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Posts Tagged ‘modelling’

Our special guest post this week comes from Dr. Liz Clark of Yale University (you may have heard of it?) in New Haven, Connecticut, USA. She is bringing some biomechanics-fu to echinoderms– the weird marine critters like seastars and sea urchins. Did you see her 9-awesome-things-about-echinoderms blog post on Anatomy to You? You should. And you should check this out– and check out our new paper on this topic, which just came out! Remember: all images below can be clicked to zoom in. That’s so fun!

Eversible Stomach-Churning Rating: 2/10; no Uni sushi here.

I remember the first time I saw one. I was at the Duke Marine Lab staring at a chunk of dredged-up oyster shells in a glass dish, when all of a sudden a mass of big, black spines obscured my view. I looked up from the microscope to see a creature with a round body the size of a nickel and a flurry of long, skinny, spiny arms skulking hurriedly across the dish. It wasn’t quite a spider- the five-fold symmetry gave its echinoderm affinity away- but it wasn’t quite a starfish, either. Starfish appear graceful as their tiny tube-feet make hurried and unseen movements underneath them to transport them slowly across the sand- appearing nearly motionless to the naked eye. This animal, on the other hand, was making rapid, whip-like strikes with its arms so that it clambered forward, rapidly and fearlessly scaling the uneven terrain of the shells in a bold attempt to escape the dish. I was hooked. I had to know who this monster was, and learn as much about it as I could.

Brittle star arm set up to study its ossicle-joint mobility with CT scanning (below).

That was the day I was introduced to the brittle star. The name “brittle star” is a bit of a misnomer, since they are really anything but. Brittleness implies rigidity and stiffness, suggesting they have a delicate nature with the impossibility of repair or to adapt, which couldn’t be farther from the truth. Their long arms are incredibly flexible, each made of around 100 tiny segments that allow them to bend in any direction or loop them around in circles. I bet that their name comes from the ease at which they can cast off their arms, which they do intentionally to escape predators or pesky researchers trying to grab them, which deceitfully suggests fragility when in fact their arms are incredibly sturdy and packed with powerful muscles. They can flawlessly regenerate their arms, and, in the meantime, even after they lose several of them, they adjust their strategy for locomotion so that they keep prowling across the seafloor unphased. Their physical flexibility and ability to repair and adapt in the face of damage makes them anything but brittle. The Japanese name for brittle star roughly translates to “spider-human-hand,” which I think much more accurately captures the ethos of this group.

Brittle stars have internal skeletons, and each segment of their arms are made of a cluster of small skeletal elements (ossicles). Researchers in the past have made the assumption that differences in the shape of these ossicles between species change how they move, but I wasn’t so sure. So, John and I decided to work together to figure it out.

We didn’t dive into the freezer for this one- sorry to disappoint all of the diehard fans of John’s freezer out there (but in my defense can you imagine how tough it would have been to even find them in the sea of rhinos, giraffes, and crocs?!). [JOHN: awwwwwww!! It’s more of a wall keeping in the wildlings, than a sea right now though!] Instead we ordered some brittle stars off the internet! The first thing we did was make some measurements of how flexible the arms of brittle stars are when they’re alive. Then we digitized their skeletons by micro-CT scanning them so we could see the articulations between the ossicles and the segments in 3D. We scanned them in a few different positions so we could see the articulations between the ossicles as their arms bend. Then we incorporated all of that data into a 3D model that allowed us to visualize what’s going on in the inside of brittle star arms as they move them around.

We made several different models using this strategy to see if different ossicle shapes change how their arms move. We looked at the differences between arm ossicles in two different speciesOphioderma brevispina and Ophiothrix angulata, which represent two of the three different major morphologies of brittle star arms.  We also looked at the difference in the movement mechanics at the tip and base of the arms in O. brevispina, since the ossicles at the tip are thin and elongated compared to wide and flat at the base.

We found that the tip of the arm of Ophioderma brevispina was more flexible than the base due, at least in part, to the shape of the ossicles. We also found several major differences between the two species, including the location of their joint center and the degree to which they could laterally flex. However, none of these differences were easily attributable to any specific morphological feature that set Ophiothrix angulata and O. brevispina apart, which cautions against making assumptions of brittle star functional capabilities by only looking at the shape of the ossicles. We also found that some of the smaller ossicles within each segment shift their position to accommodate arm flexion, when they were originally thought to limit the motion of the arm! We only looked at a few individuals of two species, but the methods for model-building we developed provide a framework to incorporate a broad sample of brittle star species in the future. We’re curious if the results we found stand when more brittle stars are brought into the mix!

It was incredible to take the journey from initially being surprised and captivated by the movement of these animals to eventually building 3D digital models to discover how they are able to do so. It made me realize that opportunities to be inspired by the natural world are around every corner, and that there are so many interesting questions out there that are still unanswered. Thanks to John and our other team members Derek Briggs, Simon Darroch, Nicolás Mongiardino Koch, Travis Brady, and Sloane Smith for making this project happen!

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As 2017 approaches its end, there have been a few papers I’ve been involved in that I thought I’d point out here while I have time. Our DAWNDINOS project has been taking up much of that time and you’ll see much more of that project’s work in 2018, but we just published our first paper from it! And since the other two recent papers involve a similar theme of muscles, appendages and computer models of biomechanics, they’ll feature here too.

