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The Response of Cranial Biomechanical Finite Element Models to Variations in Mesh Density
Author(s) -
Bright Jen A.,
Rayfield Emily J.
Publication year - 2011
Publication title -
the anatomical record: advances in integrative anatomy and evolutionary biology
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.678
H-Index - 62
eISSN - 1932-8494
pISSN - 1932-8486
DOI - 10.1002/ar.21358
Subject(s) - finite element method , convergence (economics) , polygon mesh , displacement (psychology) , quadratic equation , computer science , skull , point (geometry) , mathematics , algorithm , mathematical optimization , geometry , structural engineering , geology , engineering , psychology , economics , psychotherapist , economic growth , paleontology
Abstract Finite element (FE) models provide discrete solutions to continuous problems. Therefore, to arrive at the correct solution, it is vital to ensure that FE models contain a sufficient number of elements to fully resolve all the detail encountered in a continuum structure. Mesh convergence testing is the process of comparing successively finer meshes to identify the point of diminishing returns; where increasing resolution has marginal effects on results and further detail would become costly and unnecessary. Historically, convergence has not been considered in most CT‐based biomechanical reconstructions involving complex geometries like the skull, as generating such models has been prohibitively time‐consuming. To assess how mesh convergence influences results, 18 increasingly refined CT‐based models of a domestic pig skull were compared to identify the point of convergence for strain and displacement, using both linear and quadratic tetrahedral elements. Not all regions of the skull converged at the same rate, and unexpectedly, areas of high strain converged faster than low‐strain regions. Linear models were slightly stiffer than their quadratic counterparts, but did not converge less rapidly. As expected, insufficiently dense models underestimated strain and displacement, and failed to resolve strain “hot‐spots” notable in contour plots. In addition to quantitative differences, visual assessments of such plots often inform conclusions drawn in many comparative studies, highlighting that mesh convergence should be performed on all finite element models before further analysis takes place. Anat Rec, 2011. © 2011 Wiley‐Liss, Inc.