## Tutorial 21: how to measure the length of a centrum

### March 11, 2013

For a paper that I and Matt are preparing, we needed to measure the centrum length of a bunch of turkey cervicals. That turns out to be harder than you’d think, because of the curious negative curvature of the articular surfaces.

Above is a C7 from a turkey: anterior view on the left; dorsal, left lateral and ventral views in the middle row; and posterior on the right. As you can see from the anterior, dorsal and ventral views, the anterior articular surface[1] is convex dorsoventrally  but concave transversely; and as you can see from the lateral view, the posterior face is concave dorsoventrally and convex transversely.

This means you can’t just put calipers around the vertebra. If you approach the vertebra from the top or bottom, then the upper or lower lip of the posterior articular surface will protrude past the centre of the saddle, and give you too long a length. If you approach from the side, the same will happen with the left and right lips of the anterior articular surface.

# What are we trying to measure anyway?

But this raises the question of what it is we’re trying to measure. I said “we needed to measure the centrum length of a bunch of turkey cervicals”, but what exactly is centrum length? Why shouldn’t the upper and lower lips of the posterior articular surface count towards it?

What does centrum length mean?

The problem doesn’t only arise with bird cervicals. The same issue arises in measuring more sensible and elegant vertebrae, such as our old friend HMN SII:C8, or MB.R.2181:C8 as we must now learn to call it.

Although the back of the vertebra is nice and simple here — it’s obvious what line we’re measuring to at the back — we have three choices of where the “front” of the vertebra is, and a case can be made for any of them as being “the length of the vertebra”.

The longest measurement (here marked “T” for “total length”) goes to the front of the prezygapophyseal rami. The next one (“C” for “centrum length”) goes to the anteriormost point of the condyle. The distinction is important: as noted recently, the longest vertebra in the world belongs to Sauroposeidon if we use total length, but to Supersaurus if we use centrum length.

But in life, most of the condyle would be buried in the cotyle of the preceding vertebra. So should it count towards the length of the vertebra? If you consider a string of articulated vertebrae, the buried condyles don’t contribute to the overall length of the neck. So Matt and I call the length from the posterior margin of the condyle to the posterior margin of the cotyle the functional length (marked “F” above), which I believe is a new term.

Another way to think of the functional length is the distance from a given point on a vertebra (in this case the posterior margin of the cotyle) to the same point on the adjacent vertebra:

For our current project, Matt and I are interested in how the lengths of individual vertebrae contribute to total neck length, so for our purposes, functional length is definitely what we want.

By the way, Janensch is the only author I know of to have even recognised the importance of functional length. The measurement tables on pages 39 and 44 have columns for “Gesamtlänge des Wirbels ab Vorderende per Präzygapophyse”, “Gesamtlänge der Wirbel-Körpers in 1/2 Höhe” and “Länge der Wirbel-körpers ohne Condylus in 1/2 Höhe” — that is, “Total length of the vertebra from the anterior end of the prezygapophysis”, “Total length of the centrum measured at mid-height” and “Length of the centrum minus condyle at mid-height”. This is typical of his careful and methodical approach. Kudos!

# Hey! I thought this was about turkeys

And so it is. Here is the functional length measurement for a turkey cervical:

It’s the shortest anteroposterior distance between the two articular surfaces.

# Measuring functional length

Matt and I chatted about this at some length, and I am ashamed to say that we thought through all sorts of complicated solution involving subtracting measurements from known scaffold length and suchlike.

It took us a stupidly long to to arrive at the very obvious solution, which is just to modify the calipers to have a “tooth” that can protrude into the concavity of the anterior articulation between its left and right lips. Easily done with a flat-ended screw and a blob of wood glue:

With the measurements of all the vertebrae in my series, I can now fairly confidently expect that the sum of the individual lengths will come out at about the length of the complete neck.

You know, unless intervertebral cartilage turns out to be important or something.

# References

• Janensch, Werner. 1950. Die Wirbelsaule von Brachiosaurus brancai. Palaeontographica (Suppl. 7) 3:27-93.

