A geometric approach to study the contact mechanisms in the patellofemoral joint of normal versus patellofemoral pain syndrome subjects

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A geometric approach to study the contactmechanisms in the patellofemoral joint of normalversus patellofemoral pain syndrome subjectsKamrul Islama, Kajsa Dukeb, Tanvir Mustafya, Samer M. Adeeba, Janet L. Ronskyc & MarwanEl-Richa

a Department of Civil and Environmental Engineering, University of Alberta,EdmontonABCanadab Department of Mechanical Engineering, University of Alberta, AlbertaABCanadac Department of Mechanical and Manufacturing Engineering, University of Calgary,CalgaryABCanadaPublished online: 19 Aug 2013.

To cite this article: Kamrul Islam, Kajsa Duke, Tanvir Mustafy, Samer M. Adeeb, Janet L. Ronsky & Marwan El-Rich (2013):A geometric approach to study the contact mechanisms in the patellofemoral joint of normal versus patellofemoral painsyndrome subjects, Computer Methods in Biomechanics and Biomedical Engineering, DOI: 10.1080/10255842.2013.803082

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A geometric approach to study the contact mechanisms in the patellofemoral joint of normalversus patellofemoral pain syndrome subjects

Kamrul Islama, Kajsa Dukeb, Tanvir Mustafya, Samer M. Adeeba, Janet L. Ronskyc and Marwan El-Richa*aDepartment of Civil and Environmental Engineering, University of Alberta, Edmonton, AB, Canada; bDepartment of Mechanical

Engineering, University of Alberta, Alberta, AB, Canada; cDepartment of Mechanical and Manufacturing Engineering, University ofCalgary, Calgary, AB, Canada

(Received 5 November 2012; accepted 3 May 2013)

The biomechanics of the patellofemoral (PF) joint is complex in nature, and the aetiology of such manifestations of PFinstability as patellofemoral pain syndrome (PFPS) is still unclear. At this point, the particular factors affecting PFPS havenot yet been determined. This study has two objectives: (1) The first is to develop an alternative geometric method using athree-dimensional (3D) registration technique and linear mapping to investigate the PF joint contact stress using an indirectmeasure: the depth of virtual penetration (PD) of the patellar cartilage surface into the femoral cartilage surface. (2) Thesecond is to develop 3D PF joint models using the finite element analysis (FEA) to quantify in vivo cartilage contact stressand to compare the peak contact stress location obtained from the FE models with the location of the maximum PD.Magnetic resonance images of healthy and PFPS subjects at knee flexion angles of 158, 308 and 458 during isometric loadinghave been used to develop the geometric models. The results obtained from both approaches demonstrated that the subjectswith PFPS show higher PD and contact stresses than the normal subjects. Maximum stress and PD increase with flexionangle, and occur on the lateral side in healthy and on the medial side in PFPS subjects. It has been concluded that thealternative geometric method is reliable in addition to being computationally efficient compared with FEA, and has thepotential to assess the mechanics of PFPS with an accuracy similar to the FEA.

Keywords: patellofemoral pain; cartilage; penetration depth; contact stress; finite element modelling

1. Introduction

The patellofemoral (PF) joint is one of the major load-

bearing joints. The PF joint is beginning to garner more

attention in orthopaedic biomechanics due to such

associated instabilities as patellar maltracking, chondro-

malacia of the patella, patellofemoral pain syndrome

(PFPS), and patellar dislocation and subsequent initiation

of osteoarthritis. PFPS is one of the most common knee

disorders. In a study over a 5-year period, it was reported

that 25% of the knee problems in athletes presented to a

sports injury clinic were because of the PF syndrome

(Devereaux and Lachmann 1984). In fact, 10% of all

sports injury clinic visits are attributed to PFPS (Kannus

et al. 1987; Waryasz and McDermott 2008). Abnormal

stresses are often cited as a primary cause of different

instabilities in the PF joint, including PFPS. PFPS often

affects people who are active and/or participate in sports

(Fairbank et al. 1984; Loud and Micheli 2001; Fulkerson

2002; Powers 2003). Numerous research programmes

have been undertaken in the past to investigate the PFPS

and its associated factors (Waryasz and McDermott 2008;

Lankhorst et al. 2012). Despite what is known about this

syndrome, it is still unclear what the exact cause of PFPS is

(Fulkerson 2002).

