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Posts Tagged ‘simulation’

Today is the 210th anniversary of Charles R. Darwin’s birthday so I put together a quick post. I’d been meaning to blog about some of our latest scientific papers, so I chose those that had an explicit evolutionary theme, which I hope Chuck would like. Here they are, each with a purty picture and a short explainer blurb! Also please check out Anatomy To You’s post by Katrina van Grouw on Darwin’s fancy pigeons.

Stomach-Churning Rating: 1/10 science!

First, Brandon Kilbourne at the Naturkunde Museum in Berlin kindly invited me to assist in a paper from his German fellowship studying mustelid mammals (otters, weasels, wolverines, badgers, etc.; stinky smaller carnivorous mammals). Here we (very much driven by Brandon; I was along for the ride) didn’t just look at how forelimb bone shape changes with body size in this ecologically diverse group. We already knew bigger mustelids would have more robust bones, although it was cool to see how swimming-adapted and digging-adapted mustelids evolved similarly robust bones; whereas climbing ones had the skinniest bones.

The really exciting and novel (yes I am using that much-abused word!) aspect of the paper is that Brandon conjured some sorcery with the latest methods for analysing evolutionary trends, to test how forelimb bone shapes evolved. Was their pattern of evolution mostly a leisurely “random walk” or were there early bursts of shape innovation in the mustelid tree of life, or did shape evolve toward one or more optimal shapes (e.g. suited to ecology/habitat)? We found that the most likely pattern involved multiple rates of evolution and/or optima, rather than a single regime. And it was fascinating to see that the patterns of internal shape change deviated from external shape change such as bone lengths: so perhaps selection sometimes works independently at many levels of bone morphology?

Various evolutionary models applied to the phylogeny of mustelids.

Then there, coincidentally, was another paper originating in part from the same museum group in Berlin. This one I’d been involved in as a co-investigator (author) on a Volkswagen (yes! They like science) grant back about 8 years ago and since. There is an amazing ~290 million year old fossil near-amniote (more terrestrial tetrapod) called Orobates pabsti, preserved with good skeletal material but also sets of footprints that match bones very well, allowing a rare match of the two down to this species level. John Nyakatura’s team had 3D modelled this animal before, so we set out to use digital techniques to test how it did, or did not, move—similar to what I’d tried before with Tyrannosaurus, Ichthyostega and so forth. The main question was whether Orobates moved in a more “ancestral” salamander-like way, a more “derived” lizard-like way (i.e. amniote-ish), or something else.

The approach was like a science sledgehammer: we combined experimental studies of 4 living tetrapods (to approximate “rules” of various sprawling gaits), a digital marionette of Orobates (to assess how well its skeleton stayed articulated in various motions), and two robotics analysis (led by robotics guru Auke Ijspeert and his amazing team): a physical robot version “OroBOT” (as a real-world test of our methods), and a biomechanical simulation of OroBOT (to estimate hard-to-measure things in the other analyses, and matches of motions to footprints). And, best of all, we made it all transparent: you can go play with our interactive website, which I still find very fun to explore, and test what motion patterns do or do not work best for Orobates. We concluded that a more amniote-like set of motions was most plausible, which means such motions might have first evolved outside of amniotes.

OroBOT in tha house!

You may remember Crassigyrinus, the early tetrapod, from a prior post on Anatomy To You. My PhD student Eva Herbst finished her anatomical study of the best fossils we could fit into a microCT-scanner and found some neat new details about the “tadpole from hell”. Buried in the rocky matrix were previously unrecognized bones: vertebrae (pleurocentra; the smaller nubbins of what may be “rhachitomous” bipartite classic tetrapod/omorph structure), ribs (from broad thoracic ones to thin rear ones), pelvic (pubis; lower front), and numerous limb bones. One interesting trait we noticed was that the metatarsals (“sole bones” of the foot) were not symmetrical from left-to-right across each bone, as shown below. Such asymmetry was previously used to infer that some early tetrapods were terrestrial, yet Crassigyrinus was uncontroversially aquatic, so what’s up with that? Maybe this asymmetry is a “hangover” from more terrestrial ancestry, or maybe these bones get asymmetrical for non-terrestrial reasons.

The oddly asymmetrical metatarsals of Crassigyrinus.

Finally, Dr. Peter Bishop finished his PhD at Griffith University in Australia and came to join us as a DAWNDINOS postdoc. He blasted out three of his thesis chapters (starting here) with me and many others as coauthors, all three papers building on a major theme: how does the inner bone structure (spongy or cancellous bone) relate to hindlimb function in theropod dinosaurs (including birds) and how did that evolve? Might it tell us something about how leg posture or even gait evolved? There are big theories in “mechanobiology” variously named Wolff’s Law or the Trajectorial Theory that explain why, at certain levels, bony struts tend to align themselves to help resist certain stresses, and thus their alignment can be “read” to indicate stresses. Sometimes. It’s complicated!