# Footnotes

1. Matt and I are so used to opisthocoelous sauropod presacrals that when we’re talking about vertebrae — any vertebrae — we tend to say “condyle” and “cotyle” for the anterior and posterior articular surfaces, no matter what their morphology. When talking about crocodile cervicals or titanosaur caudals, we’re even likely to say ridiculous things like “the condyle is concave and the cotyle is convex”. Nonsense, of course: condyle means “A rounded prominence at the end of a bone, most often for articulation with another bone.” What we should say is “the condyle is at the back and the cotyle is in front”.

### 17 Responses to “Tutorial 21: how to measure the length of a centrum”

1. My first concern is always: Is the measurement meaningful?

2. Mike Taylor Says:

3. Y’know, I figured you’d “get” what is meant about “meaningful” when discussing measurements. We’ve3 had this conversation, you can’t have missed my own blog posts on making meaningful measurements, as I’ve posted them here in respose to previous discussions before.

What use is centrum length as a measurement? What is the point of that particular point on the centrum to that other point? If there is none, then there is no point to worry about whether measurement is “C” or “F”, above.

4. Matt Wedel Says:

If you have some way of measuring the length of a neck based on bones that does not involve adding up the lengths of the individual centra, we’re all ears.

5. Matt Wedel Says:

So Matt and I call the length from the posterior margin of the condyle to the posterior margin of the cotyle the functional length (marked “F” above), which I believe is a new term.

I’m sure people have derived it independently before I did–it’s a pretty intuitive concept–but I discussed it and used it a lot in the fourth chapter of my dissertation.

By the way, Janensch is the only author I know of to have even recognised the importance of functional length.

Other authors have recognized it. McIntosh frequently lists the length of the centrum “minus the anterior ball” (= “ohne condylus”), for example in his Barosaurus paper. I know that other examples exist, I just can’t name them off the top of my head.

6. Dean Says:

That sneaky articular cartilage…right when you least suspect it! :)

7. Nathan Myers Says:

Ending with a cliffhanger: your sign of quality bloggerature. Join us next week when we add up the functional lengths of all our vertebrae, and again at some indefinite time in the future for the Series Finale when we reveal the length including all that tiresome soft tissue, and compare it to our painstaking summation!

A taphonomic question: when two or more spodverts* are found miraculously articulated, is there generally a reason to distrust their relative positions? Such reasons might include there being no gap at all, or widely varying gaps in different specimens or between verts in a single specimen.

An anatomical question: what do saddle-shaped central faces suggest about differences between what a turkey does with its neck vs. something with a simple ball-and-socket? Are there other biggish birds that sport the latter?

* Feel free to use this term without attribution in refereed publications.

8. Matt Wedel Says:

A taphonomic question: when two or more spodverts* are found miraculously articulated, is there generally a reason to distrust their relative positions? Such reasons might include there being no gap at all, or widely varying gaps in different specimens or between verts in a single specimen.

That’s a good question. We do have quite a few articulated sauropod necks, and many of them seem to show little or no space between the vertebrae.

I say “seem to show” because without cutting them up, radiologically or otherwise, it’s hard to tell what’s going on between condyle and cotyle. In the best-preserved material that I have worked with, the condyle is often somewhat bell-shaped, so that if fitted into a hemispherical or ellipsoidal cotyle, the edges (rims) might be in contact but there could still be one-to-a-few millimeters of space between the articular surfaces.

So here’s another project for someone who needs one: get a sauropod cervical series that is more or less complete but where the vertebrae are preserved as separate elements (i.e., not like the Sauroposeidon proteles or Mamenchisaurus hochuanensis holotypes)–Apatosaurus CM 555 would be just perfect. Using some kind of 3D digitizing technology–point digitizer, laser surface scan, CT, whatever–capture the shapes of the condyles and cotyles and see how closely the former match the latter, and how tightly they can be articulated. My guess is that the cotyles are enough bigger than the condyles to imply a decent thickness of cartilage, but I don’t know just how thick.

