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Robert E. Carey
Department of Mechanical Engineering
and Materials Science,
Musculoskeletal Modeling Laboratory,
University of Pittsburgh,
3820 South Water Street,
Pittsburgh, PA 15203
Liying Zheng
Department of Orthopaedic Surgery,
Musculoskeletal Modeling Laboratory,
University of Pittsburgh,
3820 South Water Street,
Pittsburgh, PA 15203
Ameet K. Aiyangar
EMPA (Swiss Federal Laboratories
for Materials Science and Research),
Mechanical Systems Engineering (Lab 304),
Ueberlandstrasse 129,
Duebendorf 8400, Switzerland
Christopher D. Harner
Department of Orthopaedic Surgery,
University of Pittsburgh,
UPMC Center for Sports of Medicine,
3200 South Water Street,
Pittsburgh, PA 15203
Xudong Zhang
1
Department of Orthopaedic Surgery,
Department of Mechanical Engineering and
Materials Science;
Department of Bioengineering,
Musculoskeletal Modeling Laboratory,
University of Pittsburgh,
3820 South Water Street,
Pittsburgh, PA 15203
e-mail: xuz9@pitt.edu
Subject-Specific Finite Element
Modeling of the Tibiofemoral
Joint Based on CT, Magnetic
Resonance Imaging and
Dynamic Stereo-Radiography
Data in Vivo
In this paper, we present a new methodology for subject-specific finite element modeling
of the tibiofemoral joint based on in vivo computed tomography (CT), magnetic reso-
nance imaging (MRI), and dynamic stereo-radiography (DSX) data. We implemented and
compared two techniques to incorporate in vivo skeletal kinematics as boundary condi-
tions: one used MRI-measured tibiofemoral kinematics in a nonweight-bearing supine
position and allowed five degrees of freedom (excluding flexion-extension) at the joint in
response to an axially applied force; the other used DSX-measured tibiofemoral kinemat-
ics in a weight-bearing standing position and permitted only axial translation in response
to the same force. Verification and comparison of the model predictions employed data
from a meniscus transplantation study subject with a meniscectomized and an intact
knee. The model-predicted cartilage-cartilage contact areas were examined against
“benchmarks” from a novel in situ contact area analysis (ISCAA) in which the intersec-
tion volume between nondeformed femoral and tibial cartilage was characterized to
determine the contact. The results showed that the DSX-based model predicted contact
areas in close alignment with the benchmarks, and outperformed the MRI-based model:
the contact centroid predicted by the former was on average 85%closer to the bench-
mark location. The DSX-based FE model predictions also indicated that the (lateral)
meniscectomy increased the contact area in the lateral compartment and increased the
maximum contact pressure and maximum compressive stress in both compartments. We
discuss the importance of accurate, task-specific skeletal kinematics in subject-specific
FE modeling, along with the effects of simplifying assumptions and limitations. [DOI:
10.1115/1.4026228]
1 Introduction
Finite element (FE) modeling is a powerful tool for studying
joint and tissue mechanics, as it enables manipulation of variables
and simulation of situations that may be challenging or infeasible
to evaluate clinically or experimentally. The accuracy of FE
model solutions depends on well-defined anatomical geometry,
material properties and boundary conditions [1]. Given the consid-
erable inter-subject variability in tissue structure morphology,
personalized analyses and insights would require subject-specific
FE modeling [2]. In vivo FE modeling efforts have been limited
by difficulties in acquiring and analyzing multimodality data
for model construction and validation, including proper co-
registration and integration of all necessary data. Recent advances
in the fields of medical imaging and image reconstruction have
increased the potential to incorporate accurate tissue morphology
and boundary conditions into in vivo subject-specific models [3].
Nevertheless, the veracity of FE model predictions hinges upon
at least two challenging aspects: accurate representation of joint
kinematics during functional tasks, and validation or verification
of the model with experimentally measurable parameters obtained
in vivo. Previous in vivo tibiofemoral (TF) FE modeling efforts
have created models without sufficiently considering the func-
tional joint kinematics involved in the joint loading process [4,5].
