WOW! I knew I was dragging a bit on getting around to this vertebral orientation problem, but I didn’t realize a whole month had passed. Yikes. Thanks to everyone who has commented so far, and thanks to Mike for getting the ball rolling on this. Previous posts in this series are here and here.

First up, this may seem like a pointlessly picky thing to even worry about. Can’t we just orient the vertebrae in whichever way feels the most natural, or is easiest? Do we have to think about this?

The alarmingly 3D pelvis of the mounted brontosaur at the AMNH. Note that sauropod pubes are usually illustrated lying flat, so what usually passes for ‘lateral’ view would be roughly from the point of view of the animal’s knee.

I think we do. For sauropods, vertebrae are usually oriented for illustration purposes in one of two ways. The first is however they sit most easily on their pallets. This is similar to the problem Mike and I found for ‘lateral’ views of sauropod pelvic elements when were on our AMNH/Yale trip in 2012. In an articulated skeleton, the pubes and ischia usually lean inward by 30-45 degrees from their articulations with the ilia, so they can meet on the midline, but when people illustrate the “lateral view” of a sauropod pubis or ischium, it’s often the ventro-lateral aspect that is face-up when the element is lying on a shelf or a pallet. Photographic lateral does not equal biological lateral for those elements. Similarly, if I’m trying to answer biological questions about vertebrae (see below), I need to know something about their orientation in the body, not just how they sit comfortably on a pallet.

The other way that vertebrae are commonly oriented is according to what we might call the “visual long axis” of the centrum—so for example, dorsoventrally tall but craniocaudally short proximal caudals get oriented with the centrum ‘upright’, whereas dorsoventrally short but craniocaudally long distal caudals get oriented with the centrum ‘horizontal’, even if they’re in the same tail and doing so makes the neural canals or articular faces be oriented inconsistently down the column. (I’m not going to name names, because it seems mean to pick on people for something I just started thinking about myself, but if you go plow through a bunch of sauropod descriptions, you’ll see what I’m talking about.)

Are there biological questions where this matters? You bet! There are some questions that we can’t answer unless we have the vertebrae correctly oriented first. One that comes to mind is measuring the cross-sectional area of the neural canal, which Emily Giffin did a lot of back in the 90s. Especially for the Snowmass Haplocanthosaurus, what counts as the cross-sectional area of the neural canal depends on whether we are looking at the verts orthogonal to their articular faces, or in alignment with the course of the canal. I think the latter is pretty obviously the way to go if we are measuring the cross-sectional area of the canal to try and infer the diameter of the spinal cord—we’d want to see the canal the same way the cord ‘sees’ it as it passes through—but it’s less obvious if we’re measuring, say, the surface area of the articular face of the vertebra to figure out, say, cartilage stress. It doesn’t seem unreasonable to me that we might want to define a ‘neural axis’ for dealing with spinal-cord-related questions, and a ‘biomechanical axis’ for dealing with articulation-related questions.

Caudal 3 of the Snowmass Haplocanthosaurus, hemisected 3D model.

With all that in mind, here are some points.

To me, asking “how do we know if a vertebra is horizontal” is an odd phrasing of the problem, because “horizontal” doesn’t have any biological meaning. I think it makes more sense to couch the question as, “how do we define cranial and caudal for a vertebra?” Normally both the articular surfaces and the neural canal are “aimed” head- and tail-wards, so the question doesn’t come up. Our question is, how do we deal with vertebrae for which the articular surfaces and neural canal give different answers?

For example. Varanus komodoensis caudal.

(And by the way, I’m totally fine using “anterior” and “posterior” for quadrupedal animals like sauropods. I don’t think it causes any confusion, any more than people are confused by “superior” and “inferior” for human vertebrae. But precisely because we’re angling for a universal solution here, I think using “cranial” and “caudal” makes the most sense, just this once. That said, when I made the image above, I used anterior and posterior, and I’m too lazy now to change it.)

I think if we couch the question as “how do we define cranial and caudal”, it sets up a different set of possible answers than Mike proposed in the first post in this series: (1) define cranial and caudal according to the neural canal, and then describe the articular surfaces as inclined or tilted relative to that axis; (2) vice versa—realizing that using the articular surfaces to define the anatomical directions may admit a range of possible solutions, which might resurrect some of the array of possible methods from our first-draft abstract; (3) define cranial and caudal along the long axis of the centrum, which is potentially different from either of the above; (4) we can imagine a range of other possibilities, like “use the zygs” or “make the transverse processes horizontal” (both of which are subsets of Mike’s method C) but I don’t think most of those other possibilities are sufficiently compelling to be worthy of lengthy discussion.

