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Subject-Specific Finite Element Modeling of the Tibiofemoral Joint Based on CT, MRI and Dynamic Stereo-Radiography Data In Vivo.

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In this paper, we present a new methodology for subject-specific finite element modeling (FEM) of the tibiofemoral joint based on in vivo computed tomography (CT), magnetic resonance imaging (MRI), and dynamic stereo-radiography (DSX) data. We implemented and compared two techniques to incorporate in vivo skeletal kinematics as boundary conditions: one used MRI-measured tibiofemoral kinematics in a non-weight-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 kinematics 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 of a meniscus transplantation study subject with a meniscectomized and an intact knees. The model-predicted cartilage-cartilage contact areas were examined against 'benchmarks' from a novel in situ contact area analysis (ISCAA) in which the intersection volume between non-deformed 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 by the former was on average 82% closer to the benchmark 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.
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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 [68] 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.
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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 [1922]. 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 [17,20,2326]. 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
[1,4,6,9,23,2939]. 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 [1,2,47,9,16,23,25,30,32,33,3539,4246] with a mod-
ulus of 15 MPa [4,9,25,30,35,45] and a Poisson’s ratio of 0.46
[3133,47,48].
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
[19,21,4951]. The menisci were therefore modeled as linearly
elastic, transversely isotropic materials [1,2,4,9,10,16,25,30,
3436,39,4345,52], 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 [4,7,8,23,30,32,35,4042,48,53,54]. 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
[1,4,16,23,30,3235,3739,42,43,45,46,48,55]. 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
iffiffiffiffiffiffiffiffiffiffiffiffi
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. [3133] 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
041004-6 / Vol. 136, APRIL 2014 Transactions of the ASME
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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 [23,3335].
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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... A variety of constitutive material models have been implemented in the modeling of cartilage in the reviewed papers. Of the 79 reviewed papers, 45 used a linear isotropic elastic model (Akbarshahi et al., 2014;Akrami et al., 2018;Aksahin et al., 2017;Andriacchi et al., 2006;Atmaca et al., 2013;Besier et al., 2005Besier et al., , 2008Butz et al., 2011;Cardiff et al., 2014;Carey et al., 2014;Dong et al., 2011;Farrokhi et al., 2011;Fitzpatrick et al., 2010Fitzpatrick et al., , 2011Guess, 2012;Guiotto et al., 2014;Ho et al., 2014;Huang et al., 2018;Kang et al., 2018;Klets et al., 2016;Knecht et al., 2008;Koh et al., 2019;Lenhart et al., 2015;Li et al., 1999Li et al., , 2001Li et al., , 2020Liao et al., 2018;Liu and Zhang, 2013;Liukkonen et al., 2018;Meng et al., 2017b;Mesfar and Moglo, 2013;Mootanah et al., 2014;Orsi et al., 2016;Pal et al., 2019;Pena et al., 2005;Qi et al., 2018;Salmingo et al., 2017;Segal et al., 2012;Shah et al., 2015;Shim et al., 2016;Tang et al., 2011;Yang et al., 2009Yang et al., , 2010Yin et al., 2016;Zheng et al., 2017), which provides a simple and straightforward relation between stress, strain, and material properties, while Liukkonen et al. introduced a transversely isotropic elastic model (Liukkonen et al., 2017). One paper used the Biot model (Lin et al., 2020), while Klets et al. and Bolcos et al. implemented a transversely isotropic poroelastic model as a subclass of orthotropic materials (Klets et al., 2016(Klets et al., , 2018Bolcos et al., 2018Bolcos et al., , 2019. ...
... Higher in-plane spatial resolution and thinner slice thicknesses are further advantages of 3 compared to 1.5 T. T 1 relaxation time depends on the magnetic field strength and increases by about 30% in a 3T scanner, which in turn requires longer repetition times (TR) if one aims for the same contrast as with 1.5 when using conventional spin-echo imaging (Wood et al., 2012). Further details of the MRI acquisitions and applications are summarized in Table 12 in Appendix F. Of the 79 studies, 23 used a 1.5 T MRI (Akrami et al., 2018;Aksahin et al., 2017;Besier et al., 2005Besier et al., , 2008Fitzpatrick et al., 2010Fitzpatrick et al., , 2011Guess, 2012;Guiotto et al., 2014;Hattori-Hara et al., 2014;Knecht et al., 2008;Koh et al., 2019;Li et al., 1999Li et al., , 2001Luczkiewicz et al., 2018;Mononen et al., 2011Mononen et al., , 2012Ng et al., 2019;Orsi et al., 2016;Pal et al., 2019;Qi et al., 2018;Renani et al., 2017;Shah et al., 2015;Yang et al., 2010), 22 a 3 T MRI (Abe et al., 2013;Atmaca et al., 2013;Bolcos et al., 2018;Carey et al., 2014;Farrokhi et al., 2011;Greybe et al., 2017;Ho et al., 2014;Kang et al., 2018;Klets et al., 2016;Kłodowski et al., 2016;Lenhart et al., 2015;Li et al., 2020;Liao et al., 2018;Linka et al., 2017Linka et al., , 2019Liukkonen et al., 2017;Mootanah et al., 2014;Räsänen et al., 2013;Sagl et al., 2019;Tang et al., 2011;Yin et al., 2016;Zheng et al., 2017) and one a 1 MRI (Segal et al., 2012). One study used a 0.18 T MRI . ...
