Functional Morphology of Animal Feeding Apparata

[theropod]

There is apparently a FEA model that Infinity Blade posted some pages back, but it’s not published.
theworldofanimals.proboards.com/post/42506

There was also 2D FEA in Rayfield 2004 (Proc. R. Soc. Lond. B (2004) 271, 1451–1459, DOI 10.1098/rspb.2004.2755) and Rayfield et al. 2011 (Special Papers in Palaeontology, 86, 2011, pp. 241–253, doi: 10.1111/j.1475-4983.2011.01081.x) , for what it’s worth.

[Verdugo]

I just checked Rayfield 2011 does not have Tyrannosaurid in it. But anyway, it does not matter. I guess the we don't have any then. Which is odd since T-rex BF is one of the most studied subject, i'm surprised the no one has ever attempted to employ 3D FEA on it (Wroe never really published his T-rex 3D FEA so it does not provide any values other than an image).

Are there any studies on T-rex skull performance (strength) compared to Crocodilians (such as Gators) or to Mammalian Carnivores (like Wolf, Hyena, Big Cats)? Would be great to see how T-rex skull performs against some modern top Predators. 

Any studies on Abelisaurid's BF (such as Majungasaurus) that is not Therrien 2005? Those guys' predatory capacity is always a mystery to me. For example, Majungasaurus has a robust and broad skull, which seems to indicate a strong bite, but it's mandible is rather slender and kinetic which is not a trait you would expect from an animal with strong bite.   

[dinosauria101]

Verdugo

I think the upper head was the primary weapon in Majungasaurus; likely gripping or doing most of the damage for the lower jaw.
And Majung didn't necessarily need a strong bite; it could slice like a Komodo dragon too. Therrein got that result, I believe

[Infinity Blade]

Sept 20, 2019 8:39:17 GMT 5 Verdugo said:

Does anyone knows any T-rex BF studies that are done in 3D FEA? I know there are 3D BF studies of T-rex in Bates et al and Erickson et al but i don't think neither studies actually employed 3D FEA.

A couple months back there was a study released about kinesis in Tyrannosaurus' skull (it concluded that T. rex's skull was actually functionally akinetic). It was recently reported in the media and it turns out that it actually performed an FEA analysis on the dinosaur's skull, particularly Stan's. Here's what the paper says.

Upon this heatmap (Fig. 4), we project the regression line of Bates and Falkingham (2018), which compiled over 1,000 measured vertebrate muscles, along with plots of Bates and Falkingham’s (2012), Gignac and Erickson’s (2017), and our phylogenetically bracketed Tyrannosaurus muscle architecture data. Bates and Falkingham’s (2012) muscle force estimates used combinations of pennation angles of 0–20-degrees and fiber lengths of 0.1–0.4 times muscle length (i.e., 1/10–2/5 times muscle length), which resulted in forces below the regression line, thus corresponding to higher forces. Gignac and Erickson (2017) modeled muscles with 0-degrees pennation and a fiber length equal to muscle length, the combination of which yields the lowest possible PCSA. The PCSA estimates in Tyrannosaurus from the present study fall close to the regression line of all known vertebrate PCSAs published by Bates and Falkingham (2018), suggesting that the values we used are close to predictions from extant taxa and our bite force estimates are reasonable.

Bite forces in our Tyrannosaurus model (35,365N– 63,492N) extensively overlap with the range reported by Bates and Falkingham (2012; 18,065N–57,158N) and are about twice the magnitude predicted by Gignac and Erickson (2017; 8,526–34,522N). These differences between our results and those of Gignac and Erickson (2017) are likely due to our inclusion of pennate jaw muscles, whereas the latter authors modeled all jaw muscles as parallel fibered.

sci-hub.tw/10.1002/ar.24219

[Verdugo]

^ Just to be clear though, the BF of T-rex in the bracket is not a range of estimates but it's actually anterior and posterior BF. The paper does not make its clear on this regard. However, they did pointed out that their estimates for Gecko and Parrot represent different biting positions, so i assume it must be the same thing for T-rex:

