A new fracture assessment approach coupling HR-pQCT imaging and
fracture mechanics-based finite element modeling
Ani Urala,n, Peter Brunoa, Bin Zhoub, X. Tony Shib, X. Edward Guob
aDepartment of Mechanical Engineering, Villanova University, 800 Lancaster Avenue, Villanova, PA, USA
bBone Bioengineering Laboratory, Department of Biomedical Engineering, Columbia University, New York, NY, USA
a r t i c l e i n f o
Accepted 10 February 2013
High resolution peripheral computed
Cohesive finite element modeling
a b s t r a c t
A new fracture assessment approach that combines HR-pQCT imaging with fracture mechanics-based
finite element modeling was developed to evaluate distal radius fracture load. Twenty distal radius
images obtained from postmenopausal women (fracture, n¼10; nonfracture, n¼10) were processed to
obtain a cortical and a whole bone model for each subject. The geometrical properties of each model
were evaluated and the corresponding fracture load was determined under realistic fall conditions
using cohesive finite element modeling. The results showed that the whole bone fracture load can be
estimated based on the cortical fracture load for nonfracture (R2¼0.58, p¼0.01) and pooled data
(R2¼0.48, po0.001) but not for the fracture group. The portion of the whole bone fracture load carried
by the cortical bone increased with increasing cortical fracture load (R2Z0.5, po0.05) indicating that a
more robust cortical bone carries a larger percentage of whole bone fracture load. Cortical thickness
was found to be the best predictor of both cortical and whole bone fracture load for all groups (R2
range: 0.49–0.96, po0.02) with the exception of fracture group whole bone fracture load showing the
predictive capability of cortical geometrical properties in determining whole bone fracture load.
Fracture group whole bone fracture load was correlated with trabecular thickness (R2¼0.4, po0.05)
whereas the nonfracture and the pooled group did not show any correlation with the trabecular
parameters. In summary, this study introduced a new modeling approach that coupled HR-pQCT
imaging with fracture mechanics-based finite element simulations, incorporated fracture toughness
and realistic fall loading conditions in the models, and showed the significant contribution of the
cortical compartment to the overall fracture load of bone. Our results provide more insight into the
fracture process in bone and may lead to improved fracture load predictions.
& 2013 Elsevier Ltd. All rights reserved.
Osteoporosis is one of the prominent public health problems
affecting millions of people and leading to high medical costs in
the United States and the world (Cooper et al., 1992; Melton,
2003; Ray et al., 1997). Accurate identification of individuals
under high fracture risk is important for decreasing the preva-
lence and negative impact of fractures.
High resolution peripheral computed tomography (HR-pQCT) has
recently been proposed as a possible alternative to the current clinical
fracture risk assessment approach, dual energy X-ray absorptiometry
(DXA), based on several studies which demonstrated that bone
mineral density (BMD) measured by DXA is not sufficient to predict
future fractures (Cummings et al., 1990; Hui et al., 1988; Ott, 1993).
HR-pQCT provides three-dimensional in vivo images combining BMD,
geometry and architecture of both cortical and trabecular bone
compartments exclusively at distal radius and tibia that can be used
as early detection sites for future hip and spine fractures (Cuddihy
et al., 1999; Lauritzen et al., 1993; Mallmin et al., 1993; Owen et al.,
1982). The detailed noninvasive bone measurements by HR-pQCT
may provide additional information which can lead to a better
assessment of fracture risk.
The bone images obtained by HR-pQCT can also be converted
to finite element models to improve the mechanistic understand-
ing of the failure process in bone. The current state of the art in
HR-pQCT-based finite element modeling utilizes axial compres-
sive loading of the clinical scan region at the distal radius or tibia
and evaluates the failure load based on the percentage of
elements that exceed a certain level of strain (Pistoia et al.,
2002). This approach has been used to evaluate the structural
and mechanical properties of distal radius and tibia (Liu et al.,
2010; Varga et al., 2010), to compare bone properties between
patients with and without fracture (Boutroy et al., 2008; Melton
et al., 2007), and to determine the load distribution between the
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Journal of Biomechanics
0021-9290/$-see front matter & 2013 Elsevier Ltd. All rights reserved.
nCorresponding author. Tel.: þ1 610 519 7735; fax: þ1 610 519 7312.
E-mail address: firstname.lastname@example.org (A. Ural).
