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Finite element modeling of lumbar interbody fusion

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Title:
Finite element modeling of lumbar interbody fusion
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Chatham, Lillian S. ( author )
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Denver, CO
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University of Colorado Denver
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English
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1 electronic file (62 pages). : ;

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Lumbar vertebrae ( lcsh )
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bibliography ( marcgt )
theses ( marcgt )
non-fiction ( marcgt )

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Review:
To help reduce complications following lumbar interbody fusion, such as subsidence, there is a need for patient specific selection of device components. This thesis investigated the effects of age-related changes and the spacer material on the stress and strain in the lumbar spine after interbody fusion with posterior instrumentation. As exploratory addition compared a normal spacer with a custom fit spacer that conformed to the vertical endplates. Finite element models of the L4-L5 unit were developed from computered tomography of two cadaveric lumbar spines. The models were loaded under compression and strain and stress were observed in various locations. The models were validated with experimental testing. In one study, cortical thickness and trabecular bone material properties were altered to simulate age-related changes of cortical thinning and the loss of volumetric trabecular bone mineral density. In both models, stress increased with age at the L4 and L5 anterior bone, and in the posterior rods. One model had a similar correlation at all analyzed locations, while the other model experienced smaller changes at the bone-spacer interfaces and spacer. The stress at the L4 and L5 anterior locations, at a minimum, doubled between the 20 and 90 year old model in both subjects. In the other study, the effects of spacer materials were investigated. The effects of polyethrertherketone, titanium, self-reinforced polyphenylene (STP), and SRP simulated 70 percent porosity were tested. SRP with 70 percent porosity produced a load shift in stress from the spacer to the rods. Though titanium is approximately 25 times stiffer than PEEK, differences in stress levels at all locations were relatively small when the spacer material was changed from titanium to PEEK. However, when a factor of stiffness was reduced by 244 in SRP with70 percent porosity, stress at the bone-spacer interfaces decreased (8-15 percent) in one model. This study demonstrated variation in subject response to different spacer materials, and the changes in stress distributions between human subjects. The custom spacer implant significantly decreased stress at the bone-spacer interfaces. These findings show the effects of age-related changes and spacer materials on the mechanical environment in the bone following lumbar interbody fusion.
Thesis:
Thesis (M.S.)--University of Colorado Denver. Mechanical engineering
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Includes bibliographic references.
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Department of Mechanical Engineering
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by Lillian S. Chatham.

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Full Text
FINITE ELEMENT MODELING OF LUMBAR INTERBODY FUSION
by
LILLIAN S. CHATHAM
B.S., University of Colorado Denver, 2012
A thesis submitted to the
University of Colorado in partial fulfillment
of the requirements of the degree of
Master of Science
Mechanical Engineering Department
2014


This thesis for the Master of Science degree by
Lillian S. Chatham
has been approved for the
Mechanical Engineering Department
by
R. Dana Carpenter, Chair
Christopher M. Yakacki
Ronald A. L. Rorrer
May 2, 2014
11


Chatham, Lillian S. (M.S., Mechanical Engineering)
Finite Element Modeling of Lumbar Interbody Fusion
Thesis directed by Assistant Professor R. Dana Carpenter.
ABSTRACT
To help reduce complications following lumbar interbody fusion, such as subsidence,
there is a need for patient specific selection of device components. This thesis investigated the
effects of age-related changes and the spacer material on the stress and strain in the lumbar spine
after interbody fusion with posterior instrumentation. An exploratory addition compared a normal
spacer with a custom fit spacer that conformed to the vertebral endplates. Finite element models
of the L4-L5 unit were developed from computed tomography of two cadaveric lumbar spines.
The models were loaded under compression and strain and stress were observed in various
locations. The models were validated with experimental testing.
In one study, cortical thickness and trabecular bone material properties were altered to
simulate age-related changes of cortical thinning and the loss of volumetric trabecular bone
mineral density. In both models, stress increased with age at the L4 and L5 anterior bone, and in
the posterior rods. One model had a similar correlation at all analyzed locations, while the other
model experienced smaller changes at the bone-spacer interfaces and spacer. The stress at the L4
and L5 anterior locations, at a minimum, doubled between the 20 and 90 year old model in both
subjects.
In the other study, the effects of spacer material were investigated. The effects of
polyetheretherketone, titanium, self-reinforced polyphenylene (SRP), and SRP simulated 70%
porosity were tested. SRP with 70% porosity produced a load shift in stress from the spacer to the
rods. Though titanium is approximately 25 times stiffer than PEEK, differences in stress levels at


all locations were relatively small when the spacer material was changed from titanium to PEEK.
However, when a factor of stiffness was reduced by 244 in SRP with 70% porosity, stress at the
bone-spacer interfaces decreased (8-15%) in one model. This study demonstrated variation in
subject response to different spacer materials, and the changes in stress distributions between
human subjects. The custom spacer implant significantly decreased stress at the bone-spacer
interfaces. These findings show the effects of age-related changes and spacer material on the
mechanical environment in the bone following lumbar interbody fusion.
The form and content of this abstract are approved. I recommend its publication.
Approved: R. Dana Carpenter
IV


DEDICATION
I dedicate this thesis to all my family and friends who have been an amazing support
throughout this intensive process.
v


ACKNOWLEDGEMENTS
I wish to express my sincerest thanks to my adviser, R. Dana Carpenter, for giving me the
opportunity to research in the area of biomechanics and for his constant guidance. I want to
recognize Dr. Sam Welch and Dr. Ron Rorrer for being constant mentors throughout my
undergraduate and graduate degrees. Craig Lanning and Dr. Vikas Patel should be acknowledged
for getting me started in my research. I also want to thank Dr. Chis Yakacki for being on my
graduate committee along with Dr. Carpenter and Dr. Rorrer. I am sincerely grateful for being
selected as a National Science Foundation GK-12 Fellow. It has provided a financial support in
my last year, and I have become a better presenter of my research and learned a lot in the process.
The Tashiro Tutoring Scholarship was another financial support that deserves mentioning. There
are plenty of people that have made an impact on my education and even if they are not directly
named here, I thank all of them.
vi


TABLE OF CONTENTS
CHAPTER
I. INTRODUCTION................................................................1
Purpose......................................................................1
Outline......................................................................5
II. MODEL DEVELOPMENT OF AN L4-L5 UNIT.........................................7
Introduction.................................................................7
Methods......................................................................8
Model Preparation..........................................................8
Material Properties........................................................9
Finite Element Analysis...................................................10
Summary.....................................................................11
III. PRELIMINARY WORK.........................................................12
Introduction................................................................12
Methods.....................................................................12
Model Development.........................................................12
Material Properties.......................................................12
Finite Element Analysis...................................................14
Results.....................................................................14
Discussion..................................................................17
Summary.....................................................................17
IV. MODEL VALIDATION..........................................................19
Introduction................................................................19
Methods.....................................................................19
Model Determination.......................................................20
Convergence Study.........................................................21
Experimental Testing......................................................21
Results.....................................................................23
Discussion..................................................................25
Summary.....................................................................26
V. EFFECTS OF AGE-RELATED CORTICAL THINNING AND TRABECULAR BONE
LOSS ON THE MECHANICS OF LUMBAR SPINE FUSION..................................27
vii


Introduction....................................................................27
Methods.........................................................................29
Model Preparation.............................................................29
Material Properties...........................................................29
Finite Element Analysis.......................................................30
Results.........................................................................30
Discussion......................................................................33
Summary.........................................................................34
VI. EFFECTS OF DIFFERENT SPACERS..................................................36
Introduction....................................................................36
Methods.........................................................................37
Model Preparation.............................................................37
Material Properties...........................................................37
Finite Element Analysis.......................................................39
Results.........................................................................39
Discussion......................................................................45
Summary.........................................................................47
VII. CONCLUSIONS AND FUTURE WORK...................................................48
Conclusions.....................................................................48
Future Work.....................................................................49
REFERENCES.........................................................................50
viii


LIST OF FIGURES
FIGURE
1: Comparison of a healthy disc and degenerated disc [3]................................1
2: Example image of spacer, bone graft, and posterior instrumentation involved in lumbar
interbody fusion [4]....................................................................2
3: Meshed male (left) and female (right) models with CAD-developed spacer and posterior
instrumentation (pedicle screws and rods)...............................................9
4: Cut view of L4-L5 unit model to show shell and core compartments (gray=core, blue=shell). 11
5: Calculations of average elastic modulus based on the axial rigidity of the combined trabecular
and cortical compartments................................................................13
6: Average values of tensile principal strain and compressive principal strain of subject 1 (female-
top) and subject 2 (male- bottom)........................................................15
7: Maximum tensile strain at lateral endplate and in posterior rods with two spacer materials:
PEEK and titanium; subject 1 (female- top), subject 2 (male- bottom)....................16
8: Anterior view of L4-L5 unit with locations of strain rosettes at the spacer and L4 vertebral
body.....................................................................................22
9: Posterior view of L4-L5 unit with location of uniaxial strain gages at the rods......22
10: Comparison of experimental results and the grey-scale based FE model (p = 0.096)....24
11: Comparison of experimental results and the two-part homogeneous FE model (p < 0.001). 24
12: Mesh convergence results for L4-L5 model stiffness. Differences in model predicted stiffness
converged to less than 2% at a mesh density of 93,700 nodes..............................25
13: Vertebral body from a younger individual (top) and from an elderly individual (bottom) [15],
.........................................................................................28
14: Stress at multiple locations in the age-simulated female model at 20, 65, and 90 years old (65
was actual age of specimen)..............................................................31
15: Stress at multiple locations in the age-simulated male model at 20, 70, and 90 years old (70
was actual age of specimen)..............................................................32
16: Average maximum principal tensile and compressive strain at multiple locations in the age-
simulated female model...................................................................32
17: Average maximum principal tensile and compressive strain at multiple locations in the age-
simulated male model.....................................................................33
18: Comparison of original spacer and custom fit spacer in the male model...............39
19: Average maximum principal tensile and compressive strain at multiple locations in the female
model with various spacer materials......................................................40
20: Average maximum principal tensile and compressive strain at multiple locations in the male
model with various spacer materials......................................................41
21: Stress at multiple locations in the female model with various spacer materials......42
22: Stress at multiple locations in the male model with various spacer materials........43
23: Stress at the bone-spacer interfaces and rods in the male model with the original and custom
spacer...................................................................................44
IX


24: Stress distribution at the L5 bone-spacer interface with PEEK (left) and SRP 70% porous
(right) custom spacers..............................................................................45
x


CHAPTER I
INTRODUCTION
Purpose
Lower back pain is problematic worldwide, causing daily discomfort and restriction of
activities. It is estimated that as much as 80% of the population will experience a back problem at
some time in our lives [1]. Back pain is one of the most common reasons for missed work, and it
is the second most common reason for visits to the doctors office [2], Arthritis, poor posture,
obesity, and psychological stress are all factors in increasing the risk of back pain [2], There are
multiple issues that can occur in the back, ranging from injury of the intervertebral discs (like
herniated or bulging disc) to ligaments and nerves that can be stretched or pinched causing
various scales of pain. Degenerative Disc Disease (DDD) is a common reason for lower back
pain, and it occurs when the disc begins to degenerate, causing pain due to decreased space
between vertebrae (Fig. 1). Though this can be caused by injury or trauma, such as a car accident,
it is more common as a result of aging [3], The disc has no blood supply and therefore camiot
repair itself, so wear and tear typically develops as we age [4],
Figure 1: Comparison of a healthy disc and degenerated disc [5],
1


For extreme cases with great pain, lumbar spine fusion is the surgical solution. A spacer
or spinal cage is used to provide a fixed space between the vertebrae (Fig 2). Currently,
polyetheretherketone (PEEK) and Titanium are often used as the spacer material. Bone graft is
used in the process to stimulate bone growth to fuse the two vertebrae together, eliminating
motion in that segment. Posterior instrumentation, such as titanium screws and rods, may be used
to fixate the spinal unit during the healing process so as to restore the height of the intervertebral
disc and provide stability.
Figure 2: Example image of spacer, bone graft, and posterior instrumentation involved in lumbar
interbody fusion [6].
excessive spinal cage subsidence, lack of bone growth, and increased risk of multi-level fusions.
Spinal surgeons have experienced all of these issues post-surgery and seek to discover the cause
so that the solution may be found. Subsidence of the spinal cage is when the cage collapses a
significant amount into the vertebral body following surgery, consequentially voiding the purpose
fusion rate varies in patients and is unpredictable. In a study [7] with 32 procedures of anterior
V-
There is a clinical need to understand the fusion process better to determine the causes of
of the cage placement. The cage needs to support the vertebrae through the fusion process, but the
2


lumbar interbody fusions using a PEEK cage, 4 cases fused in 3 months, twenty-five cases fused
within 6 months, and three cases resulted in nonunion (no fusion). In the cases of nonunion, a
second surgery with additional instrumentation for fixation stability was necessary. Some patients
underwent fusion at multiple spine levels. Out of all the fused levels, subsidence was found in
five spinal units [7]. Some of the patients had spondylolisthesis, which is a condition where one
vertebra slips forward or backward, becoming misaligned with adjacent vertebrae. Though this
study was not large enough to make concrete conclusions, spondylolisthesis and obesity (high
BMI) were shown to increase the rate of cage subsidence. Another paper [8] summarized multiple
studies of the impact of subsidence on clinical outcomes and radiographic fusion rates, but that
study was limited to anterior cervical (neck) discectomy and fusion. Exploration of subsidence in
the lumbar spine is relatively limited, and a better understanding of the endplate structure and the
effects of implant material may be essential in finding the source of failure. The stiffness of
PEEK and titanium, the common implant materials, can be orders of magnitude stiffer than the
endplate of the vertebral body. Therefore, a less stiff material may provide less incidences of
subsidence. However, the material must still be able to produce efficient stability for the course of
the fusion process in which, as mentioned before, the length of time is unpredictable in patients.
An interbody cage with soft (low elastic modulus, E = 19 MPa) layers on the bone-implant
interface was tested in a finite element study of an L4-L5 segment [9], The study showed that the
peak contact pressure was significantly reduced with this cage, which could be a strategy for
decreasing the risk of cage subsidence [9],
Along with subsidence, the lack of bone growth is an issue in successful operations,
because without bone growth the fusion will not occur, resulting in a failed spine fusion and the
need for an additional operation. As briefly mentioned in one of the previous studies, nonunion
occurred in a few cases, and nonunion was due to the lack of bone growth. As a solution,
additional instrumentation was used to provide stability. Though instrumentation is thought to
3


decrease the incidences of nonunion, it still occurs in patients [10], Some possible explanations as
to why this occurs could be stress shielding, disrupted blood supply, chronic inflammation, and
bone quality [11]. Multiple studies compare instrumentation to non-instrumentation in various
fusion surgeries and there is not a solid consensus on one versus the other. What may work in one
patient may not work in another. Nonunion is difficult to quantify due to the many factors
involved. A retrospective study [12] examined the surgical outcomes of non-instrumented
posterolateral lumbar fusion (PLF) in order to compare cases with union versus cases with
nonunion. The follow-up was conducted with 42 patients and in 26% of the patients nonunion
was noted. Though bone growth is a necessity for a successful spine fusion, it is a very complex
matter and will not be directly investigated in this work.
Studies have shown that there is an increased risk of fusion in other levels in the lumbar
spine after the first spinal unit fusion [13] [14] [15] [16], It would seem that this would be a direct
relation to the altering load sharing involved in this fusion process. Posterior instrumentation is
used to carry much of the load during healing, but the devices do not serve a purpose once the
spinal unit is fused. The load must be carried elsewhere, and it is thought that the adjacent levels
are experiencing a greater load after fusion completion. In an anterior lumbar interbody fusion
(ALIF) study with six cadaveric lumbar spine specimens, the biomechanics of neighboring
unfused segments was investigated. When the lumbar spine units were loaded in 15 of flexion
with L4-L5 unit fused, there was an increase in segmental mobility at neighboring levels and
there was an increase in intradiscal pressure in all unfused segments in flexion [17], In another
study, the risk factors involved in adjacent segment degeneration after posterior lumbar spine
fusion were analyzed in 81 patients. Out of the 81 patients, 9 required a second operation where
degeneration occurred in the upper adjacent segments in 8 patients and in the lower adjacent
segments in one patient. Factors such as sex and age were used in evaluating the increased risk of
degeneration in adjacent segments, and there was a significant correlation with patients older than
4