Undaunted, Peter measured a bunch of theropod limb bones’ inner geometry and found consistent differences in how the “tracts” of bony struts, mainly around joints, were oriented. He then built a biomechanical model of a chicken to test if the loads that muscles placed on the joints incurred stresses that matched the tracts’ orientations. Hmm, they did! Then, with renewed confidence that we can use this in the fossil record to infer approximate limb postures, Peter scanned and modelled a less birdlike Daspletosaurus (smaller tyrannosaur) and more birdlike “Troodon” (now Stenonychosaurus; long story). Nicely fitting many other studies’ conclusions, Peter found that the tyrannosaur had a more straightened hindlimb whereas the troodontid had a more crouched hindlimb; intermediate between the tyrannosaur and chicken. Voila! More evidence for a gradual evolution of leg posture across Mesozoic-theropods-into-modern-birds. That’s nice.

Three theropods, three best-supported postures based on cancellous bone architecture.

If you are still thirsty for more papers even if they are less evolutionary, here’s the quick scoop on ones I’ve neglected until now:

(1) Former PhD student Chris Basu published his thesis work w/us on measuring giraffe walking dynamics with force plates, finding that they move mostly like other quadrupeds and their wobbly necks might cost them a little.

(2) Oh, and Chris’s second paper just came out as I was writing this! We measured faster giraffe gaits in the wilds of South Africa, as zoo giraffes couldn’t safely do them. And we found they don’t normally go airborne, just using a rotary gallop (not trot, pace or canter); unlike some other mammals. Stay tuned: next we get evolutionary with this project!

(2) How do you safely anaesthetize a Nile crocodile? There’s now a rigorous protocol (from our DAWNDINOS work).

(3) Kickstarting my broad interest in how animals do “extreme” non-locomotor motions, we simulated how greyhounds stand up, finding that even without stretchy tendons they should, barely, be able to do it, which is neat. Expect much more about this from us in due time.

(4) Let’s simulate some more biomechanics! Ashley Heers, an NSF research fellow w/me for a year, simulated how growing chukar birds use their wing muscles to flap their way up steeper inclines (“WAIR” for devotees), and the results were very encouraging for simulating this behaviour in more detail (e.g. tendons seem to matter a lot) and even in fossil species; and finally…

(5) Hey did you ever think about how bone shape differs between hopping marsupials (macropods) and galloping artiodactyl (even-toed) mammals? We did, in long-the-making work from an old BBSRC grant with Michael Doube et al., and one cool thing is that they mostly don’t change shape with body size that differently, even though one is more bipedal at faster speeds—so maybe it is lower-intensity, slower behaviours that (sometimes?) influence bone shape more?

So there you have the skinny on what we’ve been up to lately, messing around with evolution, biomechanics and morphology.

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This post will walk through the basic steps we take to do some of the major, ongoing research in my team. It comes from our lengthy project aiming to determine how elephant legs work at the level of individual muscle/tendon/bone organs. We need fancy computer simulations because anatomy, mechanics, physiology, neural control etc. are all very complex and not only impossible to completely measure in a living, moving animal but also extremely unethical and unjustified in the case of a rare, fragile animal like an Asian elephant. We want to do such complex things to test hypotheses about how animals work. For example, we want to estimate how fast an elephant could run if it wanted to, or why they cannot (or will not) jump or gallop like smaller mammals do— even as baby elephants (~100 kg or 220 lbs), which is an ancillary question we’re tackling. That’s cool basic science, and that’s enough for me. But the applications once such models and simulations are established are manifold– human clinical research now routinely employs such approaches to help treat “crouch gait” in patients with cerebral palsy, plan corrective surgeries, aid in rehabilitation strategies, and even potentially optimize athletic performance. Non-human research is pretty far behind this kind of confident application, because there are too damn many interesting non-humans out there to study and not many people using these approaches to study them (but it’s catching on).

Breaking up the monotony of the text with a baby elephant we met during our research in Thailand (Chiang Mai, here) in 2001. It was just a few days old and VERY cuddly and playful (chewing on everything!) but it’s mother did not want us playing with it so we only gave a quick hello.

