This document summarizes the design of attachments for a novel knee implant. It describes the design of three different peg shapes (circular, triangular, and square) to attach plates to the femur and tibia bones as part of a new knee prosthesis. Finite element analysis was performed using ABAQUS to simulate the performance of each peg design under loading conditions and over time. The results suggest that a triangular peg encourages higher bone formation compared to the other designs, as measured by strain energy density in the bone near the pegs.

1. Design of attachments for a novel
knee implant
This thesis is submitted in fulfilment of the requirements for the degree of
Master of Engineering in Engineering Science, The University of Auckland, 2015.
February 28, 2015

4. i
Abstract
Osteoarthritis is the most common form of arthritis. It is a long term disease leading to
degeneration of the knee joint and it causes stiffness, pain and swelling. The treatment
includes replacement of the damaged knee joint with an implant (Total Knee Replacement).
In a conventional knee replacement surgery, the damaged joints are replaced with materials
such as metal and plastic, allowing for the natural motion of the knee.
A new knee prosthesis has been designed recently and a prototype was built and tested under
some simple loading conditions. The prosthesis is made up of a “femur plate” and a “tibia
plate”, which are attached to either side of the femur and tibia. These plates are designed in
such a way that they wrap around the lateral and medial sides of the distal femur and
proximal tibia. The femur and tibia plates must be attached to the bone using fixators. The
design of such fixators and their performance is the central issue of investigation in this
project.
There are various factors which could lead to the failure of fixators. This project addresses
the issue of loosening of the fixators and the appropriate design of the fixators to prevent
them from loosening. Following Wolf’s Law, the strain energy density in the vicinity of the
fixators is used as a measure of strength of fixation. A higher strain energy density would
suggest formation of bone and osteointegration whereas a lower strain energy density would
indicate bone resorption and possible loosening.
Three dimensional computational models of different peg designs were created using the
SOLIDWORKS CAD software. The pegs used in this project were chosen to have three
different shapes: circular, triangular and square. They were inserted into a bone model and
imported into ABAQUS for computational Finite Element Analysis. The results of the
computer simulations were used to evaluate the performance of each design. A bone
remodelling process was simulated using Python scripting in conjunction with ABAQUS.
This enabled the evaluation of the performance of each design over a period of time. The
results suggest that a triangular peg encourages higher bone formation as compared to the
other designs.

5. ii
Acknowledgement
I would like to express my heartfelt thanks to my supervisor, Dr. Piaras Kelly for his
excellent academic support and guidance during the planning and execution stages of this
research, as well as providing me with an excellent atmosphere for carrying out my work. I
am really grateful for having such a caring mentor helping me at every stage of my research.
His remarks and suggestions helped in overall aspects of learning in the past one year. His
patience, enthusiasm and encouragement were a constant motivation throughout the course of
my research.
I would also like to thank Dr. Pranesh for his valuable inputs and sharing of his knowledge.
Thank you for your valuable feedback.
I am grateful to Mr. Xiaoming Wang for helping me understand the interaction between
Python and ABAQUS.
I would like to thank Mrs. Yuting Zhu for helping me in the experiments.
Finally I would like to thank my parents Mr. Jayasankar and Mrs. Sarala Jayasankar for their
unconditional love and support. I also want to thank brother Sandeep and my sister-in-law
Deepika for their constant encouragement in taking up this Master’s

6. iii

7. iv
Table of contents
LIST OF FIGURES .......................................................................................................VI
CHAPTER 1 ......................................................................................................................1
INTRODUCTION ............................................................................................................1
1.1 OBJECTIVE OF THIS RESEARCH......................................................................................................... 1
1.2 ANATOMY OF THE KNEE................................................................................................................. 1
1.3 TIBIA-FEMORAL JOINT ................................................................................................................... 2
1.4 PATELLA- FEMORAL JOINT .............................................................................................................. 3
1.5 ARTICULATING MOTIONS IN THE KNEE JOINT....................................................................................... 3
1.6 LIGAMENTS IN THE KNEE JOINT........................................................................................................ 4
1.6.1 Anterior cruciate ligament................................................................................................. 4
1.6.2 Posterior cruciate ligament ............................................................................................... 5
1.6.3 Medial collateral ligament ................................................................................................ 5
1.6.4 Lateral collateral ligament ................................................................................................ 5
1.7 BONE STRUCTURE AND REMODELLING............................................................................................... 5
1.8 BONE REMODELLING ALGORITHM .................................................................................................... 7
1.8.1 Pixel and Voxel Based Remodelling.................................................................................... 7
1.8.2 Apparent density remodelling ........................................................................................... 9
1.9 OSTEOARTHRITIS........................................................................................................................ 10
1.10 MATERIAL CHARACTERISTICS....................................................................................................... 12
1.11 ORTHOPAEDIC FIXATIONS........................................................................................................... 13
1.12 LOOSENING OF FIXATORS ........................................................................................................... 13
1.13 MEASURING PARAMETER IN THE PROJECT ...................................................................................... 14
1.14 CHAPTER SUMMARY ................................................................................................................. 16
CHAPTER 2 ................................................................................................................... 19
DESIGN OF PEGS ....................................................................................................... 19
2.1 NOVEL KNEE PROSTHESIS DESIGN................................................................................................... 19
2.2 CAD SOFTWARE (SOLIDWORKS).................................................................................................... 20
2.3 LOCATION AND POSITION OF FIXATION ............................................................................................ 21
2.4 CHAPTER SUMMARY ................................................................................................................... 23
CHAPTER 3..................................................................................................................... 25
FINITE ELEMENT ANALYSIS...................................................................................... 25
3.1 ABAQUS................................................................................................................................... 25
3.2 ANALYSIS OF TWO DIMENSIONAL MODEL......................................................................................... 26
3.2.1 Materials ........................................................................................................................ 27
3.2.2 Step ................................................................................................................................ 27
3.2.3 Boundary conditions........................................................................................................ 27
3.2.4 Contacts and interaction ................................................................................................. 27
3.2.5 Load................................................................................................................................ 28

8. v
3.2.6 Mesh............................................................................................................................... 28
3.3 RESULTS FROM THE TWO DIMENSIONAL MODEL ................................................................................ 29
3.4 THREE DIMENSIONAL MODEL ........................................................................................................ 30
3.5 CHAPTER SUMMARY ................................................................................................................... 34
CHAPTER 4..................................................................................................................... 37
SIMULATION RESULTS................................................................................................ 37
4.1 MODEL SETUP ........................................................................................................................... 37
4.2 SIMULATION RESULTS FOR PEG DESIGNS .......................................................................................... 38
4.3 STRAIN ENERGY DENSITY VALUES.................................................................................................... 39
4.4 CHAPTER SUMMARY ................................................................................................................... 44
CHAPTER 5..................................................................................................................... 47
BONE REMODELLING SIMULATION ........................................................................ 47
5.1 ABAQUS AND PYTHON............................................................................................................... 47
5.2 PREPARING BONE MODEL FOR SIMULATION...................................................................................... 48
5.2.1 Creation of cortical and cancellous section of the bone.................................................... 48
5.2.2 Creation of materials for the sections.............................................................................. 49
5.2.3 Load and boundary conditions......................................................................................... 49
5.3 BONE REMODELLING SIMULATION USING PYTHON SCRIPT.................................................................... 50
5.4 SIMULATION RESULTS.................................................................................................................. 52
5.5 STRAIN ENERGY DENSITY AT SELECTED NODES ................................................................................... 58
5.6 PEG HOLE WITH SQUARE PEGS....................................................................................................... 61
5.7 CHAPTER SUMMARY ................................................................................................................... 63
CHAPTER 6..................................................................................................................... 65
CONCLUSION ................................................................................................................. 65
6.1 THESIS SUMMARY AND CONCLUSIONS............................................................................................. 65
6.2 FUTURE WORK........................................................................................................................... 65
6.3 CHAPTER SUMMARY ................................................................................................................... 67
APPENDIX..................................................................................................................... 69
PYTHON SCRIPT......................................................................................................... 69
REFERENCES .............................................................................................................. 77

