Embed Size (px)
Citation preview
Computational and Experimental Analysis of the Vertebral Column for the Intervertebral Fusion Study
Ana Catarina Costa Roque Soares Pires
Thesis to obtain the Master of Science Degree in
Mechanical Engineering
Examination Committee
Chairperson: Prof. Luís Manuel Varejão de Oliveira Faria
Supervisor: Prof. Paulo Rui Alves Fernandes
Co-supervisor: Prof. João Orlando Marques Gameiro Folgado
Members of the Committee: Maria de Fátima Reis Vaz
Maio 2014
\i
Acknowledgements
First, I would like to thank my Professor, Paulo Fernandes, for all the time and patience to answer my
questions and doubts on the work to pursue and always doing it with a smile. I would also like to thank
Professor João Folgado, for the availability for computational related matters.
Paula Fernandes, for all the patience and advice not only on the experimental part but also on the
computational one.
Joana Leal and Ecorad Clinic, for the Human CT scan.
Évora’s Veterinary Hospital, particularly Professor Joana Reis and Professor José Potes, for providing
the sheep spine for the experimental part of the thesis.
Professor Fátima Vaz, for all the laboratory help, in particular providing the sandpaper and giving her
expert opinion on how the testing was going.
Professor Fernando Simões, for the interest demonstrated on the intervertebral discs.
Professor Ana Paula Dias, for the graduated cylinder used for the volume measurement of the vertebrae.
Dr. João Gamelas, for the CT scan of the sheep spine.
Mr. Pedro, at the IST machine shop, because although having a lot of work he managed to make time
for making the compressive plate and for cutting the sheep vertebrae, which obviously isn’t the most
pleasurable task one can ask for.
My family and friends for all the love and support.
ii
\iii
Abstract
The vertebral spine endures several loads during a life time and is subjected to several injuries.
Constituted by vertebrae, discs, tendons and muscles, each one with particular mechanical properties
and movements, in whole they are able to maintain an equilibrium of forces which preserve the spine
stabilized during the day.
The biomechanical study of this complex structure allows for a better comprehension of its functioning.
Not only to avoid injuries but also to be possible an upgrade of the existing surgical techniques when
these are not possible to avoid.
The mechanical properties assigned in a computational model are essential for its reliability. Because
there isn’t a clear boundary between cortical and trabecular bone, the correct property attribution to the
bone is a problem. On this thesis, the equivalent elasticity modulus of the whole vertebra was calculated
through several compression tests implemented on sheep spine, because human specimens are quite
hard to obtain.
In order to validate the obtained results, the vertebrae were designed and cut computationally with the
same geometry as for the compression test and imported into a finite element program so as to apply
the reached properties.
A computational model of a segment of a human lumbar spine was also made as well as its
biomechanical study in a finite element program and a study of range of motion.
Keywords
Spine; Experimental work; Animal model; Finite element
iv
\v
Resumo
A coluna vertebral humana suporta diversas cargas ao longo da vida e está sujeita a diversas lesões.
Constituída por vértebras, discos, tendões e músculos, cada um com propriedades mecânicas e
movimentos próprios, no seu conjunto conseguem um equilíbrio de forças que mantêm a coluna
estabilizada ao longo de todo o dia.
O estudo biomecânico desta estrutura tão complexa permite uma melhor comprensão do seu
funcionamento. Não só para evitar lesões mas também para ser possível uma evolução das técnicas
cirúrgicas existentes quando estas não são possíveis de evitar.
As propriedades mecânicas atribuídas num modelo computacional são essenciais para a sua
fiabilidade. Por não haver uma fronteira definida entre osso cortical e trabecular, a correcta atribuição
de propriedades ao osso é problemática. Nesta tese, o módulo de elasticidade equivalente de toda a
vértebra foi calculado através de ensaios de compressão realizados em colunas de ovelha, pois os
espécimes humanos são muito difíceis de obter.
De forma a validar os resultados obtidos, as vértebras foram desenhadas e cortadas
computacionalmente com a mesma geometria que para os ensaios e importadas para um programa de
elementos finitos de forma a aplicar as propriedades obtidas.
Foi também feito o modelo computacional de um segmento da coluna lombar humana e feito o seu
estudo biomecânico em elementos finitos e de amplitude de movimento.
Palavras-chave
Coluna; Trabalho experimental; Modelo animal; Elementos finitos
vi
\vii
Contents
Acknowledgements ...................................................................................................................................i
Abstract.................................................................................................................................................... iii
Resumo ....................................................................................................................................................v
Contents ................................................................................................................................................. vii
Abbreviations ........................................................................................................................................... ix
List of Figures .......................................................................................................................................... xi
List of tables ........................................................................................................................................... xv
1. Introduction ....................................................................................................................................... 1
1.1. Motivation and Work Purpose ................................................................................................. 1
1.2. Approach and Organization ..................................................................................................... 3
2. The Spine ......................................................................................................................................... 5
2.1. The Vertebra ............................................................................................................................ 6
2.2. The Intervertebral Disc ............................................................................................................ 7
2.3. Ligaments and muscles ........................................................................................................... 8
2.4. Biomechanics of the Lumbar Spine ....................................................................................... 10
2.5. Possible Lumbar Disorders ................................................................................................... 12
3. Lumbar Fusion ............................................................................................................................... 15
3.1. Spinal Implants ...................................................................................................................... 16
3.1.1. Bone grafts and Cages .................................................................................................. 16
3.1.2. Pedicle screws, Rods and Bolts .................................................................................... 17
4. Experimental Work ......................................................................................................................... 19
4.1. Differences between Sheep and Human Spines................................................................... 20
4.2. Experimental Phase .............................................................................................................. 22
4.2.1. Spine Preparation .......................................................................................................... 23
4.2.2. The Vertebral Testing .................................................................................................... 24
4.2.3. Results ........................................................................................................................... 26
5. Geometric Model ............................................................................................................................ 33
5.1. Medical Images ..................................................................................................................... 33
5.2. Segmentation......................................................................................................................... 35
viii
5.3. Conversion to Solid ............................................................................................................... 40
6. Computational Validation of the Experimental Work ...................................................................... 43
6.1. Mesh Selection ...................................................................................................................... 44
6.2. Displacement Analysis .......................................................................................................... 49
7. Finite Element Analysis .................................................................................................................. 55
7.1. Model Parameters ................................................................................................................. 55
7.1.1. Materials and Initial Conditions ...................................................................................... 55
7.1.2. Mesh Selection .............................................................................................................. 56
7.2. Range of motion .................................................................................................................... 59
7.3. Sensibility analysis ................................................................................................................ 63
8. Discussion ...................................................................................................................................... 65
8.1. Experimental Work ................................................................................................................ 65
8.2. Computational Model and Finite Element Analysis ............................................................... 66
9. Conclusion and Future Work .......................................................................................................... 71
10. Bibliography ............................................................................................................................... 73
11. Appendix – Results from the Experimental Work ...................................................................... 77
11.1. Force-Displacement Experimental Results ........................................................................... 77
11.2. Stress-Strain Experimental Results ....................................................................................... 80
11.2.1. Vertebra 1 Slice 1 .......................................................................................................... 80
11.2.2. Vertebra 1 slice 2 ........................................................................................................... 82
11.2.3. Vertebra 2 ...................................................................................................................... 84
11.2.4. Vertebra 3 ...................................................................................................................... 86
\ix
Abbreviations
PLIF – Posterior Lumbar Interbody Fusion
TLIF – Transforaminal Lumbar Interbody Fusion
ALL - Anterior Longitudinal Ligaments
PLL - Posterior Longitudinal Ligaments
ROM – Range of Motion
ROI – Region of Interest
FE – Finite Element
NP – Nucleus Pulposus
AF – Annulus Fibrosus
x
\xi
List of Figures
Fig. 2.1 – Human spine and its regions [19] ............................................................................................ 5 Fig. 2.2 – The lumbar vertebra, on the left the superior view, and the side view on the right [22] .......... 6 Fig. 2.3 – A schematic view of the spinal segment and the intervertebral disc. On the figure it can be
seen the nucleus pulposus (NP) surrounded by the lamellae of the annulus fibrosus (AF) and separated
from the vertebral bodies (VB) by the cartilaginous end-plate (CEP). It can also be seen the spinal cord
(SC), the nerve root (NR) and the apophyseal joints (AJ) [24] ................................................................ 7 Fig. 2.4 – The seven ligaments [26] ........................................................................................................ 8 Fig. 2.5 – The axes of rotation for the lumbar vertebrae [26] ................................................................ 10 Fig. 2.6 – Facet joint orientation [27] ..................................................................................................... 11 Fig. 2.7 - Range of motion through the lumbar spine. Image adapted from White and Panjabi [26] .... 11 Fig. 2.8 – Disc pressure according to position [27] ............................................................................... 12 Fig. 2.9 – How the centre of mass varies its position with adipose tissue, increasing its distant to the
intervertebral disc, increasing, as a consequence, it’s the intradiscal pressure. [27] ........................... 12 Fig. 2.10 – On the left a healthy disc and on the right, a herniated disc, compressing the nerve root,
causing back pain [29] ........................................................................................................................... 13 Fig. 3.1 - Different types of cages: on the left, MOON cage; on the centre, Stryker cage; and on the right,
BAK cage [38] ........................................................................................................................................ 16 Fig. 3.2 – Different types of prostheses: on the left, AcroFlex; and on the right, Charité [40] .............. 17 Fig. 3.3 – Example of failure of rod fixation, the patient had to be re-submitted to surgery. Image taken
from Pihlajamaki et al. Complications of transpedicular lumbosacral fixation for non-traumatic disorders
............................................................................................................................................................... 17 Fig. 3.4 – Posterior Dynamic Stabilization Devices: A) Graf system; B) Dynesys system; C) FASS
system; D) DSS system [36].................................................................................................................. 18 Fig. 4.1 – Comparison of ROM in Flexion/Extension for sheep and human spine [46] ........................ 21 Fig. 4.2 – Comparison of ROM in Lateral Bending for sheep and human spine [46]............................ 21 Fig. 4.3 – Comparison of ROM in Axial Rotation for sheep and human spine [46]............................... 21 Fig. 4.4 – Compression plate................................................................................................................. 23 Fig. 4.5 – The before and after the removal of most of the muscle attached to the spine .................... 23 Fig. 4.6 – On the left, the beginning of the separation; on the right, the vertebra and disc side by side
............................................................................................................................................................... 24 Fig. 4.7 – On the left, the second vertebra after being sanded; on the right, one of the positions in which
the vertebra was checked with the level. ............................................................................................... 24 Fig. 4.8 – Vertebra 1, experimental setup ............................................................................................. 25 Fig. 4.9 - Vertebra 2, outside and inside area on one of the sides ....................................................... 26 Fig. 4.10 – Curve and trend line from the first test on the slice 1 of vertebra 1, starting at strain zero. 27 Fig. 4.11 – Curve and trend line from the first test on slice 1 of Vertebra 1, starting at 1000 N ........... 28 Fig. 4.12 – Normal (or Gaussian) Distribution ....................................................................................... 29 Fig. 4.13 – Normal distribution for the equivalent Young’s modulus ..................................................... 30
xii
Fig. 4.14 – Normal Distribution based on 2000 random numbers......................................................... 31 Fig. 5.1 - Sequence of used programs as well as their file formats ...................................................... 33 Fig. 5.2 – Basic functioning of the CT scan [52] .................................................................................... 34 Fig. 5.3 - ROI definition for: A) Vertebra2 (C4) of the sheep spine; B) L4 vertebra in the human model
............................................................................................................................................................... 36 Fig. 5.4 - Filter application to vertebra 2 (C4) of the sheep spine ......................................................... 37 Fig. 5.5 – Deformable models, bubbles, inserted for the segmentation on L4...................................... 37 Fig. 5.6 – Automatic segmentation (bubble growth) on L4 vertebra ..................................................... 38 Fig. 5.7 - Automatic segmentation on: A) Vertebra 3 (C3) on the sheep spine, B) L5 vertebra on the
human spine .......................................................................................................................................... 39 Fig. 5.8 - Final assembly of the human spine, consisting of L4 vertebra (in red), L5 vertebra (in green)
and the intervertebral discs connecting those two vertebrae between each other and to L3 and S1
vertebra.................................................................................................................................................. 39 Fig. 5.9 – From the sheep spine: Vertebra 1 (C5) on the right, after the automatic segmentation; Vertebra
2 (C4) on the centre, after manual segmentation; Vertebra 3 (C3) on the right, after the manual
segmentation ......................................................................................................................................... 40 Fig. 5.10 – Vertebra 2 (C4) from the sheep spine; A) Before any mesh adjustments; B) In the middle of
the process, note how the staircase effect is reduced but still there; C) After Mesh Prep Wizard is
completed .............................................................................................................................................. 40 Fig. 5.11 – L4 vertebra from the human spine; A) Before any mesh adjustments; B) In the middle of the
process, note how the staircase effect is reduced but still there; C) After Mesh Prep Wizard is completed
............................................................................................................................................................... 41 Fig. 5.12 - Vertebra 2 (C4) from the sheep spine; on the left, the feature lines, still with errors; on the
right, the solid model after correction .................................................................................................... 41 Fig. 5.13 – L4 Vertebra from the human spine; A) Surface detail, still with errors; B) Feature Lines,
already with no errors; C) Solid model .................................................................................................. 41 Fig. 6.1 – Vertebra 2 (C4) after cut with 15.68 mm height .................................................................... 43 Fig. 6.2 – Vertebra 2 (C4) before and after the virtual topology tool ..................................................... 43 Fig. 6.3 – Element type C3D4 used in Abaqus ..................................................................................... 45 Fig. 6.4 – Typical curve in mesh Convergence study [57] .................................................................... 45 Fig. 6.5 – Vertebra 2; A) with mesh made of seeds of global size 3.8; B) After analysis ..................... 46 Fig. 6.6 – Convergence curve for Vertebra 2 ........................................................................................ 47 Fig. 6.7 – Convergence curve for Vertebrae 1, slice 1 and 2, and Vertebra 3 ...................................... 48 Fig. 6.8 – Displacement on: A) Vertebra 1 slice 1; B) Vertebra 1 Slice 2; C) Vertebra 2; D) Vertebra 3
............................................................................................................................................................... 49 Fig. 6.9 – Graph reaction force – displacement for vertebra 1 slice 1, taken from Abaqus .................. 50 Fig. 6.10 – Force-Displacement graph, comparison between Abaqus results and experimental work with
its trend lines and respective equations ................................................................................................ 50 Fig. 6.11 – Force-displacement evolution with the change of the Poisson’s ration .............................. 51
\xiii
Fig. 6.12 - The Poisson’s ratio study and its comparison to one of the experimental tests for vertebra 1
slice 2 ..................................................................................................................................................... 52 Fig. 6.13 – The Poisson’ ratio study and its comparison to one of the experimental tests for vertebra 2
............................................................................................................................................................... 52 Fig. 6.14 - The Poisson’ ratio study and its comparison to one of the experimental tests for vertebra 3
