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?

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Marten skull on top, opossum on bottom. Internal (medial) view of the right half of each skull.

These have been in my collection for ages, I just hadn’t gotten around to posting pictures. I don’t remember where I got them, but they were definitely purchased rather than collected. It’s funny, I remember the origin story of almost every bone and skull I’ve collected myself, but stuff I’ve bought tends to slide out of recollection.

I assume the marten is the American marten, Martes americana, but I haven’t keyed it out. The opossum is definitely Didelphis virginiana.

I think the opossum skull was already hemisected when it came to me – at least, I can’t find the other half. The marten I did myself, with a Dremel. In part because I wanted to compare the size and shape of the braincases. As you can see from the photos, the marten had a big wrinkly brain that left impressions on the inside of the skull, and these are visible externally through the thin walls of the braincase.

Now, I am an opossum fan, but I will be the first to admit that the osteological evidence does not imply a lot of brainpower for North America’s only resident marsupial. Apparently its brain was small and smooth, untroubled by any thoughts more complicated than trash can access. Images of opossum brains online confirm that impression (or maybe lack of impression, since we’re talking about braincases here).

And yet, opossums are still around, thriving in the face of placentals with our wrinkly brains, high metabolisms, regular garbage collection, and whatnot. Long may they scurry.

Vicki book arrival 3

When we last left my better half, Dr. Vicki Wedel, she was helping to identify a Jane Doe who had been dead for 37 years by counting growth rings in the woman’s teeth. That case nicely illustrated Vicki’s overriding interest: to advance forensic anthropology by developing new methods and refining existing ones. To that end, for the past few years she has been working with her PhD advisor, Dr. Alison Galloway at UC Santa Cruz, to revise and update Alison’s 1999 book, Broken Bones: Anthropological Analysis of Blunt Force Trauma. The revised and much expanded (504 pages vs 371) second edition, co-edited by Vicki and Alison, came out Monday (Amazon, Amazon.co.uk).

You can read the whole table of contents on Amazon (click to look INSIDE!), but the short short version is that the book has three major sections. The first covers the science and practice of trauma analysis (pp. 5-130), and the second classifies hundreds of common fractures throughout the skeleton, with illustrations (pp. 133-313). The chapters in these sections were all written by Vicki, Alison, and another of Alison’s former students, Dr. Lauren Zephro, solo and in varying combinations. Lauren, whom I always think of as “the Amazon cop”, is a 6-foot blackbelt forensic anthropologist for the Santa Cruz County Sheriff’s Office. If push came to shove I have no doubt that she could beat me to death with her bare hands and then produce a technical analysis of my corpse.

The final section (pp. 314-410) consists of nine case studies contributed by forensic anthropologists, pathologists, medical examiners, forensic and medical artists, and a DoD casualty analyst, based across the Anglophone world from Hawaii to Scotland. There’s some grim stuff in there: trauma to the homeless and elderly, from intimate partner violence, and from child abuse. It’s gut-churningly awful that the defenseless suffer from bone-breaking violence; it’s always been amazing to me that people like Vicki, Alison, Lauren, and the other contributors have both the courage to face these horrors and the technical chops to make the unspeakable solvable.

Beyond that unavoidable darkness, if you’re interested in the many, varied, and often just plain weird ways in which people die, the book is a treasure trove. There’s an elderly woman lying on her deathbed for six years, slowly turning into a natural mummy… (wait for it) …while her daughter went on living in the same house. There’s a classification of plane crashes with a description of what human remains will be found and over what area. There are people hit by trains; the funniest line in this very serious book is the deadpan and unsurprising, “The typical pedestrian hit by a train is male and often highly intoxicated.”

