What does it mean for a vertebra to be “horizontal”?

August 28, 2018

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). b 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 anterior 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?

Advertisements

10 Responses to “What does it mean for a vertebra to be “horizontal”?”

  1. Allen Hazen Says:

    I would think that the “articulate two copies of the same vertebra” would be likely to give bizarre results applied to something like the seventh cervical of the giraffe. After all, that vertebra is a sort-of “elbow” in the column, connecting series (dorsals and cervicals) that in life are likely to be oriented in different directions: the whole point of its key-stoned “design” is that it connects to very differently shaped vertebrae on its two sides.

    My gut instinct is that something like B is what, ideally, one would want to use — something that would be biologically significant in the living animal — but as you point out it is very hard to use (or even make precise), particularly if you don’t have an articulated series.

    Best practice, I guess, would be to include a definition of the sense of “horizontal” used in the supplemental information of any paper in which traits defined in terms of horizontality are used.


  2. Has to be “A” since that is the view you would figure. Your manuscript would refer to the slope as the viewer would see it figured.

  3. Matt Wedel Says:

    Ken, is that not begging the question? How do you know how to orient the vertebrae when putting together the figures? Mike could have titled the post, “How should we orient vertebrae when we figure them?” and all of the body of the post could remain unchanged, and us no closer to an answer (justified by anything other than fiat).

    In any case, tt’s not clear to me that the centrum ends automatically trump the neural canal – especially if the centrum ends aren’t parallel, as in the case of the giraffe C7. I mean, maybe the centrum method is better, but it would be nice to have some actual reasons.

  4. Andrea Cau Says:

    I usually assume the standard orientation as the long axis of the centrum (or the proximodistal direction along the centers of the articular facets in shortened vertebrae) to be oriented perpendicular to the direction of the gravity force vector.
    (I assume no paleontologists work in the International Space Station, so the Earth gravitational field is a natural setting share by all those reading the description of my vertebra and can use it as reference parameter).
    This is the reason in theropod osteology we consider the posterior cervical vertebrae as “titled” at articular facets of centrum and not, instead as “sloped” at zygapophyseal facets.


  5. Ah, but Matt, you sort of answered the question yourself. No one figures vertebrae as B or C, ergo A. The camel vert is a red herring because the sauropod example is anteroposteriorely short, not elongated. Your own publications show elongated cervicals as oriented with the axis through the length, so you know the answer to your own question.

    The question really is not how to illustrate a vertebra, but what criteria defines how to measure slope (although “inclined” is probably a better term). It really does not matter so long as it is defined: “midline axis of neural spine inclined 30 degrees vertical relative to plane of posterior centrum face.” Note that it really is necessary to define where the inclined axis is measured for replication.


  6. […] 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 […]

  7. Matt Wedel Says:

    Ah, but Matt, you sort of answered the question yourself. No one figures vertebrae as B or C, ergo A.

    That’s a courageous assertion, particularly in light of Borsuk-Bialynicka (1977: plate 5).

    The question really is not how to illustrate a vertebra, but what criteria defines how to measure slope (although “inclined” is probably a better term). It really does not matter so long as it is defined

    That’s only true if this is a trivial methodological problem. If there are real biological questions at stake, it does matter.

    In any case, I’m not the one arguing that we should define the orientation based on how things are illustrated!


  8. point taken on Borsuk-Bialynicka.


  9. […] now for me to dig into the interesting and important discussion on how we should orient vertebrae (here and here so far) – that will be coming soon. In the meantime, here’s something […]


  10. […] 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. […]


Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out /  Change )

Google+ photo

You are commenting using your Google+ account. Log Out /  Change )

Twitter picture

You are commenting using your Twitter account. Log Out /  Change )

Facebook photo

You are commenting using your Facebook account. Log Out /  Change )

Connecting to %s

This site uses Akismet to reduce spam. Learn how your comment data is processed.

%d bloggers like this: