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

osteoporotic (OP). The sample volume fractions (BV/TV) range from 14.6 to 51.1%.
The scans are 170x170x170 voxels at a resolution of 30µm.
Figure 1: Locations of 5x5x5mm cubic samples within the femoral head. The
nomenclature is as follows: MP – medial posterior, MSC – medial superior central,
MC – medial central, MIC – medial inferior central, MA – medial anterior, CP –
central posterior, SC – superior central, CC – central central, IC – inferior central,
CA – central anterior.
4.2 Procedure
The 5x5x5mm volumes of interest (VOIs) were directly considered as representative
volume elements as supported by an examination of the continuum assumption for
trabecular bone [23, 24, 25].
The µ-CT scans were first binarised into solid and void using an identical procedure for
all samples comprising contrast enhancement and automatic thresholding based on an
analysis of the image. A morphological analysis was then performed to determine
indices of micro-architecture including bone volume fraction (BV/TV) and trabecular
thickness (Tb.Th).
In order to perform mechanical tests on the samples, a finite element mesh was
generated from the binarised images using 10-noded tetrahedral elements. The tissuelevel
elastic properties were E = 18GPa and v = 0.3, which were applied to all elements.
Three uniaxial and three pure shear strain tests were applied independently to each
sample [26, 27]. The resulting stresses were averaged volumetrically, and from this the
full anisotropic elastic stiffness tensor was computed as
E= 1
V ∫ V
E t M dV (1)
where V is the sample volume, Et is the tissue stiffness tensor, and M is the local
structure tensor. The stiffness tensor was then optimised to find the most orthotropic
orientation, and the error in the orthotropy assumption was calculated [26]. The direct
stiffness (E1111) was also maximised separately in order to find its largest value and
direction.