These networks were used at the jaw joint (to line the articular surfaces), the occipital condyle (again, lining the articular surface), on the pterygoid buttress and apposing part of the mandible, on the teeth involved with the bite point, and at the muscle attachment surfaces. For twisting, ranked results were similar for only four models. Palin Responds To Sen. Kerry Joke: "Why The Long Face?" Dorsal view of various skulls, showing the spectrum of rostral proportions in (from top) crocodilians, odontocetes, plesiosaurs, ichthyosaurs and thalattosuchians. When shake forces were equalised to bite forces, the mandible was weaker in biting than in shaking for all species except Osteolaemus. Linear morphometric variables were selected a priori on the basis of beam theory principles. a question asked to know why someone is upset. Wireframe (left) of mandible from dorsal and lateral perspectives illustrates the change in shape along PC1 axis. To address this question, a combination of in vivo data, fluid dynamics and solid mechanics would be required to best model crocodilian jaws during prey capture. For biting, each of the teeth involved in the bite (see below) were restrained against rotation about the jaw hinge axis (dθ); additionally the two left teeth are restrained for translation along the jaw hinge axis (dZ – i.e. ΔAICc values are the difference in AICc between an explanatory model and the AICc-best explanatory model. In the latter case bite force in longirostrine forms decreases as outlever length increases, so the higher strain may indicate a more gracile mandible in these forms in addition to the effects of increased bending moments acting on the jaws. The skulls were modelled with homogeneous material property sets, with the brick elements representing bone assigned an elastic (Young’s) modulus of 13,471 MPa. How can mouth breathing make the upper jaw grow long? Whilst comparative approaches are of high value to palaeobiology, they tend to use post hoc analysis and are sometimes difficult to conduct in a way that explicitly tests hypotheses of form and function. (CSL-CW-VL-VA) – Constant symphyseal length and width, variable length and angle. The regions of high tensile (reds) and compressive (blues) stresses are shown. maximal) values (Figure 16); in the absence of validated data on actual strain values our assumption that 95% values provide a suitable basis for the analysis of results is untested but is logically sound. AICc score is a measure of the relative amount of information lost when using an explanatory model to approximate reality, taking into account both the number of parameters in the EM and the sample size. Copyright: © 2013 Walmsley et al. Speaking to a group of servicemen in Kosovo, Gov. Surface meshes were optimised to remove unwanted internal geometry (Figure 8) and to control the resolution of the final ‘tetrahedral’ solid mesh. In shaking, strain correlates with symphyseal length and PC1, whilst in twisting strain correlates with symphyseal length, length, and PC1. Second moments of area correspond to the geometry of long and short symphysis crocodilians. Specimens are plotted according to their respective PC2 values (centre right). Given that we have all been kids at some point, and we all breathe, surely this is something that should be common knowledge? Competing interests: The authors have declared that no competing interests exist. Surface meshes were used for morphometric analysis (see below) and formed the foundation upon which suitable FEA solid meshes were generated using Harpoon (SHARC). Multiple trusses were used per muscle, with the number of elements proportional to the size of the muscle. The general pattern of. https://doi.org/10.1371/journal.pone.0053873.g010. Y axis is the proportion of symphyseal length to mandibular length. Conceived and designed the experiments: CWW PDC CRM. (A), data for 82 specimens of crocodilian, data measured from photographs of museum skulls; regression line is based upon mean values for each species. I really liked this Sooz. Why the long face? Check your children. Taxa: A, Tomistoma schlegelii; B, Mecistops cataphractus; C, Crocodylus johnstoni; D, Crocodylus intermedius; E, Crocodylus novaeguineae; F, Crocodylus moreletii; G, Osteolaemus tetraspis. We thank Holger Preuschoft, Ulrich Witzel, Chris Glen and Bill Daniel for discussion on various aspects of biomechanics and Finite Element Analysis that ultimately lead to the research presented here. In all models, strain is low along the rami, and is concentrated within the symphysis. long face A facial expression denoting sadness, dissappointment, or dissatisfaction. (A), linear measurements of mandible; (B), landmark locations. David Eggerschwiler. When he sits down the bartender asks him: âwhy the long faceâ?