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Finite element analysis of two total knee joint prostheses
Article in International Journal for Interactive Design and Manufacturing (IJIDeM) · May 2013
DOI: 10.1007/s12008-012-0167-7
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2. Int J Interact Des Manuf (2013) 7:91–101
DOI 10.1007/s12008-012-0167-7
ORIGINAL PAPER
Finite element analysis of two total knee joint prostheses
T. Ingrassia · L. Nalbone · V. Nigrelli · D. Tumino ·
V. Ricotta
Received: 24 January 2012 / Accepted: 1 June 2012 / Published online: 14 June 2012
© Springer-Verlag 2012
Abstract Aim of this work is to compare two different total
knee prostheses that differ mainly in the shape of the poly-
ethylene (PE) component inserted between the femoral and
tibial plates. The best solution between them has been origi-
nally reshaped in order to reduce stress peaks. The study pro-
cedure has been divided into the following steps. First step
is the digitalisation of the shape of the prostheses by means
of a 3D laser scanner. The morphology of two prototypes
of the prostheses has been acquired by elaborating multiple
Moirè fringe patterns projected on their surfaces. Second step
consisted on the manipulation of these data in a CAD mod-
ule, that is the interpolation of raw data into NURBS sur-
faces, reducing singularities due to the typical scattering of
the acquiring system. Third step has been the setting up of
FEM simulations to evaluate the prostheses behaviour under
benchmark loading conditions given in literature. The CAD
model of the prostheses has been meshed into solid finite
elements. Different flexion angles configurations have been
analysed, the load being applied along the femoral axis. FEM
analyses have returned stress fields in the PE insert and, in
particular, in the stabilizing cam which function is to avoid
dislocation. Last step has been the integrated use of CAD
T. Ingrassia · V. Nigrelli · V. Ricotta
Dipartimento di Ingegneria Chimica, Gestionale,
Informatica e Meccanica, Università degli Studi di Palermo,
Viale delle Scienze, 90128 Palermo, Italy
L. Nalbone
Ambulatorio di Ortopedia e Traumatologia, Azienda Ospedaliera
Universitaria Policlinico Paolo Giaccone di Palermo,
90100 Palermo, Italy
D. Tumino (B)
Facoltà di Ingegneria, Architettura e delle Scienze motorie,
Università degli Studi di Enna Kore, Cittadella Universitaria,
94100 Enna, Italy
e-mail: davide.tumino@unikore.it
and FEM to modify the shape of the stabilizing cam of the
best prosthesis, in order to reduce the stress peaks in the
original prosthesis without affecting kinematics of the joint.
Good results have been obtained both in terms of stress and
contact pressure peaks reduction.
Keywords Total knee replacement · FEM simulation ·
Contact analysis
1 Introduction
Total knee joint replacement allows the patient to restore the
full functionality of the knee joint and to overcome arthritic
pain. Clinical studies are reported in literature [1] where dif-
ferent solutions are compared in terms of geometry and kine-
matics of the mating components.
Such a prosthesis consists of femoral and tibial metallic
plates rigidly bonded to the bones, separated by a plastic
spacer. Usually, femoral and tibial components are made of
titanium, while the plastic insert is made of Polyethylene
(PE).
Some cases are found [2] where an hybrid knee implant,
combining a polymer-composite with an existing stainless
steel implant system is studied: this solution is expected to
transfer load to the femur more effectively compared to con-
ventional metallic implants.
The PE insert can be shaped in a way that dislocation
of the joint for high values of flexion angles is avoided.
Prolonged use of this prosthesis can cause wearing of the
contact surfaces of PE; the creation of debris can lead to
infection and, eventually, to a reduced ability of the patient.