Journal of Biomechanics 46 (2013) 1305–1311
cortical and trabecular bone (Boutroy et al., 2008; Burghardt et al.,
2010; MacNeil and Boyd, 2007).
Although these studies were successful at several fronts,
development of new modeling techniques that can provide a
better understanding of the fracture process in bone will be
beneficial. This can be achieved by introducing a fracture
mechanics-based failure criterion and by incorporating loading
conditions that represent fall orientations in the finite element
models. The use of a fracture mechanics-based approach instead
of a strength-based approach will provide a more robust failure
criterion by explicitly modeling the crack formation process and
by integrating fracture toughness, a parameter that directly
influences the bone fracture behavior (Nalla et al., 2004;
Vashishth et al., 1997) in the models. Previous studies on bone
test specimens and idealized radius geometries by one of the
authors demonstrated the promise of this finite element techni-
que (Buchanan and Ural, 2010; Ural, 2009; Ural and Vashishth,
2006). Incorporating loading conditions that represent fall orien-
tations instead of pure axial compression in the models will
provide more accurate assessment of the fracture load and
location. In addition, the new modeling approach will make it
possible to systematically evaluate the mechanical behavior of
the cortical compartment of the bone which has been shown to
contribute significantly to the distal radius fracture load in
experimental studies (Ashe et al., 2006; Augat et al., 1998;
Augat et al., 1996; Lochmuller et al., 2002; Muller et al., 2003;
Myers et al., 1993; Myers et al., 1991; Spadaro et al., 1994).
In summary, the goals of this study were (i) to introduce a new
fracture load prediction method that couples HR-pQCT imaging
with fracture mechanics-based finite element modeling, (ii) to
incorporate realistic fall loading conditions in fracture load
assessment, and (iii) to assess the contribution of the cortical
compartment to the overall fracture load at the distal radius.
2. Materials and methods
2.1.HR-pQCT scans and finite element models
The distal radius of 20 postmenopausal women ranging from 60 to 90 years
old (mean age: 68.477.2 years) was scanned using HR-pQCT (XtremeCT, Scanco
Medical AG, Br¨ uttisellen, Switzerland) at the standard human in vivo scan location
at 82 mm isotropic voxel size resulting in a 9.02 mm section composed of 110
slices. Ten of these scans were obtained from individuals with a prior vertebral
fracture (mean age: 70.279.0 years) and the remaining ten of the scans were
from individuals with no prior fracture history (mean age: 66.574.6 years). The
cortical and trabecular compartments were separated using a manual tracing
method to accurately capture the cortical compartment at thinner regions based
on previous studies (Buie et al., 2007; Mueller et al., 2009). This resulted in two
models for each patient one of which is the whole bone model (Fig. 1a) including
both the trabecular and cortical bone compartments and the cortical bone model
(Fig. 1b) that only includes the cortical compartment of the bone.
The segmented images were converted to finite element meshes using the
ScanFE software (Simpleware, Exeter, UK) (Fig. 1c, d). The models used a
geometry-based meshing technique that generated finite element meshes using
tetrahedral elements. This approach provided smoother meshes eliminating
artificial stress concentration locations compared to voxel-based meshes while
preserving the accuracy of the geometry of the bone. The meshes generated by
ScanFE were then imported into the finite element program ABAQUS (version
6.11, 2011, Simulia, Providence, RI). The total number of elements in cortical and
whole bone models ranged between 0.99 and 1.32 million and 1.63 and 3.95
million elements, respectively. The simulations were run on a parallel cluster
using 60 and 96 processors for cortical and whole bone models, respectively. The
simulation run time for cortical bone models ranged between 3 and 6 h and
5.5 and 16 h for whole bone models.
A crack plane with cohesive elements (Section 2.2) that represent the fracture
behavior was inserted at the mid-height of all models corresponding to the
average location of the distal forearm fractures (Fig. 1e, f) (Eastell, 1996). The
models were assigned isotropic properties following previous studies (Liu et al.,
2010) with an elastic modulus of 15 GPa and a Poisson’s ratio of 0.3. The fracture
properties for the cohesive elements were taken from the literature (Section 2.2).
