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

A complete heterogeneous orthotropic model of the femur was produced with artificial
hip and knee joint structures, muscles and ligaments were included explicitly according
to the linear muscle model proposed [9] (Fig. 1, left). The geometry was extracted from
the Muscle Standardised Femur [11] and meshed with 326026 tetrahedral C3D4
elements with the same initial local orthotropic material properties (E1, E2, E3 = 3000
MPa, ν12, ν13, ν23 = 0.3, G12, G13, G23 = 1500 MPa) and orientations. The hip, patellofemoral
and tibio-femoral joints were modelled as bi-layered structures with an internal
isotropic elastic layer representing the cartilage (E = 10 MPa, ν = 0.49) and an external
isotropic elastic cortical bone layer (E = 18GPa, ν = 0.3) connected to the scaled
functional joint centres [12] by stiff elastic beam elements, in order to promote a
physiological load distribution (Fig. 1, right).
3.2 Load Cases
Three frames for three daily activities (normal walking, going upstairs and going
downstairs) were modelled, including the frame resulting in the maximum measured hip
contact forces. Segment positioning was extracted from published data [17, 18]. Body
weight was applied at the L5S1 joint and a single node on the condyle structure fixed in
the translational degrees of freedom (Figure 1, right).
3.3 Algorithm
At each iteration, , the model’s strains and stresses were found and processed. For each
element, the maximum absolute value across all frames was chosen for each of the
loading diagonal components, , of the strain tensor, . The guiding frame was
selected as the one where the maximum absolute value among these could be found and
its corresponding stress tensor, , extracted. The element material orientations were
matched with the local principal stress orientations, (Equation 1) and their associated
strain stimuli, , found (Equation 2),
eig , (1, 2)
The elements outside the remodelling plateau (1000 – 1500 µstrain) were then updated
proportionally to the absolute value of their associated strains in order to achieve a
target normal strain value of 1250 µstrain [2] (Equation 3),
with limited between 10 MPa and 30 GPa [13, 14]. E1, E2 and E3 were based on
the normal strains associated with the minimum, medium and maximum principal
stresses, respectively. Poisson’s ratios, were restricted (Equation 4) [15], and shear
moduli, , taken as a constant fraction of the average of the Young’s Moduli (Equation
5) [16]. The model was considered to achieve a state of convergence when E1, E2 and E3
remained constant at less than ±5% between iterations for at least 95% of elements and
the change in the model average elastic moduli values was less than ±1% after the
twentieth iteration. [10].
ν
0.09 ,
(3)
(4, 5)