Load applied to the knee joint during normal activity of the
patient has been clinically studied in literature. In [3] kine-
matic and loads acting on the knee are studied especially
in cases of deep flexion angles: largest values of posterior
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3. 92 Int J Interact Des Manuf (2013) 7:91–101
forces on the joint are found to be related to flexion angles
greater than90◦. Theload-deflection responseof thekneeina
fully extended configuration is studied in [4] by means, also,
of finite element analyses. Similar numerical techniques are
used in [5] to study different combination of flexion angles
with axial forces and to calculate the resulting contact areas.
The experimental measurements performed in [6] point out
that, in isokinetic knee extension, a large influence on peak
and average force values is given by torque of the knee. Other
tests performed in [7,8] have returned the force applied to the
knee joint during a gait cycle in the condition of level and
downhill walking: the latter condition is the most demanding
in terms of net forces, with a maximum load acting on the
knee equal to 15 N/kg of body mass.
Contact stress distribution in the PE insert follows from
the shape of sliding surfaces. Measurements via thin film sen-
sors are reported in [9] where, under a constant femoral load
value, the contact areas of the medial and lateral compart-
ments are calculated together with the load acting on each
compartment. Whether if the femoral load is differently split
on the two compartments, the contact pressure is similarly
distributed on the two surfaces.
In [10] finite element analyses are performed on two pos-
terior stabilised joints, one with a flat and one with a curved
post cam. Results show that the second solution reduces
peaks and average values of Von Mises stress in the PE
insert. The reduction of stress concentration gives benefits
in terms of wearing reduction of the plastic material. In the
same paper, the influence of flexion angles on the contact
stress distribution is analysed, namely increasing the flexion
leads to greater contact peaks.
Results of numerical explicit analyses can be found [11]
for a total knee replacement without a posterior cam. This
method is used to find the position of the joint for each flex-
ion angle of the gait cycle. Also loads and contact pressure
are calculated and it has been found that the maximum stress
concentration appears in proximity of the mid point of the
gait cycle.
Beneath the solution of a posterior stabilising cam has a
widespread diffusion in clinical application [12], new mod-
els are recently available that are characterised by a different
shape of the anti-dislocation system; one of these uses a third
median condyle instead of a post stabilising cam. In [13] a
clinical follow-up study of the performances of this type of
prosthesis has been performed; their results are only in terms
of functionality of the replacements on the patient. To the
author’s knowledge, no mechanical analysis has been per-
formed on the third median condyle joint and no comparison
has ever been done with the posterior stabilising cam solu-
tion, in terms of stress distribution during normal activity of
the prosthesis.
In this work two posterior-stabilized knee joint prostheses
have been compared, one with a posterior stabilising cam
and one with a third median condyle. Numerical compari-
sons have been performed in terms of contact and equivalent
stresses on the plastic insert for both models. Furthermore,
geometric modifications of the anti-dislocation element are
proposed to enhance the stress distribution and minimize the
risk of wearing and fracture damage.
2 The knee joint prosthesis
The knee prosthesis is an artificial joint made usually of
metallic alloy and plastic materials, that can replace the dam-
aged knee totally or partially [1]. The total prosthesis consists
of three components: the femoral part, the tibial part and the
plastic insert that replaces menisci in a healthy knee. Figure 1
shows a standard total prosthesis.
Two different total prostheses are objects of this work:
one is produced by Stryker Corp., the other is produced by
Tornier Surgical Implants. Both of them are considered as
posterior stabilised prosthesis because their shape is made in
a way to prevent possible dislocation of the joint due to high
flexion angles of the knee joint. Figure 2 shows the two men-
tioned prostheses. Femoral and tibial components are made
of titanium alloy Ti6Al4V, while the plastic insert is made of
Ultra High Molecular Weight Polyethylene UHMWPE.
Main differences between the two prostheses are related
to the plastic insert: in the Stryker prosthesis, the PE insert
has a central cam element that goes in contact with the mate
surface in the femoral plate when the flexion angle exceeds
a limit value; in Tornier prosthesis, the PE insert has a third
Femoral component
Tibial component
Plastic spacer
Fig. 1 The total knee replacement (courtesy of Tornier Surgical
Implants)
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4. Int J Interact Des Manuf (2013) 7:91–101 93
Fig. 2 Comparison between the systems under analysis: Stryker (left) and Tornier (right)
median condyle where a convex surface on the femoral part
can slide.
