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OPTICAL COHERENCE TOMOGRAPHY AND MICROWAVE IMAGING:

DIAGNOSTIC TECHNIQUES FOR OSTEOPOFIOSIS

presented by

Solimar Reyes Rodriguez

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5/08 K:IPrchAcc&Pres/CIRC/DaleDueindd

OPTICAL COHERENCE TOMOGRAPHY AND MICROWAVE
IMAGING: DIAGNOSTIC TECHNIQUES FOR OSTEOPOROSIS

By

Solimar Reyes Rodriguez

A THESIS

Submitted to
Michigan State University
In partial fulfillment of the requirements
for the degree of

MASTER OF SCIENCE
Electrical Engineering

2008

ABSTRACT

OPTICAL COHERENCE TOMOGRAPHY AND MICROWAVE IMAGING: DIAGNOSTIC
TECHNIQUES FOR OSTEOPOROSIS

By
Solimar Reyes Rodriguez

Osteoporosis is a disease in which bone mineral density is reduced, making the
bone brittle. Two different imaging techniques, Optical Coherence Tomography (OCT)
and Microwave imaging, are proposed for osteoporosis detection.

The OCT system was calibrated by measuring the thickness of a microscope
cover Slip. The microscope cover slip was replaced by a cortical bone sample and was
scanned. Different morphological image processing techniques were applied to the
image and the variance was found in order to identify porosity between compact bone
and cancellous bone. The variance of the compact bone was higher than that of
cancellous bone. Difference in porosity was found using OCT but more experiments will
be needed in order to determine that OCT could be used to find difference in porosity.

In order to implement the microwave technique the reflection coefficient was
calculated for a layered cylinder using Matlab and was calculated for a realistic tissue-
bone model using a finite element package. The simulations, using the finite element
package, were carried out with the permittivity and conductivity reduced by 5 percent in
the bone to simulate loss of bone density and without reducing it. There was no
difference between the total electric field calculated for both simulations. Other non-

invasive methods have to be explored.

COPYRIGHT BY
SOLIMAR REYES RODRIGUEZ

2008

ACKNOWLEDGMENTS

There were a lot of people that help me in the process to complete my complete
my Master’s degree. First of all, I have to thank my advisors, Dr. Satish Udpa and Dr.
Lalita Udpa for all their invaluable guidance through my research and course work and to
Dr. David Fischer from NASA Glenn Research Center for all his guidance, support and
help through the second part of this research. I also want to thank Dr. Rothwell for all his
guidance, electromagnetic lessons, and because everytime I had problems with my
research he gave me useful ideas to solve them. I am very grateful for all their support
and invaluable help.

I would also like to thank Dr. Kavitha Arunachalam for all her help, guidance and
interest in my research topic. While I was at NASA Glenn Research Center I met
incredible human beings that assisted me with the optical set up. I like to give special
thanks to Marius Asipauskas, William Yanis, Gordon Berger, and Chris Garcia for all
their help and support and great suggestions.

Next, I would like to thank Dr. Barbara O’Kelly and Dr. Percy Pierre and the
Sloan foundation for all their support and guidance through graduate school. I am a
Harriet G. Jenkins Fellow and this fellowship provided me with fimding for my graduate
studies. I would like to thank this program for all the financial support and all the
wonderful experiences that I was exposed to while being part of this program.

I would also like to thanks all my teachers and friends who provided me
knowledge, and emotional support through all this process. I would like to thank Priscilla

Génzalez, Alexandra Litchfield, and Giselle Agosto for all their unconditional friendship.

1V

Finally, I would like to give all my gratitude to my parents, Aida Rodriguez
Rodriguez and Samuel Reyes Saldar‘ia, my sister, my extended family, and to my
beloved, Carlos Eduardo Nifio. These people mean the most to me because they give me
all their support and all their unconditional love and the journey was very pleasant with

their presence by my side.

TABLE OF CONTENT

 

 

 

 

 

 

 

 

 

LIST OF TABLES VIII
LIST OF FIGURES IX
CHAPTER 1 INTRODUCTION 1
CHAPTER 2 BACKGROUND 5
2.1 BONE MINERAL DENSITY RESEARCH 5
2.2 OPTICAL COHERENCE TOMOGRAPHY (OCT) 9
2.3 MICROWAVE TECHNIQUES 21
2.4 TISSUE DIELECTRIC PROPERTIES 24
2.5 THE INDUCTION THEOREM 26
2.6 LAYERED DIELECTRIC CYLINDER MODEL 27

 

CHAPTER 3 SIMULATION RESULTS FOR THE MICROWAVE TECHNIQUE........ 33

CHAPTER 4 CONSTRUCTION AND CALIBRATION OF AN OPTICAL

 

 

 

COHERENCE SYSTEM 59
4.1 MICHELSON INTERFEROMETER 59
4.2 OCT SYSTEM WITH A LED AS A LIGHT SOURCE 61
4.3 OCT SOURCE 79

 

CHAPTER 5 ANALYSIS OF OPTICAL COHERENCE TOMOGRAPHY DATA ......... 87

 

 

 

 

 

 

 

5.1 CALIBRATION OF THE SYSTEM 87
5.2 EXPERIMENTAL OBSERVATIONS 93
5.3 DEPTH SCAN DATA ANALYSIS 97
CHAPTER 6 CONCLUSIONS 109
APPENDIX A 112
MATLAB CODES FOR OCT 112
A1 CODE USED To DETECI‘ AVERAGE DISTANCES 112
A2 CODE USED To APPLY MORPHOLOGICAL IMAGING TECHNIQUES TO THE BONE

IMAGES 113

 

A.3 LAB VIEW PRINT OUTS USED To COLLECT DATA IN THE OCT TECHNIQUE 1 15

vi

APPENDIX B 121

MATLAB CODES TO IMPLEMENT MICROWAVE IMAGING TECHINIIQUE............ 121
3.] CODE To DETERMINE THE DIFFERENT FIELDS FOR THE LAYERED CYLINDER ............. 121
3.2 CODE To CALCULATE THE REFLECTION COEFFICIENT FOR THE GRID 123
3.3 CODE T0 CALCULATE THE ELECTRICAL PROPERTIES OF HUMAN TISSUE .................... 124

vii

LIST OF TABLES

Table 1 Results from the experiment with the LED as a light source and both mirrors... 64

Table 2 Results from the Microscope cover slip experiment ........................................... 69
Table 3 Results of the average distance between the peaks ............................................. 98
Table 4 Varince of data after applying erosion operation ............................................... 104
Table 5 Varince of data after applying “opening” operation. ........................................ 106
Table 6 Varince of data after applying “closing” operation. .......................................... 107

viii

LIST OF FIGURES

Figure 2.1 OCT set up ...................................................................................................... 11
Figure 2.2 Interference Signal .......................................................................................... 12
Figure 2.3 In Vivo image of the aorta using OCT. ........................................................... 19

Figure 2.4 a) Shows the original problem and b) shows how the induction theorem is

applied. ...................................................................................................................... 26
Figure 2.5 Induction Theorem for a Perfect Conductor ................................................... 27
Figure 2.6 Geometry of a circular dielectrical scatterer with three layers. ...................... 28
Figure 3.1 Geometry of a circular dielectric scatter with 4 layers. .................................. 35

Figure 3.2 Graph that shows the incident field, scatter field, and reflection coefficient. 40

Figure 3.3 “Images in this thesis are presented in color”. Grid showing different
reflection coefficient numbers for different positions at 200 MHz. Each circular line
in this figure represents a different region outside the cylinder where the reflection
coefficient was calculated. The numbers on top of the lines are the reflection
coefficients for those regions. The regions inside the red line represent the skin, fat
and bone. The outer regions in the figure have the smaller reflection coefficient
(1.72). The next region has a reflection coefficient of 1.74. The reflection
coefficient in the region close to the cylinder free space boundary is 1.76. Inside
the cylinder the reflection coefficient varies fiom 1.78 to 1.86. ............................... 42

Figure 3.4 “Images in this thesis are presented in color”. Graph showing that the
reflection coefficients are less than one far away from the Skin free space boundary.
Each circular line in this figure represents a different region outside the cylinder
where the reflection coefficient was calculated The numbers on top of the lines are
the reflection coefficients for those regions. The regions inside the red line represent
the skin, fat and bone. The outer region in the figure has a reflection coeflicient of
.95. The next region has a reflection coefficient of 1. The region below has a
reflection coefficient of 1.05 and the region closer to the skin free space boundary
has a reflection coefficient of 1.1 .............................................................................. 43

ix

Figure 3.5 “Images in this thesis are presented in color”. Reflection coefficients
calculated at different positions at 100MHz. Each circular line in this figure
represents a different region outside the cylinder where the reflection coefficient was
calculated. The numbers on top of the lines are the reflection coefficients for those
regions. The regions inside the red line represent the skin, fat and bone. The outer
region has a reflection coefficient of .6. The reflection coefficient of the region
close to the cylinder free space boundary is .61. ...................................................... 44

Figure 3.6 “Images in this thesis are presented in color” (a) Shows the reflection
coefficients calculated at 200 MHz and (b) shows the reflection coefficients
calculated at 900MHz. Each circular line in this figure represents a different region
outside the cylinder where the reflection coefficient was calculated. The numbers
on top of the lines are the reflection coefficients for those regions. The regions
inside the red line represent the skin, fat and bone. .................................................. 45

Figure 3.7 Pictures that Show the air box, leg, and coax antenna used in the simulation

with HF SS. ................................................................................................................ 47
Figure 3.8 Mesh inside the structure that was simulated. ............................................... 48
Figure 3.9 Line behind the leg where the total field was measured. .............................. 49

Figure 3.10 Graph of the total electric field of the leg with regular permittivity and 5%
less permittivity for 100 MHz. .................................................................................. 51

Figure 3.11 Graphs of the total electric field of the leg with regular permittivity and 5%

less permittivity for 50 MHz. .................................................................................... 52
Figure 3.12 Graphs of the total electric fields of the leg for 200 MHz ........................... 53
Figure 3.13 Graphs of the total electric fields of the leg for 500 MHz ........................... 54

Figure 3.14 “Images in this thesis are presented in color”. Graph of the total electric
field of the leg for 500 MHz when the difference in permittivity is 25%. ............... 55

Figure 3.15 “Images in this thesis are presented in color”. Graphs of the total electric
fields of the leg with regular permittivity and 25% less permittivity for 50 MHz. .. 56

Figure 3.16 “Images in this thesis are presented in color”. Graphs of the total electric
field of the leg with regular permittivity and 25% less permittivity for100 MHz. 57

X

Figure 3.17 “Images in this thesis are presented in color”. Signals for a healthy bone
and a bone with 25% of permittivity loss for a different position of the coaxial cable
antenna. ..................................................................................................................... 58

Figure 4.1 “Images in this thesis are presented in color”. Michelson Interferometer 60
Figure 4.2 LED used for this experhent ......................................................................... 62
Figure 4.3 Set up of a Michelson Interferometer using a LED as a light source ............ 63

Figure 4.4 “Images in this thesis are presented in color”. Experimental and true

interference when an LED was the source of the OCT system. . .............................. 66
Figure 4.5 Experimental data when an LED was the source of the OCT system. ........... 67
Figure 4.6 Michelson Interferometer with a Microscope cover slip ............................... 68
Figure 4.7 Gold coated cover slip. ................................................................................... 69
Figure 4.8 Graph showing the two interference peaks. ................................................... 73
Figure 4.9 Graph that shows experimental data vs. true approximation. ........................ 75
Figure 4.10 Interference with LED as a point source and a motorized linear stage. ....... 76

Figure 4.11 “Images in this thesis are presented in color”. Graph showing experimental
and true interference. ................................................................................................ 78

Figure 4.12 Interference peaks with a LED as a point source and motorized linear stage.

................................................................................................................................... 79
Figure 4.13 Interference peaks with an OCT as a point source. ...................................... 80
Figure 4.14 Interference peaks with an OCT source and intensity around 6V. ............... 81

Figure 4.15 "Images in this thesis are presented in color”. Front surface of the
microscope cover slip. .............................................................................................. 84

xi

Figure 4.16 Bone sample used in the experiment. ........................................................... 85

Figure 4.17 Signal from the depth scan of the bone sample. ........................................... 86
Figure 5.1 OCT system built by Applied Science Innovations. ...................................... 88
Figure 5.2 Microscope cover slip coated with gold. ........................................................ 88

Figure 5.3 Image of the microscope slip cover with gold and depth scans of the
microscope cover slip. .............................................................................................. 89

Figure 5.4 Schematic that explains how the thicknesses of the microscope cover slip
cover with gold was obtained. .................................................................................. 90

Figure 5.5 Schematic of the microscope cover slips and the signal. ............................... 92

Figure 5.6 Image of the three microscope slips and depths scans for three microscope
cover slips. ................................................................................................................ 92

Figure 5.7 Picture of the three microscope cover slips used to calibrate the OCT system.
................................................................................................................................... 93

Figure 5.8 Tibia slice sample scanned. ............................................................................ 94

Figure 5.9 “Images in this thesis are presented in color”. Picture of the tibia that shows
the compact Structure and the cancellous structure of bone. .................................... 95

Figure 5.10 “Images in this thesis are presented in color.” Picture of the bone that shows

the areas of the bone that were analized .................................................................. 95
Figure 5.11 Picture of the bone that shows how it was scanned ...................................... 96
Figure 5.12 Image of dot l and its depth scans ................................................................ 97

Figure 5.13 (a) Original Image (b) Line structural element of size 2 (c) Image after
erosion ....................................................................................................................... 99

xii

Figure 5.14 (a) Original Signals and (b) Signal after erosion with size 3 structuring
element. ................................................................................................................... 100

Figure 5.15 (a) Original Signals and (b) Signal after ‘opening’ with size 2 structuring
element. ................................................................................................................... 102

Figure 5.16 (a) Original Signals and (b) Signal after ‘closing’ with size 3 structuring
element. ................................................................................................................... 103

Figure 5.17 Signals after erosion with (a) size 2 and (b) size 5 structuring element. 105

Figure A.1 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. 115

Figure A.2 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. l 16

Figure A.3 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. 117

Figure A.4 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. 118

Figure A.5 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. 1 19

Figure A.6 “Images in this thesis are presented in color”. Lab View print out of the
program made to move the linear stage. ................................................................. 120

xiii

CHAPTER 1 INTRODUCTION

Osteoporosis, one of the prevalent diseases affecting bones results in loss of bone
mineral density, rendering bones brittle and more susceptible to fractures [1]. The
incidence of osteoporosis increases with age and plagues more women than men
particularly post menopause. Besides senility and menopause, one of the major causes for
osteoporosis is long term immobilization often experienced after trauma or extended
space missions. The absence of earth’s gravity in space disrupts one of the key
functionalities of the skeletal bones to support body weight. Diagnostic methods currently
available to assess bone mass density include Dual and Single Energy X-Ray
Absorptiometry, Quantitative Computed Tomography and Quantitative Ultrasound. The
most commonly used X-Ray Absorptiometry methods are radioactive and are often less
sensitive to early. stage osteoporosis. Two different imaging techniques for quantifying
bone mass density are proposed here. The first approach employs Optical Coherence
Tomography (OCT) and the second approach investigates microwaves.

Imaging is an important tool in the medical field because it helps doctors to give
accurate diagnostics. Computed tomography, Spiral or Helical CT, Electron beam CT,
Magnetic Resonance Imaging, Ultrasound, Nuclear Medicine Technique, Microwave
Imaging, and Optical Coherence Tomography are some of the imaging techniques used in
the medical field. Optical coherence tomography (OCT) is a three dimensional imaging
technique with ultrahigh Spatial resolution even in highly scattering media. In this

technique the longitudinal locations tissue structures are determined by measuring the

l

time-of-flights delays of light backseattered from these structures. The optical delays are
measured by low coherence interferometry. Information on lateral position is provided by
transverse scanning of the probe beam. OCT is the optical analog of ultrasound, but with
greatly improved spatial resolution.

The second approach for bone density estimation employs microwaves.
Microwave is a non-ionizing penetrating energy source with enormous potential in
biomedical applications. Microwaves range from 300MHz to 300 GHz; this is between
the VHF radiowaves and the far infrared in the electromagnetic spectrum. The electrical
properties of different human tissues at RF and microwave fi'equencies are well
documented in the literature. The dielectric properties of tissues depend on their water
content and frequency. Muscle and skin have high water content and they have greater
permittivities than bone and fat that have low water content [2]. Microwave imaging
consists of illuminating the body to be imaged with a low-power coherent microwave
field and measuring the field scattered by the body on the opposite side (transmission
imaging) or on the same side (reflection imaging) as the illurninator. The measured data
can be processed using specialized reconstruction algorithms [3]. In the past decade,
efficient model based image reconstruction algorithms for active biomedical microwave
imaging systems have been developed [3]. The model based tomographic algorithms
yields 3D tomogram of the electrical properties of the internal tissue. A tomographic
setup employing microwaves was used as an alternative approach for imaging skeletal

bones.