50 years having a higher risk [16], The work of this thesis will analyze the stresses in various
locations in an L4-L5 model for evaluation of load sharing during lumbar spine fusion with
posterior instrumentation. Age and gender will be taken into account, but due to the small sample
size, no strong conclusions will be made in relation to these factors.
There is a need for patient-specific selection of device components to reduce
complications following lumbar interbody fusion such as subsidence, nonunion, and increased
risk of multi-level fusions. The purpose of this study was to develop a working L4-L5 model that
represents lumbar spine fusion with posterior instrumentation, so as to observe differences in
strain and stress in the lumbar spine due to age, gender, and various spacer materials in order to
begin to provide a quantitative rationale for the use of specific implant materials and
instrumentation on a patient-specific basis. Preliminary work led to a few hypotheses for each
study conducted in this thesis. It was hypothesized that there will be a shift in load to the posterior
rods with age-related cortical thinning and trabecular bone loss. Additionally, the vertebral cortex
will bear more of the load after trabecular bone loss. In respect to the spacer material, a spacer
with a modulus closer to trabecular bone will shift the load from the spacer and bone, to the rods.
Furthermore, a less stiff spacer will reduce stress at the bone-spacer interfaces. Even more, a
spacer that conforms to the contours of the vertebral endplates will distribute the stresses more
evenly, decreasing the stress at the bone-spacer interfaces.
Outline
Various methods were used in developing an accurate and workable model of the L4-L5
unit for strain and stress evaluation after lumbar spine fusion with posterior instrumentation.
Chapter II depicts the process taken to develop the L4-L5 unit used in this thesis. The imaging to
three-dimensional (3-D) model process, materials used, and finite element analysis are explored
thoroughly. The model development and direction of this thesis were determined from
preliminary work, which is addressed in Chapter III. Though the main purpose of this thesis is to
5


use 3-D modeling of the lumbar spine to observe changes in strain due to parameters such as age
and device material selection, the validation of the model is significant for confidence in
predictability (Chapter IV). Validation includes comparison to experimental testing and a
convergence study for appropriate mesh density for the models. The preliminary studies
prompted the final investigations, which will be presented using the final model in Chapters V-
VI. Chapter VII summarizes the material contained herein and discusses the path forward for this
research.
6


CHAPTER II
MODEL DEVELOPMENT OF AN L4-L5 UNIT
Introduction
Research into the three-dimensional distribution of mechanical stress after lumbar spine
fusion has been relatively limited. Spinal surgeons have found several complications with the
surgery, mentioned previously, and seek to find solutions. Due to the limitations of testing on
human subjects and the expense of cadaveric specimens, finite element (FE) modeling is perhaps
the best way to research the effects of patient-specific anatomy, bone quality and device design
on the process of lumbar spine fusion and to discover what variations may affect the outcome of
this surgery.
The spine is a very complex system with non-linear behavior; however, if a linear model
can be used to explore age-related effects and material implant effects on the bone, this will
provide a sufficient method of obtaining subject-specific information for proper device selection
based on modeling. To observe the effects of age-related cortical thinning and trabecular bone
loss and the effects of the spacer material properties on the stress and strain in the lumbar spine
after lumbar interbody fusion, a model needed to be developed. Lumbar spine fusion is most
commonly performed first in the L4-L5 segment of the spine. Therefore, a L4-L5 FE model was
developed.
Posterior instrumentation and a spacer were included in the model to replicate the
surgical procedure. Pedical fixation is not always included, especially in cases of anterior lumbar
interbody fusion (ALIF), and it is thought to produce greater risk of multi-level fusions due to
increased stress on adjacent levels. In a recent study [18] the effects of ALIF with and without
pedical fixation were explored using FE analysis. This study concluded that a stand-alone
interbody cage was sufficient for stability and better replicated an intact spine. Thus, ideally a
7


surgical procedure that does not require the use of posterior instrumentation would be preferred,
but for the purpose of this study aimed at simulating current procedures, they were included. The
development of the L4-L5 unit with posterior instrumentation, involving imaging of cadaveric
specimens and computing software, is explained further in the following section.
Methods
Model Preparation
Three-dimensional linear FE models of the L4 and L5 vertebrae were developed from
computed tomography (CT) data (voxel size = 0.7x0.7x0.9mm) of two cadaveric lumbar spines.
One donor was a 70-year-old male who had died from respiratory failure and sepsis and the other
donor was a 65-year-old female who had died from severe sepsis.
Quantitative CT (QCT) imaging was performed on a Gemini TF 64 (Philips, Amsterdam,
The Netherlands). A tube potential of 120 kVp was used. A QCT reference phantom (Mindways
Software, Inc., Austin TX) was used to obtain bone mineral density data from image intensity.
The data from imaging were saved as DICOM fdes, which were then imported into
ScanIP (Simpleware Ltd, Exeter, UK). Segmentation and smoothing were performed to obtain the
models of the L4-L5 unit. An interbody spacer and posterior instrumentation (pedicle screws and
6-mm or 5.5-mm diameter rods for subject 1 and subject 2, respectively) were designed using
SolidWorks (Dassault Systemes, Waltham, MA) and then integrated into the model using
Simplewares +CAD program. They were designed based on measurements of instrumentation
currently used by the clinical advisor for the study, Dr. Vikas Patel. The spacer was positioned
between the inferior surface of L4 and superior surface of L5.
Blocks were incorporated into the model to depict the urethane blocks that were used to
pot the superior endplate of L4 and the inferior endplate of L5 during mechanical testing (see
Chapter IV). In addition to recreating the experimental setup, the urethane blocks help to
8


distribute the applied loads evenly across the superior and inferior surfaces of the bones in the
model. Facet joints, including thin cartilage layers, were included in the model and assigned as a
contact pair. A contact pair was also assigned between L4 and the spacer and L5 and the spacer.
The entire assembly was then meshed with linear, four-noded tetrahedral elements using the
adaptive meshing algorithm in Simplewares +FE program (Fig. 3). This model represents the
condition immediately following surgery.
Figure 3: Meshed male (left) and female (right) models with CAD-developed spacer and
posterior instrumentation (pedicle screws and rods).
Material Properties
Homogeneous material properties were used for the trabecular core and the cortical shell
of the vertebrae. The cortical bone was assigned an elastic modulus (E) of 12 GPa and Poissons
ratio (u) of 0.3 [19], Due to the relatively low resolution provided by the clinical CT system used
to obtain the images, the cortical shell could not be directly defined based on image data. Instead,
the cortical shell thickness in the models was determined by fitting a linear relationship between
age and cortical thickness. Mosekilde [20] provided a range of cortical thickness values in die
vertebral body for age ranges 20-40 and 70-80 years. Using the linear fit equation, cortical
thicknesses of 0.27 mm and 0.29 mm were determined for the 70-year-old and 65-year-old
subject, respectively.
9


A linear relationship between QCT measurements of trabecular volumetric bone mineral
density (vBMD) in the lumbar spine and age was used to estimate vBMD loss with age [21],
Riggs et al. provided an average value of trabecular vBMD measured at the mid-portion of LI, L2
and L3 between the ages of 20-29 and then found an average 47% and 54% decrease in trabecular
vBMD from 20-90 years in a study with 323 men and 373 women, respectively [21], A linear
relationship between trabecular vBMD and elastic modulus was then used to estimate the
corresponding age-related decline in E with a p >0.01^(Eqn. 1) [22],
cm3
E = -34.7 MPa + 3230 MPa-----------p (1)
9
Elastic modulus is in units of MPa and p is the QCT density in units of-^-r. Based on this
cm3
relationship, an E of 400 MPa and v of 0.3 were assigned for the male subject. An E of 429 MPa
and v of 0.3 were assigned for the female subject.
The rods and screws were treated as titanium with an E of 110 GPa and v of 0.3 [19], The
blocks were assigned an E of 6832 MPa and a v of 0.3 (manufacturers data). Cartilage lined
facet joints were included in the model and cartilage regions were assigned an E of 6 MPa and a
v of 0.49 [23],
Finite Element Analysis
The models were exported as a readable format for Abaqus (Simulia, Providence, RI). In
Abaqus, the skin feature was used to create a homogeneous shell around the vertebrae. The shell
around the vertebrae was used to represent a thin cortex, which had a thickness less than the voxel
size of the original QCT image. A cortex of 0.27 mm and 0.29 mm were applied to the male
subject and female subject, respectively, based on published data of age-dependent cortical
thinning [20] and were later modified to simulate age-related effects (Fig. 4).
10


Figure 4 : Cut view of L4-L5 unit model to show shell and core compartments (gray=corc.
blue=shell).
The inferior end of the block attached to L5 was fixed in all directions and a 0.145 MPa
pressure was applied to the superior end of the block attached to L4. The pressure of 0.145 MPa
was obtained from taking 730 N divided by the area of the urethane block. The load of 730 N was
chosen based on in vivo measurements of a patient rising from a chair, available in the OrtlioLoad
database (www.orthoload.com) [24] [25],
Groups of elements were selected at the L4 and L5 anterior regions, anterior spacer
region, posterior rods region, and bone-spacer interface at L4 and L5 for analysis of stress and
strain. The average maximum tensile and compressive strain (maximum and minimum principal
strains, respectively) and the von Mises stress were obtained at each location.
Summary
The methods outlined in this chapter are the general methods of the model development
used in Chapters III-VI. Other specific model parameters will be specified in each chapter where
applicable. The following chapter will explore the preliminary work that directed the work
presented in this thesis.
11


CHAPTER III
PRELIMINARY WORK
Introduction
The L4-L5 model has evolved throughout the course of this thesis work. The model
began as a simple homogeneous model without the inclusion of urethane blocks or facet joints
with cartilage layers. The urethane blocks were later included to better represent the experimental
testing, and the facet joints were included to better approximate the anatomy. Though the final
model is also homogenous, the model developed for the preliminary work took an average elastic
modulus of combined trabecular and cortical compartments. The relationships between age-
related changes, including cortical thinning and trabecular bone loss, and strain in the L4-L5
model were observed. The effects of PEEK and titanium as the implant material were also tested
in the model.
Methods
Model Development
The model development outlined in Chapter II applies to this model with the only
differences being that neither the blocks nor the facet joints in combination with the cartilage
layers were included. The entire assembly was meshed with linear, four-noded tetrahedral
elements using the adaptive meshing algorithm in Simplewares +FE program. Note that these
models were developed prior to the convergence study and therefore contain a larger mesh size.
Material Properties
A homogeneous value of E was assigned to each vertebra based on the axial rigidity of
the combined trabecular and cortical compartments. Figure 5 shows how the vertebral body was
treated as an ellipse to obtain the area for use in calculations of an average elastic modulus.
12


Figure 5: Calculations of average elastic modulus based on the axial rigidity of the combined
trabecular and cortical compartments.
In a study presented at the American Society of Bone and Mineral Research 2012 Annual
Meeting [26], a homogeneous E was calculated based from trabecular bone loss and cortical
thinning with increasing age for two subjects: a male and a female. Table 1 displays the E value
assigned to each subject for a range of ages. The rods and screws were treated as titanium with an
E of 110 GPa and u of 0.3 [19], The spacer was treated as PEEK with an E of 4.6 GPa and v of
0.38 [27],
Table 1: Material properties applied to the bone for each specimen with age-related changes and
the material properties applied to the instrumentation.
Elastic Modulus (MPa) Poisson's Ratio Cortical Thickness (mm)
Male (30, 70, 90 yr) 1099.6, 715.7, 564.7 0.3 0.45, 0.29, 0.18
Female (30, 65, 90 yr) 1133.1, 761.5, 560.3 0.3 0.45, 0.27, 0.18
PEEK 4,600 0.38 N/A
Titanium 110,000 0.3 N/A
Another study, presented at Orthopaedic Research Society 2013 Annual Meeting [28],
determined the effects of spacer material in the same two subjects. Titanium and PEEK were the
materials assigned to the spacer (Table 1).
13


Finite Element Analysis
The model was exported as a readable format for Abaqus (Simulia, Providence, RI). The
inferior end of L5 was fixed in all directions and a distributed pressure was applied to the superior
end of L4. A load of 400 N was divided by the average cross-sectional area taken at the mid-
section of L4 to obtain the pressure applied: 0.38 MPa. The load of 400 N was chosen from a
recommendation for the average pre-load on the spine in a paper by Goel et al. [29].
Groups of elements were selected at the posterior rods, bone-implant interface, and lateral
endplate of L5 for analysis of average maximum tensile and compressive strain at each location.
Results
Cortical thickness and trabecular elastic modulus were varied in both models to simulate
age-related changes in the bone. As hypothesized, the strain in the bone increased with age, and
different locations experienced various levels of strain. At the endplate of L5, the maximum
tensile and compressive strain in the 90 year old was nearly double that in the 30 year old (Fig.
6). The female specimen experienced overall greater tensile strains at the bone-implant interface,
while the male specimen had greater tensile strain at the lateral endplate of L5.
14


200
0-
b
| -200-
cn
O
4-.
u
s
-400-
-600-
Principal Tensile Strain
Principal Compressive Strain
30 year old
65 year old
90 year old
Bone-Spacer Interface Lateral Endplate
JL
Principal Tensile Strain
Principal Compressive Strain
Bone-Spacer Interface Lateral Endplate

200-
100-
0-
.g -loo-
Kj
1 -200-
p
2 -300-
-400
-500-
-600-
-700 .
30 year old
n 70 year old
90 year old
Figure 6: Average values of tensile principal strain and compressive principal strain of subject 1
(female- top) and subject 2 (male- bottom).
The effects of PEEK compared to a Titanium spacer were observed in both subjects. The
trabecular elastic modulus and cortical thickness in relation to the current age of the cadaveric
specimens remained constant while only the spacer material properties were adjusted. The strain
at the lateral endplate of L4 and in the posterior rods was observed (Fig. 7).
15


Tensile strain at the lateral aspect of the inferior endplate of L4 and in the posterior rods
was greater in subject 1 for both PEEK and Titanium spacer implants. Furthermore, subject 1
experienced higher strain at both locations with a PEEK spacer implant, while subject 2 had
lower strain in the posterior rods with a PEEK spacer implant.
Figure 7: Maximum tensile strain at lateral endplate and in posterior rods with two spacer
materials: PEEK and titanium; subject 1 (female- top), subject 2 (male- bottom).
16


Discussion
The results of the first study demonstrated the effects of age-related cortical thinning and
trabecular bone loss on the mechanical environment in bone following interbody fusion.
Furthermore, the different strain levels in the two specimens demonstrate the importance of using
patient-specific information. Though it is impossible to compare the effects of gender and weight
due to small sample size, we expect that both parameters play a role in how the bone is affected.
Additionally, when the spacer material was altered, both specimens experienced
difference levels of strain in the two locations: lateral endplate and posterior rods. This further
concludes the need for patient-specific information when choosing device material. The changes
in strain in the posterior rods due to different implant materials, is of particular relevance due to
its load sharing significance.
A limitation of these results was the different alignment of the spine in both subjects that
could have altered the strain distribution. At the same time, this also helped to solidify the
importance of subject-specific information to determine the optimal mechanical environment
post-surgery. The subjects differed in gender, weight, height and age, which are all possible links
to the trabecular BMD of the lumbar spine and could be used to project optimal subject-specific
surgery procedures.
Summary
The preliminary work helped determine the direction of this thesis. The first study
demonstrated the effects of age-related cortical thinning and trabecular bone loss on the
mechanical environment in bone following interbody fusion [26], Therefore, a similar method
was applied to the final models and results are presented in Chapter V. The different effects of the
spacer material on each subject in the second study [28] began to show the importance of patient-
17


specific information for selection of device components, and this concept is explored further in
Chapter VI. All future work uses the methods outlined in Chapter II with a trabecular core and
cortical shell. Chapter IV will address the validation of these models and the process of selecting
the most useful combination of modeling methods.
18