............................................................................................................................................................... 53 Fig. 6.15 – Force-displacement of the four vertebrae with a Young’s modulus of 22.2 MPa ............... 54 Fig. 7.1 – On the left, discs with partitions (disc L5-S1 on the back, L4-L5 on the centre and L3-L4 on
the front); on the right the vertebrae with the materials separated on the outer layer .......................... 56 Fig. 7.2 – Vertebrae L4 and L5 mesh convergence study .................................................................... 57 Fig. 7.3 – Mesh convergence study for nucleus pulposus (NP), axis on the left, and the annulus fibrosus
(AF), axis on the right, for the three discs L3-L4, L4-L5 and L5-S1 ...................................................... 58 Fig. 7.4 – Comparison of calculated results with previous studies, image adapted from Kuo et al. [10]
............................................................................................................................................................... 59 Fig. 7.5 – Stress distribution on the entire model, on the left, and on the L4-L5 disc, on the right for a
460 N load ............................................................................................................................................. 59 Fig. 7.6 – Flexion and extension spine movement when subjected to a ± 5 Nm moment on the X-axis
............................................................................................................................................................... 60 Fig. 7.7 – Lateral Bending movement of the spine when subjected to a ± 5 Nm moment on the Y-axis
............................................................................................................................................................... 60 Fig. 7.8 – Rotational movement of the spine when subjected to a ± 5 Nm moment on the Z-axis ....... 60 Fig. 7.9 – Stress distribution in disc L4-L5; on the left, in extension; on the centre, in lateral bending; on
the right, in axial rotation ....................................................................................................................... 61 Fig. 7.10 – Stress distribution in the spine segment L4/L5 when subjected to a pure moment of ± 5 Nm on each axis; on the left, in extension; on the right, in lateral bending; on the bottom, two views of axial rotation ................................................................................................................................................... 62 Fig. 7.11 – Range of Motion evolution with the alteration of nucleus pulposus’ Young’s modulus ....... 63 Fig. 7.12 – Stress distribution in disc L4-L5 for discs with a nucleus’ Young’s modulus of 4 MPa; on the
left, in extension; on the centre, in lateral bending; on the right, in axial rotation ................................. 64 Fig. 11.1 – Force-Displacement graph for vertebra 1 slice 1 ................................................................ 77 Fig. 11.2 - Force-Displacement graph for vertebra 1 slice 2 ................................................................. 78 Fig. 11.3 - Force-Displacement graph for vertebra 2 ............................................................................ 78 Fig. 11.4 - Force-Displacement graph for vertebra 3 ............................................................................ 79 Fig. 11.5 - First test for Vertebra 1 slice 1 and its results ..................................................................... 80 Fig. 11.6 - Second test for Vertebra 1 slice 1 and its results ................................................................ 80 Fig. 11.7 – Third test for Vertebra 1 slice 1 and its results .................................................................... 81 Fig. 11.8 – Fifth test for Vertebra 1 slice 1 and its results ..................................................................... 81 Fig. 11.9 – First test for Vertebra 1 slice 2 and its results ..................................................................... 82 Fig. 11.10 – Second test for Vertebra 1 slice 2 and its results .............................................................. 82 Fig. 11.11 – Third test for Vertebra 1 slice 2 and its results .................................................................. 83
xiv
Fig. 11.12 – Fourth test for Vertebra 1 slice 2 and its results ................................................................ 83 Fig. 11.13 – First test for Vertebra 2 and its results .............................................................................. 84 Fig. 11.14 – Second test for Vertebra 2 and its results ......................................................................... 84 Fig. 11.15 – Third test for Vertebra 2 and its results ............................................................................. 85 Fig. 11.16 – Fourth test for Vertebra 2 and its results ........................................................................... 85 Fig. 11.17 – Fifth test for Vertebra 2 and its results .............................................................................. 86 Fig. 11.18 – First test for Vertebra 3 and its results .............................................................................. 86 Fig. 11.19 – Second test for Vertebra 3 and its results ......................................................................... 87 Fig. 11.20 – Third test for Vertebra 3 and its results ............................................................................. 87 Fig. 11.21 – Fourth test for Vertebra 3 and its results ........................................................................... 88 Fig. 11.22 – Fifth test for Vertebra 3 and its results .............................................................................. 88
\xv
List of tables
Table 2.1 – Summary of ligaments and its locations [23] ........................................................................ 9 Table 2.2 – Muscle description [23] ....................................................................................................... 10 Table 4.1 – Summary of the data and obtained results ........................................................................ 28 Table 6.1 – Vertebrae materials ............................................................................................................ 44 Table 6.2 – Number of mesh elements for each vertebra ..................................................................... 48 Table 7.1 – Material properties [10] ....................................................................................................... 55 Table 7.2 – Number of mesh elements for each component of the human model ............................... 58 Table 7.3 – Values of Range of Motion and reaction force of the spine segment when subjected to a
± 5 Nm moment on each axis ................................................................................................................ 61 Table 7.4 - Values of Range of Motion of the spine segment when subjected to a ± 5 Nm moment on
each axis when the nucleus have a Young’s modulus of 4 MPa .......................................................... 63
1
1. Introduction
Low back pain is very common among world population and it can involve bone, muscle, joints or a
combination of them. Given that the lumbar spine supports most of human bodyweight as well as its
movement during daily activities, it is often the cause of such pain whether it’s derived from heavy loads,
disc disease or even bad posture. In some cases, the pain can be reduced and even eliminated by
correcting posture, physical therapy, weight loss, among others, but in other, more severe cases, it can
only be managed by surgery. [1]
Decompression and spinal fusion are the two main types of lumbar spine surgery. The first, can be
divided into microdiscectomy and laminectomy, both involve the removal of part of the bone, disc or
ligament in order to reduce the nerve compression which is causing the back pain. The second and
most common spinal surgery consists of joining two (or in rare cases more than two) vertebrae by the
intermediate of a bone graft, reducing or completely stopping the motion of the segment. A combination
of both types of surgery is usually used with the purpose of achieving a most reliable and sustained
result. [2] [3] [4]
The first lumbar interbody fusion appearance was reported in 1940, and in 1951 several successful
cases were already described using posterior lumbar interbody fusion technique (PLIF) and later the
usage of pedicle screws, around 1960 in Europe. Transforaminal lumbar interbody fusion (TLIF)
appeared later as an alternative. [5]
No matter the treatment option, one very important aspect of spine fusion is that the basic spine functions
must be maintained, and for every single treatment, there can be literature found containing favourable
and unfavourable outcomes. These disparities in results may be due to differences in population (such
as age, sex, race, etc.) as well as bias factors and heterogeneity in the literature. [5]
1.1. Motivation and Work Purpose
Each individual has different daily routines and his spine varies in shape, size, and bone composition
and density, which means each and every disorder will be different from the next. This makes it
impossible to find a unique solution which is preferable for all individuals. As a result, different options
are still being studied and developed.
If only a decompression surgery would be used, the stability of the spine would be jeopardized. Spinal
fixation devices, which promote the spinal fusion may form a rigid fixation, restore alignment and prevent
further disruption on the segment [6], can and should be used to complement the decompression
technique.
However, one other characteristic of the lumbar spine is its flexibility and adaptability, which is lost with
this type of fixation devices. Moreover, studies have shown that some patients later develop disc
2
disorders on the adjacent discs to the treated segment due to the load reduction on the segment. To
counter this, flexible and dynamic fixation devices were designed. [7]
A biomechanical study of the lumbar spine should help us to better understand the spinal behaviour as
well as assess which device provides a better choice. For this, there are three options: in vivo, in vitro and in silico studies. The first, may provide good information specific to the subject but it has a limited
invasiveness requirement. The second, gives us the results from laboratory measurements and has
been widely used, however there are limitations to specimens usage. The latter, and most recent, refers
to the prevalent testing method used nowadays, a computer simulation. [8]
For this computer simulation, AKA in silico study, one needs data to first built the model and then an
adequate program to analyse the model. The anatomical fidelity of the model may vary according to the
precision and general of the required response [9]. For example, one may want a very precise model to
study a very specific response to a determined load or one may prefer a more general model to represent
the entire population.
On this thesis, a computer analysis is done, using a model built from CT images from a woman in her
thirties. It is an anatomical realistic model so as to obtain the most accurate results possible.
The lumbar spine is the lowest part of the human spine but more particularly, levels L4/L5 and L5/S1
are the ones which appear to be the most problematic and propitious of spinal diseases [10]. And so,
this thesis will focus on the L4/L5 segment.
When a computational model is built, it is required to assign material properties to each component of
the model. As the human body is crafted to perfection, it is close to impossible to model the exact
properties of each component in each specific millimetre and so, several simplifications are made, these
will be more closely analysed in the chapter on the geometric model and finite element analysis.
Since the material properties are only an approximation, it is necessary to validate the computational
model. To do so, ex vivo testing is done to provide us the bone properties necessary to the model.
Preferentially, human spinal specimens would be used. Beside the difficulty in finding human specimens
for testing and potential risk of infection, there is a great variation in size, anatomy and mechanical
properties from each individual due to age, sex and bone quality and so, human specimens are not an
option. [11] [12]
As an alternative for human specimens, animal spines are commonly used for in vivo, in vitro and ex vivo testing. The choices include pig, calf, sheep, baboon, deer, goat and even dog spines as good
spinal research, being the first three options the most adequate. [11] [12] [13] [14]
Several studies on the comparison of these three animals and the human spine can be found. They
show that the motion characteristics of the intact spines of calf and sheep are quite similar to the human
spine, and although sizes differ considerably, qualitatively they are similar [12]. It seems that calf spines
are the most used as a substitute for human spine for in vitro testing, closely followed by porcine spine
while sheep spines are the most used for in vivo testing. [14] [15] [16]
3
On this thesis, sheep cervical spines were used to determine the equivalent Young’s modulus of the
whole vertebra via compression testing of said spine. It is stated that sheep spines are a good model
for human cervical spines, “mainly because of the comparable cervical lordosis” [17]. A computational
model of the sheep spine was also made based on CT scans made from one of these spines.
1.2. Approach and Organization
The work is divided between the computational model of the human lumbar spine and the experimental
validation with sheep cervical spine. This thesis is presented in 7 parts besides the first chapter which
is this introduction to the problem in hand.
The second chapter contains an introduction to the human spine, where it is possible to become familiar
with its main components and its role in the human body. As well as the possible pathologies that the
lumbar spine may succumb to.
The third chapter is a theoretical introduction to the lumbar fusion. It explains why fusion is important
when a patient is subjected to surgery and how can this be accomplished with the help of the appropriate
devices, which can vary from bone grafts to dynamic fixators.
On the forth chapter, a detailed description of the experimental work is provided. Several mechanical
compressions of slices from the cervical sheep spine will allow us to obtain the equivalent Young’s
modulus of the whole vertebra, which will allow to simplify future finite element models.
On the fifth chapter, it is explained how the geometrical model is obtained. Every step of the process is
described from the CT scan, passing through the segmentation process and finishing in the solid
construction.
The sixth chapter is in the finite element validation of the experimental work. Based on a CT scan
obtained from one of the sheep spines, the exact slices were recomputed to be submitted to a finite
analysis therefore showing how the results obtained can be used on future work.
The seventh chapter is also a finite element analysis but of a human lumbar spine. On this chapter all
steps from how the properties were chosen to how the mesh was selected are described as well as the
following analysis done such as stress analysis and range of motion to compare to the literature.
The eighth and ninth chapter are the discussion and work conclusions.
4
5
2. The Spine
The spine plays an essential role supporting the upper body’s weight, still allowing movement and
flexibility, while protecting the spinal cord [18] [19]. The human spine has a natural S-shaped curvature;
the neck (cervical) and low back (lumbar) have a concave curve while the chest (thoracic) and pelvic
(sacral and coccyx) have a convex curve. This permits to stand in an upright position as well as allowing
the typical body movement and absorbing shock. [19] [20] [21]
The spine, or vertebral column, is formed by 33 vertebrae and it is divided into five regions: seven
vertebrae in the cervical region, twelve in the thoracic region, five in the lumbar region, five in the sacral
region and four in the coccygeal region. The vertebrae in the last two regions are joined during adulthood
forming two bones (the sacrum and the coccyx) whilst the other vertebrae maintain their original format.
Also, depending on the individual, there may be one extra bone in some region and compensate with
one less bone in other region, this makes no difference on the spine health of the individual. [20] [22]
For the purpose of this thesis, focus will be given to the lumbar spine and the normal distribution of
bones will be considered, particularly, 5 vertebrae on the lumbar region, named from L1, the top one, to
L5, the bottom one that connects to the sacrum. [18] [23]
Fig. 2.1 – Human spine and its regions [19]
The vertebrae are separated from one another by an intervertebral disc. Ligaments, such as the anterior
longitudinal (ALL) and the posterior longitudinal ligaments (PLL), and muscles connect the bones
together and keep them aligned, stabilizing the spine and protecting the intervertebral discs. [19]
6
2.1. The Vertebra
Although they are quite similar, there are differences on the vertebrae according to the spine region.
They are named by the first letter of their region and numbered to indicate their position on that region.
Regardless of location, a typical vertebra consist of the anterior segment, or the body, and the posterior
segment, or the neural arch, which consist of a pair of pedicles and a pair of laminae and support seven
processes. [20] [21]
Fig. 2.2 – The lumbar vertebra, on the left the superior view, and the side view on the right [22]
The body, has a cylindrical shape, with around 40-50 mm lateral diameter and 30-35 mm sagittal
diameter, and is the largest part of the vertebra, supporting most of the weight. The upper and lower
surfaces are flattened and rough and are called endplate, around 0.5 mm thick. It is composed of a thin
shell of hard, strong and dense cortical bone, estimated to be around 0.35 mm thick, and a less dense,
soft and more flexible cancellous bone, or trabecular bone, on the inside. [10] [20] [21] [22] [23]
The vertebral foramen is a triangular shaped hole in each vertebra through which passes the spinal
cord. The laminae are broad plates from the pedicles which are two strong, thick processes that project
backward on both sides of the upper part of the vertebral body. Like the vertebral body, they are made
of cortical bone on the outside and cancellous bone on the inside. Pedicles act as the lateral walls of
the spinal canal, there are concavities above and below the pedicles so that, when the vertebrae are
united, there are notches through which the spinal nerves can branch out of the vertebral canal for the
rest of the human body. [20] [22]
The superior and inferior articulate processes are well defined, projecting upwards and downwards from
the pedicle junctions with the laminae, and contain the articular facets which articulate the vertebrae
between each other; they strengthen the vertebral column and allow for movement. The facets on the
inferior process are convex, directed forward and lateralward while the facets on the superior process
are concave, directed backwards and are wider apart, since the superior processes ‘embrace’ the
inferior ones articulating the column. The transverse process, project laterally from the junction of the
pedicles with the laminae. They are long and slender on the upper three lumbar vertebrae whilst incline
a little upward in the lower two. The transverse process is a site of muscle attachment. Finally, the
7
spinous process, projects posteriorly where the two laminae join, it has the combine function of muscle
attachment and allowing spinal movement and strengthening the vertebral column. [20] [22]
As a consequence of supporting much of the upper body weight and absorbing most of the stress of
lifting and carrying objects, the lumbar vertebrae are the largest and strongest of the movable vertebrae
but are more flexible attributable to the lack of ribs in this region. For the same reasons, this segment is
also the most likely to have problems. [19] [20] [21]
2.2. The Intervertebral Disc
Situated in between vertebrae and keeping them from rubbing into each other, the intervertebral discs
are the main joints of the spine and occupy about one-third of its height. They have the mechanic
function of transmitting loads and providing the necessary flexibility for all natural movements. In the
lumbar region, they are approximately 7-10 mm thick, 40-45 mm in lateral diameter and 35-40 mm
sagittal diameter and are composed by two distinct areas: the nucleus pulposus, in the middle, and the
annulus fibrosus, around the nucleus. [23] [24]
Fig. 2.3 – A schematic view of the spinal segment and the intervertebral disc. On the figure it can be seen the nucleus pulposus (NP) surrounded by the lamellae of the annulus fibrosus (AF) and separated from the vertebral bodies (VB) by the cartilaginous end-plate (CEP). It can also be seen the spinal cord (SC), the nerve root (NR)
and the apophyseal joints (AJ) [24]
The nucleus pulposus is an elastic central mass that acts as a shock absorber to prevent the bones
from bumping into each other while under stress [18] [19] [22] [25]. It contains fibres randomly organised
and elastin fibres arranged radially. These fibres are embedded in a hydrated aggrecan-containing gel
[24]. It presents a variation of 70%-90% water and 15%-20% of collagen in average. The water
composition may vary greatly during a lifetime and even daily, reducing the disc height during normal
activities by losing water and increasing it while the individual is at rest (mainly during sleep) due to the
water reabsorption [25].
