John Arigho (X00075278) Final Project [Porcine Vertebra Simulation](Print)

Department of Mechanical Engineering

Project Title

Investigation into the Virtual Modelling of Geometrically Complex Bio Parts

via the Development of a Simulated Porcine Vertebra

Student Name: John Arigho

Student No: x00075278

Date of Submission: 24/04/2016

Supervisor: Mr. Stephen Tiernan

i

Declaration of Originality

I hereby certify, that this report, submitted as a part of the BEng (Hons) Mechanical

Engineering, is entirely the work of the author and that any resources used for the completion

of the work done are fully referenced within the text of this report.

Signature: Date: 24/04/2016

Acknowledgements

I would like to take this opportunity to thank my supervisor Mr. Stephen Tiernan for his

guidance and support throughout the process of this project. I would also like to extend my

gratitude to Mr. Colin Bright and in particular, Mr. Christopher McClelland, for affording me

the time to answer an array of questions pertaining to the field of bio-mechanics. Their

knowledge and support have been vitally important to the success of this project.

Finally I would like to thank my family and friends for their unwavering support throughout

the entirety of this project. For without their support none of this would have been possible.

ii

Abstract

Many complications surround the physical testing and analysis of the spine. Particularly when

considering the limits and problems related to the acquisition of suitable human test samples.

To overcome these difficulties a variety of novel surgical techniques such as “In-Silico

analysis”, a computerized simulation method used for medical examination have come to light

and become increasing popular in recent years. Specifically, there has been a significant

increase in the use of finite element analysis (FEA) in spinal research. The benefits of using in-

silico analysis in medical research are numerous.

Provides a non-invasive and fully repeatable means of testing without consequence to

the patient.

As a result, surgical techniques can be perfected to provide patient specific treatments.

However, this method of creating patient specific models involves creating an FEA mesh to

account for living tissue, complex geometry, material properties and changes over time which

makes this process extremely complex and time consuming. In addition, clinically approved

medical imaging software is still very expensive.

Considering this, an investigation was undertaken into the various methods of creating a FEA

mesh model from medical images.

The purpose of this project is to investigate the use and validity of freely available, open source

software packages for medical image processing and more specifically, the development of

FEA models directly from these software packages.

This project demonstrated that the freely available open source software package IA-FEMesh

proved capable in terms of creating geometrically accurate FEA meshed models. However,

the models created were restricted by limitations in the software and due to the lack of

computational power available.

iii

Table of Contents

Acknowledgements ..................................................................................................................... i

Abstract ...................................................................................................................................... ii

Chapter 1 – Aims, Objective and Methodology ........................................................................ 1

Introduction ............................................................................................................................ 1

In-Vitro Analysis: .............................................................................................................. 1

In-Vivo Analysis: ............................................................................................................... 2

In-Silico Analysis: ............................................................................................................. 2

Detailed Aims & Objectives .................................................................................................. 3

Objectives for Literature Survey ............................................................................................ 4

Methodology .......................................................................................................................... 5

Analysis & Validation............................................................................................................ 6

Chapter 2 - Literature Review .................................................................................................... 7

Introduction ............................................................................................................................ 7

Anatomy of the Porcine Spine ............................................................................................... 7

The Vertebra ...................................................................................................................... 7

The Vertebral Column ....................................................................................................... 8

Differences and Similarities of the Human and Porcine Spine ............................................ 10

Vertebral Loading Orientation ......................................................................................... 10

Vertebral Load Distribution ............................................................................................. 13

Natural Vertebral Loading Magnitudes ........................................................................... 15

Vertebral Loading Characteristics ................................................................................... 16

Vertebral Bone Density and Load Sharing Between Trabecular and Cortical Bone ....... 19

Overall Summary ............................................................................................................. 20

Acquisition of Material Properties from CT Scans .............................................................. 20

Results .............................................................................................................................. 22

Anatomical Mesh Creation Methods ................................................................................... 23

iv

IA-FEMesh ...................................................................................................................... 23

Meshing Techniques ........................................................................................................ 25

Summary .......................................................................................................................... 25

Model Validation ................................................................................................................. 26

Chapter 3 Design...................................................................................................................... 29

3D-Slicer Steps .................................................................................................................... 29

Preliminary Model ............................................................................................................... 29

Geometric Simplification ..................................................................................................... 30

Initial Geometrically Simplified Model ........................................................................... 30

Design Rework................................................................................................................. 32

Summary .......................................................................................................................... 32

Chapter 4 Finite Element Mesh Creation................................................................................. 33

Import Surface ................................................................................................................. 33

Import Image .................................................................................................................... 33

Create Building Blocks .................................................................................................... 34

Geometry Simplification .................................................................................................. 35

Assignment of Material Properties & FE Mesh Models Created .................................... 35

Chapter 5 Testing ..................................................................................................................... 37

Loading the Model ............................................................................................................... 37

Compression Test................................................................................................................. 38

Summary of Testing ............................................................................................................. 38

Chapter 6 Results ..................................................................................................................... 39

Graph of Deformation from Finite Element Analysis Results............................................. 39

Graph of Max Stresses from Finite Element Analysis Results ............................................ 41

Chart of Material Property Distribution and Range (John Custom (1.1)) ........................... 42



v

Chart Comparing the Distribution and Range of Material Properties of Custom Models... 45

Graph of Physical Distribution of Material Property Elements ........................................... 46

Graph of the Models Predicted Fracture Location ............................................................... 47

Chapter 7 Analysis of Results .................................................................................................. 48

Displacement........................................................................................................................ 48

Factors Giving Rise to Differences in Stiffness Values....................................................... 50

Different Specimen Tested .............................................................................................. 50

Mesh Density ................................................................................................................... 51

Power Law Equations Used ............................................................................................. 52

Use of Potting Material .................................................................................................... 52

Material Isotropy .............................................................................................................. 52

Validation ............................................................................................................................. 53

Material Property Distribution and Range ....................................................................... 53

Physical Location of Material Property Elements ........................................................... 56

Predicted Fracture Location ............................................................................................. 57

Burst Fractures ................................................................................................................. 58

Chapter 8 Conclusions & Future Work ................................................................................... 60

Increased Computational Power .......................................................................................... 60

Fixed Value/False Assumptions .......................................................................................... 60

Incorporation of Facet Joints ............................................................................................... 60

Chapter 9 Ethical Considerations............................................................................................. 61

Ethically Sourced Cadaver Specimens ................................................................................ 61

Future Implementation of Project on Humans ..................................................................... 61

Chapter 10 Appendix ............................................................................................................... 62

Project Plan .......................................................................................................................... 62

Post Graduate Results (Actual Compression Test) .............................................................. 64

Finite Element Analysis Results .......................................................................................... 65

vi

Elemental Material Property Distribution and Range .......................................................... 79

References ................................................................................................................................ 85

1

Chapter 1 – Aims, Objective and Methodology

Introduction

Computational modelling combines mathematics, physics and computer science to study the

behaviour of complex systems. A computational model is a simulation based on numerous

variables that distinguish a particular system’s characteristics. The fundamentals of

methodology is widely found in traditional engineering sectors such as aviation engineering.

Flight simulators used to train future pilots in their craft rely on complex equations and

theoretical assumptions to produce a realistic experience including the effects of turbulence,

air density and weather conditions. This technology also spreads to the design of the aircrafts

itself e.g. The Boeing 777 which was the first passenger aircraft to be completely designed by

digital simulation. (1)

As computational efficiencies have progressed over the years, specific methods of virtually

simulating models of musculoskeletal bodies, such as the spine, through finite element analysis

(FEA) have become solidified in clinical research and applications. The development of

complex spinal models with high architectural detail provides a convenient tool that is used to

explore the biomechanical intricacies of the spine. This approach has provided significant

biomechanical insight and, as such, is being used during the assessment of orthopaedic

pathologies, prosthetic limb design and in the negotiation of suitable complex surgical

techniques alongside the more conventional methods used previously. (2) (3)

To date there are 3 main branches of biomechanically assessing the spine:

In-Vitro Analysis:

The measurement and analysis of spinal specimens from a human cadaver. This method

produces an accurate representation of human spinal geometry and material properties.

Unfortunately this technique is limited by the restricted availability of specimens (particularly

young or prime specimens), the cost of properly prepared cadavers, the presence of a non-

homogeneous range of specimen properties (density, elasticity etc.) due to large variations in

age, weight and general physical condition while also presenting the possible exposure to life

threatening virus’s (AIDS). It is also worth noting that there are significant differences between

the material makeup of the properties of living and dead specimens.

2

In-Vivo Analysis:

The measurement and analysis of a living person’s spine presents the possibility of examining

the spine in its natural state and also re-examining the same specimens over time post treatment

to evaluate and document results. Given the nature of this technique specimens are in short

supply with testing restricted to limited invasiveness so as not to harm the test subject.

In-Silico Analysis:

The analysis of the spine via a computational simulation model allows for complete test

repeatability and specimen scalability but the level of realism produced in the simulation

heavily depends on the calibration of the model parameters (accounting for living tissue,

complex geometry, material properties and changes over time).

(4) (5)

Considering the above limitations associated with the use of human specimens, the

investigation and testing of porcine samples has been undertaken by members of IT Tallaght

and in particular the post graduate students. In 2014, a student of IT Tallaght, Mr. Christopher

McClelland, commenced the laborious and complex task of creating a porcine L-4 Vertebra

model via computer topography scans (CT scans). Christopher was successful in its creation

but due to computational and time constraints was unable to fully validate the model.

Fortunately Christopher logged a clearly laid out step by step instruction manual in his report

detailing exactly how the model was developed. (6)

The aim of this project is to use Christopher’s report as a resource to develop a similar

representational model of a porcine vertebra but within in a smaller time frame so that the main

focus of this project can be directed to the validation of the model in accordance with real world

test data supplied by post graduate students.

In addition to this, the integration of the articulated facet joints into the model will be sought

after.

Further aims of this project are to investigate alternative methods of validation such as

attempting to model specific compressive load points that are applied to the vertebra during

certain human movements e.g. walking up the stairs.

3

Detailed Aims & Objectives

1. Investigation of the various methods employed in converting (Diacom) CT scan files

into stl files while retaining grey scale properties of the specimen with particular

attention being paid to free open-source solutions e.g. 3D-Slicer

2. Investigation of the various methods of converting stl files to finite element meshes

with particular attention being paid to free open-source solutions suitable for anatomic

FE model development e.g. IA-FEMesh

3. Research of the mechanical and material properties of the porcine vertebra to aid in an

investigation into the theoretical and formulaic relationships acting between the CT

grey scale values, density and stiffness of pig bones.

4. Investigation into the behaviour and characteristics of the load distribution that effect

the vertebral body and articulated facet joints under compressional force.

5. Development of a geometrical model of a vertebral specimen including the articulated

facet joints via an image and visualisation analysis software package e.g. 3D-Slicer.

6. Development of a material mesh model via a finite element analysis software package

e.g. IA-FEMesh

7. Importation of the FE model into an environmental simulation software package e.g.

ANSYS

8. Replication of real world compression tests performed on the vertebral body and

articulated facet joints of the porcine specimen by post-graduate students.

9. Comparison of the results produced by the finite element analysis with that of real world

test data gathered by post graduate students.

10. Adjustment of the material properties within the specimen model in order to acquire

simulated results in accordance with real world test data.

11. Investigation of alternative test methods to further validate the FEA e.g. validation of

strain characteristics via strain gauging or further validation of compression

characteristics by calibrating the data produced when loads are applied over a range of

positions/angles etc.

4

Objectives for Literature Survey

The purpose of the literature review is to gain a competent and well-rounded understand of the

overall project by establishing the theoretical framework, familiarisation of key definitions and

terminology and identifying relevant literature to illustrate how the subject has been studied

previously, highlight any flaws or gaps in the preliminary project plan and also to set a direction

for project goals and any ongoing research during the project.

The literature review will be used to answer the following questions:

What is the anatomy of the porcine spine and its vertebra?

Is it reasonable to use a pig samples to investigate human loading?

What are the correct methods of creating computationally simulated models of

complex anatomic bio-parts?

What defines a fully validated model?

What process was used to retain the grey scale material properties of the specimen?

What formulas were used to link the grey scale values of the CT scans to the

material properties of the bone i.e.: bone density, elasticity? Is there a variation of

these formulas that could be used to produce more realistic results?

What are the loads applied to the vertebra during specific human activity? In what

way are the loads applied i.e. angles etc.? What are the load transfer relationships

between interconnecting vertebrae?

How are the applied load forces distributed across the vertebra itself? i.e. load

sharing between the vertebral body and facet joints.

What is the thickness ratio of trabecular bone to cortical bone in porcine vertebra?

What are the common reasons for vertebral fracture? What part of the vertebra is

most susceptible?

How have similar projects in the sector been carried out? How can they be improved

or conducted in an original approach?

What results and conclusions have people previously achieved in this sector?

What can be done to expand and further the validation of the FEA model?

5

Below is a list of resources to be used during the acquisition of information for this literature

review:

Science Direct – An archive of mostly peer reviewed research papers.

Library Resources – Help during the attainment of Journals, articles, newspaper

articles and books.

Medical Journals – A provision of professional medical conclusions.

Medical Forums – A medium by which technical questions may be answered.

YouTube - Tutorial videos for software packages. (3D-Slicer, IA-FEMesh, CREO,

ANSYS etc.)

Google: Large search engine.

Methodology

A broad system of planned procedures was developed to specify the project’s direction and

scope. From this a detailed project plan can then be developed to timetable and meter the

progress of objectives. The following list of procedures was developed in the interest of the

projects success.

Research and acquisition of quality information and resources related to any areas of

interest regarding the project to be archived in a literature review database.

Construction of a comprehensive literature review to gain a knowledgeable and well-

rounded understand of the overall project by establishing the theoretical background,

familiarisation of key definitions and terminology and identifying relevant literature to

illustrate how the subject has been studied previously, highlight any flaws or gaps in

the preliminary project plan and also to set a direction for any ongoing research during

the project.

Research, familiarisation and competency in relation to the operation of the various

software packages associated with this project such as 3D-Slicer, CREO, IA-Mesh and

ANSYS.

Creation of a geometric model of the porcine lumber vertebra. This will be achieved

through the use of a free, open source software package e.g. 3D-Slicer to convert the

CT scan of the porcine specimen to an stl file.

6

Creation of a finite element analysis (FEA) mesh model via the importation of the stl

file produced to a free, open source software package e.g. IA-Mesh.

Virtual environment replication via the ANSYS software package to simulate the real

world compression tests performed by post graduate students.