OCT technique offers a lot of advantages over other imaging techniques. OCT
offers high depth and transverse resolution, high probing depth in scattering media,
contact-free and non-invasive operation. It provides an axial (depth) resolution of roughly
10 um (depends on bandwidth of source) and a transverse resolution dictated by the beam
spot size (focusing increases resolution). Because OCT is based in interferometry, it
provides high dynamic range and sensitivity. Imaging of weakly scattering structures
even in a scattering environment is possible. OCT is widely used in ophthalmology to
diagnose retinal diseases. It is used to detect skin diseases and for the early detection of
skin cancer. OCT is also used in the cardio-vascular area to detect plaque in veins.

Microwaves also provide a lot of advantages as an imaging technique and is also
non invasive. The radiation used is not harmfirl to the patient because of the low power
employed and the equipment use by this technique is very common and already
developed in the communications field, this makes it available and relatively inexpensive.
Microwaves are used also in the medical field to shrink and detect cancerous tumors, and
to treat atrial fibrillation.

This thesis focuses on the detection of bone mineral density loss using OCT and
microwave imaging. Three major contributions of this thesis are i) the equipment is
small and relatively inexpensive and this allows that more people will be tested, ii) it is
sensitive to early stages of osteoporosis, iii) does not requires much training for
technicians.

The rest of this thesis is organized as follows. In Chapter 2, microwave imaging

and OCT techniques are explained in depth and previous work related to these techniques

3

is presented. The simulations done for the microwave technique are introduced in
Chapter 3. Chapter 4 presents construction and calibration of an OCT system. The
experimental results showing the images obtained with OCT are presented in Chapter 5.

Finally some concluding remarks are presented in Chapter 6.

CHAPTER 2 BACKGROUND

2.1 BONE MINERAL DENSITY RESEARCH

Osteoporosis is caused by the lack of physical stress on the bones because of
inactivity. This is why astronauts suffer from bone mineral density loss. Also
malnutrition and lack of vitamin C can contribute to bone mineral density loss. Vitamin
C is very important for the secretion of intercellular substances by cells [1]. Women that
go through the menopause phase experience lack of estrogen secretion. Estrogen and
vitamin C are very important because they produce osteoids. Osteoid is like a cartilage
but calcium salts readily precipitate in it. Other factors that contribute to bone mineral
density loss and osteoporosis are ageing and Cushing’s syndrome.

Bone mineral density loss is usually determined by X-ray absorptiometry
(DEXA)[4]. For this technique two different X-rays beams are used. If the bone is
strong it will not allow a great amount of X-ray radiation to pass through them. This
technique is used at the posterior-anterior and lateral lumbar spine, proximal femur and
forearm. Another type of X-ray absorptiometry is Peripheral dual energy X-ray
absorptiometry[4]. This technique measures bone mineral density loss in the arms and
legs. It is not a good technique to follow up treatment or to measure bone mineral density
loss in the hips or spine. There are other techniques that are used to detect bone mineral
density loss. Quantitative computed tomography (OCT) [4] is a densitometry technique

that measures bone mineral density loss in the spine because of the high responsiveness

of the spinal trabecular bone. QCT is also used to asses vertebral fracture risk, and to
measure the effectiveness of follow up treatments for osteoporosis and other bone related
diseases. Peripheral OCT [4] is used for the same purpose but instead of measuring bone
mineral density loss in the spine, it measures it in the arms and legs. This technique is
expensive and it uses higher radiation doses. Dual photon absorptiometry [4] uses
radioactive substances to measure bone mineral density loss in the hip and spine. The
problem with this technique is that it scans very slowly and it takes more time.
Ultrasound can be used to detect bone density loss in the heel. It can not be used to
detect bone mineral density loss alone and can not be used to measure the effectiveness
of follow up treatment. DEXA is ofien used to confirm the results.

Bone mineral density assessment is very important to detect osteoporosis and to
determine the effectiveness of the treatment selected for the patient. Research has been
done in order to determine the effectiveness of each of the methods created to measure
bone mineral status and new methods had been created. In [4] the most common
noninvasive methods for assessing bone mineral density status are compared in terms of
their respective abilities to reflect age and menopause related bone loss, and their ability
to determine bone fractures. In this study among all the different techniques that are
compared, spine computed tomography was the one that performed the best. Quantitative
Computed Tomography was also found to be very accurate to measure bone mineral
density loss after oopheroctomy [5] and also for determining the effectiveness of the

treatment.

The most common technique used to measure bone mineral density loss is DEXA.
DEXA is used to measure bone mineral density loss accurately in the lumbar Spine. This
technique is usually compared with QCT and Dual Photon absorptiometry (DPA). In [6]
the precision of DEXA was better than DPA but the ability to predict future fractures was
about the same for both methods. In the case of Lateral DEXA the diagnostic sensitivity
[7] was between that of Posteroanterior DEXA and QCT. It was also found that Lateral
DEXA has more sensitivity than QCT when anatomic abnormalities or degenerative
processes of the spine are present. Duboeuf et a1 Show [8] that the performance of
Lateral DEXA can be improved. In this case the DEXA machine was equipped with
multiple detectors and a rotating arm. Lateral projections improve the discrimination
between people with and without osteoporosis the method can also be used for early
detection of trabecular bone loss in perimenopausal women and in the elderly.

DEXA is also used to measure bone mineral density loss in the forearm but in [9]
Deodhard et al showed that the method can be used to measure bone mineral content in
the hand to asses and monitor rheumatoid arthritis. In order to accomplish this, the
technique used to measure bone mineral density in the spine was modified by hardening
the X-ray beam with a perspex aluminum plate. The method offers a quantitative way of
measuring bone mineral content and is reproducible even when the patient changes the
hand position. The procedure and is automated to avoid observer error.

Recent research shows that DEXA often provides inaccurate measurements of
bone mineral density loss. The variability in bone mineral density loss measured with

DEXA arises from soft tissue anthropometrics than to natural variations in bone mineral

7

density loss [10]. Another factor that creates false bone mineral density readings is the
fact that there can be disparities between the X-ray attenuation characteristics of soft
tissues along photon paths laterally adjacent to the bone and those on paths intersecting
the bone segment that are unavoidably assigned by DEXA to bone material[10]. Because
of this the Red Marrow and Yellow Marrow mix along any given X-ray trajectory have to
be such that their linear attenuation coefficient is less than that of the particular
extraosseous fat and lean muscle tissue mix laterally adjacent to the bone. This
absorptivity deficit is attributed by DEXA to bone mineral density loss and causes the
bone mineral density loss value to be over or under estimated. For these reasons the
inaccuracies of DEXA readings could be up to 20% [10].

Ultrasound has been found to measure different bone properties, like structure and
elasticity, than the ones that can be measured with other methods using broadband
ultrasonic attenuation (BUA) and the velocity of ultrasound through the heel (HV) [11].
Velocity of sound is related to the density and elasticity of bone and BUA to the density
and trabecular architecture of cancellous bone. Research suggests that these properties
change with age [11].

Radiographic absorptiometry (RA) is another technique that can be used to
measure bone mineral density loss. It is usually used to predict fractures in the phalanges
but Yang [12] et a1 show that the method can be used to find bone mineral density loss
successfully in hip and spine, places prone to osteoporotic fracture. This technique can

identify osteoporotic fractures as well as other techniques such as DEXA but not as well

as QCT [10]. It is an easy technique to implement and the equipment is more available
than bone densitometers and it does not require that much training for the technician [13].

Lately few new techniques to measure bone mineral density loss have been
developed. In [2] a potential new technique is presented. This study indicates the
potential that impedance spectroscopy has to measure bone mineral density loss. The
study does not compare this technique with DEXA and ultrasound but suggests doing so.
A new technique using an iterative numerical solver based on the finite volume method
for simulating the induced current impedance for two dimensional polar grid objects is
also being explored. This study shows a strong correlation between bone density
variations and the corresponding surface potentials. It is recommended only as a
complimentary method rather than an alternative technique because the values and the
distribution of surface potential is a personal unique characteristic, and requires
calibration with a conventional bone densitometry system or obtaining reference
geometry from an imaging modality before using the bio-impedance technique. The
advantage of this technique is that it is inexpensive and does not uses ionizing radiation

like DEXA or QCT [14].

2.2 OPTICAL COHERENCE TOMOGRAPHY (OCT)

OCT is a non invasive three dimensional imaging technique that has superior
spatial resolution and sensitivity than ultrasound. OCT is analogous to ultrasound but
instead of measuring the backreflection intensity of sound, it measures the backreflection

intensity of infrared light. A low time coherence light source in a Michelson

Interferometer is part of the set up. The Michelson Interferometer splits the light beam
into two different beams and recombines them with a beam splitter. The first beam is
reflected by two different mirrors while the other beam is reflected by a mirror and the
sample to be scanned. This light intensity that is recombined is directed towards a

photodetector. The intensity or irradiance that reaches the detector is given by:

ID =IR+15+2Rey(z)llJI—,Iscos(2kAl) (2.1)

Where I D is the combine signal at the detector, 1R is the intensity reflected from the

mirror, I S is the intensity reflected from the sample, k=£f , and AI is the coherence

length. If the pathlengths of both beams match to within a coherence length, interference
will occur [15]. Coherence length is the distance the light beam travels over the period of
time where the phase correlation between the two beams stays constant.

The backreflection intensity of infrared light can not be measured electronically
because of the high speed associated with the propagation of light [15]. In order to
measure backreflection intensity of light, low coherence interferometry is used. Low-
coherence interferometry utilizes a light source with low temporal coherence.

In order to optimize resolution, the OCT set up should, for convinience, have a
source with a Gaussian spectrum because the autocorrelation function of a Gaussian
source is Gaussian. In addition the source needs to have a low temporal coherence [15].

Figure 2.1 shows a common OCT set up.

10

Reference t OCT Depth

 

   

 

   

Mirror 5C3"
Low Coherence I t IS n
Light Source . _ La era ca
I «II-ll \
Beam ......
Expander ggmrc , Sample Lens

.1

-,;_,; J
.. . “JW' _

V Pinhole
Detector

 

Sample

  

 

Signal
Processing

Figure 2.1 OCT set up.
0 Fercher A F, Drexler W, Hitzenberger CK and Lasser T 2003 Rep. Prog. Phys. 66 239-303

When a Gaussian source is used the irradiance becomes:

.- -1223123.
[areal exp[ onAz'p]exp (2.2)

Where (00 is the central frequency, 0“,, is the standard deviation of the angular frequency

spectrum, Az' p is the phase delay, and Arg is the group delay. The second term of this

equation is oscillatory and is the Gaussian envelope of the autocorrelation function. This

firnction carries ranging information and is critical to obtain high resolution images [15].

Figure 2.2 shows this autocorrelation function.

11

Interference

 

 

 

 

 

 

 

 

 

 

 

 

 

0.11 T I I l i
0.108_ J _
0.106~ .
> I
'5 mi lit
E 0104~ MMWWH‘ if {Mp/WWW.
E ii i
0102— it _
0.1» ,
0091%“; 135 1.652 1.654 1.655 1.658 1.06

Position in um

4
X1 0
Figure 2.2 Interference Signal.
OCT technique offers a lot of advantages over other imaging techniques. It has
high depth resolution at sites where it is not possible with high numerical aperture beams
[l 6]. The depth and transverse resolution of the OCT technique do not depend on each

other. The depth resolution depends on the coherence length. The coherence length is

given by:

—2
21n2/1

7r 3 ( 2.3)

12

Where Ethe mean wavelength, and Al is is the spectral width. The coherence length is
influence by the amount of different frequencies and phases within the beam [15]. The
transverse resolution depends on the waist radius of the focused probe beam. The waist
radius is given by:

w
J2 +7z2w4 biz
1 P

Where WF is the waist radius, WP is the minimum beam waist radius, f is the focal

( 2-4)

length of the sample lens, and 21 is the distance of the focal plane of the sample lens from

the beam waist to the unfocused probe beam The depth resolution in the histological 1
pm range is possible [16]. Because OCT is based in interferometry, it provides high
dynamic range and sensitivity. OCT enables the imaging of weakly scattering structures
in a scattering environment and also is a non-invasive technique that allows in vivo data.

Speckle is another factor that can influence or degrade the resolution of the
images when using OCT. In order to obtained good resolution with OCT, single
backreflected light has to be detected. Speckle results from multiple scattered light from
out of focus sites [15]. If two or more of this sites are separated by a distance of odd
multiples of one half the wavelength, but within the coherence length, speckle will be
present [15]. Speckle produces grains in the image that deteriorates the images but if all
the waves backreflect from the sample volume, interfere constructively, and produce
contrast, then the OCT image improves [15].

Two different scans procedures are used in this technique. The longitudinal scan

or depth scan is performed moving the mirror. Longitudinal tissue structure is

13

detemiined by measuring the times of flight (or phase delay) of backseattered light. It
provides an axial (depth) resolution of roughly 10 um (depends on bandwidth of source).

The axial resolution is given by:

21112120
AI =—

m (25)

2.

Where A11 is the full-width at half maximum of the bandwidth. The transverse scan or

lateral scan is performed by moving the sample or by transverse scanning of the probe
beam. It is determined by how light is directed and collected from the sample [15]. The

transverse resolution is given by:

was)

Where d is the spot size on the objective lens and f is its focal length. High transverse
resolution can be obtained by using a large numerical aperture and focusing beam to
small spot size [17].

In order to choose the proper OCT light source some important considerations
need to be taken into account. Some of the important properties include: coherence, and
wavelength. One of the most commonly used light sources in OCT is a
Superluminescent diode (SLD)[15]. SLDs are diodes that become optically active and
generate amplified spontaneous emission. In contrast to laser diodes, there is not

sufficient feedback to achieve lasing action. This amplified spontaneous emission allows

l4

SLDs to be used in applications where low time coherence and high spatial coherence
light is needed as is the casex of OCT imaging. Coherence can be defined as the degree
of correlations that exist between the light fluctuations of two interference beams [15].
The wavelength selection is very important because the light penetration into the skin
depends on it. Scattering decreases when the wavelength is increased. Near Infrared
light experiences forward-directed scattering interactions in tissue [16]. This is one of the
reasons why SLDs are good sources for OCT. SLDs wavelength range goes from 675nm
to 1550nm, output powers up to SOmW and spectral widths up to 70nm.

A number of different OCT imaging techniques relying on polarization, doppler,
absorption, and elasticity OCT have been proposed [18]. Polarization OCT detects the
modified state of backreflected polarized light that the tissue generates when the light
passes through it. Normally the tissues that would produce this modifications of
backreflected polarized light are the ones that have very well organize structures. Some
of the tissues that have very well organized structures include: collagen, cholesterol
crystals, acting-myosin complexes, nerve fibers, and calcium hydroxyapatite.
Birefringence, dichroism, and optical rotation are three mechanisms used by the tissues to
modify polarization. Birefi-ingence occurs when the light propagation velocity is
dependent on the spatial orientation of the sample and is the most important mechanism.
Some factors that can affect birefringence are: molecular concentration, chemical
composition of molecules, form and intrinsic birefringence, molecular organization, and

the presence of multiple birefiingent materials. Changes in molecular type,

15

concentration, and organization can be signs of different pathological conditions and this
is why this technique is so powerful [15].

Doppler OCT measures the Doppler frequency shift in the OCT signal [15]. It
provides local velocity mapping with high spatial resolution. In comparison with
Doppler ultrasound, Doppler OCT measures the velocity resolution better than ultrasound
because the wavelength of the lightwave is shorter. Doppler OCT has been applied to
different fields like ophthalmology, dermatology, gastroenterology, cardiovascular
medicine, oncology and several others.

Absorption OCT measures the absorption spectrum of a sample [18]. It has the
goal of providing depth resolved quantitative tissue spectroscopy [19]. In order to do this
two different light sources are used These two light sources need to have center
wavelengths within and outside the water absorption band. To separate the scattering and
absorption effects, the scattering coefficients have to be similar for both sources [20]. It
has applications in the field of ophthalmology.

Elasticity OCT measures local variations of the stiffiress inside a tissue in a non-
invasive way measuring the shear elastic modulus. It quantifies microscopic
deformations of the tissues when stress is applied to them [18]. There are some
conditions that produce changes in the shear elastic modulus like edema, fibrosis, and
calcification. Elasticity OCT can be used to differentiate between hard and soft masses,
to image arterial plaque, and to evaluate how a wound is healing [18].

Research has been done in many areas using OCT imaging. One of the earliest

applications of OCT was in the field ophthalmology. A high-speed micrometer-

l6

resolution OCT system for automated in viva transpupillary measurements of the human
retina was developed[21]. The speed of the longitudinal scan was four times higher than
obtained previously. In this work the retinal and retinal nerve fiber layer thickness was
determined. The measurement is very important in order to diagnose retinal diseases
such as macular degeneration, macular hole and macular edema.

The ability of OCT to measure retinal thickness has been confirmed by several
studies. In [22] the reproducibility of retinal thickness using commercially available
mapping software of OCT was assessed. The thickness, measured by the software, was
determined by the distance between the inner borders of the inner and outer red bands of
high reflectivity. The study was performed in healthy and diabetic patients and proved
that the software allows measurements of retinal thickness in all patients with a
reproducibility of i5% in healthy subjects and 16% in diabetic patients with macular
edema.