... The results are summarized in Table 14 in Appendix H. Among the retrieved papers, there were 34 high-quality papers (Akbarshahi et al., 2014;Akrami et al., 2018;Aksahin et al., 2017;Assassi and Magnenat-Thalmann, 2016;Besier et al., 2008;Farrokhi et al., 2011;Greybe et al., 2017;Guiotto et al., 2014;Hattori-Hara et al., 2014;Ho et al., 2014;Huang et al., 2018;Julkunen et al., 2008;Klets et al., 2018;Knecht et al., 2008;Koh et al., 2019;Liao et al., 2018;Lilledahl et al., 2011;Linka et al., 2017Linka et al., , 2019Liukkonen et al., 2017Liukkonen et al., , 2018Yin et al., 2016;Luczkiewicz et al., 2018;Mootanah et al., 2014;Ng et al., 2019;Pal et al., 2019;Pierce et al., 2013Pierce et al., , 2016Räsänen et al., 2013;Segal et al., 2012;Tang et al., 2011;Yang et al., 2009Yang et al., , 2010Zheng et al., 2017), 18 medium-quality papers (Abe et al., 2013;Bolcos et al., 2018Bolcos et al., , 2019Guess, 2012;Halonen et al., 2014;Jacobs et al., 2014;Kazemi and Li, 2014;Klets et al., 2016;Kłodowski et al., 2016;Lenhart et al., 2015;Meng et al., 2017b;Mesfar and Moglo, 2013;Mononen et al., 2011Mononen et al., , 2012Mononen et al., , 2019Pierce et al., 2009;Renani et al., 2017;Safshekan et al., 2020), and 27 low-quality papers (Andriacchi et al., 2006;Atmaca et al., 2013;Besier et al., 2005;Butz et al., 2011;Cardiff et al., 2014;Carey et al., 2014;Dong et al., 2011;Fitzpatrick et al., 2010Fitzpatrick et al., , 2011Gu et al., 1998;Haemer et al., 2011;Kang et al., 2018;Li et al., 1999Li et al., , 2001Li et al., , 2020Lin et al., 2020;Liu and Zhang, 2013;Meng et al., 2017a;Orsi et al., 2016;Pena et al., 2005;Pierce et al., 2010;Qi et al., 2018;Sagl et al., 2019;Salmingo et al., 2017;Shah et al., 2015;Shim et al., 2016;Tanska et al., 2015). Of the low-quality papers, 18 did not mention any hypothesis and had fewer than three participants. ...
Article
MRI-based mathematical and computational modelling studies can contribute to a better understanding of the mechanisms governing cartilage’s mechanical performance and cartilage disease. In addition, distinct modelling of cartilage is needed to optimize artificial cartilage production. These studies have opened up the prospect of further deepening our understanding of cartilage function. Furthermore, these studies reveal the initiation of an engineering-level approach to how cartilage disease affects material properties and cartilage function. Aimed at researchers in the field of MRI-based cartilage simulation, research articles pertinent to MRI-based cartilage modelling were identified, reviewed, and summarized systematically. Various MRI applications for cartilage modelling are highlighted, and the limitations of different constitutive models used are addressed. In addition, the clinical application of simulations and studied diseases are discussed. The paper’s quality, based on the developed questionnaire, was assessed, and out of 79 reviewed papers, 34 papers were determined as high-quality. Due to the lack of the best constitutive models for various clinical conditions, researchers may consider the effect of constitutive material models on the cartilage disease simulation. In the future, research groups may incorporate various aspects of machine learning into constitutive models and MRI data extraction to further refine the study methodology. Moreover, researchers should strive for further reproducibility and rigorous model validation and verification, such as gait analysis.
... A literature review of knee kinematics and modelling techniques was preformed [4][5][6][7][8][9][10][11][12][13][14][15][16][17], to assess current methods and techniques utilised in the field. From this review, three models were developed with the appropriate loads, boundary conditions and material relations. ...