Graphical analysis via the Microsoft Excel software package will be used in the

comparison of the data produced in the model simulation to that of the results founded

in the compression tests performed by the post graduate students along with that of

other published results.

Validation of the FEA model will be performed by considering the information

presented from the graphical analysis which will give insight into the assessment and

calibration of the material properties so as to produce the desired outcomes. This is a

time consuming process requiring the need for multiple simulations to acquire results

in accordance with the research data. As such this will be the focus of the project.

Investigation of alternative methods of validation such as attempting to model specific

compressive load points that are applied to the vertebra during certain human

movements e.g. walking up the stairs.

Analysis & Validation

The overall goal of this project is to produce a fully validated FEA model that produces realistic

data in agreement with the researched results of real world test data. To prove this a graphical

analysis via the Microsoft Excel software package will be used in the comparison of the data

produced in the model simulation to that of the results found in the compression tests performed

by the post graduate students as well as with alternative published results. The accuracy of the

model will be deduced and from there decisions on further manipulation or re-simulation will

be undertaken if necessary in order to authenticate the model.

7

Chapter 2 - Literature Review

Introduction

This chapter intends to add to the researched information gathered by Mr. Christopher

McClelland in the most recently established report of this ongoing investigation. The reader

will be introduced to the porcine spinal anatomy with relevant comparisons being made to that

of the human spine. A particular investigation will be made into the mechanical relationships

present between interconnecting vertebrae and also the load distribution behaviours and

processes that accompany the application of naturally occurring forces. This chapter

additionally aims to highlight previous computational and formulaic methods, processes and

techniques that have been used to create computationally simulated models of geometrically

complex bio parts including a discussion of the criteria involved in model validation.

Anatomy of the Porcine Spine

The Vertebra

As can be seen from the researched information documented by Mr. Christopher McClelland

(6) previously, it was found that a close anatomic and geometric relationship was present

between porcine and human vertebra. Therefore the structure of the vertebrae in either case can

be briefly summarised into the following three sections:

The anterior (front side) vertebral body

Composed of hard external cortical bone encompassing within it a mass of spongy trabecular

bone. Its superior (Upper) and inferior (lower) surfaces are known as the vertebral endplates

to which connects the intervertebral disk.

The posterior (backside) arch

Consisting of the pedicle and the lamina both of which are made from cortical bone and used

to protect the spinal cord and nerve roots. In either case several process bones arise in there

formation such as the two articular processes which in themselves house the articular facet

joints that extend and house the interior facets of the neighbouring vertebra. The facet joints

contain opposing articular cartilage surfaces that provide a low friction environment so that,

along with the intervertebral disc, they can facilitate the transfer of loads. Their main function

is to guide and constrain different motions of the spine depending on their position within the

anatomy i.e. to avoid movements that could damage the surrounding spinal structures such as

the spinal cord, intervertebral disks or protruding spinal nerves. The most significant

8

anatomical difference between human and porcine vertebrae is that the porcine facet joints

are also interlocked and as a result act as a mechanical hinge. Additionally the vertebral arch

contains a prominent central spine bone known as the spinous process which is used as a

point of attachment for the spinal muscles and ligaments.

The transverse processes

Two lateral projections made of cortical bone on either side of the vertebra. These projections

serve as points of attachment for muscles and ligaments in the spine. (7) (8)

Figure 1 - The Anatomy of the Human Vertebrae (9)

Figure 2- The Superior, Inferior Facets and Laminae of a Human Vertebra (10)

The Vertebral Column

The vertebral column of a pig consists of 51 - 58 interlocking vertebrae that are organised into

a horizontal column connecting the base of the skull to the pelvis region. This range in the

number of spinal bones found present is a direct result of selective breeding tending towards

pigs with longer backs which are therefore able to provide more product. (11) The vertebral

Laminae

9

columns main function is that of the principal load carrying system in the body that works in

cooperation with a network of interconnecting disks, ligaments and muscles to provide flexible

movement and firm control throughout. Its design also provides a protective frame for the

spinal cord to be housed via the spinal canal. The porcine vertebral column can be divided into

five sections: cervical/cranial, thoracic, lumbar, sacral, and caudal depending on their position and

roles played in the anatomy. As in most mammals, there are seven cervical vertebrae present in

the neck region which are used for supporting the weight and allowing free movement of the

head. The first two of these bones encountered are known as the atlas and the axis with the

final bone of the cervical section being unique in that it contains an extremely long spinous

process along with housing its articular facet joints, used in connecting the first rib, on the

vertebral body. The next section contains 14-17 thoracic vertebrae which are used for

supporting the weight of the rib cage. These are characterised by highly projected spinous

processes in comparison to that of humans and articular costal facet joints for connecting ribs.

Adjacent to this section are 6-7 lumbar vertebrae which are characterised by their reduced

spinous processes, long transverse process and massive vertebral bodies needed for supporting

the weight and any additional stresses applied to the body. It is worth noting that the angle of

the facet joints present in this region tend towards 30° which differs considerably from that of

a human (60°) (12).This difference can be attributed to the forces encountered during human

locomotion. Neighbouring this section is the sacral region connecting the spine to the hip area.

The pig contains only 4 vertebrae lacking in complete fusion at this point which differs from

the 5 fully fused vertebrae found in this section of a human. The need for the additional bone

and solid fusion in the human is a direct result of the support problems associated with standing

erect (13). Finally, humans have 3-5 partially fused but fixed vertebrae used for integrating

ligaments and muscles in the pelvic region known as the coccyx. Pigs on the other hand have

20-23 separate caudal vertebrae which extend out into the tail. Between each vertebra lies an

intervertebral disk which allows angular movement of the vertebrae while providing the

absorption and distribution of shock as well as preventing friction between the otherwise bare

connecting vertebral bones. (14) The spinal column and its vertebrae are connected via a

network of ligaments and muscles that provide it with stability and rigidity. (7) (15) (16)

10

Figure 3 – Anatomy of the Porcine Vertebral Column (14)

Table 1 – Comparative Summary of the Variation in Vertebral Bone Numbers (14) (15)

Differences and Similarities of the Human and Porcine Spine

Further research has been undertaken into the differences and similarities between the human

and porcine spine. This section of the report will focus on the comparisons made between them

in terms of the mechanical vertebral loading and the corresponding force distribution applied

to the vertebrae. Using this information the author will attempt to further validate the use of

porcine vertebrae as reasonable models to investigate loading of the human spine.

Vertebral Loading Orientation

Considering the resemblances found in this report between human and porcine specimens

regarding the anatomy of the spine an investigation was undertaken to see if indeed both cases

transferred load through their respective vertebral columns in a similar manner.

Static Loads

It is obvious from the orientation of a bipeds (human) upright position that the main static force

experienced within the vertebral column is that of axial compression, as it lies parallel to the

force of gravity. The quadruped (porcine) spinal column on the other hand is laid horizontal

which means gravity and body weight act as axial shear loads on the spine which therefore

indicates that there is a fundamental difference in how the spine will support itself. In this case

the vertebral column is held in firm stability via complex ligament and muscular systems

connected throughout the spine. The funiculus nuchae and linea alba ligaments work alongside

Vertebral Region Human Pig

Cervical/Cranial 7 7

Thoracic 12 14 - 17

Lumber 5 6 - 7

Sacral 4 (Sacrum) 5

Caudal 3 – 5 (Coccyx) 20 - 23

Total 31 -33 52 - 59

11

a network of muscles to provide axial compression and tension, similar to that of a biped, but

instead to combat the perpendicular acting forces mentioned previously. (12)

Dynamic Loads

The dynamics of quadruped locomotion is beyond the scope of this report however research by

Theo H. Smit (12) into the translation of loads encountered via walking, trotting and galloping

was undertaken and in summary the force exerted due to the opposing torsional moments of

the pelvis and thorax during a trot alone would result in severe deformation of the spines

vertebrae if they were to resist this force alone. In conclusion this means that a system of tensile

structures such as muscles and ligaments must be present to compensate for the applied

moments. As such, this results in a transfer of loads to the spinal column via axial compression

and thus it appears that the spine of a quadruped is loaded quite similar to that of a biped. (12)

Vertebral Bone Architecture

According to Wolff (17) the structural design of a bone has a close relationship to that of its

mechanical function. This is known as Wolff’s law and it states that a bone will organise itself

in the best orientation to allow it to bear applied physiological loads. The theory is that unused

bone is recycled by the body whereas stresses applied to bone will stimulate further bone

formation. Therefore bone is said to be able to adapt and remodel itself in accordance to the

mechanical loads it is exposed to. It must be noted that bone adaptation is a slow process that

only responds to heavy and regular loading such as that of locomotion experienced on a day to

day basis which makes this a particularly strong indicator of the dominant loads applied to the

bone. This law applies to both cortical and trabecular bone but evidence is most prominent in

that of the trabecular and as such the latter was investigated further. Note the adaptation of the

cortical bone comes in the form of change to its thickness and shape in relation to the magnitude

of forces regularly applied. (17)

Discussion

In light of the previous information, a study undertaken by Ruey-Mo Lin et al (18) was

considered. This study focuses on the distribution and regional strength of trabecular bone in

the porcine lumbar spine with its comparison to that of the human lumbar spine. The study uses

2 lumbosacral porcine spines taken from heathy pigs of around 2.5 years old and also the

lumbosacral spine from a heathy 25 year old man who died in a traffic accident and had no

previous significant diseases. The vertebral bodies of the L3, L4 and L5 vertebrae of each spinal

section were separated, cleaned and prepared by slicing 3 cancellous bone segments 5mm thick

12

in transverse, sagittal, coronal planes (see Figure 4) to allow access to the trabecular bone. The

observation of the prepared specimens was made using X-rays and a zoom stereo microscope

(SZ40, Olympus optical co., Tokyo, Japan)

Figure 4 – Orientation of the Transverse, Sagittal, Coronal Planes (19)

Figure 5 - Zoom Stereo Photomicrograph of Human and Porcine Trabeculae Morphology in Lumbar Vertebrae

(17)

The results of the study are shown in Figure 5 above. It can be seen, particularly in the coronal

and sagittal sections, that the main struts of the trabecular architecture, in both the human and

the porcine samples, sit longitudinal and parallel with the axis of the spine. Due to the

13

orientation of the transverse sample, it takes a horizontal cross-section across the width of the

vertebrae and therefore does not adequately highlight the vertical characteristics of the

trabecular struts in this case. However, in each photograph the presence of horizontal cross

bridging struts used to further support the vertical struts can be seen, this is highlighted

particularly well in the transverse section. As has been discussed previously, the dominant load

applied to the biped spine is that of axial compression and therefore it is reasonable that the

bone architecture sits longitudinal and parallel with the axis of the spine i.e. endplate to

endplate to resist the forces of axial compression. Given the research undertaken into the

transfer of loads during static and dynamic quadruped locomotion along with the similarities

found by Ruey-Mo Lin et al (18) of the orientations of the trabecular morphology it is also

reasonable to say that the main static force experienced within the porcine vertebral column is

also of axial compression. These points can be further substantiated by the geometrical and size

similarities of the porcine and human vertebra found by Mr. Christopher McClelland (6) which

imply similar axial loadings experienced between bipeds and quadrupeds. It must also be noted

that in this same report by Mr. Christopher McClelland (6) the porcine specimen’s trabecular

bone was seen to be more homogenous.

Vertebral Load Distribution

Considering that the main load applied in both cases was found to be axial compression, and

also that the significant differences present in the orientation of the facet joint in either case,

caused variance in the loading of eccentric loads (such as that experienced during flexion and

extension), it was decided that only axial loading will be further investigated for the remainder

of this report. As discussed previously, the vertebrae are physically connected with each other

via the anterior column (vertebral base & intervertebral disks) and the posterior column (the

laminae articulations that house the facet joint couplings). An investigation was undertaken

into how the applied loads encountered are distributed throughout the vertebra itself. One

particular study by Aruna et al (20) was considered which focused on the transmission of load

through the neural arch of the lumbar vertebrae in humans via the comparison of areas of load

bearing regions present in the anterior (inferior vertebral base) and posterior (laminae and

articular facets) sections of the vertebrae under the assumption that the size of a given portion

of the vertebrae is related to the magnitude of the forces acting upon it i.e. Wolff’s law, as

discussed previously and also considering that resistance to pressure by a uniform structure

depends on its cross sectional area. Although basic in technique and containing assumptions,

this study also incorporates numerous other studies incorporating the use of more superior

14

techniques and presents a comparison table of all results found. Such studies include one

undertaken by Yang and King (21) where lumbar segments were instrumented with an

intervertebral load cell (IVLC) to measure disc load so that facet load could be deduced. The

study by Aruna et al (20) uses the area of the inferior surface of the vertebral body as the

anterior column parameter solely because it was the lowest and most linear but notes that a

combination including the superior surface would give better results. The areas of the inferior

articular facets were used as the first parameter of the posterior column. The cross sectional

areas of the laminae (see Figure 2) were used as the second parameter of the posterior column

as it is stated that

“The articular facets are incorporated in the laminae itself; hence the compressive forces

acting at the superior articular facets are transmitted to the inferior articular facets through

the laminae. Thus a cross sectional area of the laminae represents the magnitude of the forces

transmitted through it. In other words, the compressive forces transmitted through the laminae

are the same as that transmitted through the two articular facets.”

These measurements were carried out on forty-four disease free sets of adult male lumbar

vertebrae (total vertebrae: 220). Each of the posterior parameters were compared with the

anterior parameter and an average value was deduced from the range of posterior loads

presented. This average was then used in the comparative study by Aruna et al (20) against a

range of alternative researched data values to come up with the averaged percentages for each

vertebra seen in Table 2 below. Theses averages were averaged to estimate each case overall.

Table 2 - Percentage Area of Inferior Surface of the Vertebral Body in Comparison with Inferior Articular

Facets and Cross Sectional Area of the Lamina for Each Lumbar Vertebra

Table 3 - Comparison of Results from Various Studies of Load Percentages Transmitted by the Posterior

Column in Lumbar Vertebrae.