9. vi
List of figures
Figure 1.1:Structure of knee.................................................................................................. 2
Figure 1.2: Meniscus (Gray 1918). ....................................................................................... 2
Figure 1.3: Articulations in knee joint................................................................................... 3
Figure 1.4: The major ligaments of the knee joint: Green – patella ligament, Red – collateral
ligaments, Dark blue – anterior cruciate ligament, Light blue – posterior cruciate
ligament (Gray 1918)..................................................................................................... 4
Figure 1.5: Steps in bone remodelling process ...................................................................... 6
Figure 1.6: Microstructure of femur before and after pixel based remodelling approach
Tsubota et al. (2002) ...................................................................................................... 8
Figure1.7 : The bone remodelling process is simulated in femur after 500 loading iterations
(Jacobs et al., 1995)..................................................................................................... 10
Figure 1.6: Osteoarthritis ................................................................................................... 11
Figure 1.7: Orthopaedic screw and pin............................................................................... 13
Figure 1.8: Loosening of fixator.......................................................................................... 14
Figure 2.1: Prosthesis design (Cheong 2012)...................................................................... 19
Figure 2.2: Triangle, square and circular pegs ................................................................... 21
Figure 2.3: Screws placed in various angle (Letizia Perillo 2014)....................................... 22
Figure 3.1: A simple two dimensional model....................................................................... 26
Figure 3.2: Meshing of two dimensional model ................................................................... 29
Figure 3.3: S11 values for two dimensional model .............................................................. 30
Figure 3.4: Extruded three dimensional model.................................................................... 31
Figure 3.5: S11 values for three dimensional model............................................................ 31
Figure 3.6: Three dimensional symmetrical model .............................................................. 32
Figure 4.1: Block inserted with peg..................................................................................... 37
Figure 4.2: View cuts of the full model................................................................................ 39
Figure 4.3: Regions around the peg (view in y-z plane)....................................................... 40
Figure 4.4: Regions where the peg enters the bone (View in x-z plane)................................ 42
Figure: 5.1: The view cut model of tibia illustrating the thickness of the cortical section in
orange.......................................................................................................................... 48
Figure 5.2: Tibia-peg model applied with load and boundary conditions ............................ 49
Figure 5.3: Flow chart for bone remodelling simulation ..................................................... 51
Figure 5.4: The view cut in x-z plane................................................................................... 53
Figure 5.5: The view from y-z plane.................................................................................... 56
Figure 5.6: Strain energy density results from the final step................................................ 57
Figure 5.7: The element ID of the nodes observed............................................................... 58
Figure 5.8: The strain energy and iteration plot for element ID 97...................................... 59
Figure 5.9: The strain energy and iteration plot for element ID 1698.................................. 59
Figure 5.10: The strain energy and iteration plot for element ID 28499.............................. 60
Figure 5.11: The strain energy density around the square peg with holes............................ 61

10. vii
List of tables
Table 1: Mechanical properties of various biological materials .......................................... 12
Table 2: Dimensions of pegs ............................................................................................... 19

11. 1
Chapter 1
Introduction
1.1 Objective of this Research
The objective of this research is to analyse the effectiveness of a variety of different
pegs/fasteners, as used to fix metallic plates to bone. A number of different peg designs will
be examined. The strength of fixation of these pegs will be analysed computationally using
Finite Element Analysis (FEA). Some deductions will also be made regarding bone
remodelling (bone growth and bone decay) in the vicinity of the pegs, and the effect that this
might have on the effectiveness of the pegs over a period of time.
The particular application is the fastening of plates to the human tibial-femoral (knee) joint.
These plates are to form part of novel knee prosthesis (more details of which will be given in
the Chapter 2) and, as such, the plates may have to be fixed to the bone for many years.
As an introduction to the analysis of plates, bone and pegs, in this Chapter a brief review of
the anatomy of the knee joint, its range of motion and the bone remodelling process will be
given.
1.2 Anatomy of the Knee
The knee joint is the most important and largest synovial joint in the human body. It is the
major weight bearing joint of the human body, and is capable of various movements such as
flexion, extension and other complex rotatory movements. It consists of four bones: the
femur, tibia, fibula and patella. The joint itself acts as an articulation between the distal, i.e.
lower, end of the femur (thigh bone), the meniscus-bearing upper surface of the tibia (shin
bone), and the posterior surface of the patella (Knee Cap). This articulation is shown in figure
1.1 (to be precise, there are two articulations: the tibia-femoral articulation and the patella-
femoral articulation – see below). The fibula is the smaller bone which runs alongside the
tibia.

12. 2
1.3 Tibia-femoral joint
At the distal end of the femur, two curved bony protrusions emerge, one on either side (see
Figure 1). They are called the medial and lateral condyles. These femoral condyles articulate
with the medial and lateral condyles of tibia.
Figure 1.1:Structure of knee (WebMD, LLC)
Between the condyles of the femur and tibia is found the meniscus (see figure 1.2); the
meniscus here is a C-shaped disc consisting of a fibrocartilage structure.
Figure 1.2: Meniscus (Gray 1918).

13. 3
The menisci serve two functions:
1. To increase the articulating surface of the tibia (and to increase stability of the joint).
2. To act as a shock absorber, absorbing the shocks due to daily activities such as
walking and running.
1.4 Patella- femoral joint
The knee cap or patella and femur form a joint called the patella- femoral joint. The patella is
the triangular shaped bone (see figure 1.1) to the front of the knee joint (Gray 1918). It acts as
a shield to protect the knee. The articulation of patella and femur forms the patella-femoral
joint.
The patella is connected to the quadriceps femoris muscle, which is used to extend or
straighten the leg. The vastus intermedius muscle is attached at the base of the patella, and the
vastus lateralis and vastus medialis are attached to the lateral and medial borders of the
patella respectively.
1.5 Articulating motions in the knee joint
The human knee joint acts like a hinge. It has 6 degrees of freedom (see figure 1.3): three
rotational movements (flexion and extension, internal and external rotation, adduction and
abduction rotation) and three translational movements (anterior and posterior translation,
medial and lateral translation, compression and distraction)
Figure 1.3: Articulations in knee joint

14. 4
Flexion of the knee joint is where the femur rolls over the tibia, and the straightening of the
knee joint is called as extension. The backwards and forwards sliding of the tibia relative to
the femur is called anterior and posterior translation respectively.
In internal and external rotation, the tibia rotates around its axis, whereas, in medial and
lateral translation, the tibia translates from side to side. The movement of the femur and tibia
along their own long axes is called superior and inferior translation, respectively.
Movement towards the midline of the body is called adduction; movement away from the
midline is called abduction (Gray 1918).
1.6 Ligaments in the knee joint
Ligaments are fibrous tissue which connects bone to bone. There are four ligaments in the
knee joint (see figure), and these play a crucial role in maintaining knee joint stability. They
are listed and discussed briefly below.
1.6.1 Anterior cruciate ligament
The anterior cruciate ligament (ACL) starts from the intercondylar region of the tibia and
ends in the posterior medial side of the lateral femoral condyle. During extension of the knee
joint, the ACL prevents posterior displacement of the femur in relation to the tibia, and vice
versa. The ACL has two main bundles, the anteromedial and posterolateral bundles. The
anteromedial is relaxed in extension and tenses in flexion, while the latter is vice versa (Gray
1918).
Figure 1.4: The major ligaments of the knee joint: Green – patella ligament, Red – collateral ligaments, Dark
blue – anterior cruciate ligament, Light blue – posterior cruciate ligament (Gray 1918).

15. 5
1.6.2 Posterior cruciate ligament
The posterior cruciate ligament (PCL) starts from the posterior intercondylar area of the tibia
and ends in the lateral side of the medial femoral condyle (Gray 1918). When the knee is
flexed, the PCL is taut. It prevents posterior displacement of the tibia and the femur, and
hyper flexion of the knee. The PCL plays a crucial role when walking downhill or climbing
uphill. It stabilises the weight bearing flexed knee.
1.6.3 Medial collateral ligament
The medial collateral ligament runs from the medial epicondyle of the femur to the medial
condyle of the tibia (Gray 1918). It attaches to the medial meniscus at its midpoint. This
prevents movement and extension of the leg away from the medial plane.
1.6.4 Lateral collateral ligament
The lateral collateral ligament runs from the lateral epicondyle of the femur to the lateral
surface of the head of the fibula. It is not attached to the tibia. The lateral collateral ligament
prevents the leg moving towards the median axis of the body (Gray 1918).
1.7 Bone structure and remodelling
There are two types of bone found in the human body. They are compact bone and cancellous
bone. Compact bone is the hard outer layer of the bone. It is very dense, it has a smooth,
white and solid appearance and it constitutes 80% of the total bone mass.
The cancellous or trabecular bone is less dense, softer, weaker and less stiff than compact
bone. The porosity of cancellous bone is between 30% and 90%. The primary anatomical and
functional unit of cancellous bone is the trabecula. The interior of the bone is filled with
trabeculae (Kihn 2013). They constitute 20% of total bone mass. The cancellous bone is
made up of a structure of Harvesian systems or osteons. In the centre of each osteon is the
Harvesian canal. These canals are surrounded by collagen fibres. Inside the bone matrix,
osteocytes are found. These osteocytes are interconnected with each other.
Bone remodelling is a dynamic process of resorption and formation of the bone that occurs
throughout our life. Bone remodelling follows a sequence consisting of activation, resorption,
and formation. The bone remodelling process involves interaction of four types of cell,
namely osteoclasts, osteoblasts, osteocytes and bone lining cells. They are collectively called
basic multicellular units (BMUs). The bone lining cells, osteoclasts and osteoblasts are
located at the surface of the bone whereas osteocytes are located within the bone matrix.

16. 6
The bone remodelling process begins with bone resorption which is done by osteoclasts. It is
hypothesized that osteocytes can detect strains (micro deformations) induced in bone when it
is loaded. The osteocytes initiate an osteogenic response if the strains are above or below
strain levels which the bone was usually subjected to. Micro damage caused by the straining
to the osteocyte network is thought to disrupt osteocyte-to-osteocytes communication and
fluid flow in the local region (Ehrlich PJ 2002). This micro damage induced disruption of
cell communication and fluid flow is thought to trigger bone remodelling. This process by
which the cells convert mechanical stimulus into chemical activity is called as
mechanotransduction. This concept of stress or strain induced bone remodelling was first
proposed by the German anatomist Julius Wolff known as Wolff’s law.
Figure 1.5: Steps in bone remodelling process (wweb.utah.edu)
The figure above shows the steps involved in the bone remodelling process. In step 1
quiescent1
bone surface is shown above with osteocytes embedded in the bone matrix and
lining cells on the surface. Between step 1 and 2, when a force that exceeds the structural
integrity of the bone tissue is applied, there is an increase in strain. This causes micro crack to
occur in the bone matrix. Osteoclasts initiate the bone remodelling process by removing
1
in a state or period of inactivity or dormancy.