2.1 Shape acquisition of the prostheses
To digitally acquire the shapes of the prostheses, a 3D laser
scanner COMET 5 has been used. The scanner COMET 5 is
composed of a 11 mega-pixel camera, a laser source, a work-
station and a software, the COMETPlus, that manages all the
data, from the scanning phase to the CAD model exporting.
The system has a measuring volume that can vary from 80
to 1,000 mm3, an accuracy level (depending on the volume)
lower than 5 µm and a very reduced acquisition time (about
1 s). The acquisition procedure is here briefly summarised.
At first, surfaces to be acquired are sprayed with a mat white
colour in order to minimize reflective spurious phenomena.
Then a regular fringe pattern is projected on the object sur-
faces by means of a Laser source. Fringe pattern resulting on
the surfaces to be measured is modified according with Moirè
optical principles [14]. Multiple images have been acquired
by rotating the object around a vertical axis. All the fringe
patterns have been processed in order to obtain a point-by-
point description of the scanned surfaces.
This kind of systems are usually subjected to noise that
causes scattering in the acquired points. For this reason, these
points have been imported in the Geomagic Studio software
where they have further been filtered and interpolated into
NURBS surfaces.
Final step of this process is the conversion of the NURBS
surfaces into CAD solid models, depicted in Fig. 3.
2.2 Materials
As mentioned before, materials used for these prostheses are
titanium alloy Ti6Al4V and high molecular weight polyeth-
ylene UHMWPE, both are considered as biomaterial because
of their high compatibility with human tissues [1]. Main
Fig. 3 CAD models of the prostheses
Table 1 Elastic properties of the materials
Young Poisson Stress at
modulus (MPa) ratio failure (MPa)
Ti6Al4V 110,000 0.34 1,140
UHMWPE 2,000 0.44 60
requirements for these materials, and in particular for ortho-
paedic uses, are:
• load carrying capability and low notch sensitivity due to
stress concentration; loads generated by normal activity
of the joint should not be modified by the presence of the
prosthesis. Moreover, static, fatigue and creep resistance
are of great importance when considering a biomaterial
application;
• good tribological properties: small friction coefficients
and high wearing resistance.
Table 1 summarises elastic characteristics of the materials
used in the models.
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5. 94 Int J Interact Des Manuf (2013) 7:91–101
Fig. 4 Scheme of the loads acting on a knee
3 Loads and constraints on knee prosthesis
The determination of loads acting on the knee joint during
real working conditions is not a trivial task and requires suit-
able assumptions. A schematic representation of the human
skeleton has been defined in Fig. 4. In this scheme femur
and tibia are considered as link elements, while main artic-
ulations (hip, knee and ankle) are assumed to be cylindrical
joints [15]. Considering a general position where a person
maintains both feet on the ground, the vertical force (FB)
due to the body weight is equally split between the two legs.
When a person, instead, stays on a single foot (for example
when climbing the stairs), the whole body weight is trans-
mitted to the ground by means of only a leg.
Of course such a situation is very common and represents
one of the worst load conditions for the knee.
In this study the main interest is to evaluate the stress
and pressure values at the interface between the femoral part
and plastic insert interface, so different working conditions
have been investigated by changing the knee flexion angle φ
(Fig. 5).
3.1 Assumptions and limitations
To evaluate the maximum forces on a knee during a nor-
mal working condition, it is useful to consider the scheme
in Fig. 4. In this case, to simplify the load analysis, a sin-
gle leg support has been studied. The body force (FB) is
transmitted to the femur through the hip and can be decom-
posed into two components: one (FA) along the femoral axis
and another (FT) perpendicular to it. By imposing the equi-
librium between the femur/knee system and assuming the
lower part of the tibial component as locked (Fig. 4) [11], it
can be deduced what follows. Due to the fact that the knee
works like a cylindrical joint, it can only react to the axial load
FA, while the force FT and themoment due to it are balanced
through the muscles [15] that generate axial and transversal
forces but also a reaction moment (MM).
