Final Year Project 2015

Manchester Metropolitan University Faculty of Science and Engineering

Effects of Exercise on Artificial Hip Joints

Author

Richard Turner

Supervisor

Dr Kirstie Andrews

Unit Code: 6E6Z2001_1415_9Z6

Date Submitted: 31/3/15

2

Acknowledgements

I would like to thank Dr Kirstie Andrews for her help and guidance throughout this project and Dave

Ingham of Zimmer Orthopaedics for providing information on prosthesis components.

3

Summary

This report provides an investigation into the effects of exercise on artificial hip joint prosthesis

components. Using finite element analysis, a Charnley-style femoral stem and acetabular cup were

simulated using peak loads and angles of flexion when the body is in walking, jogging, and cycling

motion. The components were modelled using a range of materials to determine the optimum

combination of material choice for the femoral head and acetabular cup.

Results from the simulations showed that for high impact exercises with low repetition of movement, a

stainless steel femoral stem and cobalt chromium acetabular cup was the optimum combination to

prevent failure from excessive displacement and cracking in the components. For low impact exercises

with highly repetitive movement, a titanium alloy (Ti-6Al-4V) femoral stem and ceramic acetabular

cup was the optimum combination to prevent failure from excessive wear-rate of the prosthesis.

4

PROJECT MANAGEMENT REPORT 2015

CONSULTATION WITH YOUR PROJECT SUPERVISOR

September: 29 October: 6, 13, 20, 27 November: 3, 10, 17, 24

December: 1, 8, 19 January 12, 19, 26 February 2, 9, 16, 25

March: 2, 9, 16, 23

INITIATIVE

Made contact with employee of Zimmer orthopaedics to discuss prosthesis models and

materials.

Modelled hip prosthesis in two components as opposed to a complete assembly to overcome

simulation limitations.

Converged the model to find the optimum mesh size to produce the most accurate results.

NEW TECHNIQUES

Improved CAD skills and learnt how to conduct FEA on a range of components.

Used free body diagram to analyse forces present on the hip to use as values for simulation.

Using two result plots of convergence graph to identify anomalies.

CREATIVITY & INNOVATION

Used CAD to produce a scale model of an acetabular cup component to be used in

conjunction with femoral stem for simulation.

Determined angle at which resultant force at hip will act relative to the ground and

calculated the magnitude of resultant force in terms of bodyweight.

Designed method of calibrating CAD model for any exercise providing the angle of flexion

and peak load is known.

5

Contents

Nomenclature 9

Table of Figures 8

Table of Tables 10

Introduction 11

Aim 12

Objectives 12

Background

The Hip Joint 13

History of Hip Arthroplasty 16

Modern Day Hip Arthroplasty 18

Variations of Prostheses 20

Materials of Components 21

Life After Surgery 26

Method 27

Methodology

Forces Acting on Hip Joint 28

Effects of Exercise on Natural Hip 32

CAD Model

Stem Dimensions 35

Cup Dimensions 36

Finite Element Analysis

Assembled Model 37

Set-Up 38

Convergence 40

Configuration of Components for Exercise 42

Simulation Plots 44

Results 47

6

Interpretation of Results 48

Errors 51

Discussion 52

Conclusion 53

Future Work 54

References 56

Appendices 59

Preliminary Report 60

Weekly Record Sheet 69

Ethics Form 71

Risk Assessment Form 74

7

Nomenclature

𝑊 Total weight of body.

[N]

𝑚 Total mass of body.

[kg]

𝐹𝑅 Resultant force acting on hip.

[N]

𝐹𝐴 Net abductor muscle force.

[m]

𝐶 Centre of femoral head.

[-]

𝐿 Perpendicular distance from centre of femoral head to the point at

which resultant bodyweight acts on hip joint.

[N]

𝑟 Perpendicular distance from centre of femoral head to the point at

which net abductor muscle force acts.

[m]

𝛼 Angle at which net abductor force acts from the vertical.

[°]

𝜃 Angle at which resultant force acts from the horizontal.

[°]

𝛽 Angle at which femur acts from the vertical.

[°]

8

Table of Figures

Figure 1 The hip joint. [6] ..................................................................................................................... 13

Figure 3 Posterior view of hip joint. [6] ................................................................................................ 14

Figure 2 Anterior view of hip joint. [6] ................................................................................................ 14

Figure 6 Mckee-Farrar prostheses. [14] ................................................................................................ 16

Figure 7 Original Charnley prosthesis. [17] .......................................................................................... 17

Figure 8 Cross section of cemented stem in femur. [18] ...................................................................... 18

Figure 10 Substantial bone still attached to the acetabular component after revision surgery. [22] ..... 19

Figure 9 Osseointegration of bone. [21] ............................................................................................... 19

Figure 11 Comparison of cemented and uncemented methods of fixation. [25] .................................. 19

Figure 13 Prosthesis in position. [27] ................................................................................................... 20

Figure 12 McKee-Farrar prosthesis components. [27] ......................................................................... 20

Figure 14 Charnley prosthesis used to replace damaged hip joint. [29] ............................................... 20

Figure 15 Stress distribution of natural femur. [30] .............................................................................. 21

Figure 16 Stress distribution of hip prosthesis. [30] ............................................................................. 21

Figure 18 Ti-6Al-4V 40% porosity. [33] .............................................................................................. 22

Figure 17 Cancellous bone. [32] ........................................................................................................... 22

Figure 23 Ceramic on ceramic bearing. [41] ........................................................................................ 24

Figure 25 Comparison of wear rates for bearing materials. [36] .......................................................... 25

Figure 26 Free body diagram of hip joint in one-legged position. [51] ................................................ 29

Figure 27 Visualisation of forces acting on body when walking.[52] .................................................. 31

Figure 28 Planes of body. [54] .............................................................................................................. 33

Figure 29 Angle of flexion of hip. [55] ................................................................................................... 33

Figure 30 Average hip angle during gait analysis using a three dimensional musculoskeletal model

(Effect of hip angle on anterior hip joint force during gait, Lewis CL, Sahrmann SA, Moran DW,

2010.) .................................................................................................................................................... 33

Figure 31 Hip flexion-extension angle during gait cycle of human running. (Biomechanical Basis of

Human Movement, Hamill J, Knutzen KA, 2008, p. 365) ................................................................... 34

Figure 32 Hip flexion-extension angle range for cycling and other methods of activity. (Comparison

of elliptical training, stationary cycling, treadmill walking and overground walking, Damiano DL,

Norman T, Stanley CJ, Park HS, 2011 ................................................................................................. 34

Figure 33 Side view of assembled prosthesis showing angle of flexion. .............................................. 37

Figure 37 Fixed geometry on shaft and underside of flange of femoral stem. ..................................... 38

Figure 36 Fixed geometry on outer surface and ridges of acetabulum cup. ......................................... 38

Figure 43 Stem with 1.5mm mesh. ....................................................................................................... 40

Figure 42 Stem with 5mm mesh. .......................................................................................................... 40

Figure 44 Probing neck of femoral stem at split-line intersections....................................................... 40

Figure 45 Graph of convergence plot. .................................................................................................. 41

Figure 47 Resultant force position on femoral head. ............................................................................ 42

Figure 48 Resultant force position on acetabular cup. ......................................................................... 42

Figure 46 Visual configuration of components. .................................................................................... 42

Figure 51 Resultant force position on acetabular cup. .......................................................................... 42

Figure 53 Resultant force position on femoral head. ............................................................................ 43

Figure 54 Resultant force position on acetabular cup. .......................................................................... 43

Figure 55 Bar chart comparing max von Mises stress in femoral stem materials when under loading

from exercise. ........................................................................................................................................ 48

9

Figure 56 Bar chart comparing max von Mises stress in acetabulum cup materials when under loading

from exercise. ........................................................................................................................................ 48

Figure 57 Bar chart comparing max displacement in femoral stem materials when under loading from

exercise. ................................................................................................................................................ 49

Figure 58 Split bar chart comparing max displacement in acetabular cup materials when under loading

from exercise. ........................................................................................................................................ 49

Figure 59 Bar chart comparing max strain in femoral stem materials when under loading from

exercise. ................................................................................................................................................ 50

Figure 60 Split bar chart comparing max strain in acetabular cup materials when under loading from

exercise ................................................................................................................................................. 50