17. 7
normal inhibition of osteoclastic activity. This removal of inhibition sends a biochemical
signal over to the surface of the bone.
Once the biochemical signal is received, the lining cells in the affected area open up to allow
the osteoclasts to enter the area with micro damage. In steps 3 and 4 the osteoclasts mature
and start excavating a cavity in the affected area. The resorption of the bone by osteoclasts
takes about 2 weeks. After that, between step 4 and 5, osteoclasts undergo apoptosis2
.
In step 5, osteoblasts lay down new bone tissue. The osteoblasts fill in new bone matrix and
some of the osteoblasts turn into osteocytes, some turn into lining cells and the rest undergo
apoptosis. The osteocytes in the newly formed bone matrix establish a dendrite network with
neighbouring osteocytes and the bone lining cells.
The bone is remodelled continuously by the process just described above. There are a lot of
theories which speculate about bone growth. This phenomenon plays a vital role in loosening
of fixators; how this will affect them will be discussed later in this chapter.
1.8 Bone remodelling algorithm
There have been a number of studies carried out by researchers on the bone remodelling
processs using finite element methods. Different approaches can be used to simulate the bone
remodelling process. The apparent density modelling and pixel based voxel method are two
widely-used approaches.
1.8.1 Pixel and Voxel Based Remodelling
In three dimensional voxel based remodelling or two dimensional pixel based remodelling,
all the elements used are either completely bone or completely empty; no apparent density is
used in either case. The process of bone remodelling is simulated by changing the elements
which correspond to empty, to solid bone, and vice versa.
A two dimensional pixel-based finite element model was developed by Tsubota et al. (2002)
to depict the remodelling process occurring in the proximal femur. The bone growth is
dependent on the non-uniformity of the stress and strain distribution (and not as a function of
the actual stress and strain). This modelling approach is based on the idea that fluid flow is
responsible for bone growth stimulation, as the fluid flow would be caused by the stress and
2
If cells are no longer needed, they commit suicide by activating an intracellular death program. This process is
therefore called programmed cell death, although it is more commonly called apoptosis from a Greek word
meaning “falling off,” as leaves from a tree (Alberts B, J. A., Lewis J 2002).

18. 8
strain gradients. Initially, the internal distribution of bone was generated by filing the bone
randomly in a circular pattern, with same size of cancellous bone trabeculae. The model is
loaded over several time steps, with remodelling of the bone at each iteration. This procedure
was able to demonstrate the strain criteria set for the initialising the bone remodelling process
accurately predicted the generation of the complex trabecular structures seen within the
human femur.
The two dimensional model was then extended into a three dimensional voxel model by
Tsubota et al (2002). In this case, the isotropic bone structure was filled initially with
trabecular tori. This model was again able to accurately predict the trabecular structure seen
in the femur, and also predicted orientation of bone along the principal stress directions. Pixel
and voxel based approaches are successful in predicting the trabecular structure of the bone
using the non-uniformity of strain as a stimulus for bone growth. This procedure, however,
requires a very small element size. In the two dimensional approach, the proximal femur
model was required to have 0.67 million elements for computational accuracy and
convergence, while in the three dimensional model the element size was required to be 0.93
elements having a resolution of 87.5 µm. The change in bone density is illustrated in figure
1.6 below
Figure 1.6: Microstructure of femur before and after pixel based remodelling approach Tsubota et al. (2002)
The voxel approach serves for modelling the changes in bone at the trabecular level, but large
scale modelling of the entire bone or joint does not essentially require resolution at the micro
scale of the bone microstructure. At the larger scale, the apparent density method proves to be
suitable to model the bone remodelling behaviour over a specified period of time.

19. 9
1.8.2 Apparent density remodelling
In this approach a continuous density distribution is defined throughout the bone. The
apparent density is defined as the ratio of the mass of bone inside a cubic element to the
volume of that cubic element (the element consists also of empty space, or in fact bone
marrow). This is different from the actual density of the bone. The actual density of the bone
is defined as the ratio of the mass of the bone to the volume of the bone.
The apparent density can also be defined as a relative density in which a value of ‘0’
indicates the element is empty and a value of ‘1’ indicates that it consists of solid bone.
A differential equation is used to model the bone remodelling process. The bone model is
loaded for a multiple number of iterations. After each iteration, the apparent density
distribution in the bone is updated, based on the distribution of stress, strain and/or strain
energy within the bone. Usually, the strain energy density per unit mass or the average
absolute value of the principal strains is used as the bone remodelling parameter (Chen et al.,
2007, Huiskes et al., 1992). A threshold range of strain energy density values are defined. If
any element has a value above this threshold range, there will be an increase in density of that
element, and if the value is less than the threshold range there will be a decrease in density of
that element. This strain energy thresholding simulates an increase in density of the bone
(bone formation) and/or a decrease in density (bone loss).
Equation 1 shows the rate of change of apparent bone density:
d ρ
dt
= 𝐵 [
𝑆𝐸𝐷
ρ
− 𝑘]……………. Equation 1
where:
ρ apparent density
B is a constant controlling the rate of bone growth
SED strain energy density
𝑘 equilibrium level of strain energy per unit mass (which results in no bone growth)

20. 10
A relationship between the Young’s modulus and density can be obtained through
mechanical testing of actual bones. In a Finite Element Analysis, the density of the material
can be changed through its relationship with the Young’s modulus of that material. Euler’s
method of order one can be used to solve Equation 1, in which the density at the beginning of
the next iteration is equal to the density of the previous iteration plus the right hand side of
Equation 1 (times the number of iterations). Note that the loading in any one iteration
represented in Finite Element Analysis does not correspond directly to loading in real time, as
the analysis at each iteration is a static analysis. The simulation represents an arbitrary
number of similar loading cycles over an arbitrary amount of time.
Figure1.7 : The bone remodelling process is simulated in femur after 500 loading iterations (Jacobs et al.,
1995)
Initially, the apparent density is assumed to be uniform throughout the bone. After each
loading iteration, the bone grows more or less dense according to the bone remodelling
equation 1 shown in figure 1.7. This method of bone growth has been used by a number of
researchers to simulate bone remodelling in real time (see, for example, Jacobs et al., 1995).
For this project this approach is used to simulate bone remodelling process.
1.9 Osteoarthritis
Arthritis is a condition which involves damage to the joints in the human body. There are
more than 100 different types of arthritis.

21. 11
Osteoarthritis (OA) is the most common form of arthritis. It is estimated that OA affects one
in every six New Zealanders over 15 years of age.
As mentioned earlier, the cartilage which covers the surfaces of the femur and tibia in the
knee joint acts as a shock absorber, allowing the femur and tibia to glide more smoothly over
each other (Buckwalter and Mankin 1998). In Osteoarthritis, this cartilage is degenerated or
damaged, which allows the femur and tibia to rub directly against each, resulting in pain,
inflammation and restriction in movement of the knee.
There are various factors which can lead to Osteoarthritis, including:
 Age
 Obesity
 Cartilage Injury
 Mechanical wear and tear.
 Bone deformity
There is a strong correlation between age and Osteoarthritis; aging leads to changes and
deterioration in the cartilage (Buckwalter and Mankin 1998). Aging is not the only factor
which contributes to Osteoarthritis. Cartilage can also be damaged when it is subjected to
higher rates of torsional and direct loading. Certain activities will involve the cartilage being
Figure 1.6: Osteoarthritis (WebMD, LLC)
subjected to high impact loading and, over a period of time, the cartilage will become
damaged. Certain sports in which the knee joint is subjected to intense loads also lead to a
higher risk of Osteoarthritis (Floris P.J.G Lafeber 2006). However, individuals with bone and
joint deformities, and obese individuals are at greater risk of Osteoarthritis. The main reason

22. 12
for the progression of Osteoarthritis is that the cartilage is never allowed to heal: it is always
subjected to loads during everyday activities.
1.10 Material characteristics
Composites are materials which contains two or more components. Bone is a fibre composite
material because it contains collagen fibres embedded in an inorganic matrix.
When a structure such as femur is subjected to a load, it deforms due to a change in the
interatomic distances inside the femur. This change in interatomic distance is associated with
spatially dependent distributions of local internal forces and deformations (Dennis R. Carter
2001). By using a continuum model of the femur, cartilage, tibia, cancellous bone and
compact bone, it is possible to calculate the intensity of the internal forces and magnitude of
internal deformations using the stress and strain values at the specified locations. In order to
develop the continuum model, one needs to specify the macroscopic material properties. For
an elastic model, one needs to specify the Young’s Modulus and the Poisson’s Ratio. These
can be obtained from experimental tests (uniaxial tests, biaxial tests, etc.). Typical values
obtained are listed in table 1 below.
Material Young’s Modulus
(MPa)
Poisson’s ratio
Cortical Bone 19000 0.45
Ligament /Tendon 250-1000 >0.45
Cartilage 0.8 0.38
Stainless steel 193000 0.31
Table 1: Mechanical properties of various biological materials

23. 13
Once the material properties have been obtained, they can be input into numerical and
computational analysis software, such as Finite Element software. This software can be used
to predict the stresses and strains within the material, and so predict the response of the
material to various loading conditions.
1.11 Orthopaedic fixations
Orthopaedic fixation devices are used for fixation of fractures, soft tissue injuries and
reconstructive surgeries. In the context of the prosthesis discussed in the next chapter, these
fixations will need to maintain the stability of the knee implant with the bone. They must be
strong enough to hold the knee implant and bone together and allow mobilization of the
patient.
There are various types of orthopaedic fixators such screws, pegs and nails; examples are
displayed in figure 1.7 below.
Figure 1.7: Orthopaedic screw and pin reference (Ortho.in)
For this project, screws and pegs were considered for the fixation of plates to bone. This is
because the prosthesis has to be held firmly in its position and this can be achieved by screws
or pegs. The design concept of the prosthesis will be explained in the next chapter. But before
making a decision as to whether to use a screw or peg, it is important to understand one of the
important causes of failure of orthopaedic fixators, which is their loosening from the bone.
This is discussed in the next subsection below.
1.12 Loosening of fixators
After decades of research, the loosening fixators remains a subject of debate (Gefen 2002).
However, studies indicate stress shielding as an important candidate cause for this loosening
(Rik Huiskes 1992). In this section, the effect of stress shielding and strain energy density on
loosening of fixators is examined.