... Frictionless contact was assumed between all articulating surfaces [6,8,12]. ...
... The simulations of unique material prop-94 erties (300 total, 100 simulations per knee model) demonstrated 95 that the knee models using previously optimized material properties 96 represented 42% of the possible material property variations [18]. 97 Material properties were taken from previously validated finite 98 element knee models for the evaluation of tibiofemoral compres-99 sion [25,26]. The interface of bone with articular cartilage and the 100 meniscal insertions were modeled as rigid as this has a minimal 101 effect on contact solutions when evaluating quasi-static tibiofe-102 moral compression [27]. ...
... Articular cartilage was modeled as 103 homogenous, linearly elastic, isotropic materials with a modulus 104 of 15 MPa and Poisson's ratio of 0.475 to maintain the nearly 105 incompressible behavior during short loading times [28][29][30]. The 106 body of the menisci was modeled as homogeneous, linearly elas-107 tic, transversely isotropic materials [25,26,[31][32][33][34]. The modulus 108 and the Poisson's ratio in the meniscus fiber direction were 109 defined as 150 MPa and 0.3, respectively. ...
Article
Meniscal root repairs are susceptible to unrecoverable loosening that may displace the meniscus from the initial position reduced during surgery. Despite this, the effects of a loosened meniscal root repair on knee mechanics are unknown. We hypothesized that anatomic root repairs without loosening would restore knee mechanics to the intact condition better than loosened anatomic root repairs, but that loosened repairs would restore mechanics better than untreated meniscal root tears. Finite element knee models were used to evaluate changes in cartilage and meniscus mechanics due to repair loosening. The mechanical response from loosened anatomic root repairs was compared to anatomic repairs without loosening and untreated root tears. All conditions were evaluated at three flexion angles, 0°, 30°, and 60°, and a compressive force of 1,000 N to simulate return-to-activity loading. The two-simple-suture method was represented within the models to simulate posteromedial meniscal root repairs and repair loosening was derived from previous biomechanical experimental data. Loosening decreased hoop stresses throughout the meniscus, increased posterior extrusion, and shifted loading through the meniscus-cartilage region to the cartilage-cartilage region compared to the anatomic root repair without loosening. Despite differences between repairs and loosened repairs, the changes from loosened repairs more closely resembled the anatomic repair without loosening than the untreated root repair condition. Therefore, root repairs are susceptible to loosening that will prevent a successful initial repair from remaining in the intended position and will alter mechanics, although repairs that loosen appear better than leaving tears untreated.
... The results will be presented in the relevant "Results" section. Regarding the menisci roots, they are modeled as bundles of linear tension-only springs with a total stiffness value of 2000 N/mm equally distributed to each spring 33,65 . Moreover, we modeled the posterior capsule, anterolateral and arcuate ligaments. ...
Article
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Anterior cruciate ligament (ACL) tear is one of the most common knee injuries. The ACL reconstruction surgery aims to restore healthy knee function by replacing the injured ligament with a graft. Proper selection of the optimal surgery parameters is a complex task. To this end, we developed an automated modeling framework that accepts subject-specific geometries and produces finite element knee models incorporating different surgical techniques. Initially, we developed a reference model of the intact knee, validated with data provided by the Open Knee(s) project. This helped us evaluate the effectiveness of estimating ligament stiffness directly from MRI. Next, we performed a plethora of “what-if” simulations, comparing responses with the reference model. We found that (a) increasing graft pretension and radius reduces relative knee displacement, (b) the correlation of graft radius and tension should not be neglected, (c) graft fixation angle of 20∘ can reduce knee laxity, and (d) single-versus double-bundle techniques demonstrate comparable performance in restraining knee translation. In most cases, these findings confirm reported values from comparative clinical studies. The numerical models are made publicly available, allowing for experimental reuse and lowering the barriers for meta-studies. The modeling approach proposed here can complement orthopedic surgeons in their decision-making.
... In general, meniscectomy is effective at relieving pain and symptoms 25 ; however, patients who experience degenerative changes and worse clinical outcomes may have mechanical factors associated with altered joint biomechanics and overloading of the articular cartilage. 7,12,26,28 Studies have observed that 13% to 76% of patients with previous meniscectomy have persistent or recurrent pain and symptoms, and 5% to 36% are not satisfied with the outcome. 8,20,38 These high rates may reflect a need for more careful patient selection when considering meniscectomy. ...
