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

simulations are evaluated by quantitative and qualitative comparisons between the
predicted and the actual bone density of the scapula.
3. MATERIALS AND METHODS
The geometric model of the right scapula is generated from the Visible Human Male
Dataset [5]. In Solidworks®, a thin layer of cartilage is modeled at the surface of the
glenoid and at the tip of the coracoid process, which are then considered tied to the bone
in Abaqus®. The Young’s modulus and Poisson’s ratio of the cartilages are taken to be
6 MPa and 0.47, respectively. The material properties of bone result from the bone
remodeling model, considering a Poisson’s ratio of 0.3 and a maximum Young’s
modulus of 17 GPa.
The bone remodeling model used considers bone as a linearly elastic orthotropic
material obtained by the periodic repetition of a unit cell [6], as depicted in Fig. 1. In
this work, the unit cell considered consists of a cubic cell with throughout rectangular
holes with dimensions a1, a2 and a3 [7].
Fig. 1. Material model for bone.
Being the bone characterized, at each node [8], by the parameters of the microstructure
a, which are related with the bone density, and the Euler angles θ, which define the unit
cell orientation, the bone remodeling law is stated as
m
P P
u e u 0
NC H
E
P ijkl
(1)
ekl
ij
a
a
P1
where NC is the number of applied load cases, α P are the load weight factors, H
E ijkl are
the homogenized bone material properties [9], e ij and e kl are the components of the
strain filed and P
u is the set of displacements fields computed through the finite
element method. The parameters κ and m define the cost of bone maintenance and
therefore control the total amount of bone mass.
In this study, twelve load conditions including joint reaction and muscle forces at 10º,
30º, 50º, 70º, 90º and 110º of arm abduction and anterior flexion are considered. The
load applied to the scapula results from an inverse dynamic analysis of a multibody
system of the upper limb based on the same subject whose scapula is here analyzed [10,
11]. It should be noted that instead of applying the reaction forces at the scapulothoracic
joint, the nodes in the vicinity of these are constrained in all directions to avoid rigid
body motion [12]. The load weight factors α P , shown in Table 1, are defined based on
the frequencies of each movement and the arm positions during activities of the daily