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QUANTIFYING OPTICAL TOMOGRAPHY METHODS FOR BIOMOLECULAR SENSING
A Thesis
Submitted to the Faculty in partial fulfillment of the requirements for the
degree of
Doctor of Philosophy
by
JENNIFER-LYNN H. DEMERS
Thayer School of Engineering Dartmouth College
Hanover, New Hampshire
MAY 2014
Examining Committee:
Chairman__________________________ Brian W. Pogue, Ph.D.
Member__________________________ Venkataramanan Krishnaswamy, Ph.D.
Member__________________________ P. Jack Hoopes, D.V.M., Ph.D.
Member__________________________ Michael D. Morris, Ph.D.
___________________ F. Jon Kull Dean of Graduate Studies
ii
Abstract
Diffuse optical imaging techniques can be combined with standard imaging technologies
such as computed tomography (CT) and magnetic resonance (MR) imaging to allow
measurement of spectroscopic signals pertaining to the molecular components of tissue.
Some of the more promising approaches to image-guided spectroscopy rely upon
inelastic scattering or fluorescence phenomena, which directly sample molecular contrast.
Measurement of these molecular signal changes can then allow for diagnostic
determination of tissue function or disease status in vivo. Molecular signal measurement
often requires small tissue thickness and high signal intensity, yet when utilized with
tomographic recovery it is often feasible to detect even lower signals at deep tissue
depths. In this work, the range of useful signals and concentrations possible for molecular
sensing with image-guidance are identified and key application areas examined.
In order to better understand the advantages and disadvantages of each possible
tomographic signal, a series of experiments were conducted in tissue phantoms as well as
animal studies. Three imaging signals have been explored in detail: 1) Raman, 2) surface
enhanced Raman and 3) molecular fluorescence. Previous work has shown, that with the
combination of optical measurements and spatial information garnered from CT or MR
scans, a higher level of contrast-to-background could be obtained. These gains in signal
were verified for these imaging methods. Phantom measurements determined the
concentration range necessary for a linear response for each signal and system pair. In-
vivo and ex-vivo animal experiments provided data for a comparison of the signal
iii
strength and contrast with respect to the biologically relevant molecular contrast
available.
An understanding of the regions over which a linear response of the detector occurs
for each optical contrast method can be used to guide experimental design, both in
knowing the necessary level of contrast for successful tomographic imaging to occur, in
order to then guide the dosing estimates for use of extrinsic contrasts and determine
regions with sufficient Raman signal density for intrinsic contrast.
iv
Acknowledgements
I owe extreme gratitude to my thesis advisor, Dr. Brian Pogue - without his knowledge
and insight much of this work would have been impossible to complete. The lab group
that has been created at Thayer surrounding Optics in Medicine is a great group of minds,
at many levels, where students are well groomed to lead successful careers. Thanks go to
the many students, post-docs, staff and faculty members who provided opportunities for
questions, for growth, and endless hours of help during experimentation.
Additionally, my external advisor, Dr. Michael Morris shared much knowledge with
me and acted as a fantastic advisor with many interesting discussions occurring during
my multiple visits to his lab at the University of Michigan. He has also created a lab full
of wonderful post-docs who were extremely crucial to the forward movement in the
Raman imaging experiments. Drs. Francis and Karen Esmonde-White were extremely
patient and thoughtful, welcoming me into their home during my time in Michigan.
I would be remiss to not thank all the wonderful staff and employees at Thayer
School and in the Dartmouth Graduate Studies office for all their hard work and
dedication to their jobs. Without them, many of the everyday tasks would be nearly
impossible. Thank you to the Kathy’s, Roxanne, Becky and the wonderful custodial,
development and finance office staff. During my PhD I was also given opportunities to
work with the Graduate Studies Office to organize and lead the ASURE program. This
was a fantastic program that allowed me to further connect with undergraduate students.
The 13 students with whom I worked were able to really change my perspective on grad
school, and shaped my mind so that I will be sure to seek out future opportunities that are
along the lines of the work I did with them. Danielle, Joel, Iliana, Wynette, Bailey,
v
Anthony, Courtney, Ridwan, Edith, Patrick, Eileen, Andres, and Tangeria – Thank you
for all you have taught me and I look forward to hearing about the wonderful things your
futures bring.
Many thanks should also be given to the students who surrounded me at Thayer and
made this my home for the last five years. The students who started with me but have
since moved on, to those who spent every day of the last five years working together, and
those who started after me, reminding me of the excitement that I came into graduate
school with. Garet Gamache, Josiah Gruber, and Matt Pallone – you were the first ones
to get me involved in the student organizations within Thayer, for that I thank you, and
also blame some of my grey hairs on you. Kaitlin Keegan, Brad Ficko, Nan Jia, Fanling
Meng, Kelly Michaelsen, and Mike Mastanduno – you shared so many, maybe too many,
long nights with me during our first year of graduate school, and really embodied what I
consider my grad school family. Without each and every one of you beside me, graduate
school would not have been nearly as an amazing experience. Dan Schuette, Valerie
Hanson, Adam Glaser, and Christian Ortiz – you four were the people who kept me
remembering that graduate school can also be fun, and too not take myself so seriously.
Thanks for all the good times and I look forward to making many more good memories.
I also owe a huge amount of appreciation to my Upper Valley family outside of the
Thayer School. This amazing group of people are the best of friends – keeping me
grounded in the tough times, and helping to really celebrate the great times. Thank you
all - for the times spent on the river, the wonderful potlucks and food, the company in
rocking chairs by fires and all the other adventures.
vi
During my last year of graduate school, my family was involved in a serious car
accident. The gratitude for the support, emotional and monetary, that I received from
many friends, near and far, during this difficult time cannot be expressed enough. I owe
so much to the people that were there for me in this time, and to the best friends who
went way above and beyond the call. Lindsey Roper, you’re a hero for taking care of me
and sharing my story to get others, many anonymous, to help me. Andrew Graves, I
don’t know how I would have handled many days without your help. Brendan Alexander,
only you could tame the beast of Ed as frequently and surely as you’ve done.
Finally, none of this would be possible without the unconditional love and support
from my family. Most people are blessed with two great parents – I’ve been even more
blessed with the addition of fantastic step-parents and step-families who have become my
own. I have wonderful siblings and stepsiblings who have gifted me with amazing nieces
and nephews – I’m so grateful to be their Aunt and look forward to teaching them so
many weird science facts. Many meals and holidays were spent with my grandparents,
Bob and Barbara Coleman as well as some wonderful relaxation time at the lake house.
Thanks for treating me like your own and being proud of me it means the world.
I have four amazing parents who have supported me through every step of my
adventurous life. Thank you for loving me through every mistake and being there to
cheer me on at each challenge. I am who I am today because of the parents that I had.
I’m proud to be your daughter.
vii
Dedication
This work is dedicated to the cancer warriors who were not able to win the battle and
their families who have dealt with immeasurable pain. These people were the ones who
reminded me every day that research has a bigger purpose.
Carol Barry
Casey O’Neal
Ethan Max Williams
Gloria Jean Evans
viii
Table of Contents
Abstract .............................................................................................................................. ii�
Acknowledgements .......................................................................................................... iv�
Dedication ........................................................................................................................ vii�
List of Figures ................................................................................................................. xiii�
List of Tables .................................................................................................................. xxi�
Table of Acronyms ....................................................................................................... xxiii�
1� Biomolecular Imaging ................................................................................................ 1�
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2� Introduction to Light Interaction with Tissue ......................................................... 8�
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8� Fluorescence Imaging ............................................................................................. 109�
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9� Comparison of Imaging Methods .......................................................................... 125�
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References: ..................................................................................................................... 137�
10� Appendix A ............................................................................................................ 159�
11� Appendix B ............................................................................................................ 161�
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List of Figures
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����������7�( ����������� �� ����������������� ���� ���� � � ������,��K���0���/�,���"�� ������ ��K���������������������������������������������������������������������������������������������������������������������������������������������������4��
����������: (Left) Test tubes of agar and SERS nanoparticle solution with varying concentration with 1 nM in the top left down to 0.2 fM in the bottom right tube. (Center) Diagram of the heterogeneous phantoms used to determine system limits. (Right) Photograph of the system set up. The 90- and 135-degree measurements are the average of the two signals.���������������������������������������������������������������������������4��
����������: (Left) The Raman signal of the SERS particles used. (Right) The Born ratio data points separated by degree of fiber from source location for the 16 concentrations of SERS particles. The noise floor, absorption dominated point and the linear respone region are marked.�����������������������������������4)�
���������): (Left) Reconstructed diffuse images of phantoms made of Intralipid and gelatin containing SERS nanoparticles. (Right) Plot showing the linear fit of the reconstructed contrast-to-background with respect to the concentration when no prior and spatial prior information was included in the algorithm.������������������������������������������������������������������������������������������������������������������������������������������������������������������������������4)�
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���������+: (Left) MR image of the mouse head with the brain (blue) and SERS tube (green) segmented from the remainder of the head. (Center) Diffuse reconstruction of the signal shows the dominance at top-right. (Left) Reconstructed region values when including two-region spatial priors with no signal being present in the brain.�����������������������������������������������������������������������������������������������������������������������������������������������4+�
����������: Selected MRI images from the mouse models showing the variation in tumor size and location.��������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������4��
���������1: (Left) MR slice corresponding to the segmented image. (Center) Segmented image with white representing tumor, black representing brain and skull, and red representing all other background. (Right) Surface nodes of segmented mesh showing placement of source and detectors on mesh.��������41�
���������!: Reconstruction result for Mouse 12 with 3 nM injection of SERS particles. Surface artifacts are present at each source and detector position.������������������������������������������������������������������������������������������������������������41�
���������4: Nirfast simulations showing the recovered contrast given the tumor to background contrast values (T2Bkgd) and tumor to brain contrast (T2Brain) indicated above each plot. These simulations support having a tumor to background contrast near 5 in order to have a recovered signal (center plot).����������������������������������������������������������������������������������������������������������������������������������������������������������������������������������������4!�
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List of Tables
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Table of Acronyms
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1
1 Biomolecular Imaging
Biomolecular imaging has the potential to provide measurements of new biomarkers for
disease pathology from non-invasive sensing of the tissue in vivo. The National Institutes
of Health (NIH) defines biomarkers as: “key molecular or cellular events that link a
specific environmental exposure to a health outcome” and “a characteristic that is
objectively measured and evaluated as an indicator of normal biological processes,
pathogenic processes or pharmacologic responses to therapeutic intervention” [1].
Following this definition, antibodies, proteins, cell receptors, measured electrical activity
and the presence of specific molecules could all be considered biomarkers and may have
substantial relevance to human disease management if a reliable way to measure and/or
monitor them are developed. Within this body of work, the focus is on those molecules,
which can be used to image fundamental features using optical techniques, because the
optical spectrum provides a direct sampling of their signature molecular bonds.
1.1 Current State of Imaging
Currently biomolecules can be imaged using a variety of techniques in a clinical setting
including Magnetic Resonance Imaging (MRI), Single Photon Emission Computed
Tomography (SPECT), and Positron Emission Tomography (PET). SPECT and PET
scans are useful in monitoring the levels of biological activity using injections of
radioactive molecules and imaging their regions of congregation [2]. SPECT imaging
uses gamma emitting particles such as Technetium-99m and Iodine-123 or -131 and can
be targeted in order to understand the physiological processes in bone, heart, brain and
white cells [3]. The gamma rays generated by these radioisotopes are detected and their
2
origination location pinpointed due to their high energy and low likelihood of scatter by
tissue, resulting in direct light of sight transmission once the smaller scatter components
are removed. PET imaging incorporates beta emitting radionuclides including Carbon-
11, Oxygen-15, and Nitrogen-13 into biological compounds, such as water and glucose,
that are incorporated into tissues through metabolic pathways [4]. Once a beta particle is
emitted and interacts with an electron, an annihilation process occurs that generates two
511 keV photons in directly opposite directions, allowing detection and triangulation of
the origin of them [2]. Although PET and SPECT can provide useful information
regarding the state of the biological tissue, they require the injection of radioactive
materials; therefore, for each scan the potential risk and expense must be weighed against
the potential benefits.
MRI technology uses magnetic fields to perturb the magnetic moment of molecules
in tissues and measure the resulting effect [2]. It is possible to increase the signal in
regions using injections of targeted molecules, but injections are not always necessary for
image creation. The ability to image endogenous contrast is a major benefit of MRI, but
any patient with metal implants cannot be imaged. The presence of metal can be from
orthopedic implants, cardiac pacemakers, surgical clips and a variety of other procedures
– leading to potentially large reduction in the number of patients benefitting from MRI
technologies. Still, true molecular contrast is rarely imaged in clinical settings, with most
of the oncology scans using vascular contrast injection to visualize vascular abnormalities
and most soft tissue scans being largely based upon water contrast mechanisms. So while
MRI has good potential for molecular sensing, this version of it is rarely implemented in
clinical practice today.
3
The development of an imaging technique that is formed with non-ionizing radiation
and would allow for a more inclusive patient pool is a necessary development to continue
advancing the clinical standard. Alternatively, a more cost effective imaging technique
could largely change the research field of drug analysis and verification.
Research has been done to determine the validity and usefulness of Near Infrared
light as an imaging technique for in-vivo analysis [5-9]. It has been shown that light can
interact with endogenous and exogenous targets in tissues leading to the formation of
images [10, 11]. Imaging with light provides a variety of molecular information, the
specifics of which will be described further in Chapter 2.
1.2 Advantages of Biomolecular Imaging
Pulse oximetry, the most common example of light used in the clinical setting, was
developed in the 1940’s and became standard in the clinic in the 1980s [12, 13]. This
technique relies on the absorption of two different wavelengths to calculate an
approximate of the concentration of oxygen in the blood. This technology innovated the
clinical setting by replacing the previous blood test that required lengthy analysis and
allowed for better patient care.
While blood oxygenation measurements are a key physiological parameter, light can
be used in many other innovative technologies, many which are currently in the research
phase of development. A variety of non-invasive optical spectroscopy methods are being
generated with current work focused on gaining a deeper understanding of the functional
components within a tissue volume [14, 15]. Invasive methods for use in surgical
procedures, specifically in determining tumor margins are also being explored [16-18].
Diagnostic imaging on excised tissue samples or other biological samples by optical
4
probing shows promising results and due to the lack of risk to the patient, this technique
is the most easily implemented [19, 20].
Each of these techniques provides information on the tissue morphology on either
micro or macro scales. The current standard practice for understanding tissue morphology
on the micro scale uses hematoxylin and eosin (H&E) stains, but this process could be
augmented by optical spectroscopy [19, 21, 22] and addition of other molecular dyes.
Currently imaging of macro scale variation in tissue is done with PET, SPECT, and MRI
imaging as described previously. In this work, we use optical spectroscopy methods to
understand the macro scale variation in the imaging of brain tumors and bone tissue.
1.2.1 Targets in Cancer Imaging
There are many varying definitions of cancer, but a commonly accepted component of
the definition is that cancer consists of a group of abnormal cells with altered
characteristics that affect their cell homeostasis, survival and death [23]. Cancer
screening and detection, diagnosis, and treatment monitoring are all steps in the health
care pathway that could be aided by the addition of optical spectroscopy [20, 24-29].
Changes in the cellular structure and the organelles can be measured using scattering and
absorption techniques [11]. Levels of tissue chromophores, such as hemoglobin and
deoxy-hemoglobin, can be monitored with near-infrared light, additionally quantification
of the water and lipid components can be determined [30, 31]. Research has been
conducted that connects the blood volume and oxygenation levels to treatment response
for various cancers [32, 33]. Increased presence of proteins and genes can be also be an
indicator of cancer, with over expression of: prostaglandin G/H synthase linked to colon
5
cancer [34], human epidermal growth factor receptor 2 (HER2) linked to breast cancer
[35], and claudin-3 and claudin-4 are linked to ovarian cancers [36].
Overexpressed proteins, especially those on the cell surface, can be targeted for
binding of exogenous contrasts for optical imaging. Fluorescent dyes and nanoparticles
can be conjugated with proteins that interact with cell surfaces, aiding in the congregation
of these contrast agents at the tumor site [37-39]. The increased cell division rate leads to
tumor angiogenesis and this cancer vasculature structure allows greater permeability to
contrast agents [40-42]. In this work, the use of nanoparticles and targeted fluorescent
dyes will be examined and their ability to positively identify tissues of interest will be
quantified.
1.2.2 Targets in Bone Imaging
The current clinical standard of imaging of bone for diagnosis of diseases and tracking of
treatment is Dual Energy X-ray Absorptiometry (DEXA or DXA) [43, 44]. This
technique uses two distinct energies of x-rays and compares the absorption planar images
to determine the component of mineral present in the bone [45]. However, relying on a
technique that uses ionizing radiation and provides data as averages of large regions is
not ideal and an alternative method for in-vivo imaging could be useful.
Light interactions with the mineral and matrix components of bone that are
dominated by scattering events cause a change in the vibrational states and is measured
via a technique called Raman spectroscopy. Currently Raman imaging is conducted on
excised tissue samples and is not a sufficient technique for longitudinal studies in human
patients [46-48]. Additionally, light interactions can also be measured using Fourier
transform Infrared spectroscopy (FTIR) when the interaction is dominated by absorption;
6
however, this technique also is used with excised tissue samples [49]. Experiments
conducted in this work focus on the scattering technique, Raman spectroscopy, and in
quantifying the data for measuring and imaging of bone tissue in-vivo for an animal
model.
Much like in cancer imaging, bone has proteins and cell types that can be targeted
for imaging using extrinsic contrast. Targeting of fluorescent dyes to osteoblast cells,
which play a key role in the development of bone, allows for the imaging of different
stages of the biological process and understanding these processes are altered in a disease
state [50, 51]. Current Food and Drug Administration (FDA) standards do not allow for
the injection of these fluorescent dyes for human imaging. The state of imaging using
external contrast relies of the injection of radionuclides, including Fluoride-18 and
Technitium-99m methylene diphosphonate. Studies with these contrast agents have
provided information regarding the rate of blood flow affecting bone development and
the location of osteoblast activity [52, 53].
1.3 Future of Imaging
Medical imaging is a complex field with many techniques available for diagnosis, based
upon the condition expected and what is desired from the scan. The optimal imaging
system would provide high contrast and high specificity images, including both spatial
and functional information. The ideal situation for collecting the information would be to
use non-ionizing radiation techniques, which are maximally sensitive to the relevant
molecular bonds. Imaging exams would be more readily used if the scans were less risky
for cancer induction and/or if they were less expensive. By removal of the ionizing
7
radiation the number of eligible patients could increase as the risk of radiation dose is
decreased.
Creating high contrast images requires a large signal generated at the site of interest
and a decreased signal in the background regions. The further development of targeting
affibodies and discovery of potential targets on the cell surface, specifically those that are
unique to a certain biological state, would allow for this higher contrast imaging. The use
of targets can also ensure that the location of optical signal contrast is specific to the
region of interest.
This research focuses on techniques available to understand the biomolecular signals
present for the optical imaging of brain tumors and of healthy bone, as measured through
thick tissue as diagnostic data. The overall goal has been to assess which signals can be
measured and to what extent they can be specific to disease processes, focusing on
tomographic and deep tissue recovery in rodent models. This work is pre-clinical in
focus, and provides the estimation of which methods might be further developed for
systematic animal imaging or have relevance to human imaging.
8
2 Introduction to Light Interaction with Tissue
Electromagnetic waves have always been used for diagnostic purposes in medicine.
From x-rays, to visible, down to radio waves, the different energies of the signal provides
extremely different levels of contrast within tissue based upon changes in what types of
bonds the energy is absorbed into. The excitation mechanisms by photons shift with
wavelength band, such that generally: 1) x-rays and UV photons lead to ionization of
electrons, 2) visible photons lead to electronic excitations, 3) infrared (IR) photons lead
to vibrational mode excitation, and 4) microwave absorption leads to excitation of
rotational modes. Use of photon absorption or scattering at any of these wavelengths can
provide contrast coming from different tissue boundaries, or discrepancies in bone
density. There are niche areas of spectroscopy, which have become most applicable for
diagnostic measurements of tissue function and disease that are examined here. Each of
these technologies have become integral imaging techniques used every day in medicine,
but the ability to distinguish biomolecules deeper into tissue is still evolving for specific
applications. This work focuses on determining the range of utility of several different
optical tomography methods in molecular tissue imaging, focusing primarily on emerging
diagnostic signals such as Raman, enhanced Raman and molecular fluorescence which
can be used with thicker tissues, and are thought to have the most potential for molecular
specificity for given applications.
2.1 Types of Interactions
The portion of the electromagnetic spectrum in visible light, spans from 400-700nm, and
near infrared is largely 700-1400nm. Light waves in these ranges will interact with the
9
biological matrix of tissue in two broad ways, absorption or scattering. These are defined
as either the total loss of a photon in the absorption process, or the change of photon
energy or direction in the scattering process. Re-emission of some of the energy from an
absorption or inelastic scattering event is also commonly possible leading to several types
of detectable signals.
The energy of a light wave, E, is related to frequency and wavelength by,
� ���
�� �� Equation 2-1
where h is Planck’s constant, c is the speed of light in a vacuum, λ is the wavelength, and
� the frequency.
Given the wide range of components to tissue, there are many possible types of
interactions that can occur between light and tissue, within the categories of absorption
and scattering. The figure below shows some of the measurable interactions and how
these relate to the physiological parameters of interest. The figure also contains
information regarding the possible contrast agents for the phenomena separated by
whether they are intrinsic or extrinsic to tissue.
10
Figure 2.1: Diagram showing the measurement phenomena that can be measured in biomedical
applications and the physiological parameters that they allow us to view, as well as the sources of intrinsic and extrinsic contrast for these imaging phenomena.
The measurement techniques from the figure above have varying levels of occurrence
within tissue. Each photon that enters tissue will have some interaction, but the
likelihood of each type varies significantly. The probability of an interaction occurring
within a specific area is defined by the cross section. The cross section of interaction is
related to the ratio of interacted photons per solid angle to the total incident photons per
solid angle [54]. Cross section of interaction is measured as an area, with larger areas
having a higher chance of a photon crossing within that area and interacting. The table
below includes an approximation to the cross sections of interaction for the phenomena
that will be discussed here [55]. The cross section is reported per molecule and these
values have been measured in various experimental designs. We would expect a change
in the cross section for all the processes if measured in a biological tissue.
Measurement
Scatter
Absorbance
Fluorescence
Raman
Extrinsic Contrast
Fluorescent Dyes
Phosphorescent Oxygen-sensitive
Probes
PET Isotopes
SER
Nanoparticles
Envi
ronm
enta
l Se
nsiti
vity
Intrinsic Contrast
Oxy-Hb
Deoxy-Hb
Water
Tissue Pathology
Autofluorescence
Bioluminescence
Scatter Power
Scatter Amplitude
Tissue Structure
Stru
ctur
al
Mol
ecul
ar
Physiological Parameters
Blood Oxygenation
Angiogenesis Sensitivity/Volume
Antibody Antigen Interaction
Organelle and Matrix
Constituent Volumes Lipid/Stroma/Epith.
Tissue pH
Molecular Bonds
Biological
Biochem
ical
11
Table 2-1: The cross section of interaction order of magnitude estimate for each of the
electromagnetic phenomena that will be studied in this work.