In [23] OCT was used to obtain high resolution, cross-sectional images of the
retina and cells of the retinal pigment epithelium (RPE). Images of RPE are very
important because RPE is thought to be responsible for the formation of epiretinal
membranes after retinal detachment. OCT images showed RPE proliferation and
migration through the retina into regions of secondary epiretinal membranes. These
images suggest that the migration of RPE cells may be responsible for creating the
epirentinal membranes in the patients under study.

OCT has a lot of applications in the medical area. One of the most important is in

the area of cardiovascular medicine. Cardiovascular diseases are the number one leading

17

cause of death in America. OCT is used in the treatment and diagnostic of Acute
Coronary Syndromes (ACS). ACS includes myocardial infarctions and unstable angina.
OCT has been used for in vivo intravascular imaging in order to determine the thickening
of the inner layer of the arteries. Polarization OCT was used in [24] for imaging of back-
reflected light, birefringence, and fast-axis orientation simultaneously in different kinds
of atherosclerosis plaque. The research suggests that birefringence changes in plaque are
possible because of the collagen or cholesterol that is present in plaque. In [24] was
found that Polarization OCT is sensitive and that is able to characterize different kinds of
atherosclerotic plaques, has the potential to detect atherosclerosis early, and is able to
predict plaque rupture.

In [25] herniation of atheromatous plaque material into the coronary lumen was
observed in all the patients using OCT and this was not obtained with ultrasound. The
next figure shows an OCT image of a human coronary artery, the layered structure of this
artery with intimal hyperplasia is clearly identified [15]. OCT has also been use for
monitoring stent deployment. Stents are use to treat atherosclerotic plaques. In this area
it provides high resolution visualization of detailed vessel wall structure within and
adjacent to stents [25]. In Figure 2.3 a detailed image of an aorta is shown. Limitations

of the imaging method include attenuation of the response due to blood.

18

 

Figure 2.3 In vivo image of the aorta using OCT.

Another application of OCT is in the area of imaging the musculoskeletal system.
In this area OCT is used for early diagnosis and monitoring of osteoarthritis. OCT can
asses the extend of Osteoarthritis, monitor the effectiveness of chondroprotective agents
in the treatment of the disease, and monitor the effectiveness of the techniques of
cartilage repair [15]. Osteoarthritis is the number one cause of disabilities in the USA.
This disease affects cartilages the most. Cartilages are mostly made of collagen.
Collagen as was mention before has a well organized structure and because of this
Polarization OCT can be used to detect Osteoarthritis in early stages when collagen
disorganization is observed.

In [26] OCT was used to detect and monitor progression of experimentally

induced osteoarthritis in the rat knee joint. In this research thickness, surface

abnormalities, and collagen organization was observed These knee joints were imaged
with OCT and polarization sensitive OCT. In this case polarization sensitive OCT was
able to detect collagen disorganization. Collagen disorganization is an indicator that
osteoarthritis is present. This research proved the capability of OCT to assess articular
changes and observe the progression of the disease. OCT can also be used to image
tendons and ligaments. It is very useful to image the anterior cruciate ligament, the
Achilles tendon and the ligaments that make up the rotator cuff.

Research is being conduct to investigate how well OCT can detect cancer in early
stages. Gastric cancer has a high rate of sm'vival when it is detected at it is early stages.
In order to be detected at an early stage, the mucosa and submocosal diseases have to be
differentiated. The problem with the detection of this cancer at this early stage is that it is
very expensive. Images using OCT and propylene glycol as a contrast agent have shown
differences exist between the lamina propia and muscularis mucosa. In [27] OCT was
also used to identify different mucosal layers.

OCT has limited depth range but is enough to penetrate the mucosal lining of
endosc0pically accessible organs of the gastrointestinal tract and it provides images with
resolution superior to other techniques. OCT endoscopies have the potential of guiding
the selection of biopsy sites. This technique is better and cost effective if compare to the
actual technique of practicing random biopsies for early stage cancer [28]. This shows the
potential of OCT to detect early gastric malignancies in an inexpensive way. OCT
research is being conducted for other cancer types as well [29]. In [30] intraoperative

OCT is used for imaging prostate pathology in vivo. Ex vivo images suggest that OCT is

20

capable of differentiate glandular architectural morphology associated with prostate
cancer.

OCT has other potential applications in medicine. It is used in dentistry for the
diagnosis of early dental caries and assessing the adequacy of restorations [15]. It can
also be applied for prostate surgical guidance because it can reduce the impotence rates.
Nerve repair surgery is another area that is being considered because OCT has the
capability of imaging through the nerve and also distinguishes motor from sensory
nerves. OCT could also be used for surgical guidance for the precise delivery of high
power laser radiation and ablation of diseased tissue and tumors [31]. Research is being
done in the areas of vascular repair, neurosurgery, and in the area of assessing
subfertility.

OCT has also been used in other fields in addition to the medical field. OCT
research in [3 2] was done to analyze and to characterize paper as an alternative to slower,
labor intensive, expensive, and invasive techniques. This research shows how OCT is a
good alternative for paper characterization and evaluation and also to obtain information

about paper quality.

2.3 MICROWAVE TECHNIQUES

Microwaves are electromagnetic waves in the frequency range between 300 MHz

and 300 GHz. Microwave technology is very important to diagnostic and therapeutic

21

medicine. Microwave has been used for the treatment of benign prostatic hypertrophy
non-invasively. Microwaves are used to heat the prostate gland via the urethra and at the
same time dilation is made with an expansion balloon of the part of the urethra that
surrounds the prostate. This creates a safely long lasting enlarged lumens of the prostatic
urethras in one session [33]. Microwaves are used also for creating hyperthermia devices
for treating cancer. Hyperthennia treatments can increase the efficacy of conventional
radiation and chemotherapy [33]. Another application of microwaves for cancer
treatment involves the use of conformal array applicators for the treatment of breast
cancer. These conformal array applicators are design to heat superficial tumors and can
measure the temperatures of the heated tissues by measuring the thermal noise generated
by heated tissues [33]. Microwaves are also applied to the treatment of prostate cancer
using a dual microwave antenna system to heat tumors close to the urethra and the
rectum. Microwaves are also used to create pores in malignant cells to introduce
chemotherapeutic agents into the cell and destroy them [33].

The determination of the reflection coefficient and transmission coefficient at
microwave frequencies can be very helpful to detect changes in structures or human
body. In [34], [3 5] the refractive index was measured at a microwave frequency for
concrete. The refractive index was calculated for concrete a week after curing and 14
months after curing. The index of refraction showed a difference in the imaginary part
indicating that aging, in this case water desiccation, is responsible for this change in the

imaginary part.

22

Microwaves can be used to determine electric and dielectric properties of
materials using the free space technique which is contact-less. This can be used to create
more techniques to non-invasively treat or diagnose different types of diseases. In [36]
the permittivity of a material is found using the free space technique and the transmission
and reflection coefficient values. In order to do this the material sample is prepared with
large attenuation.

The free space method has been improved in order to reduce the effect of multiple
reflections and diffraction effects to measure complex permittivity and magnetic
permeability. The complex permittivity and magnetic permeability are calculated from
the reflection and transmission coefficients measured with horn lens antennas [37], [38].
Another method used to detect changes in material structures at microwave frequencies
involves the use of open ended rectangular waveguide sensors. This technique is used to
detect the minute thickness variations in laminate structures and is especially useful to
detect rust under paint. Microwaves can penetrate inside low loss dielectric materials,
like paint, and interact with their inner structure without suffering from high attenuation.
Variations in the magnitudes and phase of the reflection coefficient indicate the presence
of rust [39]. This technique and the variations in the reflection coefficients can be used in

different fields to determine changes in different structures.

23

2.4 TISSUE DIELECTRIC PROPERTIES

The relationship between electrical properties and the microstructure of trabecular
bone has been studied[2]. Some of these electrical properties are: permittivity, loss
factor, conductivity, phase angle, impedance, and dissipation factor. The pemittivity for a
dense, healthy bone is tipically high and low bone mineral density loss is associated with
high conductivity. Perrnittivity also shows a dependency with the trabecular bone
volume fraction; this parameter is strongly correlated with bone mineral density loss.
Conductivity in the trabecular bone is dependent on the fluid phase distribution and the
spatial orientation of the pores. These factors affect conductivity and the amount of
liquid phase and its spatial distribution have an impact on permittivity at low frequencies.
This effect decreases with increasing frequency [2].

The dissipation factor and relative permittivity are capable of characterize human
trabecular bone microstructure because these two are related to the amount of calcified
matrix of trabeculae [2]. There is also a relationship between mechanical properties of
bone and electrical measurements. Bones that have complex architecture and high
density have high permittivity, strength, and Young’s modulus. Bone strength was well
predicted by relative permittivity but not by conductivity [40].

Dielectric properties of tissues are necessary for simulations involving tissue
behavior towards microwave exposure. These dielectric properties are very important for
the biomedical imaging area. The dielectric properties of tissues are dependent in the

interaction between electromagnetic radiation and its constituents at the cellular and

24

molecular level [41]. The dielectric properties of the different tissues are calculated from
their complex relative permittivity in [41] which is given by:

3 = £'— jg” (2.7)
Where 8' is the relative permittivity of the material and 8" is the out of phase loss factor
which is given by:

5" = _0' ( 213)
50w

0' is the conductivity of the material, sometimes depending on the tissue there is a

contribution fi'om a frequency dependent-independent ionic conductivity 0',- , so is the

free space permittivity and a) is the angular frequency of the field.
These dielectric properties given in [42] were characterized from 10Hz to
lOOGHz accross four dispersion regions. The frequency dependence within each

dispersion region was expressed as a Cole-Cole equation:

A5,,
1+ (jan'n )(l—a)

A

8(a))=£oo +2

 

+ , l (2.9)
16080
Where A8,, is the magnitude of the dispersion and A8,, =35 — goo , 800 is the permittivity

at field frequencies where (or >>1, as is the permittivity at car << 1, and a is the low

frequency dispersion and is associated with ionic diffusion processes at the site of the

cellular membrane.

25

2.5 THE INDUCTION THEOREM

The induction theorem is used to find the scatter field when an obstacle is present

The incident field is defined as the field generated by the sources when an object is

absent and the total field is defined as that produced when the object is present. The

scatter field is defined as the difference between the field with the object present and the
incident field, that is, [43]:

1355:1549i H3=H—H‘ (2.10)

This scatter field is the field produced by the currents surrounding the object. The total

field and the incident field have the same sources. Figure 2.4 shows how the induction

  

theorem works.
E=Ei+Es Es
n n
Object )Js=Hi x n
L
$st=n x Ei
a b

Figure 2.4 8) Shows the original problem and b) shows how the induction theorem is applied.

The induction theorem can also be used to find the surface currents. In order to
do this the object is retained and the total field exists internal to it and the scatter field

exists external to it. The currents of these fields are given by:

26

Js=nx(Hs—H) MS=(ES—E)xn (2.11)
When the object is a perfect conductor the induction theorem is simplified because the

tangential total electric field is zero. Figure 2.5 shows how the induction theorem works

for a perfect conductor object. The equations of the field and current are reduced to:

anS=-ani MS=ES><n=ani (2.12)

E=Ei+Es Es

   

     
 

Perfect Perfect
Conductor Conductor
ést=n x Ei
a b

Figure 2.5 Induction Theorem for a Perfect Conductor.

2.6 LAYERED DIELECTRIC CYLINDER MODEL

The layered dielectric cylinder model is used to analyze the electromagnetic
scattering and penetration due in it when the cylinder is excited externally by a TM-
polarized plane wave. The plane wave is assumed to be propagating in the x coordinate

direction and this makes the angle of incidence zero. In the layer cylindrical geometry,

27

illustrated by Figure 2.6, the fields can be expressed in terms of cylindrical wave modes
[44]. In all the next equations a) is the external radius, a; is the internal radius, and at is

an angular variable. The plane wave is given by an infinite series of cylindrical wave

   

modes:
. co .
Ez'(p.¢)=E0 z j'MJmaclmeW (2.13)
m=—<n
Y
/I\
Boundary1
X
Boundary2

Figure 2.6 Geometry of a circular dielectrical scatterer with three layers.
The scattered electric field in the first layer, which is free space, is expressed as an

infinite number of outgoing propagating cylindrical wave modes:

28

E‘lz(p,¢)=Eo Z ClmHm‘2’(k1p)ej'"¢ (2.14)

m=-oo

The total electric field in this same layer is:

00 , 00 .
El,(p,¢)= 0 2 1""Jm(k1p)e”"¢+Eo Z ClmH‘z’mwlpvjm" (2.15)
m=—oo m=—oo

The angular component of the total magnetic field is expressed in terms of the axial
electric field:
.k 00 ._ ' ' -
H1¢(p,¢)=-;J)-l-Eo Z [J "U," (klp)+ClmH‘2)m(k1p)]eJ"'¢ (2.16)
”1 m=—oo

Where Clm is an unknown scattered modal coefficient for free space and p 2 a1.

For layer 3, which is the homogeneous lossy dielectric scatterer region, the total
electric field is expressed in terms of an infinite number of non-propagating cylindrical
wave modes:

w .
E32(p,¢) = 50 Z BameegmeW (2.17)
m=—oo
The angular component of the total magnetic field is expressed in terms of the axial
electric field:
1763 °° ' 'm¢
H3¢(p,¢) = "—150 z [133me (ks/3)]?! (218)
(0.113 "p.00

Where 33m is the unknown penetrated modal coefficient for this layer and p S 02 .

29

For the second layer, which is also homogeneous and a lossy dielectric region,
the electric field is expressed in terms of an infinite number of both propagating and non-

propagating cylindrical wave modes:

Ezz(p,¢)=Eo Z Bszm(k2P)ejm¢+Eo Z C2mH(2)m(k2/9)ejm¢ (2.19)

m=—oo m=—oo
Where B2m and C2m are unknown modal coefficients for the second layer

andaz SpSal.

The angular component of the total magnetic field is expressed in terms of the axial
electric field:

.k 00 ._ , . -
Hl¢(p:¢) = ‘ifiEO Z [J me (klp)+ ClmHm(2) (klp)]ejm¢ forp 2 a] (2.20)

mz—(D

'k 0° . , ,
H2¢(p’¢) = ‘é—szO Z [132me (k2P)+ C2mHm(2) (kzpflejm

fora S Sa
m=_oo 2 P 1

(2.21)

.k a) ' .
H3¢(P,¢)=-C{)—j350 Z [Bstm (lame/mt

m=—oo

for p 2 a2 (2.22)

The angular component of the magnetic field distributions is expressed in terms of
the cylindrical coordinate system:

30

. . ~ 16 . a .
-Jw#[pr+H¢¢]=-55¢;Ezp—55Ez¢ (2.23)

The angular component and the unknown modal coefficients can be determined if

these boundary conditions are used:

512.00%) = E22 (.0415)

”IA/”45) = H2¢(P,¢)

for .0 = 01

52200, ¢) = E32 (p45) (2'24)
H2¢(P’¢) = H3¢(.0,¢)

for ,0 = 02

Using these boundary conditions and [M][A]=[V] modal matrix equation the modal

coefficients are found. Matrix M is as follows:

 

 

H (2)m(k101) - "206201) —H(2)m(k2"l) 0
flflaymflqal) “kiJ'mUczafl -—lem(2)'(k2a1) O
2) (- )
o Jm(k2a2) H‘ m(k2a2) — mam)
k . k ' k '
0 -—2-J m(k202) —2-H(2)m(k201) “—34 m(k3‘12)
_ #2 #2 #3 _

The excitation vector V is:

p—

_ 7
-j me (k101)

 

 

_fl --m '
0
0

31

The vector A, which is the one with the unknown modal coefficients, is:
- Clm 1

(2.27)
CZm

 

 

32

CHAPTER 3 SIMULATION RESULTS FOR THE MICROWAVE
TECHNIQUE

In order to select the optimal frequency at which the experiments are to be
conducted, simulations carried out. Simulations were also conducted to determine how
much reflection was going to be obtained. We use a layered dielectric circular cylinder to
resemble a finger. Each of the layers of the cylinder represented a tissue/bone layer of
the finger. The first layer represents fiee space, the second layer represents skin, the third
layer fat, and the fourth layer represents bone. The scattered field in free space is
expressed as an infinite number of outgoing propagating cylindrical wave modes. The
scatter field in this region is given by

00
ESlz(P,¢) = E0 2 ClmH(2)m(k1p)ef'"¢ (3.1)
m=—oo
while the total field in this layer is given by

Elz(p,¢)=Eo z I‘me(klp)ejm¢+Eo 2 CImH (2)m(k1P)ejm¢ (3-2)

m=—w m=—CX)

In this equation pZal and a1 = 1.5 cm, k, which is the wavenumber, is given

byk=27rf,/p,y06,£0, where/10=472'10—7,80=8.854x10_12, ,u,=l and

r=goo +2 1_0i . This last equation, called the Cole-Cole
1+(jwz'n 6”)( a)+1w30

 

33

equation, describes the relative permittivity for different human tissues. In this equation
A5,, is the magnitude of the dispersion and A5,, = 55 — 5.Jo , 500 is the permittivity at field
frequencies where (or >1, 5 S is the permittivity at an >1, and a is the low frequency
dispersion and is associated with ionic diffusion processes at the site of the cellular

membrane. For this equation Clm is the scatter modal coefficient for free space. The

total electric field distribution for layers 2 and 3 can be expressed in terms of an infinite
number of both nonpropagating and propagating cylindrical wave modes. The total field

for layer 2 is given by

E22(10,¢)=Eo Z Bszm(k2.0)ejm¢+Eo Z szHm(2)(k2P)ejm¢ (3.3)

m=—® fizz—(1)

and for layer 3 is given by

E32 (Pa¢) = E0 2 83m] m (k3p)ejm¢ + E0 2 C3mH ”1(2) (k3.0)ejm¢ (3-4)

m=—oo mz-oo
where Bzm,C2m,B3m,C3m are unknown modal coefficients that were found for the
different dielectric regions. For layer 2,02 s p 5 al , and for layer 3, a3 3 p 5 a2 , where
02 =1.3 cm and a3 =1.1cm. For layer 4 the total electric field distribution can be

expressed in terms of an infinite number of nonpropagating cylindrical wave modes:

E4z(p,¢)=Eo Z B4me(k4p)e/""¢ (3.5)

m=-oo

34

Where p 5 a3 and B4”, is an unknown penetrated field modal coefficients for this layer.