10

Table of Tables

Table 1 Summary of bearing materials. ................................................................................................ 25

Table 2 Properties of most common prosthesis materials. .................................................................... 25

Table 3 Comparison for activities with their corresponding peak loads. [51] ...................................... 32

Table 4 Resultant force for physical activity. ....................................................................................... 32

Table 5 Angle of flexion for physical activity. ..................................................................................... 34

Table 6 Convergence results. ................................................................................................................ 41

Table 7 Stress distribution values of femoral stem. .............................................................................. 44

Table 8 Stress distribution values of acetabular cup. ............................................................................ 44

Table 9 Displacement values of femoral stem. ..................................................................................... 45

Table 10 Displacement values of acetabular cup. ................................................................................. 45

Table 11 Strain values of femoral stem. ............................................................................................... 46

Table 12 Strain values of acetabular cup. ............................................................................................. 46

Table 14 Simulation results for jogging set-up. .................................................................................... 47

Table 13 Simulation results for walking set-up. ................................................................................... 47

Table 15 Simulation results for cycling set-up. .................................................................................... 47

Table 16 Stress distribution values of femoral stem. ............................................................................ 59

Table 17 Stress distribution values of femoral stem. ............................................................................ 59

11

Introduction

Total hip arthroplasty (THA) is a form of joint replacement surgery used to replace a painful or

dysfunctional hip joint with an orthopaedic prosthesis. In England and Wales alone, there are

approximately 160,000 joint replacement procedures performed each year, half of which are specific to

hips. [1]

Hailed as ‘The Operation of the Century’, THA has revolutionised the way severe hip problems are

treated, making it arguably the most successful orthopaedic procedure to date. With advances in

bioengineering technology and manufacturing methods, modern day prostheses are expected to last a

minimum of 15 years of use depending on the materials of the components and lifestyle of the patient.

[2]

THA has always been considered a procedure predominantly associated with old age, but more recently

there has been a large increase in younger people opting for the operation. [3] This is believed to be

because of modern lifestyle changes, such as the popularity of physical exercise, particularly impact

sports such as jogging.

Current hip prostheses are designed to cope with ‘normal’ levels of loading to restore mobility to the

patient and allow them to live a pain-free life. The standard procedure of THA is that the patient abstains

from strenuous physical activity in order to prevent complications and damage to the prosthesis. [4]

High levels of loading can ‘displace’ the components of the prosthesis, which over time can degrade

the method of bonding that fixes them to the bone surfaces. As a result of this, active patients find

themselves having to limit or discontinue their favourite sports and physical activity.

The ability to exercise is a liberty, and should remain so regardless if a person has a prosthetic hip. It is

simply not fair to expect patients to change their lifestyle, especially considering THA is intended to

improve the lives of patients. Furthermore, abstaining from physical activity promotes an unhealthy

lifestyle, which studies have shown can lead to health problems such as obesity, diabetes and heart

complications. [5]

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Aim

The aim of this project is to determine the combination of materials for components of a hip

prosthesis to prevent failure occurring from exercise-induced loading.

Objectives

Research the natural hip joint and its components.

Investigate the types of hip prostheses and where they originated from.

Investigate how the prosthesis is fixed to the body.

Explore materials of components of hip prostheses and their mechanical properties.

Research the material wear-rates of each material combination.

Investigate the effects of different types of exercise on the natural hip joint.

Design a CAD model of a prosthesis.

Simulate the model under loading from methods of exercise using finite element analysis.

Determine the stress, displacement and strain of the model using different materials.

Conclude the optimum material combination for the prosthesis for each type of exercise.

13

Background – The Hip Joint

The hip joint is a multiaxial or ‘ball and socket’ joint located between the femur and pelvis, used

primarily to support the weight of the body in both dynamic and static positions. It is the largest and

strongest joint in the body, comprised of two main components; the femoral head and the acetabulum.

[6]

The acetabulum is a spherical-like socket at the lower half of each side of the pelvis, and the femoral

head is the ‘ball’ of the joint situated at the top of the femur, fitting perfectly into the acetabulum.

Between these components lies a layer of hyaline cartilage which acts as a smooth surface for the two

bones to move past each other, additionally acting as a method of shock absorbance. Amidst the layers

of cartilage, synovial membranes secrete synovial fluid to lubricate the capsule of the joint. [6]

Surrounding the entire joint is a series of ligaments that provide stability and prevent the joint from

dislocating. These ligaments can be split into two categories; instrascapular (ligaments on the inside of

the joint) and extracapular (ligaments on the outer surface of the hip joint capsule). The only

instrascapular ligament is the foveal ligament, or ligament of head of femur. This ligament connects the

acetabulum to the femoral head. [6]

There are three extracapsular ligaments each serving a different function. The illofemoral ligament,

located anteriorly, prevents hyperextenion of the hip joint. The pubofemoral ligament, located anteriorly

and inferiorly, prevents abduction and extension. Finally the ischiofemoral ligament, located

posteriorly, prevents excessive displacement of the hip joint. [7]

Femoral head

Foveal ligament

Acetabulum

Acetabular labrum

Figure 1 The hip joint. [6]

14

Each hip joint must be able to support half the total body weight as well as any other external forces

acting upon the body. Impact sports, for example, can subject the joints to massive loading, far greater

than that of bodyweight alone. The main reason why the joint is able to bear such large loads is due to

the depth of the acetabulum itself. [6]

The acetabulum is very deep and encloses nearly all of the femoral head. This allows loads to be

dispersed directly through the joint and into the femur whilst preventing the femoral head from slipping

out of the socket. Around the outside of the acetabulum is a fibrocartilaginous ring which further

increases stability of the hip by providing a large contact surface area for the femoral head. This is

known as the acetabular labrum. [6]

Hip problems

The most common hip problem is osteoarthritis - a debilitating condition which causes a great deal of

pain and discomfort in the hip joint and surrounding area. Osteoarthritis occurs when the layer of

hyaline cartilage between the femoral head and acetabulum wears away or breaks down. When this

happens, bone on bone contact begins to develop between the two surfaces of the joint and the

surrounding tissue gets inflamed. Over time this can lead to stiffness and restricted movement of the

joint, rendering the hip dysfunctional. [8]

Iliofemoral

ligament

Pubofemoral

ligament

Ichiofemoral

ligament

Figure 3 Anterior view of hip joint. [6] Figure 2 Posterior view of hip joint. [6]

Figure 4 Healthy hip joint. [8] Figure 5 Osteoarthritic hip joint. [8]

15

Osteoarthritis is most common in elderly people and usually develops over 45 years of age, although

younger people can still be affected by the condition.

Another problem, particularly present in athletic individuals, is fracturing or breaking of the hip.

Although the hip uses many different methods to absorb shock, if an impact force from exercise or a

fall is significantly high, the hip may fracture or even completely break as it simply cannot disperse

the shock from the impact. Those who have osteoporosis of the hip are at a much higher chance of

this problem occurring as the bone is brittle, although this is much more prevalent in elderly people.

[9]

Other problems [10]

Femoral head and acetabulum rubbing together due to being abnormally shaped.

Rheumatoid arthritis (similar to osteoarthritis – a condition that causes swelling and stiffness

in the joint).

A tear in the acetabular labrum.

Hip dysplasia (defect of hip joint).

Inflamed ligaments.

Infection in the area.

