The Effect of Cyclic Loading on the Articular Cartilage of the FemoroAcetabular Joint in the Absence of a Functional Labrum as Explored
through FEA
by
Taylor J. Castagna
An Engineering Project Submitted to the Graduate
Faculty of Rensselaer Polytechnic Institute
in Partial Fulfillment of the
Requirements for the degree of
Master of Engineering
Major Subject: Mechanical Engineering
Approved:
_________________________________________
Ernesto Gutierrez-Miravete, Project Adviser
Rensselaer Polytechnic Institute
Hartford, CT
December, 2013
i
CONTENTS
The Effect of Cyclic Loading on the Articular Cartilage of the Femoro-Acetabular Joint
in the Absence of a Functional Labrum as Explored through FEA .............................. i
LIST OF TABLES ............................................................................................................ iii
LIST OF FIGURES .......................................................................................................... iv
LIST OF SYMBOLS ........................................................................................................ vi
ACRONYMS AND DEFINITIONS ............................................................................... vii
ACKNOWLEDGMENT ................................................................................................ viii
ABSTRACT ..................................................................................................................... ix
1. Introduction.................................................................................................................. 1
1.1
Background ........................................................................................................ 1
1.2
Problem Description........................................................................................... 3
2. Theory and Methodology ............................................................................................ 5
2.1
Theoretical Background ..................................................................................... 5
2.2
Numerical Analysis - Modeling ......................................................................... 6
2.2.1
Parts and Part Geometry......................................................................... 7
2.2.2
Property Definition................................................................................. 8
2.2.3
Step Definition, Boundary Conditions, and Applied Loads ................ 12
2.2.4
Mesh ..................................................................................................... 22
3. Results and Discussion .............................................................................................. 24
3.1
Baseline Model Results .................................................................................... 24
3.2
Cyclic Load Results ......................................................................................... 28
3.2.1
Load Case Comparison ........................................................................ 28
3.2.2
Weight Comparison ............................................................................. 30
4. Conclusions................................................................................................................ 32
5. References.................................................................................................................. 33
ii
LIST OF TABLES
Table 2.1 Input Data for Material Property of Strain Dependent Cartilage and Labrum .. 9
Table 2.2 Data Used for Development of Polynomial Functions for Walking, Jogging
and Sprinting Loads ......................................................................................................... 15
Table 2.3 ABAQUS input data developed from Polynomial Functions for Walking,
Jogging and Sprinting (150 LB Bodyweight) .................................................................. 17
Table 2.4 Varying Weights Represented as Contact Forces for ABAQUS Input
Amplitudes....................................................................................................................... 20
Table 3.1 Tabular Results for Pore Pressure, Strain and Normal Contact Force for
Differing Load Cases ....................................................................................................... 29
Table 3.2 Tabular Results for Pore Pressure, Strain and Normal Contact Force for
Differing Weights ............................................................................................................ 30
iii
LIST OF FIGURES
Figure 1.1 (A) Diagram of the acetabular labrum (B) View of the labral attachment
points [2] ............................................................................................................................ 2
Figure 2.1 Structure of articular cartilage with representation of proteoglycans, collagen
and water concentration varying with depth [8] ................................................................ 6
Figure 2.2 Axisymmetric finite element geometry representation of the cartilage on the
femoral head (top) and the cartilage with intact labrum (bottom) which is attached to the
subchondral bone of the acetabulum. ................................................................................ 8
Figure 2.3 Material orientation assignment for the in-plane and out-of-plane material
properties in the labrum ................................................................................................... 12
Figure 2.4 ABAQUS screenshot of the interaction module (top-row) detailing the rigid
surfaces and the contact interaction surfaces. The load module is also shown detailing
the areas where pore pressure = 0 boundary condition is employed and necessary
boundary conditions for axisymmetry are shown (bottom-row) ..................................... 13
Figure 2.5 Initial contact step with applied displacement ............................................... 14
Figure 2.6 Walking, Jogging, and Sprinting Polynomial Functions as Percentage of Body
Weight.............................................................................................................................. 17
Figure 2.7 Cyclic Load Representation for 150 LB Conditions of Walking, Jogging, and
Sprinting .......................................................................................................................... 19
Figure 2.8 Graphical Representation of Varying Weights for ABAQUS Amplitude Input
......................................................................................................................................... 22
Figure 2.9 Mesh of CAX4P elements for both the intact labrum (top) and resected
labrum (bottom) ............................................................................................................... 23
Figure 3.1 Fluid velocity vectors for an intact labrum (top) and resected labrum (bottom)
for a 200 lb force being helf for 100 seconds .................................................................. 25
Figure 3.2 Normal contact force represented as vectors at each element for an intact
labrum (top) and resected labrum (bottom) at 1 second of full load application for a 200
lb load. ............................................................................................................................. 26
Figure 3.3 In-Plane strain for an intact labrum (left) and resected labrum (right) at 1
second of full load application for a 200 lb load. ............................................................ 27
iv
v
LIST OF SYMBOLS
Symbol/Variable
n
Description
Volume fraction of the voids to total volume
Units
-
Vvoids
Total volume of the voids
in3
Vtotal
Total volume of the solid matrix
in3
e0
Void ratio as defined by ABAQUS at t=0
-
λ
Lame’s first constant for the solid matrix
psi
μ
Lame’s second constant for the solid matrix
psi
𝜎𝑖𝑒
Principal elastic stressed for hyperelastic model
psi
𝜆𝑖
Principal stretch ratios for hyperelastic model
-
U
Strain energy density function
-
𝛼𝑖
Material parameter for hyperelastic model
𝛽
Material parameter for hyperelastic model
k0
Permeability at t=0
in/s
Strain dependent permeability
in/s
k(e)
M
Material constant for strain dependence
-
κ
Material constant for strain dependence
-
Ep
In-plane modulus of labrum
psi
Et
Transverse modulus of labrum
psi
νp
In-plane poisson’s ratio of labrum
νpt
νtp
Poisson’s ratio (labrum) for strain transverse
resulting from stretch normal to it
Poisson’s ratio (labrum) for strain in plane
resulting from stretch normal to it
-
-
Gp
Shear modulus, in-plane of labrum
psi
Gt
Shear modulus, transverse of labrum
psi
vi
Equation
Used
ACRONYMS AND DEFINITIONS
vii
ACKNOWLEDGMENT
Type the text of your acknowledgment here.