The bone sections were fixed in all directions at the proximal end and were loaded
at the distal surface in a fall loading orientation that accounts for 751 dorsiflexion
of the wrist and 101 internal rotation used in previous studies (Augat et al., 1996;
Myers et al., 1991). The load was incrementally increased and the fracture load
was identified at the point where the first cohesive element broke. This fracture
Fig. 1. A sample HR-pQCT bone image from a 63-year-old subject for (a) whole bone (b) cortical bone. Finite element mesh for (c) whole bone (d) cortical bone. The crack
plane tiled with cohesive elements in (e) whole bone (f) cortical bone.
Cohesive model parameters used in the simulations based on experimental data in
the literature (Brown et al., 2000; Cezayirlioglu et al., 1985; McCalden et al., 1993;
Zioupos and Currey, 1998). Note that snc, ssc(¼stc), Gnc, and Gsc(¼Gtc) are the
normal strength, the shear strength, the critical energy release rate for opening
mode, and the critical energy release rate for shear mode, respectively.
Cohesive model properties
A. Ural et al. / Journal of Biomechanics 46 (2013) 1305–1311
criterion was chosen based on our previous study that showed only 1–4% increase
in fracture load if failure of all cohesive elements were considered (Ural, 2009).
The simulations were run on 40 models including 20 whole bone models and 20
cortical bone models to obtain the whole bone fracture load (FW) and cortical bone
fracture load (FC). In addition, in order to assess the influence of crack location on
the fracture load, three randomly selected bone models were simulated with a
crack at the distal and proximal quarter of the bone section. These simulations
determined the whole and cortical bone fracture loads at the distal (FW
p) crack locations.
Geometrical properties for all models were evaluated at the most distal, most
proximal, and the crack surfaces for both whole and cortical bone models using the
ScanIP software (Simpleware, Exeter, UK). The parameters that were evaluated
included the cortical thickness, bone area, volume, and moment of inertia in
palmar–dorsal and medial–lateral directions (Table 2). In addition, trabecular bone
parameters including trabecular bone volume fraction, trabecular number, trabe-
cular thickness, and trabecular separation were evaluated for each bone (Table 2).
2.2.Cohesive finite element modeling
The fracture process was modeled with cohesive finite element modeling
which is a phenomenological traction–displacement relationship that captures the
nonlinear fracture behavior of bone. In the current study, we employed a bilinear
cohesive relationship (Fig. 2a) since the model parameters are the most important
contributors to the results rather than the shape of the traction–displacement
curve (Tvergaard and Hutchinson, 1992). The initial ascending slope of the curve is
a penalty stiffness in the numerical formulation and is generally chosen to be as
high as possible in order to obtain a very small dcvalue, satisfying numerical
convergence (Camanho et al., 2003). The cohesive model captures the material
softening via the descending part of the curve (Fig. 2a), where the traction
transferred between the material surfaces decreases as the crack opening
displacement increases. For the current study, the model has both normal (open-
ing) and shear components representing the mixed mode behavior that occurs due
to the load application direction. As a result, both the normal and shear cohesive
behavior needs to be defined considering the critical energy release rate and
strength denoted by Gnc, Gsc, Gtc, and snc, ssc, stc, respectively (Fig. 2a), where
subscript n refers to normal and subscripts s and t refer to in-plane shear
directions. The in-plane shear response is assumed to be the same in both
directions (Gsc¼Gtcand ssc¼stc).
The cohesive models are formulated as interface finite elements that have zero
initial thickness and are compatible with solid elements (Fig. 2b). The damage
initiation in a cohesive element occurs when the traction on the surfaces of the
cohesive elements reach a critical value defined by (Camanho et al., 2003)
where Tn, Ts, Ttare the current stress values in normal and shear directions and
snc, ssc, stcare critical normal and shear strengths. In each cohesive element,
damage accumulates following the traction–displacement profile. An element
forms a full crack based on the mixed mode fracture criterion (Camanho et al.,
where Gn, Gs, and Gtare the current values of energy release rate and Gnc, Gsc, and
Gtcare the critical energy release rates in normal and shear modes. The material
properties that are used to define the traction–displacement relationship are
based on experimental properties reported in the literature (Table 1) (Brown et al.,
2000; Cezayirlioglu et al., 1985; McCalden et al., 1993; Zioupos and Currey, 1998).