It is important to note that the cross section is dependent on wavelength of light as well as
the nature of the molecules involved [56].
In the following subsections, the dominant interactions tested for light-based
tomography in vivo are introduced, first as the fundamental phenomena that they
represent, and also how they are quantified in transport modeling. Each method also
includes an example of how it is relevant in biological imaging currently.
2.1.1 Absorption
Absorption occurs by quantized events, into one of the constituents of the molecules in
the tissue. The energy levels for electrons in the atom are quantized into shells around
the nucleus, and these levels dictate which photon energies can be absorbed by a specific
atom or molecule. The figure below shows a potential absorption energy level
discretization for a molecule, and the corresponding absorption plot with each absorption
interaction marked.
Process σ (cm2) Absorption 10-21
Scattering - Rayleigh 10-26 Scattering - Mie 10-10
Fluorescence 10-19
Raman 10-29 Surface Enhanced Raman 10-16
12
Figure 2.2: (Left) Diagram of absorption levels for an atom and the potential absorption transitions. (Right) Characteristic plot showing the frequency difference and intensity variation that would be
expected for the various energy discretization steps.
Tissue spectroscopy results in a spectral absorption features from many biological
molecules. The dominant chromophores, such as hemoglobin, de-oxyhemoglobin, water,
fat, and melanin, have reasonably well characterized spectra of absorption across the
visible/NIR wavelengths [11, 30]. The figure below shows the absorption parameters of
some these components at some typically found concentrations for soft human tissues.
Figure 2.3: Tissue chromophores absorption coefficient, plotted logarithmically with respect to the visible and NIR wavelengths, showing values at representative tissue level concentrations [57-60].
In biomedical optics, absorption measurements are often made using near infrared (NIR)
wavelengths, 750 – 1100 nm, as there is a drop in the magnitude of absorption from these
chromophores in this range, allowing for much greater transmission of light signal
S0
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13
through tissue [6]. Thus, using multiple wavelengths of excitation, it is possible that
these chromophores can be quantified. Previous research studies have used absorption
spectroscopy to compare the levels of de-oxyhemeglobin and oxyhemeglobin present in a
tumor throughout the course of chemotherapy treatments, in order to determine if there
exists an early indication of response [61-63].
Absorption of a tissue is typically quantified by an absorption coefficient (μa) and is
measured with units of reciprocal distance (mm-1). Phenomenologically this is the
characteristic penetration distance through which the signal is attenuated by absorption,
by a factor of 1/e. This coefficient is a strong function of wavelength, l, with absorption
bands varying for each of these chromophores across the visible/NIR, ma(l).
2.1.2 Elastic Scattering
Scattering of light occurs when a refractive index change occurs, and there is no loss of
energy, just a change in photon direction of travel. Mie scattering theory describes
scattering from spheres, which are on the same size scale as the wavelength of the
radiation, and can be approximately applied to light scattering from biological structures.
Rayleigh scattering theory describes the scatter intensity of photons refracting off
particles, which are much smaller than the wavelength, and can also approximate the
scattering from the smallest biological structures and larger molecules within tissue [64].
When using NIR light to probe the tissue, Mie scattering typically involves signals
coming from the major organelles within the cell as well as extracellular matrix, while
individual or groups of molecules cause Rayleigh scattering [65]. The combined signals
are commonly observed with Mie scatter dominating interactions in the NIR spectrum.
14
Scatter measurements can be used to determine the scatter properties of tissues. The
scattering of NIR light in tissue is dependent upon the amplitude of scatter and the scatter
power, through the equation, μs=Al-SP. A scatter power of 4 is theoretically estimated for
Rayleigh scattering, while Mie scattering has a scatter power dependent upon the particle
characteristics and the wavelength of radiation, but closer to the range of 1.0 [11]. At the
same time as obtaining absorption measurements, the simultaneous estimation of scatter
properties can further aid attempts at tissue type classification [11, 31, 61].
Figure 2.4: (Left) Photon scattering diagrams for Rayleigh and Mie scattering showing the
probability of directional scattering by the size of the arrow (Right) A plot of the best fit from an empirical model for Mie and Rayleigh scattering components over a range of wavelengths.
Elastic scattering magnitude in a medium is mathematically quantified by the scattering
coefficient (μs) and is measured with units of reciprocal distance (cm-1). The scattering
directions are typically not isotropic, meaning that scattering is quite directional. In the
diagram in Fig 2.4, the probability of the direction of scatter for Raleigh interactions
shows nearly equivalent likelihood in all directions when the scatter js caused by a small
particle. Alternatively the Mie scattering probability is much more weighted with the
majority of the scattering events from the larger particle occurring in the same direction.
As such the angular range of scatter is characterized by a phase function, f(q), where q is
the angular change of the direction. The magnitude of the directional spread is
Raleigh
Mie
��� ��� ��� ��� ��� �� ����
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15
commonly characterized by the average cosine of this scattering angle, g = <cos(q)>.
The effective diffuse scattering coefficient, or transport scattering coefficient, is then
described by μs/ = μs (1-g). This effective scattering coefficient is commonly measured
through large tissue volumes by matching measurements with diffusion theory
predictions, as will be described later in the chapter.
2.1.3 Fluorescence
Fluorescence is a phenomenon, which occurs after a photon is absorbed following the
rules of absorption discussed previously, after which a non-radiative energy transfer
occurs decreasing the vibrational energy state, which results in a photon emission with a
longer wavelength (decreased energy) as the excited electron returns to its ground state.
Figure 2.5 (Left) Energy diagram showing the absorption, and non-radiative decrease in energy (green arrow), before the emission of a fluorophore with a shifted wavelength. (Right) Characteristic plot showing the absorption curve, in blue, for a fluorophore with the peak absorbance aligned with the diagram. Also shown is the emission curve, in red, corresponding to the spectrum of light which
can be emitted, with the peak corresponding to the diagram on the left.
Molecules and compounds that exhibit fluorescence can be endogenous to the body
or exogenously administered. Autofluorescence, or endogenous fluorescence, arises in a
large part to the molecules contained or produced in the mitochondria and lysosomes
such as NADH, FAD, elastin, and porphyrins [66, 67]. Exogenous fluorophores are used
Excited States
Ground State S0
S1
S2
Frequency
Inte
nsity
S1,1�S0,0 S0,0�S1,3
16
in situations where they are chosen as a tracer or a drug such that their absorption and
emission spectra can be selected to best suit the biological imaging need, and hopefully
avoid overlap with endogenous absorbers.
In the included work discussed here, Cyto500LSS and IRDye 800CW will be used as
exogenous fluorophores. Fluorophores that are cleared for human use with FDA approval
include only indocyanine green (ICG), which has had success in many clinical trials [6,
68, 69]. Other fluorophores, with absorption and emission different then ICG, are in the
process of seeking FDA approval and have shown promise in animal studies [70, 71].
Molecular fluorophores have characteristic absorption and emission spectra. The
absorption spectra is linear with concentration, so that the molar extinction coefficient is
a constant for each biochemical environment (cm-1 M-1), and pre-measurements of this
can be used to calculate an absorption coefficient of the fluorophore, maf, for optical
modeling as long as the concentration is well known. Or vise versa, if the absorption
coefficient is measured, then the concentration could be estimated from this. There are
characteristic emission lifetimes and emission quantum yields for each molecule, which
can be important to include in transport modeling of their interactions in vivo.
Additional parameters governing fluorescence emission of a molecule include the half-
life of the fluorescent interaction and the quantum yield, which is a measure of the
number of fluorescent photons generated for each absorbed photon.
2.1.4 Inelastic Scattering: Raman
Raman scattering is an electromagnetic effect changing the vibrational and rotational
modes of molecules and compounds, occurring from the highly improbable interaction
with a virtual electronic state of the molecule. When the molecule returns to a higher
17
vibrational state than its original, a Stokes scattering event has occurred. When the
molecule returns to a lower energy ground state than it’s original, an anti-Stokes
scattering event occurred. Raman scattering has a low probability with only 1 in 10
million photons being scattered for most biologically relevant molecules. Stokes
scattering events have a much higher likelihood of occurrence than anti-Stokes, as the
population of the lower level ground states is always dominant, following Boltzmann
distribution statistics [55].
Figure 2.6: (Top) Energy diagram comparing the photon interactions for scattering as well as Stokes
and ant-Stokes Raman scattering, with the emitted photon, in green, having an energy changed by the difference in the original and final ground state. (Bottom) Characteristic plot showing the
location of Rayleigh scattering with respect to anti-Stokes and Stokes shifted spectra. The anti-Stokes peaks are lower in magnitude due to their lower population state governed by the Boltzmann
distribution.
The energy of the emitted photon is simply the difference in energy of the initial and
final vibrational energy states. The Raman photons are commonly characterized as a
wavenumber shift to identify their vibrational transition origin,
Excited State
Ground State
Virtual Level
Stokes Scattering Anti-Stokes Scattering Rayleigh Scattering
ΔE = hνR
hν0 - hνR
hν0 + hνR
S1
S0
Frequency
Inte
nsity
Anti-Stokes Stokes
Rayleigh
18
�� ��
������
��
��������
Equation 2-2
By reporting these values in wavelength shift, specific vibrational and rotational modes
always appear at the same location on the spectra regardless of excitation source.
Raman has found application in clinical imaging through microscopy imaging to
determine the structure of tissue specimens ex vivo. This imaging technique has been
applied to bone specimens [72], heart tissue [73], and many applications in individual cell
imaging [74, 75]. In our work, Raman scattering is measured in a tomographic fashion,
with a large amount of overlaying tissue. The signal of interest is measured through these
layers, which then must be interpreted relative to the probabilities for absorption and
fluorescence in order to compare their relative magnitudes in vivo.
Various data processing algorithms exist to aid in the separation of Raman signals
from overlying tissue as well as separating signals from different components and
molecules of interest. Band-target entropy minimization (BTEM) separates the signal
using singular value decomposition methods and eigenvectors [76] , other methods focus
on polynomial fitting to remove autofluorescence components and spectral fitting
methods to separate spectral components [77, 78].
2.1.5 Surface Enhanced Raman Spectroscopy
Surface enhanced Raman scattering (SERS) is caused by the use of metal surfaces, which
have high level of electronic wave interaction with the Raman scatterers, such that a
localized surface plasmon resonance (LSPR) wave occurs. When light with a wavelength
larger then the nanoparticle passes through a sample, electrons in the metal are stimulated
by the light, and as each oscillation of light passes, an LSPR if formed.
19
The LSPR amplifies the electric field component at the surface of nanoparticles, thereby
increasing the amount of incident light on the Raman materials, and additionally
increasing the amount of Raman scattered photons. Under certain conditions, this LSPR
induces a significantly higher Raman scattering cross section, enhancing the signal by up
to thirteen orders of magnitude, when all the components are tuned for the same
wavelength.
Figure 2.7: (Left) Diagram explaining the gold core center of the nanoparticle with Raman active layer coating and addition of surface proteins to the exterior of the particle. (Right) Showing how
the photon wavelength, shown in blue, can disrupt the electrons in the particle and generate an electric field through the LSPR effect.
Research with SERS has used uncoated nanoparticles to amplify the signal of cell
components they abut [79, 80] after being taken up into the cellular cytoplasm.
Nanoparticles that have been coated with Raman material prior to injection are used to
amplify the known signal, but target it to specific regions within the tissue [26, 81].
Surface enhanced Raman scattering is defined by its cross-section like Raman itself.
2.1.6 Cerenkov Emission
Čerenkov radiation is caused by charged particles traveling with a velocity greater than
the speed of light in a given dielectric medium [82]. As the particle travels through the
medium the molecules in its path are polarized and as they return to their ground state
they emit radiation in the form of photons.
Gold Core
Raman Active Layer
Surface Proteins
20
Figure 2.8: (Left) Showing the shape of the Cerenkov photon wave generated with respect to the pathway of the charged particle, at approximately θθ = 41 degrees in tissue. (Right) Representative
diagram of the spectra of light that is emitted by the Cerenkov effect with the y-axis being the number of photons in each wavelength, with a high number in the blue and a low in the red and NIR
region as the spectrum is predicted by I α 1/λ2.
Photons generated through this phenomenon exhibit a spectral dependence that is
inversely proportional to the wavelength of light squared. Therefore a majority of the
photons are generated in the ultraviolet and blue regions, which have large absorption and
scattering coefficients, inhibiting their use for deep tissue imaging. Our studies have used
a fluorophore to shift some of the Čerenkov photons to longer wavelengths allowing
increased intensity of red and NIR photons to be detected as transmission signal from the
tissue interior. Other work with Čerenkov emission, collects light in order to correlate
optical signal with dose at the surface [83], while other experiments place the detector
within the subject through a fiberscope in order to measure the optical signal [84] .
2.2 Modeling of Interactions
2.2.1 Tomography: Forward and Inverse Problems
Tomography is a method where boundary measurements of transmitted signals are used
to determine a 3D map of the interior components of the object. The most common
θ
21
implementation of tomography measurements is computed tomography (CT) scans which
use x-rays as the transmission signal. This method allows for a 3D reconstruction of the
location of the interior components rather than acquiring single planar measurements
with all the interior components stacked over one another. Tomography measurements
can be done with any signal that is capable of transmission through the object of interest,
from x-rays to ultrasound and as used here, near infrared light.
The tomographic forward problem consists of understanding how the signal will be
changed while being transmitted through the object. X-ray tomography is a simplified
problem, in that high energy x-rays are not often scattered, but are simply absorbed or
transmitted. Light based tomography however requires modeling of how scattering,
absorption and transmission affect the measured signal [85]. When light is used as an
input, the photon tracks through the object can be modeled using the Radiation Transport
Equation. Different biological tissues have been extensively studied to determine their
scattering and absorption optical properties [86]. When modeling the forward problem
the locations of the sources and detectors are known, as well as the distribution of optical
properties, and the solution provides you with information regarding the amount of light
measured at each of the detector positions.
Figure 2.9: (Left) The likely light path between a signal source and detector pair. (Right) The sum of the potential light paths for all source detector pairs. When summed the greatest number of photons
are likely to exist nearest the location of the source.
22
The forward modeling approach is used extensively to produce simulated results. The
data constructed from a forward simulation can also be used as a calibration standard for
experimental results. But knowing the exact optical properties of all internal components
at the time of imaging is an extremely complex problem.
The tomographic inverse problem then, involves using the measured transmission
data to reconstruct the optical properties corresponding to the internal components of the
object. The simulated data shown here was constructed from a homogeneous mesh, and
the inhomogeneity of the reconstructed image, while narrow in range, further illustrates
the complexity of tomography.
Figure 2.10: (Left) Example transmission data points for the mesh shown, with 5 sources and 10 detectors with nearly 2 orders of magnitude variation in the signal. (Right) Reconstructed image
form simulated data from a homogeneous object with 10% noise included.
For reconstruction algorithms, the surface boundary and the location of the sources
and detectors must be known. Other inputs include estimates of the internal optical
properties and a mesh made of the object, these inputs are discussed in more detail in
Section 2.2.5. The reconstruction problem is both ill-posed and ill-conditioned, but
techniques for increasing the accuracy and resolution of the solution can be included,
these techniques are discussed further in Section 2.2.6.
23
2.2.2 Radiation Transport Equation
Accurate modeling of the transport of light through tissues is an important tool in
biomedical engineering. As research progresses and the equipment is designed which
optically images the body need to be tested and verified, it is crucial that we are able to
accurately reconstruct the interior characteristics of a volume, solely with boundary data.
Many scientists worked towards developing solutions to transport problems, with a large
emphasis placed on the ability to model fission and fusion reactors [87]. The equations
that were developed to model atomic transport have found to be useful in describing the
propagation of light through a medium. Light transport theory was developed in order to
describe the absorption and scattering events that affect light when it is being transported
through a medium.
The transport equation (Eq.3) accounts for the number of elements flowing out of the
surface, the number of elements colliding within the volume, the change in velocity of
elements caused by collisions, and the velocity of new elements entering the model due
to a source [87].
Equation 2-3
In order to derive this equation, a few assumptions had to be made about the state of the
model; that all the nuclei in the model are at rest, that collisions between the elements are
instantaneous, that the model consists of a material that is highly scattering while being
weakly absorbing.
With an equation to model the transport of light through tissues, solving it would be
the next step. However, this equation cannot be solved analytically, therefore more
∂ψ(r ,v,t)
∂t+ v ⋅ ∇ψ(r ,v,t)+ v ⋅ σ(r ,v,t) ⋅ ψ(r ,v,t) = q(r ,v,t)+ d∫ 3
⋅ v'⋅σ(v'→ v,r) ⋅ v'⋅ψ(r ,v' ,t)
24
assumptions and approximations must be made in order to find solutions. These
assumptions lead to solutions for idealized problems, such as infinite plane geometries
and semi-infinite slabs, as well as infinite cylinders and spheres [88]. While it is a step in
the right direction, most practical models, such as humans or animals, cannot be formed
using these geometries.
2.2.3 Approximation of Light Transport Equation
In order to attempt to model practical models, it is necessary to use numerical methods to
approximate the integrals present. Other approximations come from approximating the
angular density and the phase function. Assuming that all elements have the same speed,
and that the equation is time-independent, it is possible to rewrite the transport equation
in terms of the scattering angles (Eq. 4).
Equation 2-4
Angular density approximations are typically done using orthogonal functions,
specifically spherical harmonics. Spherical harmonic expansions are used to replace the
flux and the source terms (Eqs.5 & 6).
and Equation 2-5
Equation 2-6
Legendre polynomials are used to expand the term within the integral, which takes into
account the change in angular space. This expanded term can then be written in terms of
the spherical harmonics.
Ω⋅ ∇ψ(r ,Ω)+ σ(r)ψ(r ,Ω) = 1
νq(r ,Ω)+ c(r)σ(r) ψ(r ,Ω')∫ f (Ω'•Ω)dΩ'
ψ(r ,Ω) = 2l +1
4π⎛ ⎝ ⎜
⎞ ⎠ ⎟
m =−l
l
∑l =0
∞
∑1/ 2
ψlm(r )Ylm(Ω)
q(r ,Ω) = 2l +1
4π⎛ ⎝ ⎜
⎞ ⎠ ⎟
m =−l
l
∑l =0
∞
∑1/ 2
qlm(r )Ylm(Ω)
25
Equation 2-7
Substituting all Eqs.6 and 7 into Eq. 4, we have a solvable version of the transport
equation. To derive the Diffusion Equation (Eq. 8), sum the spherical harmonic
expansions over l = 0, 1.
Equation 2-8
where,
. Equation 2-9
While the Diffusion Equation is useful for solving non-idealized models, it still has
shortcomings and areas for which the solution is not accurate. There are four major
shortcomings of the diffusion equation; discontinuities, low-scattering areas within the
medium, thin tissue regions, and anisotropic scattering [89]. Discontinuities usually
occur at barriers between two types of mediums when one of the mediums has
dramatically different optical properties. Tissues with low-scattering areas would mostly
be a problem when trying to model regions of the brain or spinal cord, as well as areas
with joints. The brain and spinal column are filled with cerebral spinal fluid (CSF) and
joints are cushioned with synovial fluid, both of these fluids have relatively high
absorption coefficients when compared with scattering. Thin tissues are any tissues that
are not as thick as the mean free path; this condition could potentially lead to the region
not being scatter dominated. The final shortcoming applies to when the light elements
within the medium cannot be modeled as coming from an anisotropic source. This
problem arises because in the derivation of the Diffusion Equation, only the isotropic
term remained, therefore the equation does not account for any other type of source.
f (Ω'•Ω) = 2l +1
4π⎛ ⎝ ⎜
⎞ ⎠ ⎟
l =0
∞
∑ flPl(Ω'•Ω) = flYlm* (Ω')Ylm(Ω)
m =−l
l
∑l =0
∞
∑
−∇ • D(r )∇ρ(r )+ σa(r )ρ(r ) = 1
υq0(r)
D(r) = 1
3σ(r) 1− c(r )μ 0{ }[ ]−1
26
Other methods have been developed, some of which, deal with the shortcomings found
using the Diffusion Equation.
2.2.4 Monte Carlo Methods
The Monte Carlo method was first proposed by Metropolis and Ulam [90], and is a
method where a single photon path is followed throughout the medium, until the photon
exits from one of the boundaries. This method works measuring the absorption and
scattering events that occur at each step through the medium. By following a very large
amount of photon paths it is possible to get an approximation of the scattering and
absorption coefficients for every node in the medium. The amount of energy absorbed at
each node is determined using random numbers and a density function. The scattering
direction of the photon after the absorption event, is calculated using an approximation to
the phase function, generally the Henyey-Greenstein equation [90],
Equation 2-10
where the value g is dependent on the level of isotropic scattering of the medium. If the
medium is completely isotropic then g will be zero, if the medium is completely
anisotropic then g will be equal to 1. Thus, by reducing the scattering phase function to a
single parameter, the knowledge of g can be simply used with this phase function to
approximate the angular scatter in tissue during Monte Carlo simulation, through random
sampling of this distribution.
Due to the fact that spherical harmonic expansions are not necessary in order to
implement this method, it is not necessary to make the assumption that the medium being
modeled is isotropic. This allows for the modeling of more practical and non-idealized
cosθ = 1
2g1+ g2 − 1− g2
1− g+ 2gξ⎡
⎣ ⎢
⎤
⎦ ⎥
2⎧ ⎨ ⎪
⎩ ⎪
⎫⎬⎪
⎭⎪
27
situations. However the implementation of this method is very computationally
expensive. Each photon path requires multiple random numbers and the storing and
update of all the absorption and scattering coefficients found calculated at each step of
the process. While this method follows the events occurring within the medium and
allows us to determine how accurate of a solution we want, by increasing the number of
paths followed, it is not a perfect method. Other methods of approximation allow for the
modeling of a medium with less necessary computations, therefore less time to reach a
solution.
In this work, Monte Carlo methods will be used to determine the source locations
within a volume when using a Linear Accelerator to generate Cerenkov photons in a
phantom. The implementation of this method will be discussed further in Chapter 6.
2.2.5 Diffusion Theory Model
Optical modeling and image reconstruction of interior information is completed with
numerical modeling software called Nirfast (www.nirfast.org) [85, 91]. This software
was developed to implement the diffusion approximation to the Radiation Transport
equation for both forward modeling and inverse modeling also referred to as image
reconstruction. A variety of models are included in the software, but the work done here
uses the fluorescent model, to reconstruct the fluorescent experiments with laser and
Čerenkov excitation, the Raman scattering experiments and the SERS experiments.
As a finite element method, a mesh of the volume is required. These meshes can be
generated from DICOM images acquired with standard images, or generated using a
simple shape algorithm. When DICOM images are used, the different regions of the
subject can be segmented prior to meshing to generate regions within the mesh, using the
28
Nirview software [91]. Each mesh has seven corresponding files containing information
about node placement, the number of elements, the locations of sources and detectors the
relationship between source and detector pairs, the regions within the mesh boundaries,
and the optical properties of the mesh.
Node information includes coordinates in Cartesian space and a distinction of
whether it is a boundary node. The element file defines the nodes, which generate each
element. Source and detector files contain the location on the mesh using Cartesian
coordinates. The link file lists the relationships between each of the source pair detectors
that are used in the data acquisition. Multiple regions can be defined within the mesh and
these are extremely important when including spatial information in the reconstruction
algorithm.