Modeled Psittacus bite force (61.78N [rostral bite position]–
96.44N [caudal bite position]) was greater than the
16.74N reported for Monk Parakeets (Myiopsitta monachus)
estimated using PCSA by Carril et al. (2015) as expected
given that the skull of P. erithacus is about twice as
large. Bite forces in our Gekko models (11.27N [rostral
bite position]–18.53N [caudal bite position]) were near
ranges reported by both Anderson et al. (2008; 10.1N–
19.1N) and Herrel et al. (2007; 10.78N–16.97N) using
bite force meters.

Which exact position is not clear but i think it's probably anterior most and posterior most. So it probably represents incisiform and molariform BF of T-rex. Caniniform is probably somewhere in between

[Infinity Blade]

That sounds pretty reasonable.

[Verdugo]

Sept 26, 2019 15:55:49 GMT 5 Infinity Blade said:

That sounds pretty reasonable.

I agree. I think the latest BF is probably the most reasonable because it takes into account some of the 'issues' of previous studies. For example, Bates (2018) pointed out that the muscle model in Bates (2012) is less volumous than that of Gignac (2017). So the muscle model of Bates (2012) might be rather conservative in volume. On the other hand, the model in Gignac (2017) assumed un-pennated muscle which is kinda unrealistic. So overall, the new BF study seems to be the best of both worlds.

The BF estimate here is still lower than the in-vivo of a similarly sized Croc (80000 N at 7000 kg of mass), which is expected because Model and In vivo probably represent different things (Static/Sustained vs Impact/Peak/Snap BF). Overall, it's quite likely that T-rex would probably at least have similar in vivo BF to a similarly sized Croc.

[theropod]

^Do note that lack of accounting for muscle pennation is among the main issues that cause these underestimates in dry-skull-based bite force estimation. And Since Bates & Falkingham’s and Cost et al.’s estimates are already over twice as high as the dry-skull based figure for T. rex from McHenry (despite that being for a slightly larger specimen) and almost twice as high as that from Gignac & Erickson, around 6 t would probably be within a realistic range for a large T. rex’ in vivo bite force.

But a few tons more is possible too. That underlines the imprecision associated with these estimates, which is not often appreciated. It is just as possible that Stan or Sue bit as hard as a 4-5 ton crocodile as it is that they bit as hard as a 7-8 t crocodile. Really just goes to show how funny the common fixation with bite force is among the AVA people, what they are not considering is that there might not even be a significant difference between whatever two animals they are comparing, if they are just comparing estimates and different methods.

[Verdugo]

Sept 26, 2019 17:30:27 GMT 5 theropod said:

^Do note that lack of accounting for muscle pennation is among the main issues that cause these underestimates in dry-skull-based bite force estimation.

Dry skull is still meaningful comparative purpose imo. While it does underestimate the BF on a whole, it can still provide some comparative senses as long as you are sure that the methodology is consistent between whatever BF you're comparing.

Sept 26, 2019 17:30:27 GMT 5 theropod said:

And Since Bates & Falkingham’s and Cost et al.’s estimates are already over twice as high as the dry-skull based figure for T. rex from McHenry (despite that being for a slightly larger specimen) and almost twice as high as that from Gignac & Erickson, around 6 t would probably be within a realistic range for a large T. rex’ in vivo bite force.

But a few tons more is possible too.

