Consideration of anisotropic elasticity minimizes volumetric rather than shear deformation in human mandible

Abstract

This article is focused on the role of anisotropic elasticity in the simulation of the load distribution in a human mandible, due to a lateral bite on the leftmost premolar. Based on experimental evidence, orthotropy of the elastic properties of the bone tissue has been adopted. The trajectories of anisotropic elasticity are reconstructed from (i) the organ's geometry and (ii) from coherent structures which can be recognized from the spatial distribution of the grey values coming from computer tomography (CT).

A sensitivity analysis comprising various three-dimensional (3D) finite element (FE) simulations reveals the relevance of elastic anisotropy for the load carrying behavior of a human mandible: comparison of the load distributions in isotropic and anisotropic simulations indicates that anisotropy seems to “spare” the mandible from loading. Moreover, a maximum degree of anisotropy leads to kind of load minimization of the mandible, expressed by a minimum of different norms of local volumetric strain, evaluated throughout the organ. The observed optimization with respect to volumetric rather than shear strain seems to confirm the frequently emphazised role of volumetric-strain-induced fluid flow for the stimulation of cellular activity.

Keywords:

• Human mandible
• Bone
• Anisotropy
• Trajectories of elasticity
• Finite element simulation
• Tissue visualization

Acknowledgements

The authors gratefully acknowledge H.-C. Hege and his team at ZIB Berlin for the good cooperation and the Amira license. The geometry reconstruction from 3D image data and all visualizations—except for the diagrams—are performed with Amira 3.1 (see, Stalling et al. 2005). Furthermore, the authors want to thank Götz Bock (Munich University of Technology) for his continuous help, especially with regards to the network. Finally, we are grateful for computational assistance by Rainer Roitzsch (ZIB Berlin) and Jens Lang (Darmstadt University of Technology).