Patellar maltracking, which is associated with

malalignment of the patella as well as an imbalance of

the knee extensor muscles, is considered to be an

important factor in the onset of PFPS (Ahmed et al.

1983; Neptune et al. 2000; Sheehan et al. 2009, 2012).

Muscle force imbalance results in a lateral shift of the

patella, causing pain in the lateral side of the PF joint

(Dhaher and Kahn 2002; Cowan et al. 2009). As such, the

main clinical concern has been that patients with PFPS

experience a higher load in the lateral facet of the PF joint.

But, interestingly, a few recent studies have shown

evidence of pain and cartilage wear in the medial side of

the PF joints as well as medial shift of the patella (Gorniak

2009; Song et al. 2011; Draper et al. 2012). These findings

have constituted a clear contradiction of the previous

reports discussing the PFPS, in which most of the research

focused on the lateral aspect (lateral malalignment/

maltracking) of the PF joints as a sole contributor of

PFPS. In addition, elevated joint contact stresses are also

considered to be a cause of PFPS (Fulkerson 2002; Mach

et al. 2002). Patients with PF pain also experience an

elevated level of bone metabolic activity at the PF joints,

which is correlated with pain intensity (Draper et al. 2012).

In vivo and in vitro quantifications of PF joint contact

stress were conducted using animal and cadaveric models

(Ahmed et al. 1983; Huberti and Hayes 1984; Ronsky et al.

1995; Lee et al. 2003). However, computational modelling

is gaining popularity in biomechanical research due to its

q 2013 Taylor & Francis

*Corresponding author. Email: [email protected]

Computer Methods in Biomechanics and Biomedical Engineering, 2013

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flexibility and manipulating capacity for joint modelling.

Complex joint characteristics and contact mechanics can

easily be investigated through computational models.

Although in vivo joint stress cannot be measured using

direct mechanical tests, computational modelling, such as

finite element (FE) method, can be readily used to quantify

stress/strain within the joints. The lack of experimental

measures coupled with the complexity of the joint has led

researchers to develop FE models of the PF joint in order

to better understand its mechanical behaviour (Elias et al.

2004; Han et al. 2005; Besier et al. 2005, 2008; Farrokhi

et al. 2011). Previous FE models of PF joints relied on

muscle forces. These muscle forces are often estimated

from electromyographic systems which have many

limitations (Sheehan et al. 2012). As PF joint contact

stress is a function of quadriceps muscle force (Schindler

and Scott 2011), inaccurate quantification of muscle force

may change the contact stress pattern.

The first objective of this study is to develop an

alternative geometric method using a three-dimensional

(3D) registration technique and linear mapping to

investigate the PF joint contact stress using an indirect

measure: the depth of virtual penetration (PD) of the

patellar cartilage surface into the femoral cartilage surface.

The second objective is to develop 3D FE models of the PF

joint in order to quantify in vivo cartilage contact stress.

The novelty of this FE approach is the use of the

registration technique and linear mapping to investigate

the PF contact stresses, rather than using muscle forces.

Finally, this study will compare the peak contact stress

location (medial/lateral) obtained from the FE models with

the location of the highest PD.

2. Materials and methods

2.1 Alternative geometric methods

This study used experimental data obtained from six

healthy (female, 26 ^ 4 years, 167.0 ^ 7.9 cm,

64.4 ^ 5.7 kg) and six pathological (PFPS) subjects

(female, 28 ^ 8 years, 167.0 ^ 4.7 cm, 59.0 ^ 5.5 kg).

Among the six healthy subjects H1–H6, the left knee of

three subjects H1–H3 and the right knee of three subjects

H4–H6 were scanned. In the case of the six PFPS subjects

P1–P6, the left knee of three subjects P1–P3 and the right

knee of three subjects P4–P6 were scanned. All the

subjects used in this study were female due to the

significant difference in the knee joint kinematics between

male and female subjects (Malinzak et al. 2001; Csintalan

et al. 2002; Biscevic et al. 2005). All subjects were

scanned using 3.0 T magnetic resonance imaging (MRI) at

158, 308 and 458 knee flexion angles. The MRI

specifications and details about the subjects were given

in Connolly (2006). A brief summary of the MRI

specifications is described here.