CHAPTER IV
MODEL VALIDATION
Introduction
Modeling of the lumbar spine can be a valuable tool for evaluating the biomechanics,
geometric orientation, and optimal implant materials and design, but validation is important for
assurance that relative differences in strain at various locations are accurately depicted.
Mechanical testing of the cadaver specimens was conducted and the experimental data were
compared with the results obtained from the FE models. Various models were explored in the
process with the goal of finding the most accurate model for estimating strain in the lumbar spine
after interbody fusion with posterior instrumentation. The model was determined by comparing
multiple approaches of defining the material properties in the lumbar spine: homogenous, grey-
scale based, and two methods of a two-part (cortical shell and trabecular core) homogeneous
model. Once the model was determined, a convergence study was conducted in order to define
the mesh density of the models. The L4-L5 unit model was validated and determined for use in all
other studies.
Methods
In order to compare to experimental data, the rods and spacer in the model were assigned
a shell of 0.01 thickness and the same assigned material properties as the instrumentation. The
shells allowed the directional surface strain to be obtained so as to more accurately model the
experimental strain gage measurements.
19


Model Determination
After preliminary work with the homogeneous L4-L5 model, a grey-scale based model
was hypothesized to produce more comparable results to experimental data. Using the grey-scale
based material type feature in Simpleware, each voxel was assigned an elastic modulus. Keyak et
al. [30] provided equations to compute E from ash density (Eqns. 2-4). All voxels under 1 mg/cc
were assigned l.OOxlO"4 MPa to eliminate all negative values representing air pockets and fat
areas.
E = 33,900 pash220 (MPa) forpash < 0.27 g cm~3 ( 2 )
E = 5307pash + 4-69 (MPa) for 0.27 < pash < 0.60 g cm~3 (3)
E = 10,200 pash2 01 (MPa) for pash > 0.60 g cm~3 ( 4 )
Using clinically realistic imaging methods, it is difficult to directly depict the cortical
shell due to its miniscule thickness, but it is important in modeling the lumbar spine because of its
role in sharing load with the trabecular bone compartment. Therefore a lumbar spine model that
represented a cortical shell and trabecular core was hypothesized to help predict strain in the
bone. A cortical shell and trabecular core was originally tested using features in Simpleware. The
pixel size of the cadaver specimen images was reduced to fit the thickness size of the cortical
shell.
The other method used to create a two-part homogenous model was the application of the
SKIN feature in Abaqus where a shell with input thickness and homogeneous E was added to the
vertebrae [31] [32] [33], The trabecular core was represented with a homogeneous E value.
20


Convergence Study
A mesh convergence study was conducted to determine the mesh density to be used in
subsequent models. Starting with a mesh size containing 26,593 nodes, the mesh was refined until
convergence was obtained. Mesh convergence was determined by measuring the vertical stiffness
of the model at the various mesh sizes until the change in stiffness was less than 2%.
Experimental Testing
After imaging the cadaveric spine, the L4-L5 motion segment was excised. A spinal
surgeon (VVP) inserted a spacer, screws, and rods into the cadaver specimen. The L4 superior
endplate and the L5 inferior endplate were then potted in urethane (Dyna-cast, Kindt-Collins
Company, Cleveland, OH). Aluminum fixtures were created to hold the vertebrae in the urethane
while it cured.
The L4-L5 segment with interbody spacer and posterior instrumentation was placed in
compression in an MTS Insight with a 30 kN load cell. Strain rosettes (L2A-06-062WW-350,
Vishay Micro-Measurements, Raleigh, NC) and uniaxial strain gages (L2A-06-125LW-120,
Vishay Micro-Measurements, Raleigh, NC) were purchased and tested prior to using. An
aluminum bar was used to check the accuracy of the strain rosettes. A 0.5395 kg weight was
suspended on the aluminum bar and the strain was predicted by beam theory using the cross-
sectional area and moment of inertia. Calculations resulted in 360 microstrain, and using the
beam theory with the published value of E (68.9 GPa [34]) for 6061 aluminum is 346 microstrain,
giving a 4% error. The strain rosettes and uniaxial strain gages were then glued with
cyanoacrylate in their respective locations on the L4-L5 segment.
Strain rosettes were placed on the anterior surface of the spacer and anterior surface of
the L4 vertebra (Fig. 8). Uniaxial strain gages were placed on the posterior sides of the rods (Fig.
9). The motion segment was tested in compression at room temperature with three different peak
21


loads (400, 730 and 1000 N). Specimens were kept hydrated throughout testing. During each trial
(three per peak load level), the applied load was increased under displacement control until the
pre-determined peak load was reached.
L4 strain
rosette
location
Spacer strain
rosette location
Figure 8 : Anterior view of L4-L5 unit with locations of strain rosettes at the spacer and L4
vertebral body.
Figure 9: Posterior view of L4-L5 unit with location of uniaxial strain gages at the rods.
22


The peak principal strains on the anterior surfaces of the spacer and L4 vertebral body
were calculated from rosettes, and the peak strain on the posterior surfaces of the rods were
measured from the uniaxial gages.
Results
After experimental testing and model data collection, the model was determined. The
measured experimental strain and the FE model strain at each location were normalized to the
corresponding peak load and plotted together. There was no correlation between the grey-scale
model and the experimental data. This led to adding a shell (using SKIN feature in Abaqus) to the
model in the same manner as the two-part homogeneous model. The strain at the L4 anterior
location was not predicted well in the grey-scale model compared to the experimental, which is
evident by the three data points farthest from the linear regression (Fig. 10). The cortical shell
was assigned the same thickness and modulus as the two-part homogeneous model so this would
show the homogeneous trabecular bone modulus represented the experimental strain better.
Therefore, the grey-scale based model still did not prove to predict strain better than the
homogenous model in comparison to the experimental data and therefore was eliminated as a
model option. The first two-part homogenous model method in Simpleware proved to be too
computationally expensive and time intensive, and therefore this method was eliminated as a
candidate. This led to using the SKIN feature in Abaqus where a shell with input thickness and
homogeneous E was added to the vertebrae. Overall, this two-part homogenous model best
predicted strain in the lumbar spine in comparison to the experimental testing results (Fig. 11).
23


Figure 10: Comparison of experimental results and the grey-scale based FE model (p = 0.096).
Figure 11: Comparison of experimental results and the two-part homogeneous FE model (p <
0.001).
24


The convergence study was done to the two-part homogeneous model. The stiffness
converged to a less than 2% difference from 93,790 nodes to 252,357 nodes (Fig. 12). The figure
shows the next mesh size as well with 377,542 nodes. There remains a less than 2% difference
even between 93,790 nodes and 377,542 nodes, where the number of nodes is 4 times greater.
The mesh density that contained 93,790 nodes was therefore chosen for all models in this study.
16000
15800
I 15600
&
C/3
tn
o
?9 15400
-4-J
15200
15000
0 100000 200000 300000 400000
Number of Nodes
Figure 12: Mesh convergence results for L4-L5 model stiffness. Differences in model predicted
stiffness converged to less than 2% at a mesh density of 93,700 nodes.
Discussion
The comparisons of the experimental strain and the FE model strain at the same locations
led to determining the model that best predicted the strain in the lumbar spine after interbody
fusion with posterior instrumentation. The grey-scale based model was hypothesized to predict
strain the best; however, the comparison to experimental data showed differently. This may have
25


been due to too many air pockets depicted in the images, lowering the elastic moduli assigned to
each voxel in the trabecular bone region. Therefore, the two-part homogeneous model was
determined to be the best option. It resulted in an R-squared value of 0.56. Thus the model had
the ability to explain 56% of the variance in measured strain. While this coefficient of
determination was rather modest, the relationship was highly significant (p < 0.001), leading us to
conclude that the model could be used in subsequent analyses to produce a realistic depiction of
strain distribution and magnitude. It is likely that a greater number of locations and specimens
would increase the correlation, and therefore additional experiments will be implemented in
future studies.
There were a few limitations in the methods used in comparing the model to experimental
results. Imaging the cadaveric specimens post-surgery could have led to better comparison
between the FE models and experimental results, because the exact location and orientation of the
spacer and posterior instrumentation would have been more accurately represented. Another
limitation to the validation was the small number of locations used for obtaining measured strain.
The trabecular core E, cortical cortex E, and cortex thickness were all applied to the model based
from published data, which could also cause a mismatch in comparison to the experimental data.
Summary
Modeling the spine is a very complex procedure, but it can be very useful in studying the
biomechanics of the lumbar spine for optimization of surgical procedures like lumbar spine
fusion as a result of DDD. The L4-L5 unit used in this work was validated in comparison to
experimental data and will be used to explore the effects of age-related changes (Chapter V) and
effects of spacer material (Chapter VI) on the strain and stress in various locations. The following
chapter will discuss how the model was developed to represent various ages and how this alters
the stress and strain distribution in the lumbar spine after fusion with posterior instrumentation.
26


CHAPTER V
EFFECTS OF AGE-RELATED CORTICAL THINNING AND TRABECULAR BONE
LOSS ON THE MECHANICS OF LUMBAR SPINE FUSION
Introduction
Age, gender, weight, and lifestyle (smoking, etc.) are all factors that affect the vertebral
bone strength, mass and structure. Age is the most dominant factor, as there is a loss in trabecular
bone density leading to an overall large decline in vertebral body strength [20], The vertebral
body is comprised of a spongy trabecular core, compact cortical shell and endplates with similar
properties to the cortical shell but with an even smaller thickness. Vertebral strength is primarily
determined by cross-sectional area, thickness of the cortical shell and endplates, and density and
structure of the trabecular core [20], Vertebral strength as a whole, will not be considered, but
rather the age-related cortical thinning of the cortex and trabecular bone loss. Figure 13 shows a
vertebral body from a young and elderly individual. It is evident in this comparison that the
vertebral body of the elderly individual is much less dense than that of the younger individual.
Though age is the most significant factor in affecting changes in the vertebral body, there
are different age-related changes among genders. Peak bone mass is reached between the ages of
25-30 in both men and women and then begins to decrease soon thereafter [20], At that point,
different relationships between age and trabecular bone loss in men and women are apparent.
Men already have greater bone mass and vertebral strength than women at their peak, and then as
they age, an increase in cross-sectional area of the vertebral bodies has been seen, which has the
ability to provide better load support [35], Additionally, once women reach menopause, they
experience accelerated bone loss. The MrOS study is a large study that evaluates many of the
factors mentioned, plus more in men and how they affect the trabecular vBMD in the lumbar
27


spine [36], Diabetes was associated with an 11% greater trabecular vBMD at the lumbar spine
and two of the strongest negative correlations were history of fracture and height.
Figure 13: Vertebral body from a younger individual (top) and from an elderly individual
(bottom) [20],
The purpose of this study was to determine the effects of age-related cortical thinning and
loss of trabecular vBMD on the stress distribution in the spine after lumber interbody fusion with
posterior instrumentation. Though additional factors could be taken mto account by adding
additional levels of complexity to the models, this study only directly looks at age-related
changes. The two cadaver specimens observed in this study differ in age, weight, and gender, but
weight and gender will only be discussed with respect to inter-individual differences and how
these factors could correlate with observed mechanical differences.
28


Methods
Model Preparation
The model preparation outlined in Chapter II applies to these models. Additionally, the
cross-sectional area was found for both subjects. The cross-sectional area was calculated by
assuming an ellipsoid and averaging the measured values across the mid-section of the L4
vertebral body using imageJ (Eqn. 5).
A = nab
(5)
A is the area of the ellipse in units of mm2, and a and b are the distances measured horizontally
and vertically, respectively, from the edge of the vertebral body to the center in mm.
Material Properties
The methods for applying the material properties outlined in Chapter II were used in
these models. However, to determine the effects of age-related changes in trabecular vBMD and
cortical thinning, trabecular bone E and cortical thickness were calculated for a 20 and 90 year
old and were assigned to the same models (Tables 2-3). For details on how the trabecular bone E
and cortical thickness were determined, see Chapter II (p. 7).
Table 2: Material properties and cortical thickness applied to the male specimen at 20, 70, and 90
years old.
Age (yr) Trabecular Bone E (MPa) Poisson's Ratio Cortical Thickness (pm)
20 567 0.3 500
70 400 0.3 270
90 333 0.3 180
29


Table 3: Material properties and cortical thickness applied to the female specimen at 20, 65, and
90 years old.
Age (yr) Trabecular Bone E (MPa) Poisson's Ratio Cortical Thickness (pm)
20 609 0.3 500
65 429 0.3 290
90 328 0.3 180
Finite Element Analysis
The FE analysis outlined in Chapter II applies to these models. A cortex with a thickness
given in Tables 2-3, dependent on age, was added as a SKIN in Abaqus. The same boundary
conditions were applied to these models.
Results
Cortical thickness and trabecular elastic modulus were varied in both models to simulate
age-related changes in the bone. A linear increase in stress in correlation with an increasing age
was evident at the L4 and L5 anterior locations and at the rods in both models. The stress in the
L4 anterior location was 8-13 times greater compared to the L5 anterior location in the male
model, while the female model experienced similar magnitudes of stress in both L4 and L5. The
stress doubled from the 20 to 90 year old in the female model at the L4 and L5 anterior bone and
in the male model at the L4 anterior bone (Figs. 14-15). The stress more than tripled in the male
model at the L5 anterior location.
The female model demonstrated a linear relationship of an increasing stress with age at
all locations. The von Mises stress at the L4 bone-spacer interface increased by about 11%
between the 20 and 90 year old model and increased about 7% between the 20 and 90 year old
model at the L5 bone-spacer interface. The female model experienced greater stress at the L4
30


bone-spacer interface than the L5 bone-spacer interface while the male model experienced similar
magnitudes at both interfaces. In the male model there was only a 3% increase and 10% increase
from the 20 year old to 90 year old model at the L4 and L5 bone-spacer interfaces, respectively.
Rod stress increased with age but there was not a direct age-related correlation with the
spacer stress in the male model. In fact, the stress at the spacer was a bit higher (3%) in the 70
year old than the 90 year old. Furthermore, the stress at the spacer only increased by a little more
than 1% between the 20 and 90 year old, while the female model experienced a 12% increase.
Nonetheless, the rods still experienced an increase (16%) between the 20 and 90 year old in the
male model and 30% in the female model.
Figure 14: Stress at multiple locations in the age-simulated female model at 20, 65, and 90 years
old (65 was actual age of specimen).
31


Figure 15: Stress at multiple locations in the age-simulated male model at 20, 70, and 90 years
old (70 was actual age of specimen).
The average maximum principal tensile and compressive strain measured at various
locations in the models was also obtained. Because the models were linear, the strain data
correlated directly with the stress results (Figs. 16-17).
Principal Tensile Strain
Principal Compressive Strain
L4-Spacer Interface L5-Spacer Interface
Spacer
Figure 16: Average maximum principal tensile and compressive strain at multiple locations in
the age-simulated female model.
32


L4-Spaccr Interface L5-Spaccr Interface
Spacer
Principal Tensile Strain
Principal Compressive Strain
Figure 17: Average maximum principal tensile and compressive strain at multiple locations in
the age-simulated male model.
The cross-sectional areas of the L4 vertebral body were 1213 mm2 and 1115 mm2 for the
male and female, respectively.
Discussion
Both subjects experienced increased levels of stress and strain at the different locations as
cortical thickness and trabecular elastic modulus varied due to the simulated increase in age. In
both models, the stress at least doubled from 20 to 90 years old at the L4 and L5 anterior bone
locations. Since gender differences have not been evaluated in the measurement of cortical
thickness, it is the same in both models at the same ages. This may have been a reason for similar
magnitudes of changes in stress in both subjects at the anterior bone. This also suggests that the
cortical thickness is a large factor in the stress at the anterior bone, which goes along with the
original hypothesis that the vertebral cortex will bear more of the load after trabecular bone loss.
Contrarily, an increase in stress from 20 to 90 years old ranged from 3-11% in the subjects at the
bone-spacer interfaces. In this case, though the cortical thickness was still the same in both
subjects, the bone-spacer interface interactions differed to a greater extent between the subjects.
The trabecular bone may therefore be playing a greater role in the effect on the stress at the bone-
33


spacer interface. Additionally, other factors (spine alignment, device placement, etc.) not directly
measured in this study, may be affecting the bone-spacer stress distribution.
The increase in stress in the rods with an increase in age showed the rods were carrying a
greater load in the older models. In the female, there was also an increase in stress at the spacer.
Overall, this shows that as a person ages, the instrumentation takes on more of the load. It would
seem that there must be a load shift from the vertebral body with age-related cortical thinning and
trabecular bone loss.
The cross-sectional area of the male was calculated to be 8% larger than the female. This
correlates with literature that shows men typically have larger vertebral cross-sectional areas than
women. However, this is not a large difference, which may be due to the female being obese. The
body mass index (BMI) of the female was 35.6 (mass = 103 kg, height = 170 cm), while the male
had a BMI of 28.9 (mass = 102 kg, height =188 m), which falls into the overweight category.
Due to the fact that only two subjects were analyzed, no conclusions can be drawn from the cross-
sectional area or BMI of the subjects. However, it is worth mentioning due to its possible
relevance, and effects of body size should be taken into account in future studies.
Summary
The results obtained in this study demonstrated the age-related effects of cortical thinning
and trabecular bone loss on lumbar interbody fusion with posterior instrumentation. The greatest
changes in stress with age were found at the L4 and L5 anterior locations. However, there were
still significant increases in stress between the 20 and 90 year old models at most locations, with
the two exceptions being the stress at the spacer and L4 bone-spacer interface in the male model.
Other than the anterior bone locations, the rods experienced the next greatest increase in stress
with a 16% increase in the male model and 30% increase in the female model. In a future
analysis, it would be useful to maintain the cortical thickness as the trabecular bone varies to
34


discern how much the cortical thickness plays a role in the stresses obtained in the lumbar spine
and instrumentation. The following chapter will analyze the affects of the spacer material on the
stress and strain distribution in the lumbar spine after fusion with posterior instrumentation.
35