Studies have incorporated skeletal kinematics from either
nonsubject-specific data [6–8] or skin surface marker measure-
ments [9,10]—the latter are prone to soft-tissue artifacts [11] due
to marker movement [12,13] and inaccurate marker positioning
on the skin relative to the bone [14,15]. Two FEM studies have
employed advanced imaging techniques to acquire skeletal kine-
matics: Beillas et al. [7,8] used X-ray imaging that required surgi-
cal implantation of radio-opaque markers into the bone; Yao et al.
[16] utilized a loading device to exert a force on the knee as it was
undergoing magnetic resonance imaging (MRI) in a supine posi-
tion. While these studies were successful attempts to incorporate
task-specific [7,8] or load-specific [16] kinematics, quantitative
verification of their FE model predictions was not conducted. Val-
idation or verification is a crucial step before making interpreta-
tions based on model predictions or using the model for clinical
applications [17,18]. Conventional measures for FE model valida-
tion, such as contact pressure [3], cannot be reliably acquired
without invasive procedures and are not applicable to in vivo
subject-specific models. However, it is possible to estimate the
contact area and centroid in vivo without invasive procedures
with a technique we present here.
This study was motivated by the need for a validated subject-
specific FE modeling methodology to study joint mechanics and
1
Corresponding author.
Contributed by the Bioengineering Division of ASME for publication in the
JOURNAL OF BIOMECHANICAL ENGINEERING. Manuscript received May 30, 2013; final
manuscript received November 18, 2013; accepted manuscript posted December 12,
2013; published online March 24, 2014. Assoc. Editor: Pasquale Vena.
Journal of Biomechanical Engineering APRIL 2014, Vol. 136 / 041004-1Copyright V
C2014 by ASME
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functions in response to various musculoskeletal injuries and their
treatments. While the methodology can be generalized to other
articulating joint structures, this study focused on the TF joint,
meniscus injury and meniscectomy. The meniscus is an integral
component of the knee, playing a vital role in stability, proprio-
ception, lubrication and load distribution [19–22]. It has been
shown that meniscectomy, a common treatment for meniscal inju-
ries and one of the most frequently performed orthopaedic proce-
dures, can lead to degenerative changes of the articular cartilage
in the knee [17,20,23–26]. In order to better understand the rela-
tionship between meniscectomy and the onset as well as progres-
sion of articular cartilage damage, it is important to first assess the
joint and tissue mechanical changes involved—a problem well
suited for investigation based on FE modeling.
Specifically, we aimed to explore subject-specific FE modeling
of the TF joint based on in vivo measurements of tissue morphol-
ogy from high-resolution MRI and three-dimensional (3D) skele-
tal kinematics from dynamic stereo-radiography (DSX). This
latter technology provides an ability to measure skeletal kinemat-
ics during functional tasks with sub-millimeter accuracy [27]. We
proposed a novel in situ contact area analysis (ISCAA) technique,
allowing the use of a subject’s own data to validate the subject-
specific FE model.
2 Materials and Methods
The knee morphological and kinematic data for FE modeling
were from an IRB-approved meniscus allograft transplantation ex-
perimental study. We used the data of one subject (female, age
19) who had previously undergone a left knee lateral meniscec-
tomy. Data for both the meniscectomized left knee and intact right
knee, collected prior to the transplantation surgery, were used. An
overview of how multimodality data (DSX, CT, and MRI) were
acquired and integrated for model creation and verification is pre-
sented in Fig. 1. The individual procedures from data acquisition
to model verification are described as follows.
2.1 Data Acquisition. A DSX system was used to acquire 3D
TF skeletal kinematics data (Fig. 2), with a precision of 0.2 mm
in translation and 0.2 deg in rotation [27]. The particular static
standing trial data used in this study were collected while the sub-
ject held a static, natural, upright posture.
A bilateral computed tomography (CT) scan (GE Medical
Systems Lightspeed Pro 16, Waukesha, WI) of the subject’s knees
was obtained with the following specifications: pixel size ¼0.586
0.586 mm
2
, slice thickness ¼1.25 mm, pixel resolution
¼512 512 pixels, field of view (FOV) ¼30.0 cm, number of
slices ¼123, excitation voltage ¼120 kV, current-time ¼402.8
mAs. The CT data were imported into Mimics 14.0 (Materialise,
Ann Arbor, MI, USA) and segmented slice-by-slice to create a 3D
bone model for both the femur and tibia. A custom model-based
tracking software program was used to create a virtual testing con-
figuration replicating that of the actual physical DSX system. The
3D bone models produced from CT were placed within the virtual
environment to, through a ray-tracing algorithm, create digitally
reconstructed radiographs (DRRs). A volumetric image-matching
algorithm was then employed in a co-registration process between
the DRRs and DSX images, optimizing the 3D position of the
DRRs relative to the corresponding bone in the DSX images for
each frame. Additional details on this model-based tracking
technique can be found in a previous publication [28].