Optical properties are defined at each node and in the case of the fluorescence model,
include absorption and reduced scattering coefficient for the excitation and emission
wavelengths, the refractive index, and the fluorophore parameters of absorption, half-life
and quantum yield. Raman and SERS experiments are also modeled with the fluorescent
toolbox, as they can be treated as an excitation photon being absorbed and altered in
wavelength. The fluorescent parameter of lifetime is set to 0.
Forward models use the diffusion approximation equation (Eq.7) and the placed
source to calculate the value of the excitation field at each detector position assuming the
photons have traversed a segment of the mesh with the associated optical properties. The
inverse model uses intensity measurements for a known wavelength at all detector
positions and determines the optical properties for each node in order to create the data
set that most matches the input measured data vector. The difference between the
29
measured and the calculated fluence fields is found using a Tikhonov minimization of the
form,
Equation 2-11
where the first sum is over the number of measurements and the second sum is over the
number of nodes in the mesh. The parameter, λ, is the regularization parameter, which
can be set as a constant or as a reducing value with each iteration. In order to minimize
Eq. 9 with respect to the optical properties, μ, the derivative of (dχ2/dμ) must be set equal
to zero, leaving,
Equation 2-12
which can be reduced to the form,
Equation 2-13
with J being the Jacobian matrix, which details how the fluence measured at the surface
of the tissue changes with respect to changes in the optical properties. The optical
properties, which are grouped within the δμ term are updated at each iteration until the
stopping criteria has been met.
2.2.6 Model of Fluorescence
The fluorescence model consists of two coupled diffusion equations; the first equation
describes the transport of the excitation photons from the source, q0,
Equation 2-14
and the second equation governs the transport of the fluorescent photons that are
generated through the absorption process, μaf,
χ 2 = (ΦiM − Φi
C )2 + λ (μ j − μ0 )2
j=1
nodes
∑i=1
meas
∑⎡
⎣⎢
⎤
⎦⎥
∂ΦC
∂μ⎛⎝⎜
⎞⎠⎟
T
ΦM − ΦC( ) − λ μ − μ0( ) = 0
JT J + 2λI( )−1JTδΦ = δμ
∇Dx (�r )∇φx (
�r,ω ) − [μax (
�r ) + iω / c]φx (
�r,ω ) = −q0 (
�r,ω )
30
Equation 2-15
The subscripts x and m are used to designate whether the variable is part of the excitation
or emission field. The fluorophore lifetime, τ, and the quantum efficiency, η, affect the
form of the emission light field.
For the forward model, the fluence field of the excitation is determined first, and
used as an input as the source term for the emission fluence field. For the inverse
reconstruction algorithm, a Jacobian matrix is developed for both the excitation and
emission fields and the values for the optical properties are updated from their initial
estimate at the completion of each iteration.
2.2.7 Inclusion of a priori Information
In multi-modal imaging, the spatial information obtained from the additional modality is
often used to guide the recovery of optical contrast. Optical measurements obtained
through diffuse optical tomography have very poor spatial resolution when reconstructed
from exterior measurement solely. The spatial information from these alternative imaging
techniques can be incorporated into the inverse problem, through inclusion of regional
information pertaining to the nodes of the mesh.
Prior to mesh generation, the DICOM images are segmented into the regions of
expected different optical properties. These region designations are then passed into the
inverse problem, and the Jacobian (Eq. 11) is altered to force homogeneous optical
properties in each of the defined regions.
Stacks of DICOM images can be created using various imaging techniques which are
clinically available. For the work discussed in this thesis the spatial information is
∇Dm (�r )∇φ, (
�r,ω ) − [μam (
�r ) + iω / c]φm (
�r,ω ) = −φx (
�r,ω )ημaf (
�r )
1 − iωτ (�r, )
1 − [ωτ (�r )]2
31
gathered via Magnetic Resonance Imaging (MRI) or Computed Tomography (CT). Both
methods generate volume snapshots of the domain that is probed optically.
CT scans have been widely used since the 1970s and are often preferred to planar x-
ray imaging because the reconstruction algorithm eliminates the overlap of the internal
anatomical structures providing for greater contrast [2, 92]. Modern CT scanners can
create image stacks with slices representing millimeter or smaller thickness and have sub-
millimeter spatial resolution [93]. Bone and other materials with high proton count, or
large Z numbers, have much greater contrast in CT scans than muscle, fat and water. The
contrast in biological materials is due to the difference in the attenuation of x-ray.
Injections of Iodine can be used to generate high signal contrast in order to measure
perfusion parameters in various organs [94].
In comparison, MRI scans were first completed in the late 1970s on whole tissues to
provide information regarding the micromagnetic properties of each voxel [2, 95, 96].
Current MR technology produces images with slices representing 2-3 millimeter
thickness and approaching millimeter spatial resolution [97]. Magnetic resonance
contrast is caused by the spin properties of the protons in the imaging field. An input
signal of radio waves perturbs the protons in the tissue, and the change in the relaxation
time before reemission of the wave for each proton is measured with antennas. Different
tissue types; fat, muscles and different organs all have varying relaxation times which
provide high contrast. Alternatively, gadolinium compounds can be injected to provide
increased contrast, as a paramagnetic material whose unpaired electrons enhance the local
magnetic field and measurable signal [98].
32
CT scans are generally considered to have high structural contrast, while MRI scans
are known for ability to generate high soft tissue contrast. When imaging the structural
components of the leg, CT is used to gather the spatial information. Measurements of the
brain, and potential tumors, are captured with MRI techniques. Detailed descriptions of
the optical components of each of these dual modality images are discussed in the
following chapter.
33
3 System Overview
Data discussed in this work was acquired with two distinct systems. Both systems were
multi-modal, acquiring standard clinical images together with optical spectroscopy
transmission measurements. The specifics of each system will be discussed in this
chapter, as well as the advantages and disadvantages of each design.
3.1 NIR-CT Imaging
The system housed at the University of Michigan, Ann Arbor is a multi-modal system
that combines x-ray computed tomography (CT) with near-infrared (NIR) light
spectroscopy. The CT system provides the spatial information from x-ray attenuation
and the NIR system provides the molecular information from Raman spectral peaks [99,
100]
3.1.1 System Specifications
Optical fiber bundles include 5 fibers and with 10 collection branches a total of 50 fibers
were integrated into the Raman spectrograph (HoloSpec f/1.8, Kaiser Optical Systems
Inc., Ann Arbor, MI, USA). The individual fibers were 100μm core and 125μm after
cladding and coating, when combined lead to a fiber bundle with an active area of
0.33mm. All fibers had a numerical aperture (NA) of 0.22. The fibers are encapsulated
with a stainless steel ferrule to increase the sturdiness of the fiber tip, for a total diameter
of 1.27mm. Low OH fibers are used to decrease the amount of extraneous signal
generated within the fibers [101], and fiber bundles were custom designed (FiberTech
Optica Inc., Kitchener, Canada).
34
Two versions of the illumination fiber bundle existed. The first generation consisted
of 19 individual fibers bundled together for easy attachment to the laser. Fibers had a
200μm core and a 220μm diameter after cladding, which when bundled had an outer
diameter of 3.0mm. The second generation, like the detection fibers, consisted of fibers
with 100um core and 125μm diameter after cladding, and a bundle diameter of 1.23mm
with the inclusion of the stainless steel ferrule. Both a 785 (Invictus, Kaiser Optical
Systems, Inc. Ann Arbor MI) and 830nm laser (Innovative Photonics Solutions,
Monmouth Junction, NJ, USA) could be coupled into the illumination fiber bundle.
These laser sources have maximum laser output around 400mW, however the ANSI
standards for lasers, Z136.1-2007, indicate that for wavelengths in the range 400-
1400nm, the maximum exposure should not exceed 200mW/cm2 for continuous
illumination on human tissue [102], when averaged over a 3mm effective spot size. In
most cases the ANSI limit was not exceeded, although this work was all carried out under
experimental animal protocols, and studies on human tissues was not completed in this
thesis.
35
Figure 3.1: Image of Raman Imaging system. The collection fibers couple into the system at the right side of the optical filtering and the light is detected by the CCD after being spectrally dispersed. The excitation light is generated with the included laser for the 785nm source or from a separate 830nm
laser.
The illumination fibers were coupled into the imaging system with a converging
lens. The Raman scattered photons were detected using an optimized HoloSpec
spectrograph that was fitted with a 100μm slit. The grating used depended on the
excitation wavelength, but was a low frequency Raman grating produced by Kaiser to
disperse light over the wavenumber region between 0cm-1 and 1800cm-1. The excitation
laser signal was removed with a long pass filter. The detector for the spectrograph was a
back-illuminated deep-depletion charge coupled device (CCD) (Andor Classic, Andor
Technologies, Belfast, United Kingdom) cooled to -75°C with 1024 x 256 pixels.
3.1.2 Data Calibration
During data acquisition, the total time per light source position exposure was completed
at 60, 180, or 300 seconds. When high noise was an issue in the signal data, frames were
taken in triplicate to reduce the noise via median filtering. The flowchart below describes
the calibration steps that were necessary to implement before Raman signal could be
Optical Filtering
CCD
Spectrograph
Laser
36
isolated from the spectra. Scripts for processing were created using MATLAB
(Mathworks, Inc., Natick MA).
Figure 3.2: Diagram describing the calibration steps necessary to process the acquired data on the
NIR-CT system before extracting Raman signal.
The original acquired signal consisted of pixel intensities for the entire CCD as it is
was read out, as shown in Fig. 3.3. Processing was completed to remove cosmic rays
spikes in individual or small clusters of pixels, which are common during long
acquisition times with cooled CCDs [103].
Figure 3.3: Example of CCD image from Raman measurements on the NIR-CT system. Red pixels
have the greatest number of photons. Individual fiber tracks can be seen for some when looking horizontally. Ten fiber bundles are distributed vertically.
Acquire Signal
Removal of Cosmic Ray Spikes
Normalize by White Light Spectra
Neon Light to Determine Window
Teflon to Determine Operating Wavelength of Laser
Subtract Dark Current
Cosmi
Deter
peratin
Dark
White
2.2
1.8
1.4
1.0
0.6
0.2
×10 4
37
Additional spectra measurements of neon and teflon were acquired during the
experiments. Light measurements for calibration were made using a HoloLab accessory
(Kaiser Optical Systems, Inc. Ann Arbor MI) The neon spectrum, which has well defined
with narrow peaks, was used to determine the wavelength region over which the data was
collected and to assign wavenumbers to each pixel. The image on the CCD of neon light
could also be used to determine if any distortion of the signal existed and to inform the
transformation to remove any distortions from the image. The teflon spectrum was used
to determine the exact operating wavelength of the laser because of its strong and well
characterized Raman peaks. Other possible materials for determination of the
wavelength include Tylenol, and sulfur [104]. Teflon and Tylenol are most frequently
used because of their general availability, and Teflon was particularly beneficial here
because it could be shaped into a tissue-like object, and has similar scattering features to
unpigmented tissue. Dark spectra acquired with no excitation signal but for equivalent
acquisition time width is measured and subtracted from spectra [105].
Figure 3.4: (Left) Example of Neon spectra used to determine the wavelength at each pixel. (Center) Teflon measurement used for determination of lasers operating wavelength, showing the dominant fluorescence as well as regular strong Raman peaks. (Right) The ten CCD panels when each of the single fibers was illuminated sequentially with white light, showing the location and distribution of
each fiber in the vertical orientation of the CCD pixels.
White light acquisition with each fiber individually, allows for visualization and
separation of the rows of the CCD to the correct fiber. When 10 fiber bundles are
displayed on the single CCD, they are represented by approximately 25 rows each. Some
38
cross talk between fiber signals can occur with this method of acquisition, so care must
be taken to ensure that the rows attributed to each fiber contain no excess signal.
Exclusion of the pixels that form the boundaries between the fibers on the CCD can be
done to ensure the removal of crosstalk, but in doing so the cumulative signal per fiber is
decreased.
The knowledge of the true spectra of the white light source can be used to determine
the response of the CCD at each measured wavelength, as shown in Fig 3.4.
Most CCDs have lower efficiency at higher wavelengths, however this is not a linear
effect. Division of the measured spectra by the true white light spectra creates a
correction factor at each pixel that is related to the wavelength efficiency, which can be
used to alter the measured spectra into the true Raman spectra. This is especially
important when the ratio of the different peaks in the Raman spectra is the desired result,
to avoid errors in the relative peak values as compared to the true absolute values.
3.2 NIR-MRI Imaging
The system housed at Dartmouth Hitchcock Medical Center at Dartmouth College is
another multi-modal system combining magnetic resonance imaging (MRI) with NIR
optical spectroscopy transmission measurements. This system was originally designed to
acquire fluorescence measurements in parallel with MRI of small animal models [106]
and has the potential for human use imaging thick tissue, because there is a single CCD
coupled to each detection fiber, enhancing the signal sensitivity.
3.2.1 System Specifications
Eight optical fiber bundles of 8-meter length were composed of 7 collection fibers
arranged in a ring with an illumination fiber centered in the bundle (Z-Light, Livani,
39
Latvia). Fibers were custom designed with a bifurcation in order to allow for connection
to the spectrograph and source-coupling array. The detection and illumination fiber were
400μm core with a 430μm diameter after cladding, with a NA of 0.37.
Figure 3.5: Specification of the custom bifurcated fiber, with a single fiber used for excitation light
transmission and seven surrounding fibers coupled into the spectrometer.
Each fiber bundle was integrated into a spectrograph (Princeton/Acton Insight:400F
Integrated Spectroscopy System, Princeton Instruments, Acton, MA, USA) with a front
illuminated CCD (Pixis 400F, Princeton Instruments, Acton, MA, USA) with 1340 x 400
pixels. Gratings in the system are 300 or 1200 1/mm, allowing for 300 or 60 nm
resolution on the chip.
The illumination pathway was coupled into a rotating stage, which was controlled by
LabView (National Instruments Corp., Austin, TX) and allowed for precise alignment of
a single input fiber with each of the bifurcated fibers. For Raman measurements, an
830nm laser (Innovative Photonics Solutions, Monmouth Junction, NJ, USA) was
coupled into the rotating stage. Fluorescence measurements were acquired using a
690nm laser (Applied Optronics, South Plainfield, NJ, USA).
In all optical methods, filtering of the signal is key in increasing the signal to noise
ratio. Raman scattering has both a low probability and low intensity, so any background
signal can easily swamp out the Raman peaks. To increase the signal to noise ratio for
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the Raman acquisition an 830nm laser line filter (ThorLabs, Newton, NJ, USA) was
included in the illumination pathway. An 850nm long pass filter was included in the
collection pathway to remove excess illumination light from entering the spectrometer
(3rd Millennium Filter, Omega Optical Inc., Brattleboro, VT, USA). An optical density
filter (OD = 4) was included in the collection pathway when excitation measurements
were acquired to allow for increased acquisition times without saturation of the detector.
For fluorescent measurements a 720 long pass filter was included in the collection
pathway, and the same OD filter was used for the excitation measurement.
3.2.2 Data Calibration
Data acquisition length varies from 15 to 60 seconds, and data frames were taken in
triplicate to reduce the noise by averaging. The flowchart below shows the major
calibration steps that occur before the Raman signal can be separated from the remaining
spectra. Processing scripts were implemented in LabView and MATLAB.
Figure 3.6: Diagram describing the calibration steps necessary for the MRI-NIR system acquired
data before extraction of Raman peaks.
The acquired signal consists of 1340 x 400 pixels, but is condensed to a 1340 x 1 data
string as the columns of data are binned as they were read off of the CCD chip
maximizing the number of pixels per wavelength.
Acquire Signal
Removal of Cosmic Ray Spikes
Neon Light to Generate Wavelength Shift
Subtract Dark Current
Cosm
nerate
Dark
41
Figure 3.7: Example of three collected spectra for a Teflon phantom, showing the random placement
and intensity variation of cosmic rays for long acquisitions.
Neon spectra were taken with each fiber spectrometer pair to determine the accurate
wavelength for each pixel (RadioShack, Fort Worth, TX, USA). The LabView software
reports the center wavelength, and the shift for each fiber spectrometer pair was
determined by the discrepancy in these two methods. Dark spectra are acquired for each
pair for the equivalent acquisition time after each experiment session and removed from
the acquired data. The design of this system allows for a greater number of pixels
acquiring per fiber and per wavelength while removing any potential crosstalk in the
hardware components.
3.3 Sequential vs. Parallel Measurements
The NIR-CT imaging system requires sequential imaging of the optical and spatial
information as the CT bore is small enough that optical fibers cannot feasibly be used
with the holder design. Additionally, the optical fibers were designed with a metal
42
ferrule, which would lead to a large image artifact. In order to have a high level of
certainty in fiber placement for reconstructions an alternative method for marking the
tissue surface needs to be implemented. To aid in the placement of fibers, a bed was
designed which allowed for optical measurements to be acquired in the same orientation
that the animal would be scanned. Additionally fiber guides built from a CT compatible
material are implemented in order to reduce the placement error, which was present when
using fiducial markers to guide fiber placement. Use of the fiber guides also allows for
knowledge of the displacement and compression of skin during imaging which is
important in the generation of the mesh and determining optical path length, as well as to
the fact that the applied pressure can affect the optical properties [107].
In comparison, the NIR-MRI imaging system allows for parallel acquisition of the
optical and spatial information. The MR bore size is not a hindrance on system design,
however, the magnetic field within the room, requires that no ferrous metal can be within
the room. Therefore, computers must also remain outside of the field, which accounts for
the length of the optical fibers used in this system. Fibers were machined with delrin
ferrules and pass through a small hole in the wall, this process requires their long length.
All fibers generate some background signal, which is dependent upon both their length
and fabrication material. The fibers in this system are not made of low OH as it is a more
costly investment, and are approximately 8 times as long as the fibers developed for the
Raman system, therefore they produce a higher fiber signal than the which is added to the
background signal. For Raman measurements, this signal can quickly become higher in
intensity then the measured Raman signal, thus increasing the lower limit of
concentrations that can be imaged.
43
Data acquisition in parallel by the NIR-CT requires a longer experimental time than
parallel measurements, but the system is more sensitive to Raman measurements and is
capable of low background with long acquisition times. The MRI-CT has the ability to
take measurements in quick succession, which is necessary for any experiments with time
sensitive measurements, such as a time course study of fluorescence uptake.
44
4 Data Processing
As in most biomedical imaging systems, a large amount of data processing must occur
after the acquisition before the data is useful. In the previous chapter the calibration steps
necessary for the two systems were discussed. This chapter will focus on describing the
steps necessary to separate and quantify the Raman peaks of interest from the entire
collected spectra as well as discussing methods to quantify the amount of fluorescence
signal present in spectra.
4.1 Autofluorescence Signal Removal
The largest contribution to the background signals measured during Raman and
fluorescence measurements is the autofluorescence generated in the tissue or phantom
material. This nonspecific light generation can obscure the signal of interest, and various
methods are in use in order to separate and remove this signal. In the work described here
two main methods are in use - polynomial fitting to the background and spectral fitting to
recover the known components.
4.1.1 Polynomial Subtraction
The simplest method for subtracting the extraneous signal is through fitting a polynomial
to the data. A simple polynomial fit can be done in MATLAB and requires only the x
and y coordinates of the data as inputs. Research groups typically use a 3rd to 6th order
polynomial for fitting and the value varies by group [78, 108, 109]. The choice of the
polynomial can lead to a large variation in the background components that are well fit to
and therefore removed from the measured signal. Through truncation of the spectra to a
region of interest it is possible to reduce fitting errors that may occur due to system
45
components, such as filter cut on and cut off or regions of the CCD that have saturated at
or near the laser line.
Figure 4.1: (Left) Logarithm in base 10 of the intensity of a Teflon and Intralipid phantom, showing the large variation in signal intensity for each fiber. (Right) The polynomial fits assigned for each of
the fibers, colors match the original spectra, plotted with respect to the wavenumber.
Polynomial fits of autofluorescence can also include fitting of any system features
and other background components within the spectra. The spectra acquired on the NIR-
CT system all have the same system components and therefore are easily fit with the
same polynomial order. The NIR-MR system with its independent fiber CCD pair has
slightly varying system components leading to varying polynomial orders generating the
lowest error value.
The disadvantage of this fitting method is that the occurrence of peaks in the data can
artificially raise the background fit, leading to negative values after subtraction of the
polynomial, and a reduction in the true height of the data peaks. Manual removal of these
regions from the fitting can be done before fitting, but requires a prior knowledge of the
expected location for peaks, which isn’t always possible and can be time consuming.
4.1.2 Iterative Polynomials
Iterative polynomials are designed to automatically remove regions with peak
information before producing the final polynomial fitting. The iterations also allow for
Log
Inte
nsity
(arb
uni
ts)
Wavenumber (cm-1)
Inte
nsity
(arb
uni
ts)
Wavenumber (cm-1)
46
the minimization of negative values in the baselined spectra. The flowchart in Fig 4.2 is
adapted from the Zhao, et. al. paper which develops a method they call I-ModPoly [110].
A similar method was concurrently developed by Cao, et. al. [78]. Both algorithms have
been recreated in house using MATLAB software.
The iterative polynomial method uses a residual calculation, based on the difference
between the polynomial fit and the data string being fit, to determine if a fit is better then
a previous model. Peak removal is included in the algorithm, which assigns any
wavelength/wavenumber and intensity pair that is above the sum of the first iterations
polynomial and the standard deviation of the residual, as a peak, removing it from the
fitting data set for all future iterations. After this designation and removal of data values
that are Raman peaks, the truncated data is used to generate a new signal.
In the diagram in Fig. 4.2 the new signal is referred to as Oi and is a Boolean
operation. Data points from the original measured signal remain only when they are
lower than the sum of the polynomial fit and the standard deviation of the residual. If this
relationship is false for a given point, the data point is reset to be equal to the sum of the
polynomial and the standard deviation of the residual. This step ensures that minimum
value is used in the next iteration, decreasing the number of points that will be below the
polynomial fit, and therefore a negative value after subtraction. These steps continue
iterating until a stopping criteria or maximum number of iterations, included as an input
into the function, is reached. A typical stopping criteria, is when the relative change in
the standard deviation of the residual is below a certain percentage, marking that the
change in the resulting polynomial fit has converged. The lower the percentage change
47
allowed, the lower the allowed variation in subsequent polynomial fits, which would
require an increased number of iterations.
Figure 4.2: Diagram of the iterative polynomial method described by Zhao et al [110], which produces a background polynomial fit by taking into account the expected variation within the
acquired signal.
Manual distinction and removal of peak data points can also be done but risks adding
inaccurate preference to regions where Raman is expected. However, in cases of low
signal and a high background, it may be necessary. An example of this algorithm is
included below, and shows 8 iterations of the polynomial fitting before a less than 5%
relative change in the standard deviation of the residual. The data used in this example
was truncated to remove regions without Raman and those suffering from signal added
by system components.
Acquired Signal, O0(λ)
Polynomial Fit, Pi(λ)
Stopping Criteria Met?