Fig 7-3 train skull

That’s from the top of page 122. At the bottom of the same page is my one contribution to the book, which also appears as the cover art (yeah, nepotism, whatcha gonna do). There’s a story behind this. This guy–yes, male, dunno if he was intoxicated–was hit by a train and his head was sheared in half, with the somewhat fractured but mostly intact facial skeleton separated by a lot of missing bone from the occipital region. With no way to obtain the deceased guy’s permission to use his mortal remains in the book, Alison and Vicki didn’t feel comfortable including their photos, so I spent a weekend bashing out a technical drawing for them to use instead. That reawakened my interest in pen-and-ink work and led to the dödö pöst.

I should say two things right here: first, that yes, I am hijacking the rest of the post to talk about myself. (Is anyone really surprised? I thought not.) Second, that I have had no training and possibly my stippling violates Art Rules or best practice guidelines of which I am ignorant. But I hope it also illustrates what can be achieved in a couple of days, with about $15 worth of supplies, by a guy whose only rule is “möre döts”.

So anyway, if you’re curious, here’s the method I use for my pen-and-ink illustrations:

  1. Get a decent-sized photo of the object to be drawn. I usually roll with $2 8x10s from MalWart, in this case one for each half of the skull.
  2. Tape the photo down to your work surface. I have a large, incredibly hard, perfectly smooth cutting board that I use for this, but in a pinch you could use just about anything, including just a larger piece of paper. Cardboard off the backs of desk calendars is nice.
  3. Over the photo, tape down a piece of tracing paper.
  4. Lightly trace the outline of the photo and all the major details in pencil.
  5. Once you’ve gone as far as you can with that, peel up one side of the tracing paper, unstick the photo from the work surface, and remove it. Stick the tracing paper back down the work surface.
  6. Using the uncovered photo as a reference, pencil in any other salient details by eye. Also contour lines for shadows. All of the pencil lines are going to be erased later, so don’t be shy.
  7. Whenever you decide you’re done with the pencil, get a good pen and start tracing, directly over the pencil lines. I tend not to be too persnicketty about my tools but decent pens are a real help here. For these recent works, I picked up a three-pack of beige-tubed Micron pens for $7 (this set).
  8. In all of the following pen-related steps, be careful to keep your big stupid hand and arm off the wet ink you just laid down–one careless smear can ruin a few hours’ work. Having a work surface that you can rotate is nice, so your pen hand can approach the drawing from any angle. Anytime I have to lay my hand on the drawing, I put down a piece of clean scrap paper first. Even if the underlying ink is dry, it just feels like a smart precaution.
  9. Once the lines are on, add döts to taste. With a little experimentation, you can get patterns of dots to not only indicate light and dark but also suggest textures. Different pen tips and amounts of pressure will yield dots of different sizes, which can also be useful. Dense, overlapping dots can produce an effect similar to scratchboard. BTW, sometimes I do “gear down” and place each dot with thought and care, but in the dense sections I just rat-a-tat-tat like a Lilliputian jackhammer. Try different speeds and see what you can tolerate.
  10. When you’re done dötting, at least to a first approximation, and you’re dead certain the ink is all dry, get a decent eraser and erase all of the pencil lines. I used one of those clicky mechanical erasers because it was cheap and soft enough to not tear up the paper.
  11. Re-ink any lines lightened by the erasing. I find that the döts are usually unaffected, but lines are often knocked down a bit by the eraser work. I suppose it would be cleaner to just draw natively in pen, with no prior pencilling and therefore no erasing, but the few times I’ve tried it, it hasn’t gone well. YMMV. If you’re drawing a 3D solid, this is a good time to employ an old illustrator’s trick, which is to make the bottom outline heavier and darker than the rest, to subtly convey a sense of weight.
  12. Scan, touch up as needed in GIMP, post to blog, bask in self-admiration.

In this case I had a few more steps, which consisted of making variants of the drawing and test-driving them by Vicki and Alison so they could pick their favorites.

Skull drawing - A

This is just embarrassing: after scanning the two drawings and doing a little touch-up, I just scooted them together until they looked like a skull. The problem is that the occiput is nowhere near anatomical position. See that flange of bone above the ear-hole, pointed down and right at a 45-degree angle? That’s the back end of the zygomatic arch, and it should be aimed at the forward stump of the arch, which is just down and back from the eye socket.