IF we accept “neural canal”, “articular surfaces”, and “centrum long axis” as our strongest contenders, I think it makes most sense to go with the neural canal, for several reasons:

  • In a causative sense, the neural tube/spinal cord does define the cranial/caudal axis for the developing skeleton. EDIT: Actually, that’s a bit backwards. It’s the notochord, which is later replaced by the vertebral column, that induces the formation of the brain and spinal cord from the neural plate. But it’s still true that the vertebrae form around the spinal cord, so it’s not wrong to talk about the spinal cord as a defining bit of soft tissue for the developing vertebrae to accommodate.
  • The neural canal works equally well for isolated vertebrae and for articulated series. Regardless of how the vertebral column is oriented in life, the neural canal is relatively smooth—it may bend, but it doesn’t kink. So if we line up a series of vertebrae so that their neural canals are aligned, we’re probably pretty close to the actual alignment in life, even before we look at the articular surfaces or zygs.
  • The articulated tails of Opisthocoelicaudia and big varanids show that sometimes the articular surfaces simply are tilted to anything that we might reasonably consider to be the cranio-caudal axis or long axis of the vertebra. In those cases, the articular surfaces aren’t orthogonal to horizontal OR to cranio-caudal. So I think articular surfaces are ruled out because they break down in the kinds of edge cases that led us to ask the question in the first places.

Opistocoelicaudia caudals 6-8, stereopair, Borsuk-Bialynicka (1977:plate 5).

“Orient vertebrae, isolated or in series, so that their neural canals define the cranio-caudal axis” may seem like kind of a ‘duh’ conclusion (if you accept that it’s correct; you may not!), but as discussed up top, often vertebrae from a single individual are oriented inconsistently in descriptive works, and orientation does actually matter for answering some kinds of questions. So regardless of which conclusion we settle on, there is a need to sort out this problem.

That’s where I’m at with my thinking. A lot of this has been percolating in my hindbrain over the last few weeks—I figured out most of this while I was writing this very post. Is it compelling? Am I talking nonsense? Let me know in the comments.

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I am still building up to a big post on vertebral orientation, but in the meantime, check out this caudal vertebra of a Komodo dragon, Varanus komodoensis. This is right lateral view–the vert is strongly procoelous, and the articular ends of the centrum are really tilted relative to the long axis. I find this encouraging, for two reasons. First, it helped me clarify my thinking on how we ought to orient vertebrae, which Mike wrote about here and here. And second, it gives me some hope, because if we can figure out why tilting your articular surfaces makes functional sense in extant critters like monitors, maybe we can apply those lessons to sauropods and other extinct animals.

This is LACM Herpetology specimen 121971. Many thanks again to Neftali Camacho for access and assistance, and to Jessie Atterholt for basically doing all the other jobs while I was faffing about with this Komodo dragon.

Left lateral view

Have we ever posted decent photos of the Brachiosaurus altithorax caudals? Has anyone? I can’t remember either thing ever happening. When I need images of brachiosaur bits, including caudals, I usually go to Taylor (2009).

Taylor (2009: fig. 3)

Which is silly, not because Mike’s diagrams compiling old illustrations aren’t good – they definitely are – but because I’m sitting on a war chest of decent photos of the actual material. I am home sick with a sore throat today, and I can’t be arsed to (1) follow up on the “Down in Flames” post, (2) add anything thoughtful to the vertebral orientation discussion, or (3) crop or color-adjust these photos. You’re getting them just as they came out of my camera, from my trip to the Field Museum in 2012.

Here are the rest of the orthogonal views:

Right lateral view

 

Anterior view

 

Posterior view

 

Dorsal view of caudal 1

 

Dorsal view of caudal 2

And here’s a virtual walkaround using a series of oblique shots. Making a set like this is part of my standard practice now for important specimens during museum visits.

 

 

 

 

 

 

 

Now, I said up top that I wasn’t going to add anything thoughtful to the vertebral orientation discussion. I have thoughts on that, but I’m tired and hopped up on cold medicine and now ain’t the time. In lieu of blather, here are a couple of relevant photos.

 

I wanted to capture for my future self the pronounced non-orthogonality of the neural canal and centrum, so I rolled up a piece of paper and stuck it through the neural canal. I haven’t run the numbers, but in terms of “angle of the articular faces away from the neural canal”, these verts look like they’re right up there with my beloved Snowmass Haplocanthosaurus.