Residual, Ri = Oi-1(λ) - Pi(λ)
Standard Deviation of the Residual, Devi if i = 1
Generate New Signal, Oi Oi-1, if Oi-1< Pi(λ) + Devi
Oi = Pi(λ) + Devi, else _____
Background Fit, Pi(λ) Pure Signal, PS(λ) = O0(λ) - Pi(λ)
i = i
+ 1
YES
NO
Peak Removal, if O0(λ) - [Pi(λ) + Devi] > 0
remove point
48
Figure 4.3: (Left) Raman spectra being fit with an iterative polynomial method, showing the entire
region of fitting, with the highlighted region being focused in on. (Right) Iterative polynomial fitting on a Raman peak, showing the large difference between the first and second iteration where the
removal of peak data occurs.
This method is ideal for Raman experiments where the data is present as narrow peaks
that have low to no overlap. However, this process would not perform well for
fluorescent experiments, as the recovered signals are much broader in nature, and would
be artificially truncated in the fitting regions.
4.1.3 Spectral Fitting
Spectral fitting of measured spectra is done in a variety of imaging fields [111, 112]. The
spectral fitting algorithm requires prior knowledge of the expected contribution from the
contrast in the tissue, whether it is a fluorescent emitter or Raman scattering elements, as
well as a measurement of the encompassing bulk background tissue. Spectral fitting of
fluorescent signals requires that each dye present in the object is described by an
independent function. When using this algorithm for Raman data processing, although
the peaks are not independent, a better overall fit result occurs when the peaks are treated
as independent functions. These functions describing the spectra are considered to be
basis spectra and are combined in order to generate the total signal measured. Additional
49
spectra from system components may also need to be included in spectral fitting
algorithms, such as CCD response curves and the locations of filter cut-ons. These ideal
basis spectra are inputs into the function along with the calibrated spectra, and the
quantity of each component is determined using a least squares regression. Algorithms
for this process were coded in house using MATLAB.
Figure 4.4: Example of spectral fitting from experiments measuring fluorescence emission with Cerenkov excitation. The width of the fluorescence peak makes quantifying the intensity very
difficult from the measured spectra, requiring knowledge of the expected signal from the fluorophore and background.
This method is highly conducive in phantom measurements, where measurements of
homogeneous models are simple to create. Application in the biomedical field requires
an optical measurement of background taken prior to the addition of the contrast agent,
which is possible for fluorescence and SERS experiments. For spontaneous Raman
measurements, although not ideal, a polynomial background fit can be used as one of the
component spectra. The sum of the residual between the spectral fit and the measured
data can be used as a check to the validity of the fit.
Disadvantages of this method include the inability to accurately fit spectra that have
been shifted or skewed by transmission through tissue. Adaptation to the algorithm has
allowed for the peak location of the fluorescence basis to shift to the location with the
Wavelength (nm) In
tens
ity (a
.u.)
Wavelength (nm)
Inte
nsity
(a.u
.)
50
best fit, however, accounting for spectral distortion caused by tissue transmission is much
more complicated.
4.2 From Spectra to Data Points
The Nirfast software requires single data values as input for each source detector pair
rather than a spectral component when doing tomographic reconstructions. The spectral
fitting or polynomial subtraction method provide information regarding the various
optical signals over an entire spectral range. For the work completed in this thesis the
spectra of both Raman and fluorescence are integrated over a narrow spectral region,
which is defined for each experiment. By keeping the wavelength region narrow, the
change in optical properties such as scattering and absorption in the integration region are
minimized. Plots of scattering and absorption and their dependence on wavelength were
presented in Figures 2.4 and 2.5.
51
5 Spatially Offset Raman Spectroscopy Imaging
The first section of this chapter is based on text from two published papers regarding the
spontaneous Raman signals generated in phantom materials. The first paper, Acquisition
and Reconstruction of Raman and Fluorescence Signals for Rat Leg Imaging, is a
collaboration of work done with the University of Michigan with the CT-NIR imaging
system. The second paper, Multi-Channel Diffuse Optical Raman Tomography, is
focused on measurements acquired with the MRI-NIR system.
The second section of the chapter focuses on the changes to the CT-NIR system that
have occurred to make data acquisition more repeatable for collection of data on an in-
vivo model. The changes are detailed and initial data from a multi-day two animal study
are reported.
5.1 Introduction
Current medical standards for bone imaging use x-rays, in the form of either standard x-
ray, computed tomography (CT), or dual energy x-ray absorptiometry (DEXA), to
determine the health of bone by measuring the mineral component. However, research
has shown that the organic component of the bone matrix, specifically the collagen
complex, is rich with information pertaining to the bone health for both cases of disease
and healing after fracture [113, 114]. The ability to measure these organic components
has the potential to significantly improve diagnostic bone imaging.
It is possible to measure organic components using spectroscopic techniques that
take advantage of Raman scattering, an inelastic scattering phenomena used for
determining the vibrational and rotational modes of molecules and compounds [24]. This
52
optical technique can be used for monitoring bone health as it has the ability to provide
information on both the organic and mineral states of the material without the addition of
chemical or fluorescent markers [9, 25, 115, 116]. Bone’s composite structure lends itself
to the generation of strong Raman bands, which can be associated with the quantities of
phosphate, carbonate and collagen amide components, as well as less intense collagen
bands associated with the amino acids, notably proline, hydroxyproline and
phenylalanine [48]. These individual components can be used to determine the
composition of the carbonated apatite and octacalcium phosphate within the bone matrix,
which are used as bone health markers [117]. Previous research using samples from both
animal models and ex-vivo human patients has shown that it is possible to determine
disease states and bone maturation from Raman scattering data [46, 48, 118]. Initial
experiments have been completed in order to compare the Raman spectra acquired
through the skin and muscle and on the exposed bone [119, 120]. As the chemical
structure of the bone alters it can be linked with shifts in the peak location as well as
changes in relative intensity, or the band area ratios. The ability to successfully translate
in-vivo Raman scattering data to accurate diagnosis of bone health could provide a
powerful tool for the clinician.
Through the pairing of Raman spectroscopy and optical tomography, it is possible to
obtain some spatial resolution for the region in which the Raman scattered photons were
emitted. Suitable light transport and inversion models are needed to compensate for the
scattering and absorption in the thin tissues, allowing an increase the spatial resolution
and reducing the effects of signal distortion with depth into the tissue.
53
Previous work on the CT-NIR system showed that transmission mode sampling was
able to reconstruct a Raman signal approximately 100-fold greater than those made in
reflection mode [121]. This difference was attributed to the ability of the transmission
measurements to collect Raman signal that was generated deeper within the tissue and
that the tissue itself attenuates the excitation signal as a function of depth, thereby
reducing background, this method is referred to as spatially offset Raman spectroscopy
(SORS) [25, 122, 123]. However, the collection of deeper signals also results in increased
levels of auto-fluorescence and increased elastic scattering events, which lead to reduced
spatial resolution upon reconstruction of the Raman signal [124].
The first study describes the first attempt at Raman tomography in a rat leg geometry
and was performed at the University of Michigan. The measurements were acquired
using an optimized multichannel, single detector system. The full results of the study can
be found in this paper:
JLH Demers, BW Pogue, F Leblond, F Esmonde-White, P Okagbare, MD Morris,
“Acquisition and reconstruction of Raman and fluorescence signals for rat leg imaging”,
Proc. SPIE 7892, Multimodal Biomedical Imaging VI, 789211 (Feb. 2011).
The second study focuses on the MRI-NIR system that combines both acquisition
modes with the intent to use MR images to generate spatial distributions. The unique
feature of this system design was that each fiber bundle is connected to an individual
spectrometer and temperature-controlled CCD, thereby allowing for higher light
throughput and hence increased sensitivity per unit time. The design is presented and
tested using teflon phantoms to assess sensitivity and ability to tomographically recover
different sized regions. The results can be found in:
54
JLH Demers, SC Davis, BW Pogue and MD Morris, “Multi-channel diffuse optical
Raman tomography for bone characterization in vivo: a phantom study,” Biomedical
Optics Express 3, 2299-2305 (2012).
5.1.1 Data Acquisition for CT-NIR
5.1.1.1 Fiber Holder Version 1
An early version of the fiber holder had a 50.75 mm stainless steel ring with 24 holes
drilled through the walls, with 12 holes in each of two planes. For each of the two planes,
the twelve positions were arranged symmetrically around the exterior with a separation of
30° between the center of two consecutive fiber holes. The interior edge of the ring had a
diameter of 25.3 mm and also contained an iris that could close around the leg of the rat
or the phantom once properly positioned. A second ring slides along the base of the
system and was used to clamp down on the foot of the rat or end of the phantom to ensure
there was no movement during the acquisition period.
Figure 5.1: Stainless steel probe with 24 fiber openings and the second rings, both the collection and
source fibers can be pushed through the openings allowing for a variety of source and detector positioning schemes.
55
5.1.1.2 Collection and Source Fibers
Ten collection branches, consisting of 5 fibers each, for a total of 50 acquisition sites
were coupled to a spectrograph, and could be placed in any orientation along the holders
24 positions. The source fiber was coupled to a 785nm laser, and could be placed in any
of the fiber locations.
5.1.1.3 Liquid Phantom
To acquire the signal acquired through a liquid phantom, the probe holder was removed
from the base and the iris was removed. The collection fibers were placed consecutively
all in the same plane and the source was placed in the location closest to the first
collection branch also in the same plane.
Figure 5.2: Stainless steel probes with the collection fibers and source fiber placed for the liquid phantom acquisition and the fiber holder placed into a liquid bath.
The liquid phantom was generated from a 20% Lyposin-II solution diluted to 1%.
The acquisition time for the liquid phantom experiment was 300ms. Data was acquired
for the fibers placed in two different arrangements, the first when the fibers were pulled
to the interior edge of the fiber holder and the second with each of the fibers moved in
5.5mm from the interior edge. The two liquid phantom experiments then had a diameter
of 25.3mm and 14.3mm, respectively.
56
Figure 5.3: The orientation of the source and collection fibers relative to the interior edge of the fiber holder for the liquid phantom experiments are shown with the fibers located around a 25.3 mm
diameter which was modeled as a semi-infinite medium. A second liquid phantom with diameter 14.3 mm was also imaged.
5.1.1.4 Rat Leg Phantom
An optically and anatomically accurate rat leg phantom was generated using molds, and a
layering technique to allow for the inclusion of a bone-like phantom with the necessary
Raman active chemical components [125]. The skin and muscle of the phantom was
constructed from a gelatin and Lyposin-II mixture and the bone component was a mixture
of gelatin and hydroxyapatite.
In order to increase the collected Raman signature the leg was oriented such that the
source was closest to bone, decreasing the distance and thus the scattering events of light
that occur prior to the interaction with the bone tissue.
57
Figure 5.4:The orientation of the collection and source fibers when imaging a rat leg phantom that contains a gelatin bone structure with chemical components necessary to create the Raman signature
from the correct interior region.
5.1.1.5 Detector Calibration
Three calibration steps were taken in order to ensure the spectrograph and CCD were
correctly aligned for Raman spectra acquisition. Each of the calibration steps was
completed for 3 frames and the average of the signals in each case was used in the
calibration step.
A white light source was acquired independently, with each of the 10 fiber branches
for 250ms in order to align each of the branches to have the same relative maximum
intensity. A neon light source was acquired for all of fiber branches for 100ms, in order to
align the known emission bands of the neon to determine the range of wavelengths being
detected by the CCD. The final step involved acquiring the spectrum of a Teflon slide
with all of the fiber branches at once for 30,000ms, which was then used to accurately
determine the wavelength at which the laser was operating.
Using the collected spectra from each of the calibration steps it was possible to align
and remove distortions [105] in the collected spectra prior to the subtraction of the auto
fluorescence from the skin and muscle. This calibration process was useful for aligning
58
the spectra but creates a fairly large region of data that is unusable near the laser line
which was removed via data truncation prior to further data analysis.
Figure 5.5: Example calibrated spectra from 14.32 mm diameter liquid phantom acquisition. Note the values of the calibrated data near the laser line were not usable due to the presence of the notch
filter. Plot only shows 5 of the 10 collection branches.
Truncated spectra were integrated to determine the amount of signal for each source
detector pair. In these experiments there was no significant Raman signal in the
phantom, therefore a region was chosen to represent the change in autofluorescence
signal occurring after the notch filter but prior to the signal fall off.
5.1.2 Data Acquisition for MRI-NIR
5.1.2.1 Experimental System Specifications
An MRI-coupled multi-spectrometer optical imaging platform was modified to facilitate
optical tomography using Raman signals [106]. One of the unique features of this system
was that each of the 8 detection fibers is coupled to its own scientific grade spectrometer
with a cooled CCD detector. Since the entire CCD chip can be used to acquire Raman
spectra, this arrangement provides superior light sensitivity and dynamic range compared
to systems which employ multi-channel detection on one CCD chip, a critical
consideration when measuring the relatively low intensities of Raman peaks. Parallel
59
detection also facilitates rapid tomographic acquisition times. For Raman imaging, the
slit widths were set to 75μm and the 1200 1/mm gratings were used, centered at 900nm.
The light source was a 200mW 830nm Raman laser (Invictus, Kaiser Optical Systems,
Ann Arbor, MI) that was multiplexed into each of the eight fibers sequentially, while the
remaining seven fibers were used to measure the light remitted from the tissue. Thus, a
total of 56 optical projections were measured and for each projection, the Raman
spectrum and the excitation intensity were measured. Light was coupled from the laser to
the fiber bundles through an automated rotary stage programmed through LabView
software with 50mW of light delivered to the surface.
Each fiber bundle contains a central illumination fiber surrounded by seven detection
fibers of 400-micron diameter and NA of 0.37. The fiber bundles were arranged at equal
angular increments around the phantom surface. In Raman imaging mode, 850nm long
pass filters were inserted in the light path at the entrance to each spectrometer. These
filters were removed when measuring the excitation intensity and a neutral density filter
with optical density = 4 was inserted in the source path. The acquisition time for each
source detector pair was determined with an automated algorithm to ensure that
saturation of the CCD did not occur. Raman measurements had a maximum acquisition
time of 50 seconds, while excitation light was measured for 5 seconds. Three replicate
data sets were taken at each source and detector location, for a total experimentation time
near 22 minutes.
5.1.2.2 Phantoms
Gelatin phantoms were constructed using agar, 1% Intralipid, 0.01% India ink (for
targeted transport scattering and absorption coefficients of μs’ = 1.0mm-1 and μa =
60
0.01mm-1), and water and had an outer diameter of 27mm to mimic the size of rat legs
and the characteristics of tissue [126]. To simulate the Raman signal from bone, teflon
rods with diameters of 5 and 12.5mm were used as inclusions within the gelatin
phantoms. A phantom with the 5mm teflon inclusion is shown in Fig. 5.7(a) placed inside
of the fiber interface with 8 fibers placed around the surface. The Raman spectrum of
pure teflon measured with a single channel of the system is shown in Fig. 5.7(b). These
three characteristic peaks arise between 1200 and 1400 wavenumbers, which is similar to
the region containing the Raman signal for the components of bone.
Figure 5.6: (a) Gelatin phantom with teflon inclusion inside fiber holder with inset image showing the
location of the inclusion. (b) Measured teflon spectrum without background subtraction.
5.1.2.3 Data Processing
For each Raman measurement, three sequential acquisitions were recorded and the
median of these three spectra was computed to reduce the appearance of spectral spikes
caused by cosmic rays [103]. These spikes appear very narrow yet with high amplitude
compared to the Raman spectrum. An example of a single 7-channel acquisition is
presented in Fig. 5.7(a) and shows these spikes in the measured spectra. The median
filtering process largely removes this noise. The resulting spectra were processed with a
16-point Hamming window to remove high frequency noise components present in the
pixel-to-pixel variations in the data over the entire measured wavenumber region of
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555cm-1 to 1295cm-1. Inter-detection wavelength calibration was then completed based on
a Neon emission calibration standard.
One of the major challenges of measuring Raman spectra from deep tissue is
extracting the relatively weak Raman signals from an often dominant background
autofluroescence. Background signal can arise from fluorescence in the fibers and filters
as well as from non-Raman interactions within the sample and dark noise of the system.
The exact origins of these signals are unknown but visible in the spectra since the
quantum efficiency of Raman scattering is on the scale of 10-7. Therefore even minor
impurities will have enough fluorescence to generate a background signal. It is common
practice in the Raman community to use a polynomial fit in order to separate these
components from the Raman signal [105, 127]. Most Raman measurements were taken
by stacking the signals one upon another along the y- axis of a CCD; so choosing a single
polynomial fit takes into account any characteristics of that detector. In this system each
channel was linked to its own spectrometer and CCD, therefore each channel may have a
different response and a different polynomial that best fits the data.
To determine the order of the polynomial to be used in each channel for this system,
spectra were acquired using a homogeneous gelatin phantom. The acquired signal,
truncated to the region of interest, 1100 to 1500 cm-1, was then fit with polynomials from
3rd order to 5th order and the cumulative error was calculated between the background
signal and the polynomial. The order of the polynomial with the lowest error for each
collection channel was stored for calculation once the teflon Raman signal was present.
All fittings were fit with 4th or 5th order polynomials, but the coefficients were
calculated for each measurement due to variations in background when the teflon
62
inclusion was added. Fig. 5.7(b) shows the variation in the polynomial fits for the
homogeneous gelatin phantom for the 8 different channels. When a Raman signal was
present in the spectrum, the data points containing the peaks are removed from
consideration before the fitting of the polynomial to ensure that the fit was not biased.
The result of the polynomial fitting was then subtracted from the processed spectra. The
result should represent the pure teflon Raman signal. This is illustrated in Fig. 5.7(c),
which shows the original spectrum, the polynomial fit to the background signal, and the
resulting teflon signal. By integrating the region underneath the Raman peaks that was
excluded during the polynomial fitting it was possible to generate a single value for each
of the 56 source detector pairs, which represents the Raman signal intensity for that
optical projection.
Figure 5.7: (a) Measured spectra from 7 parallel detection channels, showing narrow spikes present before median filtering. (b) Polynomial fits for background signal when measuring a homogeneous gelatin phantom. (c) Truncated measured signal with teflon Raman peaks; the polynomial fit to the
background and the difference between them, highlighting the portion of the spectra that is integrated in order to construct the Raman data
In addition to integrating the Raman signals, the excitation intensities are integrated
and corrected for filtering intensity. Optical data were then calibrated to the image
reconstruction model using the procedure described in Davis, et al [106]. Briefly, this
process involves dividing the Raman intensity data by the excitation intensity, which is
known as the born ratio, and then multiplying by the modeled excitation intensity
Log
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calculated by assuming the optical properties are known. Once completed, data were
ready for image reconstruction.
5.1.3 Image Reconstruction
All images were reconstructed using the open source Nirfast software package [85]. Prior
to image reconstruction, a finite element mesh, which models the tissue geometry was
created in Nirfast. This can be accomplished by segmenting DICOM images from
another imaging modality, in these experiments CT or MRI, and generating a mesh in
Nirfast or Mimics® (Materialise, Belgium), or for simple shapes like the circular
geometries used herein, by specifying the shape geometry parameters. The image
segmentation and the mesh resolution serve as inputs along with source and detector
positions, and all these parameters are output from the software as a completed mesh.
The software produces images by iteratively matching the measured data to a
diffusion model of light propagation in tissue. In this case, the fluorescence
reconstruction algorithms were used since the imaging approach was identical so far as
the modeling was concerned. This produces images of fluorescence yield, which is the
product of the quantum yield of the fluorophore and the absorption coefficient of the
fluorescent compound at the excitation wavelength. For consistency, we call this
parameter Raman yield herein. Since the optical properties are not recovered explicitly,
they must be estimated either through another modality or literature values. An initial
guess for the optical properties of the different tissue types as well as the Raman
signature were input into the algorithm but were updated at each step of the
reconstruction algorithm by the Newton-type estimation process.
64
Raman yield reconstructions were completed with two different techniques for
comparison. The mathematical difference of these methods has been explained
previously [128]. The first method used the diffusion equation and the location of surface
measurements to reconstruct interior values of Raman yield. The second method
incorporated a priori knowledge of the interior region boundaries with the surface
measurements and restricted the Raman yield results to homogeneous values.
After reconstruction, the contrast to background ratio was calculated by determining
the mean value of the reconstruction results for the nodes of the mesh within the region of
expected teflon signal and dividing by the mean value of the reconstruction for the nodes
representing the gelatin background of the phantoms.
5.1.4 Experimental Results for CT-NIR
After calibrating and processing the data acquired from the liquid phantom experiment, a
test of the validity of the data was completed. The nature of light transmission in tissue
can be approximately described as the logarithm of the product of the absorption
coefficient and the distance traveled between the source and detector. This relationship is
known as the Beer-Lambert Law. Therefore, it was expected that as the distance between
the source and the detector increases, the intensity of the light at the collection fibers and
thus being detected will decrease.
65
Figure 5.8: Logarithm of the intensity plotted versus distance between the source and collection fibers shows a negative slope as expected for both the 25.32 mm and 14.32 mm diameter liquid
phantom experiments.
The negative slope was as expected as the distance increased. Similar results are found
for the anatomically accurate phantom data.
5.1.4.1 Discussion
After calibrating the system it was possible to acquire data for both a liquid phantom
and an anatomically accurate rat leg phantom with the stainless steel fiber holder, with
the 10 collection fiber branches and 1 source fiber. After post processing of the data, the
expected negative linear trend was observed for the log of the intensity when plotted with
respect to the distance between the source and the collection fibers. Future steps for this
study and experimental setup include the measurement and reconstruction of the Raman
signature from the rat leg phantom and a comparison to the expected values. The ability
to spatially localize the origination of the Raman and Fluorescence signatures is key in
the development of future applications.
Future work will need to determine under what situations diffusion theory is an
accurate model and when a more accurate radiation transport model is necessary.
66
Additionally alterations to the system must be completed to increase the practicality of
this process for the acquisition of data from living animal models.
5.1.5 Experimental Results for MRI-NIR
Fig. 5.9(a) shows the integrated intensities of the teflon Raman signal and excitation
signal for each of the 56 optical projections through the phantom. As expected, larger
perturbations in the Raman data were observed as compared to the excitation data since
the Raman measurements describe an asymmetrical phantom with high contrast. Raman
data without a parabolic shape represent light transmission pathways that do not intersect
the area of teflon within the phantom. Similar trends in the data are seen in Fig. 5.9(b),
which plots on a logarithmic scale the Born ratio at each source detector pair for the
measured data and for the calculated data from a heterogeneous forward diffusion model.
The measured Raman data has a slightly greater change in magnitude than the modeled
data but the overall shape is in agreement.
Figure 5.9: (a) Plot of the log intensity of Raman and Excitation for each source and detector pair for 8 sources and 7 detection channels. (b) Born ratio of the measured data along with the born ratio
calculated for a heterogeneous diffusion model.
Images of teflon Raman yield recovered from both gelatin phantoms when no
interior prior information is included are shown in Fig. 5.10(c) and (d). The addition of
Source Detector Pair
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prior information results in the teflon Raman yield shown in Fig. 5.10(a) and (b), these
images also represent the true position and size of the inclusions in the phantoms.