Vertebral Set

# % Inferior Body Area % Inferior Articular Facet Area % Inferior Body Area % Lamina Cross-Section Area

L1 81.76 18.24 85.24 14.76

L2 80.25 19.75 84.55 15.45

L3 80.83 19.27 83.98 16.02

L4 80.84 19.16 83.25 16.75

L5 76.71 23.29 78.66 21.3

Average 80.078 19.942 83.136 16.856

Anterior Parameter vs Posterier Paramter 1 Anterior Parameter vs Posterier Paramter 2

Study no. Auther (year) Method% of load transmitted by posterior

coloumn in lumbar vertebrea

1 Adams & Hutton (1980) X,Y Recodered (force vs vertical displacent) 16%

2 Yang & king (1984) Intervertebral load cell (IVLD) 25%

3 Pal & Routal (1986) Comparasion of load bearing area measures 19.57%

4 Aruna et al (2003) Comparasion of load bearing area measures 18.4%

# Average 20%

15

Summary

Noticeable differences between the results of this study may be attributed to racial and ethnic

differences present between specimens of people used in each of these studies. Also in

particular significant discrepancies can be seen present due to the use of the different

methodologies used by Adams & Hutton (1980) (22) & Yang and King (1984) (21). Taking an

average value for all results yields the following conclusion about vertebral load distribution:

Vertebral body takes: 80%

Articular facet joints take: 20%

Natural Vertebral Loading Magnitudes

The magnitude of loads applied to the vertebrae are important as the heavy and regular loading

patterns of locomotion experienced on a day to day basis cause the bone adaptations discussed

in the previous section. Research and analysis of three in-vivo studies involving the

experimental detection of forces acting on the lumbar region of the spine in humans and a

quadruped (Sheep) during a range of naturally occurring activities were compared and

tabulated as follows:

Table 4 – Comparison of Human and Quadruped Vertebral Lumbar Forces over a Range of Naturally Occurring

Activities (23) (24) (25)

In the study of Wilke et al (24) the data was presented in the form of pressure (Mpa). To convert

this data into comparable units the pressures found acting within vertebrae were multiplied by

the cross sectional area of the intervertebral disk provided in the report (Force = Pressure x

Area). This method was questionable at first considering that the pressure transducer was

located within the nucleus pulpous (soft core) and didn’t consider the annulus fibrosus (tough

outer rim). Upon examination of the study by Sato (25), it seems an identical method of testing

as that found in Wilke et al (24) was used except the results had been given in the desired units

(Newton’s (N)). Comparing the results of Sato (25) to the converted results of Wilke et al (24)

using the technique mentioned above, it can be seen that similarities are present and for this

reason it was decided that the pressure-force conversion method used was valid. All Species

Activity

Sheep (Hauerstock et

al 2001)(Load Cell)

Human (Wilke et al

1999) (Pressure

Transducer)

Human (Sato (-))

(Pressure

Transducer)

Human average

Human average -

sheep %

difference

Lying Prone 212 N 198 N 144 N 171 N 23.80%

Standing 161 N 900 N 800 N 850 N 81.10%

Walking 461 N 1170 N - 1170 N 60.60%

Running/Trotting 684 N 1530 N - 1530 N 55.30%

Stare Climbing/Jumping 1290 N 2160 N - 2160 N 40.20%

16

follow the trend of increased loading with increased activity as expected. In all cases but one

(lying prone) the human experienced a significantly higher load. Sato (25) states “The spinal

load was highly dependent on the angle of the motion” which implies that the quadruped

vertebrae may experience more force when lying prone due to a more severe vertebral angle

exerted during that particular position or due to a lack of range of motion in the region.

According to Wolff’s law (17) discussed previously the structural design of a bone holds a close

relationship to that of its mechanical function. It is also stated that Wolff’s law is by no means

the most dominate factor of bone structure when compared to such things as genetics but

considering it alone it could be expected that the human bone would be able to carry larger

loads than quadrupeds such as sheep which lays the ground for the next section.

Vertebral Loading Characteristics

Considering the results discovered above, an investigation into vertebral behaviours under

uniaxial compressive loads was undertaken. To date there have been numerous experiments

conducted examining the mechanical loading behaviours and similarities of human and porcine

bone. An example of a method used by Colin Bight is that the vertebral bodies of test specimens

are dissected of all soft tissue and posterior portions of the vertebra. The specimens were then

manually cleaned so that the bone surface was not damaged. The vertebrae were mounted in

polyurethane so that the superior and inferior end plates were constrained. Testing was carried

out using the MTS Bionix Servo hydraulic Test System.

Testing process was as follows:

Pre-load 250N and hold for 60s

Load to zero

Compress at 0.25mm/s to failure

Failure is classified as 10% reduction in height

Several studies using similar testing methods and a variety of materials testing machines were

considered for this evaluation. Figures 6 & 7 below display the findings of various authors

with regards to these material behaviours.

17

Figure 6–Comparative Uniaxial Compression Test Results for the Human and Porcine L4 Vertebral Bodies (26)

(27)

Figure 7 - Comparative Uniaxial Compression Test Results for the Human and Porcine L3 Vertebral Bodies (2)

(28)

It can be seen in both cases that the porcine specimens had a greater resistance to compression

then the human counterparts. In an attempt to explain these differences the work of Mr.

Christopher McClelland (6) was consulted where a comparison table of the material properties

for human and porcine bones from various authors was compiled as follows in the Table 4

below:

18

Table 5 - Mean & (SD) values for Material Properties of Cortical & Trabecular bone for Porcine & Human Specimens (29), (30), (31), (32), (33), (34), (35), (36)

19

The study summarises the analysis of the data as follows:

“Porcine and human cortical bone display similar material properties. However the trabecular

bone of both species display both similarities and differences. Similarities where observed in

the distribution and alignment of the trabeculae throughout both specimens. The differences

between the two species was observed in the values of ultimate strength and bone density for

trabecular bone. In terms of ultimate strength the porcine trabecular bone was approximately

five times stronger than that of the human trabecular bone. The density of bone was more

homogenous in the porcine trabecular specimens. The distribution of mechanical strength was

found to be similar. However it is important to note that the bone properties vary with age.”

Referring back to the study by Ruey-Mo Lin et al (29) previously discussed in this report which

investigated the strength and distribution of trabecular bone in the porcine lumbar spine. It

states that the similarity in the Young’s moduli of both species may be attributed to the

similarities found in the bone orientation. The differences in strength of the trabecular bone

between the two specimens, may be as a result of the higher bone density and greater

homogeneity of the porcine trabecular bone.

Vertebral Bone Density and Load Sharing Between Trabecular and Cortical Bone

Considering the highlighted information regarding the role of the trabecular bone density in

the previous section an investigation was undertaken to analyse the load sharing responsibilities

of the trabecular vs the cortical bone and its effect on the overall strength of the vertebra. For

this, one study by Kilincer et al (37) was considered. The study aims to determine the debated

issue of load sharing in a vertebral body via a series of non-destructive compressive tests on

human thoracic vertebral bodies. The testing process consisted of a stepwise removal of the

vertebrae’s trabecular centrum and measurement of surface strains. The results of this study

found that the load sharing of cortical shell of a normal healthy vertebrae was 44.3±10.6 %.

Load sharing of middle thoracic vertebrae (49.4 ±10.0 %) was significantly higher than that of

lower thoracic vertebrae (42.4±8.5 %). According to general linear model analysis, test speed

and load were not found to be effectual on load sharing with the exception that osteogenic

vertebrae showed lower cortical load sharing under higher loads. The study concludes that:

“The cortical shell takes nearly 45% of physiological loads acting upon an isolated thoracic

vertebra. Load sharing between cortical shell and trabecular centrum is significantly affected

by spinal level and bone mineral density. “The load borne by trabecular bone increases

towards the lower spinal levels, and decreases by osteoporosis.” Therefore density is the

20

contributing factor in the resistance to compression and would explain the dramatic increase in

porcine compressive strength found in the research data.

Overall Summary

Considering these findings, the author has decided that it would be unreasonable to use pig

lumbar samples to investigate human lumbar loading due to the massive discrepancies and

resulting effects found in the density of the trabecular bone of the porcine samples studied. The

earlier expectation that the human bone may be able to carry larger loads when considering

Wolff’s law alone (17) seems to be invalid. The increased compressive strength in quadrupeds

could be a result of genetics and also the rapid increase in weight gain experienced in the early

growth phase, which see a large increase in bone volume (38). Although it was confirmed that

due to particular ligament and muscular influences, the quadruped spinal column is loaded

mainly in axial compression, which is similar to that of the human spinal column, it has been

deemed that the quadruped is overall an extremely complex locomotive system which little is

known about. This has been found to be particularly true during the attempts to find research

involving the activity of the integrated joints and muscles within animals, making it nearly

impossible to determine the actual loads in these living systems.

Acquisition of Material Properties from CT Scans

This section summarises the work of several authors which are referenced within, about a

particular method used to acquire the material properties of bone from CT scans.

The X-rays used during a CT scan are detected after they have passed through the bone, the

signal detected is related to a grayscale value. A radiographic Phantom consisting of known

material densities that are equivalent to the densities of the anatomic materials normally found

in and around bone is used to calibrate the data acquired from the CT scans. Hydroxyapatite

(HA) is a common example of a material used to calibrate the density of bone thus meaning

the true bone tissue density is not directly measured during a CT scan but instead the density

of a material with an equivalent mineral content to the scanned material. Placing the Phantom

in a body of water prior to scanning allows for the simulation of the soft tissue present in the

body. The Phantom is positioned, scanned, saved and exported as a DICOM file to a third party

viewing software where a mean grey scale value and standard deviation for each of the

equivalent materials can be obtained and recorded. Linear attenuation values can be derived

for each the equivalent materials using the appropriate X-Ray mass attenuation coefficients,

which can be obtained via standardized measurement bodies such as the tables provided by

21

NIST (US National Institute of Standards and Technology) (39). Note: interpolation may be

necessary to calculate the exact attenuation coefficient for the energy range of a particular X-

Ray machine which may result in slight errors. In addition to the mass attenuation coefficients,

the elemental composition and specific gravity (used to convert to density) of each of the

equivalent materials, can be obtained from the materials manufacture e.g. Gammex who

provide a specification sheet on their products (40), are used to calculate the attenuation

coefficient for each material at the X-ray machine specific energy level ranges e.g. 30 keV to

150 keV, which is found in dental CBCT X-ray machines. The grey scale values for each of

the equivalent materials present in the phantom were plotted against the relative linear

attenuation coefficients over the relevant photon energy range to reveal an approximately linear

relationship between grey scales levels and attenuation properties. Linear regression can be

applied to each energy value in the chosen range to highlight the best fit linear line (41). The

equation of this line provides a suitable means of converting grey scales into linear attenuation

coefficients and consequently into Hounsfield Units (Standard CT number) via the following

equation:

𝐻𝑈 = (1000)𝐶𝑇−𝐶𝑇𝑤

𝐶𝑇𝑤−𝐶𝑇𝑎 [HU] (31)

Where CT, CTw and CTa are the values of the material, water and air respectively.

In the next step, the material properties of bone tissue are defined by empirical equations:

Material density [kg/m3] = ρ (HU) = a1 + a2(HU)a3 + a4(HU)a5 (42),

Young modulus [MPa] = E(ρ) = b1 + b2ρ b3 + b4ρ b5 (42),

Where, ai, bi, ci (i = 1, 2, ..., 5) are coefficients dependent on bone tissue (cortical or trabecular).

Below is a table of several equations used by a range of authors in the construction of various

bone finite element models. Only equations that were involved in fully validated models have

been considered. Traceability of CT scanner calibration via an imaging phantom was also

desirable but due to the nature of clinical CT scanners the calibration cycles are far less frequent

then other CT scanners e.g. micro CT scanners and may be the reason for lack of mention in

most of these studies.

22

Results

Table 6 – Table of Material Property Equations from Various Authors. (43) (44) (45) (46) (42) (47) (48)

Species Bone Density (g/cm3) Young's Modulas (MPa) Author

Validated via

Phantom

Calibtration

Used in the

Creation of

Validated Model

Human L1 Vertebrae Tawara et al. (2010) a a

Human L1 Vertebrae ρ = 1.067 * HU + 131 Xiao et al. (2012) ? aHuman L2 Vertebrae ρ = 0.18 + 0.001244 (HU - 100) E. Morgan et al. (2013) ? a

Human Femer ρ=1.9 HU/1,700 Xin Xie (2010) ? a

Human L4 Vertebrae ρ = 1.122 ⋅ HU + 47, E = 1.92ρ – 170 Skoworodko et al. (2008) ? a

Human L4 Vertebrae ρ = 0.0132 + 0.001* HU Garduño et al. (2011) ? aHuman L4 Vertebrae ρ = 1.6 × HU + 47 Xiao (2011) ? a

Material Property Equations

= 0 𝐻𝑈 1 10−

= 0 001 = 0 0 E = 33900 0.0 < 0 E = 5307 0.27 < < 0.6E = 10200 0.6

E = 0.09882

E = 4730

E = 13.430 +1426ρ (Cortical)E = 1310ρ1.40 (Trabecular)

E = 700

E = 0.09882

23

Anatomical Mesh Creation Methods

There are a lot of meshing software’s that have been designed to accommodate simple

geometry and dimensions and thus are often incapable or inefficient when it comes to complex

anatomic structures and in particular when there is a desire for hexahedral elements. Of the

range of software’s that can provide the necessary tools for the task at hand (e.g. Mimics, Scan

FE) only a few of them can generate a mesh directly from a CT scan and most use tetrahedral

elements due to the complexities associated with the more effective hexahedral elements

possible. This section investigates a freely available software toolkit that is aimed at hexahedral

mesh generation.

IA-FEMesh

IA-FEMesh began as a project undertaken by ‘The Musculoskeletal Imaging, Modeling, and

Experimentation’ (MIMX) Program at The University of Iowa. It was development in an

attempt to facilitate the FE modelling of complex geometries such anatomic components. A

study by DeVries et al (49) was considered to highlight the validity of IA-FEMesh. This

study compares the mesh development of phalanx bone model via IA-FEMesh compared to

models created via conventional meshing techniques using commercial software

(MSC/PATRAN, Version 2005 r2) and open-source software (NETGEN, version 4.3). The

factors considered were mesh generation time, element type (hexahedral and tetrahedral),

number of zero volume elements, numbers of distorted elements and the ability to capture the

anatomical geometry. Additionally analysis of the Von Mises stress distributions was

undertaken and a table of the ideal number of nodes, number of elements, and average

element length based on an ideal mesh convergence study was used to compare with. The

results are as follows:

Figure 8 - Table of the Ideal Number of Nodes, Number of Elements, and Average Element Length Based on an

Ideal Mesh Convergence Study. (49)

Finger Bone Number of Nodes Number of elements Average Element Length (mm)

Distal Phalanx 4200 3402 0.625

Middle Phalanx 5952 4950 0.75

Proximal Phalanx 5544 4550 1

24

Figure 9 - The Number of Nodes and Elements in Each Mesh and the Corresponding Average Element Length

as well as Element Quality and Mesh Generation Time. (49)

In terms of subject specific models time is an important factor. IA-FEMesh produced a

geometrically sound hexahedral mesh in 6 minutes which is substantially quicker than the

PATRAN software but it was stated that “as the geometric complexity increases, the time

required to generate the building block structure in IA-FEMesh will increase, thereby adding

time to the meshing process”. The mesh generated using IA-FEMesh experienced fewer

distorted hexahedral elements compared to the PATRAN model, however both hexahedral

meshes had more distorted elements than the tetrahedral meshes. This was expected, since

tetrahedral elements are less sensitive to distortion. It was found that the stress distributions for

the hexahedral meshes yielded a more smooth stress distribution when compared to the

tetrahedral mesh.

