Femur Model for Predicting Strength and Fracture Risk - Computational Biomechanics of the Musculoskeletal System - page 106

To obtain more sophisticated evaluations of bone strength and the related fracture risk,
subject-specific FE analysis is particularly useful (Keyak et al., 2005; Bessho et al., 2007;
Viceconti et al., 2005). If developed properly while taking the most relevant information into
consideration, subject-specific FE modeling has the following advantages: physical properties of
bone measured noninvasively can derive the nonlinear mechanical properties of bone; paramet-
ric studies can be performed easily; heterogeneity and anisotropy can be addressed; and the mag-
nitudes and directions of loading can be varied easily. The strategies to develop subject-specific
FE models are summarized below.
9.1.1 l inear VerSuS n onlinear f inite e lement a nalySiS
Initially, most subject-specific FE models for prediction of femoral fracture load and stiffness were
established under linear assumptions (Keyak et al., 1998; Cody et al., 2000). That means linear
elastic material properties were assigned to bone tissue and small deformations were assumed.
The linear model could save a lot of computational time. The correlations predicted were statisti-
cally comparable to those reported previously for fracture load and simpler, density-based measures
because of the inability of linear models to represent the nonlinear mechanical behaviors that occur
during bone failure. In spite of this limitation of linear analysis, linear models can still be useful if
the aim is not to investigate the whole fracture process, but to verify if a certain failure criterion can
reproduce the conditions at the onset of failure (Schileo et al., 2008).
Nonlinear FE analyses were developed (Keyak et al., 2005; Bessho et al., 2007), with two kinds
of constitutive relationships developed to describe the nonlinearity of bone material. One is a bilin-
ear elastoplastic constitutive relationship, in which the asymmetric strength characteristics between
tension and compression can be taken into consideration (Bayraktar et al., 2004; Bessho et al., 2007;
Gong et al., 2012). The other is to describe the post-yield material behavior as an initial perfectly
plastic phase, then a strain-softened phase, followed by an indefinite perfectly plastic phase (Keyak
et al., 2005; Keyak, 2001).
9.1.2 i Sotropic VerSuS a niSotropic B one m aterial m odel
In most FE models an isotropic material property was assigned to bone tissue. Bone tissue at the tra-
becular level can be assumed to be isotropic, although bone at the apparent level is anisotropic (van
Rietbergen et al., 1998; Gong et al., 2007). There was also orthotropic material property assignment
adopted in some studies (Wirtz et al., 2003; Peng et al., 2006).
9.1.3 B one t iSSue H eteroGeneity
To consider bone heterogeneity, the mechanical properties of each element should be calculated
from the image grey levels or Hounsfield unit values from computed tomography (CT) scanning.
The mechanical properties can be discretized into a number of sets of material properties. There
are generally two strategies to transfer the grey level into mechanical properties. One is based on
equal density intervals (Peng et al., 2006) and the other uses a logarithmic increment of modulus
with the aim of obtaining a finer discrimination of mechanical properties at a lower stiffness value
(Perillo-Marcone, Alonso-Wazquez, and Taylor, 2003).
9.1.4 e ffectS of tHe l oadinG c ondition
Identifying the loading condition under which the femur is most likely at risk may aid in the preven-
tion of hip fracture. The effect of force direction on fracture load is a factor inherently associated
with fracture risk. There are generally two types of loading conditions investigated in the literature:
atraumatic loading, that is, loading similar to joint loading during daily activities (Keyak, Skinner,