Article
Full-text available
Background: At least 760,000 outpatient meniscectomies are performed in the United States each year, making this the most common musculoskeletal procedure. However, meniscal resection can alter the joint biomechanics and overload the articular cartilage, which may contribute to degenerative changes and the need for knee replacement. Avoiding or delaying knee replacement is particularly important in younger or more active patients. Synthetic meniscal implants have been developed in an attempt to restore the natural joint biomechanics, alleviate pain and disability, and potentially minimize degenerative changes in patients who require meniscectomy. Purpose: To evaluate the preliminary results from 2 ongoing trials that are evaluating the safety and effectiveness of a synthetic polymer meniscal implant (NUsurface; Active Implants, LLC). Study design: Cohort study; Level of evidence, 2. Methods: This was a preliminary analysis of the first 100 patients enrolled across 2 studies for 12 months: a single-arm, intervention-only study and a randomized controlled trial comparing the investigational meniscal implant with nonsurgical therapy. There were 65 patients in the implant group (30 randomized) and 35 in the control group. Outcomes included Knee injury and Osteoarthritis Outcome Score (KOOS) and adverse events (AEs) collected at baseline and follow-up visits of 6 weeks, 6 months, and 12 months. Results: No statistically significant differences were found in baseline characteristics between the implant and control groups. At 12 months, follow-up KOOS data were available for 87% of the 100 included patients. Significantly greater improvements from baseline were observed in the implant group compared with controls in all KOOS subcomponents, except for symptoms (119%-177% greater improvement at 12 months). AEs were reported at similar rates between the 2 groups, with 12 AEs among 11 patients in the implant group (16.9%) versus 5 AEs among 5 patients (14.3%) in the control group (P = .99). Conclusion: These preliminary results suggest significant improvements in pain and function scores with the implant over nonsurgical therapy and a similar adverse event rate.
... The estimated knee secondary kinematics, JCF, and soft tissue mechanical responses of a FE knee joint model can be affected by uncertainties in knee joint geometries, kinetics and primary kinematics, and material properties of tissues 52,53 . However, in a typical modeling approach, subject-specific geometries and primary/secondary kinematics can be obtained from MRI and motion analysis 54,55 . There have also been attempts to incorporate subject-specific material properties of cartilage from MRI into FE models 21,56,57 . ...
Article
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Abnormal mechanical loading is essential in the onset and progression of knee osteoarthritis. Combined musculoskeletal (MS) and finite element (FE) modeling is a typical method to estimate load distribution and tissue responses in the knee joint. However, earlier combined models mostly utilize static-optimization based MS models and muscle force driven FE models typically use elastic materials for soft tissues or analyze specific time points of gait. Therefore, here we develop an electromyography-assisted muscle force driven FE model with fibril-reinforced poro(visco)elastic cartilages and menisci to analyze knee joint loading during the stance phase of gait. Moreover, since ligament pre-strains are one of the important uncertainties in joint modeling, we conducted a sensitivity analysis on the pre-strains of anterior and posterior cruciate ligaments (ACL and PCL) as well as medial and lateral collateral ligaments (MCL and LCL). The model produced kinematics and kinetics consistent with previous experimental data. Joint contact forces and contact areas were highly sensitive to ACL and PCL pre-strains, while those changed less cartilage stresses, fibril strains, and fluid pressures. The presented workflow could be used in a wide range of applications related to the aetiology of cartilage degeneration, optimization of rehabilitation exercises, and simulation of knee surgeries.
... Material Properties. Material properties were taken from the previous studies of finite element models that were optimized and used for tibiofemoral compression [20,21]. Bone of the distal femur and proximal tibia was modeled as rigid. ...
Article
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Nonanatomic placement of posteromedial meniscal root repairs alters knee mechanics; however, little is known about how the position and magnitude of misplacement affect knee mechanics. Finite element knee models were developed to assess changes in cartilage and meniscus mechanics for anatomic and various nonanatomic repairs with respect to intact. In total, 25 different repair locations were assessed at loads of 500 N and 1,000 N. The two-simple-suture method was represented within the models to simulate posteromedial meniscal root repairs. Anatomic repairs nearly restored total contact area; however, meniscal hoop stress decreased, meniscal extrusion increased, and cartilage-cartilage contact area increased. Repairs positioned further posterior altered knee mechanics the most and repairs positioned further anterior restored knee mechanics for posteromedial root repairs. Despite this, repair tension increased with further anterior placement. Anterior placement of repairs results in more restorative contact mechanics than posterior placement; however, anterior placement also increased the risk of suture cut-out or failure following repairs. Anatomic placement of repairs remains the best option because of the risks involved with anterior placement; however, suture methods need to be improved to better restore the strength of repairs to that of the native insertion. Proper placement of repairs is important to consider with meniscal root repairs because misplacement may negatively affect cartilage and meniscus mechanics in patients.