Stomach-Churning Rating: 0/10; computer models and other abstractions.

Mussaurus patagonicus was an early sauropodomorph dinosaur from Argentina, and is now widely accepted to be a very close relative of the true (giant, quadrupedal) sauropods. Here is John Conway’s great reconstruction of it:

We have been working with Alejandro Otero and Diego Pol on Mussaurus for many years now, starting with Royal Society International Exchange funds and now supported by my ERC grant “DAWNDINOS”. It features in our grant because it is a decent example of a large sauropodomorph that was probably still bipedal and lived near the Triassic-Jurassic transition (~215mya).

In our new study, we applied one of my team’s typical methods, 3D musculoskeletal modelling, to an adult Mussaurus’s forelimbs. This is a change of topic from the hindlimbs that I’ve myopically focused on before with Tyrannosaurus and Velociraptor [in an obscure paper that I should never have published in a book! pdf link], among other critters my team has tackled (mouse, elephant [still to be finished…], ostrich, horse, Ichthyostega… dozens more to come!). But we also modelled the forelimbs of Crocodylus johnstoni (Australian “freshie”) for a key comparison with a living animal whose anatomy we actually knew, rather than reconstructed.

Mussaurus above; Crocodylus below; forelimb models in various views; muscles are red lines.

The methods for this biomechanical modelling are now standard (I learned them from their creator Prof. Scott Delp during my 2001-2003 postdoc at Stanford): scan bones, connect them with joints, add muscle paths around them, and then use the models to estimate joint ranges of motion and muscle moment arms (leverage) around joints. I have some mixed feelings about developing this approach in our 2005 paper that is now widely used by the few teams that study appendicular function in extinct animals. As a recent review paper noted and I’ve always cautioned, it has a lot of assumptions and problems and one must exercise extreme caution in its design and interpretation. Our new Mussaurus paper continues those ruminations, but I think we made some progress, too.

On to the nuts and bolts of the science (it’s a 60 page paper so this summary will omit a lot!): first, we wanted to know how the forelimb joint ranges of motion in Mussaurus compared with those in Crocodylus and whether our model of Mussaurus might be able to be placed in a quadrupedal pose, with the palms at least somewhat flat (“pronated”) on the ground. Even considering missing joint cartilage, this didn’t seem very plausible in Mussaurus unless one allowed the whole forearm to rotate around its long axis from the elbow joint, which is very speculative—but not impossible in Crocodylus, either. Furthermore, the model didn’t seem to have forelimbs fully adapted yet for a more graviportal, columnar posture. Here’s what the model’s mobility was like:

So Mussaurus, like other early sauropodomorphs such as Plateosaurus, probably wasn’t quadrupedal, and thus quadrupedalism must have evolved very close to in the Sauropoda common ancestor.

Second, we compared the muscle moment arms (individual 3D “muscle actions” for short) in different poses for all of the main forelimb muscles that extend (in various ways and extents) from the pectoral girdle to the thumb, for both animals, to see how muscle actions might differ in Crocodylus (which would be closer to the ancestral state) and Mussaurus. Did muscles transform their actions in relation to bipedalism (or reversal to quadrupedalism) in the latter? Well, it’s complicated but there are a lot of similarities and differences in how the muscles might have functioned; probably reflecting evolutionary ancestry and specialization. What I found most surprising about our results was that the forelimbs didn’t have muscles well-positioned to pronate the forearm/hand, and thus musculoskeletal modelling of those muscles reinforced the conclusions from the joints that quadrupedal locomotion was unlikely. I think that result is fairly robust to the uncertainties, but we’ll see in future work.

You like moment arms? We got moment arms! 15 figures of them, like this! And tables and explanatory text and comparisons with human data and, well, lots!

If you’re really a myology geek, you might find our other conclusions about individual muscle actions to be interesting—e.g. the scapulohumeralis seems to have been a shoulder pronator in Crocodylus vs. supinator in Mussaurus, owing to differences in humeral shape (specialization present in Mussaurus; which maybe originated in early dinosaurs?). Contrastingly, the deltoid muscles acted in the same basic way in both species; presumed to reflect evolutionary conservation. And muuuuuuch more!

Do you want to know more? You can play with our models (it takes some work in OpenSim free software but it’s do-able) by downloading them (Crocodylus; Mussaurus; also available: Tyrannosaurus, Velociraptor!). And there will be MUCH more about Mussaurus coming soon. What is awesome about this dinosaur is that we have essentially complete skeletons from tiny hatchlings (the “mouse lizard” etymology) to ~1 year old juveniles to >1000kg adults. So we can do more than arm-wave about forelimbs!

But that’s not all. Last week we published our third paper on mouse hindlimb biomechanics, using musculoskeletal modelling as well. This one was a collaboration that arose from past PhD student James Charles’s thesis: his model has been in much demand from mouse researchers, and in this case we were invited by University of Virginia biomechanical engineers to join them in using this model to test how muscle fibres (the truly muscle-y, contractile parts of “muscle-tendon units”) change length in walking mice vs. humans. It was a pleasure to re-unite in coauthorship with Prof. Silvia Blemker, who was a coauthor on that 2005 T. rex hindlimb modelling paper which set me on my current dark path.