â Whatâs probably more funny is the response of Alice. The three different contour qualities represent the 3D approximation of the mask and will form the isosurface. Image design and creation: CWW MRQ MRM CRM. Abbreviations are defined as follows: (CL, CSL; VA, VW) – Constant length and symphyseal length, variable angle and width. For shaking and twisting forces, we simulated an isometric force in the muscles (rather than isotonic fibre shortening during jaw adduction in biting) by assigning an increased elastic modulus to each truss element ; this had the effect of bracing the jaws as they hold a prey item, as occurs during actual shaking and twisting behaviours. Since we wished to determine the strength of the mandibles under load, the maximal strain values are the most useful for statistical analyses. Another important comparison is the qualitative predictions of beam models vs complex FEMs. The problem definition used to determine the equations of motion that describe the feeding behaviour associated with shaking a prey item. e53873. https://doi.org/10.1371/journal.pone.0053873.g021. September 28, 2013 at 1:51 am. In the beam models, we kept dimensions in the Y (vertical) axis constant to permit the effects of variation in geometry in the XZ plane to be explored without confounding effects from variation in beam section. https://doi.org/10.1371/journal.pone.0053873.g009, https://doi.org/10.1371/journal.pone.0053873.t004. The problem definition used to determine the equations of motion that describe the feeding behaviour associated with twisting a prey item. Background Crocodilians exhibit a spectrum of rostral shape from long snouted (longirostrine), through to short snouted (brevirostrine) morphologies. constant length and symphyseal length, variable angle and width (CL,CSL;VA, VW), constant length and width, variable symphyseal length and angle (CL, CW; VSL, VA), constant angle and width, variable symphyseal length and length (CA, CW; VSL, VL), constant symphyseal length and width, variable length and angle (CSL, CW; VL, VA). https://doi.org/10.1371/journal.pone.0053873.g006. Length is a much better predictor of strain than any other linear variable, and is also a much better predictor than multivariate measurements of shape (PC1) (Hypothesis C). For each load case in each complex FE model, strain values for the tetrahedral brick elements making up the skull and cranium were exported as text files and analysed in the R statistical programming environment . This relationship between head shape and diet has been considered reliable enough to serve as a basis to infer diet in fossil species of marine reptiles and mammals , , . here. In the upper jaw, the anterior snout has an almost tubular section and this is mirrored by the symphyseal part of the lower jaw in longirostrine crocodilians; the formation of an elongate symphysis seems to be a configuration allowing a minimal diameter of the mandible, and can be explained by hydrodynamic and/or energetic criteria. Weaker correlations are apparent between symphyseal length and biting, as well as between length and shaking, although the latter is a relatively poor explanatory model based on AICc. Yes In complex FE models, however, the maximal strain values are often associated with artefacts of the model (e.g. By combining predictions based in beam theory with data from complex FE modelling, we are able to test a priori hypotheses of the mechanical consequences of changes in morphology. School of Engineering, University of Newcastle, Newcastle, New South Wales, Australia, For biting, shaking and twisting loads, the simulated bite point was at the front of the jaw, at the largest tooth in the premaxillary row. Yes, truly. Implicit in the above hypothesis is the assumption that the biomechanics of the crocodilian mandible can be elucidated using beam theory; a secondary aim here is to quantify the extent to which that assumption is valid. Taxon labels: A, Tomistoma schlegelii; B, Mecistops cataphractus; C, Crocodylus johnstoni; D, Crocodylus intermedius; E, Crocodylus novaeguineae; F, Crocodylus moreletii; G, Osteolaemus tetraspis. Under simulated bite loads, strain in the beam models correlated positively and linearly with length when symphyseal length also varied (CA-CW-VL-VSL), and with length when symphyseal length did not vary (CSL-CW-VA-VL). https://doi.org/10.1371/journal.pone.0053873.g011, https://doi.org/10.1371/journal.pone.0053873.t005. https://doi.org/10.1371/journal.pone.0053873.g023, https://doi.org/10.1371/journal.pone.0053873.t012, https://doi.org/10.1371/journal.pone.0053873.t013. Using Finite Element software, construct a set of ‘simple’ (beam) and ‘complex’ (hi-res FE) models of each specimen, which are then analysed under simulated. Three sets of models were produced. The maximum estimated bite force, 2145 N for a rear bite by the C. intermedius ‘natural’ sized model is considerably less than that reported for that taxon (6276 N for an animal by Erickson ). Shake and twist feeding are also used to subdue prey after capture, with the use of twist feeding in crocodilians underlying the infamous ‘death roll’. Our approach allows researchers to focus on using information from first principles to identify the components of shape that are of interest and then quantify and compare the relative statistical performance of various hypotheses using model selection criteria, something that is rarely done in current studies of biomechanics. Image segmentation was largely straightforward, with the exception of the Crocodylus intermedius scan; this specimen had wire embedded in several positions within the mandible, resulting in refraction artefacts in the CT data; the affected slices were manually processed in a bitmap editor (Paintshop Pro v8, JASC) to improve image quality and reduce the influence of the artefacts (Figure 6). For twisting (TeT) loads, strain is highest at the symphyseal-rami junction, again with the exception of the Tomistoma model where the highest strains are at the anterior end of the symphysis. In people with VME, the lower third is significantly longer than the rest of the face. (see 1995 in music ). This motion is considered to be harmonic; since the skull oscillates about a neutral axis in a set period of time (); in our case this period is 0.25 seconds – i.e at a frequency () of 4 full cycles per second. For beam elements, the elastic modulus of the trusses representing muscle fibres