An anatomical question: what do saddle-shaped central faces suggest about differences between what a turkey does with its neck vs. something with a simple ball-and-socket? Are there other biggish birds that sport the latter?

All extant birds have saddle-shaped articulations in their cervical series, and kinda-saddle-shaped-grading-to-flat in their dorsals. The advantages of a saddle over a ball-and-socket, if any, are not immediately apparent to me. One would think that a saddle would bias the joint toward up-down and side-to-side motions, whereas a ball-and-socket should go as evenly in all directions, but when I have played with articulated bird necks I have not noticed any restrictions on twisting motions. My suspicion is that the zygapophyses are more important for controlling intervertebral motions than the shape of the articular surfaces on the centrum, and that saddles and sockets are both perfectly cromulent ways to skin that particular cat. But that’s just a guess. If someone knows more, please speak up!

9. Mark Robinson Says:

One would think that a saddle would bias the joint toward up-down and side-to-side motions, whereas a ball-and-socket should go as evenly in all directions,…

Matt, intuitively you might think that and certainly each dimension of curvature of the saddle-joint is pretty much restricted to a single plane of motion but, as you noticed when playing with bird necks, they can be employed in concert to allow a much fuller range. (Dodgy analogy warning) a bit like how, in theory at least, you can draw a circle with an Etch-A-Sketch even though each knob only controls movement of the drawing tool in one axis.

I think the advantage of a saddle-joint is that it permits much greater extremes of overall curvature whilst keeping the total length of the neck within acceptable limits – length as measured by an imaginary piece of string threaded thru the centre of each vert. I assume that this helps to prevent birds from snapping their own spinal cords when subjecting their necks to some of the extreme curvature that we see them regularly do.

I’d be interested in knowing when heterocoelous cervical articulation appeared on the croc to bird journey, and whether it was a singular occurrence or whether it arose in several clades independently. Come to think of it, what’s the mapping of cervical articulation type across sauropods look like?

One other difference between the articulation types is that a ball-and-socket joint permits torsion – the rotation of individual elements about their shared axis (the equivalent of us turning our heads left and right). This would obviously be restricted by cervical ribs and soft tissue but what it might mean (if anything) for sauropods, I don’t know.

10. Mike Taylor Says:

The cervical articulations in all sauropods are of the ball-and-socket type.

Excellent point that the saddle-shaped articulations of birds prevent twisting.

11. John Scanlon, FCD Says:

As far as I know, I was the first to use a rim-to-rim measurement for centrum length in snakes, for the same intuitive reasons you mention (not that much of my morphometric stuff has come out). Sticking a ‘tooth’ onto a caliper is something I never thought of, and very nifty; though I always measured a lot of other things per vertebra, and it would have got in the way for most of them. Also, it would be harder to do a centre-to-centre measurement by optical micrometer, which I had to use on the tiniest bones, while rim-to-rim was fine.

12. Matt wrote:

If you have some way of measuring the length of a neck based on bones that does not involve adding up the lengths of the individual centra, we’re all ears.

I don’t have a specific method, but I think taking a “classic” standard at face when there are ways to potentially test its efficacy is faulty methodology, as is the process of using the minimum length inside the posterior cup to anterior ball, when this measure cannot be measured without handling and personal examination (or CT, and that’s difficult for large specimens).

My concern is that a methodology should be used which incorporates some morphometric information, concern about the relative thickness of cartilage caps on centra articulations, synovial pads between articulations (which can vary in thickness), size variation along the series, relation to mass, relation to length of vertebra, relation to phylogeny, relation to posture, etc.

I personally have this silly notion that, despite birds close phyletic distance to sauropods, crocs should be involved: while crocs have short necks, they are also ball-in-socket central joints, opposing the long necks but saddle-shaped central joints. Turtles aren’t used as analogues, despite long necks, relatively massive heads in some species, and ball-in-socket central joints. And it goes on.

I am a biomechanist at heart: I look at things on a morphometric level, want to see things determined through mechanical analysis, not merely what amounts to copy-pasting of bird-like morphology onto birds as is often done by scientists for theropods. Sauropods are not birds, as you surely know: certainly, this should allow you to realize that not all structures of the neck (including spinal bifidy) are easily interpretable … one must look to other sources of data when even the strictest bracket of the EPB (Archosauria) fail to provide data.