Mouse and human legs in right side view, going through walking cycles in simulations. Too small? Click to embiggen.

We found that, because mice move their hindlimb joints through smaller arcs than humans do during walking and because human muscles have large moment arms, the hindlimb muscles of humans change length more—mouse muscles change length only about 48% of the amount that typical leg muscles do in humans! This is cool not only from an evolutionary (mouse muscles are probably closer to the ancestral mammalian state) and scaling (smaller animals may use less muscle excursions, to a point, in comparable gaits?) perspective, but it also has clinical relevance.

Simulated stride for mouse and human; with muscles either almost inactive (Act=0.05) or fully active (Act=1). Red curve goes through much bigger excursions (along y-axis) than blue curve), so humans should use bigger % of their muscle fibre lengths in walking. Too small? Click to embiggen.

My coauthors study muscular dystrophy and similar diseases that can involve muscle stiffness and similar biomechanical or neural control problems. Mice are often used as “models” (both in the sense of analogues/study systems for animal trials in developing treatments, and in the sense of computational abstractions) for human diseases. But because mouse muscles don’t work the same as human muscles, especially in regards to length changes in walking, there are concerns that overreliance on mice as human models might cause erroneous conclusions about what treatments work best to reduce muscle stiffness (or response to muscle stretching that causes progressive damage), for example. Thus either mouse model studies need some rethinking sometimes, or other models such as canines might be more effective. Regardless, it was exciting to be involved in a study that seems to deliver the goods on translating basic science to clinical relevance.

Muscle-by-muscle data; most mouse muscles go through smaller excursions; a few go through greater; some are the same as humans’.

Finally, a third recent paper of ours was led by Julia Molnar and Stephanie Pierce (of prior RVC “Team Tetrapod” affiliation), with myself and Rui Diogo. This study tied together a bunch of disparate research strands of our different teams, including musculature and its homologies, the early tetrapod fossil record, muscle reconstruction in fossils, and biomechanics. And again the focus was on forelimbs, or front-appendages anyway; but turning back the clock to the very early history of fishes, especially lobe-finned forms, and trying to piece together how the few pectoral fin muscles of those fish evolved into the many forelimb muscles of true tetrapods from >400mya to much more recent times.

Humerus in ventral view, showing muscle attachments. Extent (green) is unknown in the fossil but the muscle position is clear (arrow).

We considered the homologies for those muscles in extant forms, hypothesized by Diogo, Molnar et al., in light of the fossil record that reveals where those muscles attach(ed), using that reciprocal illumination to reconstruct how forelimb musculature evolved. This parallels almost-as-ancient (well, year 2000) work that I’d done in my PhD on reconstructing hindlimb muscle evolution in early reptiles/archosaurs/dinosaurs/birds. Along the way, we could reconstruct estimates of pectoral muscles in various representative extinct tetrapod(omorph)s.

Disparity of skeletal pectoral appendages to work with from lobe-fins to tetrapods.

Again, it’s a lengthy, detailed study (31 pages) but designed as a review and meta-analysis that introduces readers to the data and ideas and then builds on them in new ways. I feel that this was a synthesis that was badly needed to tie together disparate observations and speculations on what the many, many obvious bumps, squiggles, crests and tuberosities on fossil tetrapods/cousins “mean” in terms of soft tissues. The figures here tell the basic story; Julia, as usual, rocked it with some lovely scientific illustration! Short message: the large number of pectoral limb muscles in living tetrapods probably didn’t evolve until limbs with digits evolved, but that number might go back to the common ancestor of all tetrapods, rather than more recently. BUT there are strong hints that earlier tetrapodomorph “fishapods” had some of those novel muscles already, so it was a more stepwise/gradual pattern of evolution than a simple punctuated event or two.

Colour maps of reconstructed right fin/limb muscles in tetrapodomorph sarcopterygian (~”fishapod”) and tetrapod most recent common ancestors. Some are less ambiguous than others.

That study opens the way to do proper biomechanical studies (like the Mussaurus study) of muscle actions, functions… even locomotor dynamics (like the mouse study)– and ooh, I’ve now tied all three studies together, tidily wrapped up with a scientific bow! There you have it. I’m looking forward to sharing more new science in 2018. We have some big, big plans!

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Uh oh, a “why?” question in biology! There are many potential, and not mutually exclusive, answers to such questions. Ultimately there is a historical, evolutionary answer that underpins it all (“ostriches evolved two kneecaps because…”). But we like ostrich knees and their funky double-kneecaps (patellae; singular = patella) so we wanted to know why they get so funky. One level of addressing that question is more like a “how?” they have them. So we started there, with what on the surface is a simple analysis. And we published that paper this week, with all of the supporting data (CT, MRI, FEA).

Stomach-Churning Rating: 6/10 because there is a gooey image of a real dissection later in the post, not just tidy 3D graphics.

First author Kyle Chadwick was my research technician for 2 years on our sesamoid evolution grant, and we reported earlier on the detailed 3D anatomy of ostrich knees (this was all part of his MRes degree with me, done in parallel with his technician post). Here, in the new paper with Sandra Shefelbine and Andy Pitsillides, we took that 3D anatomy and subjected it to some biomechanical analysis in two main steps.

Ostrich (right) knee bones. The patellae are the two knobbly bits in the knee.