Figure 5.10: (a & b) Experimental reconstructed Raman yield for gelatin-based phantoms with teflon
inclusions using spatial prior information to restrict the recovered values to be homogeneous in the two regions. (c & d) Experimental reconstructed Raman yield for phantoms when no prior spatial
information is included in the iterative algorithm.
The Raman yield was recovered with high spatial correlation for both phantoms
without the inclusion of prior information. Raman yield was reconstructed with a contrast
to background ratio of 8.1 and 9.8 for the 5mm and 12.5mm sized teflon inclusions,
respectively. The size of the reconstructed teflon inclusion was smaller than the true size,
with diameters from line profiles measured as 4.3mm and 9.3mm. When prior
information was included with the phantom the contrast to background was raised to 31.7
and 57.3 while the overall maximum reconstructed value decreased.
For the reconstructions completed with no prior information, the 12.5mm teflon
inclusion has the greatest Raman signal, but also the highest background value. In the
5mm Teflon inclusion phantoms the background is very low except for areas within the
mesh domain where edge artifacts occur at the surface aligned with the source and
detector placement.
0
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5.1.5.1 Discussion
The recovered images of Raman yield in Fig. 5.10(c) and (d) show excellent agreement
with the true spatial position of the teflon inclusion and have relatively high values of
contrast to background, in agreement with earlier fluorescent experiments comparing
various reconstruction methods [128]. When spatial prior information was included when
reconstructing Raman yield the recovered contrast was increased by at least 3-fold. In this
study, geometrical information was used to determine the interior region boundaries, but
DICOM images could be used in the future for segmentation of regions.
As expected the Raman yield was greater for the 12.5mm teflon inclusion than for
the 5mm inclusion. This increase in signal can be explained by the presence of more
material to generate the Raman scattered photons. For imaging bone in vivo, the Raman
active material will not consist of such a large portion of the cross-section as the 12.5
inclusion and in some cases might consist of two smaller regions of interest.
One advantage of the multi-system parallel detection scheme used here was the
ability to measure a large dynamic range around the circumference of the tissue volume
since individual detection channels can be controlled by adjusting integration times, or
adding neutral density filters. The excitation data in Fig. 5.9(a) range over three to four
orders of magnitude. A system that arranges the collection fibers in a line at the entrance
to the spectrograph with a single CCD is unable to provide adequate dynamic range
performance to measure these signals accurately.
Additionally, single spectrometer systems, which are multiplexed sequentially,
would require significantly longer acquisition times. For example, the total scan time for
the phantoms in this study was 22 minutes. Acquiring equivalent source-detector data
69
with a single-spectrometer sequentially multiplexed system would require at least 154
minutes.
The low variation in Raman signal for source detector pairs 28 to 42 can be
attributed to the fact that the source is placed far from the Raman generating inclusion
and therefore most excitation light will not pass through the inclusion before being
detected. As the source completes it’s rotation and comes close to the teflon inclusion
again the parabolic nature of the data was restored.
The phantoms imaged in this study were relatively simple with homogeneous
background and homogeneous inclusions. In vivo imaging will be challenged by the
heterogeneity of both the bone and surrounding tissue. Some of these effects should be
reduced by the incorporation of the Born ratio when processing the data [129]. By
reconstructing the integrated Raman peaks rather than simple peak intensities we were
able to increase the amount of signal and decrease the effects of noise on the data.
Traditional methods of Raman scattering analysis use ratio techniques. These techniques
could still be applied with this method of Raman yield reconstruction. An additional
challenge when imaging Raman scattering of low intensities is reducing the background
signal collected. To address this challenge, an attempt will be made to include long pass
filtering at the collection end of the fibers.
Raman tomography was demonstrated in tissue-simulating phantoms using a multi-
channel optical tomography system with parallel spectroscopic detection for the first
time. Images of Raman yield with high contrast to background ratios and accurate spatial
resolution were recovered with and without the use of prior interior information of the
70
mesh. Parallel collection channels reduced the number and complexity of post-processing
steps necessary while increasing the dynamic range of data obtained.
5.1.6 Conclusion
These two studies demonstrated that tomography methods of light imaging can be applied
to Raman spectroscopy and that sufficient signal was generated when using models
approximating animal models. Measurements with the CT-NIR system did not include
Raman tomography results, but previous experiments with similar system components
have been successful in measuring Raman signals in reflection mode [119-121, 130,
131]. Changes to the system to aid in further studies, including in-vivo results are
discussed in detail in the next section.
Attempts to measure biologically significant levels of hydroxyapatite powder in
phantom anomalies, as well as gelatin phantoms with animal bone as inclusions with the
MRI-NIR system showed that the systems sensitivity was not sufficient for in-vivo
Raman imaging. In its current system setup, the background signals generated within the
system components were too high for separating the small component of Raman.
5.2 Implementation of New Fiber Holder Design
Both papers discussed here, use a device to hold the optical fibers in position. The MRI
coupled system used a delrin ring holder designed to fit within the coil needed. The CT
system has used a variety of designs, ranging from metal, to the current delrin model.
However, none of these holders have been able to provide the accuracy necessary for
tomography measurements.
As the CT coupled system has been shown to have higher signal of Raman, and is
developed solely for this purpose, a new fiber holder design was generated and
71
implemented. The purpose of this redesign was to allow for greater localization of fiber
placement during CT collection, decreased set up time during experimental procedures,
and inclusion of sufficient fiber locations around the exterior of the imaging domain.
5.2.1 Changes to Holder Design
The design of the micro-CT used in the CT-NIR imaging system does not allow for much
additional material to be added to the bed. The bore size is small, measuring less than 3.5
inches in diameter, ensuring that the optical imaging must be completed in a sequential
manner, to avoid putting excess strain on the fibers through bending. However, it was
extremely difficult to maintain highly accurate fiber placements for spatial imaging when
the optical imaging was completed before or after their placement.
The first generation of fiber holders was constructed from aluminum and consisted
of two independent rings. The first ring contained small plastic rings applying tension to
the fiber surface to help hold the fibers at the correct location on the surface of the animal
leg. The second ring had a closing shutter that was tightened around the ankle of the
animal to help hold the leg in the correct position throughout the extent of imaging.
72
Figure 5.11: Aluminum fiber holders created by the University of Michigan. (Left) The rear ring
contains an iris that is closed around the ankle to hold it in place; the front ring has 24 locations for fibers. (Right) Anatomically correct phantom placed inside the aluminum holder (modified from P.
Okagbare, JBO, 2012,[132])
The second generation was also made from aluminum but was able to be clipped
onto a delrin ring that was a permanent fixture on the bed used in the CT. This design
allowed for good horizontal localization of the leg because the delrin was visible in the
reconstructed CT images, however the placement of fibers and any distortion they caused
was lost with their removal after the completion of optical scanning.
The third generation was constructed fully from delrin allowing for it to be imaged
exactly as used. To further localize the fiber position on the tissue, fiber guides were
included in this design.
The delrin fiber guides were machined to have a press fit hold on the metal fiber
ferrules. The tips of the guides were beveled to allow for a tighter fit around the leg. A
slit was included in the tip to allow a view from the side through the holder to ensure that
the fiber tip was fully in contact with the skin.
The main disadvantage of this design was the maximum capacity of 12 fibers at any
given time. Additionally, with the way it was attached to the bed, the bottom fiber guides
were very difficult to access and required bending the fibers beyond their suggested
73
point. By remodeling the holder, it was possible to take all of these issues into account
and generate a holder, which was efficient and compact, while remaining versatile.
Figure 5.12: (Left) CAD drawing of the fiber guide, showing the slit at the tip, which allows the user
to see the fiber make contact with the leg. (Right) Third generation delrin holder with animal attached to bed at the entrance to the CT gantry after optical imaging.
The fourth generation fiber holder was designed with the intent that it would be created
via 3D printing technology. The advantage of printing over machining is the fiber guides
can have a smaller outer diameter allowing for a greater number of fibers to fit around the
imaging domain while remaining in a single imaging plane.
The lower 40 degrees of the holder were not fabricated to include fiber guides. These
angles were hard to use with the CT bed that the animal was laid upon. Simulation
experiments were conducted to ensure that sufficient signal could be obtained without
including positions. The results, in Fig. 5.13, indicate the difference in the summed
Jacobian, which is a property that relates to the sensitivity of the system to a specific area
of the domain.
74
Figure 5.13: Nirfast generated plots showing the normalized Jacobian, which relates to the sensitivity of the imaging system set up. The left plot shows the results for evenly distributed fiber placement. The right plot shows the results assuming no fiber placement on the bottom portion of the leg, and a
fairly homogeneous sampling in the top portion of the leg, where the bone is located.
The connection mechanism for the two pieces of the holder was altered to allow for
greater stability and easier fitting. The diagram below shows the location of the split
where the top 9 fibers and holder can quickly be placed or removed, and is held in place
by 4 set screws. When the top portion was removed a small ring still traverses the whole
ring, allowing for a more rigid design, but easier placement of the foot and leg of a rat
through the holder.
75
Figure 5.14: Diagram of the fourth generation fiber holder designed in Solidworks (Dassault
Systemes Solidworks Corp. Waltham, MA, USA) with smaller angular separation of fiber guides, and a smaller OD at the tip allowing for a total of 15 guides to be distributed around the leg, rather then the 12 in the previous model. The design has the same bed attachment in order to ensure quick
integration into the current setup.
The design of the fiber guides was changed minimally, with the wall thickness
surrounding the ferrule decreasing and the tip size also decreasing. The flat edge is to
allow for the setscrew to securely hold the position when removing or placing fibers into
the guide.
Figure 5.15: Diagram of the fourth generation fiber guides designed in Solidworks (Dassault Systemes Solidworks Corp. Waltham, MA, USA) to guide the metal ferrules in imaging, and
maintain tissue distortions for spatial imaging.
Experimental measurements were taken with this design and close attention was paid
to the usability and endurance of the materials, throughout the multiple experiments. At
76
the time of printing additional fiber guides were printed to allow for quick replacement if
a break occurred during set up.
Short setup time was necessary in order to not overly tax animals with extensive time
under anesthesia. University of Michigan Animal Protocols have maximum experiment
times of 50 minutes. Currently, with 25 minutes of Raman optical measurements and 15
minutes for CT measurements, a maximum of 10 minutes remains for setup. The
workflow for fiber setup and placement on the animal was streamlined to take 7 minutes
from the time the animal was fully anesthetized.
5.2.2 Automatic Laser Switching
Previous experiments for imaging SORS used a single fiber as the excitation source, this
was a limitation in the design and required additional time for fiber movement between
acquisition patterns. By moving the fibers manually, the likelihood of human error being
introduced in to the fiber locations was increased, and problematically the ability to know
the exact position and pressure applied to the leg from the fiber at each acquisition was
impossible, making accounting for variations in the signal nearly impossible.
The proposed solution was the incorporation of a fiber switch into the excitation
pathway. Inclusion of a 1 x 6 fiber switch would allow for individual fibers to be treated
as excitation fibers, with filtering occurring before the fiber switch. Five sources were
chosen, leading to a total of 15 fibers and fiber guides encircling the leg. The additional
channel can be used for future additional sources, or for verifying laser intensity
throughout the course of the experiment with a third party power meter (ThorLabs,
Newton, New Jersey, USA).
77
Table 5-1: Table of specifications for fiber switch from Leoni. Minimizing the cross talk, to decrease signal distortion, was the limiting factor.
Software programs were written in house for the automatic switching of the fiber
channels between acquisitions. Variations between transmitted intensities per channel
were minimal, and are shown in the table below. The crosstalk between the channels was
extremely low, with measurements of laser light in neighboring channels being near the
noise floor of detection for the power meter. Variation in each channel intensity was
below 6% change.
Channel 1 Channel 2 Channel 3 Channel 4 Channel 5 27.6 mW 26.0 mW 26.7 mW 28.6 mW 28.2 mW
Table 5-2: Showing the variation in the intensity of the fiber output when the same intensity is input into the fiber switch. Data shown is for measurements taken on January 29, 2014.
An optical board was designed to hold the elements necessary for the proper
filtering of the laser signal.
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78
Figure 5.16: (Left) Diagram of the optical set up showing the locations of filters in the path. (Right)
Photo of the board with the excitation fibers attached to the terminus of the fiber switch on the bottom center.
The laser was filtered, using a Semrock 785 laser cleanup filter (Semrock, Rochester,
NY, USA) to minimize the bandwidth prior to being passed through a 2-meter fiber made
of Cytop, a fluoropolymer [133], with strong Raman bands occurring in the region of the
CCD. The Cytop signal showed a linear relationship with the intensity of the laser signal
(see Figure 5.21). A short pass filter, Semrock 842nm, was included to remove any
Cytop bands in the wavenumber region corresponding to the bone matrix Raman signals
of interest.
Figure 5.17: Measured spectra of the Cytop fiber with and without the presence of the Semrock 842
filter.
79
Finally, the light entered the switch, and was coupled into the 5 excitation fibers. All the
optical components were wrapped in black to stop any stray light from entering the
system.
5.2.3 Filtering in the Fibers
Extensive filtering is important in Raman imaging, as any excessive light can generate
additional Raman bands. In tomography measurements, even with the use of low-OH
fibers, the passage of excitation light in the fibers generates Raman signals and
fluorescence. Any minimization of these signals allows for better signal to background
values for the Raman bands of interest.
The newest version of the fibers, constructed by FiberTech Optica (Kitchener, ON,
Canada), placed cut sections of a 785nm long pass filter, at the tip of the ferrule before
the light can enter the individual fibers. This process dramatically decreases the intensity
of the laser light entering the fibers.
Figure 5.18: (Left) Diagram of the collection fibers, with filtering included inside the ferrule surface, at the tip of the fiber. (Center) Image of two fibers showing the reflection of the laser filter to light. (Right) Head on view of the fibers showing the placement of the 5 fibers inside the bundle. of filters
in the path.
5.2.4 Experimental Results
Experiments were focused on determining the imaging limitations of the CT coupled
system with the addition of the new components. Phantom studies were conducted to
80
better understand the limitations of the imaging system and to determine the linear
response region for hydroxyapatite of bone. Animal measurements focused on validation
of the implemented components with a healthy rat model.
5.2.4.1 Phantom Measurements
As previously described, phantoms consisted of 1% Intralipid and gelatin mixture with
the anomaly region filled with a mixture including varying amounts of hydroxyapatite
mineral.
Figure 5.19: Photographs of the Raman phantoms with the anomaly containing hydroxyapatite appearing white. The concentration increases from left to right.
To determine the linearity with respect to the concentration of hydroxyapatite present in
the anomaly, light transmission measurements were taken with the source positioned
directly in front of the inclusion and detectors at various angles were analyzed.
Figure 5.20: Showing the presence of a noise floor, and that the intensity of the Raman signal is more attenuated at our highest concentration.
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The baselined intensity value for the source detector pair was determined by integrating
over the Raman peak. From this data, it appears that when the concentration of the
mineral was around 250 mg/mL we begin to see attenuation effects. This concentration is
near what we would expect in healthy biological bone tissue [134].
Additional experiments should be conducted to see if having the hydroxyapatite
anomaly represented in a more dispersed way, might aid in increased linearity, as in these
experiments the anomaly was extremely dense and the hydroxyapatite was distributed
heterogeneously.
In future work, it would be worthwhile to recreate these phantom linearity
measurements with the anatomically accurate phantoms [125], so as to mimic as best as
possible the experimental parameters.
5.2.4.2 Live and Cadaver Animal Measurements
Animal models of bone osteoporosis and other disorders are commonly used for
experimentation [47, 135]. For initial animal experiments healthy models were chosen,
ensuring the presence of typical levels of bone mineral and matrix peaks in the spectra.
Measurements were acquired over a period of 5-days using 2 rats. The first animal was
immediately sacrificed and underwent extensive experimentation to determine the best
experimental parameters while removing any anesthesia time constraints.
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Figure 5.21: (Left) Cadaver rat with fibers placed around the leg. (Right) Cadaver rat entering the
micro-CT for scanning following optical measurements.
Results regarding the minimum acquisition time and various fiber patterns were tested on
the cadaver rat. The figure below shows the results for changing the acquisition time, on
the Raman peak and the Cytop peak. The 3 data points for each measurement represent
experiments conducted for 180, 300 and 600 seconds. Linear fitting of these data points
generated a R2 value of 1 for the Raman data and 0.9992 for the Cytop data. The location
of the x-intercept on the Raman line, marked with a black x, indicates the minimum
exposure time necessary for a signal above the noise floor, which is equivalent to 69
seconds.
Figure 5.22: Comparing measurements acquired on the same animal for different acquisition times, showing that the Cytop and Raman signals scale linearly with time. The black x on the Raman fit,
corresponds to the minimum length required to have a measurable Raman bone signal.
83
Three fiber patterns were tested on the cadaver rat. Initial fiber pattern followed the
pattern used for the previous Jacobian analysis where each source fiber is separated by 2
detection fibers. This fiber pattern, however, required prior knowledge of the exact
location of the bone in the leg once the leg had been placed into the holder to acquire
high Raman signal. Since Raman scattering has such a low occurrence rate, the ideal set
up would have the laser input directly aligned with the bone to insure high fluence in this
region.
Figure 5.23: CT images with the fibers indicated as sources (yellow) or detectors (red), indicating the different fiber patterns that were used for experimentation. The left image shows the pattern
originally intended to have a homogenous probing of the leg. The right shows the pattern used for the majority of live animal measurements.
Because the approximate location of the bone was known, the second and third patterns
were implemented to try and increase the likelihood of the fiber being directly over the
bone. Pattern 2, with alternating source and detector near the bone often required a slight
rotation of the leg within the holder. This rotation of the leg added time to the setup and
required more knowledge to ensure the collection of high quality data. By moving to
Pattern 3 with three sequential sources located on the bone side of the leg, the setup time
could be minimized while the laser fluence at the bone site could be maximized.
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Figure 5.24: Diagrams showing the location of the source fibers (red) and the detectors (gray) for the 3 different fiber patterns used in experimental measurements.
In all fiber patterns, excitation fibers 4 and 5 were dispersed over the remaining portions
of the leg in order to probe regions not in the presence of bone.
Applying significant pressure to the leg of the animal and deforming the soft tissue
in order to decrease the path length between the sources and detectors was critical in
acquiring strong Raman signal. Indentations from the fiber guides were visible on the
skin of the rat after optical and CT measurements but no bruising or permanent damage
was observed. With the use of these fiber guides, the area over which the pressure was
applied to the skin was much greater than just the optical fiber tip. Additionally glycerol
was applied to the skin each day prior to fiber placement to increase optical coupling
[136]. In some cases, the excess glycerol filled the fiber guides after fiber removal. With
a similar CT contrast value to the printed plastic, it made accurately placing the fibers on
the bottom portion of the leg more difficult in NirView software [137].
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Figure 5.25: (Left) Indentations in the skin left behind after optical and CT measurements. (Center) A slice from the CT image showing how the guides show the deformation and location of fiber at the surface. (Right) Showing the bottom four fibers, with the two on the left side with glycerol filling the
void, and the two on the right with no glycerol. This highlights the difficulty and low contrast difference between the material of the holder, glycerol and muscle of the leg.
For cases with excess glycerol, measuring the distance from the start of the bevel on each
fiber guide allowed for determination of the correct plane of optical fiber placement.
Prior to further experimentation a method, potentially using fiducial markers, should be
implemented to create a greater CT contrast between the edge of the printed material and
the muscle in order to allow for automatic segmentation.
All reconstructions were completed in Nirfast using unique three-dimensional
meshes generated from CT images. Both diffuse and a priori reconstructions were done
for each data set. After reconstruction the contrast to background ratio (CBR) was
calculated by dividing the mean value of the Raman in the bone nodes by the mean value
of Raman for the muscle nodes. For Rat 1, which was sacrificed at the beginning of
experimentation, the reconstructions lead to a CBR of 2.4 ± 0.6 over three days of
measurements. Conducted experiments represent all three of the fiber patterns discussed
previously, see Fig. 5.23.
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Table 5-3: Contrast to background values (CBR) for Rat 1 (deceased) over 3 days of measurements with 3 different fiber patterns, and the resulting average value and standard deviation of CBR.
Changes in the CBR values can be affected by the fiber pattern and location with respect
to the bone, the amount of light coupled into the tissue, which was an effect of the laser
power, and the amount of pressure applied to the surface by the fibers and fiber guides.
Data from reconstructions for Rat 2, where measurements were made over 3 days with
the animal under anesthesia resulted in a CBR of 2.2 ± 0.4.
Table 5-4: Contrast to background values (CBR) for Rat 2 (living) over 3 days of measurements with the marked fiber patterns and the resulting average value and standard deviation of CBR.
After sacrificing the animal, at the end of day 3, measurements on a fourth day led to a
CBR of 3.8. It is expected that the higher CBR in this case was partially caused by a
higher pressure at the fiber tips, as the leg showed a greater deformation in the CT scans
acquired post optical measurements.
When spatial information was included in the reconstruction algorithm in the form of
priors, the CBR for the Rat 1 data increased to 1.2 ± 1.8 and the Rat 2 data increased to
6.6 ± 6.8, with the measurement after sacrifice resulting in a CBR of 24.2. With hard
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prior reconstructions all of the nodes within one region must have the same value of
Raman signal, so the CBR was no longer the division of the mean of the regions as each
region has only one signal value.
The high level of agreement between measurements acquired on different days,
shown by low standard deviations is promising for future studies. The sacrificed animal
measurements showed a maximum 28% change from the mean, and the in-vivo
measurements showed a maximum 17% change from the mean. For longitudinal
experiments further steps can be taken to reduce this variation.
5.2.4.3 Variation of Measurements with Changing Regularization
The reconstruction algorithm in Nirfast requires the input of a regularization factor that is
included in the Tikhonov minimization, as was discussed in Chapter 2. Previous
reconstructions in this chapter for animal measurements, used a regularization value of
0.1, but a variety of values could be used. To review, the algorithm calculates an update
to the optical properties of the mesh in order to minimize the difference between the
measured data and the simulated results.
Equation 5-1
The Jacobian, J, and the regularization parameter, λ, are factors in the update equation as
well as the difference in the optical properties and the fluence. Use of the Levenberg-
Marquadt method causes a reduction in the regularization parameter at each iteration
[85], whereas alternative methods hold the regularization constant.
For the Raman bone measurements, reconstructions were completed with the initial
regularization value spanning two orders of magnitude. The value was not decreased as
would be done using the Levenberg-Marquadt method, but was held constant across all
JT J + 2λI( )−1JTδΦ = δμ
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iteration. The lambda value was scaled by the maximum value of the diagonal of the
Hessian matrix before being added to the Jacobian. The resulting CBR value for the
reconstruction of data acquired across 3 days for rat 1 is tabulated below.
Table 5-5: Contrast to background ratio (CBR) for measurements acquired on different days for the same animal with the initial regularization value varying from 0.01 to 10.
The reconstructed data for Rat 2, includes measurements from four consecutive days of
experimentation with the final day measurement being acquired at 24 hours past sacrifice.
The table shows the CBR for the reconstructed Raman signal for rat 2.
Table 5-6: Contrast to background ratio (CBR) for measurements acquired on different days for rat 2 with the initial regularization value varying from 0.01 to 10.
