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A review of paleontological finite element models and their validity

Published online by Cambridge University Press:  14 July 2015

Jen A. Bright
Jen A. Bright*
Affiliation:
School of Earth Sciences, University of Bristol, Wills Memorial Building, Queen's Road, Bristol BS8 1RJ, UK,
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Abstract

Finite element analysis (FEA) is a powerful quantitative tool that models mechanical performance in virtual reconstructions of complex structures, such as animal skeletons. The unique potential of FEA to elucidate the function, performance, and ecological roles of extinct taxa is an alluring prospect to paleontologists, and the technique has gained significant attention over recent years. However, as with all modeling approaches, FE models are highly sensitive to the information that is used to construct them. Given the imperfect quality of the fossil record, paleontologists are unlikely to ever know precisely which numbers to feed into their models, and it is therefore imperative that we understand how variation in FEA inputs directly affects FEA results. This is achieved through sensitivity and validation studies, which assess how inputs influence outputs, and compare these outputs to experimental data obtained from extant species. Although these studies are restricted largely to primates at present, they highlight both the power and the limitations of FEA. Reassuringly, FE models seem capable of reliably reproducing patterns of stresses and strains even with limited input data, but the magnitudes of these outputs are often in error. Paleontologists are therefore cautioned not to over-interpret their results. Crucially, validations show that without knowledge of skeletal material properties, which are unknowable from fossilized tissues, absolute performance values such as breaking stresses cannot be accurately determined. The true power of paleontological FEA therefore lies in the ability to manipulate virtual representations of morphology, to make relative comparisons between models, and to quantitatively assess how evolutionary changes of shape result in functional adaptations.

Type
Research Article
Information
Journal of Paleontology , Volume 88 , Issue 4 , July 2014 , pp. 760 - 769
Copyright
Copyright © The Paleontological Society 

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References

Anderson, A. E., Peters, C. L., Tuttle, B. D., and Weiss, J. A. 2005. A subject-specific finite element model of the pelvis: Development, validation and sensitivity studies. Journal of Biomechanical Engineering, 127:364–373.CrossRefGoogle ScholarPubMed
Anderson, P. S. L., Gill, P. G., and Rayfield, E. J. 2011. Modeling the effects of cingula structure on strain patterns and potential fracture in tooth enamel. Journal of Morphology, 272:50–65.CrossRefGoogle ScholarPubMed
Anderson, P. S. L., Bright, J. A., Gill, P. G., Palmer, C., and Rayfield, E. J. 2012. Models in palaeontological functional analysis. Biology Letters, 8:119–122.CrossRefGoogle ScholarPubMed
Attard, M. R. G., Chamoli, U., Ferrara, T. L., Rogers, T. L., and Wroe, S. 2011. Skull mechanics and implications for feeding behaviour in a large marsupial carnivore guild: The thylacine, Tasmanian devil and spotted-tailed quoll. Journal of Zoology, 285:292–300.CrossRefGoogle Scholar
Bates, K. T. and Falkinham, P. L. 2012. Estimating maximum bite performances in Tyrannosaurus rex using multi-body dynamics. Biology Letters, 8:660–664.CrossRefGoogle ScholarPubMed
