High order finite-element analysis of the proximal femur validated by
in-vitro experiments

Zohar Yosibash

Head - Computational Mechanics Laboratory, Dept. of Mechanical
Engineering, Ben-Gurion University of the Negev, Beer-Sheva, 84105,
Israel. E-mail: zohary@bgu.ac.il

Accurate methods for predicting and monitoring in-vivo bone strength are
of major importance in clinical applications. These are nowadays
unavailable due to difficulties in obtaining individual's bone geometry
and mechanical heterogeneous and anisotropic properties, and the thin 3-D
layers that preclude the use of automatic mesh generators. An improved
method for the generation of the femur's 3D model based on quantitative
computerized tomography (QCT) scans is presented. The geometry is
represented by smooth surfaces accurately and the inhomogeneous elastic
properties are evaluated. For that purpose, the QCT data were processed
following several steps, starting from bone borders detection at each CT
slice, trough surface approximation, to solid body representation, and
finally to mesh generation.

An internal smooth surface is used to separate the cortical and trabecular
regions upon which a high-order finite element (p-FE) auto-mesh is
constructed. Within each region (cortical or trabecular)  the QCT
Housefeld Unit (HU) values are recalculated using a moving average method
regardless of the FE mesh and inhomogeneous mechanical properties assigned
by LMS approximations.  The p-version of the finite element method is
thereafter applied to obtain results with controllable numerical errors.
To validate the results we performed mechanical in-vitro experiments on
freshly frozen femurs measuring head deflection and strains at several
points. Several FE model were created and compared to
the in-vitro experiments. The generation of the FE model, the isotropic
and anisotropic material properties influence, and the comparison to the
experimental observations will be presented. A very good agreement was
observed between the predicted results and experimental observations.