CHAPTER VI
EFFECTS OF DIFFERENT SPACERS
Introduction
The spacer material is an important part of the overall fusion system. The spacer must
bear relatively high forces while fusion occurs, however, a spacer that is overly stiff could lead to
more stress on the bone, possibly leading to subsidence and the need for an additional surgery.
Titanium and PEEK are the materials used most often in posterior lumbar interbody fusions.
Vadapalli et al. [37] studied the effects of spacer stiffness in a L3-L5 segment with L4-L5 fusion
with posterior instrumentation. Peak von Mises stress in the endplates increased by at least 2.4-
fold with a titanium spacer versus PEEK. This study suggested that the chance of subsidence
would be less with PEEK spacers and the lower stiffness of PEEK did not affect the stability.
Bioactive titanium implants with 50% porosity and 116.3 MPa strength were evaluated in a
canine anterior interbody fusion model [38], Fusion was confirmed in all five dogs that received
the treated bioactive titanium implant and in 3 of the 5 dogs that received the nontreated implant.
This study concluded that the bioactive treatment enhanced the fusion ability and therefore may
be the direction for spacers. A clinical study in humans [39] using the porous bioactive titanium
had successful fusions in all five individuals aged 36-56 years old with fusion within 6 months.
The advancement in spacer materials mentioned are an attempt to correct the issues of nonunion
and subsidence; however, the load sharing is also significant. Ghouchani et al. [40] did a FE study
for optimization of material properties for an artificial lumbar disc replacement. The artificial disc
was simulated similar to an intact disc with a peripheral annulus fibrosus region and center
nucleus pulpous region. Various physiologic loading conditions were applied, leading to
predicted optimal material properties to be E=19.1 MPa and u=0.41 for the peripheral section and
E=1.24 MPa and u=0.47 for the central section. This artificial disc with these properties would
36


restore the disc height and function similar to an intact disc. Though an artificial disc replacement
could be the best solution in the future to avoid complications of lumbar spine fusion and loss of
segment motion, the work in this study is an attempt at an intermediate solution. Titanium and
PEEK were originally the materials to be compared, but an even less stiff material, one closer in
material properties to trabecular bone, was hypothesized to decrease the stress (due to shift in
load) at the bone-spacer interfaces in order to hopefully lessen the incidences of subsidence. This
chapter addresses the effects of the spacer material on the stress and strain in the bone and
posterior instrumentation and, more specifically, compares titanium, PEEK, Self-reinforced
polyphenylene (SRP), and SRP with 70% porosity as the spacer material.
Methods
Model Preparation
The model preparation outlined in Chapter II applies to these models.
Material Properties
The methods for applying the material properties of the cortical bone cortex and
trabecular bone core, outlined in Chapter II, are the same in this model. However, in this study,
multiple spacer materials were used (Table 4). Titanium and PEEK are current materials used as
the interbody spacers in lumbar spine fusion [19] [41], SRP is another material with similar
properties to PEEK and it has the ability to be manufactured with prescribed porosity. SRP was
simulated with 70% porosity by calculating the elastic modulus of the porous SRP (Eqn. 6) [42]
[43] [44], A porosity of 70% was used so as to obtain an elastic modulus similar to trabecular
bone.
37


(6)
Ec = Es{ 1 0)2
Where Es represents the modulus of the solid material, Ec represents the porous material, and 0 is
the porosity. An elastic modulus of 450 MPa, spacer modulus closest to trabecular bone, was
assigned to the spacer and will be referred to as SRP 70% porous.
Table 4: Material properties applied to the spacer [45] [41] [19],
Spacer Material Porosity Elastic Modulus (MPa) Poisson's Ratio
Titanium none 110,000 0.3
PEEK none 4000 0.36
SRP none 70% 5000 450 0.3
As an exploratory addition to this study, a model with a custom fit spacer was created in
Simpleware. The spacer was developed to conform to the curvature of the endplates to help
spread out the stress distribution along the bone-spacer interface. Figure 18 shows a comparison
between the original spacer and the custom fit spacer in the male model. The average von Mises
stress at the bone-spacer interfaces and in the posterior rods was obtained.
38


Figure 18: Comparison of original spacer and custom fit spacer in the male model.
Finite Element Analysis
The FE analysis outlined in Chapter II applies to these models. A cortical thickness and
trabecular core E were applied based from the age of the specimens, 65- and 70- year old, for the
female and male model, respectively. Boundary conditions were applied to these models as
previously explained.
Results
The spacer material was varied in both models, while all other parameters were held
constant, in order to properly analyze the effects of the spacer material. As the stiffness of the
spacer material decreased, it was hypothesized that the strain and stress would decrease at the
bone-spacer interfaces while increasing at the rods. The changes between PEEK, SRP and
titanium were very miniscule in comparison to the noticeable changes with SRP 70% porous as
the spacer material. PEEK and SRP will remain very close due to their similar material
properties; SRP was included for the purpose of comparing it to SRP with 70% porosity.
Both models experienced different levels of strain and stress at the different locations as
the spacer material varied. There was greater overall compressive and tensile strain at the bone-
39


spacer interfaces compared to other locations, which made sense due to the load-bearing
responsibility of the spacer and the bone having a lower stiffness than the other materials. The
strain and stress at the rods was taken as an average between the values collected on die posterior
side of each rod. The highest strain was found in die rods with SRP 70% porous as the spacer
material.
Though the strain in the SRP 70% porous should be greater than the other materials due
to lower stiffness, the female model experienced a very large amount of both compressive and
tensile strain (Fig 19). The female model experienced greater compressive and tensile strain at
both bone-spacer interfaces with die SRP 70% porous, which goes against the hypothesized
outcome. The L4 and L5 anterior locations experienced similar magnitudes of strain in the
female model.
Principal Tensile Strain
Principal Compressive Strain
L4-Spacer Interface L5-Spacer Interface Spacer Rods L4 anterior L5 anterior
Figure 19: Average maximum principal tensile and compressive strain at multiple locations in
the female model with various spacer materials.
Contradictory to the female model, the male model experienced less tensile and
compressive strain in the bone-spacer interface locations with SRP 70% porous (Fig. 20). Also,
there was greater tensile and compressive strain at the L4 anterior location and less at die L5
anterior location with the SRP 70% porous spacer.
40


400
SB-------
---BBhB-
3,
-200 |
PEEK
SRP
SRP 70%
Titanium
L4-Spaccr Interlace L5-Spaccr Interface Spacer
Principal Tensile Strain
Principal Compressive Strain
Figure 20: Average maximum principal tensile and compressive strain at multiple locations in
the male model with various spacer materials.
The spacer with SRP 70% porous material properties strained almost 13 times greater in
compression and almost 8 times greater in tension in the female model versus the male model.
The rods experienced greater strain with all spacer materials in the male model compared to the
female model, and consequentially the compressive strain at both bone-spacer interfaces was
greater in the female model.
Though the strain was important to observe, especially when used in comparison to
experimental results, the stress was more significant for considering how the load was distributed
in the model and the stress concentrations occurring at the bone-spacer interfaces. Coinciding
with the strain results, the stress was greater in the rods with SRP 70% porous spacer in both
subjects. For comparison of load sharing, the stress at the bone-spacer interfaces was 1-1.5 MPa
while the stress in the rods was 15-20 MPa in the female model (Fig. 21). The male model
experienced less than 1 MPa at the bone-spacer interfaces for all spacer materials while die stress
in the rods was around 40 MPa (Fig. 22).
The female experienced a decrease in stress (14%) at the spacer with SRP 70% porous
compared to SRP, yet the bone-spacer interfaces had an increase in stress (3-6%). Contrary to the
female model, the male model experienced a decrease in stress (6-12.5%) at both bone-spacer
41


interfaces with the decrease in stress (30%) at the SRP 70% porous spacer compared to SRP (Fig.
22). There was an increasing stress at the L4 anterior bone location in both models as the stiffness
of the spacer decreased. While the female model experienced similar magnitudes of stress in both
L4 and L5 anterior bone locations, the male experienced more than 12 times greater stress at the
L4 anterior location than the L5 anterior location. The female model experienced greater stress in
the spacer than the male model for all spacer materials, and the male model experienced greater
stress in the rods than the female model.
Figure 21: Stress at multiple locations in the female model with various spacer materials.
42


Figure 22: Stress at multiple locations in the male model with various spacer materials.
The effects of the custom fit spacer compared to the original spacer with PEEK and SRP
70% porous as the material properties were observed at the bone-spacer interfaces and rods. The
bone-spacer interfaces experienced higher stress with both the PEEK and SRP 70% porous
original spacers than the custom spacers (Fig. 23). The PEEK custom spacer provided a 39%
decrease in stress at the L4 bone-spacer interface compared to the original PEEK spacer, and the
SRP 70% porous provided a 41% decrease. Similar changes in stress were seen at the L5 bone-
spacer interface. Therefore, both spacer materials caused a significant decrease in stress at the
bone-spacer interfaces with the custom fit spacer.
The L4 and L5 bone-spacer interfaces experienced a 15% and 11% decrease in stress,
respectively, with the SRP 70% porous custom spacer compared to the PEEK custom spacer. The
decrease in stress at the interfaces was not as great with the original spacers when the material
43


was changed from PEEK to SRP 70% porous. There was a 12% and 6% decrease at the L4 and
L5 bone-spacer interface, respectively.
Figure 23: Stress at the bone-spacer interfaces and rods in the male model with the original and
custom spacer.
The von Misses stress at the rods was highest with the original SRP 70% porous spacer.
It is a very minimal (1%) difference between the stresses experienced at the rods with the two
SRP 70% porous spacers. However, this shows that even though there was a large decrease in the
stress at the bone-spacer interfaces with the custom spacer, the rods do not experience any large
changes in stress. In the case with the two PEEK spacers, the rods also experienced minimal
changes (< 0.5%) in stress.
Figure 24 shows the stress distribution at die L5 bone-spacer interface with the PEEK and
SRP 70% porous custom spacers. To compare the two models, a maximum limit of 1 MPa was
set. Red shows the areas of high stress and anything above the maximum. It is clear from the
figure, that the stress at the L5 bone-spacer interface is less with the SRP 70% porous custom
spacer.
44
von Mises Stress in Rods (MPa)


Figure 24: Stress distribution at the L5 bone-spacer interface with PEEK (left) and SRP 70%
porous (right) custom spacers.
Discussion
The spacer with SRP 70% porous material properties strained significantly more in the
female model than the male model. This is important to note, because the difference in strain was
very large despite the fact that the load applied and material properties of the spacer were the
same in both models. The rods experienced much greater stress overall compared to the spacer in
both the female and male models. As hypothesized, a greater stress in the rods, with SRP 70%
porous as the spacer material, was observed in both subjects, demonstrating a shift in load due to
a less stiff spacer. The overall stress in the rods was greater in the male model than the female
model, while the stress at the spacer was at least 8 times greater in the female model. Thus the
shift in load distribution was shown to be not only affected by die material used for the spacer,
but also dependent on the subject.
Additionally, the stress experienced in the rods was more dian 40 times greater dian the
stress experienced at the bone-spacer interfaces in the male model. In the female model, there was
about a 20 times greater difference. The fact that the male model experienced greater overall
45


stress in the rods was likely due to differences in the alignment of the rods in the female spine.
This may relatively reflect clinical procedures where the screws and rods are positioned to the
best abilities of the spinal surgeon, but by no means are the same in every individual.
The custom spacer, designed to conform to the contours of the vertebral endplates,
demonstrated less stress at the bone-spacer interfaces compared to the original spacer used.
Minimal stress changes were found in the posterior rods with the custom spacer, which shows
that the rods were still bearing about the same load. Both spacer materials, PEEK and SRP 70%
porous, caused a significant decrease in stress at the bone-spacer interfaces with die custom
spacer. However, the less stiff material, SRP 70% porous, resulted in the least amount of stress at
the bone-spacer interfaces. The outcome of the custom spacer analysis showed that a greater
contact area between the spacer and bone would distribute die stress beder at the bone. A spacer
that can distribute the stress beder at the bone-spacer interface is likely to decrease the chances of
subsidence.
The metiiods used to position the spacer and posterior instrumentation, as well as the
blocks, could have been a limiting factor. The spacer and posterior instrumentation were
positioned in Simpleware in the best possible location for each model. The blocks in each model
were about the same size but were positioned slightly different depending on the easiest location
that did not interfere with the rods. The orientations of the posterior instrumentation and blocks
could have had an effect on the stresses obtained. Additionally, since the bone material properties
in each specimen were based on dieir age, this could be a reason for some of the variation. There
was only a 5-year difference in their ages, but due to gender differences in age-related trabecular
bone loss, this might be a factor.
46


Summary
An increase in stress at the rods and a decrease at the spacer with the SRP 70% porous
spacer showed the shift in load occurring during lumbar interbody fusion. The subjects differed in
the observed changes at the bone-spacer interfaces, and this helps to justify the need for patient
specific information in selection of device materials. In general, the effects the SRP 70% porous
spacer had on the vertebral body show potential for porous SRP to produce more sufficient
outcomes post-surgery. The results of the custom spacer show great strides in the direction of a
new type of spacer that could improve the outcome of lumbar interbody fusion. Though the
occurrence of subsidence is still relatively unknown, the bone-spacer interfaces are likely the best
location for observance of stress and how this may predict the risk of subsidence.
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CHAPTER VII
CONCLUSIONS AND FUTURE WORK
Conclusions
Modeling of the lumbar spine is a valuable tool for evaluating stress in the bone due to
age-related changes and implant materials and design. Modeling is a non-invasive tool that can be
used to develop the selection of device materials on a patient-specific basis. This thesis explored
the effects of age-related changes as well as the effect of the implant material so as to better
quantify these factors. With age-related cortical thinning and trabecular bone loss, the load shifted
to the rods. A shift in load from the trabecular core to the cortex was also evident with an increase
in age. Though there was simultaneous cortical thinning with the trabecular bone loss, the load-
bearing responsibility of the cortex came more into play with the increase in age.
There was an increase in stress in the rods with a decrease in stress at the spacer as the
stiffness of the spacer material decreased. Therefore, the SRP 70% simulated porosity showed the
greatest shift in load. The SRP 70% simulated porosity spacer shows potential to produce more
sufficient outcomes post-surgery. However, there were variations in the stress distribution
between the two subjects used in this study, which shows a great need for patient-specific
information in determining the optimal implant materials. The custom fit spacer that was
developed in the models to conform to the curvature of the vertebral endplates showed great
strides in the direction of a new type of spacer. There is a good 6 weeks between when a patient
receives medical imaging to when they receive lumbar interbody fusion. That is plenty of time for
a custom spacer to be machined or even better, printed on a 3-D printer.
48


