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Posts Tagged ‘simulation’

Simulating Dinosaur Locomotion And Wrestling With Scepticism

Posted in Biomechanics, Exalting Archosauria, tagged , , , , , , , on September 22, 2021| 6 Comments »

We released a publication that, for me, comes full circle with research that started my career off. Back in 1995 when I started my PhD, I thought it would be great to use biomechanical models and simulations to test how extinct dinosaurs like Tyrannosaurus rex might have moved (or not), taking Jurassic Park CGI animations (for which the goal was to look great) into a more scientific realm (for which the goal is to be “correct”, even at the cost of beauty). “It would be great”, or so I thought, haha. I set off on what has become a ~26 year journey where I tried to build the evidence needed to do so, at each step trying to convince my fairly sceptical mind that it was “good enough” science. For my PhD I mainly focused on reconstructing the hindlimb muscles and their evolution, then using very simple “stick figure”, static biomechanical models of various bipeds to test which could support fast running with their leg muscles, culminating in a 2002 Nature paper that made my early career. I since wrote a long series of papers with collaborators to build on that work, studying muscle moment arms, body/segment centre of mass, and finally a standardized “workflow” for making 3D musculoskeletal models. And gradually we worked with many species, mostly living ones, to simulate walking and running and estimate how muscles controlled observed motions and forces from experiments. This taught us how to build better models and simulations. Now, in 2021, our science has made the leap forward I long hoped for, and the key thing for me is that I believe enough of it is “good enough” for me, which long held me back. This is thus my personal perspective. We have a press release that gives the general story for public consumption; here I’ve written for more of a sciencey audience.

Skeleton of the extinct theropod Coelophysis in a running pose, viewed side-on. Image credit: Scott Hocknull, Peter Bishop, Queensland Museum.

Stomach-Churning Rating: 1/10: just digital muscles.

Earlier in 2021, we simulated tinamou birds in two papers (first one here), the second one revealing our first ever fully predictive simulations, of jumping and landing; detailed here and with a nice summary article here. That research was led by DAWNDINOS postdoc Peter Bishop and featuring new collaborators from Belgium, Dr. Antoine Falisse and Prof. Friedl De Groote. Thanks to the latter duo’s expertise, we used what is called direct collocation (optimal control) simulation; which is faster than standard “single-shooting” forward dynamic simulation. The simulations also were fully three-dimensional, although with some admitted simplifications of joints and the foot morphology; much as even most human simulations do. The great thing about predictive simulations is that, unlike tracking/inverse simulations (all of my prior simulation research), it generates new behaviours, not just explaining how experimentally observed behaviours might have been generated by neuromuscular control.

OK, so what’s this new paper really about and why do I care? We first used our tinamou model to predict how it should walk and sprint, via some basic “rules” of optimal control goals. We got good results, we felt. That is the vital phase of what can be called model “validation”, or better termed “model evaluation”; sussing out what’s good/bad about simulation outputs based on inputs. It was good enough overall to proceed with a fossil theropod dinosaur, we felt.

Computer simulation of modern tinamou bird running at maximum speed. Grey tiles = 10 cm.

And so we returned to the smallish Triassic theropod Coelophysis, asking our simulations to find optimal solutions for maximal speed running. We obtained plausible results for both, including compared against Triassic theropod footprints and our prior work using static simulations. Leg muscles acted in ways comparable with how birds use them, for example, and matching some of my prior predictions (from anatomy and simple ideas of mechanics) of how muscle function should have evolved. The hindlimbs were more upright (vertical; and stiff) as we suspect earlier theropods were; unlike the more crouched, compliant hindlimbs of birds.

TENET: Thou shalt not study extinct archosaur locomotion without looking at extant archosaurs, too!
Computer simulation of extinct theropod dinosaur Coelophysis running at maximum speed. Grey tiles = 50 cm.

We observed that the simulations did clever things with the tail, swinging it side-to-side (and up-down) with each step in 3D; and in-phase with each leg: as the leg moved backward, the tail moved toward that leg’s side. With deeper analyses of these simulations, we found that this tail swinging conserved angular momentum and thus mechanical energy; making locomotion effectively cheaper, analogous to how humans swing their arms when moving. This motion emerged just from the physics of motion (i.e., the “multi-body dynamics”); not being intrinsically linked to muscles (e.g. the big caudofemoralis longus) or other soft tissues/neural control constraints (i.e., the biology). That is a cool finding, and because Coelophysis is a fairly representative theropod in many ways (bipedal, cursorial-limb-morphology, big tail, etc.), these motions probably transfer to most other fully bipedal archosaurs with substantial tails. Curiously, these motions seem to be opposite (tail swings left when right leg swings backward) in quadrupeds and facultatively bipedal lizards, although 3D experimental data aren’t abundant for the latter. But then, it seems beavers do what Coelophysis did?