Skull drawing - B

Here’s the B version, where I was working entirely off of the zygomatic arch ends, and trying to get the skull into anatomical position. Scientifically this is probably the best variant I produced (I’m not claiming it’s the best possible), but aesthetically it’s a little crowded.

Skull drawing - F1 - original on white

I’ll spare you versions C-E, all of which just scooted the back end of the skull around in an attempt to find a balance between scientific and aesthetic concerns. Here’s the winning F version, which got used for the figure, and became the seed variant for the cover.

Skull drawing - F3 - yellow no fill

For the cover, we tried a lot of things, including the white skull on a black background, and one that was simply inverted from the figure. By this point the publisher had sent Vicki some test versions of the cover, and I thought it would be cool if the drawing was in the same color as the cover text, so I sampled that color from the publisher’s sample cover image and applied it to all of the drawn bits. They knocked it down a few tones for the printed version, so happily it’s not this garish.

Incidentally, I had never tried to replace a bunch of discontinuous areas of the same color with another color in GIMP, so I had to look it up. The two key steps are Select > By color, with the threshold set to zero (or not, if you want to grab a bunch of related colors at once), and “Fill whole selection” in the Bucket tool. Hat tip to this dude and his commenters.

Skull drawing - F5 - yellow 17pc fill

One last step: I thought the bare, unfilled yellow version looked too flat, so I tried different levels of fill to make the skull pop out from the background. I didn’t use bucket fill here–too fiddly with so many dots and edges. Instead I created a new layer of solid yellow and dropped the opacity to 17%. Then went to the drawing layer and used the magic wand tool to select the whole non-skull background. Then popped back to the yellow layer and cleared that selection, leaving yellow fill only in the boundaries of the skull outline. I also tried 10% and 25% opacity for the fill layer, but 10% was too subtle and 25% was starting to swamp some of the detail in the drawing. Between goofing around with colors and opacity levels we went through 10 versions at this stage, of which the one above is the ultimate champion.

So, that’s how the cover art came to be. Back to the book. There’s a bibliography with 1237 references (Vicki knows), and an index. The book is hardbound, with a printed cover and no dustjacket, and IMHO reasonably priced at $65, currently a few bucks less on Amazon. You probably already know whether you want a copy. If so, do the right thing–it’s not too late to get it by Christmas.

References

Wedel, V.L., and Galloway, A. 2013. Broken Bones: Anthropological Analysis of Blunt Force Trauma, Second Edition. Charles C. Thomas, Springfield, 504 pp.

Wedel, V.L., G. Found, and G.L. Nusse. 2013. A 37 year-old cold case identification using novel and collaborative methods. Journal of Forensic Identification 63(1): 5-21.

Hemisected horse head

Continuing the recent theme. We’re not giving this a “Things to Make and Do” header because the spirit of that category is to showcase anatomical preparations that average people could do in the comfort of their own homes and gardens (provided they can get hold of dead wallabies, bear skulls, etc.), and freezing and band-sawing a horse is probably outside that envelope for almost everyone (I hadn’t though of that when I posted the gator!).

In the spirit of MYDHHH:

Hemisected horse head with scale

This ain’t mine, it’s a teaching specimen from our vet school, which has a no-kill policy. All of the animal cadavers used in the anatomy labs are donated by the owners at the ends of the animals’ natural lives. So no animals were harmed in the making of this science.

But I wish it was mine. And as long as I’m dreaming, I’d like a pony. Anyone want to go halvesies?

Hemisected gator

Okay, before some wag makes this point, the gator is missing a good chunk of its tail, so this is more like the left half of the anterior two-thirds of a gator. But that would make a lousy title.

We might have more to say about this in the future, but for now, I’m going to let this 1000-word-equivalent speak for itself.

Many thanks to Elizabeth Rega for the use of the gator.