I use the term model to refer to a simple abstraction of reality (such as an anatomically realistic computer graphic of a limb), and a simulation as a more complex process that is more open-ended and generally uses a model to ask a question (such as what level of extreme athletic behaviour a modelled limb could support). We use models and simulations to test how all the structures of the limb work together to produce movement. This also reciprocally gives us insight into the question, as I like to say it, of why is there anatomy? What is anatomy for? Why does it vary so much within so many groups and not so much in others? This can more easily be addressed by focusing on the consequences of a given anatomy rather than the more tricky question of why it evolved.

These approaches also can answer the frightening question of “Does anatomy really matter?” Sometimes it does not. And those “sometimes” can be impossible to predict- although sometimes they can be easy to predict, too. I think we are not at a point in the maturity of biomechanics/functional morphology to usually know a priori when either is the case.  Many factors in addition to anatomy determine function, behaviour, or performance; that’s why; and biomechanics aims to unravel those relationships. A lot of anatomists, palaeontologists, etc. assume that form can be reliably used to predict function, but plenty of studies have shown already (and if you peer deeply into the details, it comes from first principles) that one cannot be sure without either measuring what anatomy is doing in a particular behaviour or estimating that function in a computer model or simulation.

Anyway, I’ve covered my perspective on this in a paper which you can read if you want to go into deep philosophical details of the science (and read me blabbering on more about this particular hobby horse of mine?). This post will proceed mostly with pretty images and simple explanations, although I welcome comments and queries at the end. As part of this post, I’ll try to give an idea of the timespans involved in doing the research. Some steps are quick and easy; others can take dauntingly long — especially to do well, without building a digital house of cards.

I’ll start, as my posts often do, with a deceased animal, and in this case it will again be an Asian elephant. Incidentally it is the same animal from the “Inside Nature’s Giants” series (see previous post).

Above: the hindlimb viewed from the rear, showing the medial (inside) region of the thigh skinned down to the superficial musculature. The hip is toward the left of the screen, and the knee is to the far right (whitish rounded area), with the shank (still bearing most of its grey hide) heading to the bottom right corner of the picture. Muscles pictured include ST (semitendinosus) and SM (semimembranosus); major hamstring muscles; as well as the thin, sheet-like gracilis, the straplike sartorius, and the massive adductors toward the top of the image.

When collecting data from dissections for functional analysis including computer models and simulations, we dissect the muscles one by one as we identify and photograph/sketch them, then remove them and do a suite of measurements to characterize how their form relates to some basic functional parameters. From the mass (weight) of the muscle and the length and angulation (pennation) of its fibres (bundled as fascicles) we can estimate what is called the physiological cross-sectional area (PCSA) of each muscle, which is known to strongly correlate with the force the muscle can produce. Different muscles have different PCSAs; for example check out these pictures of a long-fibred, lower-PCSA muscle and a short-fibred, highly pennate and high PCSA muscle:

Above: the long muscle fibres (bands running from left to right, somewhat diagonally from the bottom left corner toward the top right) of a hip adductor muscle in our specimen. The adductors are fairly simple muscles that run from the underside of the pelvis to the inside of the thigh (femur).

Above: the tensor fasciae latae (TFL; pretty sure of ID but going from memory) hip muscle of our specimen, cut open to show the short, angled fibres (each leading at around a 45 degree angle to attach onto a thick central internal tendon). The TFL is just out of view at the top of the screen in the whole leg anatomy picture above; it is on the front outer, upper margin of the hip/thigh and runs down to the outer side of the knee, invested with thick sheets of connective tissue (fascia).

The maximal isometric force (Fmax) of a muscle is computed as the PCSA times the muscle stress (force/unit area), which is fairly conservative in vertebrates. A square meter of PCSA can produce around 200-300 kilonewtons of force, or about 60,000 cheeseburger-weights (the standard unit of force on this blog). That’s a lot of quarter pounders! And an elephant has pretty close to that many cheeseburgers worth of leg muscle (around 150 kg mass, very close to a square meter of PCSA; total Fmax would be around 80,000 cheese-burger weights!). That much muscle is important because an Asian elephant like this one weighed 3550 kg or about 9000 cheeseburger-weights. So if all the muscles in one elephant hindlimb could push in one direction at once, in theory they could hold about 9 elephants aloft. However, as the picture above shows, they do not all act in the same direction. Furthermore, there are many other factors involved in determining how hard a leg can push, such as the leverage of the muscle forces versus the actions of gravity and inertia (mechanical advantage). All those factors, again, are why we need computer models to address the complexity. But the end result is that elephants cannot support 9 times their body weight on one hind leg.

Enough talk about cheeseburgers and enough possibly savory pictures of giant steak-like leg muscles. I don’t want to be blamed for hunger-induced health problems in my beloved blog-readership, dear Freezerinos! The above steps take about a week to complete for 2 legs of a big elephant, rushing against decomposition to try to get the best quality data we can. On to the digital stuff- let’s turn the geekitude dial up to 11 with some videos of computer modelling.