Regarding the possibility of T-rex's in vivo BF. Well, the MBD method in Bates 2012 actually allows them to calculate both Impact/Peak BF (which is usually more akin to in vivo's) and Sustained/Static BF (which is usually more akin to Model's)

See Fig 2A

"Figure 2. (a) Bite force versus time for mid-jaw positions in the MDA models, showing an initial force peak representing the bite impact, before levelling off to record the sustained bite force (time normalized across models so that initiation of biting coincides).(b) Range in bite performance predictions for adult T. rex about the initial model for each parameter in the sensitivity analysis. Blue diamonds, initial model force; red squares, initial model velocity. (c) Mechanical advantage of jaw-closing muscles in the models. (d) Results of isometrically scaling all models to the mass of adult T. rex. White bars, force; grey bars, velocity. (e) Summed muscle force in the isometrically scaled models. (f) Comparison of biting forces predicted in this study with some of the largest values in the literature for terrestrial vertebrates ([4–8,12,13], grey bars are values from previous studies; white bars are from this analysis). (a,c) Lines: black, human; green, juvenile Alligator; red, adult Alligator; yellow, Allosaurus; blue, adult T. rex; purple, juvenile T. rex."

Bates 2012 also pointed out that the Impact BF for their Gators are consistent with in vivo data of those Gators:

Erickson et al. [13] reported peak forces of 500–765 N and 9000–11 125 N in alligators of equivalent size to our models. Peak forces in the initial biting impact overlap these values (figure 2a,f; juvenile 601–801 N, adult 9800–13 135 N).

I haven't done pixel measurements to figure out the exact value of T-rex Impact BF. But by eyeballing it, it seems to be ~ 80000 N. Anyway, i'm not suggesting that T-rex BF must be equal to that of a similarly-sized Croc so don't get me wrong here. I'm merely pointing out the possibility of T-rex in vivo BF according to Bates 2012. Obviously there are quite a few uncertainties here so who knows but for what we got, it seems like the hardest biting Tetrapods in the history also appear to have somewhat similar BFQ.

Sept 26, 2019 17:30:27 GMT 5 theropod said:

That underlines the imprecision associated with these estimates, which is not often appreciated. It is just as possible that Stan or Sue bit as hard as a 4-5 ton crocodile as it is that they bit as hard as a 7-8 t crocodile. Really just goes to show how funny the common fixation with bite force is among the AVA people, what they are not considering is that there might not even be a significant difference between whatever two animals they are comparing, if they are just comparing estimates and different methods.

To be fair, 2D to 2D or 3D to 3D are not always consistent in its methodology even though the results are usually quite comparable. To demonstrate what i mean: For example, both Bates 2012 and Cost 2019 used 3D methods to estimate the BF of Stan, the results from Bates 2012's MAX Model (=57000 N) is quite consistent to that of Cost 2019 (=63000 N). However, their methodologies are different in various ways. Bates 2012 used Fibre length = 0.1, while Cost 2019 used Fibre length = 2/3. Moreover, Bates 2012 used specific muscle tension = 30 N/cm2 while Cost 2019 used specific muscle tension = 25 N/cm2. Theoretically, Bates 2012 should produce higher results due to shorter Fibre length and higher specific tension. However, it's not the case here. This suggests that the Muscle Model in Cost 2019 is probably either more volumous or having longer in-level arm or both. In conclusion, while both Bates 2012 and Cost 2019 are 3D BF, it's not exactly perfect apple to apple comparison and for whatever reasons, their results happen to be quite consistent.

You can see this in Foffa 2014 and McHenry for Pliosaur BF as well. They're both 3D but they are not exactly the same thing either. McHenry used 3D FEA and un-pennated Muscles while Foffa used 3D non-FEA (contrary to popular belief, the BF from Foffa is actually not 3D FEA, the FEA in the study only used for mandible and rostrum performance) and pennated pterygoid muscles. And for whatever reasons, their BF results end up being quite consistent.

Meh, at least 3D BFs are usually consistently higher than 2D ones. So i do agree that we should only compare 2D to 2D, or 3D to 3D, or in vivo to in vivo.

[theropod]

Dry skull is still meaningful comparative purpose imo. While it does underestimate the BF on a whole, it can still provide some comparative senses as long as you are sure that the methodology is consistent between whatever BF you're comparing.

Yes it is. My point that the methods used by Bates & Falkingham and Cost et al. actually accounted for that, by taking into account pennation. That is a potential reason their figures tend to be higher than some dry-skull estimates for the same or comparable specimens would be. But of course technically there’s nothing preventing a dry skull estimate from assuming pennation as well, and indeed some do.