Article
Finite element models of the knee can be used to identify regions at risk of mechanical failure in studies of osteoarthritis. Models of the knee often implement joint geometry obtained from magnetic resonance imaging (MRI) or gait kinematics from motion capture to increase model specificity for a given subject. However, differences exist in cartilage material properties regionally as well as between subjects. This paper presents a method to create subject‐specific finite element models of the knee that assigns cartilage material properties from T2 relaxometry. We compared our T2‐refined model to identical models with homogeneous material properties. When tested on three subjects from the Osteoarthritis Initiative data set, we found the T2‐refined models estimated higher principal stresses and shear strains in most cartilage regions and corresponded better to increases in KL grade in follow‐ups compared to their corresponding homogeneous material models. Measures of cumulative stress within regions of a T2‐refined model also correlated better with the region's cartilage morphology MRI Osteoarthritis Knee Score as compared with the homogeneous model. We conclude that spatially heterogeneous T2‐refined material properties improve the subject‐specificity of finite element models compared to homogeneous material properties in osteoarthritis progression studies. Statement of Clinical Significance: T2‐refined material properties can improve subject‐specific finite element model assessments of cartilage degeneration.
Chapter
The knee is a complex 3D joint whose normal function depends on the coordination of a supporting structure made of ligaments, muscles tendons, cartilage, menisci working together to preserve stability and gait. Any disruptions of these soft tissues lead to a mechanical disadvantage, pain, and knee pathologies such as cartilage defect that might require surgery. To preserve the integrity of the knee anatomy during TKA or ligament reconstruction, it is important that the biomechanics of the knee is well understood, the role each substructure plays in our daily activities and in achieving our performance goals. The knee articulation of the femur over the tibia is also guided and driven by the patellofemoral surface articulation and muscle producing forces to balance and regulate the energy-work expenditure by muscles. This chapter objective is to describe the biomechanics of the knee and its anatomy, modeling techniques, and gait analysis use in evaluation of knee performance. Finally, use of advance techniques in imaging, FEA, and multibody dynamics to understand the in-depth role of the knee mechanics for future clinical evaluation of new prostheses design and knee repairs to restore normal knee function.
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Background: Nowadays, the total knee arthroplasty (TKA) technique plays an important role in surgical treatment for patients with severe knee osteoarthritis (OA). However, there are still several key issues such as promotion of osteotomy accuracy and prosthesis matching degree that need to be addressed. Objective: It is significant to construct an accurate three-dimensional (3D) geometric anatomy structure model of subject-specific human knee joint with major bone and soft tissue structures, which greatly contributes to obtaining personalized osteotomy guide plate and suitable size of prosthesis. Methods: Considering different soft tissue structures, MRI scanning sequences involving two-dimensional (2D) spin echo (SE) sequence T1 weighted image (T1WI) and 3D SE sequence T2 weighted image (T2WI) fat suppression (FS) are selected. A 3D modeling methodology based on CT and two sets of MRI images is proposed. Results: According to the proposed methods of image segmentation and 3D model registration, a novel 3D knee joint model with high accuracy is finally constructed. Furthermore, remeshing is used to optimize the established model by adjusting the relevant parameters. Conclusions: The modeling results demonstrate that reconstruction and optimization model of 3D knee joint can clearly and accurately reflect the key characteristics, including anatomical structure and geometric morphology for each component.