The IA-FEMesh model was further validated by comparison to the experimental testing of the

same phalanx bone via analysis of the contact areas during a compression test. The results are

as follows:

Figure 10 - The Resulting Contact Area for the Experimental Data and Finite Element Model. (49)

As the load increased from 25N to 50N, the percent error decreased from 13.17% to 3.69%.

These values are similar to the error values reported in the reviewed literature in the report

which have shown percentage error ranges from 8-36% for contact area measurements. It was

concluded that “IA-FEMesh is capable of generating anatomically accurate hexahedral

meshes of the human phalanx in significantly less time than a traditionally used commercial

mesh generator”

Meshing

Software

Element

Type

Average Element

Length (mm)

Number of

Nodes

Number of

Elements

Distorted

Elements

Zero

Volume

Elements

Mesh

Generation

Time (Min)

IA-FEMesh Hex 1 5544 4550 455 0 6

PATRAN Hex 1 6552 5434 901 1 330

PATRAN Tet 1 11366 52835 228 0 330

PATRAN Tet 2 1724 7506 55 0 330

NETGEN Tet - 808 2457 0 0 1

Load (N) Pressure Film FE Model Error (%)

25 12.36 10.73 -13.17

50 15.61 15.03 -3.69

25

Meshing Techniques

Whole Vertebra (1 stage)

Studies such as the ones undertaken by Zafarparandeh et al (50) and Kallemeyn et al (3) have

shown the creation and full validation of various vertebral models through the use of IA-

FEMesh’s multi-block approach. No comments were made about the performance of the

software nor was there mention of any issues encountered through the meshing process of the

vertebrae complex geometry.

Anterior-Posterior Separation

Another study also by Kallemeyn et al (51) illustrates through the use of a third party software

(ParaView), how the posterior region of the vertebral model can be removed. The remaining

anterior section (vertebral body) and the separated posterior region were meshed individually

and joined via node alignment of the two meshes. The study concludes that the method used

“dramatically decreases the amount of time required to mesh the spine as compared to previous

methods, while maintaining the geometrical complexities inherent to the spine.” (51)

Mapping Algorithm

A study by Ramme et al (52) show the capabilities of using an Automated Building Block

Algorithm developed using the C++ programming language, Visualization Toolkit (VTK), and

Vascular Modelling Toolkit (VMTK). The algorithm was applied to 27 different bone models

from the hand and wrist regions and found that all cases successfully generated a hexahedral

mesh appropriate for finite element analysis. The report concludes “This work represents

advancement towards automating the manual procedures in the IA-FEMesh mesh generation

protocol” but states the limitation of the algorithm is that it has only been designed to

accommodate simpler bone geometries.

Summary

A study by Grosland et al (53) provides a comprehensive overview and step by step guide on

how use the functions in IA-FEMesh. Using this, the author will attempt to mesh the vertebral

STL manually and without separation. This decision was made solely on the basis that the

scope of this project does not allow the utilization of third party software.

26

Model Validation

The final step of the finite element analysis process is the validation of the model. The objective

of validation is to examine the capabilities of the FE model at hand by comparing its predictive

results to that of real world test data which is usually acquired through cadaver experiments.

Below are examples of the resolution of validated models:

Figure 11 –Force Displacement Curves for Experimental Loading of the L1 Porcine Vertebrae vs Corresponding

FE Models (54)

0

0.5

1

1.5

2

2.5

3

3.5

0 0.1 0.2 0.3 0.4 0.5

Forc

e (k

N)

Displacment (mm)

Validated Finite Element Model - L1 Vertebrae

Pahr et al (Model 1 -L1)(2012)

Pahr et al (Experimental- L1)(2012)

Pahr et al (FE Model 2 -L1)(2012)

27

Figure 12 – Force Displacement Curves for Experimental Loading of the L2 Porcine Vertebrae vs

Corresponding FE Models (54)



0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

0 0.1 0.2 0.3 0.4 0.5

Forc

e (k

N)

Displacment (mm)


Pahr et al(Experimental -L2)(2012)

Pahr et al (FE Model 2- L2)(2012)

0

1

2

3

4

5

6

7

8

9

10

0 0.1 0.2 0.3 0.4 0.5

Forc

e (k

N)

Displacment (mm)


Pahr et al (FEModel 2 -L3)(2012)

Pahr et al (FEModel 1 -L3)(2012)

Pahr et al(Experimental -L3)(2012)

28





0

1

2

3

4

5

6

7

8

9

10

0 1 2 3 4 5

Forc

e (k

N)

Displacment (mm)


Ruth K. Wilcox (FEModel 1 - L3)(2007)

Ruth K. Wilcox(Experimental -L3)(2007)Ruth K. Wilcox (FEModel 1 - L3)(2007)

Ruth K. Wilcox (FEModel 2 - L3)(2007)

0

1

2

3

4

5

6

7

8

9

10

-0.2 0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Forc

e (k

N)

Displacment (mm)

Experimental loading of the L4 Porcine Vertebrea vs Corresponding

Colin Bright (FEModel -L4)(2014)

Colin Bright(Experimental- L4)(2014)

29

Chapter 3 Design

Due to the detail of the documented work illustrated by Mr. Christopher McClelland (6), this

chapter’s primary objective is to highlight any further actions taken in the design of a

segmented vertebrae and also any problems encountered using the software (3D-Slicer).

3D-Slicer Steps

The following flowchart outlines the steps involved in creating a model of the segmented

vertebra using 3D-Slicer.

Figure 16 - Flowchart Outlining the Step by Step Procedure Required to create a segmented model using 3D-

Slicer (6)

Preliminary Model

Following the step by step instructions detailed in the study by Mr. Christopher McClelland

(6) a successful preliminary segmented vertebral model was created as follows:

Figure 17 - Screenshot from 3D-Slicer Illustrating the Result of Generating a Segmented Model

Load DICOM Files

Crop Data to Create a R.O.I

Create a Label Map

Generate Model

Save as an STL File

30

Geometric Simplification

Learning from the experiences found by Mr. Christopher McClelland (6) in relation to the

benefits regarding the simplification of model geometry to enable or increase workability in

the future when trying to apply a finite element mesh and also for reducing computational time

for analysis, it was decided that only the artefacts of the vertebra bearing load during uniaxial

compression were of interest and all other material could be discarded. The process of

simplifying the geometry is a careful and lengthy process where the user attempts to segment

unwanted material from the main model and blend in the attachment points.

Initial Geometrically Simplified Model

Through the research in the literature survey it was found that the vertebral body and articular

facet joints carried 100 % of the axial compressive loads at an 80:20 split. For the first model

it was decided that the inferior facet joints were used only to transfer loads to the adjacent

vertebrae and could also to be discarded. The spinous process and transverse processes have

been said to have been used only for attachment point for muscles and ligament and thus were

also discarded. The bulk of the material to be discarded was removed in the crop volume model

where the ROI was parameterised about the vertebral body and articular facets joints.

Figure 18 – Re-Parameterisation of ROI to only Accommodate Articular Facets and Vertebral Body

31

With this addition implemented the guide followed until the editor section where the rest of the

unwanted material was removed using the pixel mode in the paint brush tool of the editor

module.

Figure 19 - : Slicer Editor Module Toolbar (with toolbar legend) and Paint Brush Function open

Every CT picture of each of the views was scrolled through and subsequently the unwanted

material was removed by being painted to background. This is a lengthy and delicate process

where the main objective is to remove the unwanted material and blend any major blemishes

the model way have as a result. Multiple models must be made in order to see the slight chances

that may have been made to the model upon relabelling certain pixels in the pursuit of a simple

model surface. Once satisfied a smooth model is created as per the

instruction in the review report and save as an STL surface model.

.

Figure 20 - Screenshot from 3D-Slicer Illustrating the Result of Generating a Geometrically Efficient Model

(Vertebral Body and Articular Facets)

32

Design Rework

Later the decision to remove the inferior facet joints was revoked due to the role played in

supporting the vertebrae and subsequently a second model was created with the inferior facets

reinstated. The process was again repeated as explained in the report except the inferior facets

were left intact.

Figure 21 - Screenshot from 3D-Slicer Illustrating the Result of Generating a Geometrically Efficient Model

(Vertebral Body, Inferior and Articular Facets)

It was decided that both models were sufficient for analysis at a later stage and therefore the

study will see both feature further in this study.

Summary

Due to the sound instruction provided in by Mr. Christopher McClelland (6) no major problems

were encountered.

33

Chapter 4 Finite Element Mesh Creation

The step by step process of creating the mesh using this software package is detailed heavily

in the Report provided by Mr. Christopher McClelland (6) and this section will just highlight

any significant deviations in the process.

Import Surface

The initial surface model was imported into the IA-FEMesh software package.

Figure 22 – Screenshot from IA-FEMesh Illustrating the Result of Loading the STL File of the Geometrically

Simplified Vertebrae.

Import Image

The segmented CT scan image (saved as an HDR file) was also imported to allow for the

application of material properties to the model via the grey scale per voxel attenuation level of

the CT scan.

Figure 23 - Screenshot from IA-FEMesh Illustrating the Result of Importing the CT Image.

34

Create Building Blocks

As opposed to Mr. Christopher McClelland the geometry of this anatomic shape is slightly

more complicated than the vertebral body alone because of the incorporation of the facets joint.

In particular porcine facet joint are of a difficult geometry due to the orientation of the “hinge

like” articulations as discussed in the literature review. To overcome this, the creation of 3

building blocks was required. One for the vertebral body as Mr. Christopher McClelland (6)

had done and then 2 separate blocks to accommodate each articular facet joint. IA-FEMesh

facilitates the connection of individual building blocks to form one single block. The nodes

were positioned accordingly and the results of this are as follows:

Figure 24 – Building Block Creation and Node Positioning about Surface Model

Application of Finite Element Mesh

Following the instructions in the reviewed report the mesh was applied to surface model.

Several attempts were made and upon skewing of the hexahedral mesh elements or

entanglement of the lines, the building block nodes were repositioned accordingly to improve

the model. The results of the successful meshed body are as follows:

Figure 25 – Finished meshed model including facet joints.

35

Geometry Simplification

Due to the complex shape and angles involved in this model, it was deemed unfeasible to test

in the next section. The lack of computational power available, restricted the size of the

elements resulting in skew of some elements at locations of particularly tight angles (inside of

facet joints). Skewed elements either, didn’t not regenerate when brought for testing in the next

section or regenerated but presented unrealistic, high stress concentration points across the

model. Furthermore, considering the abundance of comparable data available (both

experimental and simulated) for compression tests on just the vertebral body alone, as opposed

to with the accompanying facet joints, it was decided that the facets joints (articular and

inferior) would be removed from the model and just the vertebral body to be left for testing.

This geometry simplification was undertaken in 3D-Slicer as per the instructions laid out in the

previous chapter. Upon suitable geometry simplification the steps laid out in this chapter were

applied and the resulting meshed model can be seen below in Figure 26.

Figure 26 - Finished Meshed Model Excluding Facet Joints (Vertebral Body Alone).

Assignment of Material Properties & FE Mesh Models Created

The image based method was chosen for the assignment of material properties as opposed to

the user defined method in the interest of facilitating non-invasive, patient specific FE models.

All of the researched material property equations were trialled along with custom made

equations created by the author. The following table gives the details of each FE mesh model

created and their respective equations as follows:

36

E (MPa) = A + Bρ2

Table 7 – Table of Details for Each FE Mesh Model Created throughout the Project.

Xiao et al. (2011) (48) & Xiao et al. (2012) (44) had the same equation for E, Young’s

Modulus but as can be seen in Table 7 each equation was based on a separate density

equations to be implemented prior and thus providing a distinction between the potential E,

Young’s modulus values as a result. Unfortunately, IA-FEMesh does not allow for the

configuration of the density value and as such the models Xiao et al. (2011) (48) & Xiao et al.

(2012) (44) were therefore identical. The model created from the material property equation

provided by Xiao et al. (2012) (44) was used to represent both cases in the analysis

undertaken later in this project.

Parameters

Model Settings Name A B C E Modulus Range (MPa)

IA-FEMesh Settings 0 2875 3 1321 - 36604

Chris McClelland 0 1100 2 517 - 6220

Tawara et al. (2010) - 1 0 33900 2.2 1474 - 227951

Tawara et al. (2010) - 2 469 5307 1 4107 - 13089

Tawara et al. (2010) - 3 0 10200 2.01 4776 - 58179

Xiao et al. (2012) 0 0.09882 1.56 0.055 - 0.382

E. Morgan et al. (2013) 0 4730 1.56 2625 - 18270

Garduño et al. (2011) 0 700 1.91 340 - 3661

Xin Xie (2010) - Cortical -13.43 1426 1 964 - 3378

Xin Xie (2010) - Trabecular 0 1310 1.4 772 - 4405

SKOWORODKO et al. (2008) -170 -1.92 1 0.011 - 0.086

John Custom (1.1) 0 400 1.91 195 - 2092

John Custom (1.2) 0 400 1.91 218.2 – 1893.6

John Custom (1.5) 0 400 1.91 322.5 – 1743.5

37

Chapter 5 Testing

This chapter will detail the use of the “ANSYS” software package and illustrate how the

model was loaded whist keeping intact the assign material properties. Furthermore this

chapter will show how to obtain the necessary results.

Loading the Model

Using the “Finite Element Modeller” module in “ANSYS 15.0”, the model was able to be

uploaded. In order to keep intact the material properties, the body grouping setting was set to

“materials” and ID Handling was set to “no action”. The model was updated and the image

based material properties assigned in IA-FEMesh were retained. Figure 27 below shows the

resulting model containing the various material properties.

Figure 27 - Screenshot from ANSYS Illustrating the Result of Loading the Model Containing 95 Grouped

Materials (6).