First, we used our previous biomechanical simulation data from an adult ostrich (from our paper by Rankin et al.) to estimate the in vivo forces that the knee muscles exert onto the patellar region during moderately large loading in running (not maximal speed running, but “jogging”). That was “just” (Kyle may laugh at the “just”– it wasn’t trivial) taking some vectors out of an existing simulation and adding them into a detailed 3D model. We’ve done similar things before with a horse foot’s bones (and plenty more to come!), but here we had essentially all of the soft tissues, too.

Ostrich knee with muscles as 3D objects.

Second, the 3D model that the muscular forces were applied to was a finite element model: i.e., the original 3D anatomical model broken up into a mesh, whose voxels each had specific properties, such as resistance to shape change under loading in different directions. The response of that model to the loads (a finite element analysis; FEA) gave us details on the stresses (force/area) and strains (deformations from original shape) in each voxel and overall in anatomical regions.

Finite element model setup for our study. If you do FEA, you care about these things. If not, it’s a pretty, sciencey picture.

The great thing about a computer/theoretical model is that you can ask “what if?” and that can help you understand “how?” or even “why?” questions that experiments alone cannot address. Ostriches aren’t born with fully formed bony kneecaps; indeed those patellae seem to mature fairly late in development, perhaps well after hatching. We need to know more about how the patellae form but they clearly end up inside the patellar (knee extensor) tendon that crosses the knee. So we modelled our adult ostrich without bony patellae; just with a homogeneous patellar tendon (using the real anatomy of that tendon with the bony bits replaced by tendon); and subjected it to the loading environment for “jogging”.

The right knee of an ostrich hatchling. The patellae have yet to form; indeed there is little bone around the knee region at all, yet.

We then inspected our FEA’s results in light of modern theory about how tissues respond to loading regimes. That “mechanobiology” theory, specifically “tissue differentiation”, postulates that tendon will tend to turn into fibrocartilage if it is subjected to high compression (squishing) and shear (pushing). Then, the fibrocartilage might eventually be reworked into bone as it drops the compression and shear levels. So, according to that theory (and all else being equal; also ignoring the complex intermediate states that would happen in reality), the real ostrich’s kneecaps should be located in the same positions where the FEA, under the moderately large loads we applied, predicts the homogeneous tendon to have high compression and shear. But did the real anatomy match the mechanical environment and tissue differentiation theory’s predictions?

Tissue differentiation diagram displaying the theoretical pathways for transformation of tissues. If tendon (red) experiences high shear (going up the y-axis) and high compression (going toward the left), it should turn into fibrocartilage (purple). Transformation into bone (diagonally to the bottom right) would reduce the shear and compression.

Well, sort of. The image below takes some unpacking but you should be able to pick out the red areas on the bottom row where the patellae actually are, and the yellow shaded regions around some of those patellar regions are where the compression and shear regimes are indeed high and overlapping the actual patellar regions. The upper two rows show the levels of compression (or tension; pulling) and shear, but the bottom row gets the point across. It’s not a bad match overall for the first (“real”; common to all living birds) patella, located on top of the upper knee (femur). It’s not a good match overall for the second (unique to ostriches) patella, located below the first one (and attached to the tibia bone).

FEA results! (click to embiggen)

Kyle says, “Being a part of this project was exciting because of the application of engineering concepts to interesting biological (including evolutionary) questions. Also, it never gets old seeing people’s reactions when I tell them I study ostrich knees.

The study had a lot of nuances and assumptions. We only looked at one instant in slow running and only at one adult ostrich, not at the full development of ostrich anatomy and loading. That’s harder. We started simple. The tissue differentiation theory is used more for fracture healing than for sesamoid bone formation but there’s some reason to suspect that similar mechanisms are at play in both. And there’s much more; if you want the gory details see the paper.

So did we solve why, or how, ostriches have two kneecaps? We felt that the mechanical environment of our FEA was a good theoretical explanation of where the first patella forms. We originally expected the second patella, which evolved more recently and might be more mechanically sensitive as a result, to be a better match than the first one, but it was the opposite. C’est la science!

Enough models, let’s have some reality! I warned you this post would get messy, and here it is. Left leg (skinned) of an ostrich showing the muscles around the knee. The patellar region would be in the gloved hand of the lucky individual shown.

This study, for me, was a fun experience in moving toward more fusion of “evo-devo” and biomechanical analyses, a research goal of mine lately– but there’s still a ways to go with the “how?” and “why?” questions even about ostrich kneecaps.

We felt that the best conclusion supported by our analyses was that, rather than have homogeneous stresses and strains throughout their knee tissues (e.g. the patellar tendon), ostriches have a lot of regional diversity in how those tissues are loaded (in the condition we modelled, which is adequately representative of some athletic exertion). Look at the complex FEA coloured results above again, the top two rows: there are a lot of different shades of compression/tension and shear; not homogeneous strains. That diversity of regional loading sets those tissues up for potential transformation throughout growth and development. And thus ONE of the reasons why ostriches might have two kneecaps is that the heterogeneous loading of their knee tendon favours formation of heterogeneous tissue types.

Another, compatible, explanation is that these different tissues might have consequences for how the muscles, tendon and joint operate in movement behaviours. In due time there will be more about that. In the meantime, enjoy the paper if this post makes you want to know more about the amaaaaaazing knees of ostriches!