viii
ABSTRACT
The labrum of the femoro-acetabular provides an effective seal for the
articulating cartilage surfaces on the head of the femur and in the acetabulum. With an
increase in surgical techniques, removal of the labrum, or excision has been used to
alleviate pain in patients subjected to labrum tears. The lack of labrum providing an
adequate seal for the cartilage in the joint may lead to increased cartilage consolidation
during loading and accelerated wear, creating more pain for the patient. The commercial
finite element program, ABAQUS, was used to quantify the increase in the contact force
between the articulating surfaces in the joint subjected to increasingly strenuous
activities as well as changes in bodyweight. The results showed the normal contact force
may increase up to 200% due to lack of a functional labrum, implying a substantial risk
for an increase in wear rates of the cartilage. The results similarly showed increases in
contact forces due to greater body weight and more strenuous activity, such as jogging
when
compared
with
walking
in
ix
the
absence
of
a
labrum.
1. Introduction
1.1 Background
In recent years, the management of hip and groin injuries has broadened
significantly due to advancements in arthroscopic procedures. Minimally invasive
surgical techniques allow a relatively fast recovery for athletes in highly competitive
environments or a return to normal activity without pain. The advancements in magnetic
resonance imaging (MRI) help explain the source of pain stemming from damage or
deformities interior to the femoro-acetabular joint. A major result of advanced imaging
techniques was the evaluation of acetabular labral tears. Once left untreated, the
acetabular labrum became a main focus for research due to a lack of understanding in
regard to its function.
The labrum in the human femoro-acetabular joint, located in the capsule of the
hip, is attached to the circumference of the acetabular perimeter. As shown in Figure 1,
the transverse acetabular ligament is connected to the labrum both anteriorly and
posteriorly. The labrum is thinner in the anterior inferior section and thicker, with a
slight roundness in appearance, in the posterior section. Free nerve endings have been
identified within labral tissue, which potentially explains the pain pathway in a patient
with a labral tear [1].
1
Figure 1.1 (A) Diagram of the acetabular labrum (B) View of the labral attachment points [2]
In an attempt to fully understand the pathology and study the range of surgical
techniques to remove pain associated with acetabular labrum tears, experiments and
finite element modeling have been used to explain the labrum’s function as a part of the
femoro-acetabular joint. The results demonstrate various functions of the joint, one of
the most important shown by Ferguson et al. through a finite element model is the
labrum’s function as a seal for escaping fluid under normal loading between the articular
cartilage on the femoral head and acetabulum [3], [4]. The labrum effectively prevents
fluid from escaping the joint in order to retain a thin fluid film between the articulating
surfaces allowing lubrication and transfer of the load via fluid pressure, which prevents
premature wear of the cartilage surfaces by reducing cartilage consolidation. The authors
attempted to replicate the findings of the model using an in vitro experiment, with
similar results[5]. Song et al. used experimental results on cadaveric hips to show the
friction increase from partial removal or complete removal of the acetabular labrum,
further validating the hypothesized sealing function [6].
Using magnetic resonance imaging (MRI) techniques, a patient can be diagnosed
with an acetabular labral tear and may choose to undergo surgery. In the event that the
labrum cannot be fully repaired, excision, otherwise known as debridement, which is a
2
complete or partial removal of the torn area, is implemented to relieve the pain. The
surgery may also uncover a significant amount of work or damaged articular cartilage
and may require micro-fracturing to elicit growth of new cartilage. As previously proven
by Ferguson et al., if the labrum is no longer functioning as a seal to the joint fluid,
cartilage consolidation will greatly increase. Continued rotation of the femoral head
within the joint during walking or exercising will wear away cartilage due to the
increased friction and lack of fluid to develop hydrostatic pressure to carry the load.
Therefore, a surgical technique used to re-grow cartilage may provide short-term pain
relief but the long term effects of a debrided or damaged labrum will be problematic.
1.2 Problem Description
The function of the acetabular labrum as a seal for the femoro-acetabular joint
has been widely established through finite element modeling and in vitro
experimentation. This knowledge allows refinement of surgical techniques and physical
therapy programs for patients presenting with hip pain. If a patient requires excision of
the labrum to relieve immediate pain, the long term effects on cartilage consolidation
must be considered.
A well known principle in tribology is an increase in the normal force on a
material will lead to increased frictional forces and therefore expedite wear on the
surface of the material. This project will seek to utilize the ability of finite element
software to model a material as poroelastic, in this case the biphasic (liquid and solid)
configuration of cartilage, and how exposure to different loading conditions affect the
strains and stresses in the solid matrix. The loading conditions in this case would be
normal forces into the femoro-acetabular joint from daily activities such as walking and
3
even more strenuous conditions including jogging. The intent is to determine if there is
regimen a patient can follow after being diagnosed with a torn labrum which will limit
the wear in articular cartilage and subsequent pain.
