3D printing a crocodile

I have to say I was surprised how enthused everyone was for the 3D printed crocodile. It was the most interacted tweet I have ever done, and as promised I am ensuring all of the files are available so if people are keen they can do their own:

All files will print on a print bed that is 20x20cm, and are all scaled to the same size. However do check and scale up or down by 10 if required.

Print files:
Cranium - Lower jaw

Neck - Neck osteoderms

Forelimb (L - R)

Dorsal vertebrae and left ribs (with supports front, back) - Dorsal osteoderms
Sternal ribs fused/unfused

Pelvis and right leg, plus last dorsal vertebra and first caudal vertebra) - Pelvic osteoderms

Leg (L)

Anteriormost Caudal vertebrae

Posteriormost Caudal vertebrae

Method

So for anyone wondering how I put it together, it was fairly straight forward, albeit time consuming. If you don't have a set of 3D files (in this case ours were generated from CT scans and segmented in Mimics), there are an abundance of online 3D scans now in places like Morphosource, or phenome10k.org and even thingiverse (the Makerbot repository where I've uploaded my bits), but I strongly encourage you to check the specifics with regards to the use of their scans and to only print things you are allowed to.

The next steps involve tidying up your meshes, e.g. decimation of your mesh to make it smaller/easier to use, and remeshing to standardise triangle sizes etc. I recommend Meshlab for a lot of this as it is free. Google is also full of how-tos, but I am happy help. Feel free to reach out here or Twitter.

I then separated the sections I wanted using the select tool and deleting the unwanted bits. This could, and should, be done in segmentation if you have the scans, but I have to admit I wasn't sure how I was going to separate things when I first started. You will also likely get 3D models online that need separating, so not bad practice. In the case of the vertebral column where I separated the different regions, holes were created in the mesh (where the vertebrae were connected as a single unit). I fixed these in Blender (again a free download) by selecting the nodes in Edit Mode and making new faces to fill the holes.

For sections I wanted to fuse together I created a cylinder where an end was in a bone of interest.

Right lower leg and foot with cylinders shown between all the bones.

In the case of the osteoderms, I created a scaffold of cylinders that would sit on the vertebrae, and then vertical cylinders to attach to the osteoderms:

Scaffold for the dorsal osteoderms (from shoulders to pelvis) in the foreground, with complete scaffold with fused osteoderms for pelvis in the background.

Originally, I used the Boolean tool in Blender to union join the various parts and the cylinder:

but I found that this was not necessary for our printer/software (printing done on a Ultimaker 3 extended, Cura software) so later parts just had cylinders and bones saved together as a single obj. Your experiences may vary!

I printed all of the model on the Ultimaker 3 as I said above, using a normal 0.15mm layer thickness, automated support in the zig-zag shape with chunks enabled, and either a raft or brim support using generic PLA (2.85mm thickness) purchased from Amazon. We have the option of using 2 materials, and this probably would have been better to print using soluble material (PVA) for the support as it took a long time to manually remove the supports but as this was a test it was cheaper and far quicker to print just using the one material. It is not a perfect method and some of the smallest bits have really thin supports and broke during separation so some superglue was used to reattach them. I suspect something like a soldering iron (anything that gets up to 200C) to quickly remelt the ends could also work but please use caution and common sense!

Because our model was printed in chunks (due to the 20x20cm plate), but the original animal was obviously fully connected I created some supports for the dorsal vertebrae to get everything to the appropriate height and to ensure a realistic look. This was achieved by creating a cylinder or cube in Blender, and scaling it to be about 1.5 times wider than a single vertebrae, and a bit longer than 2 vertebrae. I then boolean subtracted the vertebrae from the cylinder, creating a vertebrae cradle. The concave surfaces of the cradle (where there are overhangs) were deleted in the edit mode (and new faces were made to fill the holes) so that the print could be slotted into the cradles.

Vertebral cradle

A disc at the horizontal level of the sternum was created and then a cylinder (other shapes available) created to connect the two (same method as for connecting bones). For the support of the vertebrae over the sternum I created a hollow where the sternum was so that the support would sit flush on the ground with the sternum passing between it by boolean subtracting a slightly enlarged sternum from the underside of the disc (the same procedure as for the vertebrae and cylinder except now for the disc).