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Last year we finally, after about 14 years of slow work, released our biomechanical model of an ostrich’s hindleg. We showed how it informed us about the potential leverages (moment arms; contributions to mechanical advantage of the joints) of all of the muscles. It was a satisfying moment, to understate it, to finally publish this work from my postdoc at Stanford. Today, we begin to deliver on that model’s promise. And it only took 4 years or so, roughly? The journal Royal Society Interface has published our study of how we used this musculoskeletal model to simulate walking and running dynamics. Those simulations join an intimidatingly broad and complex literature using similar models to study human (and some other primate) locomotion or other functions at the level of individual muscles (for whole limbs/bodies) in vast detail and growing rigor. I have Dr. Jeffery Rankin, a research fellow finishing up his post with me after ~6 years of hard work on many projects, to thank for driving this work forward, and Dr. Jonas Rubenson (now at PennState) for his patient collaboration that has continued since the early 2000’s.

Stomach-Churning Rating: 2/10; computer models of muscle actions. The underlying anatomical data are goopy, as prior ostrich-dissection-focused posts show!

Our model; in right side view (on the left) and frontal view (on the right), with muscles in red and the leg's force as the blue arrow; frozen at the middle of a step.

Our model; in right side view (on the left) and frontal view (on the right), with muscles in red and the leg’s force as the blue arrow; frozen at the middle of a running step.

Simulations like these predict things that we can’t easily measure in living animals, such as how much force muscles and tendons generate, how quickly those tissues change length, how much mechanical energy they thus contribute to the joints, limbs and whole body, how much metabolic energy their actions cost, and much more. There are more ways to use these tools than I have space or time to explain, but simply put we forced our ostrich simulation to match experimental measurements of the motions and forces of a representative walking and running ostrich stride, from contact of one foot until the next time that foot hit the ground. It then used optimization methods (minimizing target criteria like muscle stress) to estimate how the muscles and tendons were used to generate those motions and forces. This is a ways ahead of some prior ostrich simulations such as this one that I recall from classes during my PhD studies.

Any modeller worth their salt knows that their models and simulations are wrong at some level. This is much as most science is “wrong”; i.e. a simplification of reality with some errors/noise introduced by assumptions, variation, methods and such. But generally these kinds of musculoskeletal dynamic simulations hold up pretty well against experimental data. A standard “validation” is to test how closely the simulations’ predictions of muscle activity match the “real” (measured in life, also with some uncertain error) activity of muscles. Science still lacks those data for ostriches, but fortunately measurements from other birds (by Steve Gatesy and colleagues) indicate that muscles tend to follow fairly conservative patterns. Grossly speaking, avian leg muscles tend to either be active mainly when the foot is on the ground (stance phase) or off the ground (swing phase). Some studies acknowledge that this is an oversimplification and other muscles do act across those two phases of a stride, either in multiple pulses or as “transitional” (stance-to-swing or swing-to-stance) switch-hitters in their activations. Our ostrich predictions matched the qualitative patterns for avian muscle activations measured to date, so that’s good. The results also reinforced the notion of transitional or multi-phasic muscle activation as still having some importance, which bears more study.

Yet what did the simulations with our ostrich model tell us that other ostrich experiments or other bird species didn’t? Three main things. First, we could calculate what the primary functions of muscles were; they can act as motors (generating energy), brakes (absorbing energy), springs (bouncing energy back and forth) or struts (just transmitting force). We could then sum up what whole muscle groups were doing overall. The image below shows how these broad functions of groups vary across the stance phase (swing phase is harder to condense here so I’ve left it out).

Positive work can speed things up; negative work can slow things down.

Positive work can speed things up; negative work can slow things down. Solid bars are running; striped bars are walking. (from our Fig. 13) You may need to click to em-broaden this image for the gory biomechanical details.

There’s a lot going on there but a few highlights from that plot are that the hip extensor (antigravity) muscles (biarticular hip/knee “hamstrings”) are acting like motors, the knee extensors (like our quadriceps) are mainly braking as in other animals and the ankle is fairly springy as its tendons (e.g. digital flexors; gastrocnemius) suggest. We often characterize birds as “knee-driven” but it’s more accurate biomechanically to say that their hips drive (power; i.e. act as motors) their motion, whereas their knees still act as brakes — in both cases as in many other land vertebrates. Thus in some ways bird legs don’t work so unusually. Birds like ostriches are, though, a little odd in how much they rely on their hamstring muscles to power locomotion (at the hip) rather than their caudofemoral muscles, which are reduced. Zooming in on some particular muscles such as parts of the hip or knee extensors, the functions sometimes weren’t as predictable as their similar anatomy might suggest. Some muscles had parts that turned on during swing phase and other parts used during stance phase. Neural control and mechanics can produce some unexpected patterns.

Second, we looked at one important methodological issue. Simulations of musculoskeletal dynamics can vary from simple static (assuming each instant of a motion is independent from the others; e.g. ignoring acceleration, inertia, tendon effects, etc.) to more complex grades of fully dynamic flavours (e.g. assuming rigid or flexible tendons). We looked across this spectrum of assumptions, for both walking and running gaits, with the expectation that more static assumptions would work less well (vs. more dynamic ones; by various criteria) for running vs. walking. This also showed us how much tendons influence our simulations’ estimates of muscle mechanics—a fully rigid tendon will make the muscle do all of the work (force times length change) whereas a flexible tendon can literally take up some (or even all) of that slack, allowing muscles to remain closer to their isometric (high force-generating, negligible length change) quasi-optimum.