Berthaume, M. A., Dechow, P. C., Iriarte-Diaz, J., Ross, C. F., Strait, D. S., Wang, Q., and Grosse, I. R. 2012. Probabilistic finite element analysis of a craniofacial finite element model. Journal of Theoretical Biology, 300:242–253.CrossRefGoogle ScholarPubMed
Bright, J. A. 2012. The importance of craniofacial sutures in biomechanical finite element models of the domestic pig. PLoS One, 7:e31769.CrossRefGoogle ScholarPubMed
Bright, J. A. and Gröning, F. 2011. Strain accommodation in the zygomatic arch of the pig: A validation study using digital speckle pattern interferometry and finite element analysis. Journal of Morphology, 272:1388–1398.CrossRefGoogle ScholarPubMed
Bright, J. A. and Rayfield, E. J. 2011a. Sensitivity and ex vivo validation of finite element models of the domestic pig cranium. Journal of Anatomy, 219:456–471.CrossRefGoogle ScholarPubMed
Bright, J. A. and Rayfield, E. J. 2011b. The response of cranial biomechanical finite element models to variations in mesh density. The Anatomical Record, 294:610–620.CrossRefGoogle ScholarPubMed
Casas, M. J., Krimbalis, P. P., Morris, A. R., Behdinan, K., and Kenny, D. J. 2007. An experimentally calibrated finite element study of maxillary trauma. Dental Traumatology, 23:273–277.CrossRefGoogle ScholarPubMed
Chung, D. H. and Dechow, P. C. 2011. Elastic anisotropy and off-axis ultrasonic velocity distribution in human cortical bone. Journal of Anatomy, 218:26–39.CrossRefGoogle ScholarPubMed
Cox, P. G., Fagan, M. J., Rayfield, E. J., and Jeffery, N. 2011. Finite element modelling of squirrel, guinea pig and rat skulls: Using geometric morphometrics to assess sensitivity. Journal of Anatomy, 219:696–709.CrossRefGoogle ScholarPubMed
Currey, J. D. 2002. Bones: Structure and mechanics. Princeton University Press, Princeton, 436p.CrossRefGoogle Scholar
Curtis, N., Kupczik, K., O'Higgins, P., Moazen, M., and Fagan, M. J. 2008. Predicting skull loading: applying Multibody Dyanamics Analysis to a macaque skull. The Anatomical Record, 291:491–501.CrossRefGoogle Scholar
Curtis, N., Jones, M. E. H., Evans, S. E., Shi, J., O'Higgins, P., and Fagan, M. J. 2010. Predicting muscle activation patterns from motion and anatomy: Modelling the skull of Sphenodon (Diaspsida: Rhynchocephalia). Journal of the Royal Society Interface, 7:153–160.CrossRefGoogle ScholarPubMed
Curtis, N., Jones, M. E. H., Evans, S. E., O'Higgins, P., and Fagan, M. J. 2013. Cranial sutures work collectively to distribute strain throughout the reptile skull. Journal of the Royal Society Interface, 10:20130442.CrossRefGoogle ScholarPubMed
Daniel, T. L., Helmuth, B. S., Saunders, W. B., and Ward, P. D. 1997. Septal complexity in ammonoid cephalopods increased mechanical risk and limited depth. Paleobiology, 23:470–481.CrossRefGoogle Scholar
Degrange, F. J., Tambussi, C. P., Moreno, K., Witmer, L. M., and Wroe, S. 2010. Mechanical analysis of feeding behaviour in the extinct “terror bird” Andalgalornis steulleti (Gruiformes: Phorusrhacidae). PLoS One, 5:e11856.CrossRefGoogle ScholarPubMed
Donoghue, P. C. J., Bengston, S., Dong, X.-P., Gostling, N. J., Huldtgren, T., Cunningham, J. A., Yin, C., Yue, Z., Peng, F., and Stampanoni, M. 2006. Synchrotron X-ray tomographic microscopy of fossil embryos. Nature, 442:680–683.CrossRefGoogle ScholarPubMed
Dumont, E. R., Grosse, I. R., and Slater, G. J. 2009. Requirements for comparing the performance of finite element models of biological structures. Journal of Theoretical Biology, 256:96–103.CrossRefGoogle ScholarPubMed