This is the reason why a person is taller after waking up in the morning than before going to bed, at
night. The pump mechanism with the movement of the fibrous angle compresses and relaxes alternately
the pressure on the disc, pumping out water with excretions and getting water with nutrients in. [25]
8
The annulus fibrosus is a thick outer ring of fibrous cartilage and is flexible enough to allow every natural
body movement [18] [22] [24]. It is made up of 15-25 concentric rings, or lamellae, with collagen fibres
parallel with each lamella [24]. These lamellas may reach a height of 10-15 mm in the lumbar region
and have an average thickness of 1 mm [25]. These fibres are oriented approximately 60º with the
vertical axis and alternate to the left and right in which adjacent lamella. Elastin fibres lie in between the
lamellae, helping the disc returning to its original configuration after movement as well as maintaining
the lamellae together since they pass radially. [24]
The boundary between nucleus and annulus is very clear in a child, however, as the individual gets
older, the nucleus usually becomes more fibrotic and less gel-like; as a consequence, the boundary
between nucleus and annulus becomes less obvious with increasing age. Also, lamellas in the annulus
become irregular and the collagen and elastin fibres appear more disorganised. [24]
One other morphologically distinct area worth mentioning is the cartilage end-plate. Usually less than 1
mm thick, it is a horizontal layer which makes the border between disc and bone. The collagen fibres in
this region run horizontal and parallel to the vertebra. [24]
2.3. Ligaments and muscles
The main job of the ligaments is to protect the neural structure by restricting the motion of the spine.
They are also capable of absorbing energy during high speed and potentially harmful motion. Figure 2.4
shows the ligaments connecting two vertebrae between each other.
Fig. 2.4 – The seven ligaments [26]
9
The nine ligaments of the spine, their composition and their position are summarized in the following
table:
Table 2.1 – Summary of ligaments and its locations [23]
Ligament name Composition Location
Anterior Longitudinal Ligament (ALL) Collagen fibers
Originates at the base of the occiput and extends into the sacral region along the anterior surface of the spine. It is strongly attached to the vertebral bone and weakly to the disc.
Posterior Longitudinal Ligament (PLL) Collagen fibers
As the ALL, it also extends along the spine but on the posterior surface of the vertebral body, meaning between the vertebral body and the spinal cord. Contrary to ALL, it is strongly attached to disc but weakly to the vertebral bone.
Ligament Flavum (LF) Elastin
It is the most elastic ligament. It connects the anterioinferior aspect of the lamina of the upper vertebra with the posteriorsuperior aspect of the lamina of the lower vertebra, closing the gap between consecutive laminas.
Intertransverse Ligaments(ITL) Thin collagen fibers Connect the transverse processes.
Interspinous Ligaments (ISL) Thin collagen fibers Connect the spinous processes.
Supraspinous Ligament (SSL) Tendinous fibers Connect the upper region of spinous processes.
Capsular Ligaments (CL) Collagen fibers Surround each facet joint, perpendicular to the
surface of the joint.
Ligament nuchae (LN) Collagen fibers Is the continuation of SSL on the back of the head.
Facet Capsular Ligament (FCL) Collagen fibers Connect the processes on the cervical region.
On the lumbar spine, only the first seven ligaments on the table can be found. The last two ligaments
described only exist on the cervical spine, where extra ligaments are necessary because there is more
range of motion than in the rest of the spine.
Little is known about the mechanical characterization of spinal ligaments in vivo, because doing so
would require extremely invasive procedures and motion X-ray is not a suitable alternative. Their
mechanical response has, however, been study ex vivo. Their behaviour has been characterized, such
as other soft tissues, as viscoelastic with non-linear elastic responses. Also, they are capable of working
close to their failure strengths, not necessitating a great safety margin as would bones or discs would
not to have permanent damages.
10
In terms of muscles, they can be divided into two categories according to their location: postvertebral
muscles, which can be subdivided into deep, intermediate and superficial; and prevertebral muscles,
which are the abdominal muscles. Their description can be found in the following table:
Table 2.2 – Muscle description [23]
Muscle Subcategory Description
Postvertebral
Deep Short muscles, connecting spinous and transverse processes and lamina.
Intermediate Ascends from the transverse process of one vertebra and attaches to the spinous processes of the upper vertebra.
Superficial Also named Erector spinae.
Prevertebral --- Also named Abdominal Muscles. Three of them encircle the abdominal region and the other one is located at the midline.
2.4. Biomechanics of the Lumbar Spine
While muscles provide body movement, the bones allow it and the nervous system controls it. Also, and
as said before, joints are what keep bones from rubbing into each other while movements occur and on
the spine there are ligaments and facet joints limiting the movement in each segment.
On the lumbar region it is possible to find rotation movement around the axis of the spine as well as
lateral bending, consisting of a movement along the coronal plane, and flexion/extension, movements
on the sagittal plane, with contrary directions. This three movements can be schematically seen in figure
2.5.
Fig. 2.5 – The axes of rotation for the lumbar vertebrae [26]
When it comes to flexion/extension it is to be noted that it increases from the top to the bottom on the
lumbar spine. It is the movement with the greatest range of motion with an average of 12-16º; followed
by lateral bending, which is constant along the entire segment and it is about 6º. The facet orientation
on the lumbar spine, which can be seen on figure 2.6, explains why rotation is a more challenging
11
movement for this segment of the spine and can only reach about 2º, not varying much from vertebra to
vertebra. The usual degrees of motion can be seen on figure 2.7 by segments of two vertebrae. [23]
[27]
Fig. 2.6 – Facet joint orientation [27]
Fig. 2.7 - Range of motion through the lumbar spine. Image adapted from White and Panjabi [26]
The spinal movement can be characterized in three parameters: the neutral zone, where there is no
resistance; the elastic zone, where the spine begins to work and one can actually feel the resistance;
and finally the sum of both, called the range of motion. [23]
All these movements alter the intradiscal pressure. This pressure also vary with different positioning and
activities. As said before, heavy lifting can be a major cause for disc damage due to extra pressure on
the disc as well as incorrect posture while sitting. One curious fact is that even body weight distribution
can affect disc pressure, since a mass concentration on the stomach area will deviate the centre mass
and alter the normal disc pressure, leading to a higher pressure, see figure 2.7 [27]. On the following
figure, examples of disc pressure can be found according to different positions.
12
Fig. 2.8 – Disc pressure according to position [27]
Fig. 2.9 – How the centre of mass varies its position with adipose tissue, increasing its distant to the intervertebral disc, increasing, as a consequence, it’s the intradiscal pressure. [27]
2.5. Possible Lumbar Disorders
Discs degenerate earlier than other musculoskeletal tissues, signs of lumbar disc degeneration have
been found in individuals as young as 11-16 years old. Around 20% of teenagers already show some
signs of degeneration and this number increases with the ageing process, so that around 60% of 70
year old have severe degenerated lumbar discs [24] [28]. The causes may vary greatly, from small
deformities to complete rupture of the nucleus, it can be due to excessive loading, impact, low muscular
development, congenital malformation and even to a sedentary lifestyle [25].
13
Fig. 2.10 – On the left a healthy disc and on the right, a herniated disc, compressing the nerve root, causing back pain [29]
Given that cell death, cell proliferation, mucous degeneration, etc, are associated with ageing it is difficult
to separate changes that occur exclusively due to ageing, which are inevitable, from those that might
be considered pathological. [24] [28]
The major reason for disc herniation is the failure in nutrient supply [24]. In a degenerated disc, the
water content is much lower than in a healthy disc, this leads to a more rigid, lower disc height and less
disc elasticity [22] [24]. Also, they don’t behave hydrostatically like they should leading to unwanted
stress concentrations. Some studies also imply that degenerative disease may have a strong genetic
component, several articles have shown familial predisposition for this pathology. [24]
Since, disc degeneration greatly depends on the supported loads, the lumbar spine is clearly the most
affected by this pathology. This spine segment is also more likely to break down and to develop
conditions such as osteoarthritis and osteoporosis or herniated, bulging or rupture discs. [19] [30]
A ruptured or herniated disc occurs when the degenerated disc is pressed, for example due to heavy
lifting or a fall, the central mass is squeezed out of its place either tearing the annulus fibrosus or
allocating outside or over the annulus pressing on the spinal cord or on spinal nerves causing back
pain. [22]
As said before, the rapid disc water loss, when under stress, may lead to abnormal stress
concentrations. This will lead to other back problems related to muscles and ligaments, such as unusual
loading on the apophyseal joints will lead to osteoarthritic changes. It will also reduce the tensional
forces on the ligamentum flavum causing remodelling of the structure. [24]
There can also be abnormal curves on the spine, like a lateral curvature, named scoliosis, which causes
one hip or shoulder lower than the other, or an accentuated lumbar curvature called lordosis [22]. On
this thesis there will be no focus on this sort of back problem.
14
15
3. Lumbar Fusion
Since its first appearance in the 1900’s, lumbar spinal fusion has been around and about with different
approaches such as anterior lumbar interbody fusion (ALIF) and posterior lumbar interbody fusion (PLIF)
and even with a lateral approach; which although having some differences, basically consist of the same
thing. Also between static and dynamic stabilization the variety of clinical options continue to grow. [8]
[31] [32]
Despite the fact that there are differences between the surgical approaches, namely from where the
procedure is done, it fundamentally consist of the same removal of the intervertebral disc, preparation
of the bone graft, insertion of the implant into the disc space in order to restore the appropriate height
and correct alignment of the spine for a proper stabilization with help of fixation such as pedicle screws,
rods, or plates. [31]
The posterior approach (PLIF) allows for all the instrumentation to be placed through a single incision,
it would be less invasive than an anterior approach but would have risks to neural structures and
posterior musculature. The anterior approach (ALIF) would offer an extensive exposure however risking
vascular injury. Giving that one is not clearly superior to the other, the choice of one in detriment of the
other really depends on the preference of the patient and the doctor’s expertise. [31]
More recently, another approach emerged: the lateral approach. It minimalizes complications from a
vascular point of view and avoids the main ligaments, therefore being less invasive but still allowing the
removal of a great amount of disc without major complications. This approach is becoming more and
more popular. [31]
Lumbar fusion may be used as treatment of varied spinal disorders, however, it usually isn’t desirable
to sacrifice a moderately degenerated disc; many surgeons attempt to preserve the disk using
alternative devices. Preserving or not the disc, as in any surgery it comes not without risk; being some
of the most common consequences at the treated level the failure to achieve solid bony union, broken
devices (such as broken screws) and device loosening with possible migration of the implant. As so,
only a minimum of 6 months after surgery, it is safe to determine if interbody fusion has been completed
as expected. [33] [34]
To determine whether fusion has occurred or not, radiographic evaluation on spinal alignment should
be performed as well as an assessment of the device/host interface identifying new bone formation and
bone remodelling. Preferentially, evaluations should be performed sequentially over a minimum of 6
months after post-operative with dynamic motion studies and plain radiographs with the patient in
standing position. [35]
The aptitude with which fusion is met may depend on the implant’s size, configuration and porosity [35].
One other factor to keep in mind is when it comes to the materials used, on the one hand, they must be
biomechanical compatible with the human body and on the other hand they must be capable of
supporting the normal loads of the spine in order to perform their function correctly.
16
Although spinal fusion is recommended in many cases, such as in treatment of spinal instability, it
regularly results in a degeneration of the adjacent levels that were submitted to surgery. This occurs
due to differences in the biomechanical structure and the addition of spinal fixators altering the loading
conditions. [36] [37]
3.1. Spinal Implants
As said before, it is possible to have a rigid or a dynamic stabilization of the spine, and either one is
obtained with different devices. Some possibilities are bone graft substituting the intervertebral disc, a
cage and several screws and rods fixating the spine or a combination of several devices.
3.1.1. Bone grafts and Cages
As far as bone grafts go, iliac crest bone from the patient is the best option, followed by an allograft from
a cadaver to obtain fusion. However, on the first option, due to the amount of trabecular bone needed
to fill the necessary height, some complications might arise on the extraction site. On the second option,
there is the problem with the mechanical properties of the bone from being frozen and possibly becoming
dry. Given these, the procedure is not widely accepted in either case. [38]
As a complement or even an alternative to bone grafts, Bagby was responsible for the development of
the first cage the ‘Bagby basket’, which consisted of a thirty millimetre long with twenty five millimetre
diameter cylinder of stainless steel [39]. Also, other options were studied, such as the BAK cage, the
MOON cage and the Stryker cage. Several examples of cages can be seen on figure 3.1.The other
alternative to the cages and bone grafts are the prostheses such as the AcroFlex or the Charité Disc
Prosthesis which may offer bigger ROM in axial rotation when compared with cages [40]. Examples of
such prosthesis can be seen on figure 3.2.
Fig. 3.1 - Different types of cages: on the left, MOON cage; on the centre, Stryker cage; and on the right, BAK cage [38]
17
Fig. 3.2 – Different types of prostheses: on the left, AcroFlex; and on the right, Charité [40]
3.1.2. Pedicle screws, Rods and Bolts
The main reason for current treatments is to reduce back pain rather than to repair degenerative discs.
Promoting spinal fusion is a main goal on any spine surgery, for it will reduce the pain by decreasing the
segment motion.