Treating the problems:

For the most part, these problems can be managed using pain medication and anti-inflammatory

drugs. However, in severe cases such as when the hip has been fractured or cartilage has been

destroyed, surgical intervention is often required. There are multiple types of of hip surgery, each

used to fix a specific problem, but for complete replacement of the joint, a total hip arthroplasty is

required. [11]

16

History of Hip Arthroplasty

Arthroplasty as we know it has been around for over 100 years. The earliest recorded attempts at hip

replacement originated from Germany in 1891, where Professor Themistocles Glück proposed the use

of ivory to replace worn femoral heads that had been damaged by tuberculosis [12]. Since then, various

surgeons have contributed to the development of techniques and components used in THA, but none

are as renowned as Sir John Charnley. Charnley, a surgeon at the Manchester Royal Institution,

revolutionised the hip replacement surgery method through optimisation of the components and

decreasing infection from surgery. His techniques and knowledge of the subject have been taught

worldwide to many different nationalities of surgeons, and are still being taught to this day. [13]

Charnley’s prosthesis was based on a low friction design that reduced wear between the femoral head

and acetabulum of the prosthesis. Previously, surgeons had used large femoral heads, with poor long-

term results due to loosening of the joint caused by debris from friction. George Kenneth McKee, an

English orthopaedist, strongly believed the metal-on-metal configuration of the femoral head and

acetabular cup was the optimum material combination for longevity and functionality of the joint, and

that the synovial fluid in the joint was sufficient as lubrication for the prosthesis. His prosthesis was

based on a modified Thompson stem (a cemented hemiarthroplasty or ‘half arthoplasty’ prosthesis used

for fractures of the femur), and in 1961 produced the first mass production all-metal prosthesis with the

help of John Watson-Farrar. Termed the ‘Mckee-Farrar’ prosthesis, this cemented total hip replacement

was the first of its kind, and at the time was esteemed for its success. Charnley, however, was not

convinced. [14]

Charnley hypothesized that Mckee’s metal-on-metal prosthesis had a high frictional torque, and

predicted this would eventually loosen the components of the prosthesis over time. This inspired him

to look into using polymers as a low friction alternative to McKee’s all metal design. In the early 1950s,

Charnley attempted his first arthroplasty using a polytetrafluoroethylene (Teflon) bearing for a hip

resurfacing procedure. However, within two years, the components wore out. Charnley continued

working with Teflon for a further 10 years, over which time he had found that by using a smaller femoral

Figure 4 Mckee-Farrar prostheses. [14]

17

head there was less surface area for friction to occur in the joint, thus he could minimise the wear rate

of the prosthesis [14]. From the years 1958-1962 he fitted several hundred patients with different

diameter femoral heads, and found moderate success using a diameter of 22.225mm [15]. Nonetheless,

the unsatisfactory wear rates of Teflon were still prevalent, and so this presented him with a problem:

to find a material which not only has a low coefficient of friction, but is hard wearing and durable.

The breakthrough Charnley was looking for came that same year, when his assistant at the time, Harry

Craven, began experimenting with a material he had acquired from a sales technician – High Density

Polyethylene.

“John [Charnley] was going away to Zurich, I think it was, for about three weeks, and he came in and

said, ‘What are you testing?’ I replied, ‘Polyethylene’. ‘Throw the bloody stuff away,’ he said, ‘it’s no

good’. Anyway, I carried on testing it, and when he came back he asked what I was testing and I said,

‘The stuff you told me to throw away’. He asked for my graph, because I did a graph of everything I

did. ‘Well’, I said, ‘there’s your graph, a straight line all around the room and, from my figures, I have

calculated that it would last 70 years’.”

-Harry Craven on his first conversation with John Charnley about HDPE. [16]

Charnley’s third attempt at arthoplasty would be his last, where he settled with a cemented prosthesis

consisting of a HDPE acetabular cup and 22.225mm diameter femoral head. The results from this

prosthesis were unrivalled, and Charnley found great success using this in the elderly population. The

Charnley prosthesis, in essence, is the same prosthesis used today. [15]

Figure 5 Original Charnley prosthesis. [17]

18

Figure 6 Cross section of cemented stem in femur. [18]

Modern Day Hip Arthroplasty

Today’s prostheses are designed and manufactured to suit each patient’s specific needs. Produced in a

multitude of sizes and custom dimensions, prostheses are sold in three main categories; cemented,

uncemented, and hybrid.

Cemented, or press-fit prostheses, use an acrylic thermosetting polymer called

polymethylmethacrylate (PMMA) to fix the prosthesis components to the respective bone surface. In

order to achieve a good bond between the bone and cement, the surgeon will remove debris from the

area with a high pressure washer and dry the surfaces thoroughly. The cement is inserted into the

femur and forced into the spaces between the bony spicules where it is left to set under pressure. The

setting of the cement is somewhat temperamental as if the prosthesis is inserted too early, the cement

will not have cured or cooled which risks damaging the bony spicules of the inside of the femur, but

leave it too late and the prosthesis will not fix well to the cement. The cemented bond provides a

durable and reliable permanent fixation to the prosthesis. Patients can usually apply full bodyweight

to the hip and walk without support within three to six weeks of surgery. [18]

The main complication of cemented hip implants is the risk of the cement coming loose and breaking

away from the components of the prosthesis displacing. Not only can this loosen the prosthesis, but

the cement debris can irritate surrounding tissue and cause inflammation in the area. The problem

with this is when revision surgery is required. Once the cement has set, it becomes extremely hard and

very difficult to remove from the bone surface. In the occurrence where cement does have to be

removed from the bone, bone itself is often removed as a by-product of the process. Repeated revision

surgery will decrease the chance of a successful hip implant. [19]

The uncemented prosthesis is a work of modern times. The implants are designed in such a way that

the bone itself is the only source of fixation for the components of the prosthesis, with no external

bonding required. This is achieved by porous surfaces on the components of the implant which allow

Periosteum

Cancellous bone

Compact bone

Bone cement

Bony spicules

Shaft of prosthesis

19

for bone ingrowth, or osseointegration, which gets stronger as time goes on. The bonding surfaces are

usually coated with hydroxyapatite (HA) to provide a biological interface between the metal and bone

to enhance fixation. [20]

As there is no cement used in the prosthesis, the uncemented method eradicates all problems associated

with cemented implants. Younger patients with active lifestyles are generally given uncemented

implants as there is more chance of cement breaking away due to increased and more frequent loading.

The main disadvantage of an uncemented hip implant is the possibility of poor bone fixation. If this

happens, the implant will not be properly attached to the corresponding bone surfaces which can result

in loosening. Patients with uncemented implants are usually told to wait at least eight weeks before

applying bodyweight to the replaced hip(s) to ensure there is sufficient osseointegration of the bone.

[23] On the contrary, if for whatever reason the prosthesis, or components of, need to be removed, large

quantities of bone are also removed in the process due to the strong bond. Uncemented hip implants are

generally more expensive than cemented due to the manufacturing methods required to achieve the

correct surface porosity of the metal. [24]

The third type of prosthesis, the hybrid implant, combines a cemented component (usually femoral

stem) with an uncemented component. This prosthesis is a compromise between the conventional

methods of fixation to reduce the amount of cement used to secure the implant, thus reducing the

chance of loosening. [18]

Figure 8 Osseointegration of bone. [21] Figure 7 Substantial bone still attached to the

acetabular component after revision surgery. [22]

Figure 9 Comparison of cemented and uncemented methods of fixation. [25]

20

Variations of Prostheses

Each prosthesis varies based on the manufacturer’s preferences but generally follow a design based on

the McKee-Farrar and Charnley implant.

A modern day McKee-Farrar-inspired prosthesis can consist of up to 4 components; implant shaft,

femoral head, acetabular cup, and an optional acetabular cup liner to reduce friction in the joint. The

prosthesis is designed to best imitate a natural hip joint, using a large femoral head to maximise stability

for the patient [26].

Like the original prosthesis John Charnley created, the ‘Charnley’ prosthesis as it is known today

consists of two main components; a shaft with femoral head (usually as one-piece and made of a form

of metal) and acetabular cup. The distinguishing factor of these implants is the much smaller femoral

head (22-23mm) [28]

The femoral head and acetabulum of the prosthesis can be referred to as a bearing as the surfaces of

these components essentially glide over each other to allow movement. The femur of the prosthesis is

referred to as a shaft or stem.