Dumont, E. R., Ryan, T. M., and Godfrey, L. R. 2011. The Hadropithecus conundrum reconsidered, with implications for interpreting diet in fossil hominins. Proceedings of the Royal Society B, 278:3654–3661.CrossRefGoogle ScholarPubMed
Erdermir, A., Guess, T. M., Halloran, J., Tadepalli, S. C., and Morrison, T. M. 2012. Considerations for reporting finite element analysis studies in biomechanics. Journal of Biomechanics, 45:635–633.Google Scholar
Falkingham, P. L., Bates, K. T., Margetts, L., and Manning, P. L. 2011a. Simulating sauropod manus-only trackway formation using finite-element analysis. Biology Letters, 7:142–145.CrossRefGoogle ScholarPubMed
Falkingham, P. L., Bates, K. T., Margetts, L., and Manning, P. L. 2011b. The “Goldilocks” effect: Preservation bias in vertebrate track assemblages. Journal of the Royal Society Interface, 8:1142–1154.CrossRefGoogle Scholar
Farke, A. A. 2008. Frontal sinuses and head-butting in goats: A finite element analysis. Journal of Experimental Biology, 211:3085–3094.CrossRefGoogle ScholarPubMed
Fitton, L. C., Shi, J. F., Fagan, M. J., and O'Higgins, P. 2012. Masticatory loadings and cranial deformation in Macaca fasicularis: A finite element analysis sensitivity study. Journal of Anatomy, 221:55–68.CrossRefGoogle Scholar
Fletcher, T. M., Janis, C. M., and Rayfield, E. J. 2010. Finite element analysis of ungulate jaws: can mode of digestive physiology be determined? Palaeontologica Electronica, 13:21A, 15p.Google Scholar
Garwood, R., Dunlop, J. A., and Sutton, M. D. 2009. High-fidelity X-ray micro-tomography reconstruction of siderite-hosted Carboniferous arachnids. Biology Letters, 5:841–844.CrossRefGoogle ScholarPubMed
Gröning, F., Fagan, M. J., and O'Higgins, P. 2011. The effects of the periodontal ligament on mandibular stiffness: A study combining finite element analysis and geometric morphometrics. Journal of Biomechanics, 44:1304–1312.CrossRefGoogle ScholarPubMed
Gröning, F., Fagan, M. J., and O'Higgins, P. 2013. Comparing the distribution of strain with the distribution of bone tissue in a human mandible: a finite element study. The Anatomical Record, 296:9–18.CrossRefGoogle Scholar
Grosse, I. R., Dumont, E. R., Coletta, C., and Tolleson, A. 2007. Techniques for modeling muscle-induced forces in finite element models of skeletal structures. The Anatomical Record, 290:1069–1088.CrossRefGoogle ScholarPubMed
Herring, S. W., Rafferty, K. L., Liu, Z. J., and Marshall, C. D. 2001. Jaw muscles and the skull in mammals: The biomechanics of mastication. Comparative Biochemistry and Physiology Part A, 131:207–219.CrossRefGoogle ScholarPubMed
Hutchinson, J. R. 2012. On the inference of function from structure using biomechanical modelling and simulation of extinct organisms. Biology Letters, 8:117–118.CrossRefGoogle ScholarPubMed
Jasinoski, S. C., Rayfield, E. J., and Chinsamy, A. 2009. Comparative feeding biomechanics of Lystrosaurus and the generalized dicynodont Oudenodon. The Anatomical Record, 292:862–874.CrossRefGoogle ScholarPubMed
Jaslow, C. R. and Biewener, A. A. 1995. Strain patterns in the horncores, cranial bones and sutures of goats (Capra hircus) during impact loading. Journal of Zoology, 235:193–210.CrossRefGoogle Scholar
Jones, D., Evans, A. R., Siu, K. K. W., Rayfield, E. J., and Donoghue, P. C. J. 2012. The sharpest tools in the box? Quantitative analysis of conodont element functional morphology. Proceedings of the Royal Society B, 279:2849–2854.CrossRefGoogle ScholarPubMed