Regarding the possibility of T-rex's in vivo BF. Well, the MBD method in Bates 2012 actually allows them to calculate both Impact/Peak BF (which is usually more akin to in vivo's) and Sustained/Static BF (which is usually more akin to Model's)

Yes. I think another factor making the method fairly realistic. Of course since the figures they actually report (e.g. 57 kN) are sustained bite forces, not peak, that is still a factor of underestimate when compared to crocodilian in vivo data.

I haven't done pixel measurements to figure out the exact value of T-rex Impact BF. But by eyeballing it, it seems to be ~ 80000 N. Anyway, i'm not suggesting that T-rex BF must be equal to that of a similarly-sized Croc so don't get me wrong here. I'm merely pointing out the possibility of T-rex in vivo BF according to Bates 2012. Obviously there are quite a few uncertainties here so who knows but for what we got, it seems like the hardest biting Tetrapods in the history also appear to have somewhat similar BFQ.

I just did, and I’m getting something around 68 kN, measuring the uppermost end of drawn line for the T. rex curve. Of course this is fairly low-precision. The sustained BF seems to be 32 kN. That is supposed to be a mid-dentition estimate, so cannot be directly compared to their table, but the value strongly suggests this is for the initial model. Sustained BF estimates for the MAX model were about 27% higher, so scaling the peak bite force up along with that, we’d get about 86 kN for the corresponding peak BF.

Quite impressive and, I’d guess, probably quite in line with what in vivo peak bite force estimates might suggest if there were any.

To be fair, 2D to 2D or 3D to 3D are not always consistent in its methodology even though the results are usually quite comparable. To demonstrate what i mean: For example, both Bates 2012 and Cost 2019 used 3D methods to estimate the BF of Stan, the results from Bates 2012's MAX Model (=57000 N) is quite consistent to that of Cost 2019 (=63000 N). However, their methodologies are different in various ways. Bates 2012 used Fibre length = 0.1, while Cost 2019 used Fibre length = 2/3. Moreover, Bates 2012 used specific muscle tension = 30 N/cm2 while Cost 2019 used specific muscle tension = 25 N/cm2. Theoretically, Bates 2012 should produce higher results due to shorter Fibre length and higher specific tension. However, it's not the case here. This suggests that the Muscle Model in Cost 2019 is probably either more volumous or having longer in-level arm or both. In conclusion, while both Bates 2012 and Cost 2019 are 3D BF, it's not exactly perfect apple to apple comparison and for whatever reasons, their results happen to be quite consistent.

Yes, correct. What I meant was actually more that when talking about two estimates that appear to be different, the many factors that can cause errors in either directions are often forgotten. So if we have a bite force estimate for a T. rex at 5.7 t and a Pliosaurus at 4.8 t, that really isn’t even a very significant difference, and we shouldn’t consider it as such.

You can see this in Foffa 2014 and McHenry for Pliosaur BF as well. They're both 3D but they are not exactly the same thing either. McHenry used 3D FEA and un-pennated Muscles while Foffa used 3D non-FEA (contrary to popular belief, the BF from Foffa is actually not 3D FEA, the FEA in the study only used for mandible and rostrum performance) and pennated pterygoid muscles. And for whatever reasons, their BF results end up being quite consistent.

Well, in fact Foffa et al’s figures were quite a bit higher, at least their upper ones that had the pterygoid rescaled (which I’m usually going with). But that’s one more example of just what I mean.
I wouldn’t expect the bite force of P. kevani to have been much higher or lower than either that of T. rex or Kronosaurus, but different estimates vary quite a bit across these studies. It would be quite easy to cherrypick figures to support whatever conclusion about the bite forces we want, if we don’t make ourselves aware of the error margins.

Meh, at least 3D BFs are usually consistently higher than 2D ones. So i do agree that we should only compare 2D to 2D, or 3D to 3D, or in vivo to in vivo.

Yes, totally agreed.