The statistical analyses were performed using MATLAB (MathWorks, Natick,
MA). Linear correlation coefficients (R2) and the statistical significance of the
correlations (po0.05) were calculated between the whole and cortical bone
fracture loads. The correlations were reported for fracture and nonfracture groups
separately in addition to the pooled data from both groups. In addition, statisti-
cally significant differences (po0.05) in geometrical and trabecular parameters as
well as the fracture loads between fracture and nonfracture groups were assessed
using paired Student’s t-test.
Forward stepwise multiple regression analysis was performed to find the best
predictors of the whole, cortical, and the ratio of whole to cortical bone fracture
load among the geometrical and trabecular parameters investigated. In this
analysis approach, at each step, the most significant term was added or the least
significant term was removed based on an entrance tolerance of po0.05 and an
exit tolerance of p40.10. The analysis was terminated when the root-mean-
square error reached a local minimum.
Finite element simulations performed on whole and cortical
bone models successfully simulated the crack formation and
failure (Fig. 3a, b). The whole bone fracture loads ranged between
2374 and 5024 N for the fracture group and 1945–6283 N for the
nonfracture group. For cortical bone, fracture and nonfracture
groups exhibited fracture loads between 1020 and 3443 N and
498 and 4196 N, respectively. The ratios of the fracture loads
between the cortical and whole bone models ranged between
0.33 and 0.84 for nonfracture group and between 0.25 and 0.90
for the fracture group. The mean values of the cortical and whole
bone fracture loads and their ratios were larger for the nonfrac-
ture group, however, the differences did not reach statistical
significance (Table 2). In addition, the geometrical and trabecular
parameters showed statistically significant differences between
fracture and nonfracture groups only in the distal cortical
Mean values and standard deviations of the geometrical and trabecular para-
meters and the predicted fracture loads for fracture and nonfracture groups as
well as the pooled data. Note that the statistically different (po0.05) properties
between nonfracture and fracture groups are shown in bold.
Whole (FW) and cortical (FC) bone fracture load; cortical thickness at the crack surface
(CTh); cortical bone volume (VC); cortical bone area at the distal (DAC), proximal (PAC),
crack (CAC) surfaces; cortical bone moment of inertia in palmar–dorsal direction at the
medial–lateral direction at the distal (DIyy
cortical bone polar moment of inertia at the distal (DJC), proximal (PJC), crack (CJC)
surfaces; whole bone volume (VW); whole bone area in distal (DAW), proximal (PAW),
crack (CAW) surfaces; whole bone moment of inertia in palmar–dorsal direction at the
medial–lateral direction at the distal (DIyy
whole bone polar moment of inertia at the distal (DJW), proximal (PJW), crack (CJW)
surfaces; trabecular thickness (Tb.Th); trabecular separation (Tb.Sp); trabecular
number (Tb. N); trabecular bone volume fraction (BV/TV).
C), proximal (PIxx
C), crack (CIxx
C) surfaces; cortical bone moment of inertia in
C), proximal (PIyy
C), crack (CIyy
W), proximal (PIxx
W), crack (CIxx
W) surfaces; whole bone moment of inertia in
W), proximal (PIyy
W), crack (CIyy
A. Ural et al. / Journal of Biomechanics 46 (2013) 1305–1311
moment of inertia in the medial lateral direction, trabecular
thickness, and trabecular bone volume fraction (Table 2).
The fracture loads obtained from cortical and whole bone models
exhibited statistically significant correlations for the nonfracture
group and pooled data with R2¼0.58 (p¼0.01) and R2¼0.48
(po0.001), respectively, whereas the correlation was not significant
for the fracture group (Fig. 4). In addition, when the cortical fracture
load was plotted with respect to the cortical to whole bone fracture
load ratio, positive and statistically significant correlations (R2Z0.5,
po0.05) were observed for all groups (Fig. 5).
The stepwise multiple regression analysis between the geo-
metrical properties and the cortical and whole bone fracture loads
demonstrated that cortical thickness is the best and only pre-
dictor for whole bone fracture load with the exception of the
fracture group that exhibited no correlation (Table 3, Fig. 6).
Cortical thickness was the common predictor of cortical fracture
load for all groups (Fig. 6) with additional terms of distal cortical
polar moment of inertia and cortical crack area for the pooled and
fracture groups, respectively (Table 3). The fracture load ratios
were predicted by a single geometric ratio including the ratio of
cortical to whole bone crack area for pooled and fracture groups
and the ratio of cortical to whole bone moment of inertia in the
medial–lateral direction at the crack plane for the nonfracture
group (Table 3).