38

Compression Test

Each model was brought into ANSYS where loading and support surfaces were applied to

either end of the vertebral body, as seen in Figure 28 & 29 below.

The model was then tested under a purely axial static structural compression. The load was

increased in 500N increments from 0 to 10000N and the deformation and stresses were

calculated. The subsequent deformation and stress results were exported into an Excel spread

sheet for analysis and comparison with the real world test data. Figure 30 displays the results

of a simulated compression test.

Figure 30 - Screenshot from ANSYS Illustrating the Varying Deformations Using a Colour Scale. (6)

Summary of Testing

All the model created were tested with in the ANSYS software package successfully and an

overview of the results is present in Chapter 6 – Results, of this report. A complete

compilations of results is present in Chapter 10 – appendix, of this report.

Figure 29 - Screenshot from ANSYS Illustrating the

Result of Defining the Upper End Plate as the

Loading Surface. (6)

Figure 28 - Screenshot from ANSYS Illustrating the

Result of Defining the Lower End Plate as a Fixed

Support. (6)

39

Chapter 6 Results

Graph of Deformation from Finite Element Analysis Results

40

Figure 31 - Graph of the Results of Simulated Compression Testing in ANSYS, on the Models Created using IA-FEMesh.

41

Graph of Max Stresses from Finite Element Analysis Results

Figure 32 - Graph of the Results of Simulated Compression Testing in ANSYS, on the Models Created using IA-FEMesh.

42

Chart of Material Property Distribution and Range (John Custom (1.1))

Figure 33 - Chart of Material Property Distribution and Range (John Custom (1.1))

16

536

7352

6689

2633

811

23697 41 3

0

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

5500

6000

6500

7000

7500

8000

0-400 400 - 600 600 - 800 800 - 930 930 - 1100 1100 - 1300 1300 - 1500 1500 - 1700 1700 - 1900 1900 - 2100

Nu

mer

of

Elem

ents

Elastic Modulas Range (MPa)

Custom Model of Element Size 1.1 Material Property Distribution Range

Number of ElementsPresent per ElasticModulas Range forElement Size of 1.1

43



12

286

5584

4068

1889

505

128 55 17 00

1000

2000

3000

4000

5000

6000

0-400 400 - 600 600 - 800 800 - 930 930 - 1100 1100 - 13001300 - 1500 1500-1700 1700 - 19001900 - 2100

Nu

mer

of

Elem

ents




44



6

170

3024

2078

1054

174

34 10 2 00

500

1000

1500

2000

2500

3000

3500

0-400 400 - 600 600 - 800 800 - 930 930 - 1100 1100 -1300

1300 -1500

1500 -1700

1700 -1900

1900 -2100

Nu

mer

of

Elem

ents




45

Chart Comparing the Distribution and Range of Material Properties of Custom Models

Figure 36 - Chart Comparing the Distribution and Range of Material Properties of Custom Models

0

5

10

15

20

25

30

35

40

45

50

400 - 600 600 - 800 800 - 930 930 - 1100 1100 - 1300 1300 - 1500 1500 - 1700 1700 - 1900 1900 - 2100

Nu

mer

of

Elem

ents

(%

of

Tota

l)

Young's Modulus (MPa)

Distribution Range of Material Proerties Throught Models of Varied Element Size

John Custom (1.1)

John Custom (1.2)

John Custom (1.5)

46

Graph of Physical Distribution of Material Property Elements

Figure 37 – Graph of the Physical Distribution of Material Property Elements throughout a Particular Model (John Custom [1.1]).

47

Graph of the Models Predicted Fracture Location

Figure 38 - Graph of the Models Predicted Fracture Location (Red Label)

48

Chapter 7 Analysis of Results

Displacement

Comparison Table of Stiffness Values Compared to Actual Results (@ 5000N)

Model Stiffness kN/mm % Diff. With Actual

IA-FEMesh Settings 95.82583 1286.18%

Tawara - 1 734.92665 10531.13%

Tawara - 2 109.72372 1487.22%

Tawara - 3 205.72745 2875.97%

Xiao 0.00000 -100.00%

E.Morgan 79.97825 1056.93%

Xie Xin Cortical 19.96885 188.86%

Xie Xin Trabecular 19.36108 180.07%

Christopher McClelland 30.27001 337.87%

Garduno 15.16944 119.43%

John Custom (1.1) 7.90301 14.32%

John Custom (1.2) 7.07034 2.28%

John Custom (1.5) 5.72410 -17.20%

Colin Bright (Experimental - L4)(2014) 6.91297 x

Table 8 - Comparison Table of Stiffness Values Compared to Actual Results (@ 5000N)

Figure 39 - Graph of the Results of Simulated Compression Testing in ANSYS, on the Models Created using

IA-FEMesh.

49

The first model created, tested and plotted was that of Mr. Christopher McClelland (6) which

was to be used as an initial stiffness bench mark for all other models created. As can be seen

in Table 9 and Figure 39 above, the models created using the material property equations

provided by Xiao et al. (44), Tawara et al. (43), E. Morgan et al (34) and the IA-FEMesh

standard settings yielded stiffness results greater than Mr. Christopher McClelland’s

benchmark model. It must be noted that, as per Table 6, these equations were created based

on L1 & L2 vertebrae as opposed to the L4 vertebrae being used in the comparison real world

test data of Mr. Colin Bright (55) and as such were not expected to provide precise

conformance.

The model created with the material property equation from Xiao et al. (2012) (44), provided

no deformation whatsoever. As can be seen in Table 7, this can be attributed to the extremely

low young’s modulus values and range derived from the material property equation inserted

and then automatically assigned to the model in IA-FEMesh. Model created using equation

from other authors (Skoworodko et al. (2008) (42) & Xiao et al. (2011) (48) ) provided

similar characteristic in terms of the Young’s modulus and thus also yielded no deformation

upon tests. Therefore the model created via with the material property equation from Xiao et

al. (2012) (44) was plotted only to be used as an example and other models of this nature

were left out of the analysis as such.

Conversely the models created from the material property equations provided by Xie Xin et

al. (46) and Garduño et al. (47) yielded stiffness results lower then than Mr. Christopher

McClelland’s benchmark model. In particular the model created from the material property

equation provided by Garduño et al. (47) showed the highest agreement to that of the real

world test data provided by Mr. Colin Bright (55) (119.43% difference). This equation was

derived based of an L4 vertebrae and thus was expected to produce results of increased

conformance compared to other equations in Table 6.

As such this material property equation was investigated further and thus manipulated to

created three custom equations (John Custom 1.1, 1.2 & 1.5). as can be seen in Table 9 and

Figure 39 above, the resulting custom equation (John Custom 1.2) provided the highest

stiffness agreement to that of the real world test data provided by Mr. Colin Bright (55)

overall (2.28% difference).

50

Factors Giving Rise to Differences in Stiffness Values

Different Specimen Tested

The vertebrae depicted within the CT scans provided for this project were not in fact the same

vertebrae used in the mechanical testing done by Mr. Colin Bright (55). Therefore,

considering the FE models in this project have been constructed directly from the CT scans

image properties, this presents grounds for a multiplicity of variations to occur between the

simulated and experimental results.

1. Mechanical Structure

According to the research undertaken in the literature review, studies undertaken by Wolff

(17) describe a close relationship between a bones structural design and it mechanical

function stating that “that a bone will organise itself in the best orientation to allow it to bear

applied physiological loads.” (17). Although the specimen used in the CT scan and the

specimen used during testing were both from pigs of weight about 60Kg, there is no way to

verify the exact loads applied to ether specimen on a day to day basis.

2. Trabecular Bone Volume

According to the research undertaken in the literature review, studies undertaken by E. Tanck

et al. (56), describe the occurrence of accelerated trabecular bone volume during early

porcine development i.e. between 6 and 56 weeks. It was found that the resulting increase in

BV/TV ratio (bone volume/ total volume) was significant and also undefined by overall body

weight.

3. Cortical Bone Density

According to the research undertaken in the literature review, studies undertaken by Liang

Feng and Iwona Jasiuk (35), describe the increase in cortical bone mineral density to be

concurrent with the increase in age of pigs.

Although there was confirmation regarding a similarity in the overall body weight of both the

specimens used in the project, once the above information is considered it can be said that

much variation between the trabecular bone mechanical structure, trabecular bone volume

and cortical bone density could be present due to any discrepancies in age, daily mechanical

loading and genetic growth rate of either specimen.

51

Mesh Density

In order to accurately represent the material properties of bone via grey scales values attained

from a CT scan, a suitable mesh density should be incorporated. Considering an element is

assigned its material property value based on the average of all the grey scale equivalent

material property values contained with its boundaries, a finer mesh will reduce the number

of grey scale values per element ratio, giving a more precise representation of the material

properties of the bone at any particular point. Conversely, the overly course mesh used in this

project has misrepresented the material properties of bone by neglecting to facilitate small but

significant factors such as the presence of voids within the trabecular bone. This neglect is

evident due to the lack of elements containing a Young’s modulus of 0 MPa. Instead these

voids were assigned a material property based on the combined average of itself and the

surrounding grey scale values contained with its elemental boundary.

Considering the resolution of the CT scan was 0.25mm per slice, this would have been the

ideal element length to use in the mesh which would have included all minute details (Voids

etc.). Additional research suggests that the typical porcine cortical bone thickness of the L4-

L5 vertebrae can be as small as 0.45mm (57) (58). Therefore, in order to obtain any sort of

realistic results for the model in this case, an element length of no more than 0.45mm should

be used to at least provide an accurate distinction between the cortical and trabecular bone

regions. Due to the lack of computational power available during this project, the minimum

element length attained was 1.1mm (18,414 elements) and thus the models created using the

image property based techniques do not accurately represent the bones structure.

A finer meshed model consisting of an element length of 1mm (23,297 elements) was created

in IA-FEMesh with no problems, however, upon importation into ANSYS a time span of 12

hours had passed without the successful upload of the model. Computer access is only

permitted between the hours of 8am – 10pm Monday – Saturday and the computers were not

authorised to be left run over night. Additionally, the model created consisting of element

length 1.1mm (18,414 elements) already required up to two hours to upload to ANSYS and

two to four hours to process material property data and solve. Considering this, a model mesh

density of 1mm or smaller was deemed unfeasible for this project.

52

Power Law Equations Used

Several power law equation were trialled during the assignment of material properties to the

image property models created during this project. Each power law equation used, resulted in

great variation in the distribution and range of materials properties throughout each model

(this will be discussed in detail in the following section – validation). This therefore gave rise

to the major variations in stiffness experienced in these models. Unfortunately, due to the

limiting factors associated with the mesh densities, as previously discussed, it is impossible to

fully evaluate any of these power law equations. Therefore any of the models created and

trailed in this project will have been misrepresented when compared to the real world test

data, as such all and any of these models may indeed have the potential to provide

conformance once incorporated into a properly constructed meshed model. The power law

equations used in the custom models of this project were created specifically to match the

real world test data and therefore most likely would become redundant upon application to a

properly constructed meshed model. Considering this, further analysis of each power law

equation must be undertaken to define the true stiffness values associated with them.

Furthermore, as previously discussed in the “Assignment of Material Properties & FE Mesh

Models Created” section of Chapter 4, IA-FEMesh restricts the manipulation of density in the

calculation of the Young’s Modulus. Examples in the literature review showed identical

Young’s modulus equations with independent density equations that provided significantly

different results. This fixed density value automatically assigned by the IA-FEMesh software

could result in discrepancies in a model’s stiffness and should be user defined.

Use of Potting Material

During the experimental testing undertaken by Mr. Colin Bright (55), a 1mm thick potting

material was used to support either vertebral endplate within the test rig. There was no

mention of the possible variation in stiffness due to the presence of this potting material and

no significant research could be found on the matter. Therefore, a reduction in the stiffness

results may have been yielded due to the deformation of the softer potting material.

Material Isotropy

The Model is limited in that it assumes the materials involved behave in an isotropic fashion

(the same in all directions), however, in reality this is not the case. Trabecular bone for

example is by nature anisotropic and as such experiences considerable differences in its

compressive, tensile and shear strengths. The elongated ladder-like orientation of trabecular

53

bone consists of long strands of vertical trabecular bone held together by more horizontal and

oblique strands of trabecular bone. Upon compression, the vertebra decreases in height and

begins to expand around its mid riff. This provides the vertical strands of trabecular bone

with compressive strength but alternatively provides the horizontal strands of trabecular bone

with tensile stresses and in addition, provide the oblique strands of trabecular bone with shear

stresses. Additional research into a study by Sanyal et al. (59) that investigates the shear

stresses of trabecular bone has shown trabecular bone to be much stronger in compression

then in tension/shear. Furthermore, the study notes that trabecular bone tends to fail

catastrophically in tension/shear. Considering this and upon examination of Figure 39 above,

this would explain why all the simulated models behaved perfectly linearly and failed to yield

as the real world test data does upon reaching a load circa 9000 N.

Validation

Material Property Distribution and Range

The report undertaken by Mr. Chris McClelland (6) investigated the reasons behind the

differences in stiffness experienced by several models with individual material property

equations but identical mesh element density. The report concluded that similarities in

deformation can be attributed to similarities in the distribution of material properties

throughout these models. (6)

Considering this, a further investigation was undertaken into the distribution and range of

material properties throughout several models utilising an identical material property equation

but with a difference in mesh element density. An equation “John Custom” was developed by

the author which allowed the model to produce a result that coincided with the real world test

data of Mr. Colin Bright (26), as can be seen in Table 8 above. This equation was applied to

three different models containing three different element sizes (1.1mm, 1.2mm & 1.5mm) for

analysis. Details of the analysis can be seen below in Table 9 and Figure 31.

54

John Custom Element Size (1.1)



E Mod Range (MPa) No. of Elements

Element No. %

No. of Elements

Element No. %

No. of Elements

Element No. %

0-400 16 0.09 % 12 0.10 % 6 0.092 % 400 - 600 536 2.91 % 286 2.28 % 170 2.595 % 600 - 800 7352 39.93 % 5584 44.52 % 3024 46.15 % 800 - 930 6038 32.79 % 4068 32.43 % 2078 31.71 % 930 - 1100 3284 17.83 % 1889 15.06 % 1054 16.09 % 1100 - 1300 811 4.40 % 505 4.03 % 174 2.66 % 1300 - 1500 236 1.28 % 128 1.02 % 34 0.519 % 1500-1700 97 0.53 % 55 0.44 % 10 0.153 % 1700 - 1900 41 0.22 % 17 0.14 % 2 0.031 % 1900 - 2100 3 0.02 % 0 0.00 % 0 0.00 % Total 18414 12544 6552 No. of Elements Occupying Modulus Range (0 - 930) (%)

13942

9950

5278

No. of Elements Occupying Modulus Range (0 MPa - 930 MPa) Trabecular Region (%)

75.71 %

79.3 %

80.56 %

No. of Elements Occupying Modulus Range (> 930 MPa) Cortical Region (%)

24.29 %

20.68 %

19.44 %

Table 9 – Table Detailing the Young’s Modulus Distribution and Magnitude throughout the Models FE Mesh.