Nicely, our predicted muscle functions weren’t influenced much by these methodological variations. However, static assumptions  clearly were in some ways less appropriate for running than for walking, as were flexible tendons. Somewhat surprisingly, making the simulations more dynamic didn’t lower the levels of activation (and thus presumably the metabolic costs) of muscles, but actually raised those levels. There are good reasons why this might be realistic but it needs further study. It does muddy the waters for the issue of whether assuming that rapid locomotion can be modelled as static is a “bad” thing such as for estimating maximal speeds—yes, tendons can do more (elastic energy storage, etc.) if more dynamic models are used, but co-contraction of antagonistic muscles against each other also brings in some added costs and might lead to slower speed estimates. We’ll see in future work…

Finally, one often overlooked (sometimes even undiscussed!) aspect of these simulations is that they may silently add in extra forces to help muscles that are struggling to support and move their joints. The justification is typically that these extra “reserve actuators” are passive tissues, bony articular forces and other non-muscular interactions. We found that the hip joint muscles of ostriches were very weak at resisting abduction (drawing the thigh away from the body) and this needed resisting during the stance phase, so our simulations had very high reserve actuators switched on there. That fits the anatomy pretty well and needs more investigation.

Want to know more? Happily, not only is the paper free for anyone to view but so are all of the data including the models (modified slightly from our last paper’s). So, although the software (Opensim) isn’t ideal for 4-year-olds to play with (it is fancy engineering stuff), if you have the interest and dilligence it is there to play with and re-use and all that. But also watch this space for future developments, as there is more to happen with our steadily improving models of ostriches and other beasties. Anyway, while this paper is very technical and challenging to explain I am not too bashful to say it’s one of the finer papers from my career; a big stride forward from what we’ve done before. I have been looking forward for a long time to us getting this paper out.

P.S. Our peer reviewers were splendid- tough but constructive and fair. The paper got a lot better thanks to them.

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Seeking adaptations for running and swimming in the vertebral columns of ancient crocs

A guest post by Dr. Julia Molnar, Howard University, USA (this comes from Julia’s PhD research at RVC with John & colleagues)

Recently, John and I with colleagues Stephanie Pierce, Bhart-Anjan Bhullar, and Alan Turner described morphological and functional changes in the vertebral column with increasing aquatic adaptation in crocodylomorphs (Royal Society Open Science, doi 10.1098/rsos.150439). Our results shed light upon key aspects of the evolutionary history of these under-appreciated archosaurs.

Stomach-Churning Rating: 5/10; a juicy croc torso in one small photo but that’s all.

Phylogenetic relationships of the three crocodylomorph groups in the study and our functional hypotheses about their vertebrae. * Image credits: Hesperosuchus by Smokeybjb, Suchodus by Dmitry Bogdanov (vectorized by T. Michael Keesey) http://creativecommons.org/licenses/by-sa/3.0

Phylogenetic relationships of the three crocodylomorph groups in the study and our functional hypotheses about their vertebrae. * Image credits: Hesperosuchus by Smokeybjb, Suchodus by Dmitry Bogdanov (vectorized by T. Michael Keesey) http://creativecommons.org/licenses/by-sa/3.0

As fascinating as modern crocodiles might be, in many ways they are overshadowed by their extinct, Mesozoic cousins and ancestors. The Triassic, Jurassic, and early Cretaceous periods saw the small, fast, hyper-carnivorous “sphenosuchians,” the giant, flippered marine thalattosuchians, and various oddballs like the duck-billed Anatosuchus and the aptly named Armadillosuchus. As palaeontologists/biomechanists, we looked at this wide variety of ecological specializations in those species, the Crocodylomorpha, and wanted to know, how did they do it?

Of course, we weren’t the first scientists to wonder about the locomotion of crocodylomorphs, but we did have some new tools in our toolbox; specifically, a couple of micro-CT scanners and some sophisticated imaging software. We took CT and micro-CT scans of five fossil crocodylomorphs: two presumably terrestrial early crocodylomorphs (Terrestrisuchus and Protosuchus), three aquatic thalattosuchians (Pelagosaurus, Steneosaurus, and Metriorhynchus) and a semi-aquatic modern crocodile (Crocodylus niloticus). Since we’re still stuck on vertebrae (see, e.g., here; and also here), we digitally separated out the vertebrae to make 3D models of individual joints and took measurements from each vertebra. Finally, we manipulated the virtual joint models to find out how far they could move before the bones bumped into each other or the joints came apart (osteological range of motion, or RoM).

 

Our methods: get fossil, scan fossil, make virtual fossil and play with it.

Our methods: get fossil (NHMUK), scan fossil, make virtual fossil and play with it.