The next figure shows the geometry of a circular dielectric scatterer with the different

layers used in this simulation.

   

Layer1
Boundary1

Boundary2

Figure 3.1 Geometry of a circular dielectric scatter with 4 layers.
The angular component of the total magnetic field can be expressed in terms of the

axial electric field in the respective layers, and these are given by:
jkr °° --m . (2y jm¢
H1¢(p.¢) = ——E0 2 [J J m(k1p)+ ClmHm (kl/ans p 2 a1
0/11 m=—-q3

(3.6)

35

.k a) , ' _
H2¢(p,¢) = -'aj7}2-Eo 2 [13sz m (kzp) + CZmHm(2) (16219)]?! "”502 S P S a1

mz—q)

(3.7)

.k a) ' .
H3¢<p,¢)=—fl-Eo Z [Bng'm(k3p)+C3mHm‘2’(k3p>1e1"'¢a3Spsa2
toys

m=—oo
(3.3)
.k a) .
H4¢(.0,¢) = 71::1-50 Z [B4mJ 'm (k4p)]81m¢10 5 a4 (39)
m=—oo

In order to determine the modal coefficients Clm,C2m,C3m,Bzm,B3m,and B4", the

electromagnetic boundary conditions had to be enforced. Both the axial component of
the total electric field and the angular component of the total magnetic field are

continuous at the dielectric boundary. If they are continuous at the boundary then:

E12 (,0, ¢) = E22 (,0, ¢)

f = 3.10
H1¢(p,¢)=H2¢(p.¢) °”’ “1 ‘ ’

E22(pa ¢) = E3Z(pa ¢)

f = 3.11
H2¢(P,¢)=H3¢(P,¢)orp 02 ( )

E3Z(p,¢) = E4Z(p> ¢)

f = .
H3¢(P,¢) =H4¢(.0,¢) mp 03 (3 12)

The total electric field expressions and total magnetic field expressions were substituted

into the boundary conditions just stated here and in order to find the modal coefficients

36

the following modal matrix equation is obtained based on the coupled boundary condition

expressions:
[M MA] = [V] (313)
To find the elements of the [M] matrix the coupled boundary condition expressions were

solved for the Bessel function of the total electric field in layer one.

For E12 (,0, (’5) = E22 (.0: ¢) ,

j—m m(k101)+ ClmHm(2) (klal) = B2me (k2 al ) + CZmHm(2)(k201)

- (2) (2) (3'14)
-1 meU‘lal) = CrmH m (k101) -32me(k2 (11)- szH m (kzal)
The first row of the [M] matrix is:

[Hm‘2)(k1a1) —Jm(k2a1) -Hm‘2)(k2a1) o o 0]

For H 1¢(10,¢) = H2¢(p,¢),

k '- . k , k I k I
“E1 me (klal)-E1ClmHm(2) (klal) = "$82me (k201) ‘fiCZmHM(2) (kzal)

k ._ . k - k . k -
—‘J “J", (k1a1)= ——‘C1mHm‘2>(k1a1>+-leme (k2a1)+—2C2mHm<2> (kzai)
#1 #1 #2 #2

(3.15)

The second row of the [M] matrix is:

kl (2)' k2 ' k2 (2)' ]
H ka J k a] Hm k a O 0 O
[ m ( 1 l) 2 m( 2 ) 2 ( 2 l)

37

For Ezz(p,¢) = E3z(p,¢),

Bszm (kzaz) + C 2mH ma) (k202) = 193me (16302) + C3mH mm (117302)

BJk C 11(2)]: —BJk —CH(2)k -o (3'16)
2m m( 202)+ 2m m (2‘12) 3m m( 302) 3m m (302)-

The third row of the matrix [M] is:

[0 Jmaczaz) Hm‘2)(k2a2) —Jm(k3a2) -Hm(2)(k3a2) 0]

For H2¢(,0,¢) = H3¢(,0,¢),

k2

#2
k2

' k ' k l k I
Bszm (k202) ulczmHm‘Z) (k2a2)+—383me (k3 a21+4C3mHmm (ksaz) = o
#2 #2 #3 #3

l k l k D k 0
Bszm (km) 722—672mHm‘2) (km) = 733—133me (km—jaws” (16302)

(3.17)

The fourth row of the matrix is:

k ' k ' k ' k '
[0 --2-Jm(k202) -—2-Hm(2)(k202) —3-Jm(k302) "linen/€302) 0]
#2 #2 #3 #3

For E3Z(pa¢) = E4Z(p3¢) ,

BngmacsamCsmHm(2>(k3a3)=B4me(k4a3>

(3.18)
Bstm (16303) + C3mHm(2) (16303 ) - 194me (16403) = 0

38

The fifth row of the matrix is:
[0 0 0 Jm(k3a3) Hmm (1903) -Jm(k4a3)]

For H3¢(,0,¢) = H4¢(p,¢),

k I k ' k '
-434me (k 4 a3) = ——333me (k3a3)—-iC3mHm(2) (ksa3) (3.19)
#4 #3 ”3

The sixth row of the matrix is:

k . k ' k '
[o 0 o ——3-Jm(k3a3) ——3-Hm(2)(k3a3) —41m(k4a3)]
#3 #3 #4

The excitation column vector [V] has the form:

,— .-

-J'_m(k101)
k ._ I
—1 J "UM/€101)
.ul

COCO

 

 

.. .J

The unknown modal coefficients that conform matrix [A]:

 

 

39

The next figure shows the results obtained when the cylinder was used to

resemble a finger.

 

 

 

 

L-————-——.——:

 

 

 

 

 

 

 

 

 

 

 

l
g: 1——- :
1 l
0 500 1000 1500
f(MHZ)
2 , 1
_ /\\ i I
U) 1..---- --__--____:-:1‘:::~:—_—_—_— '
a : :
0 : 1
0 500 1000 1500
f(MHZ)
2 I I
\-\ : :
E1r———— ~-----—-——-‘-‘“—.‘-‘=F I ——-
o 1 1
0 500 1000 1500
f(MHZ)

Figure 3.2 Graph that shows the incident field, scatter field, and reflection coefficient.
In this figure the scatter field is more than one and the incident field, i.e. the field

when no obstacle is present, was exactly one. The transmission coefficient, scatter field,
and incident field were calculated for different fiequencies, from 100 MHz to 1.5 GHz.

To find the reflection coefficient the following equation was used.

E0 2 ClmH‘Zlmrka

 

I“ = % = ”2:1: . (3.20)
1 EO 2 1"me (kl/OW m¢
m=—oo

40

The reflection coefficient is more than one because the microwaves were concentrated
around the cylinder. In order to prove this, the cylinder model was placed in a grid and
the reflection coefficient was calculated for different positions. The reflection coefficient
was calculated for a Cartesian grid converting the original polar coordinates used for the
cylinder model into Cartesian coordinates. Figure 3.3 shows how the reflection
coefficient was decreasing while it was far away from the cylinder. The red line indicates
the boundary between the skin and free space. Figure 3.4 shows how the reflection
coefficient is less than one when it is calculated at positions very far away from the skin

and free space boundary.

41

0.01

0.005

Cylinder-Free Space Boundary

 

 

- .02
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

Figure 3.3 “Images in this thesis are presented in color". Grid showing different reflection coefficient
numbers for different positions at 200 MHz. Each circular line in this figure represents a different
region outside the cylinder where the reflection coefficient was calculated The numbers on top of the
lines are the reflection coefl'rcients for those regions. The regions inside the red line represent the skin,
fat and bone. The outer regions in the figure have the smaller reflection coefficient (1.72). The next
region has a reflection coefficient of 1.74. The reflection coefficient in the region close to the
cylinder free space boundary is 1.76. Inside the cylinder the reflection coefficient varies from 1.78 to

42

Skin-Free Space Boundary

 

0 . , -— .
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

Figure 3.4 “Images in this thesis are presented in color”. Graph showing that the reflection coefficients are
less than one far away from the skin free space boundary. Each circular line in this figure represents a
different region outside the cylinder where the reflection coefficient was calculated. The numbers on

top of the lines are the reflection coefficients for those regions. The regions inside the red line
represent the skin, fat and bone. The outer region in the figure has a reflection coefficient of .95. The
next region has a reflection coefficient of 1. The region below has a reflection coefficient of 1.05 and
the region closer to the skin free space boundary has a reflection coefficient of 1.1.

The only frequency that experienced reflection coefficients less than one at all
positions in the grid was 100 MHz as can be seen in Figure 3.5. Reflection coefficients
were more than one for all the different frequencies. The reflection coefficients were
decreasing while the frequency was increasing from 200 MHz to 900 MHz as can be seen
in Figure 3.6. At higher fi'equencies, from lGHz to 1.2GHz and from 1.3GHz to 1.5

43

GHz, the reflection coefficients remained the same and less than the reflection coefficient

recorded at 900MHz.

0.02
0.015
0.01

0.005

Cylinder-Free Space Boundary
43.02 -o.015 -o.01 43.005 0 0.005 0.01 0.015 0.02

 

-0. 02

Figure 3.5 “Images in this thesis are presented in color”. Reflection coefficients calculated at difl‘erent
positions at 100MHz. Each circular line in this figure represents a different region outside the cylinder
where the reflection coefficient was calculated. The numbers on top of the lines are the reflection
coefficients for those regions. The regions inside the red line represent the skin, fat and bone. The
outer region has a reflection coefficient of .6. The reflection coefficient of the region close to the
cylinder the space boundary is .61.

0.005

 

-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

-0.01

-0.015

 

-0.02
-0.02 -0.015 -0.01 -0.005 0 0.005 0.01 0.015 0.02

(b)
Figure 3.6 “Images in this thesis are presented in color” (a) Shows the reflection coefficients calculated at
200 MHz and (b) shows the reflection coefficients calculated at 900MHz Each circular line in this
figure represents a different region outside the cylinder where the reflection coefficient was
calculated. The numbers on top of the lines are the reflection coefficients for those regions. The
regions inside the red line represent the skin, fat and bone.

45

In order to simulate the actual shape of the leg and all the different layers High
Frequency Structural Simulator or HF SS software was used. HF SS is a software based
on finite element analysis used to calculate S parameters and 3-D electromagnetic field
simulation of high-frequency and high speed components. The shape of the leg was
drawn in Solid Works first and then was uploaded in HFSS and was drawn using an
anatomy drawing of the leg. The simulation consisted of the different layers that
constitute the leg. The piece of the leg was 50mm high and 92.06mm wide. One of the
bones was 19.994 mm wide and 39.79mm long. The other bone was 17.70mm wide and
21 .973mm long. The muscle layer was 78.882mm wide and 63.67mm. The thickness of
the layer of fat is 3.65mm and the thickness of the layer of skin is 2.1379mm. The
following figures show the simulation drawing of the leg and the actual picture of the leg.

In order to simulate the leg, the materials were defined in the software. To do
this, the relative permittivity and conductivity of each material were calculated. The real

+ 0
1+ (jam, )(l"a) 15930

 

part of this equation 5, =500 +2 was used as the relative

permittivity and the conductivity was calculated using the magnitude of 0' = (j5,.)5oa).
To simulate the free space environment, the leg was placed inside a 300mm long, 200mm
wide, and 50mm high box. Vacuum was selected as the material, already defined by the
software, to fill the box. The boundary condition applied to all the faces of the box was
radiation. This is done to simulate open space and make the waves radiate infinitely into

space and avoid reflection from the wave.

46

A coaxial cable antenna was used to illuminate the body with a low power
microwave field The inner cylinder of the coax antenna had a length of 58 mm and a
radius of .5mm and was located in the middle of the box and 1.51mm away from the leg
at its closest position. The thickness of the outer cylinder of the coax antenna was 1mm.
The material assigned to the antenna was copper and this material was already defined by
the sofiware also. The excitation used for this antenna was waveport excitation The
following figure shows the leg inside the air box and the coaxial antenna. The coaxial

antenna was placed pointing towards the middle of the leg.

 

Figure 3.7 Pictures that show the air box, leg, and coax antenna used in the simulation with HFSS.

HFSS is based on the finite elements method. In order to obtain a reliable result
the mesh had to be refined depending on the frequency employed. Figure 3.8 shows how

the mesh looks like in the model used. In this case the dimensions of the element were

chosen such that the maximum dimension was 1% or less. Where the wavelength). =%,

cis the velocity of light and f is the fi'equency. The geometry is remeshed every time

47

the frequency is changed. The simulations were carried out with the frequency varying

from 100MHz to 1.5 GHz.

  
 
  

    
   

W
D (A)
1%

u
p.24!

  

 

  

Figure 3.8 Mesh inside the structure that was simulated.

This software is based also in an adaptive solution. In order to set how many
times the simulation is going to run a maximum Delta S per pass is needed. The Delta S
is the magnitude of the change of S-parameters or scatter parameter between two
consecutive passes. If this magnitude is less than the value that was set for maximum
Delta S the simulation stops. The maximum Delta S per pass given in the simulations
was 0.0011 and the maximum number of passes was 3.

The total field was measured across the line shown in Figure 3.9. In order to

measure the scatter field the total field without the leg or incident field was measured at

48

       
   
 
 
   
   

the line. The total field was measured with the leg also. To find the scatter field the total

field with and without the leg were subtracted

 

Figure 3.9 Line behind the leg where the total field was measured.

The simulations were carried out with the permittivity and conductivity reduced
by 5 percent in the bone to simulate loss of bone density. The total field of the simulation
with regular permittivity and the total field of the simulation with five percent less

permittivity were graphed together in order to compare both of them.

49

The simulations were done for different frequencies. At 100 MHz the graph that
shows the total field of the leg without changing permittivity values of the bone is very
similar to the total field of the leg changing the permittivity of the bone by five percent.
As can be seen in Figure 3.10 and Figure 3.11 both graphs are on top of each other
showing no difference between the two signals. At 50 MHz there was no difference
between the total field of the leg when the bone did not suffer changes in permittivity and
the total field of the leg when the bone had a difference of five percent in permittivity. It
can also be observed that the shape of the graph is a deformed Gaussian because of the

presence of the bones inside the leg. This creates the antisiymmetric shape of the graph.

50

Magnitude of E (V/m) vs. Normalized Distance for 100MHz
0.29 —

 

0 regular
Siess

 

 

 

0.28 —

 

0.27

0.26

0.25

0.24

0.23

Magnitude of E (V/m)

0.22 —

0.21

  
  

 

l l l l l l J

1
0.3 0.4 0.5 0.6 0.7 0.8 0.9
Distance

0.2

—L

Figure 3.10 Graph of the total electric field of the leg with regular permittivity and 5% less permittivity
for 100 MHz.

51

Magnitude of E (Vlm) \5. Normalized Distance for 50MHz

0 regular
fifi Sless
0
Q39 \
G)

<2,
ls

0.076

I

 

0.074

I

 

 

 

I

0.072

0.07

0.068

0.066

0.064

 

Magnitude of E (Vim)

0.062

0.06

0.058

 

 

l l l l l l l l l

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance

0.056
0

Figure 3.11 Graphs of the total electric field of the leg with regular permittivity and 5% less permittivity
for 50 MHZ.

At 200 MHz there was no difference between the total field for a leg with no change
in permittivity in the bone and the total field for a leg with a five percent change in
permittivity. The results were similar for the total fields measured at 500MHz. It can be
observed from this graph that the shape of the total fields is different from the graphs at
200, 50, and 100 MHz. This difference is because of cavitation effects of the box that

simulates fi'ee space at high frequencies.

52

Magnitude of E (V/m)

0.95

0.9

0.85

.0
oo

0.75

.0
N

0.65

0.55
0

Magnitude of E (V/m) vs. Normalized Distance for 200MHz

 

0 regular
-——— 5|ess

 

 

 

I

 

 

l l l l

 

0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance

Figure 3.12 Graphs of the total electric fields of the leg for 200 MHZ.