In this study, nevertheless, it was assumed to consider only
the axial forces acting on the femur and to neglect the trans-
versal forces and the moment due to the muscles forces. This
assumption does not reduce the quality of results because
the force along the femoral axis is the one that mainly pro-
duces contact stresses between the femoral part and the plas-
tic insert of the prosthesis.
Accordingwithexperimentaltestsinliterature[6–8],three
configurations have been studied: φ = 60◦, 90◦ and 120◦.
First two values can easily be reached when climbing the
stairs (Fig. 4) with different heights of the steps, last value,
instead, is the maximum flexion angle that can be reached in
a normal use of the prosthesis, for example when squatting
down (Fig. 6). Different contact regions correspond to each
of these angles for both Stryker and Tornier joints [9]. In all
the analysed configurations, a reference load of 500 N, that
takes into account both the force FA and the axial compo-
nent of the muscles reaction forces [15], is applied on the
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6. Int J Interact Des Manuf (2013) 7:91–101 95
Fig. 5 Definition of the flexion
angle φ
femur along its axis. Same benchmark load has been used in
literature [10].
Moreover, to apply the axial load to the joint, the femo-
ral bone has been simulated as a cylindrical bar fixed to the
upper component of the knee prosthesis. This model does
not reduce the quality of the results because, as said, the only
considered load acts along the femur towards the knee joint
centre so it is not affected by the shape of the bone.
4 FEM analysis
3D models of the two prostheses have been imported in the
finite element (FE) commercial code Ansys Workbench. FE
models, depicted in Fig. 7, are meshed with esaedric eight-
noded solid elements. The total number of elements is about
140,000 for the complete model. Face-to-face contact is mod-
elled with surface contact elements; in these elements an
augmented Lagrangian method is used to avoid penetration
between the surfaces [16].
To reproduce the real working conditions of the pros-
thesis, two springs have been applied, connecting the tibial
to the femoral component. These springs mimic the behav-
iour of the collateral ligaments, restricting rotations of the
femur around its axis. Spring stiffness value has been taken Fig. 6 120◦ knee flexion angle load case
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7. 96 Int J Interact Des Manuf (2013) 7:91–101
Fig. 7 FEM models of the prostheses
from typical values measured in human ligaments, that is
K = 34 N/mm.
External boundary conditions have been applied to the tib-
ial component and to the femoral bar. The tibial component
is fixed in all directions, as found in literature [11], while the
femoral bar can only move along and rotate around its axis.
PE insert has been bonded to the tibial component, the
samebondingisappliedbetweenthefemoralbarandthefem-
oral prosthetic component. Bonding is modelled by the FE
code as a perfect constrain between the bodies in a way that
no mutual movements or rotations are permitted. Friction
contact is assumed between the PE insert and the femoral
component, with a friction coefficient of 0.01, according to
considerations in [11].
Static incremental-iterative analyses have been performed
to solve nonlinearities due to the contact behaviour. In post-
processing, attention has been paid in evaluating contact and
equivalent stresses in the PE insert to be compared with the
limitstressofthematerial.Alltheobtainedresultsarecompa-
rable with other experimental tests [9,10,17] both in terms of
Von Mises and contact stress distribution over the PE insert.
This consideration gives reliability to the procedure used in
this study, both during reverse engineering and CAD/FEM
modelling phases.
4.1 FEM results: Stryker prosthesis
In the following, contact regions and stress distributions are
shown for the PE insert under different flexion angles. Con-
tact happens usually in the two meniscal compartments and
in the anti dislocation element.