24. 14
The bone, in its natural state, carries its external loads all by itself. Fixators have the tendency
to carry the stresses transmitted to the specific bone region where they are situated. The
metallic screws have a stiffness (Elastic Modulus) in the order of 100-200GPa. Since the
stiffness of the bone is much less (~1 to 20GPa) than that of the metal screws, the internal
load is now carried by the fixator.
Figure 1.8: Loosening of fixator reference Gefen, D. A. (2002).
As discussed in the subsection named bone architecture and remodelling, the bone
remodelling process will occur only if there is a constant supply of strain detected in the
bone. When the fixator is fixed in the bone, the bone shares its load carrying capacity with
the fixator. Thus the load which was carried by the bone is now carried by the fixator (Rik
Huiskes 1992). In other words, the bone is “shielded” from carrying the normal mechanical
stresses. Thus there will be an increase in bone resorption due to a decrease in load and strain
(shown in figure 1.8) and the fixators get loosened subsequently.
It is observed that the amount of stress occurring at the edges of the screw thread is high. This
increases the stress shielding around the threads (S. Hanssona 2003). This leads to bone
resorption around the screw. Because of this phenomenon, it was decided to use pegs in this
project. Also, whereas screws must invariably have a circular cross-section, pegs can have
different cross-sectional shapes, since they are simply driven into the bone with a hammer or
similar tool. Thus different cross-sectional designs can be analysed using the peg format. In
the next chapter, suitable peg designs for the proposed prosthesis are discussed.
1.13 Measuring parameter in the project
For this project, the strain energy density will be used as an indicator of the occurrence of the
bone remodelling process. The strain energy density of a material is defined as the strain

25. 15
energy per unit volume. This strain energy is related to both the stress and strain at any
location (very qualitatively, the strain energy density is half the stress times the strain). There
is a correlation between strain energy density and the bone remodelling process (Lin 2009).
The main advantage of using the strain energy density is that it is a scalar quantity and the
directional quantities of stress and strain can be ignored (Mellal 2004).
A higher strain energy density would indicate formation of the bone whereas a lower strain
energy density would indicate bone resorption.

26. 16
1.14 Chapter summary
 The knee joint is made up of four bones: femur, tibia, patella and fibula.
 The ligaments provide stability to the knee joint. The four ligaments in the joint are:
anterior cruciate ligament, posterior cruciate ligament, medial collateral ligament and
lateral collateral ligament.
 The human knee joint acts like a hinge. It has three rotational movements and three
translational movements.
 The bone undergoes constant and continuous remodelling. The bone remodelling
involves removal of mineralized bone and the formation of new bone matrix.
 Osteocytes detect strain in the bone.
 Osteoarthritis (OA) is the most common form of arthritis. Osteoarthritis occurs in the
knee when the cartilage covering the bones in the knee joint degenerates.
 Bone is a composite material whose mechanical properties can be evaluated from
tests. These properties can be used in numerical simulations to predict the response of
bone.
 There are various types of orthopaedic fixations like screws, nails and pegs.
 Stress shielding is the main candidate cause for loosening of fixators.
 In this project, strain energy density will be used as the measuring parameter for
occurrence of bone remodelling

27. 17

28. 18

29. 19
Chapter 2
Design of pegs
As mentioned in the Introduction, this project is concerned with fixators which will be used
to attach plates to the knee joint: these fixators will play a vital role in maintaining the
stability of a knee implant, of which these plates form a part (figure 2.1). Numerous types of
fixation devices for the fixation of implants and plates to bone have emerged over the years
and, in this brief chapter, the different types of fixators used in this project will be discussed.
2.1 Novel knee prosthesis design
A new knee prosthesis has been designed recently and a prototype was built and tested under
some simple loading conditions (Cheong 2012). The prosthesis design is shown in figure 2.1
below.
Figure 2.1: Prosthesis design (Cheong 2012).

30. 20
As can be seen in Figure 2.1, the prosthesis has a “femur plate” and a “tibia plate”, which are
attached to either side of the femur and tibia. These plates are designed in such a way that
they wrap around the lateral and medial sides of the distal femur and proximal tibia. The
femur and tibia plates slide over each other, over the articulating plates which are attached to
the femur plate and tibia plate. There are large holes in the plates, which reduce the weight of
the prosthesis, without affecting its performance. There are also smaller holes visible on the
femur and tibia plates (the triangular-shaped holes) to enable the fixation of the plates to the
femur and tibia with pegs or screws. In this chapter the design specifications of these fixators
and their fixing position is discussed.
2.2 CAD software (Solidworks)
Solidworks is three dimensional mechanical computer aided design (CAD) software. It is a
solid modeller which uses a parametric feature-based approach to create models and
assemblies. In a parameter feature-based approach, the features are defined to be parametric
shapes associated with the attributes of the model. They can be shape or geometry of the
model or assembly. They can be either numerical such as length or diameter, or geometrical
such as parallel, concentric, horizontal or vertical etc.
The Solidworks software is used in this study to design the pegs. The pegs used in this project
were chosen to have three different shapes: circular, triangular and square. The circular peg is
a conventional one and square and triangular shaped shafts in pegs were used to prevent the
pegs from rotating. It is very important to prevent the rotation as this helps with the stability
of the prosthesis. The different shapes could then be tested to see which was best to use.
For each of the three designs, circular, triangular and square profiles are drawn separately.
The square and triangular profiles are drawn with the polygon tool in Solidworks with an
inscribed circle option. The dimensions of the profiles (inscribed circle or circle) are given in
the table 2 below.

31. 21
Peg Diameter of inscribed circle (mm)
Square 1.76
Triangle 2.50
Circle 4
Table 2: Dimensions of pegs
The width of the femur and tibia are approximately 66mm and 70mm respectively (Moore-
Jansen 1994). So the profiles are extruded up to 20mm in length so that pegs do not intersect
with each other when they are fixed on both the sides of the bone. One end of the profile is
chamfered for a length of 1mm and at an angle of 70⁰. The angle does not exceed 70⁰ in
order to avoid a sharp-pointed tip for the pegs. This eliminates the effect of high stress acting
at the tips. The peg images are shown in figure 2.2 below.
Figure 2.2: Triangle, square and circular pegs Reference
2.3 Location and position of fixation
The location and position of fixators play an important role in maintaining the stability and
longevity of the implant. Factors which have been reported in the literature which influence
the stability of fixators include their dimension, the shape of the fixator, their surface
characteristics and the insertion angle.

32. 22
The pegs can be placed at any location over the femur and tibia (where the plate is to be
located). However, previous research shows that the fixators should be placed at an angle of
30⁰ to 90⁰ relative to the bone for better anchorage (Niles Woodall, 2011). This is because
the pull out force on the fixators is less when compared to other angles. Figure 2.5 below
shows the fixators positioned at various angles.
Figure 2.3: Screws placed in various angle (Letizia Perillo 2014).
However, fixators placed in the implant plates at an angle of 90⁰ normal to the forces acting
have a better anchorage than fixators placed at angles of 30⁰ or 60⁰ (Letizia Perillo 2014).
When the stress acting at the tip of fixators is high, the anchorage resisting forces of the
fixators reduces. There is high stress observed for angles other than 90⁰.
Therefore, in this project it was decided to place the pegs in a direction normal to the forces
acting in the bone thereby having better anchorage, i.e. at 90⁰. This helps prevent the pegs
from loosening.

33. 23
2.4 Chapter summary
 A new knee prosthesis has been designed recently and a prototype was built and
tested under some simple loading conditions.
 The prosthesis design has a “femur plate” and a “tibia plate”, which are attached to
either side of the femur and tibia.
 The femur and tibia plates slide over each other, over the articulating plates which are
attached to the femur plate and tibia plate.
 Pegs have been chosen as the fixators, to attach the prosthesis plate to the knee bones;
three shapes for the pegs were chosen to test: circular, triangular and square.
 The pegs were designed and drawn using the Solidworks CAD software.
 The pegs are inserted to the bone in the direction normal to the forces acting in the
bone.

