Have you ever heard about using FEA in vertebrates?

During the months of the confinement due to the COVID-19 my colleagues from Transmitting Science asked me to record a short video to upload in the social networks. I decided to talk about the possibilities of Finite Element Analysis (FEA) in the field of vertebrates and when I mean possibilities, I mean different kind of elements, I mean different kind of geometries and, at the end of the street, different ways to create your FEA model. Because, of course, it is possible to use a tool from mechanical engineering to study the biomechanics of living and fossil vertebrates. It allows you for example to study locomotion or chewing and understand the evolution within their families. 

​But, what is Finite Element Analsys or FEA, which are the acronym of Finite Element Analysis? It is the matemathical way to solve problems of elasticity in complex geometries, so you can divide the geometry in tiny elements -but in a finite number- where the equations are easy to solve. Then, you can apply external forces in your model and understand how it deforms or how the inner forces are distributed inside the model. This method has been widely used in paleontology, antropology and functional morphology in general because now we can easily digitize the bony structures, so we can apply FEA in real geometries.  But, we cannot omit that we are creating models. So, Anderson et al. wrote in 2012 this sentence that today is still true:

"By definition, and in practice, models are not literal representations of reality but provide simplifications or substitutes of the events, scenarios or behaviours that are being studied or predicted. All models make assumptions. Therefore, we are creating models that maybe are not enough close to the reality but they can be very useful for our purpose."

Following the idea of simplification that Anderson was underlying, there are different kind of elements that we can use when we are creating a FEA model. The use of some of this elements imply -of course- a simplification of the reality to a simple model.  So, let me introduce you this different kind of elements and their features.

1. The element BEAM: You use them when your geometry is a line and you are working in the 3D space or in 2D. You define them creating the mesh of the elements in this line and a defining a cross-section. You can see an example of their use in Anderson et al 2007 where they simplified the skull of a fish in a linkage of four beams.
2. The element SHELL: You use them when your geometry is a surface and you are working in the 3D space. You define them creating the mesh of the element in this surface and defining a constant thickness. You can see an example of their use in my work about carpal bones (Püschel et al. 2020) because they havve a tiny layer of cortical bone with cancellous bone inside.
3. The PLANE elements: You use them when your geometry can be simplified to a surface that can lye in a 2D plane. Be careful because this elements are not 2D elements, they are called PLANE elements because they use the equations of plane elasticity. The surface is lying in a plane, the forces you apply should lye in this plane and you mAst define a thickness. The thickness play a role in the results, so you cannot avoid it and, for this reason, you cannot use the term "2D" here. You can see an example of their use in models of mandibles. For example I used them to create FEA models of the mandible of several primates in Marcé-Nogué et al 2017.
4. The SOLID elements: You use them when your geometry is a volume and you are working in the 3D space. They are the most spread and the ones people is always using when you have a real geometry from a CT-Scan, photogrammetry or laser. You can see an example of their use in thi work of Jack Tseng (2016) where he modelled the mandibles of different carnivora in three-dimensions instead of other more simplified options. ​​

Figure 1 - Example of beam, shell, plane and solid elements

These are the options you have for adapting your geometries to your FEA model. But probably you are asking yourself two questions. The first one is: Which are the differences between shell elements and plane elements? Shell elements are not lying in a plane or, if yes, they allow forces that are not in the plane, like perpendicular forces. You can see this difference in the FEA models of the skull of several Temnospondyls (Fortuny et al. 2011) where the forces I applied are perpendicular to the flat surface of the skull.
And the second one: Probably you think that if you have a ct-scan and you create a FEA model with solid elements then you have a realistic model. I regret to inform you that this is the first step when creating FEA models and there is still a lot of decisions to make. And proabably, in most of them you will need to simplify your model because always remember that models are not literal representations of reality.

References

Anderson, P.S.L.L., Westneat, M.W., 2007. Feeding mechanics and bite force modelling of the skull of Dunkleosteus terrelli, an ancient apex predator. Biol. Lett. 3, 77–80. https://doi.org/10.1098/rsbl.2006.0569
​Fortuny, J., Marcé-Nogué, J., DE Esteban-Trivigno, S., Gil, L., Galobart, Á., 2011. Temnospondyli bite club: ecomorphological patterns of the most diverse group of early tetrapods. J. Evol. Biol. 24, 2040–54. https://doi.org/10.1111/j.1420-9101.2011.02338.x
Marcé-Nogué, J., Püschel, T.A., Kaiser, T.M., 2017. A biomechanical approach to understand the ecomorphological relationship between primate mandibles and diet. Sci. Rep. 7, 8364. https://doi.org/10.1038/s41598-017-08161-0
​​Püschel, T.A., Marcé-Nogué, J., Chamberlain, A.T., Yoxall, A., Sellers, W.I., 2020. The biomechanical importance of the scaphoid-centrale fusion during simulated knuckle-walking and its implications for human locomotor evolution. Sci. Rep. 10, 3526. https://doi.org/10.1038/s41598-020-60590-6
​Tseng, Z.J., Grohé, C., Flynn, J.J., 2016. A unique feeding strategy of the extinct marine mammal Kolponomos : convergence on sabretooths and sea otters. Proc. R. Soc. B Biol. Sci. 283, 20160044. https://doi.org/10.1098/rspb.2016.0044