Future Work
The work presented in this thesis was the first attempt at creating a working L4-L5 model
that represents lumbar interbody fusion with posterior instrumentation to measure differences in
strain and stress in the lumbar spine due to age-related changes and spacer material. Only two
cadaver specimens were used in this study and therefore, a larger study will be conducted to
better quantify the affects of age-related changes and implant material, as well as how other
factors, like gender and weight, affect lumbar interbody fusion. The validation of this study
showed that the homogeneous model better represented experimental testing than the varying
material properties used in the grey-scale based model. However, a larger cadaver study will look
further into this finding to discover which model will best represent lumbar interbody fusion with
posterior instrumentation.
Future work will observe the role of cortical thickness and trabecular bone modulus more
closely. Maintaining one of these variables will help to discern how much each of them plays a
role in bearing the load in the lumbar spine. Axial loading was the only type of load included in
this model but bending and torsion should also be represented. This model assigned a constant
cortical bone cortex around the whole vertebral body but the vertebral endplates will be modeled
separately in a future model due to the different properties of the endplates and their significance
at the bone-spacer interfaces. Finally, SRP must be tested to figure out whether it could be used
as the spacer material in lumbar interbody fusion.
49


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Full Text

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FINITE ELEMENT MODELING OF LUMBAR INTERBODY FUSION by LILLIAN S. CHATHAM B S University of Colorado Denver 2012 A thesis submitted to the University of Colorado in partial fulfillment of the requirements of the degree of Master of Science Mechani cal Engineering Department 2014

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! ii This thesis for the Master of Science degree by Lillian S. Chatham h as been approved for the Mechanical Engineering Department by R. Dana Carpenter Chair Christopher M. Yakacki Ronald A. L. Rorrer May 2 2014

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! iii Chatham, Lillian S. (M.S., Mechanical Engineering) Finite Element Modeling of Lumbar Interbody Fusion Thesis directed by Ass istant Professor R. Dana Carpenter. ABSTRACT To help reduce complications fol lowing lumbar interbody fusion such as subsidence there is a need for patient specific selection of de vice component s T his thesis investigate d the effects of age related changes and the spacer material on the stress and strain in the lumbar spine after inte r body fusion with posterior instrumentation. An exploratory addition compared a normal spacer with a custom fit spacer that conformed to the vertebral endplates. Finite element models of the L4 L5 unit were developed from computed tomography of two cadaveric lumbar spines. The models were loaded under compression and strain and stress were observed in various locations. The models were validated with experimental testing. In one study cortical thickness and trabecular bone material properties were altered to simulate age related changes of cortical thinning and th e loss of volumetric trabecular bone mineral density In both models stress increased with age at the L4 and L5 anterior bone, and in the posterior rods One model had a similar correlation at all analyzed locations while the other model experienced smal ler changes at the bone spacer interfaces and spacer. The stress at the L4 and L5 anterior locations at a minimum, doubled between the 20 and 90 year old model in both subjects. I n the other study the effects of space r material were investigated The ef fects of polyetheretherketone titanium, s elf reinforced p olyphenylene (SRP) and SRP simulated 70% porosity were tested. SRP with 70% porosity produced a load shift in stress from the spacer to the rods Though titanium is approximately 25 times stiffer t han PEEK, d ifferences in stress levels at

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! iv all locations were relatively small when the spacer material was changed from titanium to PEEK. However, when a factor of stiffness was reduced by 244 in SR P with 70% porosity, stress at the bone spacer interfaces de creased (8 15%) in one model. T his study demonstrate d variation in subject respons e to different spacer materials, and the changes in stress distributions between human subjects The custom spacer implant significantly decrease d stress at the bone spacer interfaces. These findings show the effects of age related changes and spacer material o n the mechanical environment in the bone following lumbar interbody fusion The form and content of this abstract are approved. I recommend its publication. Ap proved: R. Dana Carpenter

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! v DEDICATION I dedicate this thesis to all my family and friends who have been an amazing support throughout this intensive process.

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! vi ACKNOWLEDGEMENTS I wish to express my sincerest thanks to my adviser, R. Dana Carpenter, for giving me the opportunity to research in the area of biomechanics and for his constant guidance. I want to recognize Dr. Sam Welch and Dr. Ron Rorrer for being constant mentors throughout my undergraduate and graduate degrees. Craig Lan ning and Dr. Vikas Patel should be acknowledged for getting me started in my research. I also want to thank Dr. Chis Yakacki for being on my graduate committee along with Dr. Carpenter and Dr. Rorrer. I am sincerely grateful for being selected as a Nationa l Science Foundation GK 12 Fellow. It has provided a financial support in my last year, and I have become a better presenter of my research and learned a lot in the process. The Tashiro Tutoring Scholarship was another financial support that deserves menti oning. There are plenty of people that have made an impact on my education and even if they are not directly named here, I thank all of them.

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! vii TABLE OF CONTENTS CHAPTER I. INTRODUCTION ................................ ................................ ................................ ........................ 1 Purpose ................................ ................................ ................................ ................................ ......... 1 Outline ................................ ................................ ................................ ................................ .......... 5 II. MODEL DEVELOPMENT OF AN L4 L5 UNIT ................................ ................................ ...... 7 Introduction ................................ ................................ ................................ ................................ .. 7 Methods ................................ ................................ ................................ ................................ ........ 8 Model Preparation ................................ ................................ ................................ .................... 8 Material Properties ................................ ................................ ................................ ................... 9 Finite Element Analysis ................................ ................................ ................................ ......... 10 Summary ................................ ................................ ................................ ................................ .... 11 III. PRELIMINARY WORK ................................ ................................ ................................ ......... 12 Introduction ................................ ................................ ................................ ................................ 12 Methods ................................ ................................ ................................ ................................ ...... 12 Model Development ................................ ................................ ................................ ............... 12 Material Properties ................................ ................................ ................................ ................. 12 Finite Element Analysis ................................ ................................ ................................ ......... 14 Results ................................ ................................ ................................ ................................ ........ 14 Di scussion ................................ ................................ ................................ ................................ .. 17 Summary ................................ ................................ ................................ ................................ .... 17 IV. MODEL VALIDATION ................................ ................................ ................................ ......... 19 Introduction ................................ ................................ ................................ ................................ 19 Methods ................................ ................................ ................................ ................................ ...... 19 Model Determination ................................ ................................ ................................ ............. 20 Convergence Study ................................ ................................ ................................ ................ 21 Experimental Testing ................................ ................................ ................................ ............. 21 Results ................................ ................................ ................................ ................................ ........ 23 Discussion ................................ ................................ ................................ ................................ .. 25 Summary ................................ ................................ ................................ ................................ .... 26 V. E FFECTS OF AGE RELATED CORTICAL THINNING AND TRABECULAR BONE LOSS ON THE MECHANICS OF LUMBAR SPINE FUSION ................................ .................. 27

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! viii Introduction ................................ ................................ ................................ ................................ 27 Methods ................................ ................................ ................................ ................................ ...... 29 Model Preparation ................................ ................................ ................................ .................. 29 Material Properties ................................ ................................ ................................ ................. 29 Finite Element Analysis ................................ ................................ ................................ ......... 30 Results ................................ ................................ ................................ ................................ ........ 30 Discussion ................................ ................................ ................................ ................................ .. 33 Summary ................................ ................................ ................................ ................................ .... 34 VI. EFFECTS OF DIFFERENT SPACERS ................................ ................................ .................. 36 Introduction ................................ ................................ ................................ ................................ 36 Methods ................................ ................................ ................................ ................................ ...... 37 Model Preparation ................................ ................................ ................................ .................. 37 Material Properties ................................ ................................ ................................ ................. 37 Finite Element Analysis ................................ ................................ ................................ ......... 39 Results ................................ ................................ ................................ ................................ ........ 39 Discussion ................................ ................................ ................................ ................................ .. 45 Summary ................................ ................................ ................................ ................................ .... 47 VII. CONCLUSIONS AND FUTURE WORK ................................ ................................ ............. 48 Conclu sions ................................ ................................ ................................ ................................ 48 Future Work ................................ ................................ ................................ ............................... 49 REFERENCES ................................ ................................ ................................ ............................... 50

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! ix LIST OF FIGURES FIGURE 1: Comparison of a healthy disc and degenerated disc [3]. ................................ .............................. 1 2: Example image of spacer, bone graft, and posterior instrumentation involved in lumbar interbody fusion [4]. ................................ ................................ ................................ ......................... 2 3: Meshed male (left) and female (right) models with CAD developed spacer and posterior instrum entation (pedicle screws and rods). ................................ ................................ ...................... 9 4: Cut view of L4 L5 unit model to show shell and core compartments (gray=core, blue=shell). 11 5: Calculations of average elastic modulus based on the axial rigidity of the combined trabecular and cortical compartments. ................................ ................................ ................................ ............ 13 6: Average values of tensile principal strain and compressive principal strain of subject 1 (female top) and subject 2 (male bottom). ................................ ................................ ................................ 15 7: Maximum tensile strain at lateral endplate and in posterior rods with two spacer materials: PEEK and titanium; subject 1 (female top), subject 2 (male bottom). ................................ ........ 16 8: Anterior view of L4 L5 unit with locations of strain rosettes at the spacer and L4 vertebral body. ................................ ................................ ................................ ................................ ............... 22 9: Posterior view of L4 L5 unit with location of uniaxial strain gages at the rods. ....................... 22 10: Comparison of experimental results and the grey s cale based FE model (p = 0.096) ............. 24 11: Comparison of experimental results and the two part homogeneous FE model (p < 0.001). 24 12: Mesh convergence results for L4 L5 model stiffness. Differences in model predicted stiffness converged to less than 2% at a mesh density of 93,700 nodes. ................................ ..................... 25 13: Vertebral body from a younger individual (top) and from an elderly individual (bottom) [15]. ................................ ................................ ................................ ................................ ........................ 28 14: Stress at multiple locations in the age simulated female model at 20, 65, and 90 years old (65 was actual age of specimen). ................................ ................................ ................................ .......... 31 15: Stress at multiple locations in the age simulated male model at 20, 70, and 90 years old (70 w as actual age of specimen). ................................ ................................ ................................ .......... 32 16: Average maximum principal tensile and compressive strain at multiple locations in the age simulated female model. ................................ ................................ ................................ ................ 32 17: Average maximum principal tensile and co mpressive strain at multiple locations in the age simulated male model. ................................ ................................ ................................ ................... 33 18: Comparison of original spacer and custom fit spacer in the male model. ............................... 39 19: Average maximum principal tensile and c ompressive strain at multiple locations in the female model with various spacer materials. ................................ ................................ ............................. 40 20: Average maximum principal tensile and compressive strain at multiple locations in the male model with various spacer materials. ................................ ................................ ............................. 41 21: Stress at multiple locations in the female model with various spacer materials. ..................... 42 22: Stress at multiple locations in the male model with various spacer materials. ........................ 43 23: Stress at the bone spacer interfaces and rods in the male model with the original and custom spacer. ................................ ................................ ................................ ................................ ............. 44

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! x 24: Stress distribution at the L5 bone spacer interface with PEEK (left) and SRP 70% porous (right) custom sp acers. ................................ ................................ ................................ ................... 45 !

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! 1 CHAPTER I INTRODUCTION Purpose Lower back pain is problematic worldwide, causing daily discomfort and restriction of activities. It is estimate d that as much as 80% of the population will experience a back problem at some time in our lives [ 1 ] Back pain is one of the most common reasons for missed work, and it is the second most common reason for visits to the doctor's office [ 2 ] Arthritis, poor posture, obesity, and psychological stress are all factors in increasing the risk of back pain [ 2 ] There are multiple issues that can occur in the back, ranging from injury of the intervertebral discs (like herniated or bulging disc) to ligaments and nerves that can be stretched or pinched causing various scales of pain. Degenerative Disc Disea se (DDD) is a common reason for lower back pain and it occurs when the disc begins to degenerate, causing pain due to decreased space between vertebrae (Fig. 1 ) Though this can be caused by injury or trauma such as a car accident it is more common as a result of aging [ 3 ] The disc has no blood supply and therefore cannot repair itself, so wear and tear typically develops as we age [ 4 ] Figure 1 : Comparison of a healthy disc and degenerated disc [ 5 ]

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! 2 For extreme cases wi th great pain, lumbar spine fusion is the surg ical solution. A spacer or spinal cage is used to provide a fixed space between the vertebrae (Fig 2) Currently, polyetherether ketone (PEEK) and Titanium are often used as the spacer material. Bone graft is us ed in the process to stimulate bone growth to fuse the two vertebrae together, eliminating motion in that segment. Posterior instrumentation, such as titanium screws and rods, may be used to fixate the spinal unit during the healing process so as to restor e the height of the intervertebral disc and provide stability. Figure 2 : Example image of spacer, bone graft, and posterior instrumentation involved in lumbar interbody fusion [ 6 ] There is a clinical need to understand the fusion process better to determine the causes of excessive spinal cage subsidence lack of bone growth, and increased ri sk of multi level fusions. Spinal surgeons have experienced all of these issues post surgery and seek to discover the cause so that the solution may be found. Subsidence of the spinal cage is when the cage collapses a significant amount into the vertebral body following su rgery, consequentially voiding the purpose of the cage placement. The cage needs to support the vertebrae through the fusion process but the fusion rate varies in patients and is unpredictable. In a study [ 7 ] with 32 procedures of anterior

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! 3 lumbar interbody fusions using a PEEK cage, 4 cases fused in 3 months, twenty five cases fused within 6 months, and three cases resulted in nonunion (no fusion). In the cases of nonunion, a second surgery with additional instrumentation for fixation stability was necessary. Some patients underwent fusion at multiple spine levels. Out of all the fused l evels, subsidenc e was found in five spinal units [ 7 ] Some of the patients had spondylolisthesis, which is a condition where one vertebra slips forward or backward becoming misaligned with adjacent vertebra e Though this study was not large enough to make concrete conclusions, spondylolisthesis and obesity (high BMI) were shown to increase the rate of cage subsidence. Another paper [ 8 ] summarized multiple studies of the impact of subsidence on clinical outcomes and radiographic fusion rates but that study was limited to anterior cervical (neck) discectomy and fusion. Exploration of subsidence in the lumbar spine is relatively limited and a better understanding of the endplate structure and the effect s of implant material may be essential in finding the source of failure. The stiffness of PEEK and titanium, the common implant materials, can be orders of magnitude stiffer than the endplate of the vertebral body T herefore, a less stiff material may provide less incidences of subsidence. However, the material must still be able to produce eff icient stability for the course of the fusion process in which, as mentioned before, the length of time is unpredictable in patients. An interbody cage with soft (low elastic modulus, E = 19 MPa) layers on the bone implant interface was tested in a finite element study of an L4 L5 segment [ 9 ] The study showed that the peak contact pressure was significantly reduced with this cage, which could be a strategy for de creasing the risk of cage subsidence [ 9 ] Along with subsidence, the lack of bone growth is an issue in successful operations because without bone growth the f usion will not occur resulting in a failed spine fusion and the need for an additional operation. As briefly mentioned in one of the previous studies, nonunion occurred in a few cases, and nonunion was due to the lack of bone growth. As a solution, additi onal instrumentation was used to provide stability. Though instrumentation is thought to

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! 4 decrease the incidences of nonunion, it still occurs in pa tients [ 10 ] Some possible explanations as to why this occurs could be stress shielding, disrupted blood supply, chroni c inflammation, and bone quality [ 11 ] Multiple studies compare instrumentation to non instrumentation in various fusion surgeries and there is not a solid consensus on one versus the other. What may work in one patient may not work in another. Nonunion is difficult to quantify due to the many factors involved. A retrospective study [ 12 ] examined the surgical outcomes of non instrumented posterolateral lumbar fusion (PLF) in order to compare cases with union versus cases with nonunion. The follow up was conducted with 42 patients and in 26% of the patients nonunion was noted. Though bone growth is a necessity for a successful spine fusion it is a very complex matter and will not be directly invest igated in this work. Studies have shown that there is an increased risk of fusion in other levels in the lumbar spine after the first spinal unit fusion [ 13 ] [ 14 ] [ 15 ] [ 16 ] It would seem that this would be a direct relation to the altering load sharing involv ed in this fusion process. Posterior instrumentation is used to carry much of the load during healing, but the devices do not serve a purpose once the spinal unit is fused. The load must be carried elsewhere, and it is thought that the adjacent levels are experiencing a greater load after fusion completion. In an anterior lumbar interbody fusion (ALIF) study with six cadaveric lumbar spine specimens, the biomechanics of neighboring unfused segments was investigated. When the lumbar spine units were loaded in 15¡ of flexion with L4 L5 unit fused, there was an increase in segmental mobility at neighboring levels and there was an increase in intradiscal pressure in all unfused segments in flexion [ 17 ] In another study, the risk factors involved in adjacent segment degeneration after po sterior lumbar spine fusion were analyzed in 81 patients. Out of the 81 patients, 9 required a second operation where degeneration occurred in the upper adjacent segments in 8 patients and in the lower adjacent segments in one patient. Factors such as sex and age were used in evaluating the increased risk of degeneration in adjacent segments, and there was a significant correlation with patients older than