Pedicle screws and rods of stainless steel or titanium are the gold standard when it comes to rigidity,
therefore also great for promoting spinal fusion. However, several studies have shown that these
components accelerate degeneration on the adjacent levels. Also, some potential problems specific to
the implant may appear such as mechanical failure or device migration, an example of failure can be
seen on figure 3.3. This arises some discussion on whether this is the best method. [36] [41]
Fig. 3.3 – Example of failure of rod fixation, the patient had to be re-submitted to surgery. Image taken from Pihlajamaki et al. Complications of transpedicular lumbosacral fixation for non-traumatic disorders
18
In order to combat some of these problems, semi-rigid fixation emerged. Made of polymeric or composite
rods and to be used as a complement to bone grafts and/or cages. These fixations intend to achieve
better fusion, by avoiding the stress shielding that occurs in a rigid instrumentation. [41]
To achieve spinal stabilization but without spinal fusion, dynamic fixation emerged as a new and
improved method of using pedicle screws. It can be defined as an implant that alters the movement and
load of the spinal motion segment in a favourable manner without spinal fusion. The intention of a
dynamic stabilization is solely to alter the loadbearing pattern and to control the abnormal motion of the
segment. [36]
On figure 3.4, examples can be seen of these devices. The Graf system, a nonelastic braided polyester
ligament in the form of a loop applied around the pedicle screws. Dynesys, made of titanium alloy pedicle
screws, polyester cords and polycarbonaturethane spacers. The FASS system (Fulcrum-Assisted Soft
Stabilization), consisting of polytetrafluoroethylene fulcrums and polyurethena bands. And DSS system
(Dynamic Stabilization System) made of a titanium spring rod and pedicle screws. [7] [36]
Fig. 3.4 – Posterior Dynamic Stabilization Devices: A) Graf system; B) Dynesys system; C) FASS system; D) DSS system [36]
Although these dynamic stabilizations are getting more and more popular, literature on the subject
suggests that decompression of the disc with instrumented fusion provides a better clinical outcome, a
major 90% comparing to 60% to decompression only; suggesting that dynamic stabilization is not the
best option. [5]
Also from literature review on lumbar fusion rates, although all presenting a high value; pedicular fixation
has a 99.4% rate against a lower anterior instrumentation with 94.8% and hook-rod devices of 96.9%.
[5]
19
4. Experimental Work
Whether it’s for implants study or for an increase in the general knowledge of the spine, in vitro, ex vivo
or in vivo studies are rather common. Each one having there pros and cons. For example, in vivo experiments will give the most faithful results but are very limited due to its invasiveness. Particularly for
the spine study, the in vitro experiments appeared in the 90’s and allowed a controlled environment for
the load application, however, the validity of the obtained results were questioned for not having the
fluid inflow during the unloading process and the proper recovery time. [42]
In order to solve some of this problems, in silico studies appeared. The finite element (FE) analysis
consists simply in designing the anatomic geometry that one means to study, introducing its properties
as faithfully as possible and applying the load and boundary conditions as detailed as wanted.
The properties definition on the computational model are very important for its reliability. Since that
knowing exactly where the frontier between cortical and trabecular bone is very difficult, assigning those
properties isn’t an easy task. The purpose of this experimental work was to determine the Young’s
modulus of the whole vertebra. This way it would be possible to assign a property to the whole vertebra
without distinguishing between the cortical and trabecular bone. To do so, compression tests would be
performed on the vertebrae and the results analysed.
Obviously, human cadaveric specimens would be preferably used, however, finding them, especially in
a healthy state, is very difficult. In addition, human specimens vary greatly according to gender, age,
weight and of course their health level. As a consequence, it could be difficult to establish a testing
criteria that would be equal for all specimens. [13] [43]
Animal models are usually used as a substitute in this studies. Being the most commonly used porcine,
calf and sheep among others. One consideration to have when dealing with quadruped animal models
as a comparison to human models is the weight distribution being different, considered higher in
humans. [11] [44]
For this thesis it was considered using porcine spine and efforts were made in that direction. However,
Evora’s Veterinary Hospital kindly provided sheep cervical spine for the experimental work to start. The
two cervical spines supplied were from mature healthy sheep that were killed for an anatomy class. After
dissected in anatomy class, they were frozen and only then brought to IST’s laboratory.
For future reference, if IST laboratory wishes to acquire animal material in a formal way, an authorization
from Direcção Geral de Veterinária must be asked with reference to regulation number 1069/2009 in
which must be referred where the testing will take place and how the laboratory is planning on disposal
of the by-products. For this thesis, the disposal of the by-products is not a problem for all will be returned
to Évora’s Veterinary hospital where they have the proper means to do so.
20
4.1. Differences between Sheep and Human Spines
The most obvious difference will be the load distribution, assumed to be higher on humans from being
in a standing position while sheep being quadruped animals, therefore being in a horizontal position.
However, this might not be true. Although there is no scientific proof because no measurements could
be made on this, the stress derived from muscles contraction needed to stabilize a horizontal spine is
probably higher than that needed from an already balanced vertical one. [44]
Since most humans suffer from some sort of disc degeneration after a certain age, whether it’s reduced
height, decreased water, cell death or loss of collagen. None of these symptoms occur on the sheep
spine [44]. This is usually a favourable aspect in the choice of any animal spine instead of human but in
this thesis it doesn’t matter for, although the discs were preserved, only the bone is tested.
In terms of morphometric comparison, there are several differences in all parts of the spine but only the
cervical segment is worth mentioning since this is the one being tested. The first thing noticeable in a
sheep vertebra is that it is higher than wide, considerably higher than a human vertebra, which is slightly
wider than high. However, both species present a wider than deep vertebrae, having therefore the same
oval shape. [43] [45]
Comparing the vertebral body from the cervical segment with other segments, the height, width and
depth on the sheep are the greatest whilst on the human have the smaller dimensions. The sheep
vertebral body height decreases from C2 to C7 at a regular pace, but with the anterior height usually
higher than the posterior one. [43]
Following the same trend, the pedicles are quite higher on the sheep than they are on the human spine,
and it diminishes from C2 until C7 while on the human spine it is more or less constant; in terms of width,
they have similar values all along the cervical segment. Neither processes nor facet joints report worth
mentioning differences between sheep and human cervical spines, having similar values all along the
segment. [43]
Although the motion of the entire spine is similar, the fact of these size differences pose a difficulty if
one wants to test spinal implants, for most of them will not fit the sheep spine as they would the human
spine without alterations [12]. However, this testing was outside the range of this thesis.
In terms of range of motion (ROM), there are several studies in the literature for the human spine,
however, it is difficult to use them for comparison because data vary substantially. For both human and
sheep spine, in the cervical region, typically ROM in large in all three directions however usually slightly
larger in human spine. [46]
This can be seen in figures 4.1, 4.2 and 4.3 which contain the ROM off all three motions in both spines,
the sheep spine from the study made in Wilke et al. [46] and the human data taken from previous studies.
21
Fig. 4.1 – Comparison of ROM in Flexion/Extension for sheep and human spine [46]
Fig. 4.2 – Comparison of ROM in Lateral Bending for sheep and human spine [46]
Fig. 4.3 – Comparison of ROM in Axial Rotation for sheep and human spine [46]
22
4.2. Experimental Phase
Both spines donated from Evora’s Veterinary Hospital were frozen at -20º C in the laboratory just like
they were given, meaning still surrounded by muscle. In order for the laboratory to start functioning,
some requirements had to be fulfilled such as having the material to work on the spine.
The laboratory material was acquired from VWR (their website is in reference [47]), an international
company with vast material options. For the laboratory, the following material was bought:
Disposable Nitrile Gloves – which were essential to use every time that touching the sheep
spine was necessary. The nitrile was the most adequate material to deal with animal grease;
Plastic bags – to reserve any biological waste material and any biological material yet to be
used. Note that none of the biological waste can be disposed of in a conventional matter, as so,
everything must be returned to Evora’s Veterinary Hospital;
5L container – Simple rectangular container, to leave the spine in water every time that it is not
being used or is not frozen;
Dissection Kit – Containing a scalpel, a scissor, a spatula, tweezers, a needle and a lancet. This
was necessary for taking the muscle of the spine as well as separating the vertebrae from one
another;
Extra scalpels – Each scalpel has a very sharp blade, however, these blades rapidly go to waste
and in order to guarantee precision work, changing scalpels is essential;
Pursept A disinfectant – Needed to clean all the instruments used and the workspace after work;
Hy-G-Clenz Soap – An anti-bacterial soap, recommended to wash hands after working with
biological material even if always using gloves.
For the compression test, on the laboratory there was a universal INSTRON machine, model 5544 and
there was access to two different load cells, one of 200 N and the other of 2 000 N. It was missing the
compression plate which was made specifically for the vertebrae size in the IST machine shop with Mr
Pedro. The compression plate can be seen in picture 4.4.
23
Fig. 4.4 – Compression plate
4.2.1. Spine Preparation
The spine was taken out of the freezer and left in a water bath in the fridge, at 4º C, for a 24 hour period.
After the defrosting, all the muscle was removed as far as possible as can be seen in figure 4.5.
Note that, both bone and disc should be at room temperature the least amount of time possible and they
should always be kept hydrated. As so, although the freezing and defrosting cycles may affect the
material properties, keeping them several days at the fridge is not a good option. The defrosting cycle
of 24 hours was repeated as many times as it was necessary. Also, as keeping the tissue hydrated was
a main concern, they were kept in a water bath every time that they were not frozen or being used.
Fig. 4.5 – The before and after the removal of most of the muscle attached to the spine
24
The vertebra separation was the next step. At this point, it was also considered testing the discs. The
separation was made one vertebra at a time and both vertebra and disc were separated as it can be
seen in figure 4.6. The disc was submerged in water, it was observed that it only a couple of minutes its
size had swelled substantially due to the humidification. The disc was then removed from the water and
saved in a plastic bag to be frozen.
Fig. 4.6 – On the left, the beginning of the separation; on the right, the vertebra and disc side by side
The vertebra was cleaned of all soft tissue that was then of easier access and taken to the IST workshop
to be cut. A total of three vertebrae were separated and cut and the respective discs were frozen as
described before. Two slices were cut from one of the vertebrae and one slice from each of the other
two vertebrae, meaning a total of four slices were to be tested.
Since there was not the appropriate equipment at the workshop to cut the slices of vertebrae, there was
no way of guaranteeing two parallel faces. In order to correct the possible problems of the parallelism
of the faces, the surfaces were sanded with sandpaper and levelled in several positions as best as
possible as it can be seen an example in figure 4.7.
Fig. 4.7 – On the left, the second vertebra after being sanded; on the right, one of the positions in which the vertebra was checked with the level.
4.2.2. The Vertebral Testing
The testing criteria was adapted from Buckley et al. [48]. In the article, a layer of 1.3 mm thick of bone
cement is used, ten cycles of 100 to 250 N compressive force is applied at a frequency of 0.1 Hz in a
pre-test so as to pack the cement to the bone. Following the pre-test, the actual compression test started
at a velocity of 1 mm/min until it reaches its ultimate force, around 5 kN.
25
First, on this experimental work no bone cement was used to hold the vertebra in place, that was one
of the reasons why guaranteeing the surfaces parallelism was so important, only two plastic sheets (the
blue plastic sheets that can be seen in figure 4.7, on the right) were used to protect the vertebra from
the metal in the testing process. As no bone cement was used, there was no need for the conditioning
cycles in the pre-test having such high values, so ten cycles of a load varying between 10 N to 25 N
were used at a velocity of 1 N/s. On the INSTRON machine command, there wasn’t the possibility of
controlling the velocity by frequency (Hz) hence the choice of Newton per second.
The compression test was held at a velocity of 1 mm/min, like in Buckley et al. [48]. As for stopping
criteria, the INSTRON machine allows several options; for this experiments, it was left the 40% load
reduction; which is the default option and is what is considered the consequence of the breakage of the
specimen and it was added the maximum load option as well. To gain some sensibility in terms of load,
some tests were completed with the load stopping at 100 N, 750 N, 1250 N and finally, after noting that
there was no indication of any fracture or even micro fracture (that would be noted on the graphs as a
momentary load reduction) on the vertebra and given that on other articles [48] [49] it is stated that the
ultimate load is above 2 kN (our load cell), the stopping criteria was held at 1980 N.
All slices were tested five times until 1980 N and none showed any signs of fracture. On figure 4.8, the
experimental set-up can be seen.
Fig. 4.8 – Vertebra 1, experimental setup
Note that, the bottom aluminium plates were necessary to elevate the slice of vertebra due to one of the
security features of the INSTRON machine. This security feature does not allow the compressive plate
to lower below a certain point.
The experimental results, such as time, in seconds, force, in Newton, and displacement, in millimetres
are saved in a txt file. Also, the INSTRON machine allows a possibility of automatically calculating the
Young’s modulus but given that only an estimate area was given to the machine, these Young’s modulus
values will not be considered.
26
4.2.3. Results
The data stored in txt file from the INSTRON machine was then passed into excel in order to be applied
a set of simple equations to ultimately calculate the Young’s modulus. Also, the stiffness of the
vertebrae, in kN/mm, was calculated based on the graphs force-displacement ignoring the pre-tests,
meaning considering values starting at 26 N.
In order to proceed with the calculations, the cross section area had to be calculated. For that, a program
named ImageJ was used. ImageJ is an open source program based on images to calculate the areas.
A picture was taken of the slices in a perpendicular way, with a ruler next to the vertebrae, and that said
image was imported into the program. The scale was set with the ruler and the area was design like in
figure 4.9, excluding soft tissue that was not cut off from the vertebral bone.
Note that, since the area is very irregular, the area was calculated on both sides of the slices and an
average value was used as to minimize errors. Also, the area was to be calculated by submersion in
water as well and a mean value from both calculations was to be used for the final calculations. However,
in the submersion method the error was too big to be considered an option and as a result was ignored.
Fig. 4.9 - Vertebra 2, outside and inside area on one of the sides
With the area and applied force, the stress could be calculated according with the following formula:
𝜎 =𝐹𝐴 [𝑀𝑃𝑎]
(1)
Where σ is the stress in Mega Pascal, F is the force in Newton, given by the tests and A is the area
calculate by the method described above, in square millimetres. After, the strain was calculated based
on the displacement and initial height. To calculate the displacement, however, a little adjustment had
to be made. Since there was the pre-test, the displacement associated with it had to be ignored, thus,
the displacement at the load value immediately after the cycles, meaning at the beginning of the test
27
itself was subtracted to the displacement values, making the beginning of the test a moment where the
displacement value is zero, as it can be seen in formula (2):
𝜀 =𝛥𝑙 − 𝛥𝑙(26𝑁)
𝑙4 (2)
With these results, a graph was made for each test starting just at the value where the displacement is
zero. Then, a trend line was added to the graph. Given that it is considered that the test is done at the
elastic zone of the vertebra, the inclination of this trend line should give us the value of the elastic
modulus. It can be seen both the experimental curve and the trend line in figure 4.10.
Fig. 4.10 – Curve and trend line from the first test on the slice 1 of vertebra 1, starting at strain zero
Based on this result, the elastic modulus of the vertebra would be 16.2 MPa which is a low value
comparing to the literature Young’s modulus for trabecular bone, around 100 MPa and cortical bone,
around 12 000 MPa, according to Kuo et al. [10]. From the graph analysis it can be noted that at the
beginning of the experimental curve the curvature is greater than at a higher stress value, this raises
the question if at this point can it be already evaluated the Young’s modulus or is it still the adaption of
the vertebra? Also, it can be seen that the trend line does not completely follow the experimental curve
but quite on the opposite, once again raising the same question that the beginning of the curve isn’t
valid for evaluation.
Given this, it was decided to make the same graph but only considering values higher than 1 000 N,
thus ensuring that at this point it was pass the initial curvature and already at a linear part. The trend
line was again added and the following graph was obtained:
28
Fig. 4.11 – Curve and trend line from the first test on slice 1 of Vertebra 1, starting at 1000 N
As it can be seen, the trend line perfectly follows the experimental curve and the Young’s modulus has
a higher value of 18.5 MPa. Both these graphs were made for all the tests for comparison and the same
behaviour described above was found in all other tests.
