Application of Thin-Plate Spline Transformations to Finite Element Models, or, How to Turn a Bog Turtle into a Spotted Turtle to Analyze Both

Finite element (FE) models are popular tools that allow biologists to analyze the biomechanical behavior of complex anatomical structures. However, the expense and time required to create models from specimens has prevented comparative studies from involving large numbers of species. A new method is presented for transforming existing FE models using geometric morphometric methods. Homologous landmark coordinates are digitized on the FE model and on a target specimen into which the FE model is being transformed. These coordinates are used to create a thin-plate spline function and coefficients, which are then applied to every node in the FE model. This function smoothly interpolates the location of points between landmarks, transforming the geometry of the original model to match the target. This new FE model is then used as input in FE analyses. This procedure is demonstrated with turtle shells: a Glyptemys muhlenbergii model is transformed into Clemmys guttata and Actinemys marmorata models. Models are loaded and the resulting stresses are compared. The validity of the models is tested by crushing actual turtle shells in a materials testing machine and comparing those results to predictions from FE models. General guidelines, cautions, and possibilities for this procedure are also presented.

[1]  S. Wroe,et al.  Bite forces and evolutionary adaptations to feeding ecology in carnivores. , 2007, Ecology.

[2]  A. Jacobson,et al.  Morphometric tools for landmark data , 1993 .

[3]  C. McHenry,et al.  Biomechanics of the rostrum in crocodilians: a comparative analysis using finite-element modeling. , 2006, The anatomical record. Part A, Discoveries in molecular, cellular, and evolutionary biology.

[4]  G. Rivera,et al.  Ecomorphological variation in shell shape of the freshwater turtle Pseudemys concinna inhabiting different aquatic flow regimes. , 2008, Integrative and comparative biology.

[5]  E. Paradis,et al.  A geometric morphometric assessment of the effects of environment and cladogenesis on the evolution of the turtle shell , 2003 .

[6]  Ian R Grosse,et al.  Finite-element analysis of biting behavior and bone stress in the facial skeletons of bats. , 2005, The anatomical record. Part A, Discoveries in molecular, cellular, and evolutionary biology.

[7]  Emily J Rayfield,et al.  Cranial mechanics and feeding in Tyrannosaurus rex , 2004, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[8]  G. Eble,et al.  The flourishing diversity of models in theoretical morphology: from current practices to future macroevolutionary and bioenvironmental challenges , 2008, Paleobiology.

[9]  H. David Sheets,et al.  Geometric morphometrics for biologists : a primer , 2004 .

[10]  Philip Clausen,et al.  Computer simulation of feeding behaviour in the thylacine and dingo as a novel test for convergence and niche overlap , 2007, Proceedings of the Royal Society B: Biological Sciences.

[11]  P. Stephens,et al.  Convergence, Divergence, and Homogenization in the Ecological Structure of Emydid Turtle Communities: The Effects of Phylogeny and Dispersal , 2004, The American Naturalist.

[12]  Emily J Rayfield,et al.  Using finite-element analysis to investigate suture morphology: a case study using large carnivorous dinosaurs. , 2005, The anatomical record. Part A, Discoveries in molecular, cellular, and evolutionary biology.

[13]  E. Rayfield.  Finite Element Analysis and Understanding the Biomechanics and Evolution of Living and Fossil Organisms , 2007 .

[14]  Emily J Rayfield,et al.  Patterns of morphospace occupation and mechanical performance in extant crocodilian skulls: A combined geometric morphometric and finite element modeling approach , 2008, Journal of morphology.

[15]  T. Keaveny,et al.  Evolution of the biomechanical material properties of the femur , 2002, The Anatomical record.