Applying geometric morphometrics to compare changes in size and shape arising from finite elements analyses

Abstract

We consider how the methods of geometric morphometrics (GM) might combine with functional simulations using finite elements analysis (FEA). In particular we are concerned with how the deformations arising from FEA might be compared and visualized using GM. To these ends we apply these methods to a study of coronal plane forces applied to a model of an armadillo femur. We simulate the stance phase in the hind limb where the femur is subject to bending strains due to longitudinal compressive as well as abduction loads on the greater trochanter. We use this model to examine the hypothesis that muscles attaching to the third trochanter can reduce these bending strains in the loaded femur. The analysis uses standard finite element methods to produce strain maps and examine the strains at 200 point locations on the femur, but we also use the locations of the 200 points to run novel geometric morphometric analyses to assess the gross deformation of the model under different loadings. These provide insights into the application and usefulness of geometric morphometric methods in interpreting the results of finite element analyses. With further mathematical, engineering and statistical development the combination of FEA and GMM should open up new avenues of investigation of skeletal form and function in evolutionary biology. Download the complete Yellow Book on Virtual Morphology and Evolutionary Morphometrics in the new millenium.