Figure 8 shows contact regions and contact stress map
on the PE insert for φ = 60◦; it can be noticed that contact
is restricted to external areas of the compartments and to
the central cam, where maximum peaks are present (about
37.5MPa).InFig.9,thedistributionoftheVonMisesstressis
depicted for the same case of φ = 60◦. Peaks are located in the
external parts of the cam and their values, equal to 20.7 MPa,
are nearly twice the values calculated in the meniscal com-
partments. High equivalent stress values are distributed at the
root of the cam because it behaves like a short clamped beam
under flexural loads.
Figure 10 shows contact stress map for φ = 90◦. Contact
areas on the meniscal compartments move rearwards with
respect to the case of φ = 60◦, and contact stress peaks on
the central cam reach higher values (49.9 MPa). On the cam
the pressure peak is located in a central point, while, in the
case of φ = 60◦ the peaks are located in the external areas of
the cam. Similar considerations can be done for equivalent
stresses in Fig. 11: in all the stressed areas peaks of equiva-
lent stress are higher (about 27 MPa) than those calculated
for φ = 60◦.
Last case is related to φ = 120◦. Figure 12 shows that
most of the contact load is applied at the top of the central
cam and peak values are quite high and equal to 99.6 MPa.
Pressure peaks on meniscal compartments are again moved
rearwards. Also concerning equivalent stress (Fig. 13) the
map shows that the cam is severely stressed and a maximum
value about 52.3 MPa is calculated. This configuration is the
most severe for such a prosthesis, both in terms of pressure
Fig. 8 Contour map of the contact stress in the Stryker (left) and Tornier (right) prostheses with φ = 60◦
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8. Int J Interact Des Manuf (2013) 7:91–101 97
Fig. 9 Contour map of the equivalent stress in the Stryker (left) and Tornier (right) prostheses with φ = 60◦
Fig. 10 Contour map of the contact stress in the Stryker (left) and Tornier (right) prostheses with φ = 90◦
Fig. 11 Contour map of the equivalent stress in the Stryker (left) and Tornier (right) prostheses with φ = 90◦
and equivalent stress. The central cam area is always more
stressed than the meniscal compartments.
4.2 FEM results: Tornier prosthesis
Same loading conditions have been applied to the Tornier
prosthesis. In the above mentioned Figs. 8, 9, 10, 11, 12,
and 13, contact regions and stress distributions are shown
for the PE insert under different flexion angles. Figures 8
and 9 are related to φ = 60◦. Contact is distributed over the
meniscal compartments in two symmetric areas, the central
guide is unloaded. In this case, the pressure and equivalent
stress peak values are, respectively, equal to 66 and 37.5 MPa.
Figures 10 and 11 are related to φ = 90◦. Contact is con-
centrated at the end of the central guide where a stress peak is
present, both in terms of contact (115.7 MPa) and equivalent
stress (85.7 MPa). Low stresses are present in the meniscal
compartments, but peak values are definitively lower than the
one in the central guide.
Stress concentration at the end of the central guide is more
severe in the case of φ = 120◦, as Figs. 12 and 13 reveal. In this
condition, the maximum contact pressure is about 139 MPa,
while the stress peak is equal to 150 MPa. Now the meniscal
compartments are fully unloaded and all the external load is
supported by the central guide.
4.3 FEM results: comparison of the two prostheses
Results of the analyses previously performed show that the
most stressed region of the two prostheses is the central one,
both acting as a cam (in the case of Stryker version) or as
a guide (in the case of Tornier version). Results obtained
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9. 98 Int J Interact Des Manuf (2013) 7:91–101
Fig. 12 Contour map of the contact stress in the Stryker (left) and Tornier (right) prostheses with φ = 120◦
Fig. 13 Contour map of the equivalent stress in the Stryker (left) and Tornier (right) prostheses with φ = 120◦
Fig. 14 Comparison of the maximum contact stress values for the two prostheses
for the two joints are collected in the following diagrams in
Figs. 14 and 15, where maximum contact stress and equiv-
alent stress in the PE insert are compared. For each case
meniscal compartments are not stressed as the central areas.