A summary of the data and results can be found in table 4.1, the Young’s modulus presented is the one
calculated by only considering the values starting at 1000 N.
Table 4.1 – Summary of the data and obtained results
Vertebra Area [mm2] Height [mm] Stiffness [kN/mm]
Young’s modulus [MPa]
Vertebra 1 Slice 1 1041.3 9.95
1.70 18.5 1.77 19.2 1.79 19.4 1.79 19.4 1.79 19.4
Vertebra 1 Slice 2 965.9 10.25
1.49 19.0 1.54 20.0 1.55 20.1 1.55 20.2
Vertebra 2 1190.1 15.68
1.39 22.4 1.41 23.1 1.47 23.7 1.48 23.9 1.39 23.9
Vertebra 3 826.3 11.25
1.71 26.1 1.74 24.4 1.75 26.5 1.74 26.5 1.74 26.5
29
It can be seen that in general, in each vertebra, the elastic modulus value slightly increased in each test.
This could be a consequence of not letting enough time in between tests for vertebral recovery or due
to the fact that in each test, the vertebra became less moist.
4.2.3.1. Data Analysis
Statistical analysis is the mathematical science in charge of collecting and evaluating data. Statistic is
very advantageous in the treatment of experimental data because it allows to cover for errors or lack of
information as well as take conclusions for a large population from a small sample.
The most used and common probability distribution is the normal (or Gaussian) distribution. It is
represented in figure 4.12 and it has that bell-curve shape that can be seen. In theory, it extends from
- ∞ to +∞ and the total area beneath the curve sums up to 1 (or 100%).
Fig. 4.12 – Normal (or Gaussian) Distribution
The curve is perfectly define by its mean value, µ, and its variance, σ2. The mean value, given by
equation (3) represents the higher value of the curve, it is the median, the most expected outcome and
it regulates how high the curve goes:
μ6 =∑ 𝑥9:9;<𝑁 (3)
Where 𝑥9 represents the variable to be analysed. The variance indicates the scatter of the data set from
the average, it controls the width of the curve and is given by equation (4) and its square root, σ, is
named standard deviation:
𝜎6= =∑ (𝑥9 − μ6)=:9;<
𝑁 (4)
The normal distribution is given by equation (5):
𝑓6(𝑥) =1
𝜎√2𝜋exp E−
12𝜎= (𝑥 − μ6)
=F (5)
In the normal distribution, the curve is symmetric in relation to the mean value and it has two inflexion
points in x = µ ± σ. There may be some particularities, for example, if µ = 0 and σ = 1 the distribution is
30
called standard normal distribution; also, there are logarithmic normal distribution, which do not have a
bell-curve shape.
Applying equation (3) and (4) to the attained values showed in table 6.1, the following values were
obtained for the mean and variance respectively:
μ6 = 22.22 (6)
𝜎6= = 8.15 (7)
Both these values are for Young’s modulus, as so, there units are MPa. With these two parameters,
equation (5) could be applied and the graph in figure 4.13 obtained for the normal distribution.
Fig. 4.13 – Normal distribution for the equivalent Young’s modulus
As it can be seen from the figure 4.13, the normal distribution doesn’t have exactly the bell-curve
described before. This happens because ideally, to draw the curve, several hundred values would be
used. A small sample for any statistical distribution might mislead into mistakes for not containing
enough information about the population. Unfortunately, given that this experimental work was limited
in time and numbers of slices it was not possible to get a sample as big as one would like, making
margin for errors such as the one that can be seen at the beginning of the curve.
One way around this would be to calculate the mean and standard deviation with the original sample
and then using random numbers based on these values and reploting the normal distribution graph, as
in figure 4.14. To be noted that, in this case, the errors associated with the probabilities might be slightly
different from the former graph, however, the distribution approximates better the theoretical values.
31
Fig. 4.14 – Normal Distribution based on 2000 random numbers
Looking at figure 4.14 and comparing it to figure 4.13 it can be seen improvement on the symmetry of
the curve and the beginning of the curve does not go below value zero anymore.
32
33
5. Geometric Model
The geometric models, both human and animal, were constructed as faithfully as possible from the
original form based on the CT images acquired. For this process, various programs were used. First,
ITK-Snap was used for the segmentation process of the images and the mesh files were imported into
SolidWorks where it is possible to convert them into a surface or a solid after a simplification and
smoothing of the surface and finally, the file can be imported into Abaqus, where the finite element
analysis can be performed.
With this process, a three dimensional model that is subject-specific is obtained. If a more generalized
model is wanted, some alterations could be made, such as mirroring surfaces on the sagittal plane. One
other thing to keep in mind is the difficulty in modelling muscles and tendons; however, in a finite element
model, it is not difficult to simulate the forces correspondent to those muscles but they are still seldom
used. [50]
Fig. 5.1 - Sequence of used programs as well as their file formats
5.1. Medical Images
Medical imaging is the only non-invasive way to look inside a patient without having to cut them open.
As so, it is a major tool when it comes to diagnose and treatment and it also increases our knowledge
of the human body. Some of the most commonly used are X-ray, Magnetic Resonance Imaging – MRI,
and Computed Tomography – CT scan.
The theory behind the CT scan was develop around the sixties but its successful practical
implementation was only accomplished in 1972 by Dr. Godfrey Hounsfield, who is considered the official
inventor of this technique. The first CT images were produced at the Atkinson Morley Hospital in London
and they were able to detect a cystic frontal lobe tumour. After this, it was a welcomed technique on the
medicine field and in 1979 Hounsfield together with Cormack, an engineer and physicist, were given a
Nobel Prize for their achievements. [51]
34
The Computed Tomography (tomography having its origin in the Greek “tomos” + “graphe” meaning
“slice” + “drawing”) is based on the absorption of X-ray by different tissues. A simple X-ray overlaps all
the information in one single slice and so can be of difficult interpretation, this are the cases when the
X-Ray Computed Tomography is used. However, neither of these techniques can be used too many
times due to its harmful effects on the human body because it uses ionizing radiation.
Fig. 5.2 – Basic functioning of the CT scan [52]
The X-ray source is composed by two electrodes: a cathode, acting as the electron source, and an
anode, containing the metal plate. A potential difference, which may vary between 15 and 150 kV,
depending on the application, is applied between both and the electrons have enough energy to escape
the cathode’s surface whilst being attracted to the metal surface. This will create the X-ray beam. [53]
The patient lies inside a tunnel equipped with scanner consisting of the X-ray source and the receiver
always positioned 180º across from each other. The patient’s bed slowly moves in the tunnel and stops,
the scanner circles the patient and X-rays the beam at several points. Each time the bed moves, the
scanner circles again. A computer receives the data and is capable of reconstructing a slice of the body,
nowadays, the whole 3D anatomy is reconstructed.
Most modern CT machines are able to continuously take pictures while the patient’s bed is still moving.
This Helical CT has been developed in order to avoid mistakes in the 3D reconstruction and to be more
time efficient; in order words, this spiral technique allows more slices in less time.
The sheep cervical spine images were obtained thanks to Dr. João Gamelas, in Clinica Quadrantes in
Miraflores. 405 images were taken from the cervical segment. The images are based on a greyscale.
For this thesis the human CT images were for the complete upper body of a 33 year old woman from
Ecorad Clinic done in 2013. There were 291 images for the entire spine. This images are also based on
a greyscale and there is no pathology on the lumbar region.
35
5.2. Segmentation
Typically used to identify relevant information on digital images, segmentation is the process of gathering
pixels into individual regions. There are several ways to perform the image segmentation such as a
colour base segmentation, thresholding or texture methods. In the medicine field, some of the
applications of this technique are to locate tumours or other pathologies, measure tissue volumes and
the diagnosis and study of an anatomical structure.
To help us on this process, a program named itk-SNAP was used. It is a free open source program
designed specifically for the segmentation of anatomical structures in a way that anyone would be able
to use even without a mathematical or engineer background.
The automatic segmentation method utilized in itk-SNAP is based on an active contour method that can
be described by the following equation: [54]
𝐶K(𝑡, 𝑢) = 𝐹9OKPQORS + 𝐹PUKPQORS (8)
Where 𝐶K is the contour at time t which is parameterized by u, and F are the forces acting on said contour
on the normal direction. The internal force controls the evolution based on the geometry. The external
force has the information on the image and can be calculated either through a magnitude gradient of
the image intensity or through a voxel probability map, depending on the image. [54]
By solving the equations that follow after partial differentiation of equation (1), itk-SNAP starts an
iterative process segmenting the image and allowing the user to view the reconstructed 3D image.
With the aim of having the automatic segmentation simplified, after importing the series of DICOM
images into itk-SNAP, it is important to adjust the image contrast and colour map, so that the matter that
the user wants to overlook is blackened (as far as it is possible).
Since it is not desired to segment the complete spine, the second step is to define the region of interest
(ROI). In the case of this thesis, each vertebra was done at a time in both cases, sheep and human
model, as it can be seen in the figure 5.3, vertebra 2 (C4) in the sheep spine and L4 in the human spine
as an example.
36
Fig. 5.3 - ROI definition for: A) Vertebra2 (C4) of the sheep spine; B) L4 vertebra in the human model
Now is when the segmentation process actually begins. It was chosen an intensity region method, which
is a simple thresholding method. It essentially consist in picking up a pixel, comparing it to a certain
value and if it is inside the defined values then it falls into category, otherwise, it gets overlooked.
37
The grey values which fall into category are user defined by a region filter as it can be seen in figure
5.4:
Fig. 5.4 - Filter application to vertebra 2 (C4) of the sheep spine
Ideally, the entire vertebra should be white while everything other than the bone should be blue.
However, this was not possible and the filter option represented above shows what the best option was.
At this point, the deformable models are inserted, which are called bubbles in itk-snap. Several bubbles
can be inserted and with different sizes so as to facilitate the iteration process as it can be seen in figure
5.5.
Fig. 5.5 – Deformable models, bubbles, inserted for the segmentation on L4
38
The iterative process now starts and last for as long as the user wants. The user must keep in mind that
the segmentation accuracy may vary due to the vertebra’s complex structure, unclear boundaries and
the similar structures that, although not being part of the vertebra at matter, are still within the ROI [8].
In the following figure it can be seen the iterative process of the automatic segmentation on vertebra L4
of the human model. Note how the bubbles grow and adapt to the vertebra body.
Fig. 5.6 – Automatic segmentation (bubble growth) on L4 vertebra
As it can be seen in figure 5.6, in iteration 200, the vertebra was still not complete, however, it can
already be seen pieces of the adjacent vertebrae on the facets and there wasn’t such a great difference
from iteration 150 to 200. As so, allowing the program to continue with the automatic segmentation
would not be productive. At this point, a manual segmentation is required.
As known, the trabecular bone and the cortical bone have different properties and this will be seen
through a different grey colour on the 2D slices. As so, utilizing a manual segmentation as a complement
to an automatic segmentation is always recommend even if only to adjust some boundaries [8]. The
manual segmentation has to be done slice by slice and very carefully, as a consequence, it requires a
lot of time from the user. All of the remaining L4 vertebra was segmented while the elements belonging
to other vertebrae were removed.
The same process was applied to the other two vertebrae of the sheep spine, C5 and C3, and to L5
vertebra from the human spine: ROI selection, filter application, automatic segmentation and manual
segmentation. For the L5 on the human spine, on the automatic segmentation, only after 200 iterations
did the process stabilize, as so, 250 iterations were done. The start and end result can be seen on figure
5.7.
39
Fig. 5.7 - Automatic segmentation on: A) Vertebra 3 (C3) on the sheep spine, B) L5 vertebra on the human spine
For the intervertebral disc, only needed for the human model, the process is slightly different. Since they
are made of soft tissue, they are really difficult to see on the slices, even after adjusting the filter.
Therefore only manual segmentation was applied.
On figure 5.8 it can be seen the final human model, consisting of two vertebrae and three discs. All the
parts were saved individually on a mesh file, stl format. On figure 5.9, it can be seen the three vertebrae
segmented from the sheep spine.
Fig. 5.8 - Final assembly of the human spine, consisting of L4 vertebra (in red), L5 vertebra (in green) and the intervertebral discs connecting those two vertebrae between each other and to L3 and S1 vertebra
40
Fig. 5.9 – From the sheep spine: Vertebra 1 (C5) on the right, after the automatic segmentation; Vertebra 2 (C4) on the centre, after manual segmentation; Vertebra 3 (C3) on the right, after the manual segmentation
5.3. Conversion to Solid
As it can be seen in figures 5.8 and 5.9, the segmentation leaves a staircase effect. This happens
because each slice of the CT scan on either model is separated from the next by some millimetres. The
space between each slice is divided into two and filled according to the segmentation of the immediate
following slice creating the staircase effect.
Clearly a smoothing process is required in order for the model to approximate more the human anatomy.
To do so, each file was imported individually into SolidWorks, which contains a module named
ScanTo3D that allows a smoothing of this effect.
In ScanTo3D it can be found a Wizard named Mesh Prep Wizard which contains the necessary tools to
prepare and clean up a mesh. The most used tools on this wizard were the simplification tool, global
and local, and the smoothing, global and local. The first reduces the number of vertices in the mesh
files, resulting in a smaller file; the second, corrects sharps edges and unrefined areas.
After applying both this tools, simplification and smoothing, one after the other and a few times, there
was a volume reduction but the vertebra had a geometry that was closer to the reality. Some
intermediate steps can be seen in figure 5.10 and figure 5.11.
Fig. 5.10 – Vertebra 2 (C4) from the sheep spine; A) Before any mesh adjustments; B) In the middle of the process, note how the staircase effect is reduced but still there; C) After Mesh Prep Wizard is completed
41
Fig. 5.11 – L4 vertebra from the human spine; A) Before any mesh adjustments; B) In the middle of the process, note how the staircase effect is reduced but still there; C) After Mesh Prep Wizard is completed
After the mesh preparation, another wizard is applied, Surface Wizard, which allows the conversion of
the mesh into surfaces and then into a solid model. Given the complexity of the geometry, an automatic
creation is necessary, the user only needs to choose the surface detail. In this L4 vertebra case, 1285
surfaces were obtained. After the edition of the feature lines, it was possible to delete all the errors and
create the solid as it can be seen in figure 5.12 and 5.13.
Fig. 5.12 - Vertebra 2 (C4) from the sheep spine; on the left, the feature lines, still with errors; on the right, the solid model after correction
Fig. 5.13 – L4 Vertebra from the human spine; A) Surface detail, still with errors; B) Feature Lines, already with no errors; C) Solid model
42
43
6. Computational Validation of the Experimental Work
In order to determine how faithfully the results could be used, they were introduced into Abaqus, a
commercial software program for finite element analysis released in 1978, to check if the results
matched. Using the material properties obtained in the experimental work and applying the same load,
the same displacement obtained by the software is meant to be similar, ideally equal, to the one obtained
experimentally.
After the mesh treatment in SolidWorks, the three vertebrae were cut the same way that they were for
the compression test. Meaning, with two parallel surfaces with 9.95 mm, 10.25 mm, 15.68 mm and
11.25 mm height. In figure 6.1, vertebra 2 can be seen as an example (which corresponds to vertebra
C4 on the sheep cervical spine) which was the one cut the highest.