In place in the model showing off the front support also has a gap for the sternum.

For our printer there is less support created if you change the shape up to whatever the minimum overhang angle (45-60 degrees depending on the machine) so other shapes may be better for print times/reducing support structures.

I hope this all makes sense, let me know if it doesn't and I'd love to see what you all achieve. If any of the meshes misbehave, let me know and I will try to upload corrections.

4 legs good, 2 legs better: How a dinosaur grows

The newest paper I've been involved in just came out, this time looking at Mussaurus and how it grows up (quick summary right at the end):

Otero A, Cuff AR, Allen V, Sumner-Rooney L, Pol D, Hutchinson JR. 2019. Ontogenetic changes in the body plan of the sauropodomorph dinosaur Mussaurus patagonicus reveal shifts of locomotor stance during growth. Scientific Reports.

What is Mussaurus?

Mussaurus is a sauropodomorph. If that doesn't make things any clearer, it is an early relative of the long neck, long tailed dinosaurs we know as sauropods (things like Diplodocus, Apatosaurus, Brachiosaurus, etc.). Found in Argentina, it is now dated from the early Jurassic (about 200 million years ago), having previously been dated to the Triassic.

Simplified phylogeny/family tree of sauropodomoprhs modified from Otero et al., 2015 with all silhouettes from phylopic.org

The name Mussaurus translates as "mouse lizard", and comes from the fact the first individuals found were small hatchlings that fit in the palm of your hand. In the years since its description in 1979 there have been many more individuals found covering a range of ages and associated increase in size.

Ageing a dinosaur
Dinosaurs, like trees, have rings that can be counted to determine how old they are. These lines of arrested growth (LAGs) are found particularly in long bones. It gets a bit messy with many long bones having marrow cavities (like in humans) which as the animal gets larger, so too does the marrow cavity which starts obliterating the innermost LAGs. This means that the age estimates are often given as a minimum. For our study we worked with 3 ages of Mussaurus: the smallest being palm sized and based on the sizes of eggs found nearby presumed to be hatchlings; a bigger group with individuals being determined to be under a year (no LAGs), but likely close to that age; and the largest at least 8 years old, and possibly up to 10 (which will be the age in all of my graphs below). 

Approximate sizes of the three different age groups from hatchling (bottom left), to yearling and adult.

Weighing a dinosaur

There are many ways to estimate the weight of a dinosaur but we chose 2 methods that are regularly  used in palaeontology. These are convex hulling and spline-based reconstruction:

Convex hull - this method works by building a simple geometric "box" (a hull) around bones, or series of bones to give a volume. All of the volumes are added together and multiplied by an estimated density for animals, and then multiplied by a correction factor. This correction factor is needed because the hulls are not biologically accurate (think of the amount of muscle usually on bones - see this earlier blog talking about it using lions). This method has been validated for calculating masses for mammals and birds.

Spline-based reconstructions - this method involves creating a series of hoops around various parts of the animal. For example, were the rib cage is, the hoop is built from the top of the vertebrae, around the ribs, and the gastralia/sternum. For the legs, different areas get hoops of different sizes as determined from the closest relatives of dinosaurs, birds and crocodiles (Allen et al., 2009). All of the hoops are ultimately joined together to create a 3D volume. The airways and lungs are also included. However there is variation between birds and crocodiles, and greater uncertainty with dinosaurs, so each of the segments (e.g. tail, chest, neck, arms, legs, airways/lungs) all get scaled up and down to create models with maximum and minimum estimates that are multiplied by the density of modern animals to get a mass. We can be fairly certain the real value lies somewhere between the extremes, but likely closer to the middle than the extremes.

Mass estimates between the two methods for Mussaurus.