More on that next time, I reckon. In the meantime, all these photos are yours now (CC-BY, like everything on this site [that someone else hasn’t asserted copyright over]). Go have fun.

Reference

Thanks to everyone who’s engaged with yesterday’s apparently trivial question: what does it mean for a vertebra to be “horizontal”? I know Matt has plenty of thoughts to share on this, but before he does I want to clear up a couple of things.

This is not about life posture

First, and I really should have led with this: the present question has nothing to do with life posture. For example, Anna Krahl wrote on Twitter:

I personally find it more comprehensible if the measurements relate to something like eg. the body posture. This is due to my momentary biomech./functional work, where bone orientation somet is difficult to define.

I’m sympathetic to that, but we really need to avoid conflating two quite different issues here.

Taylor, Wedel and Naish (2009), Figure 1. Cape hare Lepus capensis RAM R2 in right lateral view, illustrating maximally extended pose and ONP: skull, cervical vertebrae 1-7 and dorsal vertebrae 1-2. Note the very weak dorsal deflection of the base of the neck in ONP, contrasting with the much stronger deflection illustrated in a live rabbit by Vidal et al. (1986: fig. 4). Scalebar 5 cm.

If there’s one thing we’ve learned in the last couple of decades, it’s that life posture for extinct animals is controversial — and that goes double for sauropod necks. Heck, even the neck posture of extant animals is terribly easy to misunderstand. We really can’t go changing what we mean by “horizontal” for a vertebra based on the currently prevalent hypothesis of habitual posture.

Also, note that the neck posture on the left of the image above is close to (but actually less extreme than) the habitual posture of rabbits and hares: and we certainly wouldn’t want to illustrate vertebrae as “horizontal” when they’re oriented directly upwards, or even slightly backwards!

Instead, we need to imagine the animal’s skeleton laid out with the whole vertebral column in a straight line — sort of like Ryder’s 1877 Camarasaurus, but with the tail also elevated to the same straight line.

Ryder’s 1877 reconstruction of Camarasaurus, the first ever made of any sauropod, modified from Osborn & Mook (1921, plate LXXXII).

Of course, life posture is more important, and more interesting, question than that of what constitutes “horizontal” for an individual vertebra — but it’s not the one we’re discussing right now.

In method C, both instances are identically oriented

I’m not sure how obvious this was, but I didn’t state it explicitly. In definition C (“same points at same height in consecutive vertebrae”), I wrote:

We use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level

What I didn’t say is that the two identical instances of the vertebrae have to be identically oriented. Here’s why this is important. Consider that giraffe C7 that we looked at last time, with its keystoned centrum. if you just “articulate them together as well as we can” without that restriction, you end up with something like this:

Which is clearly no good: there’s no way to orient that such that for any given point on one instance, the corresponding point on the other is level with it. What you need instead is something like this:

In this version, I’ve done the best job I can of articulating the two instances in the same attitude, and arranged them such that they are level with each other — so that the attitude shown here is “horizontal” in sense C.

As it happens, this is also just about horizontal in sense B — the floor of the neural canal is presumably at the same height as the top of the centrum as it meets the neural arch.

But “horizontal” in sense A (posterior articular surface vertical) fails horribly for this vertebra:

To me, this image alone is solid evidence that Method A is just not good enough. Whatever we mean by “horizontal”, it’s not what this image shows.

References

I was lucky enough to have Phil Mannion as one of the peer-reviewers for my recent paper (Taylor 2018) showing that Xenoposeidon is a rebbachisaurid. During that process, we got into a collegial disagreement about one of the autapomorphies that I proposed in the revised diagnosis: “Neural arch slopes anteriorly 30°–35° relative to the vertical”. (This same character was also in the original Xenoposeidon paper (Taylor and Naish 2007), in the slightly more assertive form “neural arch slopes anteriorly 35 degrees relative to the vertical”: the softening to “30°–35°” in the newer paper was one of the outcomes of the peer-review.)

The reason this is interesting is because the slope of the neural arch is measured relative to the vertical, which of course is 90˚ from the horizontal — but Phil’s comments (Mannion 2018) pushed me to ask myself for the first time: what actually is “horizontal”? We all assume we know horizontality when we see it, but what precisely do we mean by it?