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! 5 50 years having a higher risk [ 16 ] The work of this thesis will analyze the stresses in various locations in an L4 L5 model for evaluation of load sharing during lumbar spine fusion with posterior instrumentation. Age and gender will be taken into account, but due to the small sample size, no strong conclusions will be made in relation to these factors. There is a need for patient specific selection of devi ce components to reduce complications following lumbar interbody fusion such as subsidence, nonunion, and increased risk of multi level fusions The purpose of this study was to develop a working L4 L5 model that represents lumbar spine fusion with posteri or instrumentation, so as to observe differences in strain and stress in the lumbar spine due to age, gender, and various spacer materials in order to begin to provide a quantitative rationale for the use of specific implant material s and instrumentation o n a patient specific basis. Preliminary work led to a few hypotheses for each study conducted in this thesis. It was hypothesized that there will be a shift in load to the posterior rods with age related cortical thinning and trabecular bone loss. Addition ally, the vertebral cortex will bear more of the load after trabecular bone loss. In respect to the spacer material, a spacer with a modulus closer to trabecular bone will shift the load from the spacer and bone, to the rods. Furthermore a less stiff spac er will reduce stress at the bone spacer interfaces. Even more a spacer that conforms to the contours of the vertebral endplates will distribute the stresses more evenly, decreasing the stress at the bone spacer interfaces. Outline Various methods were u sed in developing an accurate and workable model of the L4 L5 unit for strain and stress evaluation after lumbar spine fusion with posterior instrumentation. Chapter II depicts the process taken to develop the L4 L5 unit used in this thesis. The imaging to three dimensional (3 D) model process, materials used, and finite element analysis are explored thoroughly. The model development and direction of this thesis were determined from preliminary work, which is addressed in Chapter III. Though the main purpos e of this thesis is to

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! 6 use 3 D modeling of the lumbar spine to observe changes in strain due to parameters such as age and device material selection, the validation of the model is significant for confidence in predictability (Chapter IV). Validation inclu des comparison to experimental testing and a convergence study for appropriate mesh density for the models. The preliminary studies prompted the final investigations which will be presented using the final model in Chapters V VI. Chapter VII summarizes th e material contained herein and discusses the path forward for this research. ! ! ! !

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! 7 CHAPTER II MODEL DEVELOPMENT OF AN L4 L5 UNIT Introduction Research into the three dimensional distribution of mechanical stress after lumbar spine fusion has been relati vely limited. Spinal surgeons have found several complications with the surgery, mentioned previously, and seek to find solutions. Due to the limitations of testing on human subjects and the expense of cadaveric specimens, finite element (FE) modeling is p erhaps the best way to research the effects of patient specific anatomy, bone quality and device design on the process of lumbar spine fusion and to discover what variations may affect the outcome of this surgery. The spine is a very complex system with n on linear behavior; however, if a linear model can be used to explore age related effects and material implant effects on the bone, this will provide a sufficient method of obtaining subject specific information for proper device selection based on modelin g To observe the effects of age related cortical thinning and trabecular bone loss and the effects of the spacer material properties on the stress and strain in the lumbar spine after lumbar interbody fusion, a model needed to b e developed. Lumbar spine f usion is most commonly performed first in the L4 L5 segment of the spine. Therefore, a L4 L5 FE model was developed. Posterior instrumentation and a spacer were included in the model to replicate the surgical procedure. Pedical fixation is not always incl uded, especially in cases of anterior lumbar interbody fusion (ALIF), and it is thought to produce greater risk of multi level fusions due to increased stress on adjacent levels. In a recent study [ 18 ] the effects of ALIF with and without pedical fixation were explored using FE analysis. This study concluded that a stand alone interbody cage was sufficient for stability and better replicated an intact spine. Thus, ide ally a

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! 8 surgical procedure that does not require the use of posterior instrumentation would be preferred, but for the purpose of this study aimed at simulating current procedures, they were included. The development of the L4 L5 unit with posterior instrum entation, involving imaging of cadaveric specimens and computing software, is explained further in the following section. Methods Model Preparation Three dimensional linear FE model s of the L4 and L5 vertebrae were developed from computed tomography (CT) data (v oxel size = 0.7x0.7x0.9mm) of two cadaveric lumbar spine s One donor was a 70 year old male who had died from respiratory failure and sepsis and the other donor was a 65 year old female who had died from severe sepsis. Quantitative CT (QCT) imaging w as performed on a Gemini TF 64 ( Philips, Amsterdam, The Netherlands). A tube potential of 120 kVp was used. A QCT reference phantom (Mindways Software, Inc., Austin TX) was used to obtain bone mineral density data from image intensity. The data from ima ging were saved as DICOM files which were then imported into ScanIP (Simpleware Ltd, Exeter, UK). Segmentation and smoothing were performed to obtain the model s of the L4 L5 unit. An interbody spacer and posterior instrumentation (pedicle screws and 6 mm or 5.5 mm diameter rods for subject 1 and subject 2, respectively ) were designed using SolidWorks (Dassault Systemes, Waltham, MA) and then integrated into the model using S impleware's +CAD program They were designed based on measurements of instrumentati on currently used by the clinical advisor for the study, Dr. Vikas Patel The spacer was positioned between the inferior surface of L4 and superior surface of L5. Blocks were incorporated into the model to depict the urethane blocks that were used to pot the superior endplate of L4 and the inferior endplate of L5 during mechanical testing (see Chapter IV). In addition to recreating the experimental setup, the urethane blocks help to

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! 9 distribute the applied loads evenly across the superior and inferior surfa ces of the bones in the model. Facet joints, including thin cartilage layers, were included in the model and assigned as a contact pair. A contact pair was also assigned between L4 and the spacer and L5 and the spacer. The entire assembly was then meshed w ith linear, four noded tetrahedral elements using the adaptive meshing algorithm in Simpleware's +FE program (Fig. 3 ) This model represents the condition immediately following surgery. Figure 3 : Meshed m ale (left) and female ( right) m odels with CAD developed spacer and posterior instrumentation (pedicle screws and rods). Material Properties Homogeneous material properties were used for the trabecular core and the cortical shell of the vertebrae. The cortical bone was assigned a n elastic modulus (E) of 12 GPa and Poi s son's ratio ( ) of 0.3 [ 19 ] Due to the relatively low resolution provided by the clinical CT system used to obtain the images, the cortical shell could not be directly de fined based on image data. Instead, t he cortical shell thickness in the models was determined by fitting a linear relationship between age and cortical thickness. Mosekilde [ 20 ] provided a range of cortical thickness values in the vertebral body for age ranges 20 40 and 70 80 years Using the linear fit equat ion cortical thickness es of 0.27 mm and 0.29 mm were determin ed for the 70 year old and 65 year old subjec t, respectively.

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! 10 A linear relationship between QCT measurements of trabecular volumetric bone mineral density (vBMD) in the lumbar spine and age was used to est imate vBMD loss with age [ 21 ] Riggs et al. provided an average value of trabecular vBMD measured at the mid portion of L1, L2 and L3 between the ages of 20 29 and then found an average 47% and 54% decrease in trabecular vBMD from 20 90 years in a study with 3 23 men and 373 women respectively [ 21 ] A linear relationship between trabecular vBMD and elastic modulus was then used to estimate the corresponding age related d ecline in E with a > 0.01 !" (Eqn 1) [ 22 ] Elastic modulus is in units of MPa and is t he QCT density in units of !" Based on this relationship, an E of 400 MPa and of 0.3 were assigned for the male subject. An E of 429 MPa and of 0.3 were assigned for the female subject. The rods and screws were treated as titanium with an E of 110 GPa and of 0.3 [ 19 ] The blocks were assigned an E of 6832 MP a and a of 0.3 (manufacturer's data) Cartilage lined facet joints were included in t he model and cartilage regions were assigned an E of 6 MPa and a of 0.49 [ 23 ] Finite Element Analysis The model s were exported as a readable format for Abaqus (Simulia, Providence, RI). In Abaqus, the skin feature was used to create a homogeneous shell around the vertebrae. The shell around the vertebrae was used to represent a thin cortex, which had a thickness less than the voxel size of the original QCT image. A cortex of 0.27 mm and 0.29 mm w ere applied to the male subject and female subject, respectively, based on published data of ag e dependent cortical thinn ing [ 20 ] and were later modified to simulate age related effects (Fig. 4 ) ! ! !" ! !"# !"!# !"# !" ! ( 1 )

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! 11 Figure 4 : Cut v iew of L4 L5 unit model to s how shell and co re c ompartments (gray=core, blue=shell). The inferior end of the block attached to L5 was fixed in all directions and a 0.145 MPa pressure was applied to the superior end of the block attached to L4. The pressure of 0.145 MPa was obtained from taking 730 N divided by the area of the urethane block. The load of 730 N was chosen based on in vivo measurement s of a patient rising from a chair, available in the OrthoLoad database ( www.orthoload.com ) [ 24 ] [ 25 ] Groups of elements were selected at the L4 and L5 anterior region s anterio r spacer region, posteri or rods region, and bone spacer interface at L4 and L5 for analysis of stress and strain. The average maximum tensile and compressive str ain (maximum and minimum principal strains, respectively) and the von Mises stress were obtaine d at each location. Summary The methods outlined in this chapter are the general methods of the model development used in Chapters III VI. Other specific model parameters will be specified in each chapter where appli cable. T he following chapter will expl ore the preliminary work that directed the work presented in this thesis.

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! 12 CHAPTER III PRELIMINARY WORK Introduction The L4 L5 model has evolved throughout the course of this thesis work. The model began as a simple homogeneous model without the inclusion of urethan e blocks or facet joints with cartilage layers. The urethane blocks were later included to better represent the experimental testing and the facet joints were included to better approximate the anatomy Though the final model is also homogenous, the model developed for the preliminary work took an average elastic modulus of combined trabecular and cortical compartments. The relationship s between age related changes, including cortical thinning and trabecular bone loss, and strain in the L4 L5 model w ere ob served. The effects of PEEK and titanium as the implant material were also tested in the model. Methods Model Development The model development outlined in Chapter II applies to this model with the only differences being that neither the blocks nor the fa cet joints in combination with the cartilage layers were included. The entire assembly was meshed with linear, four noded tetrahedral elements using the adaptive meshing algorithm in Simpleware's +FE program. Note that these models were developed prior to the convergence study and therefo re contain a larger mesh size. Material Properties A homogeneous value of E was assigned to each vertebra based on the axial rigidity of the combined trabecular and cortical compartments. Figure 5 shows how the vertebral bo dy was treated as an ellipse to obtain the area for use in calculations of an average elastic modulus.

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! 13 Figure 5 : Calculations of average elastic modulus based on the axial rigidity of the combined trabecular and cortical c ompar tments. In a study presented at the American Society of Bone and Mineral Research 2012 Annual Meeting [ 26 ] a homogeneous E was calculated based from trabecular bone l oss and cortical thinning with increasing age for two subject s: a male and a female. Table 1 displays the E value assigned to each subject for a range of ages. The rods and screws were treated as t itanium with an E of 110 GPa and of 0.3 [ 19 ] The spacer was tr eated as PEEK with an E of 4.6 GPa and of 0.38 [ 27 ] Table 1 : Material properties applied to the bone for each specimen with age related changes and the material properties applied to the instrumentation. Elastic Modulus (MPa) Pois s on's Ratio Cortical Thickness (mm) Male (30, 70, 90 yr) 1099.6, 715.7, 564.7 0.3 0.45, 0.29, 0.18 Female ( 3 0, 65, 90 yr) 1133.1, 761.5, 560.3 0.3 0.45, 0.27, 0.18 PEEK 4,600 0.38 N/A Titanium 110,000 0.3 N/A Another study, presented at Orthopaedic Research Society 2013 Annual Meeting [ 28 ] deter mined the effects of spacer material in the same two subjects. Titanium and PEEK were the materials assigned to the spacer (Table 1).

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! 14 Finite Element Analysis The model was exported as a readable format for Abaqus (Simulia, Providence, RI). The inferior en d of L5 was fixed in all directions and a distributed pressure was applied to the superior end of L4. A load of 400 N was divided by the average cross sectional area taken at the mid section of L4 to obtain the pressure applied: 0.38 MPa The load of 400 N was chosen from a recommendation for the average pre load on the spine in a paper by Goel et al [ 29 ] Groups of e lements were selected at the posterior rods bone implant interface and lateral endplate of L5 for analysis of average maximum tensile and compressive strain at each location. Results Cortical thickness and trabecular elastic modulus were varied in both models to simulate age related changes in the bone As hypothesized, the strain in the bone increased with age, and different locations experienced various levels of strain. At the endplate of L5, the maximum tensile and compressive strain in the 90 year old was nearly double that in the 30 year old (Fig. 6 ). The female specimen experienced overall greater tensile strains at the bone implant interface, while the male specimen had greater tensile strain at the lateral endplate of L5.

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! 15 Figure 6 : Average values of tensile principa l strain and com pressive principal strain of s ubject 1 (female top) and s ubject 2 (male bottom) ! ! The effects of PEEK compared to a Titanium spacer were observed in both subjects. The trabecular elastic modulus and cortical thickness in relation to th e current age of the cadaveric specimens remained constant while only the spacer material properties were adjusted. The strain at t he lateral endplate of L4 and in the poste rior rods was observed (Fig. 7 ).

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! 16 Tensile s train at the lateral aspect of the infe rior endplate of L4 and in the posterior rods was greater in subject 1 for both PEEK and Titanium spacer implants. Furthermore, subject 1 experienced higher strain at both locations with a PEEK spacer implant, while subject 2 had lower st rain in the poster ior rods with a PEEK spacer implant. Figure 7 : Maximum tensile str ain at lateral endplate and in posterior r ods with two spacer materials: PEEK and t itanium; subject 1 (female top ), s ubject 2 (male bottom ).

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! 17 Discussion The re sults of the first study demonstrate d the effects of age related cortical thinning and trabecular bone loss on the mechanical environment in bone following interbody fusion Furthermore, the different strain levels in the two specimens demonstrate the impo rtance of using patient specific information. Though it is impossible to compare the effects of gender and weight due to small sample size, we expect that both parameters play a role in how the bone is affected. Additionally, when the spacer material was altered, both specimens experienced difference levels of strain in the two locations: lateral endplate and posterior rods. This further concludes the need for patient specific information when choosing device material. The changes in strain in the posterio r rods due to different implant materials, is of particular relevance due to its load sharing significance. A limitation of these results was the different alignment of the spine in both subjects that could have altered the strain distribution. At the sam e time, this also helped to solidify the importance of subject specific information to determine the optimal mechanical environment post surgery. The subjects differed in gender, weight, height and age, which are all possible links to the trabecular BMD of the lumbar spine and could be used to project optimal subject specific surgery procedures. Summary The preliminary work helped determine the direction of this thesis. The first study demonstrate d the effects of age related cortical thinning and trabecul ar bone loss on the mechanical environment in bone following interbody fusion [ 26 ] Therefore, a similar method was applied to the final models and results are presented in Chapter V. The different effects of the spacer material on each subject in the second study [ 28 ] began to show the importance of patient

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! 18 specific information for selection of device components, and this concept is explored further in Chapter VI. All future work uses the methods outlined in Chapter II with a trabecular core and cortical shell. Chapter IV will address the validation of these mo dels and the process of selecti n g the most useful combination of modeling methods.