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We present the first study in vivo of meniscal movement in normal knees under load. Using an open MR scanner, allowing imaging in physiological positions in near to real-time, 16 young footballers were scanned moving from full extension to 90° flexion in the sagittal and coronal planes. Excursion of the meniscal horns, radial displacement and meniscal height were measured. On weight-bearing, the anterior horn of the medial meniscus moves through a mean of 7.1 mm and the posterior horn through 3.9 mm, with 3.6 mm of mediolateral radial displacement. The height of the anterior horn increases by 2.6 mm and that of the posterior horn by 2.0 mm. The anterior horn of the lateral meniscus moves 9.5 mm and the posterior horn 5.6 mm, with 3.7 mm of radial displacement. The height of the anterior horn increases by 4.0 mm, and that of the posterior horn by 2.4 mm. In non-weight-bearing, the anterior horn of the medial meniscus moves 5.4 mm and the posterior horn 3.8 mm, with 3.3 mm of radial displacement. The anterior horn of the lateral meniscus moves 6.3 mm, and the posterior horn 4.0 mm, with 3.4 mm of radial displacement. The most significant differences between weight-bearing and non-weight-bearing were the movement and vertical
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As a step towards developing a finite element model of the knee that can be used to study how the variables associated with a meniscal replacement affect tibio-femoral contact, the goals of this study, were 1) to develop a geometrically accurate three-dimensional solid model of the knee joint with special attention given to the menisci and articular cartilage, 2) to determine to what extent bony deformations affect contact behavior and 3) to determine whether constraining rotations other than flexion/extension affects the contact behavior of the joint during compressive loading. The model included both the cortical and trabecular bone of the femur and tibia, articular cartilage of the femoral condyles and tibial plateau, both the medial and lateral menisci with their horn attachments, the transverse ligament, the anterior cruciate ligament, and the medial collateral ligament. The solid models for the menisci and articular cartilage were created from surface scans provided by a noncontacting, laser-based, three-dimensional coordinate digitizing system with an root mean squared error (RMSE) of less than 8 microns. Solid models of both the tibia and femur were created from CT images, except for the most proximal surface of the tibia and most distal surface of the femur which were created with the three-dimensional coordinate digitizing system. The constitutive relation of the menisci treated the tissue as transversely isotropic and linearly elastic. Under the application of an 800 N compressive load at 0 degrees of flexion, six contact variables in each compartment (i.e., medial and lateral) were computed including maximum pressure, mean pressure, contact area, total contact force, and coordinates of the center of pressure. Convergence of the finite element solution was studied using three mesh sizes ranging from an average element size of 5 min by 5 mm to 1 min by 1 mm. The solution was considered converged for an average element Size of 2 min by 2 mm. Using this mesh size, finite element solutions for rigid versus deformable bones indicated that none of the contact variables changed by more than 2% when the femur and tibia were treated as rigid. However, differences in contact variables as large as 19% occurred when rotations other than flexion/extension were constrained. The largest difference was in the maximum pressure. Among the principal conclusions of the study are that accurate finite element solutions of tibio-femoral contact behavior can be obtained by treating the bones as rigid. However, unrealistic constraints on rotations other than flexion/extension can result in relatively large errors in contact variables.
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Purpose: Depending on the location and extent of the meniscectomy, loading on the tibial articular cartilage alters. The main purpose of the present study was to analyze the loading on the tibial articular cartilage following medial meniscectomy performed in various location and extent, as well as in the healthy knee, via finite element analyses on the solid models. Methods: Totally, 11 finite element solid models, including the reference model, were created to investigate the effect of location (anterior, posterior, longitudinal) and extent of meniscectomy (25, 50, 75, and 100 %) on loading of tibial articular cartilage. Results: Maximum equivalent stress of the tibial cartilage was measured 0.86 Megapascal in the reference model and increased approximately by 78 % in 25 % meniscectomy group, 177.9 % in 50 %, 473.8 % in 75 % meniscectomy group, and 752.6 % in total meniscectomy. When only the amount of meniscal tissue removed was considered ignoring the location of meniscectomy, no significant difference was found in the amount of tissue excised between 25 % meniscectomy and 50 % meniscectomy, as well as between 75 % meniscectomy and total meniscectomy. Conclusion: In all meniscectomy models, the loadings on tibial articular cartilage increased. Except total meniscectomy, the highest impact was observed in longitudinal 75 % meniscectomy. During the surgical treatment, the contributions of menisci on load absorption by increasing the tibiofemoral contact area must be considered. In fact, the increase in the rate of loading on tibial articular cartilage depends on according to type and amount of meniscectomy.
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Background The posterior cruciate ligament (PCL) plays an important role in maintaining physiological kinematics and function of the knee joint. To date mainly in-vitro models or combined magnetic resonance and fluoroscopic systems have been used for quantifying the importance of the PCL. We hypothesized, that both tibiofemoral and patellofemoral kinematic patterns are changed in PCL-deficient knees, which is increased by isometric muscle flexion. Therefore the aim of this study was to simultaneously investigate tibiofemoral and patellofemoral 3D kinematics in patients suffering from PCL deficiency during different knee flexion angles and under neuromuscular activation. Methods We enrolled 12 patients with isolated PCL-insufficiency as well as 20 healthy volunteers. Sagittal MR-images of the knee joint were acquired in different positions of the knee joint (0°, 30°, 90° flexion, with and without flexing isometric muscle activity) on a 0.2 Tesla open MR-scanner. After segmentation of the patella, femur and tibia local coordinate systems were established to define the spatial position of these structures in relation to each other. Results At full extension and 30° flexion no significant difference was observed in PCL-deficient knee joints neither for tibiofemoral nor for patellofemoral kinematics. At 90° flexion the femur of PCL-deficient patients was positioned significantly more anteriorly in relation to the tibia and both, the patellar tilt and the patellar shift to the lateral side, significantly increased compared to healthy knee joints. While no significant effect of isometric flexing muscle activity was observed in healthy individuals, in PCL-deficient knee joints an increased paradoxical anterior translation of the femur was observed at 90° flexion compared to the status of muscle relaxation. Conclusions Significant changes in tibiofemoral and patellofemoral joint kinematics occur in patients with isolated PCL-insufficiency above 30 degrees of flexion compared to healthy volunteers. Since this could be one reasonable mechanism in the development of osteoarthritis (OA) our results might help to understand the long-term development of tibiofemoral and/or patellofemoral OA in PCL-insufficient knee joints.