Figure 40 – Distribution Range of Material Properties throughout Each Custom Model of Varied Element Size.

55

A study undertaken by Boyd et al. (60) in to the assessment of trabecular and cortical bone

microstructures, shows there to be an approximate ratio of 80:20 split between trabecular and

cortical bone respectively. Considering this, it can be seen in Table 10 or left of the red dashed

line in Figure 40 that 75% - 80% of the each models material properties lie below a Young’s

modulus of 930 MPa and as such this can be considered the trabecular bone region. Further

research into studyies under taken by Ashman et al. (30) and Ruey-Mo Lin et al. (29) regarding

the distribution and regional strength of trabecular bone in the porcine lumbar spine, indicate

that the typical porcine lumbar vertebrae consists of trabecular bone with a Young’s of modulus

of 91 - 665MPa. Although not unreasonable, a significant discrepancy can be seen to be present.

A study by Clarke (61) highlights that a transitional region of bone is present between the hard

cortical bone and soft trabecular bone as opposed to the assumption of a sudden and direct

change from one to another. The Young’s modulus of the transitional region increases as it

progresses from the trabecular bone to the cortical bone and as such this could have been

incorporated within the initial 80% of the young’s modulus range which has been considered

the models trabecular bone region. Therefore, this could have contributed to a significant

increase in the overall averaged Young’s modulus values found in this region.

The remaining 20% can be considered the cortical bone region of the model which ranges from

930 MPa - 1743.52MPa, 1893.6MPa, 2092.2 MPa depending on the model mesh density (1.5,

1.2, and 1.1 respectively). Additional research into a study undertaken by Feng et al. (35)

regarding the multi-scale characterization of swine femoral cortical bone, indicates that typical

porcine cortical bone has a Young’s modulus ranging from 15,240 - 23,240 MPa. Immediately,

it is evident that there is a massive discrepancy between the Young’s modulus values produced

by the model and that of the researched data. Again this can be attributed to the relatively spare

mesh densities used for this model as previously discussed. The increase in elements found

present in the cortical bone region of the model accompanies the decrease in element length

and quantity, thus indicating that a finer mesh would present a more realistic distribution of

material properties. Additionally, the reduction in element length allows for increased

concentration on the material properties found in the disproportionate cortical bone region by

increasing the ratio of cortical to trabecular bone material properties in elements present in this

particular region. Therefore the cortical bone has an increased effect on the overall value

assigned to the element and thus increases its overall material property value. The effect of this

concentration can be seen by the significant increase in the top end of the Young’s modulus

range as the mesh density is increased (See Table 11 below).

56

Model Max Young Modulus (MPa)

John Custom (1.1) 1743.5



Table 10 – Table of Custom Models Max Young’s Modulus.

Physical Location of Material Property Elements

Figure 41 - Graph of the Physical Distribution of Material Property Elements throughout a Particular Model

(John Custom [1.1]).

Figure 41 above depicts the physical location of the material property elements throughout the

model itself. As described in the literature review the typical porcine vertebrae consists of a

thin, hard exterior cortical shell encasing a soft sponge-like trabecular centre. Thus it is

expected that the material property elements of the model to be positioned in accordance to

these findings i.e. high Young’s modulus towards the exterior and low Young’s modulus

towards the centre. As can be seen in Figure 41 above the model does indeed follow the

researched information as it locates the harder material properties towards the exterior and the

57

softer material properties towards the centre. The effects of an inappropriate element size is

once again highlighted here. Due to the relatively large elements present in this particular

model, there is a problem in trying to distinguish the thin cortical shell as the elements also

encompass large areas of trabecular bone. The result is that even though the model behaves

correctly, the elements are limited in their variance and thus the whole models material property

range is skewed towards that of the amassed trabecular bone material property values.

Predicted Fracture Location

Figure 42 – ANSYS Screenshot of the Models Predicted Fracture Location (Red Label)

In an attempt to further validate this simulated model, analysis was undertaken to examine and

compare the predicted fracture location of the vertebrae against that of researched data. As can

be seen in Figure 42 above, the location of max stress, and thus the predicted fracture location,

on the model is estimated to occur in the posterior portion on the vertebral body, just under the

connection point of the right articular facet joint. The research investigation revealed the work

of Francis Denis who devised the “Three column concept of thoracolumbar spinal fractures”.

58

Denis separated and defined the vertebral column into three individual sections (anterior,

middle and posterior column) based on biomechanical studies surrounding traumatic spinal

injuries. Figure 43 below depicts Denis’s division of the vertebral column.

Figure 43 – Francis Denis’s Three Column Concept in Spinal Fracture (62)

Relating the models predicted fracture location to the Denis’s spinal fracture column concept,

it can be said that the estimated fracture location lies within the “middle column” region.

Considering this, further investigations into the types of fractures that occur in this location

yielded information about vertebral burst fractures which is explain further below.

Burst Fractures

“Burst fractures are a type of compression fracture related to high-energy axial loading spinal

trauma that results in disruption of the posterior vertebral body cortex with retropulsion into

the spinal canal.” (63)

This type of fracture is typically associated with compressive, high energy injuries resulting

from landing on the feet after falling from a significant height. This scenario is expected to

cause the intervertebral disc to apply great force on the “middle Column” of the vertebrae and

characteristically result in a loss of posterior vertebral body height.

59

Figure 44 – ANSYS Screen Shot Comparison of the Model before and After Axial Loading

Figure 44 above shows the model to experience a depression in the posterior vertebral body

similar to that characterised by a burst fracture. Furthermore, burst fractures are associated with

high stress and purely axial compression loading of the vertebrae which again describes the

conditions under which the model was loaded.

The results and likelihood of burst fractures can be categorised in the following five types:

Type A: Fracture of both endplates (24%)

Type B: Fracture of both endplates (49%)

Type C: Fracture of inferior endplate (7%)

Type D: Burst rotation (15%)

Type E: Burst lateral flexion (5%)

Figure 45 – Francis Denis Classification of Burst Fractures (63)

Considering the compared researched information it can be said that the fracture estimated to

occur is a Type C fracture.

60

Chapter 8 Conclusions & Future Work

In conclusion, creating a finite element analysis model using freely available, open source

software packages is possible but this project was limited for several reasons. The model

created in this project provided basic conformance to that of a real vertebrae. This was shown

by the realistic distribution and range of trabecular bone material properties, the physical

location of both cortical and trabecular bone material property elements and finally the

distribution and concentration of stresses via the predicted fracture location.

As such future work is needed to create a fully functioning FE model that provides an

accurate representation of a real life vertebrae.

Increased Computational Power

The material properties of the model were not accurately represented in the model. The

addition of a high power computer system would allow for an increased mesh density and

thus more realistic results. This would be the initial step needed in furthering this project.

Fixed Value/False Assumptions

IA-FEMesh incorporates assumptions regarding the density values attained from the image

properties to be used in the Young modulus equation and also falsely assumes that the

material properties are isotropic by nature. An investigation into an alternative software

which allows for these factors to be user defined would also be beneficial to this project.

Incorporation of Facet Joints

Two models, one including the articular facet joints and one including both the articular and

inferior facet joints were made during the course of this project but time constraints and

limitations in the IA-FEMesh software meant that it wasn’t feasible to include the facet joints

in the analysis. Future work would entail the incorporation of these parts of the vertebrae as

they play a significant role in the absorption and transfer of loads throughout the component.

Again, an investigation into an alternative software to IA-FEMesh, which better allows the

finite element meshing of complex geometries would be beneficial to this project.

61

Chapter 9 Ethical Considerations

Ethically Sourced Cadaver Specimens

InterNICHE 'Policy on the Use of Animals and Alternatives in Education’ describes the ethical

considerations involved in provided humane education and training within the life sciences.

This policy is set out is protest of all harmful use of animals in education and training, including

the harming and killing of animals for their cadavers, organs and tissue, for live

experimentation and skills training, for ethology and field studies, and for making alternatives.

(64) The policy promotes the use of animal cadavers and tissue obtained from animals that

have died naturally or in accidents, or who have been euthanised secondary to natural terminal

disease or non-recoverable injury. Animals that have been captured, bought, bred, kept, harmed

or killed to provide cadavers and tissue are not considered ethically sourced The use of ethically

sourced cadaver specimens is of utmost importance to ensure the no animals need to be

purposely killed for uses such as that of this project.

Future Implementation of Project on Humans

The end product of this project involves providing humans with a non-invasive, patient specific

method for surgical techniques and treatments. The initial code of ethics to consider in the

medical world comes in form of the Hippocratic Oath which sets out objectives mainly to

protect the individual receiving the treatment in this case. Ethical restraint and conduct is of

utmost important for researcher and subject alike with regards to professional demeanour,

approved permission, discretion and confidence, morally sound design conditions, respect

between all parties involved and data protection. Prior to undertaking any medical research

projects, a research ethics committee will review and confirm all of the above to ensure that all

intentions are legal, morally integral and in the interest of the research subjects. Several

directives such as the Nuremberg Code (1947) and the Declaration of Helsinki (1964) are used

to outline and ensure compliance with ethical protocols and practises.

The FEA model created in this project was based a set of CT scans supplied to the author by

the project supervisor after the review and acceptance of the project proposal by the research

ethics committee of Institute of Technology Tallaght, Dublin. Furthermore, the specimen used

in the CT scans and the specimen used in the experimental testing were both acquired through

ethically sound sources. Evaluating the considerations mentioned above, it can be said that this

project is ethically justified as it does not infringe on any ethical principles and falls in line

with the moral intensions outlined.

62

Chapter 10 Appendix

Project Plan

64

Post Graduate Results (Actual Compression Test)

Table 11 – Deformation Results of real world compression tests conducted by Mr. Colin Bright

Figure 46 -Graph of the result of real world compression testing conducted by Mr. Colin Bright

0

2000

4000

6000

8000

10000

12000

0 0.5 1 1.5 2 2.5 3 3.5 4 4.5

Load

(N

)

Displacement (mm)

Load vs Disp. (Actual Compression Test Post Grad Data)

Real World Test (Post Grad Data)

65

Finite Element Analysis Results

The data gathered from the finite element analysis was linier and for ease of reading is listed

below in a comparison table at a load of 5000N.

Comparison Table of results for a load of 5000 N

Model Deformation (mm) Max Stress (MPa)

IA-FEMesh Settings 0.05218 54.32 Tawara - 1 0.00680 47.777 Tawara - 2 0.04557 43.953 Tawara - 3 0.024304 52.713

Xiao 0.00000 54.655 E.Morgan 0.06252 50.097 Xie Xin Cortical 0.25039 45.9 Xie Xin Trabecular 0.25825 54.89

Christohper McClelland 0.16518 42.52 Garduno 0.32961 53.664 John Custom (1.1) 0.63267 57.156 John Custom (1.2) 0.70718 39.408

John Custom (1.5) 0.87350 55.644 Colin Bright (Experimental - L4)(2014) 0.72328 x

Table 12 - Comparison Table for a Load of 5000 N

66

Table 13 - Table of Displacement Results of Finite Element Analysis (IA-FEMesh Settings)

IA-FEMesh Settings

Displacement (m) Displacement (mm) Load (N)

0 0 0 5.22E-06 5.22E-03 500 1.04E-05 1.04E-02 1000 1.57E-05 1.57E-02 1500

2.09E-05 2.09E-02 2000 2.61E-05 2.61E-02 2500 3.13E-05 3.13E-02 3000 3.65E-05 3.65E-02 3500 4.17E-05 4.17E-02 4000 4.70E-05 4.70E-02 4500 5.22E-05 5.22E-02 5000

5.74E-05 5.74E-02 5500 6.26E-05 6.26E-02 6000

6.78E-05 6.78E-02 6500 7.30E-05 7.30E-02 7000 7.83E-05 7.83E-02 7500 8.35E-05 8.35E-02 8000 8.87E-05 8.87E-02 8500

9.39E-05 9.39E-02 9000 9.91E-05 9.91E-02 9500 1.04E-04 1.04E-01 10000

Table 14 - Table of Stress Results of Finite Element Analysis (IA-FEMesh Settings)

IA-FEMesh Settings

Max Stress (Pa) Max Stress (MPa) Load (N) 0 0 0

6.04E+06 6.04E+00 500 1.21E+07 1.21E+01 1000 1.81E+07 1.81E+01 1500 2.41E+07 2.41E+01 2000 3.02E+07 3.02E+01 2500 3.62E+07 3.62E+01 3000 4.22E+07 4.22E+01 3500 4.83E+07 4.83E+01 4000 5.43E+07 5.43E+01 4500 6.04E+07 6.04E+01 5000 6.64E+07 6.64E+01 5500 7.24E+07 7.24E+01 6000 7.85E+07 7.85E+01 6500 8.45E+07 8.45E+01 7000 9.05E+07 9.05E+01 7500 9.66E+07 9.66E+01 8000 1.03E+08 1.03E+02 8500 1.09E+08 1.09E+02 9000 1.15E+08 1.15E+02 9500 1.21E+08 1.21E+02 10000

67

Table 15 - Table of Displacement Results of Finite Element Analysis (Tawara - 1)

Tawara - 1

Displacement (m) Displacement (mm) Load (N) 0 0 0

6.80E-07 0.00068034 500 1.36E-06 0.0013607 1000 2.04E-06 0.002041 1500 2.72E-06 0.0027213 2000 3.40E-06 0.0034017 2500 4.08E-06 0.004082 3000 4.76E-06 0.0047624 3500 5.44E-06 0.0054427 4000 6.12E-06 0.006123 4500 6.80E-06 0.0068034 5000 7.48E-06 0.0074837 5500 8.16E-06 0.008164 6000 8.84E-06 0.0088444 6500 9.52E-06 0.0095247 7000 1.02E-05 0.010205 7500 1.09E-05 0.010885 8000 1.16E-05 0.011566 8500 1.22E-05 0.012246 9000 1.29E-05 0.012926 9500 1.36E-05 0.013607 10000