An MRI scan (Siemens Trio 3.0 T, Washington, DC) of each
knee joint was acquired while the subject was in a nonweight-
bearing, supine position using a sagittal 3D dual echo steady state
Fig. 1 A flow chart of the FE model development and verification process incorporating multi-
modality data
Fig. 2 Experimental setup for measuring 3D TF skeletal kine-
matics using a dynamic stereo-radiography system
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water excitation (DESS-WE) sequence. The MRI scan specifica-
tions were: pixel size ¼0.365 0.365 mm
2
, slice thick-
ness ¼0.7 mm, pixel resolution ¼384 384 pixels, FOV
¼14.0 cm, number of slices ¼160.
2.2 Model Geometry. The MRI data were imported into
Mimics 14.0 for creation of 3D models of the femur, tibia, femoral
cartilage, tibial cartilage, and menisci. Once the 3D models were
created, they were imported into TrueGrid (XYZ Scientific, CA,
USA) for manual linear hexahedral meshing. Each component
was meshed separately and then imported into ABAQUS CAE 6.9
(Simulia, RI, USA), where they were combined into a single FE
model for an implicit static analysis. Figure 3shows an example
of the FE model geometry development process. The numbers of
elements in the FE models of individual components in each knee
are listed in Table 1.
2.3 Material Properties. Tissue material properties were
taken from literature. The femur and tibia were modeled as rigid
structures, which greatly reduced the computational time and has
been shown to have minimal effect on the model predictions
[1,4,6,9,23,29–39]. Articular cartilage is known to be an
anisotropic, biphasic material with a time constant approaching
1500 s [40,41]. The compressive loading in this study was quasi-
static. It has been shown that under this condition, the biphasic
response of cartilage can be negligible and the single-phase linear
isotropic constitutive law be applicable [40,41]. Therefore, carti-
lage was modeled as a homogeneous, elastic, linearly isotropic
material [1,2,4–7,9,16,23,25,30,32,33,35–39,42–46] with a mod-
ulus of 15 MPa [4,9,25,30,35,45] and a Poisson’s ratio of 0.46
[31–33,47,48].
For the menisci, a transversely isotropic constitutive law was
used in order to emphasize the dominant role played by the
circumferential fibers in load distribution and function
[19,21,49–51]. The menisci were therefore modeled as linearly
elastic, transversely isotropic materials [1,2,4,9,10,16,25,30,
34–36,39,43–45,52], where the modulus and Poisson’s ratio were
20 MPa and 0.2, respectively, in the radial and axial directions,
and 140 MPa and 0.3, respectively, in the circumferential direc-
tion [4,30,45,52]. Time dependent effects of the cartilage and
menisci properties were not considered due to the quasi-static na-
ture of the models [4,7,8,23,30,32,35,40–42,48,53,54]. The ante-
rior and posterior meniscal roots for each meniscus were modeled
as linear springs with spring constants of 2000 N/mm
[9,23,25,30,35,36,45,52].
2.4 Kinematics and Loading Conditions. Two FE models
were created for each knee, one incorporating MRI-based supine
kinematics and the other DSX-based standing kinematics (Fig. 4).