Klingenberg, C. P. 2013. Visualizations in geometric morphometrics: How to read and how to make graphs showing shape changes. Hystrix, the Italian Journal of Mammalogy, 24:15–24.Google Scholar
Klingenberg, C. P. and Gidaszewski, N. A. 2010. Testing and quantifying phylogenetic signals and homoplasy in morphometric data. Systematic Biology, 59:245–261.CrossRefGoogle ScholarPubMed
Kupczik, K., Dobson, C. A., Fagan, M. J., Crompton, R. H., Oxnard, C. E., and O'Higgins, P. 2007. Assessing mechanical function of the zygomatic region in macaques: Validation and sensitivity testing of finite element models. Journal of Anatomy, 210:41–53.CrossRefGoogle ScholarPubMed
Lautenschlager, S. 2013. Cranial myology and bite force performance of Erilkosaurus andrewsi: a novel approach for digital muscle reconstructions. Journal of Anatomy, 222:260–272.CrossRefGoogle ScholarPubMed
Liu, J., Shi, J., Fitton, L. C., Phillips, R., O'Higgins, P., and Fagan, M. J. 2011. The application of muscle wrapping to voxel-based finite element models of skeletal structures. Biomechanics and Modeling in Mechanobiology, 11:35–47.CrossRefGoogle ScholarPubMed
Marinescu, R., Daegling, D. J., and Rapoff, A. J. 2005. Finite-element modeling of the anthropoid mandible: the effects of altered boundary conditions. The Anatomical Record, Part A, 283A:300–309.CrossRefGoogle Scholar
McHenry, C. R., Wroe, S., Clausen, P. D., Moreno, K., and Cunningham, E. 2007. Supermodeled sabercat, predatory behaviour in Smilodon fatalis revealed by high-resolution 3D computer simulation. Proceedings of the National Academy of Sciences, 104:16010–16015.CrossRefGoogle ScholarPubMed
Metzger, K. A., Daniel, W. J. T., and Ross, C. F. 2005. Comparison of beam theory and finite-element analysis with in vivo bone strain data from the alligator cranium. The Anatomical Record, Part A, 283A:331–348.CrossRefGoogle Scholar
Moazen, M., Curtis, N., Evans, S. E., O'Higgins, P., and Fagan, M. J. 2008. Combined finite element and multibody dynamics analysis of biting in a Uromastyx hardwickii lizard skull. Journal of Anatomy, 213:499–508.CrossRefGoogle Scholar
Moazen, M., Curtis, N., O'Higgins, P., Jones, M. E. H., Evans, S. E., and Fagan, M. J. 2009. Assessment of the roles of sutures in a lizard skull: A computer modelling study. Proceedings of the Royal Society B, 276:39–46.CrossRefGoogle Scholar
Moazen, M., Jones, A. C., Jin, Z., Wilcox, R. K., and Tsiridis, E. 2011. Periprosthetic fracture fixation of the femur following total hip arthroplasty: A review of biomechanical testing. Clinical Biomechanics, 26:13–22.CrossRefGoogle ScholarPubMed
Moazen, M., Constantini, D., and Bruner, E. 2013. A sensitivity analysis to the role of the fronto-parietal suture in Lacerta bilineata: A preliminary finite element study. The Anatomical Record, 296:198–209.CrossRefGoogle Scholar
Moreno, K., Wroe, S., Clausen, P., McHenry, C., D'Amore, D. C., Rayfield, E. J., and Cunningham, E. 2008. Cranial performance in the Komodo dragon (Varanus komodoensis) as revealed by high-resolution 3-D finite element analysis. Journal of Anatomy, 212:736–746.CrossRefGoogle ScholarPubMed
Olesiak, S. E., Sponheimer, M., Eberle, J. J., Oyen, M. L., and Ferguson, V. L. 2010. Nanomechanical properties of modern and fossil bone. Palaeogeography, Palaeoclimatology, Palaeoecology, 289:25–32.CrossRefGoogle Scholar
O'Higgins, P., Cobb, S. N., Fitton, L. C., Gröning, F., Phillips, R., Liu, J., and Fagan, M. J. 2011. Combining geometric morphometrics and functional simulation: An emerging toolkit for virtual functional analysis. Journal of Anatomy, 218:3–15.CrossRefGoogle Scholar