4
2. Theory and Methodology
2.1 Theoretical Background
A porous medium can be modelled in a commercial finite element code in which
the medium is considered a biphasic material and adheres to the effective stress principle
in order to describe its behavior. The porous medium is considered to consist of a solid
matrix and voids that can contain liquid. The constitutive behavior of the material is
governed by the response of the liquid and solid mater to local pressure, or fluid flow,
and the response of the solid matrix to effective stress. The analysis considers the total
stress acting at a point to be made up of an average pressure stress and an effective
stress, or the solid matrix stress [7].
The importance of a commercial code being able to model porous medium is critical
in analyzing geological systems such as soil containing ground water and the effect of
forces on that system. For this project, the ability to model porous media is also critical
when considering biological systems, such as articular cartilage.
Articular cartilage can be described as a soft, porous, composite material made up of
collagen, proteoglycans, and water. Visually, articular cartilage is white with a smooth,
shiny surface. The collagen and proteoglycans in the cartilage are intertwined to create a
solid matrix of material. Typically, the volume of cartilage is made up of 80% water [8].
Cartilage is found in articulating areas, such as joints, in the body. The percent
compositions of the materials which make up cartilage vary with the depth of the
cartilage, as shown in the figure below. At the surface of the cartilage, the collagen
fibers are oriented parallel to the surface, in the middle zone the orientation begins to
become more angled while in the deep zone the collagen fibers begin to orient
themselves perpendicular to the bone interface in order to properly anchor into the bone
[8].
5
Figure 2.1 Structure of articular cartilage with representation of proteoglycans, collagen and water
concentration varying with depth [8]
Due to the biphasic make up of articular cartilage, the intrinsic mechanical
properties of each phase, liquid and solid matrix, as well as the interaction between the
phases corresponds to the interesting mechanical properties of the cartilage as a whole.
Mow et al. was able to apply a linear nonhomogenous theory to accurately represent test
data for an aggregate elastic modulus and permeability of the tissue [9]. Adaptations of
these findings are used in conjunction with a commercial finite element code in order to
run complex analyses to represent joints in the human body.
2.2 Numerical Analysis - Modeling
The biphasic cartilage model detailed by Mow et al. demonstrated the
mechanical properties of articular cartilage through an analytical solution [9]. In order to
adequately analyze the joint contact mechanics within the irregular geometry of a human
joint, an appropriate finite element code is required. J.Z. Wu, W. Herzog, and M. Epstein
demonstrated the biphasic cartilage model can be implemented in the finite element code
ABAQUS. The results achieved in ABAQUS were comparable to analytical solutions as
well as other finite element codes for three numerical tests: an unconfined indentation
test, a test with the contact of a spherical cartilage surface with a rigid plate, and an axisymmetric joint contact test [10].
Since ABAQUS has previously demonstrated a capacity to analyze the biphasic
cartilage model proposed by Mow et al and contact mechanics, it will be used herein.
6
2.2.1
Parts and Part Geometry
In the ABAQUS part module, two 2D axisymmetric parts were created to
represent the joint. The parts represent the articulating cartilage surfaces in the hip with
an intact labrum and on the head of the femur, as shown in Figure 2. A second model
was built in which the labrum was removed to represent a resected labrum. The radius of
the femur was set as 1.02 in. and the bone was modelled as rigid and impermeable. The
articulating cartilage surfaces were modelled to have a thickness of 0.11 in. The joint
was modelled as being fully congruent and the labrum was modeled as being in
continuity with the articular cartilage [3].
7
Figure 2.2 Axisymmetric finite element geometry representation of the cartilage on the femoral head
(top) and the cartilage with intact labrum (bottom) which is attached to the subchondral bone of the
acetabulum.
2.2.2
Property Definition
The property module in ABAQUS allows the definition of material properties
and orientations. Two materials were created for representing each the cartilage, on both
the femur and acetabulum, and the labrum.
8
For the cartilage, a hyperporoelastic material model is used due to the porosity of
the material allowing very large volumetric changes. The hyperelastic constitutive
relation is based on the following:
𝜎𝑖𝑒 =
𝑁
𝑈= ∑
𝑖=1
𝜕𝑈
𝜕𝜆𝑖
𝑖 = 1,2,3
2𝜇𝑖 𝛼𝑖
1
𝛼𝑖
𝛼𝑖
−𝛼𝑖 𝛽
− 1)]
2 [𝜆1 + 𝜆2 + 𝜆3 − 3 + 𝛽 ((𝐽)
𝛼𝑖
Where 𝜎𝑖𝑒 and 𝜆𝑖 (i=1,2,3) are the principal elastic stresses and the principal stretch
ratios respectively; U is the strain energy function; J = 𝜆1 𝜆2 𝜆3 is the volume ratio; 𝛼𝑖 , 𝜇𝑖
(i=1…N), and β are material parameters [11]. The material parameters 𝛼𝑖 are determined
from equations 𝜆 = 4𝛼0 𝛼2 , 𝜇 = 2(𝛼1 + 𝛼2 )𝛼0, and 𝛽 = 𝛼1 + 2𝛼2 in which 𝜆=1.89 psi,
𝜇=49.2 psi, and 𝛽=0.761 [12].
