Isabelle Waterplas eindig elementenmodel Biomechanica van het kniegewricht

99 Pages·2013·6.01 MB·English

Biomechanica van het kniegewricht: een gedetailleerd
eindig elementenmodel
Isabelle Waterplas
Promotoren: prof. dr. ir. Benedict Verhegghe, dr. ir. Matthieu De Beule
Begeleiders: dr. ir. Sofie Van Cauter, ir. Wouter Devriendt
Masterproef ingediend tot het behalen van de academische graad van
Master in de ingenieurswetenschappen: biomedische ingenieurstechnieken
Vakgroep Civiele Techniek
Voorzitter: prof. dr. ir. Peter Troch
Faculteit Ingenieurswetenschappen en Architectuur
Academiejaar 2012-2013

Deze pagina is niet beschikbaar omdat ze persoonsgegevens bevat.
Universiteitsbibliotheek Gent, 2021.
This page is not available because it contains personal information.
Ghent University, Library, 2021.

Overzicht
In deze scriptie wordt een volledig eindig elementenmodel van de knie opgesteld, vertrekkend
van ruwe MR (Magnetic Resonance) beelden, met de bedoeling dit model te kunnen gebruiken in
de klinische praktijk. Hiervoor wordt op het einde van de scriptie al een eerste stap in deze
richting ondernomen, er wordt namelijk aan de hand van het model een vergelijkende studie
gemaakt tussen de anteromediale portal (AM) en transtibiale (TT) voorste kruisband
reconstructietechnieken.

Deze scriptie bestaat uit drie grote delen:

 Terminologie, anatomie en voorste kruisband
Een eerste hoofdstuk behandelt de anatomische terminologie. Een notie van deze termen
is noodzakelijk om tot een goed begrip van de rest van deze scriptie te komen. De overige
hoofdstukken van Deel 1 omvatten de literatuurstudie. Hierin worden de anatomie van de
knie, de VKB (voorste kruisband – ACL– anterior cruciate ligament) en de verschillende
aspecten van VKB letsels en reconstructies uitgebreid besproken.
 Eindig elementenmodel
In het tweede deel van deze scriptie wordt het eindig elementen model van de knie stap
voor stap opgebouwd. Een eerste hoofdstuk ervan gaat over het segmenteren en meshen
in Mimics en 3-matic. Een zijsprong wordt gemaakt naar het meshen met hexaëder
elementen in 3D Slicer. Hierna worden de gebruikte materiaalmodellen voor de
verschillende onderdelen opgesteld en de belangrijkste stappen van het model in Abaqus
overlopen. Er worden drie modellen opgebouwd: Model 1 is het model van de gezonde
knie, bij Model 2 wordt de VKB vervangen door een transplantaat zoals dit zou gebeuren
bij een AM-reconstructie operatie en Model 3 is het model van een TT-gereconstrueerde
knie.
 Simulaties
In het laatste deel worden enkele simulaties uitgevoerd. Ten eerste wordt er een
sensitiviteitsanalyse uitgevoerd om het effect van de meshdensiteit op de resultaten te
onderzoeken. Hierna worden de pivot-shift en Lachman test besproken en wordt er een
vergelijking gemaakt tussen deze beweging opgelegd op een gezonde knie en opgelegd op
een VKB gebrekkige knie. Ten slotte wordt aan de hand van deze bewegingen de
vergelijking gemaakt tussen de AM- en de TT- techniek.

Sleutelwoorden
Kniegewricht, eindig elementenmodel, voorste kruisband (VKB), transtibiale- en anteromediale
portal VKB reconstructie
vii

Biomechanics of the knee: a detailed finite element model
Isabelle Waterplas
Supervisor(s): Benedict Verhegghe, Matthieu De Beule, Sofie Van Cauter and Wouter Devriendt

This study describes a detailed three-dimensional because both tunnels may be drilled
finite element (FE) model of the human knee. The independently. This could result in a more
aim of the development of this model was anatomically  correct  placement  of  the  tunnels.  It’s  
comparing two different ACL reconstruction a safe and effective method, but has a learning
techniques, namely the anteromedial portal and the
curve. Another disadvantage is that the femoral
transtibial technique, since this is still a
tunnel should be drilled with the knee in
controversial topic in knee surgery. For this
hyperflexion, which is awkward and requires an
comparison, three models where created, one of the
extra assistant during this critical step. Although
healthy knee and two as if a reconstruction was
performed. The bones are modeled as rigid bodies, biomechanical tests show better results for the
the cartilage and menisci as linear elastic material AM technique, this is not yet clinically proven
and the ligaments as transversely isotropic. The [2]. The ideal tunnel placement remains a
model was developed with the aim to use it for other controversial topic so far.
applications in the future, like studying different
ACL grafts and investigating meniscus scaffolds.
Keywords- Human knee, finite element model,
anterior cruciate ligament (ACL), ACL
reconstruction, anteromedial portal (AM)
technique, transtibial (TT) technique.

