping up with all the good stuff on da intert00bz? The
other day Rebecca Hunt-Foster, a.k.a.
[Dinochick](http://paleochick.blogspot.com/), posted a "[mystery
photo](http://paleochick.blogspot.com/2009/07/concretionary-fun.html)"
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](https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=480&h=318 "IMG_7857"){.aligncenter
.size-full .wp-image-1904 loading="lazy" attachment-id="1904"
permalink="http://svpow.com/2009/07/20/asp-target-of-opportunity/img_7857/"
orig-file="https://svpow.files.wordpress.com/2009/07/img_7857.jpg"
orig-size="1600,1062" comments-opened="1"
image-meta="{\"aperture\":\"3.5\",\"credit\":\"\",\"camera\":\"Canon EOS DIGITAL REBEL\",\"caption\":\"\",\"created_timestamp\":\"1246988475\",\"copyright\":\"\",\"focal_length\":\"22\",\"iso\":\"400\",\"shutter_speed\":\"0.05\",\"title\":\"\"}"
image-title="IMG_7857" image-description="" image-caption=""
medium-file="https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=300"
large-file="https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=1024"
width="480" height="318"
srcset="https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=480&h=318 480w, https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=958&h=636 958w, https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=150&h=100 150w, https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=300&h=199 300w, https://svpow.files.wordpress.com/2009/07/img_7857.jpg?w=768&h=510 768w"
sizes="(max-width: 480px) 100vw, 480px"}](http://svpow.files.wordpress.com/2009/07/img_7857.jpg)

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](https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg?w=437&h=510 "camarasaurus-internal-structure"){.aligncenter
.size-full .wp-image-1905 loading="lazy" attachment-id="1905"
permalink="http://svpow.com/2009/07/20/asp-target-of-opportunity/camarasaurus-internal-structure/"
orig-file="https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg"
orig-size="437,510" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="camarasaurus-internal-structure" image-description=""
image-caption=""
medium-file="https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg?w=257"
large-file="https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg?w=437"
width="437" height="510"
srcset="https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg 437w, https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg?w=129&h=150 129w, https://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg?w=257&h=300 257w"
sizes="(max-width: 437px) 100vw, 437px"}](http://svpow.files.wordpress.com/2009/07/camarasaurus-internal-structure.jpg)(You
may remember [this
image](http://svpow.wordpress.com/2007/11/17/xenoposeidon-week-day-3-the-basic-beast-inside/)
from *Xenoposeidon* week--almost two years ago now!)

Naturally as soon as I saw ReBecca's shard of excellence, I wondered
about its
[ASP](http://svpow.wordpress.com/2009/07/18/nh-46870-strikes-back/), so
after a bit of [GIMPing](http://www.gimp.org/), voila:

[![IMG_7857
ASP](https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=480&h=318 "IMG_7857 ASP"){.aligncenter
.size-full .wp-image-1906 loading="lazy" attachment-id="1906"
permalink="http://svpow.com/2009/07/20/asp-target-of-opportunity/img_7857-asp/"
orig-file="https://svpow.files.wordpress.com/2009/07/img_7857-asp.png"
orig-size="1600,1062" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="IMG_7857 ASP" image-description="" image-caption=""
medium-file="https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=300"
large-file="https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=1024"
width="480" height="318"
srcset="https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=480&h=318 480w, https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=958&h=636 958w, https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=150&h=100 150w, https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=300&h=199 300w, https://svpow.files.wordpress.com/2009/07/img_7857-asp.png?w=768&h=510 768w"
sizes="(max-width: 480px) 100vw, 480px"}](http://svpow.files.wordpress.com/2009/07/img_7857-asp.png)

[As
usual](http://svpow.wordpress.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/),
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](http://svpow.wordpress.com/2008/09/23/theres-almost-nothing-but-nothing-there-sauroposeidon-edition-complete/),
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](http://paleochick.blogspot.com/).

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


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.

ASP target of opportunity

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.