The stepwise multiple regression analysis between trabecular
parameters and the whole bone fracture loads showed that
?su (= ?tu)
?sc (= ?tc)
Gsc ( = Gtc)
Fig. 2. Traction–displacement relationship defining the cohesive zone model in normal (n) and shear modes (t, s). Note that Tiare the tractions, sicare the critical
strengths, diare the crack opening displacements, and diuare the ultimate values of the crack opening displacements (i¼n, t and s). (b) Tetrahedral solid elements and the
compatible wedge shaped cohesive element with six nodes.
Fig. 3. Crack plane showing the damage accumulation and crack formation for
(a) cortical and (b) whole bone model for a 63-year-old subject. Note that the arrows
indicate the initial location of crack formation. Red color indicates high level of damage
and blue color indicates no damage. (For interpretation of the references to color in this
figure legend, the reader is referred to the web version of this article.)
R2 = 0.58
R2 = 0.23
R2 = 0.48
0 1000 20003000 40005000
Fig. 4. Cortical bone vs. whole bone fracture loads for fracture, nonfracture and pooled
data. Note that the blue hollow circles, red hollow squares, and black diamonds
correspond to fracture, nonfracture and pooled data, respectively. The nonfracture and
pooled data has a statistically significant correlation with p¼0.01, and po0.001,
respectively. The fracture group data did not exhibit significant correlation between the
cortical and whole bone load. (For interpretation of the references to color in this figure
legend, the reader is referred to the web version of this article.)
A. Ural et al. / Journal of Biomechanics 46 (2013) 1305–1311
trabecular thickness was a predictor of fracture group whole bone
fracture load (Table 3). However, the nonfracture group and
pooled whole bone fracture load exhibited no correlation with
the trabecular variables.
The studies on models that investigated the influence of crack
location demonstrated higher fracture loads for the proximal crack
plane and lower fracture loads for the distal crack plane (Table 4). The
predicted load ratio between cortical and whole bone at the mid-
height was closely replicated in the distal crack plane. However, at
the proximal crack plane the contribution of the cortical bone was
higher for the two models which had much thicker cortical thickness
at the proximal region (Table 4). The ratio of fracture loads between
distal, proximal and mid-height crack planes varied in proportion to
the ratio of cortical thickness on the corresponding crack surfaces.
This study presented a new approach for evaluating the
fracture load at the distal radius that combines in vivo human
images with nonlinear fracture mechanics-based finite element
modeling. Although, this technique was utilized previously on
idealized radius models (Buchanan and Ural, 2010; Ural, 2009),
this is the first study that combines HR-pQCT imaging with
cohesive finite element modeling.
Previous studies utilized only strength-based parameters and
pure axial compression loading for assessing fracture load
(Boutroy et al., 2008; Burghardt et al., 2010; MacNeil and Boyd,
2007; Melton et al., 2007; Pistoia et al., 2002; Varga et al., 2010).
Our current model determined the fracture load based on both
strength and fracture toughness and incorporated a more realistic
loading direction that represents a fall to prevent overestimation
of the fracture load due to pure axial compression loading
(Buchanan and Ural, 2010; Troy and Grabiner, 2007). In addition,
pure axial compression simulations that we ran on six sample
bone models for comparison purposes showed a narrower range
of cortical to whole bone fracture load ratios than predicted by
our modeling approach. Furthermore, the ratio of fracture loads
obtained from both approaches did not exhibit a constant value
and showed variation from model to model indicating the
possibility that the axial compression loading may not be fully
capturing the failure mechanisms in distal radius fracture.
One of the goals of our study was to provide better insight into
the contribution of cortical bone to the overall bone fracture load
by direct evaluation instead of extraction from whole bone
models (Boutroy et al., 2008; MacNeil and Boyd, 2007; Pistoia
et al., 2003). The results of our simulations showed a positive and
significant correlation between the cortical and whole bone
fracture load (Fig. 4) highlighting the possibility of estimating
whole bone fracture load based on cortical bone fracture load
Stepwise multiple regression models between the fracture loads and the geometrical and trabecular properties and the corresponding R2and p values.