The results between the 2 methods for masses are fairly similar. Hatchlings have a mass somewhere around 60-80g (about the size of a baby chicken/chick), by the time they are a year old they are 100x bigger at 8.19-8.30kg. That is an incredible amount of growth in a year. Just think about human babies being born around 3-4kg (6-8lbs) and being 300-400kg by the time they were 1 year old. For some of our domesticated birds this rate is exceeded, with modern turkeys carrying out this transition in size from 60g hatching to 8kg in 14-18 weeks (1/4 of the time) (Sogut et al,. 2016). In the next 7+ years of life for Mussaurus they continue growing at an incredible rate getting another 200x bigger reaching at least 1200-1500kg (about the size of a rhino or hippo). These growth rate are not unusual for dinosaurs, and the energetic requirements and stress associated with growing so much so quickly may be one of the major reasons there are so few "fully grown" adult dinosaurs of any species known with most dying before they attain their largest potential mass.

How can we use mass to infer posture?
Imagine you lean forward to touch your toes. Assuming you are flexible enough, this isn't too difficult. Now imagine having a really big head, or a long neck, or big arms and try again. You would likely find yourself tipping forwards. To counter this you might be able to bend your knees as if you were doing a squat and/or sticking your butt out to help keep yourself upright. However if your centre of mass gets too far forward, i.e. beyond your ability to get your foot (and by extension your knee) under your centre of mass, you will fall forward. This could be countered by reducing the mass of the front of your body (e.g. T. rex having tiny arms), having a big tail, or becoming quadrupedal (walking on all 4 limbs and using your arms to help support your mass). This simple biomechanical concept is what we applied to Mussaurus. The models allowed us to estimate the centre of mass for the different ages, and see how different regions influence the centre of mass.

We found that in the hatchlings the centre of mass is very far forward, about the length of the femur forward of the pelvis. This is the maximal theoretical limit of a centre of mass for a biped, assuming they held their femora horizontal when walking and only moved their lower legs. This of course is incredibly unlikely, and only seen in some real oddities today like penguins (who have of course become upright, and waddle), and also ignores the reality that you cannot put your knee perfectly forward of your hip as the stomach would get in the way (but you could move it to the side of your stomach, but this would have the effect of not being able to get your knee as far forward). As such we propose that Mussaurus hatchlings are quadrupedal. Through their growth the centre of mass moves back to a position that is very plausible for bipedal animals.

Centre of mass (COM) changes through ontogeny for Mussaurus. A COM of 1 would be directly between the shoulder blades, whilst a COM would be between the pelvis. 

However, having a centre of mass that is closer to your hips does not instantly make you bipedal, but our data, combined with a previous study showing that the adult Mussaurus could not get its hands flat on the ground (Otero et al., 2017), strongly suggest it was bipedal. Therefore Mussaurus follows an human-like transition from being quadrupedal when young, but becoming bipedal when adults. This transition is associated with a relative reduction in head and neck size and a relative increase in tail size.

How does this fit in our understanding of sauropod evolution?
We know that the later sauropodomorphs, the sauropods, were quadrupedal. Their giant columnar limb bones in both their arms and legs are built to support their weight. Early sauropodomorphs are smaller with much less robust forelimbs and are likely bipedal. We know there is a transition from biped to quadruped somewhere in the group but does our study help? Many studies suggest that "ontogeny recapitulates phylogeny", i.e. where your evolutionary history is reflected in how you grow. If this was the case we would expect Mussaurus to show a bipedal to quadrupedal transition not the other way round. This shows that the evolutionary history of locomotion within the sauropodomorphs is far more complicated than it first appears.

Quick conclusion
The take home/TLDR: We used computer modelling to discover a very interesting growth sequence for Mussaurus, which not only grows at a rapid rate, but transitions from being quadrupedal to bipedal during it.

References

Allen V, Paxton H, Hutchinson JR, 2009. Variation in Center of Mass Estimates for Extant Sauropsids and its Importance for Reconstructing Inertial Properties of Extinct Archosaurs. Journal of Anatomy 292, 1442-1461.

Sogut BI, Celik SI, Ayasan TII, Inci H, 2016. Analyzing Growth Curves of Turkeys Reared in Different Breeding Systems (Intensive and Free Range) with some Nonlinear Models. Rev. Bras. Cienc. Avic. 18, 619-628.

Otero A, Allen V, Pol D, Hutchinson JR, 2017. Forelimb muscle and joint actions in Archosauria: insights from Crocodylus johnstoni (Pseudosuchia) and Mussaurus patagonicus (Sauropodomorpha). PeerJ 5:e3976.