53

Magnitude of E (V/m) vs. Normalized Distance for 500MHz
1.4 ~

 

 

 

1.2~

 

0.8 -

0.6

Magnitude of E (Vlm)

 

 

l l l l l l l l g

l
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance

Figure 3.13 Graphs of the total electric fields of the leg for 500 MHZ.

The procedure was repeated changing the permittivity difference by twenty five
percent instead of five percent in order to find a significant difference between the two
signals and in this way find a new method to detect bone mineral density loss. It can be
observed that the difference of both signals is not sufficient and it is difficult detect bone
mineral density loss using this method. In Figure 3.14 it can be observed that at 500 MHz
there was no difference between the signal without change in permittivity and the signal
with twenty five percent change in permittivity. The same cavity effects that were

observed at 500 MHz for the graph with five percent less permittivity were observed in

54

this graph too. Figure 3.15 and Figure 3.16 show the results obtained for 50MHz and

100MHz.

Magnitude of E (Vlm)

1.4—

 

Magnitude of E (V/m) \5. Normalized Distance for 500MHz

 

—— regular
-—--- 25|ess

 

 

 

 

l l 1 l 1
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
Distance

1 l l l J

Figure 3.14 “Images in this thesis are presented in color”. Graph of the total electric field of the leg for

500 MHz when the difference in permittivity is 25%.

55

Magnitude of E (Vim) \5. Normalized Distance for 50MHz
0.076

I

 

——-— regular

0.074 —— 25|ess

I

 

 

 

0.072

I

I

0.07

I

2;.

g

Magnitude of E (V/m)

0.062

0.06

0.058

 

 

0.056 J l l l l l l l l l
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance

Figure 3.15 “Images in this thesis are presented in color”. Graphs of the total electric fields of the leg
with regular permittivity and 25% less permittivity for 50 MHz.

56

Magnitude of E (V/m) vs. Normalized Distance for 100MHz
0.29 —

 

—— regular
0.28 — -————— 25|ess

 

 

 

0.27

0.26

0.25

p
N
A

P
N
00

Magnitude of E (V/m)

 

 

 

0.22

0.21

02 1 1 1 r 1 1 1 1 1 1
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1

Distance

Figure 3.16 “Images in this thesis are presented in color”. Graphs of the total electric field of the leg with
regular permittivity and 25% less permittivity forlOO MHz.

The next figure shows the total field obtained when the coaxial cable antenna was
moved 0.01m to the left. It can be observed in this figure that there is a small difference
between the two signals. This small difference is not enough to make this technique

capable of distinguishing between a healthy bone and osteoporotic bone.

57

Magnitude of E (V/m) vs. Normalized Distance for 100MHz Pos -0.01m

0.29 —
0.28 —
0.27 — / 
0.26 -
0.25 —

0.24

Magnitude of E (V/m)

0.22

I

I

0.21

0.2 b

 

 

 

~———-—-— regular
——-—- 25|ess

 

l l

 

0.19 l l l l
0 0.1 0.2 0.3 0.4

Distance

Figure 3.17 “Images in this thesis are presented in color”. Signals for a healthy bone and a bone with

0.8 0.9

25% of permittivity loss for a different position of the coaxial cable antenna.

58

 

CHAPTER 4 CONSTRUCTION AND CALIBRATION OFAN

OPTICAL COHERENCE SYSTEM

4.1 MICHELSON INTERFEROMETER

In order to fully understand the concept of Optical Coherence Tomography (OCT)
it was necessary to become familiar with a Michelson Interferometer. The first phase of
this work was building an interferometer and getting interference fiinges. The Michelson
interferometer was built in two different configurations. The first configuration was with
a plate beam splitter. The second was built with a cube beam splitter. The interference
fringes were visible with both configurations. In this part of the research it was also
necessary to become familiar with the concept of collimated beams. This was done with
a laser as a light source.

In order to build a Michelson interferometer Helium-Neon 4mW class IIIa Laser
from Uniphase was used as the light source. The beam that is produced by the Helium-
Neon laser goes through a plate glass beam splitter. Two mirrors were used to reflect
their respective beams back to the beam splitter and then, ultimately, the detector.

In order to obtain a proper alignment of the beam it was necessary to make sure
that the beam was at the same height from the optical table through the path of the laser.
After the beam was at the same height the beam splitter was placed in the optical table at
a 45 degree angle. The next step was to place the two mirrors at the same distance away

from the beam splitter. One was placed at the right hand side of it and the other one was

59

placed below it. The two beams reflected from the mirrors were observed in the black
wall that was above the beam splitter. The two mirrors were adjusted until the beams
reflected from each mirror overlapped and interference was observed. The construction
of a Michelson Interferometer can be observed in Figure 4.1

Mirror #2

 

 

Light
source

 

 

m rourw

 

 

 

A

Figure 4.1 “Images in this thesis are presented in color”. Michelson Interferometer

Due to multiple reflections the plate beam splitter was substituted by a cube beam
splitter. The cube beam splitter was placed in the same place as the plate splitter. The
cube beam splitter helps to minimize reflections and makes it easier to overlap the beams.
The mirrors were adjusted once again to get interference fringes.

In a Michelson Interferometer experiment, the beam should be fairly collimated
To collimate the beam two lenses were used. These lenses were selected due to the space
available on the optical table. The focal length of the lens closer to the laser beam was -

25 mm and the focal length of the one closer to cube beam splitter was 300 mm. The first

60

lens was placed 12 m away from the laser beam and the second lens was placed 46 mm
from the cube beam splitter. One of the mirrors was placed 152 mm to the right of the
cube beam splitter. The other mirror was placed 150 mm below the cube beam splitter.
To produce a well collimated beam the distance between the lenses was 265 mm. This
distance was obtained by trial and error for simplicity. After all this was done, the

mirrors were adjusted to overlap the beams and produce interference fringes.

4.2 OCT SYSTEM WITH A LED AS A LIGHT SOURCE

For the second phase of this research the laser was substituted with a LED
because an OCT light source was not available at the time. The laser light source was
used to learn the basic principles of interference and the Michelson Interferometer. It can
not be used for OCT purposes because it is a monochromatic light source and its
coherence length is very long. This means that interference of light occurs over a
distance of meters. On the other hand, LEDs are broadband and emit light in all
directions, making them an incoherent light source as opposed to a monochromatic light
source. It has a low coherence length and interference of light occurs over a distance of
micrometers.

In order to construct this interferometer a red 10mm InGaAIP LED such as the
one in Figure 4.2 was used as a light source. This type of LED had a Alt=l8nm, lt=644nm
and a coherent length of [c = 22um. The LED was powered with 4.3 volts at 0.02
amperes. To avoid damaging the LED a 2.2 M!) resistor was connected in series to it. To

spatially filter the emitter structure of the LED and pseudo-collimate the LED beam, two

61

lenses, one with a focal length of 25.40 mm and the other with a focal length of 50.20
mm were used in conjunction with a 25 um pinhole. A micro lens was also placed 5mm
away from the LED. The 25.40mm lens was placed 22mm in front of this lens. To filter
the structure of the LED, the 25 um pinhole was placed 60 mm away from the 25.40 mm
lens. Finally, to roughly collimate the light (it is actually slightly convergent), the 50.20

mm lens was placed 50mm away from the pinhole.

 

Figure 4.2 LED used for this experiment

The distances between the mirrors and cube beam splitter were change to obtain
interference with a LED light source. The distance between the 50.20mm lens to the
cube beam splitter was 122 mm. The mirrors were placed 104mm away fi'orn the cube
beam splitter. A photodetector was used to detect the power of both beams and the
interference between the two. This device was placed 125mm away from the cube beam

splitter. In order to see the interference a Tektronix TDS 30328, 300MHz and 2.5 GS/s

62

oscilloscope was connected to the photodetector. The set up for this experiment can be

observed in Figure 4.3.

 

Figure 4.3 Set up of a Michelson Interferometer using a LED as a light source.

To test and measure the depth resolution of the system a multimeter was
connected to the photodetector, so an accurate reading of the interference intensity could
be made. The multimeter was used to measure the interference intensity of the combined
beams, as well as the intensity of each of the beam, individually. Interference can be
proven if the measurement of both beams intensities is not equal to the sum of each of the

beams intensities. Interference leads to a new term appearing in the total intensity

equation. The equation becomes 1 T = 11 + 12 + 2 * (II—1 * (II—2 *cos¢. Each of the

63

mirrors was adjusted in order to obtain the same intensity from each one of the beams.
The intensity of each of the beams individually was measured with the photodetector and
found to be 75.1 mV. The intensity of the two beams together was also measured. The
distance at which the interference was maximum was located with the oscilloscope first.
Then the multimeter was connected and intensity data was collected for that case.
Intensity data was taken 30 um before and after this point. Measurements of the
combined beam intensity and of each of the individual beam intensities were recorded
with the multimeter.

The intensity of each beam was added and this result was compared to the
measurement of the intensity of the combined beams. If the sum of the two beams was
exactly the same as the one measured, there was no interference. The results of this
experiment are shown in the next table. It can be observed from this table that at
5725um, 5726um, 5730um, 5735um, 5736um, 5737um, 5739um, 5740um, 5743um,

5745um, 5747um, 5750um, 6005um and 6010um there was interference.

Table 1 Results from the experiment with the LED as a light source and both mirrors.

 

 

 

 

 

 

 

Distance Intensity Scan Intensity Sum of each Intensity of
Mirror (mV) Regular Mirror intensity (mV) Both Beams
(mV) (mV)
5700um 75.1 75.1 150.2 150.4
5705um 75.1 75.1 150.2 150.4
5710um 75.0 75.1 150.1 150.3
5715um 75.1 75.1 150.2 150.3
5720um 75.1 75.1 150.2 150.2

 

 

 

 

 

 

Table l (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

5725um 75.0 75.0 150.0 151

5726um 75.0 75.0 150.0 149.7
5727um 75.0 75.0 150.0 150.0
5730um 75.0 75 .0 150.0 151.7
5733um 75.0 75.1 150.1 150.0
5735um 75.0 75.0 150.0 152.4
5736um 75.0 75.0 150.0 152.3
5737 um 75.0 75.0 150.0 147.7
5739um 75.0 75. 1 150.1 153.3
5740um 75.0 75.0 150.0 154.1
5743um 75.0 75.0 150.0 154.7
5745um 75.0 75.0 150.0 145.5
5747um 75.0 75.0 150.0 155

5750um 75.0 75.0 150.0 146

6005um 75.0 75.0 150.0 152.1
6010um 75.0 75.0 150.0 151.1
6015um 75.0 75.0 150.0 150.2
6020um 75.0 75.0 150.0 150.9
602511111 75.0 75.0 150.0 150.2
6030um 75.0 75.0 150.0 150.4

 

 

 

 

 

 

Using Matlab a graph was constructed to analyze these results. The yellow graph

in Figure 4.4 represents the true approximation to the experimental data. The blue graph

65

denoted by the x represents the experimental data. The true approximation is very close
to the experimental value as can be seen in this graphical representation.

Intensity (mV) vs. Distance (um)

Intensity (mV)
0
X
X
X
X
X

 

-5
-50 -4CI -31J -2D -10 0 10 2D 30 40
Distance (um)

Figure 4.4 “Images in this thesis are presented in color”. Experimental and true interference when an LED
was the source of the OCT system

66

 

1% I I r I 9 T I T

154 - {fl -
<

153 l- .

152 r

151 -

15]-

 

149-

 

 

148-

 

 

 

 

 

147i-

 

146-

 

<>
1 L l l l l I l
‘30:: 210 220 230 240 250 260 270 2&3

 

 

 

Figure 4.5 Experimental data when an LED was the source of the OCT system.

In order to prove that the system that was built worked as an OCT system, the
thickness of a micrOSCOpe cover slip was measured. The mirror in the stationary arm was
substituted with a glass cover slip as can be observed in Figure 4.6. When this was done
interference could not be detected because there was not enough light being reflected to
the photodetector. Instead a gold coated cover slip was glued to the microscope slide to
create the effect of a mirror. The back layer of the gold coated cover slip was acting as a
mirror because it was coated with a 50nm gold coat; the front layer was covered with a
5nm gold coat which made it partially transparent as shown in Figure 4.7. The thickness

of the glass cover slip was measured with a micrometer and found to be approximately

180 um thick.

67

 

Figure 4.6 Michelson Interferometer with a Microscope cover slip.

The interference was detected with the oscilloscope first. The oscilloscope time
scale was set at 40ms/division and the voltage scale was set at 20mV/division. After the
interference was detected with the oscilloscope, the intensity of each beam was measured
with the multimeter before and after interference was detected. The intensity of both
beams was measured also. Two interference patterns were observed when the mirror was
substituted with the microscope cover slip. The first pattern was observed between
7820um and 7835um. This is shown in table 2. The intensity of the beams was measured
every 2.5um fi'om 7800um to 7850um. The second interference pattern was observed
between 8075um and 8095um, also shown in table 2. The intensity of the beams was also

measured every 2.5um from 8075um to 8100um. There was no interference from

68

7.850um to 8.075 urn. The intensity was measured every 10 um when there was no

interference between the beams.

 

Figure 4.7 Gold coated cover slip.

Table 2 Results from the Microscope cover slip experiment

 

 

 

 

 

 

 

 

Distance Intensity Scan Intensity Sum of each Intensity of
Mirror (mV) Regular Mirror intensity (mV) Both Beams
(mV) (mV)
7800.0um 39.69 68.72 107.41 108.9
7802.5um 39.69 65.16 104.85 105.3
7805.0um 39.7 65.16 104.86 104.8
7807.5um 39.76 65.19 104.95 105.4
7810.0um 39.7 65.2 104.90 105.3
7812.5um 39.7 65.2 104.90 105.4

 

 

 

 

 

69

 

Table 2 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7815.0um 39.7 65.19 104.89 104.3
7817.5um 39.7 65.2 104.90 105.2
7820.0nm 39.7 65.27 104.97 110.7
7822.5um 39.7 65.32 105.20 101.9
7825.0um 39.7 65.36 105.06 107.3
7827.5um 39.7 65.5 105.20 103.7
7830.0um 39.7 65.3 105.00 105.8
7832.5um 39.7 65.3 105.00 106.7
7835.0um 39.7 65.4 105.10 106.4
7837.5um 39.7 65.3 105.00 105.3
7840.0um 39.8 65.3 105. 10 105.9
7842.5um 39.7 65.4 105.10 105.7
7845.0um 39.7 65.4 105.10 105.5
7847.5um 39.7 65.5 105.20 105.7
7850.0um 39.7 65.6 105.30 105.9
7860.0um 39.7 65.6 105.30 105.8
7870.0um 39.7 65.5 105.20 105.7
7880.0um 39.7 65.6 105.30 105.8
7890.0um 39.8 65.7 105.50 106.14
7900.0um 39.7 65.7 105.40 106

 

 

 

 

 

70

 

Table 2 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

7910.0um 39.81 65.80 105.61 106.1
7920.0um 39.82 65.7 105.52 106
7930.0um 39.7 65.8 105.50 106.07
7940.0um 39.8 65.7 105 .50 106.2
7950.0um 39.8 65.8 105.60 106.1
7960.0um 39.7 65.8 105.50 106.1
7970.0um 39.8 65.9 105.70 106.2
7980.0um 39.82 66 105.82 106.2
7990.0um 39.8 66.02 105.82 106.3
8000.0um 39.8 65.9 105.70 106.3
8010.0um 39.8 66.1 105.90 106.4
8020.0um 39.8 66.0 105.80 106.3
8030.0um 39.8 66.0 105.80 106.3
8040.0um 39.8 66.0 105.80 106.3
8050.0um 39.8 66.0 105.80 106.3
8060.0um 39.85 66.15 106.00 106.5
8070.0um 39.8 67.2 107.00 107.6
8075.0um 39.8 66.5 106.30 107.4
8077.5um 39.8 66.6 106.40 108.9
8080.0um 39.8 66.6 106.50 103.4

 

 

 

 

 

71

 

Table 2 (cont’d).

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

8082.5um 39.8 66.7 106.50 1 10.8
8085.0um 39.8 66.6 106.40 102.5
8087.5um 39.8 66.7 106.50 104.0
8090.0um 39.82 66.6 106.42 106.6
8092.5um 39.8 66.6 106.40 108.8
8095.0um 39.8 66.6 106.40 105.50
8097.5um 39.8 66.5 106.30 107.0
8100.0um 39.8 66.6 106.40 107.40
8102.5Ilm 39.8 66.5 106.30 106.80
8105.0um 39.8 66.6 106.40 107.20
8107.5um 39.87 66.7 106.57 106.70
81 10.0um 39.8 66.6 106.40 106.70
8112.5um 39.87 66.7 106.57 106.80
8115.0um 39.87 66.7 106.57 107.00
8117.5um 39.9 66.8 106.70 107.30
8120.0um 39.8 66.8 106.80 107.10
8122.7um 39.87 66.9 106.77 107.30
8125.0um 39.87 66.85 106.72 107.20

 

 

 

 

 

72

 

A graph was generated using the experimental data as well as the true data. It can
be observed in Figure 4.8 that the first interference peak occurs at a relative distance of
7820um and the second one at 8082.5um. At these distances the sum of each of the
beams was not the same as the measurement of both beams intensity. The difference of
these two numbers generated an optical path difference of 262.5um. In order to obtain
the thickness, the index of refraction of the glass was taken into account. The refraction
index of glass is 1.5. The optical path difference was divided by the refraction index

generating an experimental thickness of 17 Sum.