ABAQUS represents the volume fraction as a void ratio (e), resulting in an initial
void ratio for the cartilage of 4 based on the following:
𝑛=
𝑉𝑣𝑜𝑖𝑑𝑠
𝑉𝑡𝑜𝑡𝑎𝑙
𝑛
𝑒0 = (1−𝑛)
where e0 for cartilage is 4. The specific weight of the pore fluid is γ=0.0361008 lb/in3.
The permeability is dependent on the strain which can be related to the void ratio
and is based on the following:
𝑒 𝜅
𝑀
1+𝑒 2
𝑘(𝑒) = 𝑘0 (𝑒 ) exp { 2 [(1+𝑒 ) − 1]}
0
0
where k0=2.89355E-009 in/s, e is the void ratio, and e0 is the void ratio of the
undeformed state, as defined above. M and κ are material constants which have been
determined for cartilage to be 4.638 and 0.0848, respectively. A tabular form imported
into the ABAQUS material property definition was used to define the strain dependent
permeability over a void ratio range of 1.7 to 5 and is shown below in Table 2.1 [12].
Table 2.1 Input Data for Material Property of Strain Dependent Cartilage and Labrum
Strain Dependent Cartilage
Strain Dependent Labrum
9
Permeability (in/s)
5.20556E-10
5.50465E-10
5.8302E-10
6.18501E-10
6.57221E-10
6.99527E-10
7.45808E-10
7.96499E-10
8.5209E-10
9.13129E-10
9.80235E-10
1.0541E-09
1.13552E-09
1.22538E-09
1.32467E-09
1.43454E-09
1.55629E-09
1.69136E-09
1.84144E-09
2.00842E-09
2.19447E-09
2.40205E-09
2.634E-09
2.89355E-09
3.1844E-09
3.51082E-09
3.87771E-09
4.29069E-09
4.75626E-09
5.28191E-09
5.87632E-09
6.54951E-09
7.3131E-09
8.1806E-09
Void Ratio
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
Permeability (in/s)
1.30046E-10
1.41521E-10
1.54416E-10
1.68935E-10
1.85316E-10
2.03836E-10
2.24819E-10
2.48642E-10
2.75747E-10
3.06652E-10
3.41968E-10
3.82415E-10
4.2884E-10
4.82248E-10
5.43831E-10
6.15004E-10
6.97453E-10
7.9319E-10
9.0462E-10
1.03463E-09
1.18668E-09
1.36494E-09
1.57444E-09
1.82127E-09
2.11281E-09
2.458E-09
2.86774E-09
3.35536E-09
3.93711E-09
4.63293E-09
5.46735E-09
6.47052E-09
7.67971E-09
9.14101E-09
Void ratio
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
The permeability of the labrum was set at one-sixth of articular cartilage which is
comparable to experimental results found by Ferguson. The strain-dependence of labrum
permeability is not well defined and since the transverse properties of the cartilage
10
compared with the labrum are of the same order, the strain-depenent permeability was
adapted from the material constants of cartilage. However, an initial void ratio for the
labrum was defined as 3, in lieu of 4 for cartilage [12].
The labrum is modelled as a transversely isotropic permeable elastic material in
which the circumferential direction is out-of-plane considering the labrums unique
pathology in which fibrils run in the circumferential direction, resulting in a greater
stiffness. ABAQUS relates the stresses to the strains in each direction by the following
tensor:
where p and t stand for “in-plane” and “transverse” or out-of-plane, respectively [7].
In the case of poisson ratio νtp characterizes the strain in the plane of isotropy
resulting from stress normal to it, while νpt characterizes the transverse strain in the
direction normal to the plane resulting from stress in the plane. These quantities are
related by the following:
𝜈𝑡𝑝
𝜈
⁄𝐸 = 𝑝𝑡⁄𝐸
𝑡
𝑝
For the labrum, the specific engineering constants were defined as E p=80 psi,
Et=29000 psi, νp=0.05, νtp=0.05, νpt=0.0001, and Gt=3.77 psi [12].The shear modulus inplane, Gp, is defined by:
𝐸𝑝
𝐺𝑝 = 2(1+𝜈
𝑝)
where Gp=38 psi.
When engineering constants are used, a specific material orientation must be
defined. The transverse isotropy defined for the labrum material is then assigned with
the orientation shown below, noting the 1 and 2 directions are in-plane while the 3rd
direction, representing the circumferential oriented fibers in the labrum, is out-of-plane:
11
Figure 2.3 Material orientation assignment for the in-plane and out-of-plane material properties in
the labrum
2.2.3
Step Definition, Boundary Conditions, and Applied Loads
Since the articulating cartilage and labrum are modelled as poroelastic materials, a
coupled pore fluid diffusion and stress analysis was employed and a *SOILS step is
required. The opposing faces of cartilage are defined as contact surfaces, including the
labrum surface in the applicable model. Defining contact will allow pore fluid to flow
between the surfaces which come into contact. The degree of freedom for pore fluid flow
is 0 across surfaces as the default in ABAQUS. Since this is the case, any free surface
will employ a boundary condition which sets the pressure at this surface to zero.
Through the analysis, fluid will enter or leave this surface to maintain this boundary
condition. As previously stated, the surfaces in which the cartilage and labrum attach to
bone are made rigid and impermeable. This assumption is reasonable since the material
properties of bone are many magnitudes different compared with cartilage. The rigid
surfaces are tied to reference points on axis of symmetry. All loads and boundary
conditions are applied to these reference points since ABAQUS will define all degrees of
freedom for nodes on the rigid body by the reference node. In addition, axisymmetric
12
boundary conditions are applied along the axis of symmetry to prevent movement and
rotation.
