ARUP; ISBN: 978-0-9562121-5-3 - CMBBE 2012 - Cardiff University

A BIOMECHANICAL CONCEPT FOR CONSTRUCTION OF THE
TRAJECTORIES OF ANISOTROPIC ELASTICITY OF MAMMALIAN
BONY ORGANS, DEMONSTRATED FOR THE HUMAN MANDIBLE
1. ABSTRACT
C. Kober 1 , C. Müller 2 , P. Young 3 , A. Fritsch 4 , and C. Hellmich 5
Though tissue anisotropy is one of the key features of mammalian bone it cannot be
accessed in sufficient detail until now. A general concept for scientifically founded
approximation of these anisotropic trajectories is presented which is demonstrated for
the human mandible. Based on recent micromechanical results and experimental
evidence with regard to local orthotropic anisotropy of human bone, an algorithmic
procedure was developed for construction of the anisotropic trajectories from a
polynomial representation of the organ’s geometry and kind of inner skeleton deduced
from its inner material distribution. Finite Element simulations following the proposed
concept, based on exemplary mandibles, have already provided significant results
proving the relevance of tissue anisotropy for the mandibular load carrying behaviour.
By several FE feasibility studies, it was suggested that tissue anisotropy is not only
qualitatively relevant for the mandibular structural behaviour, but that in some sense,
“the anisotropy spares the mandible from loading”.
2. INTRODUCTION
Besides acceptable 3D-reconstruction of the organ’s geometry and realistic modelling of
the load case, an adequate material description is essential for reliable biomechanical
finite element simulation. Mammalian hard and soft tissue usually shows manifest
inhomogeneity and anisotropy. Especially, the latter one cannot be accessed in
sufficient detail until now. Therefore, a scientifically founded general concept was
developed for approximation of the anisotropic trajectories of elasticity which will be
demonstrated for the human mandible.
3. METHODS
By micro-mechanical investigation, it was shown that, collagen molecules are
responsible for the morphology of bone ultrastructure and bone tissue’s anisotropy [1-
3]. From these findings, we deduce that there is a relation between a) the skeletal
1
Professor, Faculty of Life Sciences, Hamburg University of Applied Sciences, Lohbruegger Kirchstr. 65,
D-21033 Hamburg, Germany
2
CADFEM GmbH, Marktplatz 2, D-85567 Grafing, Germany
3
Professor, Simpleware Ltd., Castle Street, Exeter, EX43PL, UK
4
Institute for Mechanics of Materials and Structures, Vienna University of Technology, Karlsplatz
13/202, A-1040 Vienna, Austria
5
Professor, Institute for Mechanics of Materials and Structures, Vienna University of Technology,
Karlsplatz 13/202, A-1040 Vienna, Austria