So the answer is: realize that mere centrum-length stacking and “margin of error for cartilage” is not enough, not good enough, and find a better way. Make a point of looking for better estimates for computing neck length reliably, as is being done for calculating body mass from single bones (femur, tibia, scapula, humerus, forelimb, linear vs circumferential vs. combination).

13. Matt Wedel Says:

Dude, what do you think we’re doing? All of this is FOR a project on how cartilage thickness affects neck length. And yes, we’re including a croc (you may remember it from this post), and a horse (this post), and as much other comparative data as possible. But surely you can see that if we want to know how much cartilage affects neck length, we need to know something about the length of the neck sans cartilage. Hence the need to measure the individual vertebrae. Hence this post.

I think taking a “classic” standard at face when there are ways to potentially test its efficacy is faulty methodology,

I have no idea what you’re talking about here. What is the classic standard, how are we taking it at face, and how should we be testing its efficacy that we’re not already? Please pay special attention to that last clause in that last sentence: if we’ve said that we’re going to do something stupid, feel free to set us straight, but don’t just assume that we’re going to do things the stupid way, as you did when you assumed that weren’t looking at anything but birds for this project, which is bigger in scope than this post. It’s not something we’ve been secretive about.

14. Mike Taylor Says:

Jaime, I can only assume from this comment that you’ve not read my and Matt’s last paper, which is freely available on PeerJ and discusses just these issues at length.

15. Matt, I’ve played with swan necks some, and the saddle does restrict torsion in them in my experience.

16. Mike Taylor writes:

Jaime, I can only assume from this comment that you’ve not read my and Matt’s last paper, which is freely available on PeerJ and discusses just these issues at length.

Yes, you discussed SOME of these issues. You did not discuss all of them, nor did you discuss any of them as a morphometric excercise. Problematically, some of your sources on these subjects are not necessarily available (e.g., in your perspective on intervertebral cartilage, you cite a study, Cobley’s, which is a thesis!). You must understand the irony of being driven to OA, publishing in an OA journal, and citing something that is barely, or not even, published! In others, the primary method you institute for neck length estimation is precisely the stand-by, summing lengths of centra, without recourse to evaluating methodlogy of length measurement, a subject I mention above, elsewhere, and whenever possible. Other soft-tissue elements, such as “discs” between centra, are not brought up at all. Morphometric perspectives are entirely absent; instead, you look at estimates of neck length in relation to perticular cervical lengths, or against total series length … and … that’s mostly it. That the paper makes a biomechanical claim (sauropods are lighter for their size, pneumatic, with greater numbers of verts and tinier heads, thus out-surpassing mammals with huge noggins) but makes no effort to cross-corellate these standards, simply relying on work of others (on mammals and birds, no less; your citations for this work involves either mammals, or birds, with a reference — Wedel and Sanders — to applying this work to sauropods, a work that still needs to substantiate claims given biomechanical loading and infrastructural analysis that HASN’T BEEN DONE for sauropod necks.

The claim I make is NOT that YOUR work is insufficient (all publications are insufficient for Science, it’s not a bar you can reach) but that to talk abotu claims of correct measurement, biomechanically or meaningful measurments, one must place those bones and necks into biomechanical perspectives. That means morphometrics. I was talking about this not a few of your posts ago when estimating musculature of the neck to help compute relative mass along the neck, a subject that almost certainly has to be done on a per-vertebra basis. It seems to me there is an attempt to short-cut this necessity in order to make potentially easier estimates and comparisons of estimates.

17. Mike Taylor Says:

Jaime, do you have any idea how close your comments approach outright trolling? I flatly reject your stupid, spurious elitist attitude to Matt Cobley’s perfectly good thesis, which is freely available on arXiv and part of the scientific record. I am too angry about that to even read, let along reply to, the rest of your comment.

Get yourself in gear, or go and comment on a different blog.