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35. 25
Chapter 3
Finite Element Analysis
This chapter describes the procedures involved in setting up a bone and peg model for a
Finite Element Analysis (FEA) using the Finite Element Method (FEM); FEM is a computer
based numerical method for solving a differential or integral equation in engineering and
applied science. It is a commonly used approach for solving partial differential equations over
complicated domains having irregular geometries and heterogeneous material properties (the
loaded and deforming bone/peg/plate problem is one of this type). A domain of interest is
represented as an assembly of finite elements. These finite elements are interconnected at
points known as nodes. Each node can be assigned with physical properties like thickness,
Poisson’s ratio, Young’s modulus, density, etc.
The true solution to the problem is approximated numerically over each element and the
values inside finite elements can be recovered using nodal or elemental values. As a result,
FEA is widely used to solve problems involving the structural mechanics of bones, their
interaction with fixators and their response.
3.1 Abaqus
Abaqus is computational software for FEA and computer aided engineering. Abaqus contains
an extensive library of elements that can model virtually any geometry. The model geometry
from many different CAD software packages such as Solidworks can be imported in Abaqus.
Using Abaqus, one should be able to use various different material models to simulate the
behaviour in bone, the pegs and at the peg/bone interface. The simulation of linear (elastic)
and nonlinear (e.g. involving friction) applications can also be done.
Abaqus/CAE (Computer Aided Engineering) gives the complete Abaqus environment that
provides the interface to create models. Abaqus/CAE is divided into modules where one can
define the geometry, assign material properties and create interaction between the various
components in the model. The boundary conditions and load profiles are assigned to the
model and the mesh is generated. Once the model is completed, Abaqus/CAE generates the
input file (.inp) and submits it to the Abaqus/Standard or Abaqus/Explicit analysis product.

36. 26
The analysis product performs the analysis and it can be monitored through Abaqus/CAE.
After the successful completion of the simulation, the output database file (.odb) is generated
and the results can be viewed.
3.2 Analysis of two dimensional model
The aim of the project is to perform an analysis of the strain energy density (SED) at the
peg/bone interface for various designs of pegs, and so choose an optimal design with the best
response. A simple two dimensional model of bone, the implant plate and a peg of length
5mm was first created and FEM was performed on these models. This two dimensional
modelling allows one to get familiar with the Abaqus software and allows one to explore the
various assumptions in the model and how these assumptions affect the final results. The
model was also created so as to validate the results which will be obtained later with fully
three dimensional models. A simple two dimension model is shown in figure 3.1.
Figure 3.1: A simple two dimensional model
The two dimensional model shown in figure 3.1 depicts the femur with two implant plates
attached to its sides with a peg attached to it. The intention was to load the models axially to
investigate the SED distribution at the pin-bone interface. The load is applied as a pressure
over the top of the central block, simulating the load acting over the femur. The plates are
fixed at the bottom as their axial movement is restricted in reality by the plates which are
fixed to the tibia from beneath.

37. 27
3.2.1 Materials
The block is taken to be bone, with isotropic and elastic properties. It was assigned the
material properties of the femur (Young’s modulus: 19000MPa and Poisson’s ratio: 0.45),
whereas the implant plate and peg are assigned the material properties of stainless steel
(Young’s modulus: 193 GPa and Poisson’s ratio: 0.31).
3.2.2 Step
The analysis step sequence for the model was next created. The step sequence provides a
convenient way to capture the changes that occur during the course of an analysis. The
analysis procedure has to be defined while creating the step. For this study, a static stress
analysis was selected. Each step is divided into multiple increments. Automatic time
increments were selected. Abaqus/Standard increments and iterates accordingly to solve for a
step. By default, the upper limit to the number of increments is 100. The increment was left at
100 as the solutions were all found under this limit.
3.2.3 Boundary conditions
In order to study the deformation of the model some degrees of freedom must be restricted. If
not, the model will behave like a free floating body and there is a possibility that the model
can undergo translational or rotational motion without experiencing any deformation. So, in
this project, the encastre option was used and applied to the bottom of the plate. This depicts
the ground forces acting through the plates attached to the tibia to the femur plates. This is
shown in figure 3.1.
3.2.4 Contacts and interaction
The contact and interaction properties must be prescribed between the block (femur) and the
plates, and between the block and peg. A contact pair is defined as two surfaces that interact
with each other. No two surfaces are allowed to have the same nodes, so the master and slave
surfaces have to be distinguished. The larger surface is usually selected to be the master
surface. The ‘Tie’ interaction was used between the block and the peg; this means that the
block and peg are attached together and move together as the body deforms. The plate is in
reality sliding over the surface of the femur, so that a “surface-to-surface” sliding/frictional
contact interaction between the block and plates would be appropriate. However, the surface-
to-surface interaction is not straight forward to implement and can be numerically
problematic and time-consuming to implement. Simulations were run with both a surface-to-
surface interaction and a tie-interaction between the bone and plate. The results showed that

38. 28
the actual interaction condition had but a small effect on the results, e.g. on the stress
distribution values around the peg. For the tie interaction and the surface-to-surface
interaction, the horizontal stress S11 was 0.0287 MPa. For this reason, it was decided to
adopt the tie-interaction for the bone/plate contact.
3.2.5 Load
In order to simulate the body weight acting on the bone, a uniform pressure distribution was
applied over the top of the block (femur). A pressure of 0.22MPa was applied over the top as
shown in figure 3.1. This magnitude is the force per unit area equivalent to an 80kg subject
standing on both legs (Cheong 2012). For this project a simple loading condition when a
subject standing in both the legs is considered.
3.2.6 Mesh
The FEM model is divided into several small elements and they are connected at key points
called nodes. All the elements and nodes in the model are numbered. This is done to establish
matrix connectivity. The elements can be one, two or three dimensional, depending on the
dimension of the model. The method by which elements are joined at nodes is called
meshing.
The two dimensional model is meshed with quadrilateral elements. Tetrahedral elements are
used in the 3 dimensional bone model. The tetrahedral elements are versatile and they are
used in automatic meshing algorithms. Since the bone model has an irregular geometry it is
convenient to mesh using tetrahedral elements.
The region of most interest is around the pegs. In order to have high resolution of results, the
region around the peg is assigned to have a lower value of seed size. This gives one a mesh
with very fine elements in that area. One also needs a relatively fine mesh in regions where
the stress and strain distributions are undergoing large changes, for example at the top of the
plate where it meets the block/bone. Other regions can have a more coarse mesh. As shown
in the figure 3.2 the seed size around the peg plate interaction region is low as compared to
the other regions.

39. 29
Figure 3.2: Meshing of two dimensional model
The seed size is assigned based on the interaction properties of the parts. The part acting as
the master in a contact pair is assigned a higher seed size value whereas the slave is assigned
a lower seed size value. Once the model is meshed, a job file is created and submitted for
analysis.
3.3 Results from the two dimensional model
The overall model was meshed with various seed sizes to check for convergence of the
results. The goal was to determine a seed-size and mesh resolution which would be fine
enough for the required accuracy, but not overly fine so as to be very computationally
expensive. The stress value (normal/direct stress) S113
was observed at the centre of the peg-
tip for various seed sizes. This was done to check for convergence of the stress in that
particular position with mesh resolution. Figure 3.3 shows a plot of the total number of nodes
in the mesh against the stress S11.
3
S11, S22 and S33 are the stresses in the global x, y and z directions respectively.

40. 30
Figure 3.3: S11 values for two dimensional model
As can be seen in Figure 3.3, the S11 values converge as the number of nodes in the model is
increased. The S11 value for the node is 0.016 MPa when the total number of nodes in the
model is 106863. In order to get a better resolution of results, a smaller value for seed size
should be assigned.
3.4 Three dimensional model
The two dimensional model was converted into a three dimensional model by extruding it
using the Solidworks software and saving it as .step file. Then the .step file was imported into
Abaqus as shown in figure 3.4. When this three dimensional model is exported into
ABAQUS, three different parts are generated: two side plates with the peg and a central
block. The same procedure is followed as before for assigning the material properties to the
parts. The step is created and the loads are applied on the top face as shown in figure 3.4.
The boundary conditions are the same as for the two dimensional model. The different parts
are meshed according to their interaction properties.

41. 31
Figure 3.4: Extruded three dimensional model
In the three dimensional model, the faces over the y-z plane are fixed in the z-direction by
applying a boundary condition ZSYMM U3=0. This is done in order to make the three
dimensional model behave like a (plane strain) two dimensional model, by arresting
movement along the z axis. The convergence of the S11 stress was also observed at the same
node (as in the two-dimensional model) for different seed sizes. The nodal stress values of
S11 observed at the peg-tip are plotted as a graph below in figure 3.5.
Figure 3.5: S11 values for three dimensional model

42. 32
It can be observed that the S11 nodal values at the peg tip again converge with an increase in
the number of nodes. The S11 value for the node is 0.02 for the seed size of 0.01 (total
number of nodes: 106863) for the peg and its surrounding region in the block. This value of
stress is also close to the value observed in the two dimensional model. These simulation
results suggest that the results of the two and three dimensional models agree, giving
confidence in the results obtained.
The three dimensional model has a large number of nodes and the computational time for
Abaqus is very high. In order to bring down the computational time and maintain the high
resolution of results, the symmetry of the three dimensional model was exploited as shown in
figure 3.6.
Figure 3.6: Three dimensional symmetrical model
The face with normal in the x direction (centre of the block) has been assigned a boundary
condition (XSYMM U1=0). This boundary condition ensures that the symmetrical model
responds in a manner similar to that of the complete three dimensional model. The S11 nodal
value at the peg-tip was found to be the 0.023, which is very close to the value in the full
three dimensional model.