was set to 0.1 MPa for biting load cases and 15 MPa for shaking and twisting load cases . The discrepancy is most likely because the jaw muscles in the FEMs are modelled as parallel fibred beams that run as straight lines between attachment points, whilst crocodilian muscles are actually pennated and run around bony structures (for example, M. pterygoidius posterior, which wraps around the ventral surface of the angular), aspects that are expected to increase total muscle force and effective inlever length. Click through the PLOS taxonomy to find articles in your field. Because ordinarily, the tongue rests on the upper palate and acts as a natural 'brace' guiding the teeth into correct position and ensuring the jaw grows sufficiently wide. Correlation with symphyseal length was positive and linear for models where symphyseal length varied (CA-CW-VL-VSL), but strain did not vary between models when symphyseal length was constant (CL-CSL-VA-VW, CSL-CW-VA-VL). The results here are somewhat encouraging for palaeobiomechanists; since simple measures of mandibular shape (length and symphyseal length) provide some insight into the mechanics of the mandible, the same measurements may be applicable to all of the above fossil reptile groups, and to marine mammals such as odontocetes, archaeocetes, and basal mysticetes , providing an answer to the functional morphologist’s question – where to put the callipers? In effect, this plot shows the allometric trajectory of ML/W for each species, with the smallest animals on the right and largest on the left of each species plot; i.e. AICc explanatory model selection indicates that symphyseal length is the best simple measurement at predicting mandibular strain under these loads, and is even better than a multivariate measure of shape (PC1 score) for twisting loads. AICc scores are shown in Tables 14, 15, 16. Strain in the first set of simple beam models, plotted against morphological variables (from top) length, symphyseal length, angle, and width, for biting (left), shaking (middle) and twisting (right) loads. Jaw adductor musculature was simulated using truss elements that carry only tensional loads between muscle origin and insertion points , , . As a result, the aquatic predators often use vigorous shaking of the prey, provided the prey is small enough to be held clear of the water. laterally). For biting and twisting simple linear measurements of the mandible provide better predictors of mechanics than a multivariate measure of shape (PC1); with overall length and symphyseal length outperforming PC1 for biting and twisting respectively. For both biting and shaking loads but not for twisting, simple beam models agree with best performance predictors in FE models. Note the longer symphyses at higher PC1 values. Stress contour plots for beam model based on M. cataphractus for biting (A), shaking (B), and twisting (C) loading regimes. Strain in the symphysis of these models is low, but strain in the rami immediately posterior to the symphysis is high, and the symphyseal-rami junction appears to be a weak point. For twist strain, the AICc-best explanatory model had symphyseal length as the sole predictor (Table 16). https://doi.org/10.1371/journal.pone.0053873.g004. Taxon: O.t, Osteolaemus tetraspis; C.ng, Crocodylus novaeguineae; C.i, Crocodylus intermedius; C.j, Crocodylus johnstoni; M.c, Mecistops cataphractus; T.s, Tomistoma schlegelii; C.m, Crocodylus moreletii. EMs within 2 of each other were considered nearly identical in information, while EMs with ΔAICc values of 4 and 8 are considered fair and EMs with a ΔAICc greater than 10 are poor . My question is, why not "Why a long face?"? The spectrum of jaw morphology in crocodilians has been interpreted as the functional trade-off between hydrodynamic agility and strength, with longirostrine skulls reflecting a low drag-high speed morphotype suited for capturing small agile prey, and meso- to brevirostrine skulls being low speed-high strength jaws better suited for killing and processing slower but larger or harder foods , , , . Skip to comments. This divergence could be due to the exclusion of sectional variance in beam models; since beam models had uniform section and real mandibles vary their section with length, this difference could be expected to change the mechanics. In the scaled models, the diameter of all beam elements was standardised. When a child cannot breathe through their nose for whatever reason (allergies, thumb sucking, nasal obstruction), they naturally open their mouths. 4.0 out of 5 stars A very interesting collection of peculiar short stories. This allows direct comparison between the results of the hi-res FE mandible models and beam modelling. In longirostrine forms, the elongated jaws provide extra reach and higher tip velocity, factors which likely contribute to success rates of capturing small agile prey. He sighs, before answering âThis is the thousandth time I have told told you. Note the strong correlation between bite and overall length, shake and symphyseal length, and twist and angle. Strain magnitude is higher under the biting loads; the difference is noticeable for longirostrine (A–C) and mesorostrine (D–F) taxa. If these loads accurately represent the magnitudes of loads used by crocodiles, then our results suggest that selection should result in increased resistance to bending loads from biting, rather than shaking or twisting, as a mandible that is strong enough to cope with a crocodile’s own bite force is already strong enough to cope with likely shaking or twisting loads. 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