Panagiotopoulou, O., Curtis, N., O'Higgins, P., and Cobb, S. N. 2010. Modelling subcortical bone in finite element analyses: A validation and sensitivity study in the macaque mandible. Journal of Biomechanics, 43:1603–1611.CrossRefGoogle ScholarPubMed
Panagiotopoulou, O., Kupczik, K., and Cobb, S. N. 2011. The mechanical function of the periodontal ligament in the macaque mandible: A validation and sensitivity study using finite element analysis. Journal of Anatomy, 218:75–86.CrossRefGoogle ScholarPubMed
Panagiotopoulou, O., Wilshin, S. D., Rayfield, E. J., Shefelbine, S. J., and Hutchinson, J. R. 2012. What makes an accurate and reliable subject-specific finite element model? A case study of an elephant femur. Journal of the Royal Interface, 9:351–361.CrossRefGoogle Scholar
Peterson, J. and Dechow, P. C. 2003. Material properties of the human cranial vault and zygoma. The Anatomical Record, Part A, 274A:785–797.CrossRefGoogle Scholar
Pierce, S. E., Angielczyk, K. D., and Rayfield, E. J. 2008. Patterns of morphospace occupation and mechanical performance in extant crocodylian skulls: A combined geometric morphometric and finite element modeling approach. Journal of Morphology, 269:840–864.CrossRefGoogle Scholar
Porro, L. B., Metzger, K. A., Iriarte-Diaz, J., and Ross, C. F. 2013. In vivo bone strain and finite element modelling of the mandible of Alligator mississippiensis. Journal of Anatomy, 218:59–74.Google Scholar
Ragazolla, F., Foster, L. C., Form, A., Anderson, P. S. L., Hansteen, T. H., and Fietzke, J. 2012. Ocean acidification weakens the structural integrity of coralline algae. Global Change Biology, 18:2804–2812.CrossRefGoogle Scholar
Rayfield, E. J. 2007. Finite element analysis and understanding the biomechanics and evolution of living and fossil organisms. Annual Review of Earth and Planetary Sciences, 35:541–576.CrossRefGoogle Scholar
Rayfield, E. J. 2011. Strain in the ostrich mandible during simulated pecking and validation of specimen-specific finite element models. Journal of Anatomy, 218:47–58.CrossRefGoogle ScholarPubMed
Rayfield, E. J., Norman, D. B., Horner, C. C., Horner, J. R., Smith, P. M., Thomason, J. J., and Upchurch, P. 2001. Cranial design and function in a large theropod dinosaur. Nature, 409:1033–1037.CrossRefGoogle Scholar
Rayfield, E. J., Milner, A. C., Xuan, V. B., and Young, P. G. 2007. Functional morphology of spinosaur “crocodile-mimic” dinosaurs. Journal of Vertebrate Paleontology, 27:892–901.CrossRefGoogle Scholar
Reed, D. A., Porro, L. B., Iriarte-Diaz, J., Lemberg, J. B., Holliday, C. M., Anapol, F., and Ross, C. F. 2011. The impact of bone and suture material properties on mandibular funtion in Alligator mississippiensis: Testing theoretical phenotypes with finite element analysis. Journal of Anatomy, 218:59–74.CrossRefGoogle Scholar
Richmond, B. G. 2007. Biomechanics of phalangeal curvature. Journal of Human Evolution, 53:678–690.CrossRefGoogle ScholarPubMed
Richmond, B. G., Wright, B. W., Grosse, I., Dechow, P. C., Ross, C. F., Spencer, M. A., and Strait, D. S. 2005. Finite element analysis in functional morphology. The Anatomical Record, Part A, 283A:259–274.CrossRefGoogle Scholar
Richmond, B.G., Wright, B. W., Grosse, I., Dechow, P. C., Ross, C. F., Spencer, M. A., and Strait, D. S. 2005. Finite element analysis in functional morphology. The Anatomical Record, Part A, 283A:259–274.CrossRefGoogle Scholar