Table 16 - Table of Stress Results of Finite Element Analysis (Tawara - 1)

Tawara - 1


4.78E+06 4.7777 500 9.56E+06 9.5555 1000 1.43E+07 14.333 1500 1.91E+07 19.111 2000 2.39E+07 23.889 2500 2.87E+07 28.666 3000 3.34E+07 33.444 3500 3.82E+07 38.222 4000 4.30E+07 43 4500 4.78E+07 47.777 5000 5.26E+07 52.555 5500 5.73E+07 57.333 6000 6.21E+07 62.111 6500 6.69E+07 66.888 7000 7.17E+07 71.666 7500 7.64E+07 76.444 8000 8.12E+07 81.222 8500 8.60E+07 85.999 9000 9.08E+07 90.777 9500 9.56E+07 95.555 10000

68


Tawara - 2


0 0 0 4.56E-06 0.0045569 500 9.11E-06 0.0091139 1000 1.37E-05 0.013671 1500 1.82E-05 0.018228 2000 2.28E-05 0.022785 2500 2.73E-05 0.027342 3000 3.19E-05 0.031899 3500 3.65E-05 0.036455 4000 4.10E-05 0.041012 4500 4.56E-05 0.045569 5000 5.01E-05 0.050126 5500 5.47E-05 0.054683 6000 5.92E-05 0.05924 6500 6.38E-05 0.063797 7000 6.84E-05 0.068354 7500 7.29E-05 0.072911 8000 7.75E-05 0.077468 8500 8.20E-05 0.082025 9000 8.66E-05 0.086582 9500 9.11E-05 0.091139 10000


Tawara - 2


4.40E+06 4.3953 500 8.79E+06 8.7906 1000 1.32E+07 13.186 1500 1.76E+07 17.581 2000 2.20E+07 21.977 2500 2.64E+07 26.372 3000 3.08E+07 30.767 3500 3.52E+07 35.162 4000 3.96E+07 39.558 4500 4.40E+07 43.953 5000 4.83E+07 48.348 5500 5.27E+07 52.744 6000 5.71E+07 57.139 6500 6.15E+07 61.534 7000 6.59E+07 65.93 7500 7.03E+07 70.325 8000 7.47E+07 74.72 8500 7.91E+07 79.115 9000 8.35E+07 83.511 9500 8.79E+07 87.906 10000

69


Tawara - 3




Tawara - 3



70

Table 21 – Table of Displacement Results of Finite Element Analysis (Xiao (2012))

Xiao

Displacement (m) Displacement (mm) Load (N) 0 0 0 0 0 500 0 0 1000 0 0 1500 0 0 2000 0 0 2500 0 0 3000 0 0 3500 0 0 4000 0 0 4500 0 0 5000 0 0 5500 0 0 6000 0 0 6500 0 0 7000 0 0 7500 0 0 8000 0 0 8500 0 0 9000 0 0 9500 0 0 10000

Table 22 - Table of Stress Results of Finite Element Analysis (Xiao (2012))

Xiao



71

Table 23 - Table of Displacement Results of Finite Element Analysis (E.Morgan)

E.Morgan



Table 24 -Table of Stress Results of Finite Element Analysis (E.Morgan)

E.Morgan

Max Stress (Pa) Max Stress (MPa) Load (N)

0 0 0 5.01E+06 5.0097 500 1.00E+07 10.019 1000 1.50E+07 15.029 1500 2.00E+07 20.039 2000 2.50E+07 25.048 2500 3.01E+07 30.058 3000 3.51E+07 35.068 3500 4.01E+07 40.077 4000 4.51E+07 45.087 4500 5.01E+07 50.097 5000 5.51E+07 55.106 5500 6.01E+07 60.116 6000 6.51E+07 65.126 6500 7.01E+07 70.135 7000 7.51E+07 75.145 7500 8.02E+07 80.155 8000 8.52E+07 85.164 8500 9.02E+07 90.174 9000 9.52E+07 95.184 9500 1.00E+08 100.19 10000

72

Table 25 - Table of Displacement Results of Finite Element Analysis (Xie Xin Cortical)

Xie Xin Cortical



Table 26 - Table of Stress Results of Finite Element Analysis (Xie Xin Cortical)

Xin Xie Cortical



73

Table 27 - Table of Displacement Results of Finite Element Analysis (Xie Xin Trabecular)

Xie Xin Trabecular



Table 28 - Table of Stress Results of Finite Element Analysis (Xie Xin Trabecular)

Xin Xie Trabecular



74

Table 29 - Table of Displacement Results of Finite Element Analysis (Christopher McClelland)

Christopher McClelland

Deformation (mm) Load (N) 0 0

0.01652 500 0.03304 1000 0.04955 1500 0.06607 2000 0.08259 2500 0.09911 3000 0.11563 3500 0.13214 4000 0.14866 4500 0.16518 5000 0.18170 5500 0.19821 6000 0.21473 6500 0.23125 7000 0.24777 7500 0.26429 8000 0.28080 8500 0.29732 9000 0.31384 9500 0.33036 10000

Table 30 - Table of Stress Results of Finite Element Analysis (Christopher McClelland)

Christopher McClelland

Max Stress (MPa) Load (N)

0 0 4.252 500 8.504 1000

12.756 1500 17.008 2000 21.26 2500

25.512 3000 29.764 3500 34.016 4000 38.268 4500 42.52 5000

46.772 5500 51.024 6000 55.276 6500 59.528 7000 63.78 7500

68.032 8000 72.284 8500 76.536 9000 80.788 9500 85.04 10000

75

Table 31 - Table of Displacement Results of Finite Element Analysis (Garduno)

Garduno



Table 32 - Table of Stress Results of Finite Element Analysis (Garduno)

Garduno



76

Table 33 - Table of Displacement Results of Finite Element Analysis (John Custom 1.1)

John Custom (1.1)



Table 34 - Table of Stress Results of Finite Element Analysis (John Custom 1.1)

John Custom (1.1)



77


John Custom (1.2)




John Custom (1.2)



78


John Custom (1.5)




John Custom (1.5)



79

Elemental Material Property Distribution and Range

Table 39 - Table of Material Property Results of Finite Element Analysis (John Custom 1.1)


Mat. No E mod (MPa) Element No.

1 194.49 1

2 315.62 2

3 335.81 2

4 356 2

5 376.19 2

6 396.38 7

7 416.57 9

8 436.75 7

9 456.94 16

10 477.13 27

11 497.32 42

12 517.51 41

13 537.7 74

14 557.88 81

15 578.07 93

16 598.26 146

17 618.45 235

18 638.64 312

19 658.83 480

20 679.01 671

21 699.2 790

22 719.39 1008

23 739.58 1201

24 759.77 1341

25 779.96 1314

26 800.14 1190

27 820.33 1015

28 840.52 910

29 860.71 802

30 880.9 749

31 901.09 739

32 921.28 633

33 941.46 651

34 961.65 569

35 981.84 526

36 1002.03 385

37 1022.22 372

38 1042.41 310

39 1062.59 279

40 1082.78 192

41 1102.97 154

80

42 1123.16 134

43 1143.35 122

44 1163.54 75

45 1183.72 80

46 1203.91 63

47 1224.1 63

48 1244.29 45

49 1264.48 37

50 1284.67 38

51 1304.85 31

52 1325.04 34

53 1345.23 29

54 1365.42 25

55 1385.61 21

56 1405.8 28

57 1425.98 20

58 1446.17 13

59 1466.36 19

60 1486.55 16

61 1506.74 10

62 1526.93 15

63 1547.11 11

64 1567.3 14

65 1587.49 8

66 1607.68 6

67 1627.87 13

68 1648.06 10

69 1668.24 4

70 1688.43 6

71 1708.62 6

72 1728.81 7

73 1749 8

74 1769.19 7

75 1789.37 2

76 1809.56 3

77 1829.75 2

78 1849.94 1

79 1870.13 3

80 1890.32 2

81 1910.51 1

82 1930.69 1

83 2092.2 1

Total 18414

81




1 218.22 1

2 325.16 1

3 360.8 5

4 378.63 2

5 396.45 3

6 414.27 2

7 432.1 1

8 449.92 3

9 467.74 8

10 485.57 13

11 503.39 15

12 521.21 17

13 539.04 41

14 556.86 33

15 574.68 67

16 592.51 86

17 610.33 102

18 628.15 154

19 645.97 199

20 663.8 372

21 681.62 438

22 699.44 510

23 717.27 582

24 735.09 716

25 752.91 869

26 770.74 864

27 788.56 778

28 806.38 677

29 824.21 586

30 842.03 591

31 859.85 522

32 877.68 473

33 895.5 426

34 913.32 435

35 931.15 358

36 948.97 333

37 966.79 296

38 984.62 263

39 1002.44 229

40 1020.26 216

41 1038.09 171

42 1055.91 157

82

43 1073.73 133

44 1091.56 91

45 1109.38 85

46 1127.2 70

47 1145.03 69

48 1162.85 67

49 1180.67 49

50 1198.49 32

51 1216.32 35

52 1234.14 23

53 1251.96 36

54 1269.79 25

55 1287.61 14

56 1305.43 24

57 1323.26 16

58 1341.08 10

59 1358.9 9

60 1376.73 12

61 1394.55 7

62 1412.37 9

63 1430.2 13

64 1448.02 10

65 1465.84 10

66 1483.67 8

67 1501.49 4

68 1519.31 2

69 1537.14 7

70 1554.96 9

71 1572.78 6

72 1590.61 6

73 1608.43 4

74 1626.25 4

75 1644.08 2

76 1661.9 2

77 1679.72 4

78 1697.55 5

79 1715.37 1

80 1733.19 7

81 1751.01 1

82 1768.84 1

83 1786.66 3

84 1822.31 1

85 1840.13 1

86 1893.6 2

Total 12544

83




1 322.55 1

2 337.66 2

3 352.78 2

4 398.13 1

5 413.25 6

6 428.36 4

7 443.48 2

8 458.6 5

9 473.72 6

10 488.83 4

11 503.95 12

12 519.07 12

13 534.18 14

14 549.3 22

15 564.42 17

16 579.53 30

17 594.65 36

18 609.77 40

19 624.88 49

20 640 89

21 655.12 138

22 670.23 169

23 685.35 194

24 700.47 261

25 715.58 271

26 730.7 312

27 745.82 357

28 760.93 390

29 776.05 418

30 791.17 336

31 806.28 327

32 821.4 275

33 836.52 259

34 851.63 239

35 866.75 226

36 881.87 205

37 896.98 204

38 912.1 159

39 927.22 184

40 942.34 184

41 957.45 161

42 972.57 110

84

43 987.69 121

44 1002.8 103

45 1017.92 85

46 1033.04 76

47 1048.15 64

48 1063.27 60

49 1078.39 48

50 1093.5 42

51 1108.62 47

52 1123.74 26

53 1138.85 18

54 1153.97 12

55 1169.09 12

56 1184.2 12

57 1199.32 8

58 1214.44 10

59 1229.55 6

60 1244.67 5

61 1259.79 9

62 1274.9 3

63 1290.02 6

64 1305.14 4

65 1320.25 1

66 1335.37 6

67 1350.49 4

68 1365.6 3

69 1380.72 4

70 1395.84 3

71 1410.96 3

72 1441.19 2

73 1456.31 2

74 1471.42 1

75 1486.54 1

76 1501.66 1

77 1516.77 1

78 1531.89 1

79 1547.01 1

80 1562.12 2

81 1577.24 1

82 1622.59 1

83 1637.71 1

84 1698.17 1

85 1728.41 1

86 1743.52 1

Total 6552

85

References

1. The Boeing 777: A look Back. Glende, Wolf L. Seattle : AGARD, September 1998,

CP-602, pp. 5-6.

2. The influence of material property and morphological parameters on specimen-specific

finite element models of porcine vertebral bodies. Wilcox, Ruth K. Leeds : ELSEVIER,

2006, Journal of Biomechanics 40, pp. 669–673.

3. IA-FEMesh: ANATOMIC FE MODELS—A check of Mesh Accuracy and Validity.

Nicole A. DeVries, Kiran H. Shivanna, Srinivas C. Tadepalli, Vincent A. Magnotta,

Nicole M. Grosland. Iowa : s.n., 2009, Iowa Orthopaedic Journal, pp. 48-54.

4. Finite element analysis of the spine: Towards a framework of verification, validation

and sensitivity analysis. Alison. C. Jones, Ruth. K. Wilcox. 2008, Medical Engineering &

Physics 30, pp. 1287-1304.

5. Limitations of the Cervical Porcine Spine in Evaluating Spinal Implants in Comparison

With Human Cervical Spinal Segments. Rene´ Schmidt, MD,* Marcus Richter, MD,*

Lutz Claes, PhD,† Wolfhart Puhl, MD,* and Hans-Joachim Wilke, PhD†. Number 11,

Ulm : Lippincott Williams & Wilkins, Inc., 2005, Vol. Volume 30, pp. 1275–1282.

6. Clelland, Christopher Mc. Porcine Vertebra Simulation (CT Scan to STL File, Solid

Model & FEA Mesh). Dublin : IT Tallaght, 2015.

7. Middleditch, Alison. Functional Anatomy of the Spine. Toronto : Elsevier, 2003.

8. Anatomical measurements of porcine lumbar vertebrae. Dath, R., Ebinesan, A.D.,

Porter, K.M., Miles, A.W. 5, 2007, Vol. 22. 0268-0033.

9. Osteology of vertebrae. medicalfreakz.ie. [Online]

http://medicalfreakz.blogspot.ie/2014/07/osteology-of-vertebrae.html.

10. Anatomy of the Spine. www.mayfieldclinic.com. [Online]

http://www.mayfieldclinic.com/PE-AnatSpine.htm#.Vj974LfhDIU.

11. Mills, Harlan Dorst. The Pig Manual. Michigan : W.C. Brown, 1963.

12. Theo H. Smit. The use of a quadruped as an in vivo model for the study of the spine –

biomechanical considerations. Amstersam : Department of Clinical Physics, 2001.

86

13. Hyatt, Lisa K. The Fetal Pig. Alexandria : Bio Corperation, 2004.

14. Jackson, Jennifer Noelle. Mechanical Properties of the Intervertebral disk as an

Estimator of Postmortem Interval. Florida : University of Central Florida,, 2003.

15. Victoria Aspinall, Melanie Cappello. Introduction to Veterinary Anatomy and

Physiology Textbook. London : Elsevier Health Sciences, 2015.