Acetabular cup

liner

Femur/shaft

Femoral head

Figure 11 McKee-Farrar prosthesis components. [27] Figure 10 Prosthesis in position. [27]

Figure 12 Charnley prosthesis used to replace damaged hip joint. [29]

21

Materials of Components

Stem

The main requirements of a material for the stem of a hip prosthesis are high strength, high hardness

and high toughness. Metals are the most suitable material for this application as they have higher values

of Young’s Modulus and are ductile, meaning they have a good resistance to fatigue and will yield

before breaking. In the case of ceramics or other materials with lower ductility, sudden breaking will

occur under loading with no warning or anticipation of it happening. Plastics are also unsuitable to be

used for implant stems due to their low resistance to fatigue. [30]

For a long time, the go-to choice for the material of the implant stem was stainless steel. In the early

days of arthroplasty, stainless steel was regarded as the best material choice due to its high resistance

to corrosion, hardness and strength. However, as stainless steel is an alloy of nickel, it poses the risk of

complications with patients who have nickel allergies. [30] Another complication with stainless steel is

a result of its high Young’s modulus, where stresses from loading are transmitted along the stem as

opposed to being distributed evenly as is the case with cancellous bone. This is known as stress

shielding. The consequence of this is the bone adapting to this change through a reduction in density,

or bone resorption. [31]

Cobalt-chromium-molybdenum (Co-Cr-Mo) has somewhat replaced stainless steel due to its increased

wear resistance and strength, but the high hardness of the material makes it is much more difficult to

machine, therefore increasing the cost of the metal. A small percentage of patients that receive these

implants will have allergic reactions to the cobalt and chromium which is a cause for concern. Another

downside of Co-Cr-Mo is the risk of metal poisoning, especially when used in a two-piece prosthesis

with a Co-Cr-Mo acetabular cup. [30]

Stress distribution

Stress transmitted

through femur

Less stress

transmitted through

femur

F F

Figure 13 Stress distribution of natural

femur. [30]

Figure 14 Stress distribution of hip

prosthesis. [30]

22

Titanium alloys have become the most common stem material due to its high strength, hardness,

corrosion resistance and biocompatibility. Out of all metals, titanium is considered the most

biocompatible due to its ability to stay inert inside in the body and its compatibility with

osseointegration for use in uncemented stems. Titanium also has a very high strength to weight ratio

and a Young’s modulus value much closer to that of natural bone, thus reducing stress shielding in the

femur. Instead of using commercially pure titanium, elements aluminium and vanadium at 6 and 4

percent by respective weight are used to increase toughness and improve resistance to fatigue. This

alloy of titanium is known as Ti-6Al-4V. A large downside with titanium is the cost – at almost 5 times

the price per kg than that of stainless steel it works about out to be almost three times as expensive for

the same sized stem. A huge advantage with titanium is the ability to control its porosity in the

manufacturing process. When the alloy is being treating during sintering, air can be formed in the

molten metal to create a sponge-like structure. A porosity of 40% creates a material with properties

very similar to that of the cancellous bone structure of the femur, known as Ti-6Al-4V 40% porosity.

[30]

Figure 16 Cancellous bone. [32] Figure 15 Ti-6Al-4V 40% porosity. [33]

Figure 19 Young’s Modulus – Density materials comparison. [30] Figure 20 Young's Modulus - Fracture Energy materials

comparison. [30]

23

Bearings

Modern day bearings are manufactured using state of the art materials and highly advanced

manufacturing processes. There are a large number of material configurations on the market, each

serving a specific purpose or application. Manufactures of hip prostheses generally base their bearings

on four basic material categories:

Metal on plastic (Me-on-PE)

Metal on metal (Me-on-Me)

Ceramic on ceramic (C-on-C)

Ceramic on plastic (C-on-PE)

Metal on plastic bearings are the longest tried and tested material combination. Ever since John

Charnley discovered the potential orthopaedic applications of high density polyethylene, the Me-on-PE

configuration has grown to succeed nearly all other bearing surfaces. The current plastics used for these

bearings are ultra-high molecular weight polyethylene (UHMWPE) and ultra-high cross-linked

polyethylene (XLPE), both very reliable and stable materials which are cost effective. [34]

Despite the advances in polyethylene from the 1950’s, this material combination is notorious for its

high material wear rate, at least when compared with other bearings. The debris caused from the

polyethylene may cause osteolysis in the femur and pelvis which occurs when foreign particles and

bodies in the area are seen as a source of infection, and over time the bone is dissolved from the body’s

natural defence mechanism. [36]

In metal on metal prostheses, both the femoral head and acetabular cup are made of a wear resistant

metal such as a cobalt chromium alloy. Cr-Co-Mo is the most popular alloy, with molybdenum added

to the metal to increase wear resistance and hardness of the component. This alloy is far more wear

resistant than any form of polyethylene which makes this bearing a popular choice for many surgeons.

[35]

Metal on metal bearings are somewhat controversial in the orthopaedic industry due to evidence that

suggests these bearings cause metal poisoning, or metallosis. [35] When the metal components of the

prosthesis wear away, they produce debris in the form of soluble particulates, known as metal ions.

These ions are absorbed into the bloodstream and cause damage to the surrounding tissue, bone, and

24

nervous system. Over time this can lead to deterioration of the hip and ultimately implant failure. This

is especially prevalent in the case of large femoral heads with increased wear rate. [37]

One example of how catastrophic the effects of metallosis can be in metal on metal implants is the 2010

DePuy recall. On the 24th of August, 2010, the orthopaedic company DePuy issued a voluntary recall

of two of their most popular metal on metal implants; the ASR™ XL Acetabular Hip System and the

ASR™ Hip Resurfacing System. [38] The company received approximately 300 complaints from

patients who had been given ASR implants since 2008, and data from the UK joint registry in 2010

revealed that approximately 13% of all ASR patients had undergone revision surgery within 5 years of

their operation. The main complications patients experienced were loosening components, metal

sensitivity, pain, and increased metal ions in the blood, resulting in nerve damage, necrosis and tissue

damage. There are currently lawsuits ongoing between DePuy and the effected people involved. [39]

Ceramic on ceramic bearings are primarily used in very active and/or younger individuals due to the

incredibly low wear rates of the material, often alumina (aluminium oxide) or zirconia (zirconium

oxide), known as OXINIUM in the orthopaedic industry. [40] The main concerns with ceramic on

ceramic bearings is the possibility of cracking, chipping and squeaking occurring in the prosthesis. Over

the years, the materials used in ceramic prostheses have vastly improved, which have greatly reduced

the cracking and chipping problems mainly associated with impact loads from exercise, but the

squeaking issues are still a cause of concern for some patients. Ceramic heads make up a total of half

the prostheses used in central Europe, but usage is much lower in the UK alone.

A Ceramic on plastic, or hybrid bearing, is a type of bearing which consists of a ceramic femoral head

and a plastic uncemented acetabular cup. The advantage of a hybrid bearing is that it offers a

compromise between the high hardness of C-on-C bearings and the reliability of polyethylene. Hybrid

prosthesis are particularly useful for younger patients as revision surgery using the uncemented

acetabular cup prevents bone loss of the acetabulum. [36]

Figure 21 Metal on plastic

bearing. [41] Figure 24 Ceramic on

plastic bearing. [41] Figure 22 Metal on metal

bearing. [41]

Figure 17 Ceramic on

ceramic bearing. [41]

25

Table 1 Summary of bearing materials.

Table 2 Properties of most common prosthesis materials.

Prosthesis Advantages Disadvantages

(Me-on-PE) -Renowned for its high

reliability.

-Cost effective.

-Most widely available

overall.

-The debris from the

polyethylene can lead to aseptic

loosening of the joint.

(Me-on-Me) -Durable and strong.

-Reduced wear than metal on

polyethylene.

-Danger of metallosis.

-Somewhat bad reputation in

the orthopaedic community.

(C-on-C) -Lowest friction bearing with

minimal wear and debris

-Theoretically posing the

longest lifespan.

-Improved lubrication.

-Most expensive out of all the

prostheses.

-Possibility of cracking and

fracturing due to brittle nature

of material.

-Squeaking may occur.

(C-on-PE) -Useful in younger patients

that may require revision

surgery in the future.

-Less wear rate than metal on

polyethylene.

-Very few trials performed on

this bearing.

-Lack of trials to support

theoretical advantages.

Component Material Property

Young’s

Modulus

(GPa)

Poisson’s

Ratio

Shear

Modulus

(GPa)

Mass

Density

(𝑘𝑔/𝑚3)

Tensile

Strength

(MPa)

Yield

Strength

(MPa)

Stem Stainless

Steel [42]

200 0.29 86 8000 505 215

Titanium Ti-

6Al-4V [43]

113.8 0.342 44 4430 950 880

Acetabular

cup

UHMWPE

[44]

0.7 0.46 0.32 926 48 21

Co-Cr-Mo

[45]

201 0.38 68 8430 758 345

Zirconia [46] 205 0.31 78.2 5740 450 276

0.1-0.5mm/year

0.0001mm/year

0.01mm/year

0.1mm/year

Figure 18 Comparison of wear rates for bearing materials. [36]

26

Life After Surgery

For the most part, life after a total hip replacement is very much the same as life prior to encountering

pain and restriction of the natural hip joint. The surgeon and/or orthopaedic unit that perform the

operation will often issue limitations and guidelines for the patient to follow as a method of reducing

complications after surgery.