Above: Video of a single virtual inter-vertebral joint from the trunk of Pelagosaurus typus (NHMUK) showing maximum osteological range of motion in the lateral direction (video). Note the very un-modern-croc-like flat surfaces of the vertebral bodies! (modern crocs have a ball-and-socket spinal joint with the socket on the front end)

While this was a lot of fun, what we really wanted to find out was whether, as crocodylomorphs became specialized for different types of locomotion, the shapes of their vertebrae changed similarly to those of mammalian lineages. For example, many terrestrial mammals have a lumbar region that is very flexible dorsoventrally to allow up-and-down movements during bounding and galloping. Did fast-running crocodylomorphs have similar dorsoventral flexibility? And did fast-swimming aquatic crocodylomorphs evolve a stiffer vertebral column like that of whales and dolphins?

Above: Video of how we modelled and took measurements from the early crocodylomorph Terrestrisuchus gracilis (NHMUK).

Our first results were puzzling. The Nile croc had greater RoM in side-to-side motions, which makes sense because crocodiles mostly use more sprawling postures and are semi-aquatic, using quite a bit of side-to-side motions in life. The part that didn’t make sense was that we found pretty much the same thing in all of the fossil crocodylomorphs, including the presumably very terrestrial Terrestrisuchus and Protosuchus. With their long limbs and hinge-like joints, these two are unlikely to have been sprawlers or swimmers!

So we started looking for other parts of the croc that might affect RoM. The obvious candidate was osteoderms, the bony scales that cover the back. We went back to John’s Freezer and got out a nice frozen crocodile to measure the stiffness of its trunk and found that, sure enough, it was a lot stiffer and less mobile without the osteoderms. If the fairly flexible arrangement of osteoderms in crocodiles had this effect on stiffness, it seemed likely that (as previous authors have suggested; Eberhard Frey and Steve Salisbury being foremost amongst them) the rigid, interlocking osteoderms running from head to tail in early crocodylomorphs would really have put the brakes on their ability to move their trunk in certain ways.

Testing stiffness of crocodile trunks to learn the effects of osteoderms, skin, muscles, and ribs. We hung metric weights from the middle of the trunk and measured how much it flexed (Ɵ), then removed bits and repeated.

Testing the stiffness of (Nile) crocodile trunks to learn the effects of osteoderms, skin, muscles, and ribs. We hung metric weights from the middle of the trunk and measured how much it flexed (Ɵ), then removed bits and repeated. Click to em-croccen.

Another cool thing we found was new evidence of convergent evolution to aquatic lifestyles in the spines of thalattosuchians. The more basal thalattosuchians, thought to have been near-shore predators, had stiffness and RoM patterns similar to Crocodylus. But Metriorhynchus, which probably was very good at chasing down fast fish in the open ocean, seems to have had greater stiffness. (The stiffness estimates come from morphometrics and are based on modern crocodiles; see here again, or just read the paper already!) A stiff vertebral column can be useful for a swimmer because it increases the body’s natural frequency of oscillation, and faster oscillation means faster swimming (think tuna, not eel). The same thing seems to have happened in other secondarily aquatic vertebrate lineages such as whales, ichthyosaurs, and mosasaurs.

So, our results were a mixed bag of adaptations particular to crocs and ones that seem like general vertebrate swimming specializations. Crocodylomorphs are important because they are the only group of large vertebrates other than mammals that has secondarily aquatic members and has living members with a reasonably similar body plan, allowing us to test hypotheses in ways that would arguably be impossible for, say, non-avian dinosaurs and birds. The take-home message: crocodylomorphs A) are awesome, and B) can teach us a lot about how vertebrates adapt to different modes of life.

Another take on this story is on our lab website here.

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…a daily picture of anatomy! And today it is five pictures; zza-zza-zee! ♫

Welcome back againagain, (gasp, pant) and again to Freezermas

I’m letting the dogs out today. Science gone barking mad! Hopefully my puns will not screw the pooch.

Stomach-Churning Rating: 4/10; a dog cadaver’s leg (not messy), then just tame digital images of anatomy.

I am working with Rich Ellis, a former MSc student at Univ. Colorado (see his cool new paper here!), for a fun new collaboration this year. He was awarded a prestigious Whitaker Foundation scholarship to do this research, which focuses on how different animals stand up from a squatting position, with the legs about as bent as they can be.

We want to know how animals do this standing up movement, because it is in some ways a very demanding activity. Very flexed/bent limb joints mean that the muscles (and some tendons) are stretched about as far as they ever will be. So this places them at disadvantageous lengths (and leverage, or mechanical advantage) for producing force. We know almost nothing about how any animal, even humans, does this-– how close to their limits of length are their muscles? Which muscles are closest? Does this change in animals with different numbers of legs, postures, anatomy, size, etc? Such fundamental questions are totally unaddressed. It’s an exciting area to blaze a new trail in, as Rich is doing. So far, we’ve worked with quail, humans, and now greyhounds; in the past I did some simple studies with horses and elephants, too. Jeff Rankin from my team and other collaborators have also worked on six species of birds, of varying sizes, to see how their squat-stand mechanics change.  Thus we’ve covered a wide diversity of animals, and now we’re learning from that diversity. “Diversity enables discovery,” one of my former PhD mentors Prof. Bob Full always says. Too true.

Greyhounds are interesting because they are medium-sized, long-legged, quadrupedal, quite erect in posture, and very specialized for fast running. Fast runners tend to have big muscles with fairly short fibres. Short fibres are bad for moving the joints through very large ranges of motion. So how does a greyhound stand up? Obviously they can do it, but they might have some interesting strategies for doing so- the demands for large joint motion may require a compromise with the demands for fast running. Or maybe the two demands actually can both be optimized without conflict. We don’t know. But we’re going to find out, and then we’ll see how greyhounds compare with other animals.