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! 19 CHAPTER IV MODEL VALIDATION Introduction Modeling of the lumbar spine can be a valuable tool for evaluating the biomechanics, geometric orientation, and optimal implant materials and design, but validatio n is important for assurance that relative differences in strain at various locations are accurately depicted Mechanical testing of the cadaver specimens was conducted and the experimental data w ere compared with the results obtained from the FE models. Various models were explored in the process with the goal of finding the most accurate model for estimating strain in the lumbar spine after interbody fusion with posterior instrumentation. The model was determined by comparing multiple approaches of defining the material properties in the lumbar spine: homogenou s, grey scale based, and two methods of a two part (cortical shell and trabecular core) homogeneous model. Once the model was determined, a convergence study was conducted in order to define the mesh density of the models. The L4 L5 unit model was validate d and determined for use in all other studies. Methods In order to compare to experimental data, t he rods and spacer in the model were assigned a shell of 0.01 thickness and the same assigned material properties as the instrumentation. The shells allowed the directional surface strain to be obtained so as to more accurately model the experimental strain gage measurements.

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! 20 Model Determination After preliminary work with the homogeneous L4 L5 model, a grey scale based model was hypothesized to produce more comparable results to experimental data. Using the grey scale based material type feature in Simpleware, each voxel was assigned an elastic modulus. Keyak et al. [ 30 ] provided equations to compute E from ash density (Eqns. 2 4). All voxels under 1 mg/cc were assigned 1.00x10 4 MPa to eliminate all negative values representing air pockets and fat areas. Using clinically realistic imaging methods, it is difficult to direct ly depict the cortical shell due to its miniscule thickness, but it is important in modeling the lumbar spine because of its role in sharing load with the trabecular bone compartment. Therefore a lumbar spine model that represented a cortical shell and tra becular core was hypothesized to help predict strain in the bone. A cortical shell and trabecular core was originally tested using features in Simpleware. The pixel size of the cadaver specimen images was reduced to fit the thickness size of the cortical s hell. The other method used to create a two part homogenous model was the application of the SKIN feature in Abaqus where a shell with input thickness and homogeneous E was added to the vertebrae [ 31 ] [ 32 ] [ 33 ] The trabecular cor e was represented with a homogeneous E valu e ! !! !"" ! !" ! !" !"# !"# !" ! ! !" ! !" ! ( 2 ) ! !"#$ !" ! !"# !"# !"# ! !" ! ! !" ! ! !" ! !" ! ( 3 ) ! !" !"" ! !" ! !" !"# !"# ! !" ! ! !" ! !" ! ( 4 )

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! 21 Convergence Study A mesh convergence study was conducted to determine the mesh density to be used in subsequent models. Starting with a mesh size containing 26,593 nodes, the mesh was refined until convergence was obtained. Mesh convergence was determined by measuring the vertical stiffness of the model at the various mesh sizes until the chan ge in stiffness was less than 2 %. Experimental Testing After imaging the cadaveric spine, the L4 L5 motion segment was e xcised. A spinal surgeon (VVP) inserted a spacer, screws, and rods into the cadaver specimen. The L4 superior endplate and the L5 inferior endplate were then potted in urethane (Dyna cast, Kindt Collins Company, Cleveland, OH). Aluminum fixtures were creat ed to hold the vertebrae in the urethane while it cured. The L4 L5 segment with interbody spacer and posterior instrumentation was placed in compression in an MTS Insight with a 30 kN load cell. Strain rosettes (L2A 06 062WW 350, Vishay Micro Measurements, Raleigh, NC) and uniaxial strain gages (L2A 06 125LW 120, Vishay Micro Measurements, Raleigh, NC ) were purchased and tested prior to using. An aluminum bar was used to check the accuracy of the strain rosettes. A 0.5395 kg weight was suspended on the alum inum bar and the strain was predicted by beam theory using the cross sectional area and moment of inertia. Calculations resulted in 360 microstrain and using the beam theory with the published value of E (68.9 GPa [ 34 ] ) for 6061 aluminum is 346 microstrain giving a 4% error. T he strain rosettes and uniaxial strain gages were then glued with cyanoacrylate in their respective locations on the L4 L5 segment. Strain rosettes were placed on the anterior surface of the spacer and anterior surface of the L4 vertebra (Fig. 8 ) Uniaxial strain gages were placed on the posterior sides of the rods (Fig. 9 ) The mot ion segment was tested in compression at room temperature with three different peak

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! 22 loads (400, 730 and 1000 N). Specimens were kept hydrated throughout testing. During each trial (three per peak load level) the applied load was increased under displaceme nt control until the pre determined peak load was reached. Figure 8 : Anterior view of L4 L5 unit with locations of strain rosettes at the spacer and L4 vertebral body. ! Figure 9 : Posterior view of L4 L 5 unit with location of uniaxial strain gages at the rods.

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! 23 The peak principal strains on the anterior surfaces of the spacer and L4 vertebral body were calculated from rosettes and the peak strain on the posterior surfaces of the rods were measured from the uniaxial gages. Results After experimental t esting and model data collection the model was determined. The measured experimental strain and the FE model strain at each location were normalized to the corresponding peak load and plotted together Ther e was no correlation between the grey scale model and the experimental data. This led to adding a shell (using SKIN feature in Abaqus) to the model in the same manner as the two part homogeneous model. The strain at the L4 anterior location was not predict ed well in the grey scale model compared to the experimental, which is evident by the three data points farthest from the linear regression (Fig. 10). The cortical shell was assigned the same thickness and modulus as the two part homogeneous model so this would show the homogeneous trabecular bone modulus represented the experimental strain better. Therefore, t he grey scale based model still did not prove to predict strain better than the homogenous model in comparison to the experimental data and therefor e was eliminated as a model option The first two part homogenous model method in Simpleware proved to be too computationall y expensive and time intensive, and therefore this method was eliminated as a candidate. This led to using the SKIN feature in Abaqu s where a shell with input thickness and homogeneous E was added to the vertebrae Ove rall, this two part homogenous model best predicted strain in the lumbar spine in comparison to the experimental testing results ( Fig. 11 )

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! 24 Figure 10 : Com p arison of experimental results and the grey scale based FE model ( p = 0.096 ) Figure 11 : Comparison of e xperim ental results and the two part homogeneous FE m odel (p < 0.001).

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! 25 The convergence study was done to the two part homogeneous model. The stiffness converged to a less than 2% difference from 93,79 0 nodes to 252,357 nodes (Fig. 12 ). The figure shows the next mesh size as well with 377,542 nodes. There remains a less than 2% difference even between 93,790 nodes an d 377,542 nodes, where the number of nodes is 4 times greater. The mesh density that contained 93,790 nodes was therefore chosen for all models in this study. Figure 12 : Mesh convergence results for L4 L5 model stiffness. Diffe rences in model predicted stiffness converged to less than 2% at a mesh density of 93,700 nodes. Discussion The comparisons of the experimental strain and the FE model strain at the same locations led to determining the model that best predicted the stra in in the lumbar spine after interbody fusion with posterior instrumentation. The grey scale based model was hypothesized to predict strain the best; however, the comparison to experimental data showed differently. This may have

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! 26 been due to too many air po ckets depicted in the images, lowering the elastic moduli assigned to each voxel in the trabecular bone region. Therefore, t he two part homogeneous model was determined to be the best option. It resulted in an R squared value of 0.56. Thus the model had t he ability to explain 56% of the variance in measured strain. While this coefficient of determination was rather modest, the relationship was highly significant (p < 0.001), leading us to conclude that the model could be used in subsequent analyses to prod uce a realistic depiction of strain distribution and magnitude. It is likely that a greater number of locations and specimens would increase the correlation, and therefore additional experiments will be implemented in future studies. There were a few limi tations in the methods used in comparing the model to experimental results. Imaging the cadaveric specimens post surgery could have led to better comparison between the FE models and experimental results, because the exact location and orientation of the s pacer and posterior instrumentation would have been more accurately represented. Another limitation to the validation was the small number of locations used for obtaining measured strain. The trabecular core E, cortical cortex E, and cortex thickness were all applied to the model based from published data, which could also cause a mismatch in comparison to the experimental data. Summary Modeling the spine is a very complex procedure but it can be very useful in studying the biomechanics of the lumbar spi ne for optimization of surgical procedures like lumbar spine fusion as a result of DDD. The L4 L5 unit used in this work was validated in comparison to experimental data and will be used to explore the effects of age related changes (Chapter V) and effects of spacer material (Chapter VI) on the strain and stress in various locations. The following chapter will discuss how the model was developed to represent various ages and how this alters the stress and strain distribution in the lumbar spine after fusion w ith posterior instrumentation.

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! 27 CHAPTER V EFFECTS OF AGE RELATED CORTICAL THINNING AND TRABECULAR BONE LOSS ON THE MECHANICS OF LUMBAR SPINE FUSION Introduction A ge, gender, weight, and lifestyle (smoking, etc.) are all factors that affect the vertebral bone st rength mass and structure Age is the most dominant factor as there is a loss in trabecular bone density leading to an overall large decline in vertebral body strength [ 20 ] The ve rtebral body is comprised of a spongy trabecular core, compact cortical shell and endplates with similar properties to the cortical shell but with an even smaller thickness Vertebral strength is primarily determined by cross sectional area, thickness of the cortical shell and endplates, and density and structure of the trabecular core [ 20 ] V ertebral strength as a whole will not be considere d but rather the age related cortical thinning of the cortex and trabecular bone loss. Figure 13 shows a vertebral body from a yo ung and elderly individual. It is evident in this comparison that the vertebral body of the elderly individual is much less de nse than that of the younger individual. Though age is the most significant factor in affecting changes in the vertebral body, there are different age related changes among genders. Peak bone mass is reached between the ages of 25 30 in both men and women and then begins to decrease soon thereafter [ 20 ] At that point, different relationships between age and trabecular bone loss in men and women are apparent. Men already have greater bone mass and vertebral strength than women at their peak and then as they age, an increase in cross sectional area of the vertebral bodies has been seen, which has the ability to provide better load support [ 35 ] Additionally, once women reach menopause, they experience accelerated bone loss. The MrOS study is a large study that evaluates many of the fact ors mentioned plus more in men and how they affect the trabecular vBMD in the lumbar

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! 28 spine [ 36 ] Diabetes was associated with a n 11% greater trabecular vBMD at t he lumbar spine and two of the strongest negative correlations were history of fracture and height. Figure 13 : Vertebral body from a younger individual (top) and from an elderly individual (bottom) [ 20 ] The purpose of this study was to determine the effects of age related cortical thinning and loss of trabecular vBMD on the stress distribution in the spine after lumber interbody fu sion with posterior instrumentation. Though additional factors c ould be taken into account by adding additional levels of complexity to the models this study only directly looks at age related changes. The two cadaver specimens observed in this study diff er in age, weight, and gender but weight and gender will only be d iscussed with respect to inter individual differences and how these factors could correlate with observed mechanical differences

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! 29 Methods Model Preparation The model preparation outlin e d in Chapter II applies to these model s Additionally, the cross sectional area was found for both subjects. The cross sectional area was calculated by assuming an ellipsoid and averaging the measured values across the mid section of the L4 ver tebral body using imageJ (Eqn. 5) A is the area of the ellipse in units of mm 2 and a and b are the distance s measured horizontally and vertically, respectively, from the edge of the vertebral body to the center in mm. Material Properties The methods for applying the material properties outlined in Chapter II were used in these models However, t o determine the effects of age related changes in trabecular vBMD and cortical thinning, trabecular bone E and cortical thickness were calculated for a 20 and 90 year old and were assigned to the same model s (Table s 2 3 ) For details on how the trabecular bone E and cortical thickness were determined, see Chapter II (p 7 ) Table 2 : Material propert ies and cortical thickness applied to the male specimen at 20, 70, and 90 years old. Age (yr) Trabecular Bone E (MPa) Pois s on's Ratio Cortical Thickness ( !m) 20 567 0.3 500 70 400 0.3 270 90 333 0.3 180 ! ! !" ( 5 )

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! 30 Table 3 : Material proper ties and cortical thickness applied to the female specimen at 20, 65, and 90 years old. Age (yr) Trabecular Bone E (MPa) Pois s on's Ratio Cortical Thickness ( m) 20 609 0.3 50 0 65 429 0.3 29 0 90 328 0.3 18 0 Finite Element Analysis The FE analysis outl in ed in Chapter II applies to these model s A cortex with a thickness given i n Table s 2 3 dependent on age, was added as a SKIN in Abaqus The same boundar y conditions were applied to these model s Results Cortical thickness and trabecular elastic modul us were varied in both models to simulate age related changes in the bone. A linear increase in stress in correlation with an increasing age was evident at the L4 and L5 anterior locations and at the rods in both models The stress in the L4 anterior locat ion was 8 13 times greater compared to the L5 anterior location in the male model while the female model experienced similar magnitudes of stress in both L4 and L5. The stress doubled from the 20 to 90 year old in the female model at the L4 and L5 anterio r bone and in the male model at the L4 anterior bone (Fig s. 14 15 ). The stress more than tripled in the male model at the L5 anterior location. The female model demonstrated a linear relationship of an increasing stress with age at all locations The von M ises s tress at the L4 bo ne spacer interface increase d by about 11% between the 20 and 90 year old model and increased about 7% between the 20 and 90 year old model at the L5 bone spacer interface. The female model experien ced greater stress at the L4

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! 31 bone spacer interface than the L5 bone spacer interface while the male model experience d similar magnitudes at both interfaces. In the male model there was only a 3% increase and 10% increase from the 20 year old to 90 year old model at the L4 and L5 bone space r interfaces, respectively. Rod stress increased with age but there was not a direct age related corre lation with the spacer stress in the male model. In fact, the stress at the spacer wa s a bit high er (3%) in the 70 year old than the 90 year old Further more, the stress at the s pacer only increased by a little more than 1% between the 20 and 90 year old while th e female model experience d a 12 % increase. Nonetheless, t he rods still experience d an increase (16%) between the 20 and 90 year old in the male m odel and 30 % in the female model. Figure 14 : Stress at multiple locations in the age simulated female model at 20, 65, and 90 years old (65 was actual age of specimen).

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! 32 Figure 15 : Stress at multi ple locations in the age simulated male model at 20, 70, and 90 years old (70 was actual age of specimen). The average maximum principal tensile and compressive strain measured at various locations in the models was also obtained Because the models wer e linear, the strain data correlated directly with the stress results (Fig s 16 17 ). Figure 16 : Average maximum principal tensile and compressive strain at multiple locations in the age simulated female model.

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! 33 Figure 17 : Average maximum principal tensile and compressive strain at multiple locations in the age simulated male model. The cross sectional areas of the L4 vertebral body were 1213 mm 2 and 1115 mm 2 for the male and female, respectively. Discussi on Both subjects experienced increased levels of stress and strain at the different locations as cortical thickness and trabecular elastic modulus varied due to the simulated increase in age In both models the stress at least doubled from 20 to 90 years old at the L4 and L5 anterior bone locations. Since gender differences have not been evaluated in the measurement of cortical thickness, it is the same in both models at the same ages. This may have been a reason for similar magnitudes of changes in stres s in both subjects at the anterior bone. This also suggest s that the cortical thickness is a large factor in the stress at the anterior bone, which goes along with the original hypothesis that the vertebral cortex will bear more of the load after trabecula r bone loss. Contrarily, an increase in stress from 20 to 90 year s old ranged from 3 11% in the subjects at the bone spacer interfaces. In this case, though the cortical thickness was still the same in both subjects, the bone spacer interface interactions differed to a greater extent between the subjects. The trabecular bone may therefore be playing a great er role in the effect on the stress at the bone

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! 34 spacer interface. Additionally, other factors (spine alignment, device placement, etc.) not directly meas ured in this study, may be affecting the bone spacer stress distribution. The increase in stress in the rods with an i ncrease in age showed the rods were carrying a greater load in the older models In the female, there was also an increase in stress at the spacer. Overall, t his shows that as a person ages, the instrumentation ta kes on more of the load It would seem that there must be a load shift from the vertebral body with age related cortical thi nning and trabecular bone loss. The cross sectional ar ea of the male was calculated to be 8% larger than the female. This correlates with literature that shows men typically have larger vertebral cross sectional a reas than women. However, this is not a large difference, which may be due to the female being ob ese. The body mass index ( BMI ) of the female was 35.6 ( mass = 103 k g height = 170 cm), while the male had a BMI of 28.9 ( mass = 1 02 kg, height = 188 m), which falls into the overweight category. Due to the fact that only two subjects were analyzed, no con clusions can be drawn from the cross sectional area or BMI of the subjects. H owever, it is worth mentioning due to its possible relevance, and effects of body size should be taken into account in future studies. Summary The results obtained in this study demonstrated the age related effects of cortical thinning and trabecular bone loss on lumbar interbody fusion with posterior instrumentation. The greatest changes in stress with age were found at the L4 and L5 anterior locations. However, there were still significant increases in stress between the 20 and 90 year old models at most locations with the two exceptions being the stress at the spacer and L4 bone spacer interface in the male model. Other than the anterior bone locations, the rods experienced the next greatest increase in stress with a 16% increase in the male model and 30% increase in the female model. In a future analysis, it would be useful to maintain the cortical thickness as the trabecular bone varies to

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! 35 discern how much the cortical thickn ess plays a role in the stresses obtained in the lumbar spine and instrumentation. The following chapter will analyze the affects of the spacer material on the stress and strain distribution in the lumbar spine after fusion with posterior instrumentation.