One complication encountered by patients is subluxation and dislocation of the prosthesis. [47] If the

hip is bent past a certain angle, then depending on the size of the femoral head and acetabular cup, the

head may partly or completely exit away from the pelvis. Not only does this render the prosthesis

completely useless, but the force concentrations at the point of dislocation can damage the components.

As a result of this, patients are advised to not bend their leg(s) past a certain point to ensure the prosthesis

never approaches the critical angle of dislocation. [48]

A second complication is the danger of fracturing and cracking of the prosthesis components as a result

of high impact loads. High impact loads occur in situations where the normal reaction forces of the

patient’s bodyweight are multiplied either by an accident or a form of injury from exercise. Younger

patients who play sports or are physically active are at the highest risk of this problem occurring due to

the increased chance of being involved in such impacts. Exercises such as weight training, rugby, and

even jogging are all excellent examples of high impact sports. [49]

The third complication, again primarily concerning younger patients, is the reduced life of the prosthesis

due to increased wear rates of the component(s). This problem is a result of continuous, repetitive

movement of the prosthesis for long periods of time. An example an exercise which could cause this

problem is cycling, where the hip undergoes tens of thousands of cycles of movement in a relatively

short space of time. [49]

27

Method

1. Create a free body diagram of the body in one-legged position to calculate resultant force on

hip joint and angle at which it acts.

2. Research the peak loads of different exercises and activities and summarise these as resultant

force equations in terms of bodyweight.

3. Use data from a UK census or anthropometrics survery to calculate the resultant force of the

hip for a male of average weight when exercising.

4. Determine the angle the femur extends when the body is exercising.

5. Produce a scale model of a prosthesis using SolidWorks using dimensions of components

from reputable orthopaedic implant manufacturers.

6. Configure the models for a simulation using the peak forces of exercises and the angles at

which the femur is extended.

7. Converge one of the models to determine the optimum mesh size for the simulation.

8. Run a series of simulations using different materials for the femoral stem and acetabular cup.

9. Record relevent plots and record the results in a series of tables to compare data.

10. Produce graphs of the relationship between materials of components and relevent plots of the

simulation.

28

Methodology

Forces Acting on the Hip Joint

To explore the effects of exercise on the the prostheses components, biomechanical research was first

made into how exercise effects the natural hip joint. By studying the hip at at stationary points of

different stances, the resultant force and the angle at which it acts can be determined.

Two-legged stance:

When the body is stationary, it can be said that it is in a two-legged stance where each leg constitutes

one sixth of the total bodyweight to make a combined total of two sixths of the total bodyweight, or

1/3W. The resultant force of the bodyweight, 2/3W, is equally distributed across each hip. Therefore it

can be said that each hip carries 1/3W, with little or no muscle contraction used to support this load.

[50]

One-legged stance:

To calculate the forces acting on the hip in a two legged stance, a free body diagram can be used.

Firstly, because only one leg is supported by the ground, it can be said that the total weight acting on

the hip is five sixths times the bodyweight, or 5/6W, at a perpendicular distance 𝐿 from the centre of

the femoral head, 𝐶. This force is balanced by muscle contractions in the surrounding area of the hip,

which stabilizes the pelvis by counteracting the leverage given by the bodyweight. [50]

For simplicity, the forces of these muscle contractions can be represented by a single force, known as

the net abductor muscle force 𝐹𝐴, which acts towards the gluteus muscles to the rear of the pelvis, at a

perpendicular distance 𝑟 from 𝐶. The angle at which this force acts from the vertical can be

represented by 𝛼. A normal value for this angle is 20°. [50]

The total force acting on the hip, or resultant force, can be expressed as a single component that acts

between the femoral head and the acetabulum at angle 𝜃 to the ground. This force, 𝐹𝑅, is proportional

the ratio of 𝐿 over 𝑟, which is usually a value of 2.5. Angle 𝛽 is known as the Q-angle of the

quadriceps of the femur and ranges from 10-14° in males and 15-17° in females as a result of

difference in hip width. [51]

29

Resolving x components:

∑ 𝐹𝑥 = 0

𝐹𝑅 cos 𝜃 − 𝐹𝐴 sin 𝛼 = 0

(1)

Resolving y components:

∑ 𝐹𝑦 = 0

𝐹𝑅 sin 𝜃 − 𝐹𝐴 cos 𝛼 −

5

6𝑊 = 0 (2)

Moments about centre of femoral head:

∑ 𝑀𝐶 = 0

𝐹𝐴 × 𝑟 −

5

6𝑊 × 𝐿 = 0

𝐹𝐴 =

5

6𝑊 (

𝐿

𝑟)

(3)

𝟓

𝟔𝑾

𝒓 𝑳

𝑭𝑨

𝑭𝑹

𝜶

𝒚

𝒙

𝑪

𝜷

Figure 19 Free body diagram of hip joint in one-legged position. [51]

30

Using (3):

𝐹𝐴 =5

6𝑊 (

𝐿

𝑟)

𝐹𝐴 =5

6𝑊 × 2.5

𝐹𝐴 = 2.083𝑊

Using (1): 𝐹𝑅 cos 𝜃 − 𝐹𝐴 sin 𝛼 = 0

𝐹𝑅 =𝐹𝐴 sin 𝛼

cos 𝜃

𝐹𝑅 =2.083𝑊 sin 𝛼

cos 𝜃

Using (2):

𝐹𝑅 sin 𝜃 − 𝐹𝐴 cos 𝛼 −5

6𝑊 = 0

sin 𝜃 =𝐹𝐴 cos 𝛼 +

56

𝑊

𝐹𝑅

sin 𝜃 =2.083𝑊 cos 𝛼 +

56

𝑊

2.083𝑊 sin 𝛼cos 𝜃

sin 𝜃 =2.083𝑊 cos 𝛼 +

56

𝑊

2.083𝑊 sin 𝛼cos 𝜃

sin 𝜃 =2.083𝑊 cos(20) +

56

𝑊

2.083𝑊 sin(20)cos 𝜃

sin 𝜃 =1.957𝑊 +

56

𝑊

0.712𝑊cos 𝜃

31

Figure 20 Visualisation of forces acting on

body when walking. [52]

sin 𝜃 = 3.917 cos 𝜃

∴ 𝜃 = tan−1(3.917) = 75.7°

Using (1):

𝐹𝑅 =2.083𝑊 sin 𝛼

cos 𝜃

𝐹𝑅 =2.083𝑊 sin(20)

cos(75.7)

𝐹𝑅 =0.712𝑊

0.247

𝑭𝑹 = 𝟐. 𝟖𝟖𝟎𝑾

2.880W

2.083W

𝟓

𝟔𝑾

32

Effects of Exercise on Natural Hip

Peak Loads

In certain activities where the hip joint is required to support the weight of the body, the resultant

force of the joint is multiplied by a factor proportional to the intensity of the activity or exercise. This

multiplying force varies based on the position of the hip at the particular point in the exercise but acts

at the same point on the hip for each exercise providing the hip is not abducted or adducted. It can be

said that the maximum multiplicative resultant force, or peak load, occurs at the point where the

exercise is at its most strenuous or where the largest load from impact is experienced.

Table 3 Comparison for activities with their corresponding peak loads. [51]

Using this information the resultant force of the hip joint can be calculated for any person providing

their bodyweight is known. A sample calculation was performed using the average male body mass in

the UK using 2010 data from the Office for National Statistics (ONS). [53]

Body mass 𝑚 = 83.6kg

Body weight 𝑊 = 𝑚g

Resultant force (walking) = 9.504𝑊

𝐹𝑅 = 9.504 × 83.6 × 9.81 = 7794.38𝑁

Table 4 Resultant force for physical activity.