With the exception of the case of φ = 60◦, where the cen-
tral guide of the Tornier prosthesis is unloaded, for the other
load cases it is clearly shown that the Stryker prosthesis is
subjected to lower stress peaks. This aspect leads to a higher
resistance to wearing and static failure of the PE insert.
4.4 FEM results: improvement of the Stryker prosthesis
In the previous paragraph, it has been proved that, in terms
of maximum stresses in the PE insert, the Stryker prosthesis
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10. Int J Interact Des Manuf (2013) 7:91–101 99
Fig. 15 Comparison of the maximum equivalent stress values for the two prostheses
20°
Fig. 16 Shape differences between the original Stryker cam and the
modified one
should be preferred with respect to the Tornier one. Starting
from the fact that contact stresses depend on the shape of the
mating surfaces [10], the central cam of the Stryker joint has
been redesigned in order to reduce peaks of contact stress.
In Fig. 16 a comparison between the original version and the
modified one is shown.
In the original version, the posterior surface of the cam
has a tangent plane almost vertical; in the modified version
this plane has been rotated up to a value of 20◦. This value
has been chosen in an arbitrary way, by considering that too
low values could have no considerable effect on the results,
whereas too high values could obstruct the normal rotations
of the knee.
This modification leads to a better distribution of contact
without any modification of the kinematics of the joint.
Same load cases have been studied for this modified ver-
sion of the Stryker prosthesis. Contact and equivalent stress
maps obtained are quite similar to those seen for the original
Stryker version, especially for φ = 60◦ and φ = 90◦. Of great
interest is the comparison of the maximum stress obtained
for the two versions of this prosthesis. Diagrams in Figs.
17 and 18 show that the modified Stryker version is charac-
terised by a marked reduction of the peak stress in the case of
φ=120◦,whiletheotherloadcasesareessentiallyunchanged.
In particular, in this case, pressure and equivalent stress peak
values are, respectively, 61.7 and 38.7 MPa. Being this case
the most dangerous in terms of specific stress on the cam, a
reduction of 38 % to the contact pressure and of 26 % to the
equivalent stress means a great improvement with respect to
the original version of the joint.
5 Conclusions
In this work a comparison has been proposed of the per-
formances of two total knee prostheses, one produced by
Stryker Corp. and the other by Tornier Surgical Implants.
Both prostheses are shaped in a way to give posterior sta-
bility to the joint, i.e. to avoid joint dislocation under high
flexion angles of the knee. Geometries of the prostheses have
been acquired via 3D laser scanner techniques. CAD models
obtained by interpolation of point-by-point raw acquisition
data, have been imported into a FEM software where, under
some loading and boundary assumptions, contact and equiv-
alent stress fields have been computed. Numerical analyses
simulate loading on the joint for different flexion angles.
Results reveal that the Stryker prosthesis is subjected to
lower peak stresses; this reduces the risk of wearing of the
polyethylene insert and the resultant creation of dangerous
debris.
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11. 100 Int J Interact Des Manuf (2013) 7:91–101
Fig. 17 Comparison of the maximum contact stress in the cam for the original and the modified version of the Stryker prosthesis
Fig. 18 Comparison of the maximum equivalent stress in the cam for the original and the modified version of the Stryker prosthesis
Last step of this work has been the redesign of the Stryker
prosthesis in order to enhance its behaviour at high flexion
angles. The posterior cam of the PE insert has been reshaped,
by giving a different tangent angle of 20◦, and smoothed.
Lower contact stress peaks have been obtained for this mod-
ified version with respect to the original one, without any
affection on the kinematics of the original knee joint.
This analysis procedure will be adopted to study different
load cases, for example to numerically simulate the case of
a complete gait cycle, applying effective loads as the flexion
angle varies. Then, considerations about the wearing and
fatigue prediction of the prosthesis during his life-cycle could
be done.
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