Fig. 6.1 – Vertebra 2 (C4) after cut with 15.68 mm height
This geometry was then imported into Abaqus. When the vertebrae are imported into Abaqus as solid
parts, their surfaces are already subdivided. After error corrections with the help of geometry edit tool,
these divisions were removed using Abaqus’s tool virtual topology for they were not necessary for the
vertebra design and would complicate the generation of the mesh. In figure 6.2, vertebra 2 can be seen
before and after the application of the virtual topology tool.
Fig. 6.2 – Vertebra 2 (C4) before and after the virtual topology tool
44
To simulate the compression test, two analytical rigid parts were created. This surfaces are considered
much more rigid than the rest of the model so that their deformation is negligible. A reference point is
assigned to each plate for a rigid body constrain, that is, every property of the reference point is extended
to the whole part. Analytical rigid part have no computational impact and do not need to be meshed.
[55]
Both plates were introduced into the assembly with the slice of vertebra and interaction properties were
introduced for the contact between them and the vertebra. The bottom plate was encastre as a boundary
condition (on the reference point) and the upper plate was subjected to a force on the Z-axis,
perpendicular to the vertebra, of 1980 N just as in the compression test.
A set was created for the bottom plate for the reaction force and another set for the upper plate for
displacement. The history output was specified for both this variables.
The vertebrae were all modelled as a mechanical elastic and isotropic material. For each geometric
representation of the slice, the mean value of the tests made on that slice was introduced as the Young’s
modulus and the Poisson value used was the same for all of them, 0.3. On table 6.1 the properties for
each vertebra can be seen.
Table 6.1 – Vertebrae materials
Young’s modulus [MPa] Poisson Coefficient
Vertebra 1 (C5) – Slice 1 19
0.3 Vertebra 1 (C5) – Slice 2 18 Vertebra 2 (C4) 23 Vertebra 3 (C3) 26
6.1. Mesh Selection
The finite element method is based on the concept that by connecting several small straight lines a circle
can be obtain; likewise, connecting several simple equations over small domains can approximate a
more complex one over a larger domain.
The set of finite elements is called the finite element mesh and for every finite element there is an
equation that relates physical quantities at certain points, the nodes. Through continuity or equilibrium
of physical quantities, these equations are assembled together.
In general, the differential equation which the solution we are looking for is:
𝑢 ≈W𝑢X𝜓XO
X;<
(9)
The values of 𝑢 at the element nodes are represented by 𝑢X and 𝜓X are the interpolation functions. [56]
45
Geometrically, a simple mesh will be applied to the vertebra before any analysis is done. Abaqus has
several types of elements and in general quadratic give more accurate results than linear, however, they
do not work well on parts with interactions due to pressure contacts. In terms of hexahedral (bricks)
versus tetrahedral elements, the first do not form such robust meshes and so are not adequate for
complex structures, nevertheless, tetrahedral elements have problems with plasticity and bending.
Considering the possibilities, the mesh on these vertebrae was made of four node linear tetrahedron
elements (C3D4) in Abaqus, which are those on figure 6.3. Note that, every adjacent elements share
the degrees of freedom at connecting nodes, making a cohesive part.
Fig. 6.3 – Element type C3D4 used in Abaqus
The following step is to select the refinement of the mesh. A balance needs to be met between how
detailed the mesh is, to give the best results and the CPU power required to give such results. To do
this study, first the vertebrae properties must be applied.
The convergence of the mesh. Ideally, a value would be assigned to the mesh, make an analysis, re-
mesh with smaller elements and remake the same analysis. A specific point on the model would be
chosen, preferably one with high stress value but not a singular one and plot a graphic (Stress – mesh
refinement) with the evolution of the stress at that point. The analysis would be repeated as many times
as necessary until two runs of difference meshes give the same results, meaning, convergence would
have been achieved. The curve would resembled something like figure 6.4. [57]
Fig. 6.4 – Typical curve in mesh Convergence study [57]
46
After a global mesh refinement on the entire part is done, a local mesh refinement can be done. If the
model has a specific area that needs to be carefully evaluated but the rest of the model is quite simple,
it might be useful to apply a simple global mesh and only refine the mesh locally. However, this is not
the case of these models. Since the geometry of the vertebrae is extremely irregular it makes no sense
to use local refinement.
For these models, the mesh control used was seeding. Seeds are markers that are placed along the
edges of a part, the mesh then approximates these seeds. The seeds were positioned uniformly along
the edges with a certain distance between each other. The part was then meshed freely.
The first global seed size used was 3.8, which gives a large mesh, as can be seen in figure 6.5 A). The
analysis was run and stress results can be seen in figure 6.5 B).
Fig. 6.5 – Vertebra 2; A) with mesh made of seeds of global size 3.8; B) After analysis
As it can be seen on figure 6.5 B) the area with higher stress value is the encircled one, it has an irregular
material distribution making it one of the areas with higher stress values. The point chosen for the
convergence analysis was from this area. A cut was made parallel to the Z-axis through the middle of
the vertebra and a node coordinate was chosen from the middle of that area. A query on the elements
around that node was made and the one with the highest stress value was the one considered.
The mesh was remade 13 times until the seeds had a global size of 1 and the process repeated. Finding
the node with the coordinates closest to the first mesh, query the elements around and consider the one
with the highest stress value. The convergence curve was then obtained, on figure 6.6 is represented
for vertebra 2.
47
Fig. 6.6 – Convergence curve for Vertebra 2
As it can be seen from the convergence curve in figure 6.6, the stress slightly rises with the refinement
of the mesh, but not significantly after the 40000 elements. One should always consider the CPU effort,
since having too many elements could become counterproductive. An equilibrium should be found.
For vertebra 2, the fourth point from the right was chosen for the mesh. From this point on, there’s not
a great difference in stress on the selected elements and so it makes no sense to use more CPU power.
The mesh chosen had seeds with global size of 1.8 and the vertebra had 55182 elements.
The same analysis was made for vertebra 1, slice 1 and 2, and for vertebra 3. The coordinates chosen
for analysis were again those of high stress on each vertebra, which do not coincide with the same
location as in vertebra 2. However, it is not important to have them all done at the same coordinates,
not only because they are different models but also because a mesh refinement to a particular area will
not be done, the mesh will be equally refined all along the vertebra. The convergence curves can be
found on figure 6.7.
48
Fig. 6.7 – Convergence curve for Vertebrae 1, slice 1 and 2, and Vertebra 3
As it can be seen, for Vertebra 1, slice 1, when the seeds have a greater global size than 2.2 the stress
values don’t go much higher than 1.82 MPa, so that was the mesh chosen. The stress value in vertebra
1, slice 2, has some irregularities at the beginning, but after, it also stabilizes with seeds with global size
of 2. Vertebra 3, has the most ‘well behaved’ stress values, they only vary from 1.9 to 2.08, and they
rise gradually, which makes it the hardest to define the point where the curve stabilizes is. Analysing the
stress values instead of the curve, it is possible to see a decreasing on the rising of the stress values
from seeds with global size 1.8, with 2.07 MPa, onward. In seeds with 1.6 and 1.4 sizes, stress increases
to 2.08 MPa and then it decreases back to 2.07 MPa, as so, the seed size chosen was 1.6.
The mesh elements for each vertebra are shown in table.
Table 6.2 – Number of mesh elements for each vertebra
Seeds global size Number of elements
Vertebra 1, Slice 1 2.2 23 887
Vertebra 1, Slice 2 2 26 564
Vertebra 2 1.8 55 182
Vertebra 3 1.6 46 699
49
6.2. Displacement Analysis
Each vertebra has a bigger displacement on a specific area, due to having less material on that area or
not having it perpendicular to the compression plates. Figure 6.8 shows the different vertebrae and their
displacements with their respective meshes.
Fig. 6.8 – Displacement on: A) Vertebra 1 slice 1; B) Vertebra 1 Slice 2; C) Vertebra 2; D) Vertebra 3
In order to compare values to the experimental work, the plate displacement was used instead of the
vertebra displacement. This way, the general displacement of the whole vertebra was considered, just
like in the experimental work.
In Abaqus, a graph was plotted with the reaction force from the lower plate VS the displacement of the
upper plate and the results were exported into a text file and then into Excel. A trend line and its equation
were also added to the graph, as it can be seen in figure 6.9.
50
Fig. 6.9 – Graph reaction force – displacement for vertebra 1 slice 1, taken from Abaqus
This displacement value is lower than what was found on the experimental work. Ignoring the pre-test,
like it was done on chapter 4, in Results, the same curve force-displacement was made for one of the
experimental tests in vertebra 1 slice one. On figure 6.10, the latter curve can be seen added to the
same graph.
Fig. 6.10 – Force-Displacement graph, comparison between Abaqus results and experimental work with its trend lines and respective equations
51
This result disparity may be attributable to the material properties selection. In Abaqus it was chosen to
model the vertebrae as mechanical elastic and isotropic materials when in reality vertebrae are more
complex than that. As an alternative, it would be an option to model the bone considering it a
homogeneous material with anisotropy and porosity.
Another possibility is the fact that the experimental Young’s modulus was calculated ignoring the values
before reaching 1 000 N. A way to counter this would be to introduce in Abaqus several different Young’s
modulus following the trend of the experimental curve. A practical option would be to formulate the
model with a hyperelastic material in which it is given the nominal stress and strain from the experimental
work starting at strain zero. This implicates some changes is the model such as changing to hybrid
elements.
The other thing that is a variable in the Abaqus model, is the Poisson’s ratio, which quantifies how much
does the material expand in the two directions when it is being compressed in a third direction and it is
given by equation (10):
𝜈 = −𝜖U𝜀\= −
𝜖]𝜀\
(10)
The Poisson’s ratio for an isotropic, linear elastic material may vary between −1 < 𝜈 < 0.5, being 0.5
the value of a perfectly incompressible material. In this case, it was varied from 0.3, the value at which
the mesh convergence analysis took place, to 0.25, 0.2 and 0.15. The displacement gradually increased,
having its final value closer to the experimental work, however still not the same. Lowering the Poisson’s
ratio even more would not be realistic, simply because 0.3 is the estimated value for the cortical bone
and 0.2 is the estimated value for the trabecular bone and our result should be somewhere in the middle
of those values. The evolution can be seen on figure 6.11.
Fig. 6.11 – Force-displacement evolution with the change of the Poisson’s ration
52
The same analysis was done for vertebra 1 slice 2, vertebra 2 and vertebra 3 and can be found in figure
6.12, 6.13 and 6.14 respectively.
Fig. 6.12 - The Poisson’s ratio study and its comparison to one of the experimental tests for vertebra 1 slice 2
Notice how, once again, the displacement value is still lower in the Abaqus theoretical model than on
the experimental result.
Fig. 6.13 – The Poisson’ ratio study and its comparison to one of the experimental tests for vertebra 2
53
Vertebra 2 was the only one where the displacement of the experimental work is lower than in the
Abaqus model.
Fig. 6.14 - The Poisson’ ratio study and its comparison to one of the experimental tests for vertebra 3
Vertebra 3 has almost the same graph as vertebra 1 slice 1. Also, they are very similar to vertebra 1
slice 2.
In terms of qualitative evolution with the change of Poisson’s ratio, all four vertebrae show the same
evolution, however, vertebra 2 shows significantly higher displacements on the Abaqus model which
might be attributable to being considerably higher than the others.
Maintaining the 0.3 Poisson’s ratio, each vertebra was analysed with the average Young’s modulus of
the entire experimental work, 22.2 MPa. The displacement obtained for each vertebra is in figure 6.15.
For vertebra 1, both slice 1 and 2, the stiffness slightly increased for the Young’s modulus was also
higher than the one used before.
54
Fig. 6.15 – Force-displacement of the four vertebrae with a Young’s modulus of 22.2 MPa
55
7. Finite Element Analysis
Many finite element models have been made on every functioning spine unit of the human vertebral
column, meaning every segment composed of at least two vertebrae and their respective discs.
However, a lot of them have simplified models such as a quarter of a vertebrae and discs or half a
vertebrae or a regular shape based on the symmetry on the sagittal plane. [10]
In a real human spine, irregularities are present in all the vertebrae and discs, and scientist are now
concerned on how this irregularities would affect its biomechanical behaviour. In the model used on this
thesis, since the geometry is based on the CT scan of an individual, it was tried to be kept as faithful as
possible to its original form, meaning the irregularities of the human vertebra are not ignored.
After the solid creation in chapter 4, the files for both vertebrae L4 and L5 from the human model as well
as the discs for levels L3-L4, L4-L5 and L5-S1 were imported into Abaqus. The same way as in the
vertebrae from the sheep model, several errors had to be corrected with the help of geometry edit tool
from Abaqus. The next step, was to apply the Virtual Topology tool to clean up the unnecessary lines
that would complicate the mesh at the expense of loss of some precision, just like on the sheep model.
7.1. Model Parameters
7.1.1. Materials and Initial Conditions
For the finite element analysis materials must be defined and sections assigned to which component
of the model.
To approximate the materials of the discs, a partition had to be made with an ellipse shape and
approximately 30% of the total cross sectional area of the disc [42] [58]. The interior was modelled with
material properties characteristics of the nucleus pulposus while the rest of the disc, representing the
annulus fibrosus with other material properties. The separation of cortical from the trabecular bone was
made through the mesh on the outer layer on each of the vertebrae. On table 7.1, the material properties
are specified.
Table 7.1 – Material properties [10]
Young’s modulus [MPa] Poisson’s ratio
Cortical Bone 12 000 0.3 Trabecular Bone 100 0.2 Nucleus Pulposus 1 0.4999 Annulus Fibrosus 4.2 0.45
56
Note that all of these materials were considered linear elastic as well as isotropic. On figure 7.1, the
properties separation on each component can be seen.
Fig. 7.1 – On the left, discs with partitions (disc L5-S1 on the back, L4-L5 on the centre and L3-L4 on the front); on the right the vertebrae with the materials separated on the outer layer
Also, other partitions had to be made on each component in order to apply interactions later on the
assembly to link the parts together. Tie constrains were used between each vertebra and their respective
disc, which allow to fuse together two regions even with different meshes, allowing the two surfaces to
move together. Another interaction was defined between the vertebral facets as a contact interaction,
so that they would have a tangential motion.
Finally, two reference points were defined and associated to the upper surface of disc L3-L4 and the
lower surface of disc L5-S1 as coupling constrains, which allows the transfer of motion from the points
to the whole surfaces. These reference points allow for the application of loads or displacements in an
easier manner. The reference point associated with disc L5-S1 will be encastre during all analysis.
7.1.2. Mesh Selection
For the mesh selection, the same method applied for the sheep model was used: the convergence
method. First, the convergence study was made for the vertebrae since they were limited in terms of
elements number due to the program application for the material properties separation. A mesh with a
global seed size of 2 was given to every disc and the analysis for the vertebrae took place. On figure
7.2, both convergence curves can be seen.
57
Fig. 7.2 – Vertebrae L4 and L5 mesh convergence study
Both vertebrae have clear points where the stress values stabilize. These are the number of mesh
elements chosen of each one of the vertebrae.
For the disc, the analysis should be slightly different. Since the annulus and nucleus have such different
properties, when subjected to a load, they will have very different reactions, so instead of choosing just
one point for the stress concentration to be analysed, two points will be chosen: one at the annulus and
the other at the nucleus, both of them with high stress values. Also note that, although the nucleus has
a Poisson’s ratio of a nearly incompressible material, it will still be modelled with linear tetrahedral
elements.