Activity Resultant force on hip joint (N)

Walking 7794.38

Jogging 11809.67

Cycling 5668.64

Activity Peak load on hip joint Resultant force in terms of body weight

Walking 3.3 2.880𝑊 × 3.3 = 9.504𝑊

Jogging 5.0 2.880𝑊 × 5.0 = 14.4𝑊

Cycling 2.4 2.880𝑊 × 2.4 = 6.912𝑊

Ascending stairs 5.5 2.880𝑊 × 5.5 = 15.84𝑊

Descending stairs 5.1 2.880𝑊 × 5.1 = 14.688𝑊

Standing up 2.2 2.880𝑊 × 2.2 = 6.336𝑊

Sitting down 2.0 2.880𝑊 × 2.0 = 5.76𝑊

Stumbling 8.7 2.880𝑊 × 8.7 = 25.056𝑊

33

Figure 23 Average hip angle during gait analysis using a three dimensional musculoskeletal model (Effect of

hip angle on anterior hip joint force during gait, Lewis CL, Sahrmann SA, Moran DW, 2010.)

Angles of flexion

During these activities the leg is flexed outwards by a specific amount depending on the movement of

the body. This flexion acts through what is known as the sagittal plane – the plane of movement from

anterior to posterior - and creates an angle with the neutral position of the hip. The value of this angle

reaches a maximum when the peak load from the corresponding exercise occurs.

Activities that are repetitive or incorporate cyclic motion such as walking can be studied using a

process known as gait analysis. When the body is in motion, or gait, the movement of limbs and

biomechanics associated with the motion can be determined by observation and instrumentation in the

various planes of the body. The angle of flexion between the extended leg and neutral position of the

hip can be measured by observing gait in the sagittal plane using a combination of cameras and/or

sensors focussed on the area of interest.

Below shows gait cycle data for three types of exercise

Sagittal Coronal

Transverse

Anterior Posterior

𝜃

Line of neutral

Figure 21 Planes of body. [54] Figure 22 Angle of flexion of hip. [55]

34

Table 5 Angle of flexion for physical activity.

Exercise Angle of Flexion (°)

Walking 20-25

Jogging 40

Cycling 70

Walking, jogging and cycling were chosen as methods of exercise due to their differences in

principals making them ideal exercises to compare the effects of each on the hip joint. Walking, for

example, is low loading and requires slow movement of the hip joint, jogging is high load and higher

movement, and cycling is low load but very high movement.

The next step of the project was to create CAD models of a femoral stem and acetabular cup to apply

the resultant forces to the prosthesis.

Figure 24 Hip flexion-extension angle during gait cycle of

human running. (Biomechanical Basis of Human Movement,

Hamill J, Knutzen KA, 2008, p. 365)

Figure 25 Hip flexion-extension angle range for cycling and other methods of activity. (Comparison

of elliptical training, stationary cycling, treadmill walking and overground walking, Damiano DL,

Norman T, Stanley CJ, Park HS, 2011

35

CAD Model - Stem Dimensions

127°

110mm

25mm

22.23mm

37°

25mm

50mm

154mm

36

CAD Model - Cup Dimensions

22.73mm

2.50mm

21.5mm

∅44mm

∅42mm

47.75m

m

∅45.5mm

37

Figure 26 Side view of assembled

prosthesis showing angle of flexion.

CAD Model – Assembled Prosthesis

Femoral component courtesy of GrabCAD user Tanay [56] - designed to the measurements of a

cemented two-part Charnley style prosthesis with a single piece stem and acetabular cup. Angle of

stem is that of a normal male Q-angle (12°). Blue shaded region of stem shows the iconic ‘cobra’

design of Charnley implants using a large surface area to bond the stem to the top of the femur.

Acetabular cup designed based on dimensions of Smith and Nephew XLPE acetabular cup model

7135-8001. [57] The red shaded region of the acetabular cup indicates the area of tapering where it

sits in the acetabulum of the pelvis.

12°

Figure 34Front view of assembled

prosthesis with acetabulum cup

flange highlighted in red.

Figure 35 Rear view of assembled

prosthesis showing flared neck of

stem highlighted in blue.

38

Finite Element Analysis Set-up

The femoral stem and acetabular cup were simulated as two separate components to overcome the

limitations of assembly simulations within SolidWorks. When the simulation was attempted on the

completed assembly, SolidWorks encountered errors where the femoral head and inside surface of the

acetabular cup were mated. This is thought to be because of the 0.5mm space between the two surfaces.

The acetabular cup was ‘fixed’ relative to the femoral stem to replicate the real-life setup of a hip

prosthesis, where the acetabular of the pelvis is stationary and fixed inside the acetabulum and the

femur is allowed to move. Constraints were applied to the respective locations of each component

using fixed geometry – a feature that prevents displacement of the particular surface or edge in any

given direction.

The stem was modelled in three variations to provide an angle of flexion for each exercise and a

position to apply the resultant force through the use of a split-line, essentially dividing the femoral

head into two sections so a force concentration at the centre of the head could be applied. This split-

line was made using a 21.23mm diameter circle sketched perpendicular to the centre of the femoral

head, leaving a distance of 0.5mm between the area where the force is applied and the edge of the

femoral head. To calculate the position at which the split-line acts, an arc was sketched across the face

of the femoral head in parallel with the line of neutral of the body. The angle of the arc was set to that

of the angle of flexion of the hip for each exercise and at the end of the arc a point was applied to the

surface of the femoral head to provide a reference point for the perpendicular plane to be allocated.

Figure 28 Fixed geometry on outer surface and

ridges of acetabulum cup. Figure 27 Fixed geometry on shaft and underside of flange of

femoral stem.

39

Figure 40 Femoral head with resultant force

direction plane angled to the ground.

To specify the angle at which the resultant force is applied, a combination of planes and axes were

created for both the acetabular cup and femoral stem. A central axis was created for each component

to provide a reference point for a plane perpendicular to the corresponding faces. This allowed a plane

to be created at an angle relative to a chosen axis, which in the case of the resultant force angle is

75.7°.

The models were now ready to be simulated using the resultant force values and angles of flexion for

walking, jogging and cycling.

75.7°

75.7°

Figure 38 Arc sketched on surface of

femoral head. In this case a flexion angle

of 20°.

Figure 39 Face perpendicular to end point of arc

and split-line of diameter 21.23mm.

Figure 41 Acetabular cup with resultant force

direction plane.

40

Convergence

Before generating results from the simulation, the models were converged to find the point at which

accuracy in the simulation did not change despite the increase in computing time. By probing an area

of interest, results from the simulation could be compared with the required computational time and a

graph could be made to show where the model has converged. To achieve a consistent probing

location, a split-line was added to the neck of the femoral stem to create intersections which could be

probed.

A test force of 5000N was applied to the femoral head using the walking angle set-up (20° angle of

flexion). A series of simulations were then run using different mesh sizes starting at 5mm, decreasing

by increments of 1mm until a point where the computational time increased exponentially. At this

point the mesh was refined by small increments to reduce anomalies in the graph. A curvature-based

mesh was used as oppose to a standard mesh due to the complex nature of the stem and its circular

geometry.

Figure 30 Stem with 5mm mesh. Figure 29 Stem with 1.5mm mesh.

Figure 31 Probing neck of femoral stem at split-line intersections.

41

0.00E+00

2.00E+08

4.00E+08

6.00E+08

8.00E+08

1.00E+09

1.20E+09

1.40E+09

1.60E+09

0 50000 100000 150000 200000 250000 300000 350000

von

Mis

es S

tres

s (P

a)

No. of nodes of simulation

Convergence Plot

von Mises stress (Pa) Top of neck von Mises stress (Pa) Bottom of neck

Table 6 Convergence results.

Mesh size

(mm)

No. of

nodes

Element

no.

Degrees of

freedom

von Mises stress (Pa) Solver

time (s) Top of neck Bottom of neck

5 8259 5025 18156 1.127e+009 1.310e+009 00:00:01

4.5 8886 5421 19725 1.085e+009 1.245e+009 00:00:01

4 10382 6410 23550 9.900e+008 1.290e+009 00:00:01

3.5 13057 8183 30342 1.131e+009 1.360e+009 00:00:01

3 18520 11871 44286 1.053e+009 1.360e+009 00:00:01

2.5 31897 20967 79128 1.056e+009 1.314e+009 00:00:01

2 54880 36785 140166 1.095e+009 1.326e+009 00:00:03

1.5 115146 78995 303150 1.094e+009 1.341e+009 00:00:06

1 325613 227457 880542 1.101e+009 1.334e+009 00:00:17

0.9 419475 294328 1141716 1.102e+009 1.348e+009 00:00:22

0.8 545384 383927 1490802 1.103e+009 1.340e+009 00:00:30

0.7 775993 549030 2135772 1.105e+009 1.340e+009 00:00:43

0.6 1152678 818404 3186528 1.106e+009 1.339e+009 00:01:02

0.5 1742896 1241623 4846719 1.100e+009 1.340e+009 00:01:39

0.4 2775995 1985935 7763196 1.106e+009 1.339e+009 00:05:54

0.3 4792441 3437792 13438668 1.104e+009 1.339e+009 00:07:19

The results from the convergence plot show a steady line from 54880 nodes to 325613, indicating the

theoretical solution is achieved between a 2mm and 1mm mesh. Therefore it can be said that the

optimum mesh size in terms of accuracy in the simulation and required computational time is 1.5mm.