Delta intensity (mV) vs. Distance (um)
111 ~

1105

109

I

108 -

107 ~ M

1... ll

105 W 1'

104—

 

 

 

Delta Intensity (mV) ,

 

 

103

I

 

 

102 —

 

101 1 1 1 l 1 1 1
7800 7850 7900 7950 8000 8050 8100 8150

Distance (um)

Figure 4.8 Graph showing the two interference peaks.

73

Because the interference data sub-samples the intensity in the interference region,
a true approximation was made creating a Gaussian interference envelope based upon the
specifications of the LED and superimposed on the graph that was made with the
experimental data. The two peaks of the Gaussian beam were subtracted and the result
was divided by the index of reflection of glass. The first one occurred at relative position
of Guru and the second one at 265nm. The optical path is, in this case, 265nm. When this
number is divided by the refraction index it generated a thickness of 176.6667 um. Both
experimental thicknesses were very close to the true one of 180um. This graph is shown
in Figure 4.9. These results prove that the OCT system would work for measuring

thickness. This means that the system would be able to scan the sample.

74

Delta Intensity (mV) 15. Distance (um): Theoretical Comparison
111 —

109 —

1 l
107 ~ .

 

Delta intensity (mV)
8

103 r

 

 

 

 

 

101 . 1 1 1 1 v 1 1
-50 0 50 100 150 200 250 300 350
Distance (um)

Figure 4.9 Graph that shows experimental data vs. true approximation.

In order to take more samples the scan mirror was placed in a miniature linear
stage. The intensity was recorded every 3.028urn. The data was collected through the
computer using LabView. The data was saved in a text file and analyzed with Matlab.
The Virtual Instrument (VI) consisted of four main parts. The first one was created to
control the movement of the linear stage. The second part recorded the position and the
third one the intensity. In the fourth one a graph with the intensity values was created.

The experiment was conducted and in Figure 4.10 it can be observed the
interference plot that was captured when the linear stage was used. The motorized linear
stage increases the accuracy and the data points in the experiment and Figure 4.10 shows

75

it. When the experiment was conducted with a motorized linear stage the interference

was detected between positions 10,510um and 10,560urn approximately.

interference
O. 1 1 l l I I j

 

0.108~ -

0.106 — _

 

0.104 — WWW“ i —

 

 

 

 

Intensity in V

 

 

 

0.102 _ 11 i

 

 

0.1~ —

 

 

 

0098 1 1 1 l 1
1.048 1.05 1.052 1.054 1.056 1.058 1.06

Position in um 4
X1 0

 

Figure 4.10 Interference with LED as a point source and a motorized linear stage.

In Figure 4.11 the yellow graph is the true approximation to the experimental
data. The blue graph denoted by the x represents the experimental data. The true
approximation is very close to the experimental value as can be seen in this graphical
representation for this experiment. This graph also shows the precision that can be

achieved with the motorized linear stage and the LED as a point source. Many data

76

points were lost but still the interference could be distinguished when the micrometer was
used instead of the motorized linear stage.

The graph in Figure 4.12 shows two interference points. The first one is the
surface of the cover slip and the second is the back surface of the cover slip, which is
coated with gold. The first peak occurred at 10293um and the second one at 10545um
and the thickness is 252nm, which when divided by the index of refraction is 168nm.
The difference between the true thickness and the experimental thickness of the cover
slip was of about 6% when the motorized linear stage was used and between the
experimental thicknesses using the motorized linear stage and the micrometer is about

4%.

77

Intensity (mV)

‘8

1*

 

$01

Intensity (mV) vs. Distance (um)

, X

Distance (um)

Figure 4.11 “Images in this thesis are presented in color”. Graph showing experimental and

true interference.

78

Interference
O. 1056 I l | l I l I

 

0.1054 — _

0.1052

1
1

0.105 — _

0.1048 — _

.1... 1 _ ‘
“1°” ‘1’1’0f11liiva V V VFW WU —

0.1042

I

 

Intensity in V

 

 

I

 

0.104 - 4

 

 

 

 

0.1038 1 1 1 1 1 1 1
1.02 1.025 1.03 1.035 1.04 1.045 1.05 1.055 1.06

Position in um

 

4
X10

Figure 4.12 Interference peaks with a LED as a point source and motorized linear stage.

4.3 OCT SOURCE

The next step in this research was to use an OCT source as a point source. This
source had a wavelength of 820 nm, a 3 dB bandwidth and an operating current of 220
mA. To focus the beam a lens with a focal lens of 25.40mm was used after the source
and a lens with a focal length of 75mm was used before the photodetector. In Figure 4.13
interference peaks were observed at position 105 86um and 10844um. The subtraction of

these two was equal to 258 um and when was divided by the index of refraction of glass

79

was 172nm. The difference between the true and experimental thickness was about
4.44%. Figure 4.13 show that the modulation in both arms is not the same. The other
problem with this experiment is that the power was not strong enough for experiment

purposes with bones because the intensity was about lOmV.

Delta Intensity (V) 1.5. Distance (um)
0.0106 1

0.0105

I

0.0104

I

I

 

0.0103

 

 

Delta Intensity (V)

0.0102

0.0101

I

 

l l l l l l

0.01 l l 1 1
1.01 1.02 1.03 1.04 1.05 1.06 1.07 1.08 1.09 1.1 1.11
Distance(um) 4
X10

 

Figure 4.13 Interference peaks with an OCT as a point source.

In order to increase the intensity another experiment was conducted and power
was increased to a peak value of 6.1V but the modulation was again not the same in both
arms, as can be seen in Figure 4.14. The difference between the peak in position 5189um

and the one in position 5438um was 249um and divided by the index of refraction was

80

166nm. The difference with the true thickness of the cover slip was around 5.55%. The
difference between the peaks in position 543 8um and position 5693um, and after dividing

by the index of refraction, was l70um.

Interference
6.3 . 1 . 1 r 1

 

6.2 ~ _

6.11— ~

5.9 - z

Intensity in V

5.8 ~ a

WWW” 11114.4.) WW1 “1M -

5.6 — ~

 

 

 

5. 5 l l l l l 1
4600 4800 5000 5200 5400 5600 5800 6000

Position in um

 

Figure 4.14 Interference peaks with an OCT source and intensity around 6V.

In order to achieve both interference and the same modulation in both arms the
lens was changed to an infrared lens with a diameter of 25.4mm and a focal length of
50.0mm. After this was done no interference was found. The reason that no interference
was found was because the source was polarized The direction of the electric field was
horizontal and that was causing the problem. To solve the problem the source was
rotated vertically, after this was done interference was found. Also the modulation in

each arm was about the same.

81

The problem after the infrared lens was installed was that a lot of data points
could not be found. This was caused because the power reflected back from the mirror
was higher than the one reflected from the cover slip and the interference was not strong.
In order to solve this problem an absorptive neutral density filter with a neutral density of
0.1 was placed in front of the mirror. After this was done the intensity of the mirror was
less than the intensity reflected by the cover slip and the interference was now stronger.

Interference was found around 1600um, l850urn and 2100um. The difference
between the first and second interference peaks was 250nm and the difference between
the second and third peaks was 250nm. If both are divided by the index of refraction the
experimental thickness is 166.67um. Each interference peak represents the interaction of
the beam with each of the surfaces. The first interference peak at 1600um corresponds to
the beam hitting the front surface of the cover slip, the second interference peak at 1850
um, which was very strong, corresponds to the beam hitting the back surface, which is
cover with gold, of the cover slip. The third interference peak corresponds to the first of
multiple bounces of the beam. From this position on interference peaks can be found
every 250nm, which will be of less intensity because of the beam bouncing back and
forth.

After the OCT system was built and the thickness of the microscope cover slip
was calculated an image of the microscope cover slip was obtained. In order to do these
two linear stages were used to scan the microscope cover slip. The scan mirror was
placed on top of one of the stages and the arm with the microscope cover slip was placed

on top of the other stage.

82

For this experiment an infrared lens of a focal length of 30mm was used 35mm
away from the source. The distance from the lens to the prism was about 340m and the
distance from the prism to the photodetector was 160mm. The V1 had to be modified in
order to acquire the data from the additional stage and make the scan quicker.

In Figure 4.15 the scan of the microscope cover slip can be appreciated. The fi'ont
surface of the microscope cover slip can be observed in this figure. In order to observe
both front and back surfaces of the microscope cover slip the intensity of the beams
needed to be increased and the alignment could have been improved. Alignment is very
important in order to obtain perfect interference and also accurate results with this

technique.

83

 

1002003004005006007008009001000

Figure 4.15 "Images in this thesis are presented in color”. Front surface of the microscope cover slip.

In order to use the bone as a sample it was necessary to add another infrared lens
between the prism and the sample arm. This was done to focus the beam that was
coming into the bone sample. If this is done the beam will not overlap and a better lateral
scan will be achieved. Figure 4.16 shows the bone sample used for the experiment. The
sample is a thin slice of bone from a cadaver. It was dye in magenta because it was used
for another experiment and it was necessary to take pictures of it. Figure 4.17 shows the
signal obtained when a depth scan was done to the sample. The figure shows a very
noisy signal that doesn’t show any interference peaks that were expected when pores or

holes in the bone were found. Interference peaks were expected at each discontinuity in

84

the bone. The results were not as expected because when the infrared lens were placed
between the prism and the sample it was very difficult to align the system to find strong
interference. The intensity of the interference was not as strong as for the other
experiments. Alignment and good interference was very important for this experiment
because the bone doesn’t reflect back that much light as a gold coated microscope cover
slip does. It was also very difficult to obtain a good signal from the bone because it did
not reflect a lot of light. The reason it did not reflected a lot of light was because the pink

dye in the bone absorbed much of the light.

 

Figure 4.16 Bone sample used in the experiment.

85

Delta Intensity (V)

Delta intensity (V) \8. Distance (urn)

2.98 ~

'8

.~
58

2.92 -

2.9 —

2.88 ~

 

2_ 86 1 1 1 1 1 l 1 1 g
0 10 20 30 40 50 60 70 80 90

Distance (um)

 

Figure 4.17 Signal from the depth scan of the bone sample.

86

CHAPTER 5 ANALYSIS OF OPTICAL COHERENCE

TOMOGRAPHY DATA

5.1 CALIBRATION OF THE SYSTEM

The first image taken with the OCT system, built by Applied Science Innovations
Inc., was the image of the microscope cover slip. The OCT system is shown in Figure
5.1. The microscope cover slip was used to calibrate the OCT system that was built in
the laboratory as well as the commercial system. The experimental system with
microscope cover slip coated with gold is shown in Figure 5.2 and the signals showing
reflections from the front and back of this microscope cover slip is presented in Figure
5.3. The typical depth resolution for this system is around 10 um. The depth dimension
of the display in Figure 5.3 is 2.4 mm and the lateral dimension is 273nm. The distance
between samples along the depth dimension was obtained by dividing 2.4 mm by the
total number of samples (280) which is equal to 8.6 pm. The depth location was then

found by multiplying the sample number by 8.6 pm.

87

 

Figure 5.1 OCT system built by Applied Science Innovations.

 

Figure 5.2 Microscope cover slip coated with gold.

88

Typical depth scans of the microscope cover slip can be observed in Figure 5.3.
The distance between the two highest peaks circled in red was found to be 172 pm. In
the schematic presented in Figure 5.4 the peaks locations can be observed. The first
peak, which represents the front layer of the microscope cover slip, is located at 266.7
um and the second peak, which represents the back layer of the microscope cover slip, is
located at 524.7 um. The distance between the two peaks is 258m. Dividing this value
by the refractive index of glass which is 1.5, gives the thickness of the cover slip as
172nm. The true thickness of the microscope cover slip measured with a micrometer and
found to be 180 um. Both numbers are very similar with a percentage of error around

4.44%.

.sNOO-§U'la>\lm®

   

20406080100120140160180200220 ° 50° 1°00 150° 200° 250°
Depth Loeation(um)

Figure 5.3 Image of the microscope slip cover with gold and depth scans of the microscope cover slip.

89

258um

A

 

266um 524.7um

 

Figure 5.4 Schematic that explains how the thicknesses of the microscope cover slip cover with gold was
obtained

Another method used to calibrate the equipment was to scan three microscope

cover slips that were not coated with gold. Figure 5.5 shows a schematic of the 3

90

microscope cover slips and the expected signal. The schematic shows that the first peak,
labeled A, represents the front layer of the microscope cover slip labeled A and the
second peak represents the back of the microscope cover slip labeled C. The true

thickness of the three microscope cover slips was found to be 160 pm when measured

with a micrometer. Figures 5.6 (a) and (b) show the b-scan image data from the three
microscope cover slips and some of the typical a-scan signals. Figure 5.6 (b) shows the
depth scans of the microscope cover slips. The experimental thickness between the two
peaks circled in red in the figure was calculated The first peak, located at 258.1 um,
represents the fi'ont layer of the first cover slip and the second peak, located at 524.7um,
represents the back of the third cover slip. The experimental thickness was found to be

177.73 ,um. Figure 5.7 shows a picture of the three microscope cover slips used in the

experimental setup.

9]

 

 

8]

 

ii .

258.1um 524.7um

 

 

 

 

 

 

Figure 5.5 Schematic of the microscope cover slips and the signal.

 

’. r--~_-“‘-a-. .

   

2040 60 80100120140160180 200 20

Depth Location (um)

(a) B-Scan Image (b) A—Scan Signals

Figure 5.6 Image of the three microscope slips and depths scans for three microscope cover slips.

92

 

Figure 5.7 Picture of the three microscope cover slips used to calibrate the OCT system.

5.2 EXPERIMENTAL OBSERVATIONS

The thin slice of the tibia bone sandwiched between two acrylic layers shown in
Figure 5.8 was scanned in different areas. Each of the black dots in the bone represents
the different areas where it was scanned. The bone has two different structures. The
compact structure of the bone is shown in Figure 5.9 between the two red lines in the
picture. The cancellous structure of the bone is the inner area of the bone shown in
Figure 5.9. This area is also known as spongy bone. The compact structure of the bone
is usually found in the shafts of long bones and surrounds the marrow cavities. It consists
of cylindrical units called osteons [45]. Osteons are bone deposits that occur in a
concentric form inside the tunnels left by the osteoclast [1]. Each osteon contains
concentric layers of hard, calcified matrix with osteocytes, which are bone cells that
do not divide into more bone cells and become entrapped in the osteoid [1], they are
located in spaces between the layers. The spongy or cancellous bone is made up of a

93

network of fine interlacing partitions, which is called the trabeculae [45]. The
network of interlacing partitions encloses fatty marrow [45]. Based on this
observation the bone slice image can be divided in different sections 1 (compact), 2
(cancellous) and 3 (cancellous). The depth scans obtained from the regions labeled 1,
2, 12 were analyzed in terms of the porosity in the corresponding region. The

different sections can be observed in Figure 5.10.

 

Figure 5.8 Tibia slice sample scanned.

94

 

Figure 5.9 “Images in this thesis are presented in color”. Picture of the tibia that shows the compact
structure and the cancellous structure of bone.

 

Figure 5.10 “Images in this thesis are presented in color." Picture of the bone that shows the areas of the
bone that were analized.

95

 

Figure 5.11 Picture of the bone that shows how it was scanned.

Figure 5.12 shows the scans from the dot labeled as number 1. The line parallel
to the x-axis, in the image represents a strong reflection from the first layer of acrylic
covering the bone. In the graph, which represents the depth scans at this particular dot,
the highest peak in the figure represents the discontinuity between the acrylic material
and bone material. The peaks located after this high peak represents the bone
discontinuities. These peaks are marked in red in Figure 5.12. The reflection from the
second acrylic layer can not be observed because of the attenuation of the signal and also
due to the scattering from the bone. Since there were no samples of bone with
osteoporosis, the depth scan data from different regions (labeled 1, 2, and 3) of the single
bone slice were analyzed in terms of the porosity of the corresponding region. These

results are presented in the following sections.

96

   

20 40 60 80 100 120 140 160 180 200 20
Depth Location (um)
Figure 5.12 Image of dot l and its depth scans.

5.3 DEPTH SCAN DATA ANALYSIS

The bone slice image can be divided in different sections 1 (compact), 2
(cancellous) and 3 (cancellous). Compact bone is assumed to have small holes because
is more dense and cancellous bone is assumed to have larger holes because the bone is
less dense and has a texture such as that of a sponge. The distances between the holes in
the compact region should be shorter because of the small holes and the distance between
the holes in the cancellous region should be greater because of the large holes.