16. Sisson, Septimus. A Textbook on Veterinary Anatomy. Stanford : Stanford

University, 1957.

17. Christopher Ruff, Brigitte Holt, Erik Trinkaus. Who’s Afraid of the Big Bad

Wolff?:‘‘Wolff’s Law’’and Bone Functional Adaptation. Baltimore : AMERICAN

JOURNAL OF PHYSICAL ANTHROPOLOGY, 2006.

18. Ruey-Mo Linl, Kuen-Horng TsaF, GuamLiang Chang. distribution and regional

strength of trabecular bone in the porcine lumbar spine. Taiwan : Elsevier, 1997.

19. buddy, anatomy study. sagittal-transverse-and-coronal-planes.

www.anatomystudybuddy.wordpress.com. [Online] [Cited: 16 11 2015.]

https://anatomystudybuddy.wordpress.com/2012/09/19/sagittal-transverse-and-coronal-

planes/.

20. Transmission of the weight through the neural arch of lumbarvertebrae in man.

Aruna. N, *Rajeshwari, T and Rajangam, S. 2, Bangalore : Department of Anatomy, St.

John's Medical College, 2003, Vol. 52.

21. Mechanism of facet load transmission as a hypothesis for low back pain. Yang, K.H.

and King, A.I. 1684.

22. Adams, M.A. and Hutton, W.C. The effect of posture on the role of apophyseal joints

in resisting intervertebral compressive force. s.l. : Journal of Bone and Joint, 1980.

23. Telemetric Measurement of Compressive Loads in the Sheep Lumbar Spine.

Hauerstock, D, *Reindl, R and +*Steffen, T. Montreal, : Orthopaedic Research Society,

2001, Vol. TELEMETRIC MEAUREMENT OF COMPRESSIVE LOADS IN THE

SHEEP LUMBAR SPINE.

87

24. New In Vivo Measurements of Pressures in the Intervertebral Disc in Daily Life.

Hans–Joachim Wilke, PhD,* Peter Neef, MD,† Marco Caimi, MD,‡ Thomas Hoogland,

MD,§ and Lutz E. Claes, PhD*. Mu¨ nchen : Lippincott Williams & Wilkins, 1999.

25. In vivo intradiscal pressure measurement in healthy individuals and in patients with

ongoing back problems. Sato K1, Kikuchi S, Yonezawa T.

26. Development of a Porcine FE Model for the Investigation of Spondylolytic Vertebral

Fractures. Colin Bright, Stephen Tiernan, Fiona McEvoy. Dublin : s.n., 2014.

27. The Role of Cortical Shell and Trabecular Fabric in Finite Element Analysis of the

Human Vertebral Body. Yan Chevalier, Dieter Pahr, Philippe K. Zysset. Vienna : s.n.,

2009.

28. Determinants of the Mechanical Behavior of Human Lumbar Vertebrae After

Simulated Mild Fracture. Wegrzyn, Julien, Jean-Paul Roux, Monique E. Arlot,

Stéphanie Boutroy, Nicolas Vilayphiou, Olivier Guyen, Pierre D. Delmas, Roland

Chapurlat, and Mary L. Bouxsein. Massachusetts : Harvard University, 2011.

29. Clinical Biomechanics "Distribution and regional strength of trabecular bone in the

porcine lumbar spine". Ruey-Mo Lin, Kuen-Horng Tsai, Guan-Liang Chang. 5, Tainan :

Elsevier Science Limited, 1997, Vol. 12.

30. Clinical Biomechanics (Relationship between CT intensity, miocro-architecture and

mechanical properties of porcine vertebral cancellous bone). Jeremy C.M. Teo, Kuan

Ming Si-Hoe, Justin E.L. Keh, Swee Hin Teoh. Singapore : Elsevier , 2005, Vol. 21.

31. Clinical Biomechanics (Examination of several techniques for predicting trabecular

elastic modulus and ultimate strength in the human lumbar spine). J Y Rho, J E Zerwekh,

R B Ashman. New York : Butterworth-Heinemann, 1994, Vol. 9.

32. Bone (Normal vertebral body size and compressive strength: Relations to age and to

vertebral and iliac trabecular bone compressive strength). Mosekilde, Lis. Mosekilde, Leif.

3, Aarhus : Elsevier, 1986, Vol. 7. 8756-3282.

33. Journal of Biomechanics (Yield strain behavior of trabecular bone). David L.

Kopperdahl, Tony M. Keaveny. San Francisco : Elsevier, 1998, Vol. 31.

88

34. Trabecular bone modulus–density relationships depend on anatomic site (Journal of

Biomechanics 36 (2003) 897–904). Elise F. Morgan, Harun H. Bayraktar, Tony M.

Keaveny. Berkeley : Elsevier Science, 2003, Vol. 36.

35. Journal of Biomechanics (Multi-scale Characterization of Swine Femoral Cortical

Bone). Liang Feng, Iwona Jasiuk. Illinois : Elsevir, 2011.

36. Bone (Tibial Ultrasound Velocity Measured In Situ Predicts the Material Properties of

Tibial Cortical Bone). S. C. Lee, B. S. Coan, M. L. Bouxsein’. 1, Boston : Elsevier, 1997,

Vol. 21.

37. Load Sharing within a Human Thoracic Vertebral Body: An In Vitro Biomechanical

Study. Cumhur Kilincer, Serkan Inceoglu, Moon Jun Sohn, Lisa A FErrara, Nadi

Bakirci, Edward C. Benzel. Belek-Antalya : Turkish Neurosurgery, 2005.

38. Increase in Bone Volume Fraction Precedes Architectural Adaptation in Growing

Bone. E. Tanck, J. Homminga, G. H. Van lenthe, and R. Huiskes. Nijmegen : Elsiever,

2001.

39. NIST. http://www.nist.gov/. [Online] http://www.nist.gov/pml/data/xraycoef/.

40. Gammex. Equivilant tissue Compositions . [Online]

file:///C:/Users/X00075278/Downloads/Tissue%20Equivalent%20Materials%20Gamme

x%20450,%20452,%20453,%20454,%20455,%20456,%20481,%20482%20Data%20Sh

eet%20(1).pdf.

41. Deriving Hounsfield units using grey levels in cone beam computed tomography. P

Mah*, 1, TE Reeves1,2 and WD McDavid1. Texas : s.n., 2008.

42. Preoperative planning and post-operative estimation of vertebroplasty using

CT/CAD/CAE systems. JÓZEF SKOWORODKO1*, KONSTANTY SKALSKI1,

WOJCIECH CEJMER2, KRZYSZTOF KWIATKOWSKI2. Warsaw : Warsaw

University of Technology, 2008.

43. Daisuke Tawara. Analysis, Mechanical Therapeutic Effects in Osteoporotic L1-

Vertebrae Evaluated by Nonlinear Patient-Specific Finite Element. Ryukoku : s.n.,

2010.

89

44. Biomechanical evaluation of three surgical scenarios of posterior lumbar interbody

fusion by finite element analysis. Zhitao Xiao1, 2, Liya Wang2, He Gong1,2* and Dong

Zhu3. Jilin : Jilin University, 2012.

45. Simulation of the behaviour of the L1 vertebra for different material properties and

loading conditions. Ibrahim Erdem, Ph.D, P.E.1, Eeric Truumees, MD2, and Marjolein

C.H. van der Meulen,. Ithaca : NIH, 2013.

46. COMBINED MUSCULO-SKELETAL MULTIBODY DYNAMICS/FINITE

ELEMENT ANALYSIS OF SEVERAL ERGONOMICS AND BIO-MECHANICS

PROBLEMS. Xie, Xin. Clemson : s.n., 2010.

47. Finite Element Evaluation of Vertebral Stiffness Behavior in the Lumbar Region.

Dipl.-Ing. Luis G. Garduño S. a*, Dipl.-Ing. Vadym Yemelyanova, M. Eng. Norbert

Babela*, Prof.-Dr. Roland Mastela. Esslingen : s.n., 2011.

48. A non-linear finite element model of human L4-L5 lumbar spinal segment with three-

dimensional solid element ligaments. Zhitao Xiao, 1 Liya Wang,1 He Gong,1, a) Dong

Zhu,2, b) and Xizheng Zhang3. Changchun : s.n., 2011.

49. IA-FEMesh: ANATOMIC FE MODELS—A check of Mesh Accuracy and Validity.

Nicole A. DeVries, Kiran H. Shivanna, Srinivas C. Tadepalli, Vincent A. Magnotta,

Nicole M. Grosland. Iowa : The University of Iowa.

50. Development of a Finite Element Model of the Human Cervical Spine. Iman

zafarparandeh1, Deniz U. Erbulut 1, Ismail Lazoglu1, Ali Fahir Ozer2. Istanbul : s.n.,

2013.

51. A NOVEL METHOD FOR PATIENT SPECIFIC FINITE ELEMENT MESH

DEVELOPMENT OF THE SPINE. Nicole A. Kallemeyn, Kiran H. Shivanna, Nicole M.

Grosland. Iowa : The University of Iowa.

52. Automating Hexahedral Finite Element Meshing of Bony Structures. Ramme, A J,

1Magnotta, V M and +1Grosland, N M. Iowa : The University of Iowa.

53. IA-FEMesh: An open-source, interactive, multiblock approach to anatomic finite

element model development. Nicole M. Groslanda, b,c,*, Kiran H. Shivannac, Vincent A.

Magnottad,c, Nicole A. Iowa : The University of Iowa, 2009.

90

54. Clinical versuspre-clinical FEmodelsfor vertebral body. Dieter H.Pahra, n,

JakobSchwiedrzikb, EnricoDall’Araa, PhilippeK.Zyssetb. Vienna : s.n., 2012.

55. Developement of a Porcine FE Model for the Investigation of Spondylolytic Vertebral

Fractures. Colin Bright, Stephen Tiernan, Fiona McEvoy. Prague : s.n., 2014.

Proceedings of the International Conference on Biomedical Engineering and Systems.

56. BONE (Increase in Bone Volume Fraction Precedes Architectural Adaptation in

Growing Bone). E. TANCK, J. HOMMINGA, G. H. VAN LENTHE, R. HUISKES. 6,

Nijmegen : Elsevier Science, 2001, Vol. 28. S8756-3282(01)00464-1.

57. Akahoshi S, Sakai A, Arita S, Ikeda S, Morishita Y, Tsutsumi H, Ito M, Shiraishi A,

Nakamura. Modulation of bone turnover by alfacalcidol and/or alendronate does not

prevent glucocoticoid-induced osteoporosis in growing minipigs. s.l. : T J Bone Miner

Metab, 2005.

58. Kato N, Koshino T, Saito T, Takeuchi R. Estimation of Young's modulus in swine

cortical bone using quantitative computed tomography. s.l. : Bull Hosp Jt Dis, 1998.

59. Arnav Sanyal1, Atul Gupta1, Harun H. Bayraktar1, Ronald Y. Kwon1, and Tony

M. Shear Strength Behavior of Human Trabecular Bone. Berkeley : J Biomech, 2012.

60. Nishiyama KK1, Boyd SK. In vivo assessment of trabecular and cortical bone

microstructure. Toronto : s.n., 2011.

61. Physiology, Normal Bone Anatomy and. Bart Clarke. 2008.

62. Three column concept of spinal fractures. al., Dr Tim Luijkx and Dr Roberto

Schubert et. s.l. : radiopaedia.

63. Rockwood and Green’s Fractures in Adults. Bucholz RW, Heckman JD, Court-

Brown C. 6, Philadelphia : Lippincott Williams & Wilkins, 2006.

64. InterNICHE. Policy on the Use of Animals and Alternatives in Education and

Training. s.l. : InterNICHE, 2011.

65. Human anatomy organs. www.aireurbano.com. [Online]

http://www.aireurbano.com/labeled-diagram-of-vertebral-column/.

91

66. Anatomy of large animal spines and its comparison to the human spine: a systematic

review. Sun-Ren Sheng, Xiang-Yang Wang, Hua-Zi Xu, Guo-Qing Zhu, Yi-Fei Zhou.

2009, Eur Spine J, Vol. 19, pp. 46-56.

67. Reduction in segmental flexibility because of disc degeneration is accompanied by

higher changes in facet loads than changes in disc pressure: a poroelastic C5–C6 finite

element investigation. Mozammil Hussain, Raghu N. Natarajan, Howard S. An, Gunnar

B.J. Andersson. 12, 2010, The Spine Journal, Vol. 10, pp. 1069-1077.

68. Monkhouse, Stanely. Clinical Anatomy (Master Medicine. London : Churchill

Livingstone, 2001.

69. Netter, Frank H. Atlas of Human Anatomy. New Jersey : Icon Learning Systems,

2003.

70. Augustus A. White, Manohar M. Panjabi,. Clinical Biomechanics of the Spine.

London : J.B. Lippincott Company, 1990.

71. Journal of Biomechanics (The influence of material property and morphological

parameters on specimen-specific finite element models of porcine vertebral bodies).

Wilcox, Ruth K. 3, Leeds : Elsevier, 2007, Vol. 40.

72. 3D-Slicer. http://www.slicer.org. [Online] [Cited: 29 10 2014.]

http://www.slicer.org/pages/Introduction.

73. Degenerative disc and vertebral disease – basic sciences (Orthopaedics II: spine and

pelvis). Adams, Michael A. 7, Oxford : Elseveir, 2009, Vol. 27.

74. Radiologyinfo.org(Computed Tomography (CT) - Body).

http://www.radiologyinfo.org/. [Online] [Cited: 18 November 2014.]

http://www.radiologyinfo.org/en/info.cfm?pg=bodyct.

75. http://bastech.com/sla/techtips/stlfiles.asp. http://bastech.com. [Online] [Cited: 18

November 2014.] http://bastech.com/sla/techtips/stlfiles.asp.

76. Cowin, Stephen C. Bone Mechanics Handbook. Washington : CRC Press, 2001.

77. vertebral_compression_fracture. hwww.emedicinehealth.com. [Online] [Cited: 14 10

2014.]

http://www.emedicinehealth.com/vertebral_compression_fracture/page2_em.htm.

92

78. BONE (Increase in Bone Volume Fraction Precedes Architectural Adaptation in

Growing Bone). E. Tanck, J. Homminga, G. H. Van lenthe, and R. Huiskes. 6,

Nijmegen : Elsevier Science, 2001, Vol. 28. S8756-3282(01)00464-1.

John Arigho (X00075278) Final Project [Porcine Vertebra Simulation](Print)

Documents

Transcript of John Arigho (X00075278) Final Project [Porcine Vertebra Simulation](Print)