Ross, C. F., Patel, B. A., Slice, D. E., Strait, D. S., Dechow, P. C., Richmond, B. G., and Spencer, M. A. 2005. Modeling masticatory muscle force in finite element analysis: Sensitivity analysis using principle coordinates analysis. The Anatomical Record, Part A, 283A:288–299.CrossRefGoogle Scholar
Ross, C. F., Berthaume, M. A., Dechow, P. C., Iriarte-Diaz, J., Porro, L. B., Richmond, B. G., Spencer, M., and Strait, D. 2011. In vivo bone strain and finite-element modelling of the craniofacial haft in catarrhine primates. Journal of Anatomy, 218:112–141.CrossRefGoogle ScholarPubMed
Seki, Y., Kad, B., Benson, D., and Myers, M. A. 2006. The toucan beak: Structure and mechanical response. Materials Science and Engineering C, 26:1412–1420.CrossRefGoogle Scholar
Seki, Y., Mackey, M., and Myers, M. A. 2012. Structure and micro-computed tomography-based finite element modeling of toucan beak. Journal of the Mechanical Behavior of Biomedical Materials, 9:1–8.CrossRefGoogle ScholarPubMed
Slater, G. J. and Van Valkenburgh, B. 2009. Allometry and performance: The evolution of skull form and function in felids. Journal of Evolutionary Biology, 22:2278–2287.CrossRefGoogle ScholarPubMed
Slater, G. J., Dumont, E. R., and Van Valkenburgh, B. 2009. Implications of predatory specialization for cranial form and function in canids. Journal of Zoology, 278:181–188.CrossRefGoogle Scholar
Soons, J., Herrel, A., Genbrugge, A., Aerts, P., Podos, J., Adriaens, D., de Witte, Y., Jacobs, P., and Dirckx, J. 2010. Mechanical stress, fracture risk and beak evolution in Darwin's ground finches (Geospiza). Philosophical Transactions of the Royal Society B, 365:1093–1098.CrossRefGoogle ScholarPubMed
Soons, J., Herrel, A., Genbrugge, A., Adriaens, D., Aerts, P., and Dirckx, J. 2012a. Multi-layered bird beaks: A finite-element approach towards the role of keratin in stress dissipation. Journal of the Royal Society Interface, 9:1787–1796.CrossRefGoogle ScholarPubMed
Soons, J., Lava, P., Debruyne, D., and Dirckx, J. 2012b. Full-field optical deformation measurement in biomechanics: Digital speckle pattern interferometry and 3D digital image correlation applied to bird beaks. Journal of the Mechanical Behavior of Biomedical Materials, 14:186–191.CrossRefGoogle ScholarPubMed
Stayton, C. T. 2009. Application of thin-plate spline transformations to finite element models, or, how to turn a bog turtle into a spotted turtle to analyse both. Evolution, 63:1348–1355.CrossRefGoogle ScholarPubMed
Strait, D. S., Wang, Q., Dechow, P. C., Ross, C. F., Richmond, B. G., Spencer, M. A., and Patel, B. A. 2005. Modeling elastic properties in finite-element analysis: how much precision is needed to produce an accurate model? The Anatomical Record, Part A, 283A:275–287.CrossRefGoogle Scholar
Strait, D. S., Richmond, B. G., Spencer, M. A., Ross, C. F., Dechow, P. C., and Wood, B. A. 2007. Masticatory biomechanics and its relevance to early hominid phylogeny: An examination of palatal thickness using finite element analysis. Journal of Human Evolution, 52:585–599.CrossRefGoogle ScholarPubMed
Tanner, J. B., Dumont, E. R., Sakai, S. T., Lundrigan, B. L., and Holekami, K. E. 2008. Of arcs and vaults: the biomechanics of bone-cracking in spotted hyenas (Crocuta crocuta). Biological Journal of the Linnean Society, 95:246–255.CrossRefGoogle Scholar
Taylor, J. D. and Layman, M. 1972. The mechanical properties of bivalve (Mollusca) shell structures. Palaeontology, 15:73–87.Google Scholar
