Biomedical Engineering Reference
In-Depth Information
treatment for ACL injuries uses a tendon graft to replace the torn ACL. Despite the
generally good outcomes of the current method, several research and clinical re-
ports have documented limitations of the treatment such as the high economic cost,
donor-site morbidity, and the risk of osteoarthritis development (Wilder et al.,
2002
;
NationalSurvey,
2004
; Salgado et al.,
2004
; Roos,
2005
;Moffatetal.,
2008
). A crit-
ical concern of the current tendon graft is that it is stiffer than the ACL it is replacing
and, therefore, it is over-designed for its application. These limitations have led re-
searchers to investigate the possibility of utilizing a tissue engineered ACL graft for
ACL reconstruction. Recent work shows tissue engineered grafts have great poten-
tial to meet this unmet clinical need to restore native ACL anatomy and function
(Goulet et al.,
2004
; Fan et al.,
2008
;Maetal.,
2012a
).
An important goal of tissue engineering grafts for ACL replacement is that the
biomechanical response of the graft match that of the native ACL. For the past
few decades, efforts have contributed to elucidating the biomechanical behavior, re-
modeling process and failure mechanisms of native ACL and ACL grafts (Butler
et al.,
1992
; Danto and Woo,
1993
; Jackson et al.,
1993
). However, researchers have
faced many challenges such as inaccurate strain and stress field measurements and
the difficulty of mimicking a physiological loading condition (Weiss and Gardiner,
2001
). Therefore, computational biomechanics has become an increasingly impor-
tant tool to provide information to fill this gap. To further investigate the biome-
chanical response of the native ACL and to design and evaluate possible grafts in
a 3D finite element framework, a constitutive model that can accurately describe
the nonlinear viscoelastic behavior of the native and engineered ACLs is required to
prescribe the material properties in the finite element analysis (FEA). Ligaments and
tendons have nonlinear viscoelastic responses that can be characterized via stress-
strain, load-unload, stress relaxation, and creep tests. Recent work has demonstrated
that the viscoelastic responses of ligaments and tendons are both time and strain de-
pendent and various viscoelastic constitutive laws have been proposed to capture
these responses (Provenzano et al.,
2001
; Duenwald et al.,
2009
;Maetal.,
2012a
).
The generalized Maxwell model that is shown schematically in Fig.
25.1
consists
of multiple spring and dashpot combinations. It has been used to model inorganic
polymer viscoelasticity and has been proposed for soft tissue (Corr et al.,
2001
; Tang
et al.,
2011
; Sopakayang et al.,
2012
). In the latter modeling approach the multiple
spring-dashpot elements are often thought of as representing the aligned fibrous
structures of ligament or tendon. A generalized description of the model in 1D is
expressed in Eq. (
25.1
), where
k
i
is the Young's modulus of the
i
th linear spring and
η
i
the viscosity of the
i
th linear dashpot. The advantage of this model is that it is
simple and convenient to implement into computer programs and to auto-search the
parameters to fit the experimental data. However, this model requires a fairly large
number of parameters in order to capture both the load-unload and stress relaxation
responses. Because the parameters are determined by fitting specific test data, these
parameters often do not fully describe the responses of the specimen under different
boundary conditions (Sopakayang et al.,
2012
). The generalized description of the