The scanning was carried out using a 3.0 TMRI with the

following specifications: repetition time, 17ms; echo time,

3ms; flip angle, 908; image resolution, 0.625 £ 0.625mm2;

field of view (FOV), 16 £ 16 cm2 and slice thickness, 3mm.

The MRI machine software produced large number of

sequential digital imaging and communications in

medicine (DICOM) images of the experimental subject

which were imported into the 3D image modelling

software, MIMICS (Materialise NV, Leuven, Belgium).

Sagittal plane images were used to segment the PF joint

surface, including cartilage boundaries, and the other two

planes were utilised for better visualisation of the full joint

surface. Three-dimensional reconstructed geometries of

the patella and femur for 158, 308 and 458 knee flexion

angles were also created using MIMICS. The surfaces of

the models were not smooth in texture. However, in order

to obtain an accurate cartilage surface geometry and

thickness, no further smoothing of the models was

completed.

Following the digitisation, two data-sets of 3D

geometry for the patella and femur (158 and 308, 158 and

458) were imported into the Geomagic Studio 12

(Raindrop Geomagic, Inc., NC, USA) simultaneously as

the input for registration. The patella at the 158 position

was chosen to be registered with the patella at 308 and 458,

whereas the femur was considered as a fixed object in each

case. Using the two built-in registration methods

(‘manual’ and ‘automatic’), the patella at 158 (reference

position) was linearly transformed from its original

position to the 308 and 458 patellar positions (final

position). The ‘manual registration’ method was first used

to find an approximate position of alignment for the two

geometries of the patella (reference and final positions).

The ‘automatic registration’ built-in algorithm in Geoma-

gic 12 was then used to fine tune the alignment. In this

‘automatic registration’ method, the built-in algorithm

checks and minimises the average deviation of all points of

comparison.

The proximal relationship between the patella and

femur is pertinent to the PF joint stability investigation.

In this study, following the incorporation of the

registration technique, the patellar surface (i.e. patella

that was previously at 158 position) intersects the surface

of the flexed femur (i.e. femur at 308 and 458 positions). In

this case, the PD becomes the measure of proximity as the

two objects (patella and femur) intersect one another

virtually. This virtual PD represents the indirect measure

of the PF joint contact deformation, indicating that the PD

between the patellar and femur surface scan can be

considered as an indirect measure of the stress developed

along the interface. To the best of the researchers’

knowledge, this study constitutes the first attempt to

quantify stress in terms of PD in computational

biomechanics research. The PD was measured using five

different methods according to the following five

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definitions: (a) PD1, cubic root of intersection volume; (b)

PD2, highest thickness of intersection; (c) PD3, ratio of the

intersection volume to the projected surface area in

contact; (d) PD4, ratio of the intersection volume to the

total volume of patella (non-dimensional) and (e) PD5,

shortest translational distance required that brings two

objects in contact. Among the five methods, only PD2 has

been used to evaluate the difference between the medial

and lateral sides of the PF joint. Table 1 shows the details

of the five different methods used in this study.