Stepwise multiple regression models
Pooled whole bone fracture load vs. Geometric properties: FW¼5144.8 CTh?488.6
Fracture group whole bone fracture load vs. Geometric properties: none
Nonfracture group whole bone fracture load vs. Geometric properties: FW¼5339.1 CTh?684.3
Pooled cortical bone fracture load vs. Geometric properties: FC¼4807.0 CTh ?2.34 DJC?1017.1
Fracture group cortical bone fracture load vs. Geometric properties: FC¼6815.5 CTh?1.6 CACþ306.5
Nonfracture group cortical bone fracture load vs. Geometric properties: FC¼5255.6 CTh?2450.4
Pooled cortical/whole bone fracture load ratio vs. Geometric properties: FC/FW¼1.30 (CAC/CAW)?0.270
Fracture group cortical/whole bone fracture load ratio vs. Geometric properties: FC/FW¼1.56 (CAC/CAW)?0.476
Nonfracture group cortical/whole bone fracture load vs. Geometric properties: FC/FW¼1.41 (CIxx
Pooled whole bone fracture load vs. Trabecular properties: none
Fracture group whole bone fracture load vs.Trabecular properties: FW¼78861.9 Tb.Th?521.7
Nonfracture group whole bone fracture load vs. Trabecular properties: none
Whole (FW) and cortical (FC) bone fracture load; cortical thickness at the crack surface (CTh); cortical bone polar moment of inertia at the distal surface (DJC); cortical bone
area at the crack surface (CAC); whole bone area at the crack surface (CAW); cortical bone moment of inertia in medial–lateral direction at the crack surface (CIxx
bone moment of inertia in medial–lateral direction at the crack surface (CIxx
mm, CACand CAWare in mm2, DJC, CIxx
W); trabecular thickness (Tb.Th). Note that the units of FWand FCare in N, CTh and Tb.Th are in
C, and CIxx
Ware in mm4.
R2 = 0.50
R2 = 0.60
R2 = 0.51
Fig. 5. Cortical bone fracture load vs. ratio of cortical to whole bone fracture load
for fracture, nonfracture and pooled data. Note that the blue hollow circles, red
hollow squares, and black diamonds correspond to fracture, nonfracture and
pooled data, respectively. The nonfracture, fracture and pooled data has a
statistically significant correlation with p¼0.02, po0.01 and po0.001, respec-
tively. (For interpretation of the references to color in this figure legend, the reader
is referred to the web version of this article.)
R2 = 0.77
R2 = 0.49
FC, FW (N)
Fig. 6. Correlation between pooled cortical and whole bone fracture load vs. the
cortical thickness at the crack location (po0.001). The cortical thickness was the
best single predictor for the cortical and whole bone fracture loads.
A. Ural et al. / Journal of Biomechanics 46 (2013) 1305–1311
with substantially less computational cost. Patients to whom this
approach can be applied may be identified by the distal cortical
moment of inertia in the medial–lateral direction that exhibited a
statistically significant difference between fracture and nonfrac-
ture groups. In addition, a significant and positive correlation
between the cortical bone fracture load and the cortical to whole
bone fracture load ratio showed that the portion of the whole
bone fracture load carried by the cortical bone increases with
cortical bone fracture load. This relationship indicates that a more
robust cortical bone structure carries a larger percentage of the
whole bone fracture load (Fig. 5) which may be an evidence for
the importance of the integrity of the cortical compartment on
The simulation results showed that the cortical geometrical
properties can identify not only the cortical fracture load but also
the whole bone fracture load (Table 3). The cortical thickness was
found to be the most important predictor of whole bone fracture
load with the exception of the fracture group. Previous studies
also found cortical thinning to be the most influential factor on
bone strength compared to trabecular bone properties (Pistoia
et al., 2003). In addition, it was shown that the thicker cortical
thickness may enable the cortical compartment to carry a higher
percentage of the load applied to the bone and may lead to lower
rates of fracture (Walker et al., 2011). The lack of any single
geometrical predictor for the fracture group whole bone fracture
load may be due to the compromised cortical structure that
cannot contribute significantly to the overall mechanical response
of bone. As a result, the fracture group may try to derive its
fracture resistance from the trabecular compartment as high-
lighted by the correlation between the whole bone fracture load
and trabecular thickness in the fracture group. This observation is
also supported by our simulations that did not find any significant
correlation between the cortical and whole bone fracture load in
the fracture group.