The results for mesh sizes lower than 1mm show a very small difference in results but an exponential

increase in solver time. For mesh size 0.3mm the accuracy increased by 0.95% but the time increased

by 98.6%.

Theoretical solution at mesh size 1.5mm

Figure 32 Graph of convergence plot.

42

Figure 35 Visual configuration of

components.

Figure 49 Visual configuration of components.

Configuration of Prosthesis for Exercise

Walking

Jogging

20°

Figure 33 Resultant force position on femoral head.

40°

Figure 50 Resultant force position on femoral head.

Figure 36 Resultant force position on acetabular cup.


43

Figure 52 Visual configuration of components.

Cycling

Due to the similar appearance of the simulation plots for all three exercises, the images of the

simulation were taken using the resultant force and angle of flexion for walking. The material of the

stem was stainless steel and the material of the acetabular cup was UHMWPE. To save space, the

remaining images are included in the appendices.

70° Figure 37 Resultant force position on femoral head.


44

FEA Simulation Plots

Von Mises Stress Distribution

Table 7 Stress distribution values of femoral stem.

Name Type Min Max

Femoral Stem – Stainless

Steel

VON: von Mises Stress 0.00408884 N/m^2

Node: 54448

1.15417e+009 N/m^2

Node: 4042

Table 8 Stress distribution values of acetabular cup.

Name Type Min Max

Acetabular Cup - UHMWPE VON: von Mises Stress 119588 N/m^2

Node: 53775

2.60344e+007 N/m^2

Node: 52905

45

Resultant Displacement Plot

Table 9 Displacement values of femoral stem.

Name Type Min Max


Steel

URES: Resultant Displacement 0 mm

Node: 3

0.426039 mm

Node: 30426

Table 10 Displacement values of acetabular cup.

Name Type Min Max

Acetabular Cup - UHMWPE URES: Resultant Displacement 0 mm

Node: 83

0.131926 mm

Node: 53491

46

Strain Plot

Table 11 Strain values of femoral stem.

Name Type Min Max


Steel

ESTRN: Equivalent Strain 1.90391e-014

Element: 53227

0.00448644

Element: 33086

Table 12 Strain values of acetabular cup.

Name Type Min Max

Acetabular Cup - UHMWPE ESTRN: Equivalent Strain 0.000245036

Element: 13647

0.0304277

Element: 13853

47

FEA Results

Table 14 Simulation results for walking set-up.

Table 13 Simulation results for jogging set-up.

Table 15 Simulation results for cycling set-up.

Component Material Min Max Min Max Min Max

Stainless steel 0.000202541 1.16E+09 0 0.458267 1.03E-15 0.00459031

Titanium Ti-6Al-4V 0.0014725 1.16E+09 0 0.800781 1.37E-14 0.00838289

UHMWPE 86972.5 1.89E+07 0 0.0959456 0.00017821 0.022129

Co-Cr-Mo 39138.9 1.96E+07 0 0.000389185 2.98E-07 7.63E-05

Zirconia 143562 2.03E+07 0 0.000404392 7.12E-07 7.32E-05

Stem

Cup

VON: von Mises Stress (N/m^2) Displacement (mm) Equivalent Strain




UHMWPE 181195 3.94E+07 0 0.199889 0.00037127 0.0461026

Co-Cr-Mo 81540.2 4.08E+07 0 0.00081081 6.21E-07 0.00015894

Zirconia 299100 4.22E+07 0 0.0008425 1.48E-07 0.0001525

VON: von Mises Stress (N/m^2) Displacement (mm) Equivalent Strain

Stem

Cup




UHMWPE 119588 2.60E+07 0 0.131926 0.00024504 0.0304277

Co-Cr-Mo 53816.5 2.69E+07 0 0.000535134 4.10E-07 0.0001049

Zirconia 197399 2.79E+07 0 0.000556044 9.78E-07 0.00010067

Equivalent Strain

Stem

Cup

VON: von Mises Stress (N/m^2) Displacement (mm)

48

Interpretation of Results

Von Mises Stress

Figure 39 Bar chart comparing max von Mises stress in femoral stem materials when under loading from exercise.

The von Mises stress stayed practically constant for each exercise, especially in the femoral stem

simulations. This could be attributed to the fact stress is force over area, therefore because the area of

each component did not vary, the total von Mises stress is proportional to the force applied. This also

explains the characteristic increase in stress with higher loading.

One explanation for the highest stress in Zirconia and the lowest in UHMWPE is the different values

of Young’s Modulus for each material. Between these materials, the stress fluctuated by an average of

2.8MN𝑚−2, approximately 6.6%. Although these differences are not significant, they are still a factor

to take into account in addressing the material’s response to high loading.

0.00E+00 5.00E+08 1.00E+09 1.50E+09 2.00E+09 2.50E+09

Cycling

Jogging

Walking

von Mises Stress (N/m^2)

Exercise - Stress

Titanium Ti-6Al-4V Stainless steel

Figure 40 Bar chart comparing max von Mises stress in acetabulum cup materials when under loading from exercise.

0.00E+00 1.00E+07 2.00E+07 3.00E+07 4.00E+07 5.00E+07

Cycling

Jogging

Walking

von Mises Stress (N/m^2)

Exercise - Stress

Zirconia Co-Cr-Mo UHMWPE

49

Displacement

Figure 41 Bar chart comparing max displacement in femoral stem materials when under loading from exercise.

Figure 42 Split bar chart comparing max displacement in acetabular cup materials when under loading from exercise.

Displacement concentrations were primarily focussed around the area at which the force was applied

to the components. The displacement of the femoral stem, for example, effected nearly the whole of

the head of the component, with the highest concentrations at the centre of the head, diminishing

towards the centre of the neck (see Table 9). Ti-6Al-4V showed a displacement average 1.75 times

greater than stainless steel, with the highest reading of 1.312mm in jogging. This is surprising

considering the high praise this alloy has in the orthopaedic community.

The displacement plot of the acetabular cup displays exactly as what would be expected for the

components in contact with each other – highest displacement on the inside face and a less focused

area of displacement on the face of the cup parallel with the femoral head. UHMWPE recorded a

significantly higher value of displacement than Zirconia or Co-Cr-Mo, with a maximum value of

almost 2mm.

0 0.2 0.4 0.6 0.8 1 1.2 1.4

Cycling

Jogging

Walking

Displacement (mm)

Exercise - Displacement


50

Strain

Figure 43 Bar chart comparing max strain in femoral stem materials when under loading from exercise.

Figure 44 Split bar chart comparing max strain in acetabular cup materials when under loading from exercise

UHMWPE recorded the highest strain, with a factor of 0.046 under loading from jogging, almost 300

times greater than the next highest value of strain for the acetabular cup. The simulation plot for the

acetabular cup (Table 12) shows this deformation occurs directly on the inside face, which is as

expected from components under loading.

The simulation plot of the femoral stem (Table 11), however, shows the highest strain occurring at the

centre of the neck. This could be a cause for concern as the neck may potentially thin out or not

behave as intended from repeated loading over time. Compared with the acetabular cup, however, the

maximum strain value is significantly lower for Ti-6Al-4V – for jogging this value is approximately

3.3 times smaller than the max strain seen in the acetabular cup for the same exercise.