Three notions of “horizontal”

The idiosyncratic best-preserved caudal vertebra of the Snowmass Haplocanthosaurus MWC 8028, illustrating three different versions of “horizontal”. A. horizontality defined by vertical orientation of the posterior articular surface. B. horizontality defined by horizontal orientation of the roof of the neural canal (in this case, rotated 24˚ clockwise relative to A). C. horizontality defined by optimal articulation of two instances of the vertebra, oriented such the a line joining the same point of both instances is horizontal (in this case, rotated 17˚ clockwise relative to A). Red lines indicate exact orthogonality according to the specified criteria. Green line indicate similar but diverging orientations: that of the not-quite-vertical anterior articular surface (A) and of the not-quite-horizontal base of the neural canal (B).

There are at least three candidate definitions, which we can see yield noticeably different orientations in the case of the Snowmass Haplocanthosaurus vertebra that Matt’s been playing with so much recently.

Definition A: articular surfaces vertical

In part A, I show maybe the simplest — or, at least, the one that is easiest to establish for most vertebrae. So long as you have a reasonably intact articular surface, just rotate the vertebra until that surface is vertical. If, as is often the case, the surface is not flat but concave or convex, then ensure the top and bottom of the surface are vertically aligned. This has the advantage of being easy to do — it’s what I did with Xenoposeidon — but it conceals complexities. Most obviously, what to do when the anterior and posterior articular surfaces are not parallel, in the 7th cervical vertebra of a giraffe?

Cervical vertebra 7 of Giraffa camelopardalis FMNH 34426, in left lateral view. Note that the centrum is heavily “keystoned” so that the anterior and posterior articular surfaces are 15-20˚ away from being parallel.

Another difficulty with this interpretation of horizontality is that it can make the neural canal jagged. Consider a sequence of vertebrae oriented as in part A, all at the same height: the neural canal would rise upwards along the length of each vertebra, before plunging down again on transitioning from the front of one to the back of the next. This is not something we would expect to see in a living animal: see for example the straight line of the neural canal in our hemisected horse head(*).

Definition B: neural canal horizontal

Which leads us to the second part of the illustration above. This time, the vertebra is oriented so that the roof of the neural canal is horizontal, which gives us a straight neural canal. Nice and simple, except …

Well, how do we define what’s horizontal for the neural canal? As the Haplocanthosaurus vertebra shows nicely, the canal is not always a nice, neat tube. In this vertebra, the floor is nowhere near straight, but dishes down deeply — which is why I used to the roof, rather than the floor of the canal. Rather arbitrary, I admit — especially as it’s often easier to locate the floor of the canal, as the dorsal margin is often confluent with fossae anteriorly, posteriorly or both.

And as we can see, it makes a difference which we choose. The green line in Part B of the illustration above shows the closest thing to “horizontal” as it would be defined by the ventral margin of the neural canal — a straight line ignoring the depression and joining the anteriormost and posteriormost parts of the base of the canal. As you can see, it’s at a significantly different angle from the red line — about 6.5˚ out.

And then you have human vertebrae, where the dorsal margin of the neural canal is so convex in lateral view that you really can’t say where the anteriormost or posteriormost point is.

Left sides of hemisected human thoracic vertebrae, medial view. Note how ill-defined the dorsal margin of the neural canal is.

So can we do better? Can we find a definition of “horizontal” that’s not dependent of over-interpreting a single part of the vertebra?

Definition C: same points at same height in consecutive vertebrae

I’ve come to prefer a definition of horizontal that uses the whole vertebra — partly in the hope that it’s less vulnerable to yielding a distorted result when the vertebra is damaged. With this approach, shown in part C of the illustration above, we use two identical instances of the vertebrae, articulate them together as well as we can, then so orient them that the two vertebrae are level — that a line drawn between any point on one vertebra and its corresponding point on the other is horizontal. We can define that attitude of the vertebra as being horizontal.

Note that, while we use two “copies” of the vertebra in this method, we are nevertheless determining the horizontality of a single vertebra in isolation: we don’t need a sequence of consecutive vertebrae to have been preserved, in fact it doesn’t help if we do have them.

One practical advantage of this definition is that its unambiguous as regards what part of the vertebra is used: all of it; or any point on it, at the measurement stage. By contrast, method A requires us to choose whether to use the anterior or posterior articular surface, and method B requires a choice of the roof or floor of the neural canal.

Discussion

I have three questions, and would welcome any thoughts:

  1. Which of these definitions do you prefer, and why?
  2. Can you think of any other definitions that I missed?
  3. Does anyone know of any previous attempts to formalise this? Is it a solved problem, and Matt and I somehow missed it?

Answers in the comments, please!

References

(*) Yes, of course we have a hemisected horse head. What do you think we are, savages?