Tseng, Z. J. 2009. Cranial function in a late Miocene Dinocrocuta gigantea (Mammalia: Carnivora) revealed by comparative finite element analysis. Biological Journal of the Linnean Society, 96:51–67.CrossRefGoogle Scholar
Tseng, Z. J., McNitt-Gray, J. L., Flashner, H., Wang, X., and Enciso, R. 2011. Model sensitivity and use of the comparative finite element method in mammalian jaw mechanics: Mandible performance in the gray wolf. PLoS One, 6:e19171.CrossRefGoogle ScholarPubMed
Tseng, Z. J. 2013. Testing adaptive hypotheses of convergence with functional landscapes: A case study of bone-cracking hypercarnivores. PLoS One, 8:e65305.CrossRefGoogle ScholarPubMed
Van Staden, R. C., Guan, H., and Loo, Y. C. 2006. Application of the finite element method in dental implant research. Computer Models in Biomechanics and Biomedical Engineering, 9:257–270.CrossRefGoogle ScholarPubMed
Viceconti, M., Olsen, S., Nolte, L-P., and Burton, K. 2005. Extracting clinically relevant data from finite element simulations. Clinical Biomechanics, 20:451–454.CrossRefGoogle ScholarPubMed
Wang, Q., Smith, A. L., Strait, D. S., Wright, B. W., Richmond, B. G., Grosse, I. R., Byron, C. D., and Zapata, U. 2010. The global impact of sutures assessed in a finite element model of a macaque cranium. The Anatomical Record, 293:1477–1491.CrossRefGoogle Scholar
Witmer, L. M. 1995. The extant phylogenetic bracket and the importance of reconstructing soft tissues in fossils, p. 19–33. InThomason, J. J.(ed.), Functional Morphology in Vertebrate Paleontology. Cambridge University Press, Cambridge.Google Scholar
Wood, S. A., Strait, D. S., Dumont, E. R., Ross, C. F., and Grosse, I. R. 2011. The effects of modeling simplifications on craniofacial finite element models: The alveoli (tooth sockets) and periodontal ligaments. Journal of Biomechanics, 44:1831–1838.CrossRefGoogle ScholarPubMed
Wroe, S. 2008. Cranial mechanics compared in extinct marsupial and extant African lions using a finite-element approach. Journal of Zoology, 274:332–339.CrossRefGoogle Scholar
Wroe, S., Clausen, P., McHenry, C., Moreno, K., and Cunningham, E. 2007. Computer simulation of feeding behaviour in the thylacine and dingo as a novel test for convergence and niche overlap. Proceedings of the Royal Society B, 274:2819–2828.CrossRefGoogle ScholarPubMed
Yang, W., Kashani, N., Li, X.-W., Zhang, G.-P., and Myers, M. A. 2011. Structural characterisation and mechanical behavior of a bivalve shell (Saxidomus purpuratus). Materials Science and Engineering C, 31:724–729.CrossRefGoogle Scholar
Young, P. G., Beresford-West, T. B. H., Coward, S. R. L., Notaberardino, B., Walker, B., and Abdul-Aziz, A. 2008. An efficient approach to converting three-dimensional image data into highly accurate computational models. Philosophical Transactions of the Royal Society A, 366:3155–3173.CrossRefGoogle ScholarPubMed
Young, M. T., Rayfield, E. J., Holliday, C. M., Witmer, L. M., Button, D. J., Upchurch, P., and Barrett, P. M. 2012. Cranial biomechanics of Diplodocus (Dinosauria, Sauropoda): Testing hypotheses of feeding behaviour in an extinct megaherbivore. Naturwissenschaften, 99:637–643.CrossRefGoogle Scholar
Zapata, U., Metzger, K., Wang, Q., Elsey, R. M., Ross, C. F., and Dechow, P. C. 2010. Material properties of mandibular cortical bone in the American alligator, Alligator mississippiensis. Bone, 46:860–867.CrossRefGoogle ScholarPubMed
Zienkiewicz, O.C., Taylor, R. L., and Zhu, J. Z. 2005. The finite element method: Its basis and fundamentals (sixth edition). Elsevier Butterworth-Heinemann, Oxford, U.K., 733p.Google Scholar