In the current study, both the average cortical and whole bone
fracture load were larger in the nonfracture group compared to the
fracture group. Although the differences did not reach statistical
significance, most likely due to the small sample group used in the
study, the difference may indicate a more robust bone structure for
the nonfracture group. On the other hand, the fracture group in this
study is composed of women who had prior vertebral fractures. The
current results may also support previous findings in the literature
that showed a weak predictive capability of vertebral fractures in
women based on distal bone strength (Vilayphiou et al., 2010).
One of the limitations of the current study is the sample size
used for fracture and nonfracture subgroups. In this study, our
main goal was to establish a new HR-pQCT-based cohesive finite
element modeling approach and to demonstrate the feasibility of
using this approach for fracture risk assessment. Due to the
computational time involved in the simulations particularly with
the whole bone models, we selected a limited subgroup sample
size to demonstrate the novel components of our approach
compared to previous studies. In the future studies based on this
approach, larger subgroup sizes will need to be utilized to further
confirm the observed group differences.
The simulations were performed using a predetermined crack
plane which corresponds to the average location of distal forearm
fractures reported in the literature (Eastell, 1996). Investigation of
the influence of crack location on the results at proximal and
distal locations showed that the fracture load varied proportional
to the ratio of cortical thickness between the corresponding crack
location and the average crack location. This indicates that the
limiting distal radius fracture load can be estimated based on the
average crack location used in the current simulations and the
ratio of the cortical thickness at the distal and proximal locations
to the cortical thickness at the crack plane. Selection of the
predetermined crack plane provides a good estimate of the
fracture load while avoiding the selection of the whole bone
section as a crack domain that is computationally very expensive
and that may lead to convergence issues based on the possible
activation of cohesive elements at various sites.
In this study, homogeneous material properties were utilized for
both elastic and cohesive properties. Various relationships that relate
the elastic modulus to densitometric measures (Helgason et al., 2008)
or attenuation values of bone (Homminga et al., 2001) have been
proposed in the literature. However, there is substantial site and
specimen specific variation between these relationships (Austman
et al., 2008; Helgason et al., 2008; Morgan et al., 2003). Furthermore,
the fracture toughness and strength variation with attenuation have
not been reported in the literature. As a result, a systematic study is
needed to establish reliable relationships between HR-pQCT attenua-
tion values and elastic modulus, strength and fracture toughness to
incorporate spatial variation of these values in finite element simula-
tions. Further advancement on the local material measurements can
easily be incorporated in our model to represent spatial and age-
related material and fracture property changes in future studies. The
additional information on densitometric parameters can also be
combined with structural and microarchitectural parameters in the
multiple regression analysis for predicting fracture load.
In summary, this study introduced a new modeling approach that
coupled HR-pQCT imaging with nonlinear fracture mechanics-based
finite element simulations, incorporated a realistic loading direction
that mimic fall conditions, and showed the significant contribution of
the cortical compartment to the overall fracture load of bone. The
results provide more insight into the fracture process and evaluation
of fracture load at the distal radius.
Conflict of interest statement
The authors have no conflict of interest.
We would like to thank Dr. Elizabeth Shane for providing the
HR-pQCT images. This work was supported in part by National
Institutes of Health grants AR051376 and AR058004. The
Fracture load and cortical thickness ratios between distal and proximal crack
surfaces and the average crack surface of three bone models. Ratios of cortical to
whole bone fracture load at the average, distal and proximal crack surfaces. Bone
Model 1, 2, and 3 refer to the three randomly selected bone models that were used
to evaluate the influence of the crack location.
Fracture load and cortical thickness ratio
Bone Model 1
Bone Model 2
Bone Model 3
Cortical to whole bone fracture load ratio
Bone Model 1
Bone Model 2
Bone Model 3
Whole bone fracture load at the average crack surface (FW); whole bone fracture
load at the distal crack surface (FW
d); whole bone fracture load at the proximal
crack surface (FW
cortical bone fracture load at the distal crack surface (FC
load at the proximal crack surface (FC
p); cortical thickness at the average crack
surface (CTh); cortical thickness at the distal crack surface (CThd); cortical
thickness at the proximal crack surface (CThp).
p); cortical bone fracture load at the average crack surface (FC);
d); cortical bone fracture
A. Ural et al. / Journal of Biomechanics 46 (2013) 1305–1311
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