Figure 2.4 ABAQUS screenshot of the interaction module (top-row) detailing the rigid surfaces and
the contact interaction surfaces. The load module is also shown detailing the areas where pore
pressure = 0 boundary condition is employed and necessary boundary conditions for axisymmetry
are shown (bottom-row)
2.2.3.1 Initial Contact Step
The first step of the analysis is used to ensure good contact between the faces due to
any differences in geometry. A small displacement of 0.002” is used on the reference
point (RP) of the femur. This boundary condition will be active in this step and then
13
removed in all subsequent steps for load application. A separate boundary condition is
applied and propagated to all subsequent steps to prevent left-right movement of the RP.
A simply supported boundary condition (U1=U2=0) is applied to the RP of the
acetabulum to prevent rigid body motion. For this step, a time period of 1s is used and
the steady-state consolidation assumption is used since the transient affects of fluid flow
are not required at this point.
Figure 2.5 Initial contact step with applied displacement
14
2.2.3.2 Load Application Step
Once initial contact has been established, the necessary loads can be applied. All
loads were derived from the Fz direction detailed in [13] for the walking load case. Data
points were developed from the hip contact force, as a % of bodyweight, over a
normalized time scale (Table 2.2). A conservative estimate of cycle time for the gait
cycle at a moderate walking pace was taken to be 1s. The data points were fit to a 6th
order polynomial which will be used to develop the tabular input to be used in ABAQUS
as an amplitude function (Figure 2.5). To develop load conditions for jogging and
sprinting, the walking loads were amplified by 150% BW and 200% BW, respectively.
The time scale was also modified from 1s to 0.8s for a jogging cycle and 1s to 0.55s for
a sprinting cycle. Each cycle is taken to be from initial heel contact to the next increment
of heel contact on the same leg.
Table 2.2 Data Used for Development of Polynomial Functions for Walking, Jogging and Sprinting
Loads
Gait Time
(Sprinting)
0
0.022
0.0275
0.0385
0.0495
0.055
0.0605
0.066
0.0715
0.07425
0.077
0.0825
0.088
0.0935
0.099
0.1045
0.11
0.1155
0.132
Force % BW
Walking
75
140
150
170
195
200
205
211
213
215
216
217
219
220
220
221
222
221
219
Force % BW
Jogging
75
210
225
255
292.5
300
307.5
316.5
319.5
322.5
324
325.5
328.5
330
330
331.5
333
331.5
328.5
15
Force % BW
Sprinting
75
280
300
340
390
400
410
422
426
430
432
434
438
440
440
442
444
442
438
0.143
0.1485
0.154
0.1595
0.165
0.1705
0.198
0.209
0.22
0.231
0.2365
0.242
0.2475
0.253
0.264
0.286
0.308
0.33
0.341
0.4675
0.55
218
217
215
213
210
208
204
204
204
205
205
203
199
196
189
172
156
120
100
30
75
327
325.5
322.5
319.5
315
312
306
306
306
307.5
307.5
304.5
298.5
294
283.5
258
234
180
150
45
75
16
436
434
430
426
420
416
408
408
408
410
410
406
398
392
378
344
312
240
200
60
75
Combined % BW Loading With Trendlines
Walking % BW
500
450
Jogging % BW
% Load (Magnitude)
400
350
Sprinting % BW
300
250
Poly. (Walking % BW)
y = -27962x6 + 87465x5 - 103145x4 + 58370x3
- 17298x2 + 2580x + 66.19
R² = 0.9898
Poly. (Jogging % BW)
200
150
100
y = -204262x6 + 505163x5 - 473217x4 +
213052x3 - 49737x2 + 5749.6x + 68.754
R² = 0.9943
Poly.
(Sprinting
% BW) 4
6
5
50
0
0
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
Time (seconds)
1
y = -2,858,684.55x + 4,840,189.92x - 3,109,233.71x +
960,451.21x3 - 153,272.39x2 + 12,035.17x + 71.32
R² = 1.00
Figure 2.6 Walking, Jogging, and Sprinting Polynomial Functions as Percentage of Body Weight
The polynomial functions developed for the three load cases are based on %BW
(percentage of bodyweight) they are appropriately scaled to represent the bodyweight of
a 150 lb human. A model was created for all three cases, one set of each for the resected
and intact labrum, totaling six models in all. The tabular data developed from the scaled
polynomial functions (Table 2.3) was input into ABAQUS as an amplitude function and
applied at the Femur RP. Each load case was applied over five cycles (Figure 2.6). These
inputs represent a consolidated system of various load conditions which can be imparted
on the hip during daily activity or physical exertion.