The first FE model developed for each knee was based on the MRI
data using the procedure described above, resulting in a model in
the supine MRI position. In order to incorporate the standing,
DSX-based kinematics, the DSX-acquired kinematics had to be
transformed into the MRI-based coordinate system. For both the
femur and tibia, the CT-based 3D model was co-registered to the
MRI-based 3D model using Geomagic Studio 10 (Geomagic,
North Carolina, USA). A manual n-point registration was com-
pleted by choosing three landmark points on the surface of the CT
3D bone model and then choosing the same three points on the sur-
face of the MRI 3D bone model. This was done to create a close
initial estimate for an automatic global registration process. The
automatic global registration process was then executed, minimiz-
ing the co-registration error between the two 3D models. The aver-
age ( 6SD) error in the co-registration process for the bones was
0.472 (60.305) mm. This procedure output a transformation ma-
trix from the CT coordinate system to the MRI coordinate system
(CT-MRI). One output of the model-based tracking process was a
transformation matrix from the laboratory coordinate system to the
CT coordinate system (lab-CT). The lab-CT and CT-MRI transfor-
mation matrices for each respective bone were combined to yield a
transformation matrix from the laboratory coordinate system to the
MRI coordinate system (lab-MRI). These transformations were
then applied to each knee’s MRI-based supine position FE model
to create a model in the DSX-based standing position. The tibial
side lab-MRI transformation was applied to the tibia, tibial carti-
lage and menisci, while the femoral side lab-MRI transformation
was applied to the femur and femoral cartilage.
For both the MRI-based and DSX-based models, the tibia was
held in a fixed position while the femur was allowed to move in
response to an axial force of half the subject’s body weight (275
N) applied to the proximal end of the femur towards the tibia.
This force, along with contact pairs and prescribed boundary con-
ditions, determined the “final position” of each model. For the
model in the MRI-based supine position, five degrees of freedom
(DOF) were allowed for the femur while the flexion-extension
was fixed. For the model in the DSX-based standing position,
since the prescribed position of the femur relative to tibia is a
final, known position from the experimental data, the only DOF
permitted was an axial translation, allowing the femur to settle
into its final position in response to the force applied. The femoral
and tibial cartilage components were tied to the femur and tibia
surfaces, respectively, while hard, frictionless contact was
assumed for cartilage-cartilage and cartilage-meniscus interfaces
[1,4,16,23,30,32–35,37–39,42,43,45,46,48,55]. In all models, a
large-strain formulation was used [38,46] to account for poten-
tially substantial strains in the soft tissue components. The contact
area between the femoral and tibial cartilage from the resulting
FE analysis was used as the measure for verification. The contact
centroid was determined on the tibial cartilage for each compart-
ment based on a transverse view of the superior cartilage surface.
Fig. 3 FE model geometry development sequence for the tibia
Table 1 Numbers of linear hexahedral elements in individual
model components
Meniscectomized Knee Healthy Knee
Femur 41,984 76,308
Tibia 61,440 87,852
Femoral Cartilage 5,632 3,648
Tibial Cartilage 11,264 2,816
Lateral Meniscus 16,896 2,352
Medial Meniscus 16,896 2,112
Total 154,112 175,088
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2.5 Verification. An in situ contact area analysis (ISCAA)
method was developed in order to verify the predictions of the FE
models using cartilage-cartilage contact as the measure. The femoral
and tibial cartilage in the DSX-based standing position was utilized.
The cartilage surfaces in the MRI-based supine position were
imported into MATLAB 2012a (MathWorks, Massachusetts, USA).
Cartilage was transformed into the DSX-based standing position by
applying the lab-MRI transformation. The overlapped area between
nondeformed femoral and tibial cartilage (Fig. 5) was calculated and
projected onto a single transverse plane determined as the least-
squares-fit plane of the tibial cartilage, which provided a common
reference for comparing the FE model-predicted and ISCAA-
assessed contact centroids. The depth of overlap can be used as a
surrogate measure of total cartilage strain [56]. The contact centroid
for the ISCAA (C
ISCAA
) result was calculated and compared to the
contact centroids obtained from the MRI-based supine position
model (C
MRI
) and the DSX-based standing position model (C
DSX
).
For the FE models, the contact centroid (C
MRI
or C
DSX
) was
found by projecting the tibial cartilage on the aforementioned
least-squares-fit plane and determining the geometric center in
two dimensions (2D). For the ISCAA, the C
ISCAA
was found by
discretizing the contact area into grid sections (size: 0.368 mm
2
)
and then identifying the section with the smallest weighted-
average Euclidean distance to all other sections. Numerically, C
IS-
CAA
was located by the grid section ID (i) resulting from the
following optimization procedure:
argmin
iffiffiffiffiffiffiffiffiffiffiffiffiffi
X
N
j¼1
s2
ij
d2
i
v
u
u
t(1)
where sis the distance from one grid section ito another grid sec-
tion j;dis the localized cartilage depression (i.e., the depth of
overlap) at a grid section, and Nis the total number of grid sec-
tions. Note that when cartilage depression dis uniform across the
entire contact area, the solution from Eq. (1) would be the geomet-
ric center as in the case for C
MRI
and C
DSX
.