The data matrix comprising depth scans at a specific region was first reduced in
size by eliminating the peak corresponding to front surface reflection. The peak to peak

distances of the thresholded data was used as a measure of pore diameter. In order to

97

calculate the distance between the peaks the variance of each column was computed

N 2
asal-2 =—Z(xi—,ui) . Where N is the number of samples, and p,- is the mean.
i=1
Using a threshold a. = 202 the data of each column in the data matrix was thresholded.
Table 3 summarizes the values obtained at the different scan areas, represented by dots

numbered 1 through 12, in the 3 regions. There were some dots that were in between the

two different regions that were not analyzed such as dot number 2, 8 and 12.

Table 3 Results of the average distance between the peaks.

 

 

 

 

 

 

Region 1 (Compact Bone) Region 2 (Cancellous Bone) Region 3 (Cancellous Bone)
Average Distance (um) Average Distance (um) Average Distance (um)
Dot 1 23.03 Dot 4 21.86 Dot 7 20.93
Dot 3 21.66 Dot 5 22.54 Dot 10 22.75
Dot 6 21.60
Dotll 21.63

 

 

 

 

 

 

As can be observed from table 3 the average distances of the peaks were very
similar in all the different regions. These results were not useful to distinguish between
regions in the bone or to determine different porosities in the bone. A second approach

using morphological image processing techniques was also investigated. Erosion,

98

 

Opening and Closing were some of the morphological operations used to analyze the
images [46].

Erosion is defined as A9B={z

 

(B)z g A}. “This equation indicates that the

erosion of A by B, translated by z, is contained in A”[46]. Erosion eliminates irrelevant
detail from the image and it shrinks the image by a certain amount specified by the
structuring element[46]. The structuring element used in this thesis is shown in Figure
5.13. The size of the structuring element was varied from 2 to 5. Figure 5.14 shows how

the signal change after erosion is applied.

l he. term ‘~'\'£ilCT‘~hC‘LI rcl‘m‘s m

:l ridge l'nnt Lll\1dcf\ (trszls

drained by di l-‘lEl‘c‘Y‘ll river
5.}; s. [cm s.

 

Figure 5.l3 (a) Original Image (b) Line structural element of size 2 (c) Image afler erosion.

99

 

 

 

 

 

 

 

 

 

 

 

500 1000 1500 2000 2500
Depth Location (um)

(8)

 

 

 

 

 

 

 

 

\w

 

 

f

 

 

L A l

1000 1500 2000 2500
Depth Location (um)

g _

(b)
Figure 5.14 (a) Original Signals and (b) Signal afier erosion with size 3 structuring element.

Opening operation “smoothes contours, break narrow isthmuses, and eliminates
small islands and sharp peaks’ ’ and is defined as A o B = (A9 B) EBB [46]. “The opening
A by B is the erosion of A by B followed by the dilation of the result by B”[46]. Dilation
enlarges objects in the image. Figure 5.15 shows the original signals and the signals
after opening was applied. Closing operation “smoothes contours, fuses narrow breaks
and long thin gulfs, and eliminates small holes” and is defined as A. B = (A EBB) 9B
[46]. “The closing of set A by B is the dilation of A by B, followed by the erosion of the
result by B”[46]. Figure 5.16 shows the original signals and the signals after closing was

applied.

101

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3W“
2M. .3 - .
the
0M; . z - . .
O 500 aggl-mfimzfi 2000 2500
(b)

Figure 5.15 (a) Original Signals and (b) Signal afier ‘opening’ with size 2 structuring element

102

10F

 

 

 

 

 

 

 

o -| N 0’ & (II a, ‘1 O ‘0
<
<
> ‘%
lb
’ W
,

O 500 1000 1500 2000 2500
Depth Location (um)

(a)

 

 

 

 

 

 

 

 

ii

0 500 1000 1500 2000 2500
Depth Location (um)
(b)

Figure 5.16 (2) Original Signals and (b) Signal alter ‘closing' with size 3 structuring element.

103

After the erosion, Opening and closing were applied to the raw image with the

different structuring elements sizes the variance of the new matrix consisting of 116 rows

and 179 columns was calculated. The mean of the variance is summarized in Table 4. It

can be observed from this table that the average variance is always greater for region 1

(compact bone). It can also be observed that when structuring elements of size 2 and 3

were used, the average variance was higher than that obtained using structuring elements

of size 4 and 5. This is because in the latter case the signal features were erased or

eroded. It can also be observed that dot 1 and 5 have similar results even though they are

not in the same regions. Figure 5.17 shows the results on data at dot 11 when size 2 and

5 structuring elements were used.

Table 4 Varince of data after applying erosion operation.

 

 

 

 

 

 

 

 

Region 2 Region 3
Region 1 (Compact Bone) (Cancellous Bone) (Cancellous Bone)
Structure
Length
Average Variance Average Variance Average Variance
Dot 1 Dot 3 Dot 6 Dot 11 Dot 4 Dot 5 Dot 7 Dot 10
2 0.0017 0.0024 0.0026 0.0026 0.0013 0.0016 0.0010 0.0015
3 0.0017 0.0024 0.0026 0.0026 0.0013 0.0016 0.0010 0.0015
4 0.0013 0.0018 0.0020 0.0018 9.008e-4 0.0010 6.816e—4 0.0011
5 0.0013 0.0018 0.0020 0.0018 9.008e-4 0.0010 6.816e—4 0.0011

 

 

 

 

 

 

 

 

 

104

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

500 1000 1500 2000 2500
Depth Location (in)
(a)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

0 \f\‘ a a t J
0 500 1000 1500 2000 2500
Depth Location (um)

(b)
Figure 5.17 Signals alter erosion with (a) size 2 and (b) size 5 structuring element.

105

Table 5 shows corrpesonding results for the compact and cancellous bone when
“opening” operator is applied to the image. This table shows results similar to table 4.
The compact bone region has higher average variance than cancellous bone region and
dots l and 5 have similar results. It can also be observed that when structuring elements
of size 2 and 3 were used, the average variance was higher than that obtained using
structuring elements of size 4 and 5. The average variance numbers obtained when the
opening technique is applied are larger than that obtained when erosion technique was
applied. This is because erosion shrinks an image and opening just smoothes the contour

of objects in the image.

Table 5 Varince of data after applying “opening” operation.

 

 

 

 

 

 

 

 

Region 2 Region 3
Region 1 (Compact Bone) (Cancellous Bone) (Cancellous Bone)
Structure
Length
Average Variance Average Variance Average Variance
Dot 1 Dot 3 Dot 6 Dot 11 Dot 4 Dot 5 Dot 7 Dot 10
2 0.0020 0.0027 0.0029 0.0030 0.0015 0.0019 0.0012 0.0017
3 0.0020 0.0027 0.0029 0.0030 0.0015 0.0019 0.0012 0.0017
4 0.0015 0.0023 0.0024 0.0024 0.0012 0.0013 8.213e-4 0.0013
5 0.0015 0.0023 0.0024 0.0024 0.0012 0.0013 8.213e-4 0.0013

 

 

 

 

 

 

 

 

 

106

 

Table 6 shows the results that were obtained when “closing” was applied to the
raw image. As observed in the previous cases, average variances for compact bone are
greater than those calculated for cancellous bone. It can also be observed that when

structuring elements of size 2 and 3 were used, the average variance was higher than that

obtained using structuring elements of size 4 and 5.

Table 6 Varince of data after applying “closing” operation.

 

 

 

 

 

 

 

Region 2 Region 3
Region 1 (Compact Bone) (Cancellous Bone) (Cancellous Bone)
Structure
Length
Average Variance Average Variance Average Variance
Dot 1 Dot 3 Dot 6 Dot 11 Dot 4 Dot 5 Dot 7 Dot 10
2 0.0019 0.0029 0.0030 0.0031 0.0017 0.0020 0.0013 0.0017
3 0.0021 0.0029 0.0030 0.0031 0.0017 0.0020 0.0013 0.0017
4 0.0019 0.0026 0.0028 0.0029 0.0014 0.0019 0.0011 0.0014
5 0.0019 0.0026 0.0028 0.0029 0.0014 0.0019 0.0011 0.0014

 

 

 

 

 

 

 

 

 

 

After analyzing the results presented in the last three tables it can be concluded
that there is a difference in the average variance of eroded, opened and closed images in
the compact and cancellous regions of the bone. This difference could be used to identify
and quantify porosity in the bone but more experimental data are needed to validate this
observation conclusively. Dot 1 and 5, have similar variance values but are from

different areas in the bone. One reason for this could be that dot 1 is close to the

107

 

cancellous bone region. The analysis techniques must be validated with more
experimental data in order to corroborate this conclusion. Finally experiments using skin,
fat and bone will have to be conducted to determine if OCT could be used to
noninvasively detect bone mineral density loss. In a realistic situation, attenuation and

penetration depth of optical signals could pose a significant problem.

108

CHAPTER 6 CONCLUSIONS

Two techniques were investigated in this thesis tO identify differences between
healthy bone and a porous or osteoporotic bone. The two techniques used were OCT and
Microwave Imaging. In the OCT technique a bone sample was scanned in different areas
with an OCT system. Different techniques were applied on the measured data tO identify
or quantify porosity in the bone. Morphological image processing was applied to the
irnagem data and variance Of the processed data was calculated. The variance Of the
compact bone was seen tO be higher than that Of cancellous bone. Difference in porosity
was found using OCT but more experiments will be needed in order to conclusively state
that OCT could be used to find difference in porosity. However the more important
problem is to study the feasibility Of using OCT noninvasively for detecting bone mineral
density loss.

Microwave technique was simulated using a layered cylinder model, (representing
a finger), tO determine the reflection coefficients at different frequencies. This was done
tO determine the Optimum frequency for conducting the experiments. In order to have a
more accurate representation, a realistic tissue-bone model that resembled a leg was
simulated using HFSS. Two different simulations were performed using the tissue-bone
model. One Of the simulations was performed using the permittivity calculated for bone
and the other simulation was performed after reducing that permittivity by five percent.
The change in permittivity represented the difference in porosity. Both fields had the

same magnitude or their difference was not strong enough to differentiate between

109

healthy and osteoporotic bone. A more rigorous evaluation and validation of the model
needs to be performed using simple calibration sample geometries for which analytical
results can be clauclated.

As future work Other non-invasive methods such as ultrasonic techniques will be

explored for noninvasively determining bone mineral density loss.

llO

APPENDICES

111

APPENDIX A
MATLAB CODES FOR OCT

A.1 Code used to detect average distances

clc

clear all

close all

[yl] = imread('reference.bmp');

[y2] = imread('fifthdot.bmp');

y3=y2-y1; %%Resto las dos imagenes porq la original q es reference
tiene unas lineas q el equipo afiade

y3=y3(34:l49,41:179);
figure

image(y3);
colormap('gray')
figure

image(y2);
colormap('gray’)

I1 = im2double(y1);

12 = im2double(y2);

I3 = im2double(y3);
x=(0:1:279)*(((2.4*lO“—3)/10“—6)/279);
varianza=var(I3);
treshold=2*(varianza);

for i=1:1:1l6
for j=1:l:139
if I3(i,j)>treshold(j)
I4(i,j)=1;
else
I4(i,j)=0;
end
end
end
for j=1:l:139

findingones=find(l4(:,j));

distl=abs(findingones(l:(length (findingones)—l))—findingones(2:(length
(findingones))));

convirtiendo=dist1*8.6;

promedio(j)=mean(convirtiendo);

112

clear findingones;
clear distl;
clear convirtiendo;

end

promedio_matriz=mean(promedio);

A.2 Code used to apply morphological imaging techniques to the

bone images

clc
clear all
close all

[y2] imread('tendot001.bmp');

dotl imread('tendot001.bmp’);
se = strel('line',5,0);
IM2 = imclose(dot1,se);

imshow(dotl), figure (2), imshow(IM2)

de_column=10;
vspace_l=0.4;
figure(3)
hold on

13 = im2double(y2);
x=(0:1:279)*(((2.4*10“—3)/10“-6)/279);
for i=1:1:235/de_column;
k=i*de_column;
yy=I3(:,k)+(i—1)*vspace_l;
plot(x,yy)
Xlabel('Depth Location (um)')
end

figure (4)
hold on

I4 = im2double(IM2);
x=(0:1:279)*(((2.4*lO“—3)/10“-6)/279);

113

for i=1:1:235/de_column;
k=i*de_column;
yy=I4(:,k)+(i-1)*vspace_l;
plot(x,yy)
xlabel('Depth Location (um)')
end

I6=IM2(34:149,41:179);
figure(S)

image(16);
colormap('gray')

I7=im2double(I6);

de_column1=5;

vspace_11=0.4;

figure(6)

hold on

x1=(0:1:115)*(((2.4*10“—3)/lOA—6)/115);

for i=l:1:139/de_columnl;
k=i*de_columnl;
yy=I7(:,k)+(i-1)*vspace_ll;
plot(xl,yy)
xlabel('Depth Location (um)')

end

figure (7)
image(y2);
colormapt'gray')
hold on

varianza=var(I7);
varianza_prom=mean(varianza)

114

A.3 Lab View print outs used to collect data in the OCT technique

 

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Figure A.1 “Images in this thesis are presented in color”. Lab View print out of the program made to
move the linear stage.

115

 

 

Figure A.2 “Images in this thesis are presented in color”. Lab View print out of the program made to
move the linear stage.

116

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m '_--‘,‘.'.'." __. ..
WEQLJ "~

 

Figure A.3 “Images in this thesis are presented in color”. Lab View print out Of the program made to
move the linear stage.

117

 

 

 

 

 

 

    

 

 

 

 

 

 

 

 

 

 

Figure A.4 “Images in this thesis are presented in color”. Lab View print out of the program made to
nmvedwhnuusmge

118

'fiii‘lrirf',

agauizuraa

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Figure A.S “Images in this thesis are presented in color”. Lab View print out of the program made to
move the linear stage.

119

 

Figure A.6 “Images in this thesis are presented in color”. Lab View print out Of the program made to
move the linear stage.

120

APPENDIX B
MATLAB CODES TO IMPLEMENT MICROWAVE IMAGING

TECHNIQUE
B.l Code to determine the different fields for the layered cylinder

clear all
% close all

load k1fs.mat;
kvl k1; clear kl
mul 4*pi*le-7;

load k25kinwet.mat;
kv2 k2; Clear k2
mu2 4*pi*le—7;

load k3fat.mat;
kv3 k3; clear k3
mu3 4*pi*le—7;

load k4bone.mat;

kv4 = k4; clear k4
mu4 = 4*pi*1e-7;
c0 = 3e8;
a1=1.5e—2;
a2=l.3e-2;
a3=1.1e-2;

% al = 3e-2;

% a2 = 2.5e—2;

% a3 = le—2;

r0 = 4e-2;

phiO = pi;

L = 15;

f = [1:L]*le8;
Ei = zeros(L,1);
Es = zeros(L,1);
M = 25;

for n = 1:L

kl
k2

kvl(n);
kv2(n);

121

k3 = kv3(n);
k4 = kv4(n);
for m = —M:M

arl = [besselh(m,2,kl*al), —besselj(m,k2*al), -

besselh(m,2,k2*a1), 0, 0, 0];

ar2 = [0, besselj(m,k2*a2), besselh(m,2,k2*a2), -

besselj(m,k3*a2), besselh(m,2,k3*a2), O];

ar3 = [0, 0, O, besselj(m,k3*a3), besselh(m,2,k3*a3), -

besselj(m,k4*a3)];

end

.9

a41 = k1/mu1*(besselh(m-1,2,k1*a1)-besselh(m+1,2,k1*al))/2;
a42 -k2/mu2*(besselj(m-1,k2*al)—besselj(m+l,k2*a1))/2;

a43 -k2/mu2*(besselh(m—1,2,k2*al)-besselh(m+1,2,k2*al))/2;
ar4 = [a41, a42, a43, 0, 0, 0];

a52 = k2/mu2*(besselj(m-1,k2*a2)-besselj(m+1,k2*a2))/2;

a53 = k2/mu2*(besselh(m—1,2,k2*a2)-besselh(m+1,2,k2*a2))/2;
a54 = -k3/mu3*(besselj(m-1,k3*a2)-besselj(m+l,k3*a2))/2;

aSS = —k3/mu3*(besselh(m-1,2,k3*a2)—besselh(m+1,2,k3*a2))/2;

arS = [0, a52, a53, a54, ass, 0];

a64 = k3/mu3*(besselj(m-1,k3*a3)—besselj(m+l,k3*a3))/2;

a65 k3/mu3*(besselh(m-1,2,k3*a3)—besselh(m+1,2,k3*a3))/2;
a66 -k4/mu4*(besselj(m-1,k4*a3)-besselj(m+l,k4*a3))/2;
ar6 = [0, 0, 0, a64, a65, a66];

% Modal solution
A = [ar1; ar2; ar3; ar4; ar5; ar6];
[ —j“-m*besselj(m,kl*al)
O
0
-kl/mul*j“—m*(besselj(m~1,k1*a1)-besselj(m+l,k1*al))/2
0
O

0'
ll

];
coef = A\b;

% Incident and scattered fields
Ei(n) = Ei(n) + j“—m*besselj(m,k1*r0)*exp(j*m*phiO);
Es(n) = Es(n) + coef(1)*besselh(m,2,kl*r0)*exp(j*m*phiO);

s reflection coefficient

Gamma(n) = Es(n)/Rim);