Article
Background: Quantifying the in vivo cartilage contact mechanics of the knee may improve our understanding of the mechanisms of joint degeneration and may therefore improve the surgical repair of the joint after injury. Objective: To measure tibiofemoral articular cartilage contact kinematics during in vivo knee flexion. Study Design: Descriptive laboratory study. Methods: Orthogonal fluoroscopic images and magnetic resonance image-based computer models were used to measure the motion of the cartilage contact points during a quasi-static lunge in 5 human subjects. Results: On the tibial plateau, the contact point moved in both the anteroposterior and the mediolateral directions during knee flexion. On the medial tibial plateau, flexion angle did not have a statistically significant effect on the location of the contact points. The total translation of the contact point from full extension to 90 degrees of flexion was less than 1.5 mm in the anteroposterior direction, whereas the translation in the mediolateral direction was more than 5.0 mm. In the anteroposterior direction, the contact points were centered on the medial tibial plateau. On the lateral tibial plateau, there was a statistically significant difference between the location of the contact point at full extension and the locations of the contact points at other flexion angles in the anteroposterior direction. No significant difference was detected between the location of the contact points at other flexion angles. The overall range of contact point motion was about 9.0 mm in the anteroposterior direction and about 4.0 mm in the mediolateral direction. The contact points were primarily on the inner half of the medial and lateral tibial plateaus (the half closest to the tibial spine). The contact points on both femoral condyles were also on the inner half of the condyles (near the condylar notch). Conclusions: The tibiofemoral contact points move in 3 dimensions during weightbearing knee flexion. The medial tibiofemoral contact points remained within the central portion of the tibial plateau in the anteroposterior direction. Both the medial and lateral tibiofemoral contact points were located on the inner portions of the tibial plateau and femoral condyles (close to the tibial spine), indicating that the tibial spine may play an important role in knee stability. Clinical Relevance: The results of this study may provide important insight as to the mechanisms contributing to the development of osteoarthritis after ligament injuries.
Article
The purpose of the current study was to evaluate influences of radial tears and partial meniscectomy of lateral meniscus on the knee joint mechanics during normal walking by using computational modeling. A 3D geometry of a knee joint of a healthy patient was obtained from our previous study, whereas the data of normal walking were taken from the literature. Cartilage tissue was modeled as a fibril reinforced poroviscoelastic material, whereas meniscal tissue was modeled as a transverse isotropic elastic material. The realistic gait cycle data were implemented into the computational model and the effects of radial tears and partial meniscectemy of lateral meniscus on the knee joint mechanics were simulated. Middle, posterior, and anterior radial tears in lateral meniscus increased stresses by 300%, 430%, and 1530%, respectively, at the ends of tears compared to corresponding areas in the model with intact lateral meniscus. Meniscus tears did not alter stresses and strains at the tibial cartilage surface, whereas partial meniscectomy increased contact pressures, stresses, strains and pore pressures in the tibial cartilage by 50%, 44%, 21%, and 43%, respectively. Increased stresses and strains were observed primarily during the first ∼50% of the stance phase of the gait cycle. The present study suggests that anterior radial tear causes the highest risk for the development of total meniscal rupture, whereas partial meniscectomy increases the risk for the development of OA in lateral tibial cartilage. Highest risks for meniscus and cartilage failures are suggested to occur during the loading response and mid-stance of the gait cycle. In the future, the present modeling may be further developed to offer a clinical tool for aid in decision making of clinical interventions for patients with knee joint injuries. © 2013 Orthopaedic Research Society Published by Wiley Periodicals, Inc. J Orthop Res 9999:1-10, 2013.
