FEA Diagram

FEA result of a papilliform minckleyi jaw. Blue represents areas of low stress, followed by green, white, yellow, and red, representing areas of increasingly higher stresses.

November, 2006 - Abstract for PURA grant application

Hericthys minckleyi is a unique species of Cichlid fish found in Cuatro Cienegas, Mexico. Its habitat is isolated, and H. minckleyi experiences fierce competition with other members of the species and with the hard-shelled snails that are its prey. H. minckleyi is trophically polymorphic, which means that as a species it produces two types of individuals with differing diets: those that excel at shredding plants, and those that excel at crushing hard-shelled snails with their pharyngeal jaws. A polymorphism is a genetic trait that varies within the same species, like hair color, eye color, nose shape, etc. in humans. This trophic polymorphism in minckleyi is unusual in that it comprises such an extensive change in diet and jaw design. The snail-crushing individuals, known as molariforms, have large and flat teeth, very robust jaws, and strong jaw muscles, whereas the plant-shredding individuals, known as papilliforms, have sharp and pointed teeth, gracile jaws, and weaker muscles. The snails crushed by molariforms are some of the hardest in the world, presumably because they are continuously evolving to resist crushing by minckleyi, while the minckleyi continuously evolve to be able to crush them. Because of this, the forces routinely used by molariforms to crush snails would immediately break the jaws of papilliforms if their muscles were able to produce them!

Such an extensive polymorphism within a species provides a unique opportunity to study how a trait evolves, and I have been studying how the jaw structure differs in molariforms and papilliforms in an effort to understand what aspects of the molariform jaw structure allow it to resist the forces required to crush these hard-shelled snails.

In 2006, I investigated the application of a technique called Finite-Element Analysis (FEA) to the problem of strength analysis of pharyngeal jaws. Computed-tomography scans of the jaws were used to generate 3D models, and FEA was used to simulate the stresses in the jaw during crushing of a snail. I developed methods for setting up the simulations, determining parameters, and identifying unrealistic artifacts of the simulation in the results. This fall, I improved these methods with the addition of novel simulation and analysis techniques, and am currently developing software in MATLAB to analyze the FEA results.

Using the software I am developing, I am performing an analysis of how stress and jaw structure vary between molariform and papilliform H. minckleyi groups. A unique aspect of this study is that FEA results from large groups of individuals are being compared, giving statistical power to the results. Because of the large variability within each morph, between individuals of the same size and throughout ontogeny, this type of analysis is necessary to understand what differences between molariform and papilliform jaws give them such extremely different force-resisting capabilities. This knowledge will ultimately help us understand how this trait evolved, and also the molecular and mechanical mechanisms behind force-mediated jaw and bone remodeling in general.

June, 2006 - Progress report for PURA grant

The Cichlidae comprise an amazingly diverse family of fish that evolve very rapidly and feed on all trophic levels. Herichthys minckleyi, a member of the cichlid family, has an oral jaw, which captures prey, and a pharyngeal jaw modified from gill arches, which processes prey. H. minckleyi is unique in that two distinct pharyngeal jaw morphologies exist within the same species. Molariform individuals, which primarily crush very hard snails with extreme force, have a robust jaw with large, flat teeth. Papilliform individuals, which mainly eat plant matter, have a much thinner, more delicate jaw with small, sharp teeth and smaller muscles (Hulsey et al, 2005). Finite Element Analysis (FEA) was used to simulate biting stresses in the jaws of H. minckleyi, using computational tomography (CT) scans to generate 3D models. With FEA, biting experiments were performed “in silico", and the strength of the jaw in resisting these biting forces was measured. Figure 1, below, shows the general form of the FEA simulations performed.

FEA was performed under the guidance of Angela Lin in Dr. Guldberg’s Micro-CT lab. FE experiments were performed on a number of minckleyi of varying size, as well as on individuals from several other species with molariform and papilliform pharyngeal jaw morphologies. Three sets of experiments were performed. The purposes of the first set were to determine the best way to convert the CT data into a 3D model and to learn the FEA software. To convert the data into a 3D model, a procedure was developed to carry out on each CT measurement that removed noise from the data, reduced the resolution so that FE calculations would finish in a reasonable amount of time, and set up where the jaw would be constrained and where the force would be applied. Material properties of bone were also determined from the literature to give the model the correct Young’s modulus and Poisson’s ratio. Capabilities of the software, especially FE settings and image manipulation commands were investigated and applied to improve the realism of the model.

The second and third sets of experiments were performed on a sample set of various sizes of molariform and papilliform minckleyi, and on several individuals of other species. The second set of experiments applied the developed procedure to the sample set. The strength was determined from the peak stress in the jaw. Theoretically, this metric should work, because when two jaws are subjected to the same force, the one that shows lower peak stress levels is the strongest. Stress concentrations where the jaw was constrained and where the force was applied made this metric impossible to apply properly, however. Stress concentrations are areas of very high stress in the model that exist because constraints can only be applied to flat, on-axis, surfaces, or to single points. When all the force on the jaw is transmitted through a single point, very high stress exists in that point and the surrounding area, when in actuality the joint or muscle attachment spreads the force out over a larger area. It turned out to be impossible to eliminate the stress concentrations entirely, so it was decided that data around the stress concentrations would have to be discarded. Another problem to be solved was that stress concentrations in the tooth extended below the tooth, rendering it impossible to accurately determine the strength of the jaw structure supporting the tooth.

To address these problems, the experiments were performed again with some modifications. In the third set of experiments, constrains were modified to be consistent among all samples. Previously, constraints had been positioned to attempt to reduce stress concentrations, but it is believed that doing so made the simulations somewhat unrealistic in other aspects. Instead, stress concentrations were removed in processing the results. The stress concentration in the tooth could not be discarded, because measuring the strength of the tooth-bearing jaw surface was desired, and the stress concentration extended into this surface. Instead, the tooth cap was simulated as a very hard material. This is in fact the same solution evolved in living organisms: When an organism is biting, all the stress from the food item is concentrated on a small area of the tooth, and an extremely hard enamel tooth cap serves to distribute the force onto a larger area of softer dentin underneath the enamel. Finally, in order to gain more insight into what features of the jaw contribute to its strength, and to be able to compare features between individuals, the resulting data was broken down into several regions: the horns, the keel, the suture line, and the tooth bed. The horns are the muscle attachment points, the end of the keel comprises the joint, the suture is a line extending from the back of the jaw towards the front along the centerline, and the keel is the ridge that starts where the suture ends and extents to the joint at the front of the jaw. The tooth bed holds the teeth in place, and resists the force that would push the teeth through the jaw. These regions are shown in Figure 1, which is an FEA result of a papilliform minckleyi. This jaw is being subjected to the load routinely used by molariform individuals to crush snails. The red areas are under stresses that would cause bone to fail, indicating that the papilliform jaws are not remotely able to withstand the forces required to crush snails.

At this time, the third set of experiments is being performed, and data has not yet been analyzed from it. This research project will be continued over the summer, during which time more experiments will be performed and more data collected so that the strength of each of these features can be compared between minckleyi morphs and other species. Additionally, experiments are being performed on very small, immature minckleyi that are believed to have been too small to eat snails. If very small molariform individuals show higher jaw strength, we may be able to conclude that there is a genetic basis for increased jaw strength in the molariform phenotype. These results will ultimately help us understand the molecular mechanisms and mechanical properties of force-mediated jaw and tooth remodeling, as well as the evolution of these phenotypes.