To find out, we first have to measure some dogs standing up. We’ve done that for about 8 greyhounds. Here is an example of a cooperative pooch:

Those harmless experiments, if you follow me on Twitter, were live-tweeted under the hashtag #StandSpotStand… I dropped the ball there and didn’t continue the tweeting long after data collection, but we got the point across– it’s fun science addressing useful questions. Anyway, the experiments went well, thanks to cooperative pooches like the one above, and Rich has analyzed most of the data.

Now the next step involves the cadaver of a dog. We could anaesthetize our subjects and do this next procedure to obtain subject-specific anatomy. But it really wouldn’t be ethically justified (and if I were an owner I wouldn’t allow it either!) and so we don’t. A greyhound is a greyhound as far as we’re concerned; they’ll be more like each other than either is like a quail or a human. Individual variation is a whole other subject, and there are published data on this that we can compare with.

We get a dead dog’s leg — we don’t kill them; we get cadavers and re-use them:

Greyhound hindlimb for CT

We study the hindlimb because birds and humans don’t use their forelimbs much to stand up normally, so this makes comparisons simpler. We’re collecting forelimb data, though, as we work with quadrupeds, for a rainy day.

We then CT scan the leg, getting a stack of slices like this– see what you can identify here:

It’s not so clear in these images, but I was impressed to see that the muscles showed up very clearly with this leg. That was doggone cool! Perhaps some combination of formalin preservation, fresh condition, and freezing made the CT images clearer than I am used to. Anyway, this turned out to be a treat for our research, as follows.

We then use commercial software (we like Mimics; others use Amira or other packages) to “segment” (make digital representations in 3D) the CT scan data into 3D anatomy, partitioning the greyscale CT images into coloured individual objects– two views of one part of the thigh are shown below.

What can you identify as different colours here? There are lots of clues in the images (click to embiggen):

Hindlimb segmentation of greyhound

And here is what the whole thigh looks like when you switch to the 3D imaging view:

Quite fetching image, eh?!

The next steps after we finish the limb segmentation are to apply the experimental data we observed for greyhounds of comparable size by importing the model and those data into biomechanics software (SIMM/OpenSim). We’ve done about 40 models like this for various species. I detailed this procedure for an elephant here.

Then, at long last, science will know how a greyhound stands up! Wahoo! Waise the woof! Stay tuned as we hound you with more progress on this research-as-it-happens. Rich just finished the above thigh model this week, and the rest of the leg will be done soon.

Many thanks to Rich Ellis for providing images used here. And thank you for persevering my puns; they will now be cur tailed.

Happy Freezermas! Sing it: “On the fifth day of Freezermas, this blo-og gave to me: one tibiotarsus, two silly Darwins, three muscle layers, four gory hearts, a-and five stages modelling a doggie!” ♪

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Party time! Let the media onslaught begin! We’ve published a paper in Nature on the limb motions of Ichthyostega (and by implication, some other stem tetrapods). Since we did use some crocodile specimens from Freezersaurus (see below) in this study, I figured WIJF could cover it to help celebrate this auspicious event. Briefly. Particularly since we already did a quasi-blog on it, which is here:

http://www.rvc.ac.uk/SML/Research/Stories/TetrapodLimbMotion.cfm

and some juicy fossily images at:

http://www.rvc.ac.uk/SML/Research/Stories/TetrapodImages.cfm

However I want to feature our rockin’ cool animations we did for the paper, to squeeze every last possible drop of science communicationy goodness out of them. So here they are in all their digital glory. Huge credit to Dr. Stephanie Pierce, the brilliant, hardworking postdoc who spearheaded the work including these videos! Dr. Jenny Clack is our coauthor on this study and the sage of Ichthyostega and its relatives- her website is here. Also, a big hurrah for our goddess of artsy science, Julia Molnar, who helped with the videos and other images. Enjoy!

The computer model

The forelimb model

The hindlimb model

We used some of my Nile crocodile collection to do a validation analysis of our joint range of motion (ROM) methods, detailed in the Supplementary info of the paper, which I encourage anyone interested to read since it has loads more interesting stuff and cool pics. We found that a bone-based ROM will always give you a greater ROM than an intact fleshy limb-based ROM. In other words, muscles and ligaments (and articular cartilage, etc.). have a net effect of reducing how far a joint can move. This is not shocking but few studies have ever truly quantitatively checked this with empirical data from whole animals. It is an important consideration for all vert paleo types. Here is a pic of one of the crocodiles from the study, with (A) and without muscles (B; ligaments only):

I’ll close with Julia Molnar’s jaw-droppingly awesome flesh reconstruction from our model. Why Nature wouldn’t use this as a cover pic, I’ll never understand, but I LOVE it! When I first saw it enter my email inbox and then opened it to behold its glory, my squeal of geeky joy was deafening.

(edit: Aha! Fellow Berkeley alum Nick Pyenson’s group made the Nature cover, for their kickass study of rorqual whale anatomy, including a “new” organ! Well, we don’t feel so bad then. Great science– and a win for anatomy!!!)

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