A sensitivity analysis was performed to assess how sensitive
C
MRI
and C
DSX
predictions would be to changes in assumed mate-
rial properties of the articular cartilage, menisci, and meniscal
roots. Seven material property values (elastic modulus and Pois-
son’s ratio of articular cartilage, elastic modulus and Poisson’s ra-
tio of meniscus in the circumferential direction, elastic modulus
and Poisson’s ratio of meniscus in the axial and radial directions,
spring stiffness of the meniscal roots) were each varied by 65%
and 610%, resulting in a total of 28 model variants.
3 Results
When overlaying the FE model predictions for contact centroid
with the ISCAA results, the DSX-based position models were in
better agreement with the ISCAA results compared to MRI-based
position models, as evidenced in Fig. 6by the alignment of the FE
contact area prediction with the areas of greater contact depth in
the ISCAA.
With C
ISCAA
as the benchmark estimate for the contact cent-
roid, C
DSX
predicted the contact centroid more accurately than
C
MRI
(Fig. 7). The mean absolute distance from C
FE
to C
ISCAA
was 6.395 mm (SD: 2.296 mm, range: from 3.242 mm to
8.234 mm) for the MRI-based FE models, and 0.747 mm (SD:
0.457 mm, range: from 0.205 mm to 1.307 mm) for the DSX-
based FE models. C
DSX
estimate was closer to C
ISCAA
by 85%
(617%), on average, than C
MRI
(See Table 2).
Once the model in the DSX-based position was verified, contact
area between the femoral and tibial cartilage (reported as a per-
centage of the superior surface area of the tibial cartilage), maxi-
mum compressive stress and maximum contact pressure were
extracted from the FE results and compared between the menis-
cectomized and healthy knees (Table 3). All three variables, in
both the lateral and medial compartments, were greater for the
meniscectomized knee compared to the healthy knee. It was also
noted that the differences in these three variables between healthy
and meniscectomized states were much greater in the lateral
compartment than in the medial compartment.
The sensitivity analysis showed that variations of material prop-
erties by 65% and 610% had no marked effect on the average
model-predicted contact centroid locations (Fig. 8). The conclu-
sion that the DSX-based model outperformed the MRI-based
model and provided accurate predictions holds for the range of
material property variations considered.
Fig. 4 Lateral and anterior views of FE models of the meniscectomized knee in (a)
MRI-based and (b) DSX-based positions
Fig. 5 In situ contact area analysis (ISCAA) to determine the
contact area, defined as the intersection between femoral and
tibial cartilage, by co-registering the MRI-acquired cartilage
models with DSX-acquired bone models
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4 Discussion
The current study presents a novel approach to creating subject-
specific FE models of the tibiofemoral joint. This approach
distinguishes itself from past efforts in two ways: (a) physiologi-
cally realistic weight-bearing states are modeled with high
morphological and kinematic fidelity, and (b) the model is
verified, in vivo, with a unique technique using the subject’s own
data.
Fig. 6 Left: meniscectomized knee ISCAA results overlapped with (a) MRI-based position and
(b) DSX-based position FE model predictions. Right: healthy knee ISCAA results overlapped
with (c) MRI-based position and (d) DSX-based position FE model predictions. The green area
represents the FE model contact area predictions, while the other colors are the color coded
ISCAA estimate. Penetration depth increases from blue to red. M 5Medial, L 5Lateral,
A5Anterior, P 5Posterior.
Fig. 7 Left: contact centroid of ISCAA estimation and (a) MRI-based and (b) DSX-based FE
model predictions for left, meniscectomized knee plotted on FE tibial cartilage. Right: contact
centroid of ISCAA estimation and (c) MRI-based position and (d) DSX-based position FE model
predictions for right, healthy knee plotted on FE tibial cartilage. M5Medial, L 5Lateral,
A5Anterior, P 5Posterior.
