Biomedical Engineering Reference
In-Depth Information
and Fleming, 2001; Bessho et al., 2007; Schileo et al., 2008), and fall loading, simulating impact
from a fall (Keyak et al., 1998; Verhulp, van Rietbergen, and Huiskes, 2008). Keyak, Skinner, and
Fleming (2001) investigated the effect of force direction and found that for the fall configuration, the
force direction with the lowest fracture load corresponded to an impact to the posterolateral aspect
of the great trochanter, and for atraumatic loading, the lowest fracture loads for the force directions
occurred when the load was similar to conditions while standing on one leg or climbing stairs. In
this chapter, subject-specific, image-based, nonlinear FE modeling of the proximal femur is intro-
duced to predict proximal femoral strength and failure location.
9.2
develoPment oF Femur modelS to PredICt Strength
and FraCture rISk
9.2.1 q
uantitatiVe
ct S
canninG
p
rocedure
Quantitative CT (QCT) scans were made of the hip region. The settings for the QCT scanning were
80 KVp, 280 mA, and 512 × 512 matrix in spiral reconstruction mode with 0.9375 mm pixel size
and 2.5 mm increments (GE Medical Systems/lightspeed 16, Wakesha, Wisconsin). To calibrate CT
Hounsfield units to equivalent bone mineral concentration, a calibration phantom containing known
hydroxyapatite concentrations was included in each scan (Image Analysis, Columbia, Kentucky).
The calibration phantom extending from the L1 vertebral body to the mid-femoral shaft was posi-
tioned under each subject. The phantom contained calibration cells of 0, 0.075, and 0.15 g/cm
3
equivalent concentration of calcium hydroxyapatite (Gong et al., 2012).
9.2.2 t
Hree
-d
imenSional
m
odelinG
of
tHe
p
roximal
f
emur
Three-dimensional reconstruction and surface meshing of the proximal femur was performed in
MIMICS software (Materialise Inc., Leuven, Belgium) from the femoral head to 1 cm below the lesser
trochanter; then it was imported into ABAQUS software (Simulia Inc., Waltham, Massachusetts) to
convert the triangular surface mesh into a four-node tetrahedral elements mesh. The largest average
element edge length was 1.76 mm, which could achieve a sufficiently precise prediction.
9.2.3 B
one
t
iSSue
H
eteroGeneity
To account for bone tissue heterogeneity, bone material in the whole proximal femur was divided
into approximately 170 discrete sets of materials so that the modulus of each material increased
in an increment of 5% over the modulus of the previous material (Keyak et al., 1998; Perillo-
Marcone, Alonso-Wazquez, and Taylor, 2003). All bone materials in the proximal femur were set
with a Young's modulus of 22.5 GPa. Relationships between ash density and elastic modulus can be
obtained from the literature (see Table 9.1). The apparent density of each element can be determined
from the linear regression relationship of the Hounsfield units of the calibration phantom to their
apparent density, and its ash density can be obtained from its apparent density using a relationship
between ash density and apparent density reported in the literature (Keyak et al., 1998). Then, which
bone material an element was assigned with can be determined.
A specific nonlinear constitutive relationship was assigned to each bone material. A four-
parameter bilinear constitutive model was used to describe the nonlinear constitutive relationship
of each bone material (Gong, Zhang, and Fan, 2011; Gong et al., 2012). The four parameters in the
constitutive model were tensile yield strain ( ε
t
T
), compressive yield strain ( ε
c
T
), pre-yield Young's
modulus (
E
), and post-yield modulus (
E
u
, assuming that the post-yield modulus in compression was
equal to that in tension) (Gong, Zhang, and Fan, 2011). The schematic of the bilinear constitutive
model of one bone material is shown in Figure 9.1.
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