The standard deviation across the different regularization parameters is below 0.5 for
nearly all reconstructed data sets. The single data set with a standard deviation greater
than 1, the first measurement for Rat 1, comes from a data set with high variability and
few data points above the noise floor for the Raman data.
These sets of reconstructions, with varying initial regularization values indicate that
when the data was of high quality the change in the CBR value was low and additionally
that the final iterations of the reconstruction reproduce similar results. This is a promising
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result as prior to this analysis, little was known about how this regularization parameter
would affect the resulting solution for the Raman reconstructions.
5.3 Summary of Results
We have shown that the measurement of Raman signals from bone can be done non-
invasively and that sufficient signal can be measured for tomographic reconstructions.
This work was the first reconstruction completed using 360 degrees of data collection
rather than simply reflection measurements. The additional hardware components have
made the acquisition of these Raman signals possible, and initial results regarding the
repeatability of the data collection are promising.
Excitation and detection fibers have small diameters allowing for dense placement at
the surface. Inclusion of laser line filtering at the tip of the collection fiber is done here,
for the first time on such a small fiber tip. Use of this technology can greatly reduce the
noise generated in the fiber for a variety of future applications.
The non-invasive measurement of bone signal in an in-vivo setting has many
implications for the future of imaging. This technique and system can be scaled in order
to collect data on the human scale. The ability to collect data from a biological tissue
without the addition of an extrinsic contrast mechanism reduces many of the restraints
from the FDA in transitioning this technique to a more clinical setting.
5.4 Future Directions
With the completion of measurements on healthy rat models, work can begin on imaging
and reconstructing the Raman signal for a more complex bone model. Implementation of
additional hardware components and alteration of methods are necessary to ensure that
the pressure applied is consistent across multiple imaging experiments and that the
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change in data from variation in setups will be minimalized. For the two live
measurements of Rat 2, using Pattern 3, a change of 8% was seen from the average CBR
values. Alternative data analysis could be done on the pure Raman spectra to further
analyze the variation in the fiber-to-fiber measurements separate from the day-to-day
variation.
Generation of a diseased model would allow for testing to determine if the system
components allow for sufficient quality data collection. Future work will focus on
imaging the change in the bone mineral and matrix components after fracture and during
the healing stages.
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6 Surface-Enhanced Raman Imaging
Surface enhanced Raman scattering (SERS) uses the localized surface plasmon resonance
(LSPR) effect within specially designed particles as a tool to amplify the signal of the
adjacent Raman-active material. Researchers have shown that amplification can increase
signal from cell components or Raman-active material that has been included in the
nanoparticles of gold [79-81].
6.1 SERS Nanostars
Creating nanoparticles or nanostars that are capable of SERS amplification requires
multiple processing steps. The gold core is first coated with the Raman active layer
before being encapsulated within a silica shell. Conjugation of proteins to the exterior of
the silica allows for the addition of targeting, alternate contrast types, or PEGylation to
decrease the likelihood of the nanoparticle being targeted for degradation within the
biological system [138]. One type of SERS particle, used previously by collaborators,
used a trans-1,2-bis(4-pyridyl)-ethylene coating for the Raman-active material, but a
variety of organic materials could be used [81, 139]. In some of their published work,
gadolinium chloride hexahydrate was bound to the surface of the particle providing MR
contrast due to Gd+3 being a relaxation enhancer [81]. Alternatively, fluorescent markers
could be conjugated to the particle surface to act as an optical contrast. The particles used in these experiments were developed by collaborators at Memorial
Sloan Kettering Cancer Center (Moritz Kircher, MD PhD research group), and are
currently in the process of being patented. The particles are also designed to have
multiple sources of imaging contrast, with absorption for photoacoustics, a Raman
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reporter for SERS, and the potential for gadolinium conjugates for MRI. The particles
consist of a gold star center of approximately 50 nm diameter with approximately 30 nm
silica coating, for a total diameter near 120 nm. The figure below includes TEM images
for single and grouped particles.
Figure 6.1: Potential design of particle designed from information provided by Kircher Lab at
Memoral Sloan Kettering.
The Raman active layer is typically an organic material that is coated directly on to
the gold core. Because these particles are currently in the patent process the exact
material used is unknown. However, from the large Raman band at approximately 950
cm-1 that could correspond to a backbone vibrations in C-O-C or to a stretch of phosphate
(PO4) as well as the presence of the multiple peaks between 1050 - 1150 cm-1, which
appear from the stretching in C-O, C-C, and C-N bonds, it can be guessed that the
molecule used to coat the particles is a type of phosphorylated polysaccharide.
Particles are stored in a buffer solution, composed of 10 milliMolar (mM) 4-
morpholineethanesulfonic (MES) acid that can be diluted to alter the solutions
nanoparticle concentration or injected directly into the subject being imaged.
6.1.1 Phantom Measurements
In order to test tomographic imaging of these, the SERS particles were mixed with agar
in order to create a series of tubes with a serial dilution from a high concentration of 1
Design of Particle�
93
nanoMolar (nM) to a low concentration of 0.2 femtoMolar (fM). The tubes with high
particle content were darker to the visible eye, whereas low concentrations where beyond
the lower limit of the imaging system.
Figure 6.2: (Left) Test tubes of agar and SERS nanoparticle solution with varying concentration with 1 nM in the top left down to 0.2 fM in the bottom right tube. (Center) Diagram of the heterogeneous
phantoms used to determine system limits. (Right) Photograph of the system set up. The 90- and 135-degree measurements are the average of the two signals.
Intralipid and gelatin phantoms were designed with an inclusion sized for the premixed
solutions of SERS particles. The tube was aligned with the source fiber and the seven
other fibers were used as detectors. Spectra collected from the 45-degree were not used in
the analysis. Symmetry in the phantom allowed for the 90- and 135-degree spectra to be
averaged.
Processing of the measured spectra included the subtraction of the gelatin and
Intralipid background signal, in order to baseline the signal. Data points were determined
by integrating the area under the Raman peak occurring at 950 cm-1. The Born ratio was
calculated for each fiber position and each concentration of SERS particles, by dividing
the Raman value by the excitation value. Born ratios for each tube concentration were
plotted and the noise floor and absorption dominated regions were determined.
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Figure 6.3: (Left) The Raman signal of the SERS particles used. (Right) The Born ratio data points separated by degree of fiber from source location for the 16 concentrations of SERS particles. The
noise floor, absorption dominated point and the linear respone region are marked.
Full tomographic data sets, with each of the fibers acting as the source for a total of
56 data points, were acquired for the 4 concentrations, from 1.37 to 37.0 pM, which were
within the linear response of the system. Reconstructions were completed with and
without spatial priors, and the reconstructed values were also linear. By including spatial
priors in the reconstruction algorithm, the recovered contrast-to-background was greater
and therefore the fit line for the prior reconstruction is steeper.
Figure 6.4: (Left) Reconstructed diffuse images of phantoms made of Intralipid and gelatin
containing SERS nanoparticles. (Right) Plot showing the linear fit of the reconstructed contrast-to-background with respect to the concentration when no prior and spatial prior information was
included in the algorithm.
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6.1.2 Animal Measurements
Initial animal experiments used a cadaver mouse, with the SERS agar tubes inserted into
the mouth of the animal. In this way, it was possible to image more realistic samples, and
determine if the signal was sufficient for injection and imaging of an animal tumor
model.
Figure 6.5: (Left) MR image of the mouse head with the brain (blue) and SERS tube (green)
segmented from the remainder of the head. (Center) Diffuse reconstruction of the signal shows the dominance at top-right. (Left) Reconstructed region values when including two-region spatial priors
with no signal being present in the brain.
The Raman spectra were isolated from other tissue and system signals using the spectral
fitting analysis described previously. Diffuse reconstructions were heavily surface
weighted, which is unsurprising as there was little tissue between the tube and the fibers.
The inclusion of spatial prior information in the reconstruction led to accurate
localization of the Raman signal with no signal being attributed to the brain region. Data
collected with the 1.37 pM concentration showed very little Raman signal and was unable
to be reconstructed. The recovery was linear with concentration for these tests and the
localization was outstanding for diffuse tomography and hard-prior recovery in vivo.
However the limitation of these experiments was that there was clearly very little
background from SERS particles anywhere else, as the only signal was from the localized
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eppendorf tube. Thus the next phase of testing required a more biologically relevant
tumor model test.
An in vivo animal model was established by implanting the U87 tumor line into a
nude mouse model. The tumors were grown for 3 weeks with an average diameter of 2.5
mm before imaging with the SERS particles. Mice were injected with the SERS particle
solution prior to imaging. All mice were given 150 uL injections of the particle solutions
– three mice at 3 nM and seven mice at 1 nM. Two mice were given no SERS injection
and were used as controls.
After anesthetizing the animal, gadolinium contrast injections were given in order to
increase the contrast of the tumor in the MR images. MR and optical data was acquired
in parallel. The Raman acquisitions were repeated 3 times and had a maximum
acquisition time of 50 seconds for a total collection time of 27 minutes per animal. Each
animal with SERS injection was measured at an early time point, between 7 and 17
hours, and again at a later time point, between 17 and 24 hours. After imaging of the
mice, the brains were sliced and prepped for pathology, which would be imaged ex vivo
for correlation testing with reconstructed images.
Figure 6.6: Selected MRI images from the mouse models showing the variation in tumor size and
location.
MR images were used to segment the mouse head into three regions: brain, tumor and
background head. The MR scan was also used for accurate placement of the fibers on the
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surface of the mesh. Spectral fitting was done to separate the Raman data from the other
signals.
Figure 6.7: (Left) MR slice corresponding to the segmented image. (Center) Segmented image with
white representing tumor, black representing brain and skull, and red representing all other background. (Right) Surface nodes of segmented mesh showing placement of source and detectors on
mesh.
6.1.3 Reconstruction of Animal Models
Attempts to reconstruct the data from the mouse models with the high concentration of
SERS particles met with difficulties in localizing the signal. Inclusion of spatial prior
information in the reconstruction algorithm was unable to reconstruct signal into the
tumor portion of the brain. These complications are likely caused by higher than normal
levels of signal in the background regions of the tissue sample.
Figure 6.8: Reconstruction result for Mouse 12 with 3 nM injection of SERS particles. Surface
artifacts are present at each source and detector position.
An alternative data processing method was implemented, the differencing method [140].
This method attempts to subtract the autofluorescence background from the measured
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signal. Results from this implementation showed a reduction in surface artifacts at the
source locations, but we were still unable to accurately localize the signals origin. These
results further indicate that these experiments did not have sufficient particle localization.
Presence of non-negligible nanostar concentration in the normal brain is expected to be
very minimal because the blood brain barrier remains intact. The solution is not targeted,
but after 24 hours, the majority of particles in circulation should be removed to either the
tumor, which has a depleted blood brain barrier, or taken up into the kidneys and liver for
clearing. Nirfast simulations were performed to evaluate what levels of contrast would be
necessary in order to reconstruct images of the tumor given some level of signal in the
background.
Figure 6.9: Nirfast simulations showing the recovered contrast given the tumor to background
contrast values (T2Bkgd) and tumor to brain contrast (T2Brain) indicated above each plot. These simulations support having a tumor to background contrast near 5 in order to have a recovered
signal (center plot).
With the current experimental set up, ex vivo images, both optical and histology can only
be taken on the brain and tumor slices, giving no estimate of the tumor to background
levels. The nirfast simulations and reconstructions show that a tumor to background
contrast of approximately 5 is necessary to see any effect of its presence using diffuse
reconstructions. This is a rather unfortunate need for high contrast in this geometry.
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6.2 Summary of Results
It was shown that particles can be measured and quantified using tomography for
phantom and cadaver animal measurements. Previous work with SERS nanoparticles use
reflection geometries, like Raman microscopes in order to image the signals [17, 141,
142]. Here we show that with sufficient quantity it is possible to measure the SERS
particles using tomographic methods. These findings can further direct the application of
SERS particles for use in imaging studies with a focus on non-invasive techniques as the
SERS cross section is nearly 10 orders of magnitude greater than Raman signals allowing
for imaging of much lower concentrations.
6.3 Future Directions
If particle localization issues were overcome and tomographic reconstructions were
reproducible in an animal model, the diagnostic potential of these particles could begin to
be exploited. Particle localization could be altered by the addition of targeting proteins
on the surface of the particle.
Particle distribution within the animal could be tracked with optical measurements
taken at the location of interest over a time course. However, these measurements would
not be extremely useful, if the signals origin could not be accurately reconstructed from
the data sets. Alternatively by slicing the head of the mouse, at time points post injection,
and measuring the particle signal in various regions of the head, one could better
understand the flow of particles in the animal model and thus determine the ideal time
frame for imaging.
The diagnostic potential would be greatly increased, if the particles could have
varying Raman signals as well. Future work could focus on imaging multiple particles in
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single inclusions, as well as in various inclusions, and testing the ability of the system to
accurately reconstruct the concentrations of the various particles present. Initial
experiments would be conducted in gelatin and Intralipid phantoms, similar to the
experiments discussed previously. If promising results are found, then particles could be
used for animal studies, where particles are targeted to multiple regions of interest.
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7 Cerenkov Excited Fluorescence Tomography Using External Beam
Radiation Treatment
This chapter is adapted from the text of the following paper:
JLH Demers, SC Davis, R Zhang, DJ Gladstone and BW Pogue, “Cerenkov excited
fluorescence tomography using external beam radiation,’ Optics Letters 38, 1364-1366
(2013).
Measurements were acquired with the optical components of the NIR-MR system, which
was used in conjunction with a Linear Accelerator in Dartmouth Hitchcock Medical
Center’s Radiation Therapy Department.
Unlike the Raman spectroscopy methods, this experiment was designed to determine
the validity of generating photons within a media in order to excite a fluorescent dye.
Fluorescence measurements were taken on the exterior surface and tomographic
reconstructions were completed. A linear response was seen for the four fluorescent
concentrations tested, however sufficient concentrations were not tested to determine the
full region of linear response.
7.1 Introduction
External beam radiation therapy (EBRT) is used in the treatment of many cancers, but the
methods for monitoring changes in the tumor volume during the course of treatment are
dependent on image guidance by computed tomography or magnetic resonance imaging
[143], and the ability to guide therapy based upon molecular signals has been heavily
examined yet remains unsuccessful to date. A course of treatment lasts 2–10 weeks with
daily radiation treatment fractions; ideally, image guidance or molecular response would
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be measured during treatment, maximizing the targeting of radiation and individualizing
therapy based upon tumor volumes and molecular signals.
In this study, a method is proposed that combines EBRT with optical measurements
taken during treatment to measure the signal of a targeted fluorophore with excitation by
the phenomenon known as Cerenkov radiation [82]. When charged particles travel with a
velocity greater than the speed of light in a dielectric medium they generate C erenkov
photons. Charged particles with these properties are produced with linear accelerators
(LINACs). C erenkov emission generated from a LINAC treatment beam has previously
been used for both absorption and fluorescence emission imaging using single-fiber
measurements [144, 145].
Photons emitted through C erenkov radiation exhibit a spectral dependence that is
inversely proportional to the wavelength squared. A majority of the photons generated
are in the ultraviolet and blue regions of the spectrum; however, these wavelengths are
largely absorbed in tissue. Therefore the ability to measure C erenkov light in patients is
limited to shallow depths of light generation and longer wavelengths. By targeting a
large-Stokes-shift fluorophore to the tumor region, it is possible to shift some of the
Cerenkov photons to longer wavelengths, increasing the intensity of surface
measurements [146, 147]. This principle has been shown previously by using radioactive
probes to excite fluorescence on quantum nanoparticles through C erenkov radiation
energy transfer [146].
An ideal fluorophore would have a large Stokes shift with large absorption in the
shorter wavelengths and emission within the near infrared window, where light can
propagate further through tissue. In this study, Cyto500LSS (Cytodiagnostics,
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Burlington, Ontario, Canada) was used (absorption maximum 500 nm and emission
maximum 630nm), which can be readily conjugated to targeting agents and has a large
Stokes shift.
7.2 Methods
Experiments were conducted using a cylindrical tissue-equivalent phantom containing
1% Intralipid with a height of 164mm and diameter of 86mm. An anomaly with height
114mm and 33mm diameter was placed 13 mm from the outer boundary of the phantom
wall [Fig. 7.1(c)]. The anomaly was filled with 1% Intralipid inclusions with varying
concentrations of fluorophore ranging from 0.1 to 0.8mg/mL to represent different
binding rates.
Figure 7.1: (a) Schematic of the experimental setup shows the location of the phantom and measurement devices. (b) The phantom schematic shows the region of the phantom where C erenkov light would be generated in a three-dimensional volume. (c) The top view of the phantom has a white-
light image of the experimental setup with the phantom exterior highlighted with red.
Thirteen fiber bundles were placed around the exterior of the phantom to collect
surface spectra. Fiber bundles contained seven 400μm detection fibers with NA of 0.37
and 13m length. Each bundle has an individual spectrometer and cooled CCD on an
Imaging Cart
Intralipid Phantom
Anomaly
Čerenkov Light Top View Side View Side Viewe Viee View Top View
Radiation Beam
Phantom
a
b c
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imaging cart kept outside of the lead treatment door in order to decrease noise in the
measurements due to scattered radiation. Individual detection channels allow for varying
collection times and large flexibility in fiber placement. The fiber arrangement for these
measurements can be seen in Fig. 7.2(c). Fibers were placed 88 mm above the treatment
couch, and data was collected for 30s during LINAC treatment to the phantom with a
6MV photon beam from 500 to 800nm.
The LINAC beam size and shape can be altered to match a treatment plan for
individual patients using a multileaf and collimator system. Beam size is measured at the
isocenter, located 1m from the source, but in this experiment measurements were
acquired at 1.36m. The beam size was expanded to include the angular variation, leading
to a square beam with sides of length 58mm (40mm at isocenter). Beam size and shape
were restricted only by the requirement of not passing directly through a collection fiber
as large amounts of Cerenkov radiation would be generated within the fiber and detected
by the CCD.
Measured spectra were subject to dark signal subtraction prior to correction for the
spectral response of the optical components. This correction factor was determined by
dividing a measured white light source by its known spectra for each fiber bundle.
Butterworth filters were used to decrease the spectral noise and pixel- to-pixel variations.
A least squares fitting algorithm was used to separate the signal from the fluorophore
from the signal generated by the C erenkov radiation. A basis spectrum of the background
Cerenkov radiation level was generated by measuring surface data when the anomaly was
filled with a 1% Intralipid vessel. Determining the background spectra for a more
complex imaging domain could either be performed before the administration of
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fluorescence or modeled by accounting for scattering and absorption parameters of tissue
(i.e., water, HbO, deoxyHb).
7.3 Results
Figures 7.2(a) and 7.2(b) are examples of least squares fitting of the measured spectra and
its two basis functions, the background Cerenkov and the fluorophore emission curve.
The emission curve of the fluorophore was allowed to shift up to 5nm in order to get the
best fit. Previous work has shown that a distortion of the emission spectra is expected
when generated at depth in tissue [148]. Figure 7.2(c) is a two-dimensional representation
of the slice containing the detection fibers. The blue square represents the beam size and
Cerenkov light field region, and the fiber positions are numbered. Figure 7.2(d) shows the
result of integrating a 20nm region centered on the emission peak maximum for each of
the 13 detectors for the four concentrations of fluorophore. A poor least squares fit for
detector 1 in the 0.1mg/mL concentration caused by poor fiber contact with the phantom
surface led to the removal of that data point prior to reconstruction.
Figure 7.2: Least squares fitting of the background C erenkov radiation and the fluorophore emission spectrum were done for each detector location shown in (c). (a) Example of 0.1mg/mL concentration
fitting. (b) Example of 0.8mg/mL concentration fitting. (d) Integrated intensity of the signal measured in each detector for increasing concentrations of fluorophore in the anomaly.
Images of the fluorophore distribution were generated using the Nirfast software
package [85, 149]. Reconstructions were completed with and without the addition of
spatial priors on a finite element mesh, created using simple shape geometries and a
Wavelength (nm)
Inte
nsity
(a.u
.) a
Detector Number
Inte
grat
ed In
t. (a
.u.)
d
11 11111
1 2
3
5 7
9
13
10
8 6
4
12
Detector Placement
c b
Wavelength (nm)
Inte
nsity
(a.u
.)
106
defined mesh resolution. Nodes within the anomaly region were marked. Optical
properties were applied to each node of the mesh as the average values over the 20 nm
region described previously. For patient experiments, mesh generation and region
assignment could be determined through DICOM files provided from previous imaging
studies of the patient.
The reconstructions used an iterative process to match the measured surface data to a
diffusion model of light propagation. Unlike traditional fluorescence tomography
measurements, where excitation is done with a laser entering the medium at the surface,
our fluorophore was excited by Cerenkov radiation, which was generated throughout the
interior of the phantom. To approximate the excitation field, distribution, and photon
intensity, Monte Carlo modeling was performed using GAMOS [150, 151]. The resultant
field calculations were interpolated onto our mesh and used in the diffusion forward
model; see Fig. 7.3(a).
Figure 7.3: (a) Calculated field of C erenkov radiation is shown in the plane of the detection fibers. (b) The reconstructed images are shown when using no spatial information for each of the
concentrations marked. (c) The linear relationship between the concentration of the anomaly and the reconstructed values are shown in the graph.
7.4 Discussion
The fluorescence yield recovered for the various concentrations had high spatial
correlation without the inclusion of spatial information, although the values were surface
Concentration (mg/mL)
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107
weighted as is sometimes encountered in tomographic reconstructions. A linear
relationship exists between the concentration of fluorophore and the difference between
the mean reconstructed value in the anomaly region and the mean reconstructed value in
the background for both the no-priors and hard-priors reconstruction results. The bias in
this relationship could arise from a variety of factors; in this case it is likely caused by
data-model mismatch or incorrect optical properties during reconstruction. C erenkov
light was generated throughout most of the phantom due to the beam location and size,
but through spectrally resolving the two light components, C erenkov and fluorescence;
reconstructions of the signal were calculated with relatively high contrast to background
values (4.5–6 for no priors and 20–28 for priors).
Using a single light source, in this case the C erenkov light field, creates a different
reconstruction problem than typical fluorescence molecular tomography, which uses
multiple-source projections to build up a data set [152, 153]. A single source generated
beneath the surface of the imaging domain is similar to the bioluminescence problem that
is known to be more difficult to reconstruct [154-157]. Additional difficulties in
reconstruction of the fluorescence signal and location lie in the amount of signal
generated per treatment, complexity of least squares fitting, and accounting for any
degradation of the fluorophore over time due to photobleaching from prolonged
Cerenkov light generation due to treatment by the LINAC beam.
7.5 Summary of Results
Measurement of fluorescence signal generated by EBRT was done previously with a
single fiber. The results published here indicate that the fluorescence signal can be
measured tomographically with the reconstructed signal able to quantify the amount of
108
fluorescent present for the Cyto500LSS dye. This work also combined GAMOS results
with Nirfast in order to effectively generate the location and extent of the field of
Cerenkov generated photons. This was a significant addition to the field of EBRT as it
allows for the potential measurement of biomarkers in the subject – measurements can be
taken prior to, during and post treatment.