43. 33
The symmetrical model involves very much less computational time than the three
dimensional model. Because of its similarity and accuracy, this symmetrical model was used
for further simulations involving pegs and their analysis, thereby saving computational time
without losing the resolution of the results. This will be discussed in the Chapter 4.

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3.5 Chapter summary
 Abaqus was chosen as the Finite Element Analysis (FEA) software for this project.
 A two dimensional model was created in Abaqus. Prior to the simulation the model
had to be set up by assigning the material properties, step and mesh elements. The two
dimensional model was then submitted for analysis.
 A three dimensional model was created in Solidworks and imported into Abaqus. The
model was set up with the same procedures as used for the two dimensional model.
Mesh convergence studies were carried out in order to validate the results.
 The results from the two dimensional and three dimensional models agreed.
 A “half-model” was created, using the symmetry of the problem, thus reducing the
computational time required.

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46. 36

47. 37
Chapter 4
Simulation results
In this chapter each peg design is subject to a finite element analysis using the ABAQUS
software. The strain energy densities around each design of pegs are analysed. As discussed
in chapter 2, a higher strain energy density indicates bone growth whereas lower strain
energy density indicates bone resorption. In this chapter the strain energy densities around
each peg design are analysed and the peg design which better promotes bone formation
around it will be determined.
4.1 Model setup
The three dimensional model depicting the femur and implant plate are created using
Solidworks software. The model is then saved as .step file so that it can be imported into
ABAQUS software as shown in figure 4.1.
Figure 4.1: Block inserted with peg

48. 38
In the model the implant plate and the peg are assigned the material properties of stainless
steel. These material properties are discussed in chapter 1.
The boundary conditions are applied as discussed in chapter 3. The top face of the central
block is applied with a pressure (due to body weight) of 0.22MPa. The bottom face of the
implant is fixed using ‘ENCASTRE’ option. The faces of the block in the x axis are fixed to
arrest their motion along the axis. Since a symmetrical model is being used in this project, the
face of the block is arrested in y axis as well.
The interaction properties in the model are then defined. The ‘Tie’ option is used. As
discussed in chapter 3, the central block is selected as master and implant plate is selected as
slave. In the interaction between the block and peg, the block is selected as master and the
peg as slave. Similarly, in the interaction between the plate and peg the implant plate is
selected as master and the peg is selected as slave. The method of selecting the master and
slave surfaces is discussed in chapter 3.
The entire model is now meshed, a job file is created and they are submitted for analysis.
Once the job file is submitted, ABAQUS solves the entire model and the results can be
viewed in the ‘Visualisation’ window. This is the procedure followed for all the three models
fitted with the three different peg designs.
4.2 Simulation results for peg designs
After the job is completed, the results are viewed in the ‘Visualisation’ module in ABAQUS.
The .odb (Output database) file is created after every successful completion of the job file.
The .odb files are named accordingly with the job file names. The .odb files are opened for
each of the models in the ‘Visualisation’ module. They can be selected accordingly using the
dropdown box on top of the window.
Once the model is opened, it can be zoomed, rotated, panned so that a clear view of the
region to be observed is obtained.
The model can also be sliced in order to observe the changes inside the model. For instance,
in this project the regions around the pegs should be observed. To facilitate this, the ‘View
cut’ option found under the tools window can be used. This helps to slice and view the model
in the desired axis. In this project the model is observed from the top view and side view. So
the ‘View cut’ option is used in the z-axis and x-axis respectively. This is illustrated in figure
4.2 below.

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Figure 4.2: View cuts of the full model
4.3 Strain energy density values
The strain energy density values are to be observed at the region where the peg is entering the
block and the region around the peg in the block. The strain energy density values for each
model can be viewed by selecting the ‘Field output’ from ‘Result’ menu. Then ESEDEN
(strain energy density) is selected from the ‘Field output’ menu window.
In this subsection the strain energy density for both the regions for all three peg designs are
observed.

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Figure 4.3: Regions around the peg (view in y-z plane)

51. 41
In the figure 4.3 shown in the page above the strain energy density for the region in which the
circular, triangular and square peg enters the block. The view shows the y-z plane in the
model. The same view is maintained for all the peg designs in order to maintain uniformity.
This helps one to compare each design with one another.
In figure 4.3, it can be observed that the strain energy density is almost the same for all the
three pegs. The strain energy density is higher in the region normal to the load applied in x-y
plane. It is found along the axial direction of the bone and it is highlighted with an arrow in
figure 4.3.
However in the region where the peg enters the bone, the strain energy values around the
square peg are found to be high when compared with the other two designs. This is
highlighted with an arrow mark in figure 4.3.
The view in the x-z plane where the peg enters the bone gives more details.
In figure 4.4, regions around the peg where it enters the bone is observed. The bone growth in
this region is very crucial in maintaining the stability of the fixator in the bone model. Using
the ‘Display group’ option from the ‘Tools’ menu the view of the region where the peg enters
the bone is observed. This option helps to remove any part instance displayed in the model. In
this case, the plate is removed because it blocks the view of the region where the peg enters
the bone. This is view is observed for all the three peg designs. The results from this view
help determine the best out of square, triangular and circular peg.

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Figure 4.4: Regions where the peg enters the bone (View in x-z plane)

53. 43
The above results from figure 4.4 shown in the previous page the strain energy distribution
around the peg, when the model is observed in x-z plane. It is very evident that the strain
energy is high for the square peg. The bands of orange and yellow can be seen above and
below for the circular and triangular peg. But for the square peg, the region of red is observed
over the top face of the peg and a band of orange can be noted below the peg. The region is
highlighted with a black circle. However, the distribution patterns around the triangular and
circular peg are more or less the same, without any notable difference.
It is evident from both the views that the strain energy density is high for the square peg when
compared to triangular and circular pegs. This suggests that for square peg there may be
better bone growth in the regions around the peg and also in the region where the peg enters
the bone.
However these pegs should be tested and simulated in the bone model. In the next chapter the
pegs will be placed in a realistic bone model and a bone remodelling process will be
simulated. This will give a clearer insight regarding bone growth around each design.

54. 44
4.4 Chapter summary
 The model has been set up with each of the peg designs placed in the same position in
the block.
 All three models are meshed with the same seed size in order to maintain uniformity
and consistency in results.
 The job file is created and submitted for analysis. Once the job is executed
successfully the results are viewed in ‘Visualisation’ window using the .odb file.
 The display group is used to display selected parts of the model.
 The regions observed in the model are the region around the pegs and the region in
which the peg enters the bone.
 There is a notable difference in both the views between the square peg and the other
two designs.
 The square peg has a higher strain energy density than the other pegs.
 This suggests that the square peg encourages higher bone formation around it.

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Chapter 5
Bone remodelling simulation
In this chapter the effect of the bone remodelling process on the pegs will be presented. The
bone remodelling process is simulated using the ABAQUS finite element analysis. The
analysis helps to determine the stability and performance of pegs over a period of time. The
results from the simulation will be discussed at the end of the chapter.
5.1 ABAQUS and Python
The ABAQUS GUI has been used in the work reported in previous chapters, where relatively
straight forward finite element analysis was performed. Now, however, the full bone
remodelling simulation has to be carried out, and in every time step the material properties of
the bone have to be updated accordingly. This process had to be automated due to its
complexity, using the subroutine functionality available within ABAQUS.
Each subroutine in ABAQUS has its own functionality; the UMAT subroutine was found to
be useful for the purposes of this project. The functionality of the UMAT subroutine is that,
after every job is completed successfully, the strain energy density values are read
individually for every element and the material property of the element may be updated in
that iteration. However, in order to use subroutines in ABAQUS, a FORTRAN compiler is
required. This has several compatibility and set-up issues with respect to ABAQUS and
therefore an alternative possibility was explored: Python scripting
Using Python scripts, it is possible to read and write ABAQUS input and output files. For this
process, the ABAQUS output file has to be read and the material properties have to be
updated. Since ABAQUS has an inbuilt Python interpreter and compiler, it was decided to
use this approach in this project.

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5.2 Preparing bone model for simulation
Before simulating the bone remodelling process in the bone, the Python code was developed
to deal with the following tasks:
 Creation of cortical and cancellous section of the bone
 Assigning appropriate material properties for cortical and cancellous sections
These code blocks were created and tested individually and later combined to simulate the
bone remodelling simulation. The Python code is attached in the Appendix.
5.2.1 Creation of cortical and cancellous section of the bone
An anatomically accurate model of the tibia was provided by Dr. Vickie Shim of the
Auckland Bioengineering Institute. It was not possible to have different types of bone (e.g.
cancellous and cortical) in this model as it was. Having a layer of cortical bone over the
surface of the bone was important, as this would strongly affect the response of a peg. It was
necessary to create “sections” of separate bone within the model. The cortical elements are
created and the ‘View cut’ of the bone having the cortical elements is shown in figure 5.1
below.
Figure: 5.1: The view cut model of tibia illustrating the thickness of the cortical section in orange.
The cancellous elements were created as a set named ‘corticalElementLabels’. All the other
elements are cancellous elements.