2.2 Finite element modelling

The geometries of the bony structures and soft tissues in

this study were obtained following the procedures

described in the previous section. In order to obtain

smoothed surfaces for finite element analysis (FEA), the

binary stereolithography (STL) file generated in MIMICS

was imported into Geomagic Studio 12. After further

refinement of the 3D geometry, a registration technique

similar to the one explained above was used. The purpose

of the registration technique is to use the undeformed

patella (i.e. patella at 158 position), as the cartilage on the

patellar surface at the 308 and 458 positions is assumed to

be already deformed with respect to the patella at 158

position. Finally, the non-uniform rational B-spline

surfaces produced by Geomagic were exported to the

initial graphics exchange specification (IGS) format, and

the refined 3D PF joint geometry was imported into

HyperMesh (Altair Engineering, Inc., Troy, MI, USA). FE

meshes of the 3D-digitised models of the femur, patella,

patellar cartilage and femoral cartilage were created using

HyperMesh. The articular cartilage of the patella and

femur was modelled as a homogeneous isotropic material

with a modulus of elasticity of 12.0MPa and a Poisson’s

ratio of 0.45 (Mesfar and Shirazi-Adl 2005). Similarly, the

femur and patella were modelled as linear elastic isotropic

materials with a modulus of elasticity of 12.0GPa and a

Poisson’s ratio of 0.38 (Donahue et al. 2002). As we are

not interested in fluid exudation and matrix consolidation,

modelling the cartilage as linear elastic was deemed

sufficient to capture the in vivo mechanical behaviour of

the joint (Carter and Beaupre 1999; Carter and Wong

2003). The articular cartilage geometry was discretised

using tetrahedral elements, whereas shell elements were

used for the geometry of the cortical bone layers of the

femur and the patella. In this study, we are interested to

quantify the stress in the cartilage surface; therefore, for

bony structures (patella and femur), we did not

differentiate between cortical bone and cancellous bone.

The bony structures have large stiffness, and are

considered rigid compared with the cartilage. An average

element size of 1mm was used for tetrahedral elements,

whereas an average element size of 2mm was used for

shell elements. The element sizes were chosen based on

the previous study (Donahue et al. 2002). The patellar

cartilage had 18,000 elements, whereas the femoral

cartilage had 83,000 elements. Surface-to-surface contact

was assumed based on the hard contact constraint, and the

default penalty method was used for simulations using

ABAQUS 6.10 (Simulia, Providence, RI, USA). A very

low coefficient of friction of 0.002 was assumed for the

contact modelling (Adeeb 2004). For all simulations,

the femur was constrained in all six degrees of freedom at

the proximal end. Following application of the registration

technique, it should be noted that the patellar cartilage

surface virtually intersects the femoral cartilage surface.

Moreover, prior to initiation of the simulations, the patella

was moved in the anterior direction to separate both the

objects (i.e. femur and patella) from each other. The same

amount of displacement was applied as a displacement-

controlled loading. All the four FE models were developed

for the left knees of one healthy (female, 32 years,

166.4 cm, 63.5 kg) and one PFPS subject (female, 38 years,

172.7 cm, 61.2 kg) for 308 and 458 knee positions. Figure 1

depicts the modelling approach followed in this study, and

Figure 2 depicts the meshed 3D model of the PF joint.

Table 1. Five different methods for quantifying PD.

Method Formula Unit Schematic diagram

PD1

ffiffiffiffiffiffi

V 33p ffiffiffiffiffiffiffiffiffiffi

mm33p

PD2 t mm

PD3VA

mm3

mm2

PD4VVp

mmmm

PD5 d mm

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2.3 Statistical analyses

Statistical analyses were carried out using SPSS 17.0

(SPSS, Inc., Chicago, IL, USA). A one-tailed t-test was

conducted, and significance was set at p , 0.05 to

compare the PD between healthy and PFPS subjects.

Besides the t-test, the Wilcoxon signed-rank non-

parametric statistical test was carried out to verify the

results obtained from the t-test as the sample sizes were

small. The Wilcoxon signed-rank test assumed that the

samples were distribution free. A significance level of 0.1

was used to compare the difference in PD between healthy

and PFPS subjects.

3. Results

3.1 Alternative geometric methods

The PD of healthy and PFPS subjects for the left and right

knee is shown in Tables 2 and 3, respectively. The

different measurement techniques used to calculate the PD

rendered different results. Figures 3 and 4 depict the

variation in the PD between the lateral and medial sides of

the PF joints for both healthy and PFPS subjects using the

measurement technique described by PD2. In Figures 3

and 4, each column represents the PD of a different

subject. All techniques (i.e. PD1–PD5) provided clear

distinction between healthy and PFPS subjects at 308 and

458 knee positions. However, only PD2 was able to

distinguish between medial and lateral compartments of

the PF joint, so it was selected for further analysis.