7.6 Future Directions
Future work will require further optimization of the least squares fitting to include
absorption properties and other optical parameters of the system allowing for the addition
of bio- logically relevant material to the phantom (i.e., blood). It is expected that
measurements regarding the presence of the fluorophore would still be effective due to
the Stokes shift to longer wavelengths. Additional experiments will look at varying the
beam size and shape as well as changing the size, position, or number of anomalies
present within the tissue-mimicking phantom.
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8 Fluorescence Imaging
Imaging with fluorescent dyes is done routinely in some medical fields with the FDA
clinically approved indocyanine green (ICG) and methylene blue [158-160]. Through
injection of these dyes into the blood stream it is possible to track blood flow or vessel
morphology, or by directly injecting into the tumor periphery it is commonly used for
sentinel lymph node mapping in the course of breast surgery [18, 161, 162]. More
recently, it has been shown that the conversion of δ-aminolevulinic acid (ALA) into
protoporphyrin IX (PpIX) can be used as an fluorescent marker for determination of
tumor margins in some brain cancers [163]. The difficulty with these dyes however is
that they can be quickly cleared from the system and do not have specific uptake, rather
they can be found everywhere within the injected subject in varying concentrations.
Fluorescent dyes depend on the circulation system to evenly distribute them, and any
pooling would be due to a breakdown in the physiological status of the circulatory system
and tissues [66, 164, 165]. With these injection methods it has been shown that long
circulation times can aid tumor congregation due to the presence of leaky vasculature, but
background signal strength varies greatly depending on the clearance characteristics [166,
167].
The widespread use of methylene blue and PpIX as fluorophores is limited by the
low emission yield, with the peak emission wavelength occurring around 700nm. To be
used for biological imaging, light must be able to propagate through centimeters of tissue;
therefore with excitation and emission in this wavelength region it can be difficult to
sufficiently excite the fluorophore. Additionally tissue autofluorescence is much greater
for these measurements than if the fluorophore emission occurred in the NIR [67, 168].
110
Also, the ambient room lights have about 10x less intensity in the NIR wavelengths near
800nm, than they do at 700nm, so the reduction in background interference would be
substantial as well.
For biological imaging, ICG does meet the requirements for excitation and emission
in the NIR but it is still not ideal. ICG is not stable for long period of times and must be
created, injected, and imaged in a time period of less than a half-day and can form
aggregates that would adversely alter the circulation and signal generation [169]. The
quantum yield of ICG is low, approximately 0.012 in whole blood [170], meaning the
number of photons that must be absorbed for emission of a fluorescent photon is high.
Another important issue with ICG is that the chemical structure lacks a location for
irreversible conjugation binding to a protein for a targeting agent [169].
These three FDA approved agents are all used in imaging methods today, but none of
them have the ideal components to maximize value in molecular imaging. The ideal
fluorescent imaging technique would allow high fluorescent signal in the region of
interest, and low or no fluorescence in the adjacent tissues. Several other fluorescent
dyes, currently in varying stages of FDA approval, could be used for animal imaging
studies. In this work, IRDye800CW is utilized as one candidate dye, which has been
developed to have high quantum efficiency, excitation and emission in the NIR window.
The chemical structure is designed to allow ester or maleimide binding with other
molecules in a stable covalent bond.
8.1 Fluorescence Targets
By conjugating fluorescent dyes to peptides, such as affibodies, antibody fragments, or
full antibodies, it is possible to be highly selective in where they bind and congregate,
111
because these are manufactured to bind with high affinity to receptors of interest. The
specificity of localization is what increases the signal in the area of interest, and
decreases the amount of signal in background tissues [171]. Extensive cancer biology
research is focused on understanding cellular protein expression, signaling proteins,
extracellular matrix structures and the overall microenvironment in order to guide the
development of targeting agents [171-174]. This drug discovery process is perhaps the
largest area of cost and time in oncology today, and through choice of a few suitable
cancer-specific cell receptors, this work focuses on assessing the viability of imaging
based upon these.
In the brain tumor cell line used in this work, U251-GFP (supplied by Dr. Mark
Israel, Norris Cotton Cancer Center, Dartmouth-Hitchcock Medical Center), it is known
that the tumor cells over express the Epidermal Growth Factor Receptor (EGFR) in a
higher density than normal brain cells [27, 175]. Thus, much of the work presented here
focuses on assessing the ability to target this fairly ubiquitous cancer cell receptor. The
transfection of DNA to express Green Fluorescent Protein (GFP) in the cells allowed
analysis of the tumor location with simple green fluorescence ex-vivo analysis [176,
177]. So the cells used here are denoted as U251-GFP.
8.2 Experimental Design
For these experiments, the fluorescent dye used, IRDye800CW (LI-COR Biosciences,
Lincoln, NE, USA), was conjugated to anti-EGFR affibody protein following the
procedure described in Sexton et al [39]. This dye was chosen because both its excitation
and emission maximums are within the Near Infrared band, allowing deep penetration
into tissue.
112
Figure 8.1: Absorption and emission spectra of LI-COR IRDye800CW with the location of the laser excitation source (solid line) and optical filtering (dashed line) [178].
A 690 nm laser was used for excitation of the fluorophore and a 720 LP filter was
located at the entrance to the spectrograph to decrease the amount of laser entering the
enclosure. The 690 nm had an output intensity of 0.8 mW at the fiber tip.
Phantoms were created from 1% Intralipid and gelatin, and optical measurements were
acquired for a significant concentration gradient of dye to determine the region of linear
response for the system as well as determining the lower limit of visible fluorophore.
Brain tumors were implanted orthotopically in nude mice by injecting 1 million
U251-GFP cells into the brain and allowing growth for approximately 3 weeks. Mice
with good tumor growth were assessed by gadolinium enhanced MRI scans, to visualize
the tumor progression. Once the tumors were of suitable size, the mice where used for
imaging studies. Tail vein injections of 0.1 nanomole were used to introduce the
fluorescent compound into the biological systems. Optical measurements were taken
concurrently as post-injection MR scans, using the MR coupled cart to garner the spatial
information and allow high accuracy placement of the fibers on the mouse head,
Measurements were acquired either 1 hour after injection or 24 hours after injection.
IR Dye 800 1.0 0.5 0.0
Nor
mal
ized
Inte
nsity
Wavelength (nm) 250 350 450 550 650 750 850
Absorbance Emission
113
8.3 Experimental Results
Processing of data was done using spectral fitting methods to extract the component of
dye present in the spectra. The second basis function for the spectral fitting was based on
measurements of the autofluorescence signal in each mouse prior to the injection of dye.
The combination of these two basis spectra generated fits with low error and good
isolation of the amount of signal present from each of the two components.
Figure 8.2: Spectral fitting of the components in the signal for a measurement in a mouse brain. Basis functions include the fluorescent signal and the pre-injection autofluorescence
signal.
The fitting was done on a truncated region of the spectra with the filtering components
removed but the inclusion of the entire IRDye800CW signal peak.
8.3.1 Phantom Measurements
Dye solutions were made in small tubes that hold 2mL of solution and could be inserted
into the phantom to easily alter the concentration without changing the fiber locations.
The concentrations measured in the phantom varied from 1.7 to 105 pM. The phantom
had a diameter of 25.5mm and the inclusion was placed 7.5mm from the edge.
114
Figure 8.3: Intralipid and gelatin phantom with a tube containing 1% Intralipid and IR800 dye solution with the location of the source and the angles used for concentration analysis marked.
Comparing the amount of signal measured to the concentration it is possible to determine
which concentrations fall within the linear response of the spectrograph. It is also
possible to determine the location of the noise floor and if any of the concentrations fall
within the attenuation region, where scattering and absorption by the fluorophore lead to
a decreased signal.
Figure 8.4: Plotting the logarithm of the concentration versus the logarithm of the measured signal divided by the transmission signal, was used to determine the region of linear response for the CCD detector and this fluorophore. The region where attenuation begins to dominate the signal was not
yet reached in going up to 150 nM.
Although the upper limit of the fluorescence response was not included within the
concentrations that were tested, the highest concentration that we would expect to see an
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115
in-vivo setting was included within the data set (100 nM). If future work increases the
concentration of fluorophores, it is possible that a higher concentration may be possible
and the true upper limit for the linearity of the CCD can be determined.
8.3.2 Animal Measurements
Mice with sufficient tumor growth were injected with the affibody conjugated fluorescent
dye. Optical measurements were made with 8 fibers placed around the mouse’s head.
Each source was used to acquire signal for a maximum of 10 seconds, for both
fluorescent and excitation scans, up to a maximum acquisition time of 160 seconds. The
short optical scan time coupled with a longer MRI time, allowed for the fiber locations to
be monitored with MRI scans and any adjustments to be made in order to alter the
location of the fibers and increase their probing of the plane of the tumor. T1 weighted
MR scans also provided the spatial information needed to generate 3D meshes of the
mouse head. Gadolinium contrast scans were used to determine the extent of the tumor
and to aid in segmentation (Magnevist, Bayer HealthCare, Whippany NJ, USA) and
required 200μL injections per mouse. Meshes consisted of three regions: tumor, brain
and muscle sections.
Figure 8.5: The MRI workflow with an emphasis of at least 10 minutes necessary between the
injection of the Gadolinium contrast agent and the second MR scan to allow for sufficient highlighting of the tumor region. The tumor is highlighted in the upper left quadrant of the image.
Gadolinium Injection
T1W Contrast MRI
T1W MRI
10 mins.
116
Optical tomography data was acquired at 1 hour or 24 hours post fluorescence
injection and the animal was sacrificed directly following tomography data collection.
The autofluorescence of the mouse model was acquired prior to the injection of the
fluorescent dye solution. For the 24 hour mouse, it was impossible to have the fibers
located in exactly the same position for the pre- and post-injection scans, but care was
taken to have them as similar as possible.
Figure 8.6: Diagram representing the fluorescence and optical timeline. The autofluorescence signal
was acquired prior to the injection of fluorophore, and the fluorescence can be seen in the second spectra. The animal was sacrificed directly after the completion of optical tomography and the
completion of MR scans.
The entire mouse head was frozen and later sliced for 2D ex-vivo imaging for
comparison. Slicing of the entire head decreased the deformation of the brain tissue and
increased the number of biological landmarks present to align the 2D slices with
corresponding slices from MR and optical imaging.
Fluorescence data from optical tomography was isolated with spectral fitting
methods and the area under the curve was integrated over a 20nm window. Each
tomographic data set consisted of 56 fluorescence data points and the 56 corresponding
laser measurements. The Born ratio, or the fluorescence signal divided by the excitation
Pre Injection Fluorescence
Pre Injection Transmission
Post Injection Transmission
Animal Sacrificed
Fluorophore Injection
Post Injection Fluorescence
1 hr or 24 hrs.
117
signal, was used as an input into the reconstruction algorithm. All reconstructions were
completed in Nirfast using unique 3-dimensional, three region meshes. Diffuse and a
priori reconstructions were completed for both animals.
Two different values were calculated for the contrast to background ratios (CBR),
the tumor to brain contrast and the tumor to background contrast. As previously stated the
CBR values were calculated using the mean reconstructed value in each of the regions.
The tumor to brain contrast provided information about the level of contrast in the tumor
region compared to the rest of the brain which is a measure of both how well the
fluorophore binds to the tumor cells over the normal brain cells and if the vasculature
breakdown in the tumor is significant. The tumor to background contrast was a measure
of the amount of signal in the tumor divided by the signal in the region outside of the
brain. This background region was inclusive of many sub-regions: skin, muscle, eyes and
all vasculature outside the brain.
Optical measurements were taken at 1 and 24 hours post injection to determine if a
longer period between injection and imaging would allow more targeted fluorophore to
be present in the brain tumor and if a reduction in the background signal would be
present. For diffuse reconstructions the difference in the CBR for the tumor to brain and
for the tumor to background did not increase at 24-hour measurements but was steady.
The CBR for tumor to brain was 0.9 and tumor to background was 0.6 with a
regularization value of 0.1 for both measurements times. For all cases with diffuse
reconstructions the tumor region had the lowest signal of all three regions. When
including the spatial information from the MRI in the reconstruction algorithm the both
data sets had an increase in the tumor signal. For the 24 hour data point the tumor had a
118
signal that was 1.8 times the brain signal, with a background signal that remained at a
CBR of 0.6. Reconstructions for the 1 hour data point had an increase in the CBR for
both, but the tumor to brain value remained at 1, meaning there was no visible distinction
between the 2 regions. The CBR values for the spatial priors cases are tabulated below.
Table 8-1: The contrast to background ratio (CBR) for the two data sets of targeted fluorescent dye in the mouse brain when using prior information to guide the reconstruction. The values are defined as the signal in the tumor divided by the signal strength in the remaining brain or the
background section.
Figure 8.7: Slices from the reconstructed 3D volume of fluorescence signal in the mouse head. Each image is independently normalized by its maximum fluorescence yield, to emphasize contrast
difference. The value located in the brain tumor was enhanced relative to the background normal brain in the 24 hour images, but not the 1 hour images.
The images of the reconstructed fluorescence signal are taken from the center slice
over which the fibers are placed. Contrast between the tumor and brain is only visible for
the data set acquired at 24 hours and when spatial priors are included in the
reconstruction. All other reconstructions show the difficulty of separating the signals. It
Hard Priors Tumor/Brain Tumor/Bkg 1 Hour 1.0 0.9
24 Hours 1.8 0.6
1.0 0.812 0.625 0.438 0.250
1 Hour 24 Hour
Diff
use
Prio
rs
119
is worth noting in the diffuse reconstruction on 1 hour post injection, that all of the areas
of high concentration of signal are occurring outside of the tumor and brain.
By increasing the amount of time between injection and imaging for the brain tumor
case studied here it was possible to increase the tumor contrast level. Ideally, the diffuse
reconstructions would show similar results but there is the potential that more work with
the targeting component of the fluorophore or even longer circulation times can aid in the
increasing the contrast.
Further analysis was completed, to determine how the CBR changed when varying
the regularization parameter. The regularization parameter is used in the update equation
that is calculated during the Tikhonov minimization process, and is discussed more in
depth in Chapter 5.3.4.3. For the fluorescence measurement the reconstructions were
completed with the regularization parameter varying over two orders of magnitude.
Table 8-2: The contrast to background ratio (CBR) for each mouse fluorescence measurement and
how they vary with changes in the regularization parameter. The standard deviation was calculated for each animal and each type of contrast value.
The standard deviation was calculated based on the recovered CBR across the four
regularization parameters. The data for both the 1 and 24 hour post injection had low
standard deviations with nearly identical reconstructed values, but with none of the
results indicating higher signal in the tumor. The low standard deviation infers that the
Regularization Parameters Tumor/Brain 0.1 1 5 10 St. Deviation
1 Hour 0.9 0.9 0.9 0.9 0.0 24 Hours 0.9 0.8 0.8 0.8 0.1
Tumor/Bkg 0.1 1 5 10 St. Deviation 1 Hour 0.6 0.7 0.8 0.8 0.1
24 Hours 0.6 0.5 0.6 0.7 0.1
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data is of high quality. However, the best way to understand the fluorescence distribution
within the mouse model is through the imaging of the 2D ex-vivo slices that are created
from the sacrificed animals.
8.4 Agreement with 2D Ex-Vivo Data
The 2-dimensional slices were created after the sacrificed animal was frozen. The entire
head of each mouse was sliced with slice thickness between 1 and 2 mm on in-house
designed frozen sectioning equipment. After slicing the fluorescence present from the
injected dye was measured using the Odyssey Infrared Imaging System (LI-COR
Biosciences) for each slice containing brain tissue. The 800nm channel was used to
capture the targeted fluorescence signal. No method of autofluorescence subtraction is
included in this image capture.
The tumor line, U251-GFP, was chosen because the GFP could also be imaged. The
GFP signal was measured using the Typhoon 9410 Variable Mode Imager (GE
Healthcare, Milwaukee, WI, USA). GFP signal and hematoxylin and eosin (H&E) of
adjacent slides has been done previously to show that this method shows good agreement
in tumor delineation [39].
Post processing of the captured images allowed for the aligning by biological
landmarks and display of the various signals as different color changes in RGB images.
For the generation of the RGB matrix for display of the images, the GFP signal are
represented by the green channel, the targeted IR800 dye measured in the 800 channel are
represented by the red channel, and fluorescent measurement in the 700 channel are
represented in the blue channel. The intensity of each channel in the final image is
121
determined by normalizing each channel by its maximum value. Pixels that appear purple
represent the 700 and 800 channel have similar intensities relative to their maximum.
Image groupings displayed in black and white are representative of the GFP image
on the right and the signal from the 800 channel is shown on the left. The resolution of
the GFP signal is much higher than the IR800 fluorescent signal.
All slices including brain tissue were imaged, but only those with strong GFP signal
are included in the figures below. The background regions of the mouse head have
similar levels of fluorescence in the slices farther from the tumor. For the images from
the 1 hour post injection, the intensity in the background regions is high and in shades of
purple with a much lower intensity in the brain, and nothing visible in the tumor. These
results are comparable with the images created via reconstruction of the tomography data.
Figure 8.8: Three representative slices from an animal sacrificed 1 hour after the injection of the targeted fluorescent dye. The RGB signals are representative of the different imaged channels and relate to the concentration of signal from each in the snapshot. Green is the GFP, Red is the IR800
targeted dye and the blue channel is the 700 channel. These images shows that the blue and red portions have high signal in the regions outside of the brain with the red channel being stronger for large portions of the slides and that the GFP signal is the greatest in the region defined by the brain
tumor.
The results here show that a large amount of the fluorophore is present in the skin as
much of the signal is surface weighted.
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Figure 8.9: Images on the left represent the GFP signal and images on the right of each grouping represent the 800-channel signal for the 1 hour time point post injection. Little to no signal can be
visualized within the brain space.
Comparing the 1 hour and the 24 hour data set, there is a large change in the amount of
signal present at the surface. The 24 hour data has a larger GFP, green channel, signal at
the surface. Regions with high fluorescence are still visible in the background in both the
700 and 800 channel in this later time point and appear to be highly spatially correlated.
Figure 8.10: Three representative slices from an animal sacrificed 24 hours post injection of the targeted fluorescent dye. Green is the GFP, Red is the IR800 targeted dye and the blue channel is the 700 channel. These images shows that the blue and red portions of the have high signal in the regions
outside of the brain and are highly correlated, and that the GFP signal is the greatest in the region defined by the brain tumor.
However the brain section of the slices shows a signal that contains signals in the blue
and red channels especially in the second and third slice included in the figure.
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Figure 8.11: Images on the left represent the GFP signal and images on the right of each grouping represent the 800-channel signal for the 24 hour time point post injection. The second grouping
shows fluorescence signal well correlated with the presence of the tumor in the brain.
By increasing the amount of time between injection of the fluorescent dye and the
imaging a change in the distribution of the fluorophore, and the recovered contrast is
seen. The 2D slices imaged ex-vivo show trends that agree with those from the recovered
tomography images.
8.5 Conclusions
Phantom measurements with anomalies containing fluorescent dye IRDye800CW,
showed a linear response of the detection system for concentrations between 3.7 and
150nM. Previous research results have shown concentrations within these bounds in a
mouse brain tumor model [179].
In-vivo imaging to determine tumor contrast upon injection of an affibody
conjugated fluorescent dye showed a contrast greater than 1 between the tumor and brain
when optical imaging was performed 24 hours post injection. A contrast less than 1 was
calculated from reconstructed images for the contrast between the tumor and brain for
optical imaging at 1 hour post injection, as well as for the tumor to background values for
both 1 and 24 hour imaging sessions. The 1 hour time point likely has low contrast due to
the presence of the dye in much of the vasculature system which can be cleared more
effectively prior to the 24 hour measurement.
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8.6 Summary of Results
The phantom measurements to determine concentration did not fully determine the linear
response region for the IR800 dye with this system component, with lower concentrations
included is this titration not reaching the noise floor. Further classification of the system
should be done to determine the full region of linearity.
Work to compare the tomographic results with ex-vivo slices of the brain was useful
in understanding the true location of fluorescence and its change with length of
circulation. Additionally, the agreement between tomographic images and the 2D slice
images provides validation of the tomographic results.
8.7 Future Directions
Future work should place an emphasis on development of a fluorescent dye and targeting
pair that has high selectivity to the tumor but that can be cleared from the remaining
tissues in a timely manner. Work by Hsu, et al. with a different fluorophore and binding
target showed that at 2 hours after injection the brain tumor to normal tissue ratio was the
highest with a fall of to a ratio of 1 at 24 hours [180]. This work shows that the best time
for imaging might fall between the two times chosen for these animals.
125
9 Comparison of Imaging Methods
Phantom and animal measurements were acquired for optical biomolecular techniques
with a determination of the linear response region for each contrast mechanism.
Fluorescence and Surface Enhanced Raman Spectroscopy experiments were conducted
on a MRI-NIR coupled system. Raman Spectroscopy experiments were conducted on a
CT-NIR coupled system.
9.1 Measured Signal versus Concentration
For comparison of the various measured optical signals the absolute signals have been
converted to a signal strength, which is calculated as the order of magnitude difference
from the lowest concentration to the highest concentration in the region of linear
response. Concentrations were determined for each contrast type and are reported here as
molarity, moles of contrast per liter of solution, and range from the pM to mM. To
determine the concentration gradient over which a linear response was generated,
phantoms with optical scattering and absorption properties were imaged in a tomographic
setting with only the optical parameters changing within the inclusion.
For fluorescence measurements, shown in orange in Fig. 9.1, the minimum
concentration measured remained within the linear response region, so to determine the
true lower limit where the concentration becomes attenuated, further imaging
experiments would need to occur. In phantom experiments, the Raman spectroscopy
anomalies were generated with varying concentrations of powdered hydroxyapatite (HA)
dissolved in gelatin. Surface enhanced Raman spectroscopy nanoparticles were built
from a gold core and were coated with Raman-active materials at Memorial Sloan
126
Kettering. Fluorescence markers consisted of LI-COR IR800 dye conjugated to anti-
EGFR proteins. Ideally, for each contrast type the lowest concentrations imaged were far
below the noise floor and the highest concentration would be above the attenuation
region. Results for phantom were reported independently in Chapters 5, 6 and 8.
Figure 9.1: Concentrations measured in phantoms that exhibited a linear response plotted versus the total order or magnitude change from the minimum concentration to the maximum concentration.
The concentrations measured and determined linear are included for the three biomolecular imaging techniques tested.
The results presented above were specific to the contrast mechanism used in these
experiments. Changes to the SERS particles, inclusion of a different fluorescent dye,
targeting agent, or biological Raman target would potentially affect the region over which
a linear response is seen. Alternatively different imaging systems, with different light
sources or detectors could further affect the linear response.
For the sources of contrast presented in this work the region of linearity were
independent. Determination of the necessary concentration of each type of molecule
could be used to govern their use in experiments where light measurements were to be
Concentration (M) 10-9 010-12
Sign
al S
treng
th
(ord
ers o
f mag
nitu
de)
10-6
1 –
40 p
M
0.5
1.5
2.0
1.0 1
– 15
0 nM
100
- 550
mM
Surface Enhanced Raman Spectroscopy
Fluorescence Raman Spectroscopy
10-3
1
100
127
completed in a tomographic fashion. Ntziachristos, et al., have shown that approximately
0.28% of injected contrast makes it to a tumor site [181], combining this information with
the concentrations from the plot above can further guide experimental design and
determine appropriate injected doses.