Table 2.3 ABAQUS input data developed from Polynomial Functions for Walking, Jogging and
Sprinting (150 LB Bodyweight)
Gait Time
(Walking)
0
Force 150
LB
Bodyweight
Walking
75
Gait
Time
(Jogging)
0
Force 150
LB
Bodyweight
Jogging
75
17
Gait Time
(Sprinting)
Force 150 LB
Bodyweight
Sprinting
0
75
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
475.382502
487.563288
472.934088
401.788152
239.23725
82.394712
76.955508
113.173368
475.382502
487.563288
472.934088
401.788152
239.23725
82.394712
76.955508
113.173368
475.382502
487.563288
472.934088
401.788152
239.23725
82.394712
76.955508
113.173368
475.382502
487.563288
472.934088
401.788152
239.23725
82.394712
76.955508
113.173368
475.382502
487.563288
472.934088
401.788152
239.23725
82.394712
76.955508
113.173368
18
0.025
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0.55
0.6
0.65
0.7
0.75
0.8
0.85
0.9
0.95
1
1.05
1.1
1.15
1.2
1.25
1.3
1.35
1.4
1.45
1.5
1.55
1.6
1.65
1.7
1.75
1.8
1.85
1.9
1.95
2
2.05
435.355608
655.7532681
645.6154286
633.2655763
586.4965276
468.603782
293.5648472
132.9782621
74.7623191
133.6134844
113.2245169
435.355608
655.7532681
645.6154286
633.2655763
586.4965276
468.603782
293.5648472
132.9782621
74.7623191
133.6134844
113.2245169
435.355608
655.7532681
645.6154286
633.2655763
586.4965276
468.603782
293.5648472
132.9782621
74.7623191
133.6134844
113.2245169
435.355608
655.7532681
645.6154286
633.2655763
586.4965276
468.603782
293.5648472
132.9782621
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
2.1
2.15
2.2
2.25
2.3
2.35
2.4
2.45
2.5
2.55
2.6
2.65
2.7
2.75
74.7623191
133.6134844
113.2245169
435.355608
655.7532681
645.6154286
633.2655763
586.4965276
468.603782
293.5648472
132.9782621
74.7623191
133.6134844
113.2245169
Combined Load Conditions (150 LB)
700
600
% Load (Magnitude)
500
400
Sprinting
150 Lb
300
Walking
150 Lb
200
Jogging
150 LB
100
0
0
1
2
3
Time (seconds)
4
5
6
Figure 2.7 Cyclic Load Representation for 150 LB Conditions of Walking, Jogging, and Sprinting
As a comparison, walking loading conditions were developed for a 200 lb and
250 lb human (Table 2.4). This requires creating two models each for an intact and
19
resected labrum and providing the necessary inputs as an amplitude function. Similar to
the varying load conditions for walking, jogging and running, these loads are applied
over 5 cycles and in this case is a 5s total step time.
These conditions will serve to represent the affect on weight for intact and
resected labrums. Inherently an increase in weight is an increase in contact force since
the formulation used is based on %BW.
Table 2.4 Varying Weights Represented as Contact Forces for ABAQUS Input Amplitudes
Gait Time
(Walking)
Force 150
LB
Bodyweight
Walking
Force 200
LB
Bodyweight
Walking
Force 250 LB
Bodyweight
Walking
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
1.2
1.3
1.4
1.5
1.6
1.7
1.8
1.9
2
2.1
2.2
2.3
2.4
2.5
2.6
99.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
132.38
400.224376
436.794464
432.082304
413.574496
355.505
247.842656
125.013424
54.357344
84.320216
152.38
400.224376
436.794464
432.082304
413.574496
355.505
247.842656
125.013424
54.357344
84.320216
152.38
400.224376
436.794464
432.082304
413.574496
355.505
247.842656
165.475
500.28047
545.99308
540.10288
516.96812
444.38125
309.80332
156.26678
67.94668
105.40027
190.475
500.28047
545.99308
540.10288
516.96812
444.38125
309.80332
156.26678
67.94668
105.40027
190.475
500.28047
545.99308
540.10288
516.96812
444.38125
309.80332
20
2.7
2.8
2.9
3
3.1
3.2
3.3
3.4
3.5
3.6
3.7
3.8
3.9
4
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
5
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
300.168282
327.595848
324.061728
310.180872
266.62875
185.881992
93.760068
40.768008
63.240162
114.285
125.013424
54.357344
84.320216
152.38
400.224376
436.794464
432.082304
413.574496
355.505
247.842656
125.013424
54.357344
84.320216
152.38
400.224376
436.794464
432.082304
413.574496
355.505
247.842656
125.013424
54.357344
84.320216
152.38
21
156.26678
67.94668
105.40027
190.475
500.28047
545.99308
540.10288
516.96812
444.38125
309.80332
156.26678
67.94668
105.40027
190.475
500.28047
545.99308
540.10288
516.96812
444.38125
309.80332
156.26678
67.94668
105.40027
190.475
Combined Weights for Walking
600
500
Load (Lbs)
400
200 Lb Human
150 Lb Human
300
250 Lb Human
200
100
0
0
0.1
0.2
0.3
0.4
0.5 0.6
Time (s)
0.7
0.8
0.9
1
Figure 2.8 Graphical Representation of Varying Weights for ABAQUS Amplitude Input
2.2.4
Mesh
Figure 2.5 details the mesh refinement required for an accurate result. A mesh
convergence study was performed resulting in the mesh density used. CAX4P, 4-noded
axisymmetric quadrilateral, bilinear displacement, bilinear pore pressure elements were
used to handle the effective stress of coupled pore pressure diffusion and stress analysis.
4-noded elements were used in lieu of 8-noded since the 4-noded elements behave better
in contact. This resulted in a much denser mesh due to half the number of nodes used for
each element.
22
Figure 2.9 Mesh of CAX4P elements for both the intact labrum (top) and resected labrum (bottom)
23
3. Results and Discussion
3.1 Baseline Model Results
As a baseline, to ensure the properties and boundary conditions were reasonable, a
200 lb load was applied over 1 second and then held for 1000 seconds. Specifically, the
fluid velocities represented as vector quantities at each node, the normal contact force
between the articulating cartilage surfaces, and the in-plane strains were evaluated for an
intact and resected labrum.
The baseline model showed expected results for fluid velocities and normal contact
forces; however it did present an unexpected result for strain. Numerical results are not
tabulated for these results since the intent was to show representative strain, force, and
fluid velocity results for an arbitrary load. The results are only for a comparison of visual
representations of requested field variables.