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5.2.2 Creation of materials for the sections
The cortical and cancellous material properties should be created for the appropriate elements
in the bone model. The material properties of the cortical bone is applied to the
‘corticalElementlabels’ set. All the other elements are applied the material property of
cancellous bone.
5.2.3 Load and boundary conditions
The bone model was opened using the SOLIDWORKS software and the pegs were inserted,
before the model was saved in .step file format. It should be noted all pegs should be inserted
in the same position in the bone, in order to maintain uniformity and consistency in results. A
simple loading condition when a subject is standing on both the legs have been considered.
The tibia-peg model was next imported into ABAQUS. The procedure explained in chapter 3
is followed here for creating contact interaction, defining assembly, applying load and
meshing the model. The boundary condition ‘ENCASTRE’ is used over the bottom face of
tibia and the load is applied over the top of the tibia as shown in figure 5.2.
Figure 5.2: Tibia-peg model applied with load and boundary conditions

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5.3 Bone remodelling simulation using Python script
The bone remodelling process was discussed in chapter 1. As discussed there, the hypothesis
is that, if there is an increase in strain energy density, there will be formation of bone, and a
decrease in strain energy density causes bone resorption. The algorithm used to implement
the bone-remodelling strain energy hypothesis in the finite element simulation is illustrated in
figure 5.3 below (it is discussed further below in next page).

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Figure 5.3: Flow chart for bone remodelling simulation

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The algorithm used is as follows (see figure 5.3): The job file is created and the model is
submitted for analysis. After the completion of the job, the output database file generated is
opened. The strain energy density values for each element in the cancellous list are read. If
the strain energy density value for any particular element exceeds a particular threshold
range, the Young’s modulus of that element is increased whereas, if it falls below the
threshold range, the Young’s modulus of the element is reduced. The result is that, if the
strain energy density is high (which corresponds to a high strain, if the stress is fairly
constant), above the threshold, the Young’s Modulus increases (the bone stiffens), the strain
is reduced and the state is brought back down towards the threshold (and vice versa for the
low strain energy density) After updating the material properties a new job file is created and
submitted for analysis. The simulation is executed for as many iterations as are required (each
iteration can be thought of as one step in time, or as one loading cycle). In this project, it was
found that 5 iterations produced quantifiable results. The job files created are named
according to the number of the iteration running, in order to view changes in the bone model
sequentially. After the completion of five iterations the ABAQUS file is saved. The Python
script file is shown in Appendix 1.
5.4 Simulation results
The .odb files are opened in in the Visualisation window. The view cut is made in the x-z
plane. The results for all three pegs are arranged sequentially and illustrated in figure 5.4 in
page below.

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Figure 5.4: The view cut in x-z plane
In the previous chapter, using the block model, the circular peg was determined to have a
higher strain energy density distribution (in the vicinity of the peg) as compared with the
other designs. These results are in contrast to those obtained here for the bone model, as can
be seen in figure 5.4. The simulation results for the bone model indicate high strain energy
when using a triangular peg as compared to a square or circular peg. It can be noted that, for
all the designs, there is a gradual decrease in strain energy density throughout the iterations
until the end of each simulation is reached. The strain energy density patterns are similar for
different planes cut through the bone model, through the peg.

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The highest strain energy density for the circular peg is observed in step-1. The grey region
represents the highest value in the ESEDEN plot. This region is observed in relatively few
areas away from the tip of the peg. The red and orange contours are observed in areas closer
to the tip of the peg and are surrounded by a yellow region. Step 4 is totally devoid of any
grey region. The orange contour at the centre of circular peg in step-1 starts changing to
green towards step-5. There is a notable decrease in strain energy density at the tip of the
circular peg where shades of orange and yellow are present. There is decrease in strain energy
density in the central region around the circular peg (it starts with yellow in step-1 and ends
with green in step-5).
For the square peg, the grey region is larger than for the circular peg. In step-1 it is present
closer to the red contours which are found at the tip of the peg. The centre of the peg region is
surrounded by contours of red whereas the central region of the peg is surrounded by regions
of yellow. In step-4 the green region creeps inside the yellow region. This denotes there is a
decrease in strain energy density values at the regions around the centre of the square peg. In
the final step the grey region is removed and it is replaced with regions of red. The peg is
now surrounded by regions of orange. This denotes the strain energy density has reduced
from step-1 to step-5. When compared to the circular peg, there is no notable difference in the
regions around the centre of the peg. But the tip of the square peg has a higher strain energy
density than the circular peg.
The triangle peg has the highest strain energy density when compared to other designs. In
Step -1 the grey region is around the tip of the peg. The central regions around the pegs have
contours of red which indicate a high strain energy density when compared to the square and
circular pegs. The tip of the triangular peg is devoid of grey regions towards the end of step-4
and it moves away. The region around the tip is dominated by red contours unlike those seen
in the circular peg. In the final step the central regions around the square pegs have regions of
red and yellow. This is high in comparison to the contours found in the circular peg. The
region after the cortical section is dominated by thin contours of green followed by yellow.
This shows the triangular peg has a higher strain energy density in the desired regions of
interest.
From the discussion it is clear that there is a notable difference between the triangular peg
and other designs.

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The contrast of the results presented here and those from the previous chapter is attributed to
the geometry of the bone model and also the presence of a cortical section in the bone (recall
that, with the simple block models, there was only a uniform bone/block structure, not an
outer stiffer layer corresponding to cortical bone). In order to investigate the region where the
peg enters the bone, the bone model is viewed in y-z plane to get a clear view of the region.
The view from all the steps is illustrated in the figure 5.5 below.

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Figure 5.5: The view from y-z plane
From the above results, there is no significant change in strain energy density values between
each iteration/step for each design. There are very minor changes in one or two elements
between each step. In order to help determine the peg with the highest strain energy density,
the results from the final step are magnified and presented in figure 5.6 below.

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Figure 5.6: Strain energy density results from the final step
It is very evident from the above figure that the strain energy density is higher for the circular
and triangular pegs when compared to square peg. The regions of high strain energy (grey)
are found around the circular and triangular peg whereas the square peg is surrounded with
regions of blue, green and red. When comparing the triangular peg with the circular peg, we
can clearly observe that the regions of red are found around the circular peg. The strain

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energy density values are a bit higher for the triangular peg when compared to the circular
peg.
5.5 Strain energy density at selected nodes
The change in strain energy density at selected nodes is tracked from the initial iteration to
the final iteration. The elements are selected at the areas of significance in the bone model.
Three elements were selected: at the region where the peg enters the cancellous section of the
bone model, below the peg and at the tip of the peg. The elements selected in the bone model
are marked in figure 5.7 below.
Figure 5.7: The element ID of the nodes observed
The elements were manually selected and their element ID is noted using the ‘Query’ tool.
Using the element ID the strain energy density is observed for each of design of the peg. The
change in strain energy density for each design at each of these elements is plotted in figures
5.8-5.10. The strain energy is plotted as a function of the number of iterations. The values for
the circular peg are denoted in blue, the triangular peg is denoted in orange and the square
peg is denoted by green.

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Figure 5.8: The strain energy and iteration plot for element ID 97
Figure 5.9: The strain energy and iteration plot for element ID 1698

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Figure 5.10: The strain energy and iteration plot for element ID 28499
In element ID 1698 (tip of the peg), the triangular peg has the highest strain energy density
when compared to all other designs. However the strain energy density for the square peg at
element ID 97 is higher than for the triangular peg. The simulation results observed
previously showed the strain energy density around the pegs in the cortical section of the
bone. However the strain energy density for pegs at all element IDs decreases towards the last
step of the iteration.
From the above simulations we can conclude that the triangular peg has a higher strain
energy density in the regions of interest. It is predicted that the triangular peg will have more
bone growth in those regions. This is followed by the square peg with the circular peg having
least bone growth around it. This would seem to suggest that the triangular peg will help with
osteointegration, more so than the other designs.
It should be mentioned that the thresholds used for the bone growth/resorption analysis are,
essentially, unknown. Sensible limits were chosen so that bone growth/resorption was
observed. Strain energy density value is noted at the observing node under normal loading
conditions without the peg. And the limits for bone resorption/growth was set based on this
value. The analysis must be run and the results tested experimentally for validity. A full
osteointegration experimental study would be necessary for this, for example a 10-week

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study of peg osteointegration in live animal studies. However, this was outside the scope of
this project. The purpose here was to estimate in a straightforward way the likelihood of one
design promoting osteointegration over other designs, based on the strain energy density
thresholding bone-remodelling hypothesis. The analysis seems to suggest that the triangular
peg would be best, based on this single criterion at least, and that all pegs will show some
loosening over time.
5.6 Peg hole with square pegs
Figure 5.11: The strain energy density around the square peg with holes

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The square pegs were re-designed with holes and analysed whether there is any change in
strain energy density. The bone remodelling process was simulated. From the above figure
5.11 it is clear that the strain energy density increased significantly.
It is reported that porous Tantalum coatings increased volume of tissue ingrowth and
considerably reduced stress shielding (Josa A. Hanzlik 2013). This result indicates that the
size and the structure of these pores play an important role in safe and early bone growth.

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5.7 Chapter summary
 The bone model is imported into ABAQUS.
 The cortical section of the bone is created using Python scripts.
 Sections are created for each element in the model to facilitate changes in material
properties (stiffness) during the bone remodelling simulation.
 If the strain energy density value for any element is beyond the threshold range the
material property of the element is changed. If it exceeds the threshold range, the
Young’s modulus is increased, and if it is below the threshold range, it is decreased.
 From the simulations, it is observed that the triangular peg has a higher strain energy
density distribution in its vicinity, followed by the square and then the circular peg.
 All pegs show a gradual decrease in strain energy, suggesting that there will perhaps
be some loosening of the pegs over time.
 The square peg with holes was designed and subject to bone remodelling simulation.
The strain energy density was found to be high when compared to other designs and
this indicates the porous surface over the pegs will have higher strain energy density
than normal pegs.