The convergence curve for both the nucleus pulposus and the annulus fibrosus for the three disc are in
figure 7.3.
58
Fig. 7.3 – Mesh convergence study for nucleus pulposus (NP), axis on the left, and the annulus fibrosus (AF), axis on the right, for the three discs L3-L4, L4-L5 and L5-S1
For disc L3-L4 both curves are difficult to analyse on this graph, their stress values don’t vary quite so
much, however, there is a difference in the curve slope, for a more horizontal slope, after seeds with
global size 2, so that is the chosen mesh. Disc L4-L5 is an easy choice, for both curves show a complete
change in behaviour after the same point, 8 777 is the number of elements. On disc L5-S1, the curves
change the curve slope at a different point, however, the curve associated with the annulus fibrosus
never really stabilizes, it continues with a slight slope, and so, the mesh choice was made on the curve
of the nucleus pulposus.
Table 7.2 – Number of mesh elements for each component of the human model
Number of elements
Vertebra L4 48 246
Vertebra L5 57 217
Disc L3-L4 12 869
Disc L4-L5 8 777
Disc L5-S1 6 115
In order to verify these meshes and validate the model, the value of the intradiscal pressure at the
second level, meaning, in this case, in disc L4-L5, was compared with previous studies when under the
axial compressive forces of 300 N, 460 N and 600 N. [10]
59
Fig. 7.4 – Comparison of calculated results with previous studies, image adapted from Kuo et al. [10]
Note that, the calculated values are rather similar to those calculated on Kuo et al. [10], which is the
article from which the material properties were taken. However, both these values appear to be lower
than the other studies but not so low as to invalidate the model. On figure 7.5 the stress distribution can
be seen for the entire model and for disc L4-L5 individually when subjected to a load of 460 N.
Fig. 7.5 – Stress distribution on the entire model, on the left, and on the L4-L5 disc, on the right for a 460 N load
7.2. Range of motion
Like it was said in chapter 2.4, there are three basic spinal movements: flexion/extension, lateral bending
and axial rotation. Although on daily basis the human being frequently uses a combination of the three,
it is interesting to analyse how the spine segment responds under pure moments in each axis. The
responses will be analyse in range of motion, ROM, and intradiscal pressure. In figure 7.6, 7.7 and 7.8
the flexion/extension, lateral bending and axial rotation movements respectively are represented.
60
Fig. 7.6 – Flexion and extension spine movement when subjected to a ± 5 Nm moment on the X-axis
Fig. 7.7 – Lateral Bending movement of the spine when subjected to a ± 5 Nm moment on the Y-axis
Fig. 7.8 – Rotational movement of the spine when subjected to a ± 5 Nm moment on the Z-axis
61
The range of motion values, in degrees, for the L4/L5 lumbar spine segment when subjected to a ± 5 Nm
pure moment in each of the principle axis are summarized in table 7.3.
Table 7.3 – Values of Range of Motion and reaction force of the spine segment when subjected to a ± 5 Nm moment on each axis
Range of Motion (Degrees)
Flexion 13.25
Extension 16.79
Lateral Bending Left 8.28
Right 8.65
Axial Rotation Left 2.80
Right 2.80
The motion corresponds to the sum of movement of the entire segment, being the intervertebral discs
the parts that most deform to allow distortion. As it can be seen in table 7.3, the axial rotation is
significantly lower than the other spine movements, but it is typical of the lumbar spine to have restricted
motion in turn of the Z-axis, as it was explain in chapter 2.4.
On Wilke et al. [33], a study of ROM in the three movements for pure moments of ± 7.5 Nm was made
for in vitro segments of the lumbar spine and provides a good base for comparison. The ROM values
obtained for both extension/flexion and lateral bending, left and right, were significantly higher in this
computational model than in Wilke et al. [33] experimental work. On the other hand, the axial rotation is
within the same range.
In figure 7.9, the stress distribution in disc L4-L5 can be seen for each of these loads. Note that, the
scale of the stress distribution in lateral bending, the centre figure, is different from the others, for the
stresses were, in general, lower. Also note how the different properties from the nucleus and the annulus
are very noticeable, particularly in lateral bending and axial rotation.
Fig. 7.9 – Stress distribution in disc L4-L5; on the left, in extension; on the centre, in lateral bending; on the right, in axial rotation
Both stress values in extension and rotation are lower than those found in Kuo et al. [10] and in
Rohlmann et al. [50], that were around 0.4 MPa and 0.3 MPa respectively for extension and rotation.
Qualitatively, the stress distribution matches the literature. The intradiscal pressure for extension and
flexion has the highest values, closely followed by axial rotation and finally, lateral bending with lower
values.
62
Even though the range of motion appears to be fairly high for the applied moment, the stress distribution
in the disc, which is a major factor in every computational model for spine study, appears to be a little
lower than in the literature.
The stress distribution in the vertebrae is also consistent with the literature. In Kuo et al. [10] the stress
values presented for the stress distribution in the vertebrae agree with this computational model,
reaching only around 3 MPa on the vertebral body, particularly on the lower one, L5, and much higher
values on the facet joints. These higher values in the facet joints can be explained due to the contact
between them when the segment is subjected to motion.
On figure 7.10 the stress distribution due to a pure moment of ± 5 Nm on each axis. Note how the stress
is concentrate on the front of the vertebral body in extension, while it is concentrated laterally in lateral
bending and in axial rotation, the stress is equally distributed all around the vertebral body.
Fig. 7.10 – Stress distribution in the spine segment L4/L5 when subjected to a pure moment of ± 5 Nm on each axis; on the left, in extension; on the right, in lateral bending; on the bottom, two views of axial rotation
63
7.3. Sensibility analysis
Although it is clear that the nucleus pulposus and the annulus fibrosus have different properties, some
discussion still persist on exactly which are they. Also, the fact that the range of motion in chapter 7.1 is
higher than what is found in the literature might also suggest that some adjustment is required.
Therefore, a sensibility analysis as to how the material properties of the nucleus pulposus influence the
model was made. The properties of all discs were altered and the range of motion of extension, right
lateral bending and right axial rotation were evaluated.
The nucleus’ Young’s modulus was varied from 1 MPa, its original value, to 4 MPa, approaching the
annulus Young’s modulus of 4.2 MPa. The variation can be seen in figure 7.11.
Fig. 7.11 – Range of Motion evolution with the alteration of nucleus pulposus’ Young’s modulus
As it can be seen, the computational model shows a great variation of range of motion, particularly in
extension when the nucleus’ Young’s modulus is varied. In table 7.4, the range of motion for a Young’s
modulus of 4 MPa is shown.
Table 7.4 - Values of Range of Motion of the spine segment when subjected to a ± 5 Nm moment on each axis when the nucleus have a Young’s modulus of 4 MPa
Range of Motion (Degrees)
Flexion 7.89
Extension 7.96
Lateral Bending Left 5.16
Right 5.90
Axial Rotation Left 0.30
Right 0.30
64
The ROM decreased considerably with the increase of the Young’s modulus, particularly the ROM for
extension. For both extension and lateral bending, the ROM obtained was within the range of the values
obtained in Wilke et al. [33] but on the higher end and, given that the applied moment was lower in the
computational model, it would have been expected that the ROM would have also been lower. Once
more, the axial rotation has a significantly lower range of motion.
In figure 7.12, the stress distribution on the discs also for a nucleus with a Young’s modulus of 4 MPa.
Fig. 7.12 – Stress distribution in disc L4-L5 for discs with a nucleus’ Young’s modulus of 4 MPa; on the left, in extension; on the centre, in lateral bending; on the right, in axial rotation
Once again, the scale in the lateral bending is different from the other two disc for the stress distribution
is lower. Notice how the difference between nucleus pulposus and annulus fibrosus is not perceptible
anymore. The stress values are still the same magnitude but higher, even higher than what was referred
in Kuo et al. [10].
65
8. Discussion
8.1. Experimental Work
The experimental work of this thesis aimed at assembling the laboratory for mechanical testing of
biological material as well as developing and implementing a method for quantifying the stiffness of a
whole vertebra.
So that compression tests could begin, the vertebrae had to be clean of all soft tissue, separated
individually and cut with parallel surfaces. The preservation of the discs was also a prime concern for
future work and extra care had to be taken during the separation of each vertebra for that reason.
The first challenge appeared at this time, for there were no means of cutting the vertebrae ensuring the
parallelism of their surfaces. To compensate the possible unevenness of the surfaces of the vertebra,
as well as to secure the vertebra in place during the compression test, bone cement could be used.
However, bone cement, no matter how thin the layer might be, still has its own mechanical properties
and would, therefore, influence the compression test, and introduce errors in the stiffness measurements
of the bone.
It was decided not to use any bone cement. Sanding the vertebrae were the best option giving the
material that we had access to. Also, as no moments or extension was to be applied to the bone,
securing the vertebra in place for the compression test would not be a problem as long as the surfaces
would be parallel to each other.
The experimental procedure was based on Buckley et al. [48]. A pre-test was used to accommodate the
vertebra to the compression plates and the compression test was taken until 1 980 N. INSTRON saves
the load applied as well as the displacement of the grip.
Preferentially, the displacement would have been measured in the vertebra itself, with an extensometer
for their errors are extremely small. However, several extensometers would be needed and would rise
the problem of securing them around the vertebra. Also, on the laboratory, two load cells exist, one of
200 N, the other of 2 000 N. Although the error of a load cell increases with its load capacity however,
with a limit 200 N it was not possible to do the experimental testing and the one of 2 000 N had to be
used. Other errors that might also be present in the test concern the precision and accuracy of the
INSTRON machine as well as software calibration errors. Even when all added up, all these errors are
still a small percentage. Nevertheless their existence should be kept in mind.
The experimental results can be found on table 4.1. Unfortunately, only three articles were found with
similar studies, meaning analysing the vertebra not separating the cortical from the trabecular bone and
all of them were made for human specimen. They can be found in reference [48], [49] and [59], including
the one in which the experimental work was based on.
66
Looking at the results in table 4.1 just by themselves, which give an average of E = 22.2 MPa and a
variance of 8.15 MPa, they seem extremely low values for bone elastic modulus comparing to cortical
and trabecular Young’s modulus of 100 MPa and 12 000 MPa from Kuo et al. [10]. In Masri et al. [59],
a small block of 12 X 10 X 3 mm was subjected to a compression test; the average of the obtained
results was 374 MPa which is much higher than the results on this thesis and closer to the values of the
cortical and trabecular bone individually. Nevertheless, the fact that only such a small block is used
poses the question if the results are reliable, for the natural proportion of cortical bone to trabecular bone
might not be respected.
In both the other studies, Buckley et al. [48] and Kopperdahl et al. [49], the stiffness values are only
presented in kN/mm. The area of the vertebra is never calculated. For comparing with this results, the
graph to analyse is the one taken directly from the compression test, force-displacement. All the graphs
of the vertebrae tested on this thesis and the equations of their trend lines can be found in the appendix.
In Buckley et al. [48], most vertebrae tested present a stiffness between 2 kN/mm and 5 kN/mm and
some may reach 10 kN/mm. On Kopperdahl et al. [49], the vertebrae were taken to their ultimate force,
whose average value is 5.67 kN and the average structural stiffness calculated was 15.4 kN/mm. Which
are, in both articles, also higher than our test results, which vary from 1.3 kN/mm to 1.8 kN/mm.
Note that on both these articles a relatively thick layer, around 1 mm, of bone cement was used whilst
on this thesis, no bone cement was used.
Several articles can be found on morphological and range of motion comparison between sheep spine
and human spine however, none can be found comparing stiffness. As so, the lower values might be
due the fact that the specimens used are derived from a sheep spine while on the other studies are from
human specimens.
It would also have been interesting to do a sixth compression test on each vertebra, to take them to their
ultimate force, however, on the laboratory, a 2 000 N load cell was the highest and as said in Kopperdahl
et al. [49], higher loads were necessary for failure.
8.2. Computational Model and Finite Element Analysis
A computational model allows to simulate any scenario and obtain very realistic responses.
Nevertheless, there are limitations to the computational simulation. It is only as good as the inserted
properties, as well as how geometrically accurate it is.
Both CT images series obtain for this thesis, had a small distance in between slices, particularly in the
sheep spine series, there were 405 images only for the cervical segment. This meant that, even though
after the segmentation process the staircase effect was noticeable, it wasn’t excessive. If the staircase
effect were much greater, an oversampling would have been necessary. A program such as MeVisLab
could have been used in order to do it. Taking into account the proximity of the CT slices, adding an
intermediate process, would possibly slightly alter the features of the spine and, as a consequence, be
counterproductive.
67
The segmentation process requires a great deal of anatomy knowledge from the user. Deciding where
to place the deformable models and how large to make them depends on the user’s experience. The
automatic segmentation can vary its performance greatly with this deformable models, but unfortunately,
there is no algorithm to set them, it only depends on the sensibility of the user. But even for an
experienced user, automatic segmentation isn’t enough, and the manual segmentation is always
necessary particularly on the edges of the ROI, where it was not possible to exclude other vertebral
structures; the anatomy knowledge is needed to differentiate what is what.
Although the CT images are fairly good for separating bone from the rest, discs are almost not visible
on them. The user not only needs to be able to understand what he sees in the images but also what
he does not see and do a manual segmentation on it. If carefully done and apart from the scaled effect,
the segmentation process can give a great representation of what is on the CT scan, but there is margin
for a great amount of errors in the process.
The stl files were then exported from itk-SNAP to SolidWorks for mesh treatment. The simplification and
smoothing process of the mesh leads to a volume reduction of the part being treated. If not done with
moderation, these processes can lead to a great alteration of the shape of the structure. In the human
model, another problem might exist. Since all these adjustments are made on each structure individually,
some alterations may have occur on the surfaces that will interact with other parts, as a consequence,
when putting the parts together and applying the interactions some problems may come up. All of these
was taken into account when applying the Mesh Wizard, however, in order to cancel the scaled effect
from the segmentation process, some volume reduction had to take place.
The mesh elements selection for the finite element analysis was made in chapter 6.1 and can also
introduce some errors in the model. The virtual topology allows to combine several faces into one, and
it is useful for the mesh to freely adapt to the part without having to adjust to the details of each surface.
In other words, applying the virtual topology will allow a more uniform mesh but it won’t reflect such a
detailed geometry.
The tetrahedron elements are more appropriate for complex structures and for models where there are
interactions between parts (which is the case of the human model) but they are elements of constant
stress. In order for these elements to give a suitable response in a stress analysis, the mesh refinement
should be carefully selected. On the human model, there is also the problem of the nucleus pulposus
having a 0.4999 Poisson’s ratio, which is of a nearly incompressible material. This poses the question
if for the nucleus pulposus other elements should be used.
For selecting the mesh refinement to avoid problems in stress analysis, a mesh convergence was held
for both models (chapter 6.1 for the sheep spine and 7.1.2 for the human model). The convergence of
the mesh should be done on the point with the higher stress value. If another point was used, one with
an average stress value for example, the mesh convergence could change and another mesh could
have been chosen.