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! 36 CHAPTER VI EFFECTS OF DIFFERENT SPACERS Introduction The spacer material is an important part of the overall fusion system. The spacer must bear relatively high forces while fusion occurs, however, a spacer that is overly stiff could lead to more st ress on the bone possibly leading to subsidence and the need for an additional surgery Titanium and PEEK are the materials used most often in posterior lumbar interbody fusions. Vadapalli et al. [ 37 ] studied the effects of spacer stiffness in a L3 L5 segment with L4 L5 fusion with posterior instrumentation. Peak von Mises stress in the endplates increased by at least 2.4 fold with a titanium spacer versus PEEK This study suggested that the chance of subsidence would be less with PEEK spacers and the lower stiffness of PEEK did not affect the stability. Bioactive titanium implants with 50% porosity and 116.3 MPa strength were evaluated in a canine anterior inte rbody fusion model [ 38 ] Fusion was confirmed in all five dogs that received the treated bioactive titanium implant and in 3 of the 5 dogs that received the non treated implant. This study concluded that the bioactive treatment enhanced the fusion ability and therefore may be the direction for spacers A clinical study in humans [ 39 ] using the porous bioactive titanium had successful fusions in all five individuals aged 36 56 years old with fusion within 6 months. The advancement in spacer materials mentioned are an attempt to correct the is sues of nonunion and subsid ence; however the load sharing is also significant. Ghouchani et al. [ 40 ] did a F E study for optimization of material properties fo r an artificial lumbar disc replacement The artificial disc was simulated similar to an intact disc with a peripheral annulus fibrosus region and center nucleus pulpous region Various physiologic loading conditions were applied, leading to predicted optimal material properties to be E=19.1 MPa and = 0.41 for the peripheral section and E=1.24 MPa and = 0.47 for the central section. This artificial disc with these properties would

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! 37 restore the disc height an d function similar to an intact disc. Though an artificial disc replacement could be the best solution in the future to avoid complications of lumbar spine fusion and loss of segment motion the work in this study is an attempt at an intermediate solution. Titanium and PEEK were originally the materials to be compared but an even less stiff material, one closer in material properties to trabecular bone, was hypothesized to decrease the stress ( due to shift in load ) at the bone spacer interfaces in order to hopefully lessen the incidences of subsidence. This chapter addresse s the effects of the spacer material on the stress and strain in the bone and posterior instrumentation and more specifically compares titanium, PEEK, Self reinforced polyphenylene (SRP ) and SRP with 70% porosity as the spacer material. Methods Model Preparation The model preparation outlin ed in Chapter II applies to these model s Material Properties The methods for applying the material properties of the cortical bone cortex and trab ecular bone core, outlined in Chapter II, are the same in this model However, i n this study, multiple spa ce r materials were used (Table 4) Titanium and PEEK are current materials used as the interbody spacers in lumbar spine fusion [ 19 ] [ 41 ] SRP is another material with similar properties to PEEK and it has the a bility to be manufactured with prescribed porosity SRP was simulated with 70% porosity by calculating the ela stic modulus of the porous SRP (Eqn. 6) [ 42 ] [ 43 ] [ 44 ] A porosity of 70% was used so as to obtain an elastic modulus similar to trabecular bone.

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! 38 Where ! repre sents the modulus of the solid material ! represents the porous material, and is the porosity. An elastic modulu s of 450 MPa, spacer modulus closest to trabecular bone, was assigned to the spacer and will be referred to as SRP 70% porous. Table 4 : Material properties applied to the spacer [ 45 ] [ 41 ] [ 19 ] Spacer Material Porosity Elastic Modulus (MPa) Pois s on's Ratio Titanium none 110,000 0.3 PEEK none 4000 0.36 SRP none 70% 5000 450 0.3 As an exploratory addition to this study, a model with a custom fit spacer was created in Simpleware. The spacer was developed to conform to the curvature of the endplates to he lp spread out the stress distribution along the bone spacer interface. Figure 18 shows a comparison between the original sp acer and the custom fit spacer in the male model. The average von Mises stress at the bone spacer interfaces and in the posterior rod s was obtained. ! ! ! ! ! ! ( 6 )

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! 39 Figure 18 : Comparison of original spacer and custom fit spacer in the male model. Finite Element Analysis The FE analysis outlined in Chapter II applies to these models. A cortical thickness and trabecular core E were applied based from the age of the specimens, 65 and 70 year old, for the female and male model, respectively. B oundary condition s were applied to these models as previously explained. Results The spacer material was varied in both models whil e all other parameters were held constant in order to properly analyze the effects of the spacer material. As the stiffness of the spacer material decreased, it w as hypothesized that the strain and stress would decrease at the bone spacer interfaces while i ncreasing at the rods The changes between PEEK, SRP and titanium were very miniscule in comparison to the noticeable changes with SRP 70% porous as the spacer material PEEK and SRP will remain very close due to their similar material properties; SRP was included for the purpose of comparing it to SRP with 70% poro s ity Both models experienced different levels of strain and stress at the different locations as the spacer material varied. There was greater overall compressive and tensile strain at the bone

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! 40 spacer interfaces compared to other locations which made sense due to the load bearing responsibility of the spacer and the bone having a low er stiffness than the other materials The strain and stress at the rods was taken as an average between the valu es collected on the posterior side of each rod. The highest strain was found in the rods with SRP 70% porous as the spacer material. Though the strain in the SRP 70% porous should be greater than the other materials due to lower stiffness, the female mode l experienced a very large amount of both compressive and tensile strain (Fig 19 ) The female model experienced greater compressive and tensile strain at both bone spacer interfaces with the SRP 70% porous which goes against the hypothesized outcome. The L4 and L5 anterior locations experienced similar magnitudes of strain in the female model. Figure 19 : Average maximum principal tensile and compressive strain at multiple locations in the female model with various spacer materi als. Contradictory to the female model, the male model experienced less tensile and compressive strain in the bone spacer interface locations with SRP 70% porous (Fig. 20 ) Also, there was greater tensile and compressive strain at the L4 anterior location and less at the L5 anterior location with the SRP 70% porous spacer.

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! 41 Figure 20 : Average maximum principal tensile and compressive s train at multiple locations in the male model with various spacer materials. The spacer with SR P 70% porous material properties strain ed almost 13 times greater in compression and almost 8 times greater in tension in the female model versus the male model. T he rods experienced greater strain with all spacer materials in the male model compared to th e female model, and consequentially the compressive strain at both bone spacer interfaces was greater in the female model. Though the strain was important t o observe, especially when used in comparison to exp erimental results, the stress was more signific ant for considering how the load was distributed in the model and the stress concentrations occurring at the bone spacer interfaces. Coinciding with the strain results, the stress was greater in the rods with SRP 70% porous spacer in both subjects. For co mparison of load sharing, the stress at the bone spacer interfaces was 1 1.5 MPa while the stress in the rods was 15 20 MPa in the female model (Fig. 21). T he male model experienced less than 1 MPa at the bone spacer interfaces for all spacer materials whi le the stress in the rods was around 40 MPa (Fig. 22 ). The female experienced a decrease in stress (14 %) at the spacer with SRP 70% porous compared to SRP, yet the bone spacer interfaces had an increase in stress (3 6 %) Contrary to the female model, the male model experienced a decrease in stress (6 12.5%) at both bone spacer

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! 42 interfaces with the decrease in stress (30%) at the SRP 70% porous spacer compared to SRP (Fig. 22). There was an increasing stress at the L4 anterior bone location in both model s as the st iffness of the spacer decreased. While the female model experienced similar magnitudes of stress in both L4 and L5 anterior bone locations, the male experienced more than 12 times greater stress at the L4 anterior location than the L5 anterior locat ion. The female model experienced greater stress in the spacer than the male model for all spacer materials, and t he male model experienced greater stress in the rods than the female model. Figure 21 : Stress at multiple location s in the female model with various spacer materials.

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! 43 Figure 22 : Stress at multiple locations in the male model with various spacer materials. ! The effects of the custom fit spacer compared to the original spacer with PEEK and SRP 70% porous as the material properties were observed at the bone spacer interfaces and rods T he bone spacer interfaces e xperienced h igher stress with b oth the PEEK and SRP 70% porous original spacers than the custom spacers (Fig. 23) The PEEK custom s pacer provided a 39% decrease in stress at the L4 bone spacer interface compared to the original PEEK spacer, and the SRP 70% porous provided a 41% decrease. Similar changes in stress were seen at the L5 bone spacer interface. Therefore, both spacer materi als caused a significant de crease in stress at the bone spacer interface s with the custom fit spacer. The L4 and L5 bone spacer interfaces experienced a 15% and 11% decrease in stress respectively, with the SRP 70% porous custom spacer compared to the P EEK custom spacer. The decrease in stress at the interfaces was not as great with the original spacers when the material

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! 44 was changed from PEEK to SRP 70% porous. There was a 12% and 6% decrease at the L4 and L5 bone spacer interface, respectively. Figur e 23 : Stress at the bone spacer interfaces and rods in the male model with the original and custom spacer. The von Misses stress at the rods was highest with the original SRP 70% porous spacer. It is a very minimal (1%) differenc e between the stresses experienced at the rods with the two SRP 70% porous spacers. However, this shows that even though there was a large decrease in the stress at the bone spacer interfaces with the custom spacer, the rods do not experience any large cha nges in stress. In the case with the two PEEK spacers, the rods also experienced minimal changes (< 0.5%) in stress. Figure 24 shows the stress distribution at the L5 bone spacer interface with the PEEK and SRP 70% porous custom spacers. To compare the t wo models, a maximum limit of 1 MPa was set. Red shows the areas of high stress and anything above the maximum It is clear from the figure, that the stress at the L5 bone spacer interface is less with the SRP 70% porous custom spacer.

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! 45 ! Figure 24 : Stress distribution at the L5 bone spacer interface with PEEK (left) and SRP 70% porous (right) custom spacers. Discussion The spacer with SRP 70% porous material properties strained significantly more in the female model than the ma le model. This is important to note, because the difference in strain was very large despite the fact that the load applied and material properties of the space r were the same in both models. T he rods experienced much greater stress overall compared to the spacer in both the female and male models. As hypothesized, a greater stress in the rods with SRP 70% porous as the spacer material, was observed in both subjects demonstrating a shift in load due to a less stiff spacer. T he overall stress in the rods was greater in the male model than the female model, while the stress at the spacer was at least 8 times greater in the female model. Thus the shift in load distribution was shown to be not only affected by the material used for the spacer, but also depend ent on the subject. Additionally, t he stress experienced in the rods was more than 40 times greater than the stress experienced at the bone spacer interfaces in the male model. In the female model, there was about a 20 times greater difference. The fact t hat the male model experienced greater overall

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! 46 stress in the rods was likely due to differences in the alignment of the rods in the female spine. This may relatively reflect clinical procedures where the screws and rods are positioned to the best abilitie s of the spinal surgeon, but by no means are the same in every individual. T he custom spacer, designed to con f o r m to the contours of the vertebral endplates demonstrated less stress at the bone spacer interfaces compared to the original spacer used Mini mal stress changes were found in the posterior rods with the custom spacer, which shows that the rods were still bearing about the same load. B oth spacer materials PEEK and SRP 70% porous, caused a significant de crease in stress at the bone spacer interfa ce s with the custom spacer. However, the less stiff material, SRP 70% po rous, resulted in the least amount of stress at the bone spacer interfaces. The outcome of the custom spacer analysis showed that a greater contact area between the spacer and bone wo uld distribute the stress better at the bone. A spacer that can distribute the stress better at the bone spacer interface is likely to decrease the chances of subsidence. The methods used to position the spacer and posterior instrumentation, as well as th e blocks, could have been a limiting factor. The spacer and posterior instrumentation were positioned in Simpleware in the best possible lo cation for each model The blocks in each model were about the same size but were positioned slightly different depen ding on the easiest l ocation that did not interfere with t he rods. The orientations of the post eri or instrumentation and blocks could have had an effect on the stresses obtained. Additionally, s ince the bone material properties in each specimen were based on their age, this could be a reason for some of the variation. There was only a 5 year difference in their ages, but due to gender differences in age related trabecular bone loss, this might be a factor.

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! 47 Summary An increase in stress at the rods and a d ecrease at the spacer with the SRP 70% porous spacer showed the shift in load occurring during l umbar interbody fusion. T he subjects differed in the observed changes at the bone spacer interfaces, and this helps to justify the need for patient specific inf ormation in selection of device materials. In general, the effects the SRP 70% porous spacer had on the vertebral body show potential for porous SRP to produce more sufficient outcomes post surgery. The results of the custom spacer show great strides in th e direction of a new type of spacer that could improve the outcome of lumbar interbody fusion. Though the occurrence of subsidence is still relatively unknown, the bone spacer interfaces are likely the best location for observance o f stress and how this ma y predict the risk of subsidence. ! ! ! ! ! !

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! 48 CHAPTER VII CONCLUSION S AND FUTURE WORK ! Conclusions Modeling of the lumbar spine is a valuable tool for evaluating stress in the bone due to age related changes and implant materials and design. Modeling i s a non invasive tool that can be used to d evelop the selection of device materials on a patient specific basis. This thesis explored the effects of age related changes as well as the effect of the implant mat erial so as to better quantify these factors W ith age related cortical thinning and trabecular bone loss, the load shifted to the rods. A shift in load from the trabecular core to the cortex was also evident with an increase in age. Though there was simultaneous cortical thinning with the trabecular b one loss, the load bearing responsibility of the cortex came more into play with the increase in age There was an increase in stress in the rods with a decrease in stress at the spacer as the stiffness of the spacer material decreased. Therefore, the SRP 70% simulated porosity showed the greatest shift in load. The SRP 70% simulated porosity spacer shows potential to produce more sufficient outcomes post surgery. However, there were variations in the stress distribution between the two subjects used in th is study, which shows a great need for patient specific information in determining the optimal implant materials. The custom fit spacer that was developed in the models to conform to the curvature of the vertebral endplates showed great strides in the dire ction of a new type of spacer. There is a good 6 weeks between when a patient receives medical imaging to when they receive lumbar interbody fusion. That is plenty of time for a custom spacer to be machined or even better, printed on a 3 D printer.

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! 49 Futur e Work The work presented in this thesis was the first attempt at creating a working L4 L5 model that represents lumbar interbody fusion with posterior instrumentation to measure differences in strain and stress in the lumbar spine due to age related chan ges and spacer material Only two cadaver specimens were used in this study and therefore, a larger study will be conducted to bet ter quantify the affects of age related changes and implant material, as well as how other factors, like gender and weight, af fect lumbar interbody fusion. The validation of this study showed that the homogeneous model better represented experimental testing than t he varying material properties used in the grey scale based model. However, a larger cadaver study will look further into this finding to discover which model will best represent lumbar interbody fusion with posterior instrumentation. Future work will observe the role of cortical thickness and trabecular bone modulus more closely. Maintaining one of these variables will help to discern how much each of them pla ys a role in bearing the load in the lumbar spine. Axial loading was the only type of load included in this model but bending and torsion should also be represented. This model assigned a constant cortical bone cor tex around the whole vertebral body but the vertebral endplates will be modeled sep arately in a future model due to the different properties of the endplates and their significance at the bone spacer interfaces. Finally, SRP must be tested to figure out wh ether it could be used as the spacer material in lumbar interbody fusion.

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