NHM 46870 Strikes Back: ASP

University of Portsmouth

Mike Taylor

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:

::: {#attachment_355 .wp-caption .alignnone shortcode="caption" style="width: 510px"}
[![Fig. 1. Sushi plate, poorly preserved due to
predation](https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg?w=500&h=500){.size-full
.wp-image-355 aria-describedby="caption-attachment-355" loading="lazy"
attachment-id="355"
permalink="http://svpow.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/plate-500px/"
orig-file="https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg"
orig-size="500,500" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="Sushi plate, poorly preserved due to predation"
image-description=""
image-caption="Sushi plate, poorly preserved due to predation
"
medium-file="https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg?w=300"
large-file="https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg?w=500"
width="500" height="500"
srcset="https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg 500w, https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg?w=150&h=150 150w, https://svpow.files.wordpress.com/2008/08/plate-500px.jpeg?w=300&h=300 300w"
sizes="(max-width: 500px) 100vw, 500px"}](http://svpow.files.wordpress.com/2008/08/plate.jpeg)

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:

::: {#attachment_356 .wp-caption .alignnone shortcode="caption" style="width: 510px"}
[![av, avocado; cs, crab-stick; pf, pneumatic foramen; pr,
prawn.](https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg?w=500&h=250){.size-full
.wp-image-356 aria-describedby="caption-attachment-356" loading="lazy"
attachment-id="356"
permalink="http://svpow.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/drawing-500px/"
orig-file="https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg"
orig-size="500,250" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="drawing-500px" image-description=""
image-caption="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.
"
medium-file="https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg?w=300"
large-file="https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg?w=500"
width="500" height="250"
srcset="https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg 500w, https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg?w=150&h=75 150w, https://svpow.files.wordpress.com/2008/08/drawing-500px.jpeg?w=300&h=150 300w"
sizes="(max-width: 500px) 100vw, 500px"}](http://svpow.files.wordpress.com/2008/08/drawing.jpeg)

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)](https://svpow.files.wordpress.com/2008/08/howto-500px.jpeg){.alignnone
.size-full .wp-image-364 attachment-id="364"
permalink="http://svpow.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/howto-500px/"
orig-file="https://svpow.files.wordpress.com/2008/08/howto-500px.jpeg"
orig-size="" comments-opened="1" image-meta="[]"
image-title="howto-500px" image-description=""
image-caption="Fig. 3. From Wedel (2005:fig. 7.5)
"
medium-file="https://svpow.files.wordpress.com/2008/08/howto-500px.jpeg?w=300"
large-file="https://svpow.files.wordpress.com/2008/08/howto-500px.jpeg?w=1024"}](http://svpow.files.wordpress.com/2008/08/howto.jpeg)

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

::: {#attachment_358 .wp-caption .alignnone shortcode="caption" style="width: 510px"}
[![Fig. 4. Spring-onion California roll depicted in figure 2, with solid
material drawn in black and pneumatic space in
white.](https://svpow.files.wordpress.com/2008/08/asp-500px.png?w=500&h=500){.size-full
.wp-image-358 aria-describedby="caption-attachment-358" loading="lazy"
attachment-id="358"
permalink="http://svpow.com/2008/08/12/air-space-proportion-in-pneumatic-sushi/asp-500px/"
orig-file="https://svpow.files.wordpress.com/2008/08/asp-500px.png"
orig-size="500,500" comments-opened="1"
image-meta="{\"aperture\":\"0\",\"credit\":\"\",\"camera\":\"\",\"caption\":\"\",\"created_timestamp\":\"0\",\"copyright\":\"\",\"focal_length\":\"0\",\"iso\":\"0\",\"shutter_speed\":\"0\",\"title\":\"\"}"
image-title="asp-500px" image-description=""
image-caption="Fig. 3. Sushi roll depicted in figure 2, with solid material drawn in black and pneumatic space in white.
"
medium-file="https://svpow.files.wordpress.com/2008/08/asp-500px.png?w=300"
large-file="https://svpow.files.wordpress.com/2008/08/asp-500px.png?w=500"
width="500" height="500"
srcset="https://svpow.files.wordpress.com/2008/08/asp-500px.png 500w, https://svpow.files.wordpress.com/2008/08/asp-500px.png?w=150&h=150 150w, https://svpow.files.wordpress.com/2008/08/asp-500px.png?w=300&h=300 300w"
sizes="(max-width: 500px) 100vw, 500px"}](http://svpow.files.wordpress.com/2008/08/asp.png)

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

- [Wedel, Mathew J.  2005.  Postcranial skeletal pneumaticity in
 sauropods and its implications for mass estimates.  pp. 201-228 in
 Wilson, J. A., and Curry-Rogers, K. (eds.), The Sauropods: Evolution
 and Paleobiology.  University of California Press,
 Berkeley](http://sauroposeidon.net/Wedel_2005_pneumaticity-plus-table-and-figs.pdf).

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.

Postagens de Rogue Scholar

Free papers you should read: Martin and Palmer (2014) on ASPs of pterosaur wing bones

Tutorial 24: variables for tubular bones, ASP, MSP, and bone density

ASPs for Alamosaurus

ASP target of opportunity

NHM 46870 Strikes Back: ASP

Tutorial 6: Air-space proportion in pneumatic sushi