In chapter 6.2, a displacement analysis was done in Abaqus on the sheep vertebrae with the properties
calculated on the experimental work. In graph 6.10, linear trend lines and their equations are presented
68
from both Abaqus results and one of the experimental tests for vertebra 1 slice 1. As it can be seen, the
stiffness of the vertebra is higher on the Abaqus model, around 2 kN/mm, which is closer to the values
mentioned before.
This two displacement curves probably don’t coincide due to the fact that the experimental Young’s
modulus was calculated based on values from 1 000 N and higher instead of based on the entire
experimental curve. A solution could have been to use a hyperelastic material in Abaqus and introducing
the stress and strain of the complete test as data instead of the Young’s modulus. However this would
require several alterations in the model, such as the change in the type of elements used and the step
used.
The Poisson’s ratio used for the sheep vertebrae was 0.3, the same as cortical bone. Since the
computational model was based on the experimental work, there was no particular value for the
Poisson’s ratio, and so it was lowered as to approximate the computational result to the experimental.
The Poisson’s ratio was lowered as far as 1.5 and, except for vertebra 2, it still did not reach the
displacement values in the experimental work. The choice of these values relates with the usual values
of the bone’s Poisson’s ratio, 0.3 for cortical bone and 0.2 for trabecular bone. It would be expected a
Poisson’s ratio for the whole vertebra somewhere in between those numbers.
For the human model, after mesh selection, some validation was necessary. In figure 7.4, several
studies taken from literature can be found relating intradiscal pressure with a compressive load. Just
like in Kuo et al. [10], it was applied 300 N, 460 N and 600 N on the Z-axis. Although on the bottom of
the graph, all three values approximate the literature.
A range of motion study, in degrees, was next. A pure moment of ± 5 Nm was applied on each axis in
order to obtain the positive and the negative of each of the three basic movements: extension/flexion,
lateral bending and axial rotation. All results were quite elevated and, compared to Wilke et al. [33], in
extension/flexion, almost doubled what would have been expected. On the other hand, the stress
distribution in the discs is lower than expected. According to the values from Kuo et al. [10], they should
be around 0.3-0.4 MPa and in this model the stress values can be found between 0.1-0.2 MPa.
The fact that nucleus and annulus were modelled with such different properties is very evident in the
stress distribution. Although clearly they have very distinct properties, as it was perceptible at the
laboratory even with no testing, there is still some discussion on this subject. Some computational
models are done with a higher Young’s modulus for the nucleus and so a sensibility analysis was made
for the nucleus’ Young’s modulus. The ROM was drastically reduced for extension, and moderately
reduced for both the other movements.
When it comes to stress analysis of the entire L4/L5 segment, it should be mention that some high stress
values that were found on the facet joints in every analysis. These peaks have to do with the contact
between surfaces not being as smooth as it should, it is probably related with the geometry alterations
done in SolidWorks. The interaction choice between facets was surface to surface with small sliding.
69
Other interactions could have been chosen, such as node to surface, but it would allow some penetration
of the mesh into the other surface causing even more peak stresses.
Another alteration that could have been made in the computational model for the human spine is the
mesh elements. Some mesh elements such as hybrid elements or a more rigid element than a four node
tetrahedral (C3D4) element could have been more appropriate solution for the nucleus pulposus and
might have provide a better solution in terms of ROM.
70
71
9. Conclusion and Future Work
In this thesis, an experimental method for calculating the equivalent Young’s modulus for the entire
vertebra was developed. The method was based on Buckley et al. [48] and the obtained results
compared with that same study and two others.
The experimental work was carried out on sheep spine thanks to Evora’s Veterinary Hospital. It
consisted of a simple compression test of slices of vertebrae until a maximum load of 1 980 N. Although
the testing handed the necessary data for obtaining the results, it would have been interesting to take
the vertebrae to their ultimate force. For that a higher load cell is required for the laboratory.
Alongside with the experimental work, a computational model based on a CT scan also of a sheep spine
was analysed under the same conditions in order to compare results with the experimental work.
In the human model, a functional spinal unit constituted of two vertebrae and three discs was studied.
The segments range of motion as well as the discs stress distribution were studied and compared to
literature. A sensibility analysis to the properties of the nucleus was also done.
It would have been interesting to perform the same analysis on the entire lumbar segment, from L1 to
S1. Also, one could implement the forces due to the ligaments in the spine. These can be modelled as
springs with a certain rigidity, a sensibility analysis for these properties can also be done.
The L4/L5 segment of the spine is one which has a lot of problems. As so, as it was described in chapter
3, there are also several existing surgical options to deal with those problems and several more that are
just being developed. Analysing medical devices, such as their impact in stress distribution and range
of motion is very important and something that can always be done.
On the same note, for the experimental work, since the INSTRON machine at the laboratory is
compression/extension only, an experimental set-up could be developed to apply eccentric loads. This
way, range of motion of a segment could be studied due to the application of an eccentric load. Also, if
possible, the testing of medical devices on spines.
72
73
10. Bibliography
[1] “http://www.spineuniverse.com/,” [Online]. [Accessed January 2014].
[2] “http://www.spine-health.com/,” [Online]. [Accessed January 2014].
[3] “http://www.nhs.uk/,” [Online]. [Accessed January 2014].
[4] “http://www.webmd.com/,” [Online]. [Accessed January 2014].
[5] Boos and Webb, “Pedicle screw fixation in spinal disorders: a European view,” vol. 6, pp. 2-18,
1997.
[6] Chen et al., “Stress analysis of the disc adjacent to interbody fusion in lumbar spine,” Medical Engineering & Physics, vol. 23, pp. 483-491, 2001.
[7] Rohlmann et al., “Comparison of the effects of bilateral posterior dynamic and rigid fixation devices
on the loads in the lumbar spine: a finite element analysis,” Eur Spine, 2007.
[8] H. Li, “An approach to lumbar vertebra biomechanical analysis using the finite element modeling
based on CT images”.
[9] Zhang and Merkle, “A high-fidelity model for lumbar spine injury investigation during under body
blast loading”.
[10] Kuo et al., “Biomechanical analysis of the lumbar spine on facet joint force and intradiscal pressure
- a finite element study,” BMC Musculoskeletal Disorders, vol. 11, 2010.
[11] Sheng et al., “Anatomy of large animal spines and its comparison to the human spine: a systematic
review,” Eur Spine J, 2010.
[12] Kettler et al., “Are the spines of calf, pig and sheep suitable models for pre-clinical implant tests?,”
Eur Spine J, vol. 16, pp. 2186-2192, 2007.
[13] Wilke et al., “Biomechanical in vitro evaluation of the complete porcine spine in comparison with
data of the human spine,” Eur Spine J, 2011.
[14] Wilke et al., “Load-displacement properties of the thoracolumbar calf spine: experimental results
and comparison to known human data,” Eur Spine J, 1997.
[15] Wilke et al., “Biomechanical comparison of calf and human spines,” Journal of Orthopaedic Research, 1996.
74
[16] Schmidt et al., “Limitations of the cervical porcine spine in evaluating spinal implants in comparison
with human cervical spinal segments,” SPINE, 2005.
[17] Kandziora et al., “Comparison between sheep and human cervical spines,” SPINE, vol. 26, pp.
1028-1037, 2001.
[18] “http://www.innerbody.com/,” [Online]. [Accessed February 2014].
[19] “http://www.mayfieldclinic.com/,” [Online]. [Accessed February 2014].
[20] H. Gray, Anatomy of the human body, 1918.
[21] “http://www.knowyourback.org/,” [Online]. [Accessed February 2014].
[22] P. Tate, Seeley's Principles of anatomy & physiology, McGraw Hill, 2009.
[23] M. Kurutz, “Finite element modeling of the human lumbar spine”.
[24] Urban and Roberts, “Degeneration of the intervertebral disc,” Arthritis Research & Therapy, 2003.
[25] Silvestre et al., “Morfologia dos discos intervertebrais e abordagem clínica das discopatias: uma
revisão bibliográfica”.
[26] White and Panjabi, Clinical Biomechanics of the Spine, J. B Lippincott, 1978.
[27] Banton et al., “Biomechanics of the spine,” Journal of the Spinal Research Foundation, vol. 7, pp.
12-20, 2012.
[28] Antoniou et al., “The human lumbar intervertebral disc,” 1996.
[29] “http://physioworks.com.au/,” [Online]. [Accessed February 2014].
[30] “http://www.cedars-sinai.edu/,” [Online]. [Accessed February 2014].
[31] Cappuccino et al., “Biomechanical analysis and review of lateral lumbar fusion consruct,” Spine, vol. 35, pp. S361-S367, 2010.
[32] Zhong et al., “Finite element analysis of the lumbar spine with a new cage using a topology
optimization method,” Medical Engineering & Physics, 2006.
[33] Wilke et al., “Biomechanical evaluation of a new total posterior-element replacement system,”
Spine, 2006.
[34] Denozière and Ku, “Biomechanical comparison between fusion of two vertebrae and implantation
of an artificial intervertebral disc,” Journal of biomechanics, vol. 39, pp. 766-775, 2004.
75
[35] Burkus et al., “Surgical Interbody Research Group - radiographic assessment of interbody fusion
devices: fusion criteria for anterior lumbar interbody fusion,” Neurosurg Focus, vol. 10, pp. 1-9,
2001.
[36] Shin et al., “Biomechanical study of lumbar spine with dynamic stabilization device using finite
element method,” 2007.
[37] Kumar et al., “Correlation between sagittal plane changes and adjacent segment degeneration
following lumbar spine fusion,” Eur Spine J, vol. 10, pp. 314-319, 2001.
[38] T. S. Madhu, “Posterior and anterior lumbar interbody fusion,” Current Orthopaedics, vol. 22, pp.
406-413, 2008.
[39] P. C. McAfee, “Current concepts review - Interbody fusion cages in reconstructive operations on
the spine,” The Journal of Bone & Joint Surgery, vol. 81, pp. 859-880, 1999.
[40] B. W. Cunningham, “Basic scientific considerations in total disc athroplasty,” The Spine Journal, vol. 4, pp. 219S-230S, 2004.
[41] Galbusera et al., “Rigid and flexibel spinal stabilization devices: A biomechanical comparison,”
Medical Engineering & Physics, vol. 33, pp. 490-496, 2011.
[42] Schmidt et al., “Response analysis of the lumbar spine during regular daily activities - A finite
element analysis,” Journal of Biomechanics, 2010.
[43] Wilke et al., “Anatomy of the Sheep Spine and Its Comparison to the Human Spine,” The Anatomical Record, 1997.
[44] Alini et al., “Are animal models useful for studying human disc disorders/degeneration?,” Eur Spine J, vol. 17, pp. 2-19, 2008.
[45] McLain et al., “Comparative morphometry of L4 vertebrae,” Spine, vol. 27, pp. E200-E206, 2002.
[46] Wilke et al., “Are sheep a valid biomechanical model for human spines?,” Spine, 1997.
[47] “https://pt.vwr.com/app/Home,” [Online]. [Accessed November 2014].
[48] Buckley et al., “An improved metric for quantifying the stiffnesses of intact human vertebrae,” vol.
223, pp. 537-543, 2009.
[49] Kopperdahl et al., “Biomechanical Consequences of an Isolated Overload on the Human Vertebral
Body,” Journal of Orthopaedic Research, vol. 18, pp. 685-690, 2000.
[50] Rohlmann et al., “Realistic loading coditions for upper body bending,” Journal of Biomechanics, 2009.
76
[51] “http://netforum.healthcare.philips.com/,” [Online]. [Accessed January 2014].
[52] “http://www.fda.gov/,” [Online]. [Accessed March 2014].
[53] A. Webb, Introduction to Biomedical Imaging, 2003.
[54] Yushkevich et al., Anatomical structures with ITK-snap.
[55] “http://www.tu-chemnitz.de/projekt/abq_hilfe/docs/v6.12/,” Abaqus Simulia. [Online]. [Accessed
April 2014].
[56] J. N. Reddy, “An Introduction to the Finite Element Method,” McGraw-Hill, 1993.
[57] “http://www.nafems.org/join/resources/knowledgebase/001/,” [Online]. [Accessed April 2014].
[58] Meakin et al., “Replacing the nucleus pulposus of the intervertebral disc,” Clinical Biomechanics, vol. 16, pp. 560-565, 2001.
[59] Masri et al., “Apparent Young's modulus of vertebral cortico-cancellous bone specimens,”
Computer Methods in Biomechanics and Biomedical Engineering, vol. 15, pp. 23-28, 2012.
77
11. Appendix – Results from the Experimental Work
11.1. Force-Displacement Experimental Results
Vertebra 1 Slice 1
Fig. 11.1 – Force-Displacement graph for vertebra 1 slice 1
Trend lines equations:
Test 1: y = 1698.1x - 153.04 Test 2: y = 1770.9x – 136.12
Test 3: y = 1789.8x – 135.87 Test 4: y = 1791.0x – 136.76
Test 5: y = 1788.0x – 137.25
78
Vertebra 1 Slice 2:
Fig. 11.2 - Force-Displacement graph for vertebra 1 slice 2
Trend line equations:
Test 1: y = 1485.6x – 163.16 Test 2: y = 1539.6x – 171.3
Test 3: y = 1547.8x – 173.06 Test 4: y = 1547.8x – 173.99
Vertebra 2:
Fig. 11.3 - Force-Displacement graph for vertebra 2
Trend line equations:
Test 1: y = 1387.1x – 164.66 Test 2: y = 1412.5x – 130.08
Test 3: y = 1466.3x – 105.84 Test 4: y = 1475.8 – 106.82
Test 5: y = 1387.1x – 164.66
79
Vertebra 3:
Fig. 11.4 - Force-Displacement graph for vertebra 3
Trend lines equations:
Test 1: y = 1718.2x – 92.404 Test 2: y = 1744.7x – 84.928
Test 3: y = 1745.2x – 87.741 Test 4: y = 1744.6x – 86.002
Test 5: y = 1742.5x – 87.003
80
11.2. Stress-Strain Experimental Results
11.2.1. Vertebra 1 Slice 1
Fig. 11.5 - First test for Vertebra 1 slice 1 and its results
Fig. 11.6 - Second test for Vertebra 1 slice 1 and its results
81
Fig. 11.7 – Third test for Vertebra 1 slice 1 and its results
Fig. 11.8 – Fifth test for Vertebra 1 slice 1 and its results
82
11.2.2. Vertebra 1 slice 2
Fig. 11.9 – First test for Vertebra 1 slice 2 and its results
Fig. 11.10 – Second test for Vertebra 1 slice 2 and its results
83
Fig. 11.11 – Third test for Vertebra 1 slice 2 and its results
Fig. 11.12 – Fourth test for Vertebra 1 slice 2 and its results
84
11.2.3. Vertebra 2
Fig. 11.13 – First test for Vertebra 2 and its results
Fig. 11.14 – Second test for Vertebra 2 and its results
85
Fig. 11.15 – Third test for Vertebra 2 and its results
Fig. 11.16 – Fourth test for Vertebra 2 and its results
86
Fig. 11.17 – Fifth test for Vertebra 2 and its results
11.2.4. Vertebra 3
Fig. 11.18 – First test for Vertebra 3 and its results
87
Fig. 11.19 – Second test for Vertebra 3 and its results
Fig. 11.20 – Third test for Vertebra 3 and its results
88
Fig. 11.21 – Fourth test for Vertebra 3 and its results
Fig. 11.22 – Fifth test for Vertebra 3 and its results