For the fluid velocity, the field variable was taken at 100s into the 1000s step. The
fluid velocity vectors, as shown in Figure 3.1, for an intact labrum show the labrum
effectively “choking” the fluid as it is forced from the articulating cartilage surface. The
velocity significantly decreases at the interface and dissipates as the fluid continues into
the cross section. There is a significant increase in the fluid velocity vectors on the
periphery of the labrum over a very short length. Compared with the resected labrum,
the fluid is escaping over a much larger area, which is congruent with the boundary
conditions set for the free surface.
24
Figure 3.1 Fluid velocity vectors for an intact labrum (top) and resected labrum (bottom) for a 200
lb force being helf for 100 seconds
The normal contact force field variable was evaluated after the 1 second ramp load
was applied, as shown in Figure 3.2, to obtain the maximum contact force before the
cartilage began to consolidate as the fluid began to redistribute itself. As expected, the
labrum adds a significant amount of contact area to the articulating cartilage surface of
the femur. This allows the force to be more evenly distributed over the femoral head
25
cartilage, resulting in a relatively smaller contact force. Since the model with the
resected labrum has a diminished contact area, the contact force showed a higher peak
force and a distribution which shifted the force towards the centerline of the joint.
Figure 3.2 Normal contact force represented as vectors at each element for an intact labrum (top)
and resected labrum (bottom) at 1 second of full load application for a 200 lb load.
Similar to the normal contact force field variable, the in-plain strain was evaluated
after 1 second, which is the maximum value prior to cartilage consolidation. The results
26
showed a higher strain in the femoral and acetabular cartilage in the resected labrum
model compared with the intact labrum as expected, however the area of highest strain
contour was of particular interest. As shown in figure 3.3, the areas of highest strain
were at the cartilage to bone interface, not at the articulating surface. The lack of strain
at the cartilage surface does not explain how patients will present with degraded and
worn cartilage in the acetabulum cartilage. The significance in this case is even with the
baseline model it shows the normal contact force will be the driving component when
evaluating cartilage wear.
Figure 3.3 In-Plane strain for an intact labrum (left) and resected labrum (right) at 1 second of full
load application for a 200 lb load.
27
3.2 Cyclic Load Results
For comparison of the results, the field variables of pore pressure (POR), maximum
strain (LE Max Principal), and normal contact force (CNORM) are extracted from the
steps at the peak of each load cycle. The results are broken into two separate sections for
comparison in order to correlate between the differing load cases of walking, running
and sprinting as well as the effect of the increase in weight on the extracted field
variables from the analyses.
3.2.1
Load Case Comparison
As shown in table 3.1, the pore pressure, strain, and normal contact force are reported
at the peak load application in each model.
The pore pressure is shown in order to demonstrate the lack of transient effects from
the loading and unloading in the joint. The pressure is fairly constant at the peak of each
load cycle, dictating the load carried by pore pressure does not change through the
cycles. Also, the pore pressure is much higher in models with a resected labrum but the
pore pressure maximum occurs at the centerline of the joint dictating the freely draining
surfaces do not expunge enough fluid to lower the pore pressure at the joint centerline.
Since the intact labrum, although providing a reasonable seal in the baseline model,
represents an area in which the fluid may redistribute itself into causing pressures on the
order of magnitude of 20% smaller between the model with the resected labrum and
intact labrum.
The maximum strain, as previously shown in the baseline model, occurs at the bone
interface which does not explain degradation of cartilage on the articulating surfaces.
Since this is the case, the maximum strain is reported in the table just as informational to
show the loss of a labrum will also increase the maximum strain gradient which may
eventually propagate to the articulating surface which increasing loads.
Of particular interest, based on results from the baseline model, is the contact force.
The contact force, between the intact labrum model and resected labrum model, shows
an average percent increase of 160%, 170%, and 155% for walking, jogging and
sprinting.
28
Table 3.1 Tabular Results for Pore Pressure, Strain and Normal Contact Force for Differing Load
Cases
150 Lbs
Walking
Intact Labrum
Step Time
(s)
0.2
1.2
2.2
3.2
Pore Pressure
(psi)
149.7
149.2
148.3
147.0
LE Max.
Principal
0.092
0.091
0.091
0.090
Contact
Force (Lbs)
0.276
0.277
0.276
0.274
150 Lbs
Walking
Resected
Labrum
4.2
0.2
1.2
2.2
3.2
146.8
173.6
175.3
172.8
172.0
0.090
0.127
0.128
0.128
0.127
0.274
0.756
0.709
0.709
0.707
150 Lbs
Jogging
Intact Labrum
4.2
0.2
1.0
1.8
2.6
170.9
222.4
220.9
220.0
220.0
0.126
0.136
0.135
0.135
0.135
0.705
0.359
0.359
0.358
0.358
150 Lbs
Jogging
Resected
Labrum
3.4
0.2
1.0
1.8
2.6
218.9
257.6
257.6
288.3
254.7
0.134
0.189
0.189
0.188
0.186
0.358
0.974
0.976
0.971
0.967
150 Lbs
Sprinting
Intact Labrum
3.4
0.1
0.65
1.2
1.75
253.6
296.0
296.6
293.9
293.9
0.187
0.181
0.181
0.180
0.180
0.966
0.446
0.447
0.445
0.446
150 Lbs
Sprinting
Resected
Labrum
2.3
0.1
0.65
1.2
1.75
293.5
344.2
347.3
345.7
346.1
0.180
0.471
0.471
0.471
0.471
0.446
1.135
1.132
1.143
1.145
2.3
345.7
0.470
1.145
Load Case
29
3.2.2
Weight Comparison
Similar to the comparison for load cases, the increase in weight has a significant
impact on the normal contact force in the joint. The contact force, between the intact
labrum model and resected labrum model, shows an average percent increase of 160%,
220%, and 170% for the differing weights shown in table 3.2. Again, the pore pressure
and maximum strain are reported but are not of particular interest. For the weight
comparison, the pore pressure and maximum strain show equivalent traits to the
information provided in paragraph 3.2.1.