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The FE model of the subject in a standing posture, developed
by integrating CT, MR and DSX images, was compared to an
MRI-based FE model incorporating supine kinematics—a tech-
nique applied in past FE studies investigating tibiofemoral
mechanics [4,5]. The contact centroid was used as a benchmark
variable to discern the differences between the two FE models.
The contact centroid was selected as a variable for verification/
comparison since contact pressure and stress are currently infeasi-
ble to measure in vivo without surgically invasive procedures
(which would also inevitably alter the characteristics of the con-
tact itself). Further, accurate material properties, which are diffi-
cult to determine in vivo for the various components in the TF
joint, are necessary for prediction of contact pressure and stress.
On the other hand, the contact centroid remains largely unaffected
by the choice of material properties.
Application of highly accurate task-specific kinematics is criti-
cal for achieving accurate FE model predictions, as demonstrated
by results from the current study. Creating a model in a weight-
bearing state using nonweight-bearing kinematics [4,5] incurs an
artifact of joint congruity change, as evidenced by the differences
in predicted contact area as well as the contact centroid. This
could compromise the accuracy of predictions of the TF mechani-
cal response and potentially obscure the true effects of structural
alteration due to an injury or treatment. Customized loading devi-
ces have been used to emulate weight-bearing conditions during
the MRI scan [16,57] but these alternatives are much less flexible
in accommodating a variety of functional kinematics as compared
to the dynamic X-ray imaging we used.
Experimental studies by Bingham et al. [58], Li et al. [59], and
Van de Velde et al. [60] using biplane X-ray images of subjects in
a full-extension weight-bearing position have showed that the
contact centroids lie anterior to the anterior-posterior (AP) midline
of the cartilage for both the lateral and medial compartments.
Contact centroid estimation by the DSX-based model in the cur-
rent study was consistent with those previous findings. However,
studies using a supine position from MR imaging have provided
different and often inconsistent estimates. For example, Perie
et al. estimated the contact location to be anterior in the medial
compartment, but toward the center in the lateral compartment,
based on estimates of hydrostatic stress distribution from a supine
MRI-based FE model of a healthy knee [5]. The discrepancy in
the location of contact in the lateral compartment is similar to the
prediction from the MRI-based FE model of the healthy knee in
the current study. On the other hand, experimental investigations
by Shefelbine et al. [57] and Von Eisenhart-Rothe et al. [61]
predicted the contact centroid to be posterior in the medial com-
partment and anterior on the lateral side with respect to the AP
midline of the cartilage. A collective look at these studies conclu-
sively establishes the potential for erroneous predictions when FE
models rely on nontask-specific kinematics. Small changes in the
positioning of the bones can cause substantial inaccuracies in FE
model predictions, as shown by a previous sensitivity analysis
[16].
The demonstration of a viable approach to verifying FE model
predictions using subject-specific data is another unique contribu-
tion of this study. To our knowledge, there has not been any tibio-
femoral joint FE model employing a subject’s own in vivo data to
verify the model predictions. Pe~
na et al. [31–33] developed sev-
eral 3D FE models that considered in vivo functional kinematics
using weight-bearing MRI, but all of these models lacked valida-
tion or verification against data from the same subjects. Instead,
verification was done by comparing the model results with litera-
ture data, some of which were based on in vitro cadaveric data.
Considering the morphometric variations across individuals [13]
and the discrepancies between in vitro and in vivo modalities in
relation to sometimes subtle effects or differences, conventional
verification can serve at best as a qualitative “reality check.” With
access to or the ability to acquire in vivo data, validating a
subject-specific FE model by the subject’s own data obviates
errors arising from inter-individual morphological variations. As
in vivo measurements of joint pressure and stress continue to be a
formidable challenge, we believe the in situ contact area analysis
proposed in the current study offers a viable alternative for quanti-
tative verification of subject-specific FE models based on in vivo
data.