I. INTRODUCTION
Fig.1. A comparison of ACL graft tunnel orientation: AM
(anatomic) versus TT [2]
The knee is the most complex ligament of the
human body. It serves as a hinge between the
The objective of this study is to make a
femur and the tibia. The knee is held together by
comparison between those two techniques based
four ligaments: two collateral ligaments (lateral
on a detailed FE model.
and medial) and two cruciate ligaments (anterior
and posterior). The ACL is one of the most II. METHODS
frequently injured ligaments in the knee, this can
range from a small tear to a completely torn ACL. The created model is based on MR (magnetic
In the US, the occurrence of ACL injury is resonance) images of the right knee of a female
estimated at 200.000 annually, of which 100.000 cadaver. MR images are chosen because the
are treated surgically [1]. The most common visibility of the ligaments is much better
reasons are a sudden stop, turn or change in compared to CT (computed tomography) images.
direction. These kind of movements are common Segmentation of the bones, cartilage, menisci and
in certain sports, such as football, basketball and ligaments is done in Mimics v15.01. A
skiing, so people who practice these sports have a disadvantage of the MR images is that the
higher risk of an ACL injury. In some cases, an segmentation in Mimics has to be done more
ACL reconstruction is necessary, where an auto-, manually compared to CT, because no preset
or allograft replaces the natural ACL. With an windows are available. Creating volume meshes
ACL reconstruction, two tunnels should be is done in 3-matic v7.01 for tetrahedral and in
drilled, one in the femur and one in the tibia. The 3DSlicer v3.6.3 for hexahedral elements.
drilling of these tunnels can be done by means of Afterwards, three models are created in Abaqus
two common techniques: the transtibial technique v6.10. Model 1 is the model of the healthy knee,
or the anteromedial portal (anatomic) technique, Model 2 and Model 3 are an adaptation of Model
shown in Figure 1. With the TT technique, the 1 as if an ACL reconstruction operation with
femoral tunnel is drilled through the tibial tunnel, respectively the AM and TT technique were
with the consequence that the two tunnels are performed. To make the comparison, two
dependent from each other. This technique is movements were imposed: the pivot shift test and
easy, fast and the most familiar to many surgeons. the Lachman test. These are tests used to detect a
With the anteromedial portal technique, as the torn ACL. The pivot-shift movement, which is 30
name implies, the femoral tunnel is drilled degrees of flexion and 20 degrees of torsion, is
through an anteromedial portal. This technique imposed by applying two moments to the tibia
offers a greater degree of freedom to the surgeon and  fixing  the  six  degrees  of  freedom  (DOF’s)  of
the femur. The Lachman test was imposed by
flexing the femur 30 degrees, while fixing the
DOF’s  of  the  tibia  and  subsequently  applying  an  
anterior displacement to the tibia, while fixing the
DOF’s  of  the  femur  en  some  DOF’s  of  the  tibia.  
III. MATERIALS
The bones are modeled as rigid bodies. The
cartilage and menisci as lineair elastic materials, Fig.2. Comparison of pivot-shift test imposed on Model 1
with   a   Young’s   modulus   of   E=10MPa   and (ACL intact and ACL deficient), Model 2 and Model 3
E=59MPa respectively and a Poisson ratio of
=0.46 and =0.49 respectively [3][4]. The The comparison between a linear and a quadratic
ligaments as well as the grafts are modeled as geometric order of the ligaments results in
transversely isotropic materials, since their fiber minimal differences, except the smaller standard
structure makes them much stronger in the deviation with the quadratic geometric order.
longitudinal direction than in the transverse Because the hexahedral mesh should be
direction. In Abaqus this is defined by the investigated more thoroughly first, we decide to
engineering constants, which are described in continue with the tetrahedral model with the
Table 1 [5][6]. The material orientation is defined coarsest mesh, since convergence has occurred.
by one or more local coordinate systems.
Model 1 Model 1
ACL intact ACL deficient
Table 1. Material constants for ligaments and graft
ACL/PCL/M Patellar tendon
CL/LCL graft
E (E ) 34,5 MPa 22,5 MPa
1 p
E (E ) 34,5 MPa 22,5 MPa
2 p
E (E) 345 MPa 225 MPa
3 t
 ( ) 0,22 0,27
12 p
 ( ) 0,022 0,027
13 pt
 ( ) 0,022 0,027
23 pt
G (G ) 14 MPa 8,9 MPa
12 p
G (G) 168 MPa 109,5 MPa
13 t
G (G) 168 MPa 109,5 MPa
23 t Model 2 Model 3
AM TT
IV. RESULTS
Model 1 of the healthy knee is used to perform a
mesh sensitivity analysis. The element type
(tetrahedral and hexahedral elements) as well as
the mesh density and the geometric order (linear
versus quadratic) are investigated. For the
tetrahedral mesh the maximum triangle edge
length (MTEL) is varied from 10 mm, 2 mm, 1.5
mm to 1 mm. The hexahedral mesh density is
altered by varying the edge length from 1 mm to
0.7 mm, a finer mesh made the model instable.