Our next step, often featured on this blog because I do this so often, is to take CT (and/or MRI) scans of the specimen that we wisely did before we cut it to bits, and use those to make a computer model. That’s the easy step; a scan nowaways takes me less than an hour to complete, including moving the specimen back and forth between the freezer and imaging centre. MRI scans can take quite a bit longer. Here is a CT scan of a similar hindlimb (right leg for the toes up to the knee, from a juvenile elephant; the above leg was too big for our scanner!). See what you can identify here:

And then here is a resulting computer model of the same animal (just knee down to toes), showing how we took each CT slice of even the muscles and turned them into fully or partially 3D digital organs, in our case using commercial software that makes this procedure (a step called segmentation) very easy:

The segmentation step for bones is usually incredibly simple; it can take anywhere from an hour to a day or so, depending on anatomical complexity and image quality. For muscles, this is harder because the images are often more hazy and muscles tend to interweave with each other, segue into tiny tendons, take sudden turns through bones or other narrow spaces, or even fuse with other muscles. So when we do this kind of musculoskeletal modelling, it gets pretty laborious, and can take weeks or months to finish.

Ahh, but once you’re done with the basic anatomy, the real fun begins! We take the 3D images of bones, muscles, etc. and import them into our biomechanics software. We use two packages: one commericial item called SIMM (Software for Integrative Musculoskeletal Modeling) for making models, and a nice freebie called OpenSim for doing simulations (although actually we’re finding SIMM is often better at doing both modelling and simulation for more unusual animals). Quite a bit more anatomical work is required to get the joints to move properly, then position the muscles in accurate or at least realistic 3D paths (depending on segmented image quality), then check the muscles to ensure they move properly throughout the joints’ ranges of motion, then import all the PCSA and Fmax and other data we need from dissections, then do a lot more debugging of the model… this takes months, at least.

But the greatest joy and pain comes in getting the biomechanics done with the models and simulations. You can get quite simple data out of the models alone; such as the leverages (moment arms) of individual muscles and how these change with limb joint position, across a gait cycle, etc… That’s pretty interesting to us, and can just take a few days to crank out from a finished model. Yet the ultimate goal is to do either a tracking simulation, in which we make the model try to follow forces and motions that we measured in experiments from the same or a similar animal (standard, harmless gait analyses), or a theoretical simulation, in which we set the model a task and some rules (‘optimization criteria’) and then set it to run (for hours, days or weeks) to solve that task while following the rules. In both cases, the simulations estimate the muscle activation timings (on/off and intensity) and forces, as well as the kinematics (motions) and kinetics (forces) of the limbs. Then we check the results, play around with the inputs (unknown parameters) as part of a sensitivity analysis, and re-run the analyses again, and again, and again… Here is a draft of a tracking simulation we’ve run for our elephant’s hindlimb:

Above: again, a right hindlimb of an Asian elephant. This test of our tracking simulation is replicating real experimental data (from motion capture and force platform analysis) of an elephant running at near its top speed; over 4 meters/second (>10 mph/16kph). The red lines are the individual muscles, and the green arrow is the ground reaction force, equal and opposite to the force that the limb applies to the ground. In a fast elephant that force can exceed the elephant’s body weight, so the muscles need to crank out kilo-cheeseburger-units of force!

And that’s about as far as I’ll get today. My team’s previous research (explore links for some fun videos) has shown that elephants can run about 7 meters/second (~15mph; 24kph) and that they have pretty poor mechanical advantage when they do run, so their muscles must have to work pretty hard (about 6 times more cheeseburger units in a fast run vs. a slower walk). So how do they do it? And what prevents them from going faster? What would happen if they jumped? What limits speed more; muscles, tendons or bones? Stay tuned. I’m still not sure how much longer this final step of the research will take… (presumably will precede the heat death of the universe by a long shot) But overall, the whole process when everything works nicely can take a year or so to do, proceeding from whole limbs to a simulated limbs.

As a final teaser, here is work we’ve done on using a different kind of model, called finite element analysis (FEA), to estimate how many cheeseburgers it would take to break an elephant’s femur (thigh bone), for example. How “overbuilt” are bones vs. muscles or tendons? This is still a poorly resolved question in biology. We’ve established some rigorous methodology for doing this, now we just need to see what answers it gives us…

(the colour shows the strain (deformation) in the bone in a simple bending experiment; “hot” colours are higher strain. The visualization of the strain is greatly exaggerated; in the real results they are barely visible, as bone only bends a tiny amount before fracturing)

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