Once the validity has been established, the model can be used
with confidence to analyze the contact pressure and stress distribu-
tion in the joint complex. The subject modeled in this work had
previously undergone a meniscectomy of the lateral meniscus on
the left knee. The predicted contact area, maximum contact
pressure and maximum compressive stress in both the lateral and
medial compartments were all greater in the meniscectomized
knee than in the right, healthy knee during the static, standing
trial. The difference was most evident in contact area in the
lateral compartment. The trends found in this study—increased
Table 2 Distances (mm) between FEM-predicted and ISCAA-estimated contact centroids
Meniscectomized Knee Healthy Knee
Lateral Compartment Medial Compartment Lateral Compartment Medial Compartment
MRI-based FE model 7.95 6.15 8.23 3.24
DSX-based FE model 0.84 0.21 0.64 1.31
Table 3 DSX-based FE model predictions of contact area, max-
imum contact and compressive stresses in meniscectomized
and healthy knees
Meniscectomized
Knee
Healthy
Knee
Contact Area (%) Medial 8.3 8.2
Lateral 5.8 0.4
Maximum Contact
Pressure (MPa)
Medial 2.95 2.69
Lateral 4.32 0.70
Maximum Compressive
Stress (MPa)
Medial 2.86 2.27
Lateral 3.96 0.56
Fig. 8 Average distances between FEM-predicted and ISCAA-
estimated contact centroids at different levels of material prop-
erty variation for both MRI-based and DSX-based models
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cartilage-to-cartilage contact area, increased maximum contract
pressure and increased maximum compressive stress in the menis-
cectomized versus healthy knee—were consistent with prior
reports based on FE analysis [23,33–35].
While the contact centroid locations predicted by the FE model
in DSX-based bone positions were in close agreement with those
from the ISCAA, the actual contact area resulting from the
ISCAA was noticeably greater than the area predicted by the cor-
responding DSX-based FE model. This discrepancy may be attrib-
utable to two simplifying assumptions. First, in the ISCAA, the
intersection between nondeformed cartilage volumes was assumed
to represent the total volume in contact (i.e., experiencing stress).
Had the deformation been taken into account, which is not yet
achievable in vivo, the total volume or area in contact would
likely be smaller, considering there would be deformed but non-
contacting cartilage areas. Second, material properties used in the
FE models were taken from literature on the subject of TF FE
modeling, which may have contributed to the inaccuracy in pre-
diction of contact area. in vivo subject-specific material properties
remains the “holy grail” in biomechanics and having such prop-
erty values for model development as well as validation would
greatly reduce the putative error caused by use of generic “one-
size-fits-all” data. It must be pointed out that for a “within-model”
comparative evaluation as done in the current study, the use of
generic but consistent property values would be much less conse-
quential, as confirmed by the sensitivity analysis conducted.
The cruciate ligaments (ACL, PCL) and collateral ligaments
(MCL, LCL) were not included in the models in this study. It is
understood that the ligaments play a central role in maintaining
joint stability and therefore can affect the kinematics [62]. Inclu-
sion of these ligaments in the DSX-based models would not have
any effect on the kinematics, which was prescribed from experi-
mental data. Inclusion of the ligaments in the MRI-based models
might have an effect on the contact centroid predictions as the
model permitted a large number of DOFs. Given that the MRI-
based models saw only small femoral movement relative to the
tibia (displacement <1 mm) in response to the quasi-static load-
ing, and that the standing position is considered the most “neutral”
position in terms of ligament tensions and effect, we believe the
effect would be minimal. However, caution must be exercised
when the proposed methodology is applied to modeling a joint in
more dynamic acts and/or deviate positions. Another limitation of
this study was the assumption of the loading condition applied to
the TF joint. One-half of the body weight was administered only
in the axial direction. Although we elected to use a simple loading
scenario in order to minimize possible interaction effects on pre-
dicted joint mechanical responses and loading “bias” in model
comparison, the actual loading would be more complex than a
uniformly applied axial load. Our ongoing work involves the use
of a musculoskeletal dynamic modeling tool OpenSim [63]to
determine a more realistic ensemble force input for the FE model.
Acknowledgment
The authors acknowledge the generous support by the Musculo-
skeletal Transplant Foundation (MTF), NIH (R03-AR059939),
and a University of Pittsburgh Department of Mechanical Engi-
neering & Materials Science Graduate Tuition Scholarship. The
authors also thank Dr. Scott Tashman, Mr. Eric Thorhauer, and
Dr. Snehal Shetye for their technical assistance.
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