[Verdugo]

Sept 27, 2019 4:48:34 GMT 5 theropod said:

I just did, and I’m getting something around 68 kN, measuring the uppermost end of drawn line for the T. rex curve. Of course this is fairly low-precision. The sustained BF seems to be 32 kN. That is supposed to be a mid-dentition estimate, so cannot be directly compared to their table, but the value strongly suggests this is for the initial model. Sustained BF estimates for the MAX model were about 27% higher, so scaling the peak bite force up along with that, we’d get about 86 kN for the corresponding peak BF.
Quite impressive and, I’d guess, probably quite in line with what in vivo peak bite force estimates might suggest if there were any.

Holy crap! 86 kN is higher than i expected. It's even more crazy to think that the figure is supposed to be mid-dentition position, which means that the BF at the molariform would probably be even higher. Plus, the MAX estimate from Bates 2012 is not even as high as that in Cost 2019. Anyway, of course we should not take this with absolute certainty but it does at least, like i said above, suggest somewhat similar BFQ between T-rex and those big Crocs.

Sept 27, 2019 4:48:34 GMT 5 theropod said:

Well, in fact Foffa et al’s figures were quite a bit higher, at least their upper ones that had the pterygoid rescaled (which I’m usually going with).

Are you sure about that though? Have you checked for the difference in Bite positions (out-level arm length)? I'm concerned it may play a role in explaining the BF difference between two studies here as the posterior BF in Foffa appears to be more posterior than that of McHenry's. But i may be wrong here, i'm not really familiar with specific tooth positions in Pliosaur (Foffa provided BF at the nth tooth positions but i don't where those tooth positions actually lie in the mandible)

I'm going with the pterygoid rescale here too, for sure. Parallel-fibre Model just does not seem really realistic to me.

[Verdugo]

Just came across this paper by chance, not sure if it has been posted before. This paper (Sellers et al 2017)used Gators and compared 3D level arms (seems to be a similar method to Cost et al 2019 if my understanding is correct) to FEA and to in vivo BF. They concluded that the results of 3D level arms and FEA are identical. Both Modelled methods, when compared to in vivo, underestimate the BF of larger individuals but overestimate the BF of smaller individuals. Moreover, the study also explains the difference between Peak/Impact/Snapping BF vs Static/Modelled/Sustained BF, similar to Foffa et al but clearer:

We found that modeled forces matched in vivo data well for intermediately sized individuals, and somewhat overestimated force in smaller specimens and underestimated force in larger specimens, suggesting that ontogenetically static muscular parameters and bony attachment sites alone cannot account for all the variation in bite force.

First, the mechanism of bite force production in our models differs from the direct measurements of Erickson et al. (2003). Whereas we modeled static, crushing bites, Erickson et al. (2003) included some unknown amount of momentum: the maximum force during ‘aggressive, snapping’ bites. Therefore, the peak force reported by these authors likely included some degree of impact force resulting from rapid mandibular deceleration. Daniel and McHenry (2001) suggested that ‘dynamic loading due to rapid deceleration’ likely plays a role in maximal forces experienced by the skull. Because the present study modeled static, crushing bites, which have no momentum contribution from impact forces, estimated maximum bite forces are presumably below peak forces experienced by the cranium

Given of what we know by now, it seems likely that the in vivo BF of T-rex would be even higher that of Modelled estimates.

[Grey]

Basically at this stage, which taxa appears to be the champion of heavy biters ? Tyrannosaurus, Deinosuchus or Purussaurus ? Since the method involved is always different. Or were there all in a similar department ?

[theropod]

Basically, thex are in a similar region, I don't think we can really confidently say which bit harder, but based on the peak bite force data from Bates and Falkingham, I'd be inclined to give a large T. rex individual the edge over the largest currently known Purussaurus, and probably also Deinosuchus.

[Grey]

Thank you. Thus, to get confidently higher bite forces we need to look at the theoretical big pliosaurs. Sachicasaurus seems well preserved to perform this type of analysis.