Table 3.2 Tabular Results for Pore Pressure, Strain and Normal Contact Force for Differing
Weights
Step Time
(s)
0.2
1.2
2.2
Pore Pressure
(psi)
149.7
149.2
148.3
LE Max.
Principal
0.092
0.091
0.091
CNORM
(Lbs)
0.276
0.277
0.276
3.2
147.0
0.090
0.274
4.2
0.2
1.2
2.2
3.2
146.8
173.6
175.3
172.8
172.0
0.090
0.127
0.128
0.128
0.127
0.274
0.756
0.709
0.709
0.707
4.2
0.2
1.2
2.2
170.9
198.8
197.3
197.1
0.126
0.122
0.121
0.121
0.705
0.334
0.333
0.333
3.2
195.7
0.120
0.333
200 Lbs
Walking
Resected
Labrum
4.2
0.2
1.2
2.2
3.2
195.8
228.7
228.3
227.3
227.6
0.120
0.311
0.311
0.310
0.311
0.333
0.978
1.083
1.063
1.056
250 Lbs
Walking
Intact Labrum
4.2
0.2
1.2
2.2
228.4
241.8
248.0
245.1
0.310
0.152
0.152
0.150
1.092
0.387
0.389
0.385
3.2
245.4
0.150
0.380
Load Case
150 Lbs
Walking
Intact Labrum
150 Lbs
Walking
Resected
Labrum
200 Lbs
Walking
Intact Labrum
30
250 Lbs
Walking
Resected
Labrum
4.2
0.2
1.2
2.2
3.2
244.8
284.4
283.9
283.6
283.0
0.150
0.390
0.390
0.390
0.389
0.380
1.093
1.031
1.017
1.015
4.2
282.6
0.389
1.011
31
4. Conclusions
Many findings can be made from this research. Specifically, the cyclic loads, although
repetitive in nature, do not influence the cartilage as much as the magnitude of the loads.
The most significant finding from the results of the research was the large increase of
normal contact forces between models with a labrum and without a labrum. The model
results suggest the presence of a labrum creates a much larger contact area for
distribution of loads, prevents the exudation of fluid, and allows the fluid an area to
redistribute to when under load. In the case of the model without the labrum, the solid
phase of the cartilage would be required to carry a great percentage of the load.
It is well established the friction force is proportional to the normal load and the
constant of proportionality which relates the two is the coefficient of friction. An
increase in contact force in the model with the resected labrum can be correlated to an
increase in resulting frictional forces. Although the model did not provide any rotational
motion, one can visualize the effect of rotation on the joint in the case of increasing
contact forces. The larger the frictional force would provide a greater force to shearing
of the articulating surfaces of the cartilage, resulting in pain through many cycles and
evolutions. The cartilage on the articulating surfaces would wear away at an accelerated
rate with increasing normal contact loads.
The results of the research, through the different loading conditions and weight
comparisons, show in the absence of a functional labrum or in the case of a labrum
which has been surgically removed that the normal contact forces increase with an
increase in weight and more strenuous activities. For patients, this would mean a strict
diet to maintain a reasonable weight and avoiding strenuous activities for long periods of
time may lend to limited pain later on in life.
32
5. References
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Labral Pathology,” Hip Arthrosc., vol. 15, no. 3, pp. 239–246, Jul. 2005.
[2] C. L. Lewis and S. A. Sahrmann, “Acetabular Labral Tears,” Phys. Ther., vol. 86,
no. 1, pp. 110–121, Jan. 2006.
[3] S. J. Ferguson, J. T. Bryant, R. Ganz, and K. Ito, “The acetabular labrum seal: a
poroelastic finite element model,” Clin. Biomech., vol. 15, no. 6, pp. 463–468, Jul.
2000.
[4] S. . Ferguson, J. . Bryant, R. Ganz, and K. Ito, “The influence of the acetabular
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Biomech., vol. 33, no. 8, pp. 953–960, Aug. 2000.
[5] S. J. Ferguson, J. T. Bryant, R. Ganz, and K. Ito, “An in vitro investigation of the
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178, Feb. 2003.
[6] Y. Song, H. Ito, L. Kourtis, M. R. Safran, D. R. Carter, and N. J. Giori, “Articular
cartilage friction increases in hip joints after the removal of acetabular labrum,” J.
Biomech., vol. 45, no. 3, pp. 524–530, Feb. 2012.
[7] “ABAQUS 6.11 Documentation.” .
[8] A. Neville, A. Morina, T. Liskiewicz, and Y. Yan, “Synovial joint lubrication —
does nature teach more effective engineering lubrication strategies?,” Proc. Inst.
Mech. Eng. Part C J. Mech. Eng. Sci., vol. 221, no. 10, pp. 1223–1230, Jan. 2007.
[9] V. C. Mow, S. C. Kuei, W. M. Lai, and C. G. Armstrong, “Biphasic Creep and
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