The average ‘maximum principal stresses’ of the
Fig.3. Comparison of Lachman test imposed on Model 1
ACL with their standard deviations are compared, (ACL intact and ACL deficient), Model 2 and Model 3
as well as the stability and the stress distribution
visually. It can be concluded that the hexahedral The pivot-shift as well as the Lachman test are
mesh gives lower average ‘maximal principal
much less hindered when the ACL deficient knee
stresses’, which can be caused by the
model is compared to the ACL intact model. This
oversmoothing that has been performed to obtain
indicates that those two movements are adequate
a working model.
for investigating the influence of the graft
(placement) with ACL reconstruction techniques.
The comparison between the healthy knee, the modeling the grafts, since the virtual placement
ACL deficient knee and the AM- and TT- occurs much more straightforward than in reality,
where it is patient-specific fitting. As a result, a
reconstructed knees shows that both grafts hinder
simplification of reality was required in this study
the movements much less than an intact ACL, to
which made the modeling possible but the results
the extent that the AM-reconstructed model has
less reliable. This makes the comparison of the
almost no difference compared to the ACL reconstructed knees not yet very validated and
deficient knee. Figure 2 and 3 show the positions more investigations are recommended.
of the knee after respectively the pivot-shift and
REFERENCES
Lachman test were imposed on the healthy knee,
the ACL deficient knee and the AM- and TT-
[1] AAOS. (2009, september). ACL Injury: Does
reconstructed knees. This can be caused by the
it require surgery?, consulted April 2013, from
small diameter of the graft or the insufficient
OrthoInfo: http://orthoinfo.aaos.org/
material model. Since those uncertain parameters
are the same with both reconstruction models,
[2] Potter, M. S., Werner, F. W., Sutton, L. G., &
comparing only those two makes more sense. The
Schweizer, S. K. (2012, juli). A comparison of
AM graft hinders both movements less than the
Anterior Cruciate Ligament graft tunnel
TT graft, especially with the pivot shift test,
orientation: Anatomic vs. transtibial. Clinical
resulting in lower stresses in the graft but higher
Biomechanics, 27(6), 602-606.
stresses in the other ligaments.
[3] Hart, A. N., Minns, R. J., Nabhani, F. N., &

V. DISCUSSION Muckle, D. S. (1999). An examination of the
internal stresses in articular cartilage of the human
The result of this study is a working detailed finite patella. The Knee, 6(3), 171-174.
element model that can be used in clinical
practice to study different aspects of the human [4] Peña, E., Calvo, B., Martinez, M. A., Palanca,
knee, although some more research in the future is D., & Doblaré, M. (2005). Finite element analysis
recommended, especially when modeling the
of the effect of meniscal tears and menisectomies
materials and the grafts.
on human knee biomechanics. Clinical
Biomechanics, 20(5), 498-507.
Since material investigations into human tissues
are scarce, it was difficult to compose a validated
[5] Wilson, T. W., Zafuta, M. P., & Zobitz, M.
material model for the ligaments and graft. We
suggest that more research should be done or (1999). A Biomechanical Analysis of Matched
potentially performing new material tests when Bone-Patellar Tendon-Bone and Double-Looped
developing a FE model of the knee, to overcome Semitendinosus and Gracilis Tendon Grafts. The
this problem. A second recommendation is doing
American Journal Of Sports Medicine, 27(2),
more research into the hexahedral mesh since
202-207.
literature suggest these elements are better in
stress analyses. Due to the limited scope of this
[6] Myer Kutz, & McGraw-Hill. (2003). Standard
paper, this path was not studied thoroughly. At
Handbook of Biomedical Engineering & Design.
the moment there is a big tradeoff between virtual
functionality and anatomic accuracy when New York.