In both healthy and PFPS subjects for both left and

right knees, PD1, PD2, PD4 and PD5 show an increase in

their values as the knee flexion angle increases. PD3 has an

opposite trend for the left and right knees of healthy

subjects, as well as for the left knee of PFPS subjects. PD

is greater for PFPS subjects at 308 for both left and right

knees, but results of the t-tests and Wilcoxon signed-rank

test suggest that the differences between healthy and PFPS

subjects at a 308 knee flexion angle are not statistically

significant (Tables 4 and 5). A significant difference was

found between healthy and PFPS subjects ( p , 0.05) for

the left knee using PD1 and PD3 at 458 knee flexion angle

(Table 4). In the case of the right knee, PFPS subjects have

significantly higher PD ( p , 0.05) than the healthy

subjects using all techniques (i.e. PD1–PD5) (Table 4).

Similar results were found using theWilcoxon signed-rank

test (Table 5), but the test showed significant difference

between healthy and PFPS subjects ( p ¼ 0.109) at the 308

right knee flexion angle using PD3, as well as a significant

difference between healthy and PFPS subjects

Figure 1. Computational model pipeline of PF joint.

Figure 2. Finite element model of the PF joint (meshed model).

Table 2. PD for left knee of healthy and PFPS subjects atdifferent knee positions.

Knee angleposition

PD1

(ffiffiffiffiffiffiffiffiffiffi

mm33p

)PD2

(mm)PD3

ðmm3=mm2ÞPD4

(mm/mm)PD5

(mm)

308 healthy subjectH1 6.08 1.95 1.10 0.97 2.20H2 6.97 1.98 1.54 1.95 2.80H3 6.50 1.90 1.16 1.81 2.40

458 healthy subjectH1 6.88 2.20 1.10 1.41 2.60H2 7.50 2.10 1.24 2.43 3.00H3 7.32 1.98 1.10 2.58 2.50

308 PFPS subjectP1 7.13 3.18 1.33 2.27 2.95P2 6.93 3.00 1.52 1.46 2.90P3 5.30 2.00 0.67 1.04 1.90

458 PFPS subjectP1 7.59 3.36 1.36 2.75 3.10P2 8.25 3.38 1.39 2.50 2.92P3 7.68 2.20 1.36 3.10 2.90

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( p ¼ 0.109) at the 308 left knee flexion angle using PD2

(Table 5).

A higher PD occurred on the medial side of the PFPS

joint at a 308 flexion using PD2, and it was statistically

significant ( p ¼ 0.018) for the left knee (Figure 3). For

the 458 knee flexion angle, a slight increase in PD was

obtained using PD2, and it was statistically significant

( p ¼ 0.04) for the right knee (Figure 4).

3.2 Simulation results of finite element modelling

The contact pressure, von Mises stress and maximum

principal stress in cartilage were shown to increase with

flexion in both healthy and PFPS joints, and the largest

values were obtained in the PFPS joint (Figures 5 and 6).

Higher contact pressure occurred on the medial side of the

PFPS joint and shifted to the lateral side for the healthy

joint (Figure 5). A similar trend was obtained for von

Mises stress (Figure 6). Figure 7 depicts the von Mises

stress distribution in the patellar cartilage surface for

healthy as well as symptomatic PF joint at 308 and 458

knee flexion angle conditions. The results of the FEA for

healthy and PFPS subjects at 308 and 458 knee flexion

angle conditions are shown in Tables 6 and 7, respectively

(only peak stresses at the cartilage surface are included).

4. Discussions

The purpose of this study is to quantify the contact stresses in

thePF joints for healthy and symptomatic joints. To fulfil this

purpose, the FEAs of the PF joints for healthy and

pathological subjects at two different knee flexion angles

were investigated. In addition to the FEA, another geometric

approach was developed to investigate the joint contact

behaviour for both healthy andPFPS subjects. FEAwas used

to generate stress maps in which stresses are generally

quantified based on the gradients of the deformation of the

model. In the alternative geometric method, the same 3D

geometry that was used in FEA was utilised. However, the

location of high gradients of deformation was identified

without the cumbersome task of generating FEA models in

which material property, FE meshing of the complex 3D

geometry, muscle forces, joint lubrications, appropriate

boundary conditions and contact stresses – which are subject

to user discretion – must be dealt with. The drawback of this

approach is that only the contact stresses can be inferred,

whereas other mechanical variables such as strains in

different layers of cartilage cannot be quantified.