%transmission coefficient

122

transcoeff(n)=l+abs(Gamma(n));

%angle reflection coefficient
angl_reflec_coeff=angle(Gamma);

end

figure(l);

subplot(311); plot(f/le6,abs(Ei),'r'); xlabel('f (MHz)');
ylabel('|E_i|‘);grid on; hold on

subplot(312); plot(f/1e6,abs(Es),‘r'); xlabel('f (MH2)');
ylabel('lE_s|‘);grid on; hold on

subplot(313); plot(f/le6,abs(Gamma),'r'); xlabel('f (MHz)');
ylabel('|\Gammal‘);grid on; hold on

figure(2);

subplot(21l);
plot(f/1e6,abs(transcoeff),'r');xlabel('f(MHz)');ylabel('|transmission
coefficientl‘);grid on; hold on

subplot(212);
plot(f/le6,angl_reflec_coeff,'r');xlabel('f(MHz)');ylabel('angle of
reflection coefficient');grid on; hold on

B.2 Code to calculate the reflection coefficient for the grid

lc
clear all
clear all

x=0:0.001:0.02;
=—0.02:.OOl:0.02;

for m=1:length (y)
for n=l:length (x)
XC=x(n)
YC=y(m)
[phi0,r0] = cart2pol(XC,YC);
[Gamma]=solimar1(r0,phiO);
yy(n,m,:)=Gamma;
end
end

clc

close all

figure
R_COEF(1:length(x),1:length(y))=yy(:,:,15);

123

[C,h]=contourf(y,x,R_COBF);
set(h,’ShowText','on','TextStep',get(h,'LevelStep')*2)
hold on
l=(0:1:360)*pi/180;
R=0.015;
for m=1:length(l)
x1(m)=R*cos(l(m));
y1(m)=R*sin(1(m));
end
plot(x1,y1,'r*')

B.3 Code to calculate the electrical properties of human tissue

clc
close all
clear all

epsilon_inf=[2.5 2.5 4.0 4.0] ; %%infinite epsilon from table 1 for
bone, fat, muscle and skin respectively

sigma=[0.0700 0.01 .2000 0.0004]; %%static ionic conductivity for
bone, fat, muscle and skin respectively

epnot=8.854e—12; %% permittivity of free space
delta_eps=[ 18 300 2e4 2e7; %delta epsilon for BOne
3 15 3.3e4 1.0e7 %delta epsilon for Fat
50 7000 1.2e6 2.5e7; %delta epsilon for Muscle
39 280 3e4 3e4]; %delta epsilon for Skin
tau=[ 13.26e—12 79.58e—9 159.15e—6 15.915e—3; %time constant
for Bone
7.96e—12 15.92e-9 159.15e-6 7.958e-3; %time constant
for Fat
7.23e-12 353.68e-9 318.31e-6 2.274e-3; %time constant
for Muscle
7.96e-12 79.58e-9 1.59e—6 1.592e—3]; %time constant
for Skin
alpha=[ .22 .25 .20 0; elaxation regions for Bone

.10 .10 .10 0; ~ elaxation regions for Muscle

%r
.20 .10 .05 .01; %relaxation regions for Fat
or
.10 0 .16 .20]; trelaxation regions for Skin

u0=(4*pi)*10“—7; %permeability of free space

124

%f_all=[25 50 75 100 200 300 400 500 600 700 800 900 1000 1500];
%vector of frequencies for the simulations

f_all=[100 200 300 400 500 600 700 800 900 1000 1100 1200 1300 1400
1500];

for i=1:4 %for loop for choosing the
values of epsilon_inf, sigma, delta_eps, tau, alpha 4 differents
materiasl

for l=1:length(f_all) %for loop for to evaluate each
frequency
asd=0; %initializing the summation
for n=l:4 %for loop for the summation
f=f_all(l)*1e6; %calculating the frequency in
terms of MHz
w=2*pi*f; %calculating w
asd=asd+((delta_eps(i,n))/(1+(j*w*(tau(i,n)))“(1-
alpha(i,n)))); %calculating the summation of the cole cole eqt.

end
ew(l,i)=asd+epsilon_inf(i)+(sigma(i)/(j*w*epnot));
%c*lculating the cole cole equation
sig_x(l,i)=abs(imag(ew(l,i))*w*epnot);
%calculating the conductivity sigma
k(l,i)=(w*sqrt(ew(l,i)*1*u0*epnot));
kbonedifper(l,i)=(w*sqrt((.95*(ew(l,i)))*1*u0*epnot));

end
end
e_rel_100=real(ew); %calculating the relative
permitivity
e_rel_25_less=0.75*real(ew); %calcu1ating the relative

permitivity with a loss of 25 percent

sig_x_100=sig_x;

sig_x_25_less=0.75*sig_x; %calculating the conductivity
with a loss of 25 percent

125

REFERENCES

126

[ll

[21

[31

I41

[51

I6]

[71

[9]

A. C. Guyton and J. E. Hall, Textbook of Medical Physiology, 10th ed.
Philadelphia Saunders, 2000.

J. Sierpowska, M. A. Hakulinen, J. Toyras, J. S. Day, H. Weinans, I.
Kiviranta, J. S. Jurvelin, and R. Lappalainen, "Interrelationships between
electrical properties and microstructure of human trabecular bone," Physics
in Medicine and Biology, vol. 51, pp. 5289-5303, 2006.

P. M. Q. F. G. Meaney, S.D.; Streltsov, A.V.; Paulsen, K.D.,, "3D scalar
microwave image reconstruction algorithm," Microwave Symposium Digest,
2002 IEEE M TT-S International, vol. 3, pp. 2269-2272, 2002.

S. Grampp, H. K. Genant, A. Mathur, P. Lang, M. Jergas, M. Takada, C.-C.
Gluer, Y. Lu, and M. Chavez, "Comparisons of Noninvasive Bone Mineral
Measurements in Assessing Age-Related Loss, Fracture Discrimination, and

Diagnostic Classification," Journal of Bone and Mineral Research, vol. 12, pp.
697-711, 1997.

H. K. Genant, C. E. Cann, B. Ettinger, and G. S. Gordan, "The Classic:
Quantitative computed tomography of vertebral spongiosa: a sensitive
method for detecting early bone loss after oophorectomy. 1982," Clin Orthop
Relat Res, vol. 443, pp. 14-8, 2006.

M. A. Hansen, C. Hassager, K. Overgaard, U. Marslew, B. J. Riis, and C.
Christiansen, "Dual-Energy X-ray Absorptiometry: A Precise Method of
Measuring Bone Mineral Density in the Lumbar Spine," J Nucl Med, vol. 31,
pp. 1156-1162, 1990.

G. Guglielmi, S. K. Grimston, K. C. Fischer, and R. Pacifici, "Osteoporosis:
diagnosis with lateral and posteroanterior dual x-ray absorptiometry
compared with quantitative CT," Radiology, vol. 192, pp. 845-850, 1994.

F. Duboeuf, R. Pommet, P. J. Meunier, and P. D. Delmas, "Dual-energy X-
ray absorptiometry of the spine in anteroposterior and lateral projections,"
Osteoporosis International, vol. 4, pp. 110-1 16, 1994.

A. A. Deodhar, J. Brabyn, P. W. Jones, M. J. Davis, and A. D. Woolf,
"Measurement of hand bone mineral content by dual energy x-ray
absorptiometry: development of the method, and its application in normal

volunteers and in patients with rheumatoid arthritis," Ann Rheum Dis, vol.
53, pp. 685-690, 1994.

127

[10]

[11]

[121

[13]

[14]

[151

[16]

[17]

[131

[19]

H. H. Bolotin and H. Sievanen, "Inaccuracies Inherent in Dual-Energy X-
Ray Absorptiometry In Vivo Bone Mineral Density Can Seriously Mislead
Diagnostic/Prognostic Interpretations of Patient-Specific Bone Fragility,"
Journal of Bone and Mineral Research, vol. 16, pp. 799-805, 2001.

R. J. M. Herd, G. M. Blake, T. Ramalingam, C. G. Miller, P. J. Ryan, and I.
Fogelman, "Measurements of postmenopausal bone loss with a new contact
ultrasound system," Calcified Tissue International, vol. 53, pp. 153-157, 1993.

S. O. Yang, S. Hagiwara, K. Eugelke, M. S. Dhillon, G. Guglielmi, E. J.
Bendavid, 0. Soejima, D. L. Nelson, and H. K. Genant, "Radiographic

absorptiometry for bone mineral measurement of the phalanges: precision
and accuracy study," Radiology, vol. 192, pp. 857-859, 1994.

M. Takada, K. Eugelke, S. Hagiwara, S. Grampp, M. Jergas, C. C. Gluer,
and H. K. Genant, "Assessment of osteoporosis: comparison of radiographic
absorptiometry of the phalanges and dual X-ray absorptiometry of the
radius and lumbar spine," Radiology, vol. 202, pp. 759-763, 1997.

S. Kati, S. Zlochiver, and S. Abboud, "Induced Current Bio-impedance
Technique for Monitoring Bone Mineral Density—A Simulation Model,"
Annals of Biomedical Engineering, vol. 34, pp. 1332-1342, 2006.

M. Brezinski, Optical Coherence Tomography Principles and Applications,
First ed. New York: Elsevier, 2006.

A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, "Optical
coherence tomography - principles and applications," Reports on Progress in
Physics, vol. 66, pp. 239-303, 2003.

M. E. Brezinski and J. G. Fujimoto, "Optical coherence tomography: high-
resolution imaging in nontransparent tissue," Selected Topics in Quantum
Electronics, IEEE Journal 0], vol. 5, pp. 1185-1192, 1999.

J. M. Schmitt, "Optical coherence tomography (OCT): a review," Selected
Topics in Quantum Electronics, IEEE Journal of, vol. 5, pp. 1205-1215, 1999.

V. V. Tuchin, Hanbook of Coherence Domain Optical Methods Biomedical

Diagnostics, Environmental and Material Science, vol. 2: Kluwer Academic
Publishers, 2004.

128

[20]

[211

[22]

W]

l241

[25]

[26]

[271

M. Pircher, E. Giitzinger, R. Leitgeb, A. Fercher, and C. Hitzenberger,
"Measurement and imaging of water concentration in human cornea with

differential absorption optical coherence tomography," Opt. Exgpress, vol. 11,
pp. 2190-2197, 2003.

E. A. Swanson, J. A. Izatt, M. R. Hee, D. Huang, C. P. Lin, J. S. Schuman, C.
A. Puliafito, and J. G. Fujimoto, "In-vivo retinal imaging by optical
coherence tomography," Opt. Lett., vol. 18, pp. 1864, 1993.

P. Massin, E. Vicaut, B. Haouchine, A. Erginay, M. Paques, and A. Gaudric,
"Reproducibility of Retinal Mapping Using Optical Coherence
Tomography," Arch Ophthalmol, vol. 119, pp. 1135-1142, 2001.

D. N. Zacks and M. W. Johnson, "Transretinal Pigment Migration: An
Optical Coherence Tomographic Study," Arch Ophthalmol, vol. 122, pp. 406-
408, 2004.

W. C. Kuo, J. J. Shyu, N. K. Chou, C. M. Lai, H. C. Huang, C. Chou, and G.
J. Jan, "Imaging of human aortic atherosclerotic plaques by polarization-
sensitive optical coherence tomography," presented at Engineering in
Medicine and Biology Society, 2004. IEMBS '04. 26th Annual International
Conference of the IEEE, 2004.

B. E. Bouma, M. Shishkov, K. H. Schlendorf, S. L. Houser, I. K. Jung, and G.
J. Tearney, "Monitoring coronary artery stent deployment in living human
patients with optical coherence tomography," presented at Lasers and
Electro-Optics, 2001. CLEO '01. Technical Digest. Summaries of papers
presented at the Conference on, 2001.

N. A. Patel, J. Zoeller, D. L. Stamper, J. G. Fujimoto, and M. E. Brezinski,
"Monitoring osteoarthritis in the rat model using optical coherence
tomography," Medical Imaging, IEEE Transactions on, vol. 24, pp. 155-159,
2005.

F. I. Feldchtein, V. M. Gelikonov, G. V. Gelikonov, R. V. Kuranov, N. D.
Gladkova, A. M. Sergeev, N. M. Shakhova, I. A. Kuznetzova, A. N.
Denisenko, and O. S. Streltzova, "Design and performance of an endoscopic
OCT system for in vivo studies of human mucosa," presented at Lasers and
Electro-Optics, 1998. CLEO 98. Technical Digest. Summaries of papers
presented at the Conference on, 1998.

129

[23]

[29]

I301

[311

l32]

l33l

134]

[35]

[36]

J. A. Izatt, M. D. Kulkarni, W. Hsing-Wen, K. Kobayashi, and M. V. Sivak,
Jr., "Optical coherence tomography and microscopy in gastrointestinal
tissues," Selected Topics in Quantum Electronics, IEEE Journal of, vol. 2, pp.
1017-1028, 1996.

P. Hsuing, C. Chudoba, C. Pitris, X. D. Li, T. Ko, and J. G. Fujimoto, "In
vivo colposcopic imaging of neoplastic tissues using Optical Coherence
Tomography," presented at Lasers and Electro-Optics, 2001. CLEO '01.
Technical Digest. Summaries of papers presented at the Conference on, 2001.

P. Hsiung, T. H. K0, X. D. Li, J. G. Fujimoto, M. Weinstein, A. V. D'Amico,
and J. R. Ritchie, "Intraoperative imaging using optical coherence
tomography," presented at Lasers and Electro-Optics, 2002. CLEO '02.
Technical Digest. Summaries of Papers Presented at the, 2002.

S. A. Boppart, J. M. Herrmann, C. Pitris, B. E. Bouma, and G. J. Tearney,
"Interventional optical coherence tomography for surgical guidance,"
presented at Lasers and Electro-Optics, 1998. CLEO 98. Technical Digest.
Summaries of papers presented at the Conference on, 1998.

E. Alarousu, L. Krehut, T. Prykari, and R. Myllyla, "Study on the use of
optical coherence tomography in measurements of paper properties,"
Measurement Science & Technology, vol. 16, pp. 1131-1137, 2005.

F. Sterzer, "Microwave medical devices," Microwave Magazine, IEEE, vol. 3,
pp. 65-70, 2002.

K. Sato, T. Manabe, J. Polivka, T. Ihara, Y. Kasashima, and K. Yamaki,
"Measurement of the complex refractive index of concrete at 57.5 GHz,"
Antennas and Propagation, IEEE Transactions on, vol. 44, pp. 35-40, 1996.

S. N. Kharkovsky, M. F. Akay, U. C. Hasar, and C. D. Atis, "Measurement
and monitoring of microwave reflection and transmission properties of
cement-based specimens," Instrumentation and Measurement, IEEE
Transactions on, vol. 51, pp. 1210-1218, 2002.

M. Zhihong and S. Okamura, "Permittivity determination using amplitudes
of transmission and reflection coefficients at microwave frequency,"
Microwave Theory and Techniques, IEEE Transactions on, vol. 47, pp. 546-
550, 1999.

130

[37]

[38]

I39]

[401

[41]

I421

[43]

[44]

[451

[461

D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan, "Free-space
measurement of complex permittivity and complex permeability of magnetic

materials at microwave frequencies," Instrumentation and Measurement,
IEEE Transactions on, vol. 39, pp. 387-394, 1990.

D. K. Ghodgaonkar, V. V. Varadan, and V. K. Varadan, "A free-space
method for measurement of dielectric constants and loss tangents at
microwave frequencies," Instrumentation and Measurement, IEEE
Transactions on, vol. 38, pp. 789-793, 1989.

N. Qaddoumi, L. Handjojo, T. Bigelow, J. Easter, A. Bray, and R. Zoughi,
"Microwave corrosion detection using open ended rectangular waveguide
sensors," Materials Evaluation ; VOL. 58 ; ISSUE: 2 ; PBD: Feb 2000, pp.
page(s) 178-184, 2000.

J. Sierpowska, M. A. Hakulinen, yr, J. s, J. S. Day, H. Weinans, J. S.
Jurvelin, and R. Lappalainen, "Prediction of mechanical properties of
human trabecular bone by electrical measurements," Physiological
Measurement, vol. 26, pp. 8119-8131, 2005.

C. Gabriel, S. Gabriel, and E. Corthout, "The dielectric properties of
biological tissues: 1. Literature survey," Physics in Medicine and Biology, vol.
41, pp. 2231-2249, 1996.

S. Gabriel, R. W. Lau, and C. Gabriel, "The dielectric properties of
biological tissues: III. Parametric models for the dielectric spectrum of
tissues," Physics in Medicine and Biology, vol. 41, pp. 2271-2293, 1996.

R. F. Harrington, Time Harmonic Electromagnetic Fields. New York: Wiley
Interscience, 2001.

K. Umashankar and A. Taflove, Computational Electromagnetics, 1st ed.
Boston: Artech House, Inc., 1993.

J. M. Vaughan, The Physiology of bone Second ed: Oxford : Clarendon Press,
1975.

R. W. Rafael Gonzalez, Digital Image Processing. Upper Saddle River, NJ:
Prentince Hall, 2002.

131

     

   
 
 

 
  

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