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Chapter 6
Conclusion
6.1 Thesis summary and conclusions
In this project, a number of different types of fixator for fixing plates to knee bone were
analysed and compared; pegs with different cross-sectional geometries (circular, square and
triangular) were tested. The fixators were designed and developed using SOLIDWORKS
CAD software and subjected to Finite Element Analysis using ABAQUS. Bone remodelling
was simulated using strain energy thresholding concepts, through the execution of python
scripting in conjunction with ABAQUS. The analysis and results showed that the triangular
geometry tended to encourage the most bone deposition and growth around the fastener,
indicating a longer life-span than the other designs, before any loosening might occur.
6.2 Future work
There are a number of ways in which the present work can be extended, to help us better
understand fixators and osteointegration, and to determine the most suitable fastener for the
plates of the novel knee prosthesis discussed in this thesis.
First, it is recommended that a full-scale experimental program be conducted. A number of
pegs of each design would be driven into bone and tested for pull-out strength (through
straight pull-out, shearing and fatigue). A sufficient number of pegs would be tested to make
the findings statistically significant and variability (in, for example, thickness of cortical
bone) would be accounted for. The results would indicate whether the designs gave the same
order of strength, or better, than conventional orthopaedic screws.
A more sophisticated testing program would involve live sheep trials. Pegs could be used to
fasten plates to the bone and the bone could be examined after 6-10 weeks for signs of
osteointegration or bone resorption.
The designs themselves can also be improved and enhanced. For example, the pegs could be
coated in a porous surface. This would have two effects:

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1. It would encourage osteointegration through bone growth into the meshing of the peg
(for example, it is reported that porous Tantalum coatings increase volume of tissue
ingrowth and considerably reduce stress shielding (Josa A. Hanzlik 2013)), and
2. When driven into the bone, the meshing would aid fixation through being “squeezed”.
Numerical modelling of meshed pegs would be challenging, since the scale of such pores is
small, and would have to be modelled and meshed. However, as an indication of what may
result can be garned from simple models of pegs with larger holes, as shown in the figure
below. For example, in this example, there is an increase in strain energy density when
compared to the results for the square pegs discussed in chapter 5. Future work could focus
and refine such studies.
Another area where this work can be extended is through the integration of “macro” Finite
Element modelling and “micro” modelling of bone. The macro FEA model can be used to
determine the macro stress and strain fields. These can be fed into micromechanical models
of bone, where bone remodelling can be carried out with a more physical basis. The bone
remodelling at this scale can then feed back into changes in the stiffness of the macro model.
This and similar research will help us understand fixators and osteointegration more
clearly, with the ultimate objective of choosing the most appropriate fixator for the
purpose required.

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6.3 Chapter summary
 A number of different types of fixator for fixing plates to knee bone were analysed
and compared.
 The analysis and results showed that the triangular geometry tended to encourage the
most bone deposition and growth around the fastener.
 There are a number of ways in which the present work can be extended.
 A full-scale experimental program be conducted involving live sheep.
 Another area where this work can be extended is through the integration of “macro”
Finite Element modelling and “micro” modelling of bone.

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Appendix
Python script
from part import *
from material import *
from section import *
from assembly import *
from step import *
from interaction import *
from load import *
from mesh import *
from job import *
from sketch import *
from visualization import *
from connectorBehavior import *
from odbAccess import *
import numpy
# Accessing the .cae file and the bone part
mdb=openMdb('square_cortical')
model = mdb.models['Model-1']
partName = 'Bone'
corticalElementLabelList = []
corticalNodeLabelList = []

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modelElements = model.parts[partName].elements
num_model_elements = len(modelElements)
print "CHECKING PROGRESS OF FINDING SURFACE ELEMENT NODE VERTICES"
index_list = [0,1,2]
# Finding the surface elements
for i, element in enumerate(modelElements):
adjacentElements = element.getAdjacentElements()
if len(adjacentElements) < 4:
curr_elem_edges = element.getElemEdges()
for edge in curr_elem_edges:
edgeNodes = edge.getNodes()
xCoords = [node.coordinates[0] for node in edgeNodes]
yCoords = [node.coordinates[1] for node in edgeNodes]
zCoords = [node.coordinates[2] for node in edgeNodes]
most_variant_dim = numpy.argmax([numpy.max(xCoords) -
numpy.min(xCoords), numpy.max(yCoords) - numpy.min(yCoords),
numpy.max(zCoords) - numpy.min(zCoords)])
coord_argmax_dim_list = [node.coordinates[most_variant_dim] for
node in edgeNodes]
temp_index_list = list(index_list)
temp_index_list.remove(numpy.argmax(coord_argmax_dim_list))
test_coord_argmax_dim_list = [coord_argmax_dim_list[j] for j in
temp_index_list]
test_coord_argmax_index =
numpy.argmax(test_coord_argmax_dim_list)

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remove_node_label =
edgeNodes[temp_index_list[test_coord_argmax_index]].label
for node in edgeNodes:
if node.label != remove_node_label:
corticalNodeLabelList.append(node.label)
del remove_node_label
print float(i)/num_model_elements
print "CHECKING PROGRESS OF FINDING SURFACE ELEMENTS"
# Elements attached to surface elements
for i, element in enumerate(modelElements):
curr_elem_edges = element.getElemEdges()
detect_node_list = []
for edge in curr_elem_edges:
edgeNodes = edge.getNodes()
xCoords = [node.coordinates[0] for node in edgeNodes]
yCoords = [node.coordinates[1] for node in edgeNodes]
zCoords = [node.coordinates[2] for node in edgeNodes]
most_variant_dim = numpy.argmax([numpy.max(xCoords) -
numpy.min(xCoords), numpy.max(yCoords) - numpy.min(yCoords),
numpy.max(zCoords) - numpy.min(zCoords)])
coord_argmax_dim_list = [node.coordinates[most_variant_dim] for
node in edgeNodes]
temp_index_list = list(index_list)
temp_index_list.remove(numpy.argmax(coord_argmax_dim_list))
test_coord_argmax_dim_list = [coord_argmax_dim_list[j] for j in
temp_index_list]

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test_coord_argmax_index = numpy.argmax(test_coord_argmax_dim_list)
remove_node_label =
edgeNodes[temp_index_list[test_coord_argmax_index]].label
# Creating sections for cortical and cancellous elements
for node in edgeNodes:
if (node.label != remove_node_label) and (node.label not in
detect_node_list):
detect_node_list.append(node.label)
del remove_node_label
all_nodes_in_list = 0
for nodeLabel in detect_node_list:
if nodeLabel in corticalNodeLabelList:
all_nodes_in_list += 1
elementLabel = str(element.label)
curr_elem_set = model.parts[partName].SetFromElementLabels('SET_' +
elementLabel, [element.label])
curr_elem_mat = mdb.models['Model-1'].Material('MAT_' +
elementLabel)
if all_nodes_in_list == 4:
corticalElementLabelList.append(element.label)
curr_elem_mat.Elastic(table =
model.materials['Cortical'].elastic.table)
else:
curr_elem_mat.Elastic(table =
model.materials['Bone'].elastic.table)
model.HomogeneousSolidSection(name = 'SEC_' + elementLabel,
material = 'MAT_' + elementLabel)

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model.parts[partName].SectionAssignment(sectionName = 'SEC_' +
elementLabel, region = curr_elem_set)
print float(i)/num_model_elements
model.parts['Bone'].SetFromElementLabels(name='corticalElementLabels
', elementLabels=corticalElementLabelList)
print "sections created";
# Specifying number of loops the simulation should run
i=0
while(i<5):
print "job creating";
# printing job
# Naming the .odb file. The name of the file is followed by
iteration number
jobname = 'square_cortical_feb5_1' +str(i)
myJob = mdb.Job(name=jobname, model=model)
myJob.submit()
myJob.waitForCompletion()
odb=openOdb(jobname + '.odb')
print "job created";
eseden_values = odb.steps['Step-
1'].frames[1].fieldOutputs['ESEDEN'].values
print "eseden values read";
# Reading strain energy density values from .odb file
for eseden_val in eseden_values:
if partName.upper() in eseden_val.instance.name:
elementLabel = str(eseden_val.elementLabel)

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if eseden_val.elementLabel not in corticalElementLabelList:
eseden_data = eseden_val.data
# Defining the ESEDEN threshold values
if eseden_data > 0.00001:
curr_matProp_table = model.materials['MAT_' +
elementLabel].elastic.table
curr_E = curr_matProp_table[0][0]
curr_E += 10
curr_matProp_table = ((curr_E, curr_matProp_table[0][1]),)
model.Material('MAT_' + elementLabel).Elastic(table =
curr_matProp_table)
elif eseden_data < 0.000001:
curr_matProp_table = model.materials['MAT_' +
elementLabel].elastic.table
curr_E = curr_matProp_table[0][0]
curr_E -= 10
curr_matProp_table = ((curr_E, curr_matProp_table[0][1]),)
model.Material('MAT_' + elementLabel).Elastic(table =
curr_matProp_table)
print "property changed";
i=i+1
mdb.save()
print "cae saved";

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