Tail swings this-a-way (by Peter Bishop)
Computer simulation of extinct theropod dinosaur Coelophysis running at maximum speed, shown from behind to exemplify tail lateral flexion (wagging). Grey tiles = 50 cm.

The tail motions, and the lovely movies that our simulations produce, are what the media would likely focus on in telling the tale of this research, but there’s much more to this study. The tinamou simulations raise some interesting questions of why certain details didn’t ideally reflect reality: e.g., the limbs were still a little too vertical, a few muscles didn’t activate at the right times vs. experimental data, the foot motions were awkward, and the forces in running tended to be high. Some of these have obvious causes, but others do not, due to the complexity of the simulations. I’d love to know more about why they happen; wrong outputs from such models can be very interesting themselves.

Computer simulation of modern tinamou bird (brown) and extinct theropod dinosaur Coelophysis (green) running at maximum speed. Grey tiles = 10 cm for tinamou, 50 cm for Coelophysis.

Speaking of wrong, in order to make our Coelophysis walk and run, we had to take two major shortcuts in modelling the leg muscles. The tinamou model had standard “Hill-type” muscles that almost everyone uses, and they’re not perfect models of muscle mechanics but they are a fair start; it also had muscle properties (capacity for force production, length change, etc.) that were based on empirical (dissection, physiology) data. Yet for our fossil, because we don’t know the lengths of the muscle fibres (active contractile parts) vs. tendons (passive stretchy bits), we adopted a simplified “muscle” model that combined both into one set of properties rather than more realistically differentiating them. It was incredibly important, then, that we try this simple muscle model with our tinamou to see how well it performed; and it did OK but still not “perfect”, and that simple muscle model might not work so well in other behaviours. That was the first major shortcut. Second, again because we don’t know the detailed architecture of the leg muscles in Coelophysis, we had to set very simple capacities for muscular force production: all muscles could only produce at most 2.15 body weights of force. This assumption worked OK when we applied it to our simulation of sprinting in the tinamou (vs. average 1.95 body weights/muscle in the real bird), so it was sufficiently justifiable for our purposes. In current work, we’re examining some alternative approaches to these two shortcuts that hopefully will improve outputs while maximising realism and objectivity.

Computer simulation of extinct theropod Coelophysis running at maximum speed, shown alongside running human (at 4 m/s) for scale and context. Image credit: Peter Bishop.

If you pay close attention, our simulations of Coelophysis output rather high leg-forces, and it’s unclear if that’s due to the simple muscle model, the simple foot modelling, or is actually realistic due to the more vertical (hence stiff) hindlimbs; or all of these. Another intriguing technical finding was that shifting the body’s centre of mass forwards slowed down the simulation’s running speed, as one might expect from basic mechanics (greater leg joint torques), but unlike some prior simulations by other teams.

Computer simulation of extinct theropod Coelophysis shown alongside running human for scale and context. Shown from above to illustrate tail wagging behaviour. Image credit: Peter Bishop.

Users of models and simulations are very familiar with catchphrases like “all models are wrong, but some are useful” or the much more cynical (or ignorant) “garbage in, garbage out”; or the very dangerous attitude that “if the mathematics is correct, then the models can’t be that wrong” (but if the biology is wrong, fuggedaboutit!). These are salutary cautionary tales and catechisms that keep us on our toes, because the visual realism that realistic-looking simulations produce can seduce you into thinking that the science is better than it is. It’s not a field that’s well-suited for those fearful of being wrong. I’ll never think these outputs are perfect; that is a crazy notion; but today I feel pretty good. This was a long time coming for me, and it is satisfying to get to this stage where we can push forwards in some new directions such as comparing simulations of different species to address bigger evolutionary questions.

The wrestling with scepticism never ends, but we can make progress while the match goes on.

from WWE… I could not resist

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Darwin Day 2019: Some Papers In Evolutionary Biomechanics

Posted in Biomechanics, Exalting Archosauria, Freezermas, Frozen Mammals, Two-Dog-Night Tetrapods, tagged , , , , , , , , , on February 12, 2019| 1 Comment »

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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How to Turn an Elephant Hindlimb Into a Biomechanical Computer Simulation

Posted in Geeking Out, tagged , , , , , , on May 16, 2012| 18 Comments »

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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