Table 3. PD for right knee of healthy and PFPS subjects atdifferent knee positions.

Knee angleposition

PD1

(ffiffiffiffiffiffiffiffiffiffi

mm33p

)PD2

(mm)PD3

ðmm3=mm2ÞPD4

(mm/mm)PD5

(mm)

308 healthy subjectH4 3.46 1.3 0.53 0.27 1.1H5 5.36 1.6 0.74 0.887 1.8H6 4.098 1.29 0.58 0.48 1.3

458 healthy subjectH4 5.274 1.6 0.93 0.96 1.9H5 5.9 1.97 0.78 1.2 2.15H6 4.313 1.47 0.46 0.56 1.35

308 PFPS subjectP4 4.44 1.8 0.47 0.62 1.72P5 4.14 1.47 0.37 0.5 1.35P6 4.54 1.2 0.45 0.62 1.15

458 PFPS subjectP4 7.83 3.6 1.284 3.41 3.55P5 6.73 3.61 1.1 2.05 3.53P6 6.31 2.38 0.83 1.7 2.3

Figure 3. PD (millimetre) in lateral (L) and medial (M) sides of the PF joint for healthy and PFPS subjects at the 308 and 458 left kneepositions using the PD2 method.

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From this study, we have demonstrated that the contact

deformation is related to the PD of the joint’s femoral and

patellar cartilage surfaces, measured using the 3D

registration and linear mapping of the patella from 158

(reference position) to 308 and 458 knee flexion angles.

The MRI data for this study were obtained from a previous

study by Connolly (2006). As the MRI data were not

available for the fully extended knee position, we used the

patellar shape at 158 as the reference shape. By doing this,

we ignored the PF contact forces at 158.

Five different measurement techniques were used to

measure PD in six healthy and six PFPS female knee

joints. Contact areas between the femur and patellar

cartilage surfaces are extended from the medial to the

lateral side of the PF joints (Clark et al. 2002). Therefore,

the location of the maximum contact stress could be in the

lateral, central or medial side of the contact surface. In this

study, the location of the peak contact stress was found in

the lateral side of the patellar cartilage surface for a

healthy subject using FE models, which is consistent with

those reported in the literature for healthy subjects (Besier

et al. 2005; Farrokhi et al. 2011). In addition, we found that

the PD was also greatest on the lateral side for five of the

six healthy knees at 308 and 458 knee flexion angles. One

healthy subject showed a higher PD on the medial side at

308 knee flexion angle, and another healthy subject showed

a higher PD on the medial side at 458 knee flexion angle.

Contact stresses, von Mises stresses and maximum

principal stresses increased with knee flexion from 308 to

458. PD also increased with knee flexion from 308 to 458.

Contact stresses reported in the literature for PFPS

subjects are controversial and generally higher in the

lateral side of the PF joints (Farrokhi et al. 2011).

However, this study has shown PFPS subjects to have

higher PD on the medial side than healthy subjects, and the

values were statistically significant. The current FEA

showed higher stresses in the medial side of the PFPS

subject, which is consistent with the results obtained from

the alternative geometric method. One recent study has

found increased bone metabolic activity in the posterior

side of the patella (Draper et al. 2012), as well as increased

bone metabolic activity on both the medial and lateral

sides of the patella for subjects with chronic knee pain

(Draper et al. 2012).

Table 4. Statistical analysis results (p values from t-test).

Knee angle position PD1 PD2 PD3 PD4 PD5

Left knee308 healthy and PFPS 0.465 0.076 0.350 0.492 0.388458 healthy and PFPS 0.019 0.059 0.013 0.11 0.133

Right knee308 healthy and PFPS 0.464 0.346 0.092 0.445 0.492458 healthy and PFPS 0.035 0.020 0.0008 0.047 0.011

Table 5. Statistical Analyses results (p-values from Wilcoxonsigned-rank test).