Article
Background: In recent years, with technological advances in arthroscopy and magnetic resonance imaging and improved biomechanical studies of the meniscus, there has been some progress in the diagnosis and treatment of injuries to the roots of the meniscus. However, the biomechanical effect of posterior lateral meniscus root tears on the knee has not yet become clear. The purpose of this study was to determine the effect of a complete radial posterior lateral meniscus root tear on the knee contact mechanics and the function of the posterior meniscofemoral ligament on the knee with tear in the posterior root of lateral meniscus. Methods: A finite element model of the knee was developed to simulate different cases for intact knee, a complete radial posterior lateral meniscus root tear, a complete radial posterior lateral meniscus root tear with posterior meniscofemoral ligament deficiency, and total meniscectomy of the lateral meniscus. A compressive load of 1000 N was applied in all cases to calculate contact areas, contact pressure, and meniscal displacements. Results: The complete radial posterior lateral meniscus root tear decreased the contact area and increased the contact pressure on the lateral compartment under compressive load. We also found a decreased contact area and increased contact pressure in the medial compartment, but it was not obvious compared to the lateral compartment. The lateral meniscus was radially displaced by compressive load after a complete radial posterior lateral meniscus root tear, and the displacement took place mainly in the body and posterior horn of lateral meniscus. There were further decrease in contact area and increases in contact pressure and raidial displacement of the lateral meniscus in the case of the complete posterior lateral meniscus root tear in combination with posterior meniscofemoral ligament deficiency. Conclusions: Complete radial posterior lateral meniscus root tear is not functionally equivalent to total meniscectomy. The posterior root torn lateral meniscus continues to provide some load transmission and distribution functions across the joint. The posterior meniscofemoral ligament prevents excessive radial displacement of the posterior root torn lateral meniscus and assists the torn lateral meniscus in transmitting a certain amount of stress in the lateral compartment.
Article
The menisci and their insertions into bone (entheses) represent a functional unit. Thanks to their firm entheses, the menisci are able to distribute loads and therefore reduce the stresses on the tibia, a function which is regarded essential for cartilage protection and prevention of osteoarthrosis. The tissue of the hypocellular meniscal body consists mainly of water and a dense elaborate type I collagen network with a predominantly circumferential alignment. The content of different collagens, proteoglycans and nonproteoglycan proteins shows significant regional variations probably reflecting functional adaptation. The meniscal horns are attached via meniscal insertional ligaments mainly to tibial bone. At the enthesis, the fibres of the insertional ligaments attach to bone via uncalcified and calcified fibrocartilages. This anatomical configuration of gradual transition from soft to hard tissue, which is identical to other ligament entheses, is certainly essential for normal mechanical function and probably protects this vulnerable transition between 2 biomechanically different tissues from failure. Clinical treatment of meniscal tears needs to be based on these special anatomical and functional characteristics. Partial meniscectomy will preserve some of the load distribution function of the meniscus only when the meniscal body enthesis entity is preserved. Repair of peripheral longitudinal tears will heal and probably preserve the load distribution function of the meniscus, whereas radial tears through the whole meniscal periphery or more central and complex tears may be induced to heal, but probably do not preserve the load distribution function. There is no proof that replacement of the meniscus with an allograft can reestablish some of the important meniscal functions, and thereby prevent or reduce the development of osteoarthrosis which is common after meniscectomy. After implantation, major problems are the remodelling of the graft to inferior structural, biochemical and mechanical properties and its insufficient fixation to bone which fails to duplicate a normal anatomical configuration and therefore a functional meniscal enthesis.
Article
We investigated the in vivo cartilage contact biomechanics of the tibiofemoral joint in patients after reconstruction of a ruptured anterior cruciate ligament (ACL). A dual fluoroscopic and MR imaging technique was used to investigate the cartilage contact biomechanics of the tibiofemoral joint during in vivo weight-bearing flexion of the knee in eight patients 6 months following clinically successful reconstruction of an acute isolated ACL rupture. The location of tibiofemoral cartilage contact, size of the contact area, cartilage thickness at the contact area, and magnitude of the cartilage contact deformation of the ACL-reconstructed knees were compared with those previously measured in intact (contralateral) knees and ACL-deficient knees of the same subjects. Contact biomechanics of the tibiofemoral cartilage after ACL reconstruction were similar to those measured in intact knees. However, at lower flexion, the abnormal posterior and lateral shift of cartilage contact location to smaller regions of thinner tibial cartilage that has been described in ACL-deficient knees persisted in ACL-reconstructed knees, resulting in an increase of the magnitude of cartilage contact deformation at those flexion angles. Reconstruction of the ACL restored some of the in vivo cartilage contact biomechanics of the tibiofemoral joint to normal. Clinically, recovering anterior knee stability might be insufficient to prevent post-operative cartilage degeneration due to lack of restoration of in vivo cartilage contact biomechanics. © 2012 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 30:1781-1788, 2012.