0 0.002 0.004 0.006 0.008 0.01 0.012 0.014 0.016

Cycling

Jogging

Walking

Strain - Exercise


51

Errors

Although finite element analysis generated reliable data, it only serves as an estimation for the solution

to the problem. To validate the results, an experiment could be performed on a hip prosthesis using

hydraulic testing apparatus to apply loading to each component. Using the same materials and peak

forces, theoretical results could be compared with practical-based results to verify whether the values

for stress, displacement and strain are in a sensible region. To verify the maximum stress in the model,

a brief hand calculation could be used to determine whether the results are in the same range. Providing

the area at which the force is applied to the components, the formula 𝜎 = 𝐹/𝐴 will determine the stress

as a result of the peak load from a given exercise.

An important factor to discuss is how the prosthesis was simulated. For a start, the components were

simulated individually as opposed to being assembled, therefore any interaction between the contact

surfaces of the acetabular cup and femoral stem could not be explored. Furthermore, the models were

simulated without taking into account the surrounding bone or cement that would be present in a real-

life prosthesis. As a result of this, stress-shielding was not investigated, thus the results of the

simulations are likely to be different to actual stress, displacement and strain values present in a

prosthesis inside a body. Moreover, as the 21.23mm diameter split line was only a representation of the

diminishing force at the outside edge of the head of the femoral stem, the results will differ from that

of an actual prosthesis where the outside edge of the sphere would experience zero loading and the

centre would experience the concentrated resultant force.

Despite the fact each model was converged, it is still likely that the majority of the errors in the

simulation were due to meshing errors of each model. Around areas with high stress concentrations,

such as the neck of the femoral stem, the mesh density could be increased to provide a greater number

of elements and nodes for the simulation to acquire results from. This process, known as mesh

refinement may reduce anomalies in the results.

52

Discussion

The results from the simulation of the femoral stem show that stainless steel is the best choice of

material for resisting displacement and strain when load is applied to the femoral head. However, when

the stem is fixed inside the femur, some displacement is not necessarily bad as it reduces the stress

shielding against the bone surfaces. Therefore it could be said that stainless steel is, in fact, not suitable

to be used as the material of a femoral stem. On the contrary, for patients with a very active lifestyle,

particular those who partake in regular high impact exercise, stress shielding of the femur may be of

less concern than constant displacement of the femoral stem as is the case with titanium alloy Ti-6Al-

4V. Although this alloy has a far greater biocompatibility than stainless steel, if the femoral stem is

displaced and under strain for repeated exercise, the prosthesis is far more likely to fail. Furthermore,

if a porous titanium alloy such as Ti-6Al-4V 40% porosity is used, the repeated high displacement and

deformation of the component may even loosen the bond of osseointegration of the surface of the femur.

Nonetheless, for a low loading exercise, Ti-6Al-4V is perfectly suitable to be used as femoral stem,

especially considering there is no danger of the patient suffering an allergic reaction to the material

unlike with nickel used in stainless steel.

The results from the simulation of the acetabular cup make it very clear that ultra-high molecular weight

polyethylene is unsuitable for active patients. Although the material is cost effective and reliable, the

massive displacements of the inside surface in contact with the femoral head are a huge cause for

concern. It is simply impractical for younger patients to use an acetabular cup that poses the risk of

dislocation or subluxation due to the high deformation when under loading. Additionally, due to

UHMWPE having the highest material wear-rate out of the materials studied, under exercise with high

cyclic loading such as cycling, the acetabular cup will wear out extremely fast. Combined with high

deformation, this repetitive motion could cause premature loosening of prosthesis which for younger

patients is extremely dangerous as the need for revision surgery will be very high.

Realistically, Zirconia and Co-Cr-Mo are the only suitable acetabular cup materials regardless of what

loading they are subjected to. However, Zirconia would be better suited to a patient with an interest in

cycling as the material is very much suited to high repetition-low load exercises. Due the extremely

hard nature of the material, Zirconia could resist the many thousands of revolutions of the leg during a

short space of time, and as the resultant force on the hip is relatively low during cycling, it poses no

danger of potentially cracking or fracturing the ceramic from a high impact load. Likewise, Co-Cr-Mo

is much more suited to lower repetition-high load exercise. Although there is a danger of metallosis

occurring from debris of the components rubbing against each other, it could be argued that a far greater

problem would be an acetabular cup cracking, as could be the case with Zirconia used for such exercises.

53

One important factor to discuss is the inability to simulate the femoral head as a different material

such as ceramic or an alternative metal. As explained, technical difficulties were encountered within

SolidWorks when trying to run the simulation on an assembly of mated components. As a result of

this, the femoral head and shaft were kept as one component and the acetabulum as another. It would

have been futile to simulate the femoral head as a separate component to the stem as result plots in the

simulation would not show how stress, displacement and strain are distributed from the head across

the neck of the stem.

Conclusion

Overall the use of finite element analysis was successful as the simulations were able to provide a

value of maximum stress, displacement, and strain of the prosthesis components when under loading

from exercise. The results from the simulations are sufficient to fill the gap in current research made

into this topic, and offer a strong starting point for anyone wishing to further explore the effects of

exercise on hip prostheses. To summarise, the optimum material combination for high impact loading

is a stainless steel femoral stem and a Co-Cr-Mo acetabular cup, and for low impact but high

frequency loading, a titanium Ti-6Al-4V femoral stem and Zirconia acetabular cup.

Using this information, orthopaedic surgeons could decide which materials of components to use in

the prostheses for active patients.

54

Future Work

One important factor to explore is how exercise effects the material wear-rate of the prosthesis

components. In this project, the hip was analysed in a stationary position with the peak load of the

exercise occurring at the maximum angle of flexion of the leg, but did not include cyclic loading from

the exercise that the hip would experience in real-life. The FEA package ANSYS offers a way to

perform this simulation through a process known as time dependent loading. By calculating the load of

the hip joint through each angle of flexion for the exercise, it would be possible to calculate the wear-

rate of the components providing the coefficient of friction is known for each contact surface.

Alternatively, the assembled prosthesis could be analysed using a cyclic loading machine, which are

currently used to compare material wear-rates between of the components, but are costly and require a

lot of time to generate results.

Another aspect to consider is the effect of fatigue on the components. If the maximum and minimum

load on the hip joint experienced is known, a fatigue analysis simulations could be performed on the

prosthesis between this range of force. The results of these simulations could then be plotted in a series

of graphs to compare factors such as the time taken for the component to fail. Using this information,

surgeons could confidentially select materials of components based on how active the patient is, e.g

using a Zirconia acetabular cup for patient a who cycles frequently.

In order to keep the finite element analysis results relevant, simulations should be repeated with ‘future’

materials of components. With the increasing advances in bioengineering technology, orthopaedic

companies use materials tailored to suite every requirement of the component in order to stay

competitive with other products. I made contact was made with Mr. Ingham, an employee of Zimmer

Orthopaedics, to discuss future materials in hip prosthesis components. Mr. Ingham emailed me

brochures of their newest components using state of the art materials. Trabecular Metal™ boasts up to

80% porosity and has an extremely low coefficient of friction making it one of their most innovative

products. [21] Simulating materials such as these would be a good way of comparing how future

materials compare with conventional materials of components and could provide surgeons with the

information to decide on whether these implants are effective.

The effects of exercise on hip prostheses could also be explored using a different style prosthesis and a

different method of exercise. The Mckee-Farrar prosthesis, for example, would produce different

simulation results to the Charnley prosthesis due to the increase in femoral head size, and an exercise

such as weightlifting would exert a far larger peak load on the hip. A study on the relationship between

types of prostheses and how they distribute loading could be made to compare these variables.

55

Lastly, the hip prosthesis could be improved either by changing the shape or size of each component. It

is already standard knowledge that a larger diameter femoral head will increase wear in between the

acetabular cup, but how would this effect displacement or deformation in areas with high force

concentration. By investigating the factor of safety (FOS) of the design for each model, either from trial

and error or biomechanical assessment, the prosthesis components could be modified to increase the

minimum value which would prove it is X times stronger than it needs to be. A study could then be

made into the minimum FOS value of each prosthesis required to safely subject the hip to loading from

exercise.

56

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59

Appendices

Distribution plots for jogging and cycling


Name Type Min Max


Steel

VON: von Mises Stress 0.00074351N/m^2

Node: 54448

1.993673e+009 N/m^2

Node: 4042


Name Type Min Max


Steel

VON: von Mises Stress 0.000202541N/m^2

Node: 54448

1.16427e+009 N/m^2

Node: 4042

60

Plan

of A

ctivities: Gan

tt chart

Documents

Final Year Project 2015