Knee angle position PD1 PD2 PD3 PD4 PD5

Left knee308 healthy and PFPS 0.593 0.109 0.593 1.0 0.593458 healthy and PFPS 0.109 0.109 0.102 0.109 0.285

Right knee308 healthy and PFPS 1.0 1.0 0.109 1.0 1.0458 healthy and PFPS 0.109 0.109 0.109 0.109 0.109

Figure 4. PD (millimetre) in lateral (L) and medial (M) sides of the PF joint for healthy and PFPS subjects at the 308 and 458 right kneepositions using the PD2 method.

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It has been reported that due to muscle imbalance, the

patella shifts and tilts laterally, causing an overloading in

the lateral facet (Lee et al. 2002; Wilson et al. 2009). This

study confirmed the lateral shift of the contact area using

the alternative geometric method and FEA. On the other

hand, peak stresses and PD location were observed in

the medial side for PFPS subjects, which is in

contradiction to most of the current literature. It is very

important to note that higher forces do not necessarily

equate to higher contact stresses. The contact stresses

depend also on the congruency between the contacting

areas and it is possible that a lateral shift of the patella

leads to a more congruent lateral side and a less congruent

medial side. This in turn would lead to higher stresses on

the medial side.

Recent experimental results reported in the literature

support our observation that contact stresses increase in the

medial side. Although Sawatsky et al. (2012) have shown

that the muscle imbalance associated with PFPS did not

cause shifting in the contact pressure, a recent study by

Draper et al. (2012) has found an increased bone metabolic

activity on the medial side for a few subjects. Gorniak

(2009) found greater cartilage wear on the medial side than

on the lateral side of PF joints of the cadaveric specimen,

and Song et al. (2011) also reported in their review article

that symptomatic patella did not consistently show lateral

Figure 5. Patellar cartilage von Mises stress distribution for (a) healthy knee at 308 (max. stress of 2.1MPa at lateral side), (b) healthyknee at 458 (max. stress of 5.80MPa at lateral side), (c) PFPS knee at 308 (max. stress of 2.55MPa at medial side) and (d) PFPS knee at 458(max. stress of 6.55MPa at medial side).

Figure 6. Contact pressure in lateral (L) and medial (M) sides of the PF joint at 308 and 458 flexion for healthy and PFPS joints at (a)femoral cartilage surface and (b) patellar cartilage surface.

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malalignment or maltracking. These findings support our

results, demonstrating that higher stresses occur in the

medial side of the PF joint in PFPS subjects. PD estimation

using the alternative geometric method reveals trends

similar to those in the FEA results. The similarity in the

results is naturally due to utilising the same initial and final

geometries for both the geometric approach and the FEA

approach, which shows that some of the mechanical

measures can be inferred from the geometrywithout having

to conduct the FEA.

Other previous studies have found the octahedral shear

stresses to be higher in the patellar cartilage surface than in

the femoral cartilage surface (Besier et al. 2005; Farrokhi

et al. 2011), and higher bone metabolic activity in the

patella than in the femur (Draper et al. 2012). In this study,

we also found higher stresses in the patellar cartilage

surface in both healthy and PFPS subjects.

PD estimated using various methods (PD1–PD5) is

greater in PFPS subjects. FE models also show higher

stresses in the PFPS subjects, a result which corresponds to

the quantification of the PD using the alternative geometric

method. In both FEA and the alternative geometricmethod,

this study found that the PFPS subjects experienced higher

stresses than the healthy subjects, which is consistent with

the literature (Farrokhi et al. 2011). Our results reveal that

contact stress is related to PD. FEA and the alternative

geometric method show similar trends in both the healthy

and PFPS subjects. Moreover, the alternative geometric

method could be a reliable useful tool to assess PFPS.

This study has shown, using both FEA and the

alternative geometric method, that PFPS subjects experi-

ence higher stress on the medial side of the PF joint than

healthy subjects, which is contrary to the clinical idea that

the greatest load occurs through the lateral facet, thereby

causing higher stress in the lateral side and not in the

medial side. According to earlier studies, as the PF joint

reaction force is directed laterally, it will create higher

pressure in the lateral facet (Hirokawa 1991; Hefzy and

Yang 1993). In this study, we were not focusing on the

ligament/muscle force, rather we were interested in the

stress in the PF joint cartilage which is dependent on the

orientation and shape of the articulating surface.

Current treatments are aimed towards fixing the

malalignment/maltracking through strengthening the

vastus medialis muscles to control the lateral shift/tilt of

the patella. However, the results of our work should be

taken into consideration in dealing with individuals who

have medial patellar malalignment/maltracking. In this

article, we presented the importance of the medial aspect

of the symptomatic PF joints, which is sometimes

completely ignored clinically while treating the PFPS.

There are certain limitations in this study. It is to be

noted that all the subjects used in this study were tested

in a supine condition during MRI, and the applied load

Table 6. Peak stresses (MPa) for healthy and PFPS subjects atpatellar cartilage surface.

Kneeangleposition Subject

Contactpressure

vonMisesstress

Max.principalstress

308 Healthy 3.84 2.10 4.61458 6.23 5.80 6.98308 PFPS 5.37 2.55 7.05458 5.76 6.55 12.18

Table 7. Peak stresses (MPa) for Healthy and PFPS subjects atfemoral cartilage surface.

Kneeangleposition Subject

Contactpressure

VonMisesstress

Max.principalstress

308 Healthy 3.77 1.81 4.47458 4.71 3.24 6.98308 PFPS 4.32 2.66 6.08458 6.73 3.63 5.60

Figure 7. Maximum von-Mises stresses (MPa) in lateral (L) and medial (M) side of the PF joint: (a) femoral cartilage surface and (b)patellar cartilage surface for healthy and PFPS subjects at different knee positions.

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was less than the body weight of the test subject during

MRI. The results of this small sample size show general

trends that were statistically confirmed with the t-test

and Wilcoxon test, but additional subjects will be

investigated in the future in order to further substantiate

these findings. In addition, future studies will utilise the

patellar position at the fully extended knee as the

reference geometry.

Another limitation of our study is the relatively rough

surface of the generated geometries of the patellar and

femoral cartilage layers. The roughness is attributed to the

slice thickness of the MRI images, which is a limitation of

any similar study. In our study, we have chosen not to

utilise any smoothing technique and to be as careful as

possible during the digitisation process. In addition, our

results were consistent for all the subjects. Future studies

will utilise the recent advances in MRI and the availability

of strong MRI magnets that are able to generate higher

resolution images with a small slice thickness. We believe

that the availability of such imaging techniques will enable

the development of accurate geometric assessment

methods that would infer on the stresses without having

to conduct cumbersome FEAs.

5. Conclusions

The results presented in this article should be considered

as a ‘proof of concept’. The alternative geometric method

proposed in this study is based on the initial and final

geometries of the patella. An accurate reconstruction of

3D models from MRI is an important issue in the present

approach. Results of the present approach also depend on

how accurately the patellar cartilage boundary and the

femoral cartilage boundary are identified. This study

stands as the first study which numerically demonstrated

the evidence of significant higher medial stress/pen-

etration in the PFPS patients than the lateral side of the

joints which could eventually lead to higher medial pain.

One clear distinction from the previous study was found in

terms of the location ofmaximum stress for PFPS subjects.

In previous studies, the lateral side of the PF joints was

mentioned as critical for PF pain. This study found the

medial side of the PF joints for PFPS subjects to be

significant. It should be noted that this study primarily

focused on the magnitude and location of the maximum

contact stress, as well as PD. The results of this study have

shown that the medial side of the PF joint is also important

in terms of PF pain, a finding which was not reported in

previous studies. However, the proposed alternative

geometric method to investigate the PFPS is computa-

tionally efficient compared with the conventional FEA,

and has the potential to effectively assess PFPS. Future

work is required to evaluate the present approach on more

subjects to establish it as a ‘gold-standard’ diagnostic/

computational tool for patients with PFPS.

Acknowledgement

This research work was partially supported by the NaturalSciences and Engineering Research Council (NSERC) of Canada.

Conflict of interest statement: The authors have no conflict ofinterest to declare.

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