9.2 Comparing Imaging Techniques
Raman scattering is an ideal contrast mechanism for biomolecular imaging as it relies on
contrast, which occurs naturally in tissues. Bone is an ideal candidate for imaging with
Raman spectroscopy as the dense tissue and crystalline structure provides for strong
contrast. However, due to the intrinsic nature, it can be difficult to image if the
concentration falls outside of the linear region of response for a detector. Cancellous
bone and cortical bone have varying concentrations and densities due to the nature of
their structures, so imaging of different regions of bone should allow for imaging of
concentration gradients.
Fluorescence and surface enhanced Raman spectroscopy methods both require the
use of extrinsic contrast mechanisms. Extrinsic contrast can be beneficial for imaging
when the use of targeting mechanisms can allow for high signal in the region of interest
and low or no signal in the untargeted regions, after sufficient time to allow for
localization. Additionally, use of an injectable contrast allows for a true understanding of
the normal background signals, which can be measured prior to the administration of
contrast.
Biomolecular imaging with SERS nanoparticles can be done in two ways.
Administration of particles with a Raman-active coating directly on the gold core that is
affected by the LSPR and can be measured externally, or nanoparticles with no coating
128
which then increase the signal of any Raman-active tissues with which they come into
contact with. The second type of particles was not used in this work. Particles can be
coated with various Raman-active materials, which can allow for multiplex imaging, as
the Raman spectra are very narrow and occur in specific wavenumber locations.
Concentration of nanoparticles in the region of interest can be varied by changing the
injection concentration and by the use of targeting agents and other surface proteins to
shorten or lengthen circulation time.
Fluorescence imaging of biomolecular signals requires the use of targeting proteins
to localize the signal to the biomolecule of interest. The use of targeting and an
understanding of how circulation time affects concentration in the plasma can aid in
generating concentrations within the linear region of response for the detector. Imaging
with multiple fluorescent dyes, for multiplexing, can be done, but requires complex
spectral fitting algorithms as fluorescence signals are very wide in nature with emission
spectra spanning many wavelengths.
The use of Raman, surface enhanced Raman, and fluorescence contrast mechanisms
for the imaging of biomolecules in-vivo, seems promising given the preliminary results
reported here. The advantages and constraints of each imaging technique should be
understood prior to the experimental design as well as an understanding of the expected
level of contrast, and which method is best suited for measurements in that concentration
range.
9.3 Expected Biological Contrast
The determination of regions of linear response and their corresponding concentrations
are extremely useful for phantom experiments but may lose some significance if they are
129
not within the bounds of expected biological contrast. A review of the literature would
find many articles discussing the concentrations of various contrast mechanisms in
tissues.
Bone is typically measured in an ex-vivo environment once a biopsy has been
extracted from the subject. Measurements of the concentration of mineral present in the
bone can be completed using various imaging techniques with the results being reported
generally as mg of hydroxyapatite per cubic centimeter. Table 9-1 contains the bone
signal results for various imaging techniques.
Phantom experiments resulted in a region of linear response from 144 to 531.5mM,
which is equivalent to a range of 67 to 267mg/cm3 of hydroxyapatite powder. Kalender,
et al. report cancellous bone, the spongy bone present in long bones and containing high
levels of blood vessels and bone marrow, has a calcium hydroxyapatite present in 50-
200mg/cm3 when imaged with DEXA technology [134]. Comparison of this method to
other light based imaging techniques is difficult as the typically report in terms of mineral
to matrix ratios, not concentrations.
Surface Enhanced Raman Spectroscopy nanoparticles are used for research purposes,
with all studies using animal models. Nanoparticles of other types were included in
Table 9-2 in an attempt to further understand the distribution and reasonable
concentrations expected for biological experimentation.
The in-vitro models indicated that by including targeted proteins on the nanoparticle
surface, the concentration in the cell could be increased dramatically, up to 600% for one
case [182, 183]. Mouse models of the U87MG tumor lead to 13 times as many targeted
nanoparticles as untargeted nanoparticles [139]. An across reference comparison of these
130
methods results with the nanoparticle used for SERS experimentation is difficult due to
no knowledge of the molecular weight of the nanoparticles used in either cases.
However, SERS experimentation in this work used injections of 1.37 to 37.0pM, using
the Sigma-Aldrich (Sigma-Aldrich, St. Louis, MO, USA) reported molecular weight for a
60nm gold particle of 196.97g/mole, injections were approximately on the order of
microgram per mL which is above the in-vivo and in-vitro data presented here. However,
these approximate calculations could change dramatically with an understanding of the
properties of the nanoparticles used in our experiments.
Fluorescence imaging can be done in human patients with a limited number of
fluorescent dyes, with many dyes existing in the research realm of imaging. The
conjugation of proteins to dyes for targeting of the molecules to the cells of interest
shows an added benefit in terms of increased contrast within the region of interest [184].
Table 9-3 contains of results acquired with four different fluorescent dyes, some of which
include targeting proteins.
Phantom experiments determined a region of linear response between 3.7 and
150nM, with the potential for continued linearity above 150nM. In a 9L gliosarcoma
mouse model, a recovered contrast of 110 ± 30nM was reported falling within the
phantom generated bounds [179]. Injected concentrations varied from 1 to 6nmols, an
order of magnitude higher than injected dose for the animal models in Chapter 8, which
lead to a recoverable contrast of 1.8 for the tumor to brain signal that is slightly lower
than is reported by Zaak, et al [184, 185].
131
For the three optical imaging methods tested; Raman, SERS, and Fluorescence; and
for the optical systems used for data acquisition, the concentrations needed for a linear
response fell within the published literature values for typical concentrations.
9.3.1 Tables of collected papers
132
Table 9-1: Literature review of the biological concentrations of bone mineral and matrix. References include Kalender [134], Block [186], Lang [187], McCreadie [46], Bi [188], Louis [189] and Rowland
[190].
Target Tissue Probe
Measured Signal
Imaging Technique
Ref.
Cortical B
one C
alcium H
ydroxyapatite 200-500 m
g/cm3
DEX
A
Kalender
Cancellous B
one C
alcium H
ydroxyapatite 50-200 m
g/cm3
DEX
A
Kalender
Cortical B
one C
alcium H
ydroxyapatite M
ax 1,200 mg/cm
3 D
EXA
K
alender
Cancellous B
one Potassium
Phosphate 162 ± 25.9 m
g/ml (30-39 years)
102.6 ± 25.8 mg/m
l (60-69 years) qC
T B
lock
Cancellous B
one Potassium
Phosphate 119.3 ± 23.9 m
g/cm3
qCT
Lang
Proximal Fem
ur Integrated Potassium
Phosphate 272.6 ± 55.5 m
g/cm3
qCT
Lang
Iliac Crest C
ortical C
arbonate/Phosphate Ratio
0.154 (Control)
0.184 (Fractured) N
IR R
aman
McC
readie
Femur (m
ouse) Phosphate/Proline R
atio 16-20
NIR
Ram
an B
i Fem
ur (mouse)
Calcium
Hydroxyapatite
1400-1500 mg/cm
3 qC
T B
i
Cadaver R
adius C
alcium H
ydroxyapatite 150-450 m
g per 2.5 mm
section of cortical bone
Flame A
tomic A
bsorption Spectrom
etry Louis
Femur C
ortical C
alcium H
ydroxyapatite 0.9 - 1.44 g/cm
3 X
-ray R
owland
Bone M
ineral and Matrix Signal �
133
Table 9-2: Literature review of the biological concentrations of nanoparticles from in-vitro and in-vivo experimentation. References include El-Sayed [183], Davda [182], Keren [139], Zevaleta [141],
and Petri-Fink [191].
Target Tissue Probe
Concentration (Injected)
Measured Signal
Imaging Technique
Ref.
Hum
an Oral Squam
ous C
ell Carcinom
a in-vitro anti-EG
FR nanoparticles
0.3 nM gold
particles Increased absorption at 0.06
600% greater affinity
Light Microscope (w
hite light)
El-Sayed
Hum
an Um
bilical Vein Endothelial C
ell in-vitro polym
er nanoparticles 10 - 300 μg/m
L 5-50 μg/m
g cell protein after 30 m
inutes incubation Pierce B
CA
Protein Assay/
Confocal M
icroscopy D
avda
U87M
G Tum
or Mouse
Model
SERS nanoparticles
60 pmol
0.0204 ± 0.0087 (Targeted) 0.0016 ± 0.0005 (U
ntargeted) R
aman M
icroscope K
eren
Mouse M
odel, Liver C
learing SER
S nanoparticles (m
ultiplexed) 200 - 500 pm
ol 0.00001 - 0.0002 A
U
Ram
an Microscope
Zevaleta
Hum
an Melanom
a Cells
in-vitro Super Param
agnetic Iron O
xide Particle (SPION
) 0 - 145.2 μg Fe/m
L 0.1 - 1.9
Absorbance at 690 nm
Petri-Fink
SER
S and Nanoparticle Signal �
134
Table 9-3: Literature review of the biological concentrations of bone mineral and matrix. References include Zaak [185], Gurfinkel [184], Ntziachristos [179], Kossodo [192], Kovar [193].
Target Tissue Probe
Concentration (Injected)
Measured Signal
Imaging Technique
Ref.
Transitional Cell
Carcinom
a in Hum
an B
ladder
5-Am
inolevulinic Acid to
PpIX
1.5 gm
Fluorescence Ratio
1.67 ±0.12 (Inflamm
ation) 2.09 ± 0.11 (Tum
or) Fluorescence Endoscopy
Zaak
Kaposi's Sarcom
a M
ouse Model
Cy5.5 D
ye 6 nm
ol 1.66 (Targeted) 1.3 (U
ntargeted) W
ide Field Fluorescence G
urfinkel
9L Gliosarcom
as in M
ouse Model
Cathepsin-B
probe coupled w
ith Cy5.5 dye
2 nmol
110 ± 30 nM
Fluorescence Molecular
Tomography
Ntziachristos
Hum
an R
habdomyosarcom
a A
673 Mouse M
odel IntegriSense680
2 nmol
20 pmoles
VisEn FM
T2500 K
ossodo
Protstate Tumor PC
3M-
LN4 M
ouse Xenografts
IR D
ye 800 CW
EGF
1 nmol
10 - 16 SNR
LI-C
OR
Biosciences Sm
all A
nimal Fluorescence
Imager
Kovar
Fluorescence in-vivo Signal �
135
9.4 Future Directions
The promising results from phantom measurements and preliminary animal models
suggest that both the CT-NIR and MRI-NIR systems have sufficient sensitivity and are
capable of measuring biologically relevant concentrations of biomolecular contrast.
The SERS imaging with in-vivo testing did not provide data that was adequate
quality to allow tomographic reconstructions. Future work in this project should be
focused on altering the surface molecules of the nanoparticles. Changes in the molecules
to allow protein targeting for cell binding and the addition of molecules to extend the
circulation time are anticipated to lead to higher concentration of particles in the region of
interest [194, 195].
Fluorescence molecular imaging with targeted dyes exhibited promising results when
injected 24 hours prior to optical imaging. Future work for imaging brain cancer lines
with fluorescent markers needs to focus on increasing the contrast of the tumor to
background and brain signals. Experiments to determine the ideal circulation time for
conjugated fluorescent dyes may aid in increasing contrast [193]. Use of surface proteins,
known to have high expression in the tumor line being used, can also aid in the specific
uptake by tumor cells [175]. Techniques involving multiple fluorescent dyes have also
been developed and are useful in removing the non-specific fluorescent signals to allow
increased recovered contrast [196].
Raman spectroscopy for molecular imaging has a high potential due to its use of
endogenous contrast. Spectra of bone, including mineral and matrix peaks, were
successfully measured for healthy rat models. Imaging of disease states, bone healing
and determination of maturation remain as problems to be addressed with an in-vivo
136
imaging system. A continued collaboration with the University of Michigan will aim to
gain understanding about the healing stages of bone after surgically induced fracture and
placement of autograft.
Figure 9.2: X-ray image of a rat leg with an autograft included to aid in the healing process after the surgically induced fracture. Raman spectroscopy measurements will be conducted to determine the
change in the mineral and matrix signals for a rat model.
Complications with Raman imaging for this state, and other diseases, is the extremely
small region of linearity for the current optical system. Changes to the CCD or other
optical components to increase Raman throughput would require additional phantom data
collection to correctly quantify the measured signals.
137
References:
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159
10 Appendix A
The final plot shown in Chapter 9 can also be created with the y-axis giving information
about the measured signal divided by the transmission signal. This is how each of the
phantom results was reported independently in the Chapters, previously. When plotting in
this fashion, as the Born ratio of the measurements, we get a spread occurring in both the
horizontal and vertical directions. The Born ratio gives information about how many
contrast photons are created per number of transmission photons measured.
The Raman spectroscopy method seems to have the highest Born ratio, however it is
imperative to remember that for the Raman imaging that the transmission signal was
measured as the number of Cytop Raman scattered photons being transmitted after being
generated in the transmission fiber pathway. Raman events generating Cytop should
occur at approximately the same rate as Raman events with Bone, hence a near 1 to 1
signal.
SERS and Fluorescence spectroscopy methods have similar cross sections of
interaction, as reported in Table 2-1 and therefore we would expect similar localization
on the Born ratio axis. The variation seen here is likely caused by improper
characterization of laser filtering which would lead to incorrect transmission signal
measurements.
160
Figure 10.1: Concentrations measured in phantoms that exhibited a linear response plotted versus the measured signal divided by the measured transmission value, also known as the Born ratio. The
concentrations measured and determined linear are included for the three biomolecular imaging techniques tested.
Concentration (M) 10-9 010-12
Sign
al/T
rans
mis
sion
10-6
10-8
Surface Enhanced Raman Spectroscopy Fluorescence Raman Spectroscopy
10-3 100
10-6
10-4
10-2
10 0
161
11 Appendix B
11.1 Matlab Code referenced in Chapter 3
function data = MRI_processing_13(file_string, loginfo, plotflag) % Assumes the files are ended with .raw and loads the columns of the % data into the respective source and detector pairs. Both of the % inputs should be put in as string formats % loads the loginfo file if it hasn't been loaded if ischar(loginfo) == 1 [loginfo] = load_log_file([file_string]); end if nargin == 2 plotflag = 0; end % ensures that the files are correct if isfield(loginfo,'link') == 1 ns = size(loginfo.sources,1); nd = size(loginfo.meas,1); else print('No link file included in loginfo'); end src = find(loginfo.sources == 1); det = find(loginfo.meas == 1); k = 1; for i = 1:length(src) temp=load([file_string,'_s',num2str(src(i)),'_rep1.raw']); data{i}.src= src(i); data{i}.det = find(temp(1,:)~=0); data{i}.data = temp(:,data{i}.det); data{i}.time = loginfo.exp_times(data{i}.det,src(i)); end %wavelength to wavenumber laserline = 670; center = loginfo.centerwv(det); if loginfo.grating(det(1)) == 1200 start = center - 30; stop = center + 30; pix = 60; % nm section on spectrometer else start = center - 150; stop = center + 150; pix = 300; end spread = pix./(length(data{1}.data)-1); % nm per pixel of data
162
for i = 1:length(det) values(:,det(i)) = start(i):spread:stop(i); % wavenumber(:,det(i)) = (1./laserline -1./values(:,det(i))).*10^7; end for i = 1:length(src) % data{1,i}.wavenumber = wavenumber(:,data{1,i}.det); data{1,i}.wavelength = values(:,data{1,i}.det); end if plotflag == 1 figure('Name', file_string ,'NumberTitle','off') for i = 1:length(src) % data{1,i}.wavenumber = wavenumber(:,data{1,i}.det); data{1,i}.wavelength = values(:,data{1,i}.det); if length(src) == 8 subplot(2,4,i), plot(data{1,i}.wavelength, data{1,i}.data) xlim([min(data{1,i}.wavelength(1,:)),... max(data{1,i}.wavelength(end,:))]) title(['Source Number ', num2str(src(i))]) xlabel 'wavelength' elseif length(src) == 4 subplot(2,2,i), plot(data{1,i}.wavelength, data{1,i}.data) xlim([min(data{1,i}.wavelength(1,:)),... max(data{1,i}.wavelength(end,:))]) title(['Source Number ', num2str(src(i))]) xlabel 'wavelength' else plot(data{1,i}.wavelength, data{1,i}.data) xlim([min(data{1,i}.wavelength(1,:)),... max(data{1,i}.wavelength(end,:))]) title(['Source Number ', num2str(src(i))]) xlabel 'wavelength' end end end
163
function [loginfo] = load_log_file(data_fn) % Assumes log file is formatted with text at the top and a matrix of % spectrometer/camera parameters. The list 16 columns of this matrix % are the exposure times used where each column corresponds to a source % position and each row a detector. An exposure time = zero indicates % that source-detector pair was not used. % s. c. davis 2007 logtemp = importdata([data_fn,'.log']); loginfo.exp_times = logtemp.data(:,end-15:end); loginfo.filters = logtemp.data(:,end-31:end-16); loginfo.cameratemp = logtemp.data(:,3); loginfo.centerwv = logtemp.data(:,7); loginfo.sources = logtemp.data(:,1); loginfo.meas = logtemp.data(:,2); loginfo.grating = logtemp.data(:,6); for i = 1:numel(loginfo.grating) if loginfo.grating(i) == 1 loginfo.grating(i) = 1200; elseif loginfo.grating(i) == 2 loginfo.grating(i) = 300; end end % create a nirfast-style link matrix based on sources and detectors % selected in the acquisition program temp_src = loginfo.sources; temp_meas = loginfo.meas; % % in0 = []; % for i = 1:numel(temp_src) % if temp_src(i) == 0 & temp_meas(i) == 0 % in0 = [in0 i]; % end % end % temp_src(in0) = []; temp_meas(in0) = []; % loginfo.sources(in0) = NaN; loginfo.meas(in0) = NaN; % cs = 1; cd = 1; % ns = []; nd = []; % for i = 1:numel(temp_src) % if temp_src(i) == 1 & temp_meas(i) == 1 % ns = [ns,cs]; nd = [nd,cd]; % elseif temp_src(i) == 1 & temp_meas(i) == 0 % ns = [ns,cs]; nd = [nd,0]; % elseif temp_src(i) == 0 & temp_meas(i) == 1 % ns = [ns,0]; nd = [nd,cd]; % end % cs = cs+1; cd = cd+1; % end % biuld link file based on sd_pairs
164
% sd_ind = 1:length(ns); cn = 1; for j = 1:size(loginfo.sources,1) for i = 1:size(loginfo.meas,1) if loginfo.sources(j) == 1 && loginfo.meas(i) == 1 loginfo.link(cn,:) = [j,i,1]; else loginfo.link(cn,:) = [j,i,0]; end cn = cn + 1; end end end % sd_ind = 1:length(ns); % cn = 1; % for i = 1:length(ns) % if ns(i) ~= 0 % loginfo.link(cn,:) = nd([(i+1):end, 1:(i-1)]); % cn = cn+1; % end % end %loginfo.link;
165
function CorrImage = FiberUnspike(InitImage) % function [CorrImage, PixelCount] = FiberUnspike(InitImage) % This function removes cosmic ray spikes from CCD images captured % during Raman transmission measurements if (ndims(InitImage)>2) imSz=size(InitImage); CorrImage = zeros(imSz(1:2)); % PixelCount=zeros([imSz(1),imSz(2)]); GoodPixels = false(size(InitImage)); sImage = squeeze(std(InitImage,[],3)); mImage = squeeze(median(InitImage,3)); for i=1:size(InitImage,3) GoodPixels(:,:,i)=abs(InitImage(:,:,i)-mImage)<=3*sImage; end % check where spikes show up: imagesc(sum(~GoodPixels,3)) InitImage=shiftdim(InitImage,2); GoodPixels=shiftdim(GoodPixels,2); mImage = repmat(reshape(mImage,[1,imSz(1),imSz(2)]),[10,1,1]); InitImage(~GoodPixels)=mImage(~GoodPixels); % replace all bad pixels by the median before calculating the mean % for i=1:imSz(1); % for j=1:imSz(2); % TempData2=InitImage(:,i,j); % GoodPixels = abs(TempData2-mImage(i,j))<3*sImage(i,j); % GoodPixels = within(TempData2,median(TempData2),3*std(TempData2)); % if sum(GoodPixels(:,i,j)) > 0 % CorrImage(i,j)=mean(InitImage(GoodPixels(:,i,j))); % else % if isnan(CorrImage(i,j)) % =mean(InitImage(GoodPixels(:,i,j))); % CorrImage(i,j)=0; % end % PixelCount(i,j)=sum(GoodPixels); % end % end CorrImage=squeeze(mean(InitImage,1)); % badpixels = isnan(CorrImage); % =mean(InitImage(GoodPixels(:,i,j))); % CorrImage(badpixels)=0; else CorrImage=InitImage; end % function BoolList = within(list,value,distance) % % Function Within % % % % This function finds all values in the list within a specified % % distance of the specified value, and returns a bool % % vector with the elements identified. % % % % Usage: [BoolList]=within(list,value,distance); % % Francis Esmonde-White, Oct 11, 2009 % BoolList=abs(list-value)<distance;
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%% Code to take data from measured signal to a per second measurement % for each individual fiber. Based on the NIR-MIR system at DHMC. % Removal of dark current signal, shifting of the wavelengths to % correct for error, removal of background signal, and the option to % plot results % This example is specifically done for the SERS Brain tumor research % example mouse_num = 12; mouse_hr = 24; time = 'Morning/'; name = [time,'mouse_',num2str(mouse_num),'_',num2str(mouse_hr),'hour_']; for tt = 1:size(tubes,2); t = tubes(tt); clear dark_med data_med dark filt %% Dark files for j = 1:3 files = ['SERS_Brain_Tumors/05032013/']; filename = [files,'Morning/morning_dark_trans']; dark_foo = MRI_processing_12_3reps_2013(filename,'loginfo',j); darkcube(:,:,j) = dark_foo{1}.data; files = ['SERS_Brain_Tumors/05032013/']; filename = [files,name,'fl']; foo = MRI_processing_12_3reps_2013(filename,'loginfo',j);
for i = 1:8 datacube{i}(:,:,j) = foo{i}.data; end end for j = 1:1 filename = [files,name,'trans']; laser_foo = MRI_processing_12_3reps_2013(filename,'loginfo',j); for i = 1:8 lasercube{i}(:,:,j) = laser_foo{i}.data; end end dark_med = dark_foo; dark_med{1}.data = median(darkcube,3); data_med = foo; laser_med = laser_foo; for k = 1:8 data_med{k}.data = median(datacube{k},3); figure(1); plot(data_med{k}.data), title(['Src ',... num2str(data_med{1}.src)]) laser_med{k}.data = lasercube{k}; end %% background subtraction dark = dark_med{1}.data; for i = 1:8 for j = 1:7 det = data_med{i}.det(j)/2; data_med{i}.data(:,j) = data_med{i}.data(:,j) - dark(:,det); laser_med{i}.data(:,j) = laser_med{i}.data(:,j) - dark(:,det);
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end end %% shifting wavelength found with Neon measurement laserline = 830; load('wavelength_shift.mat'); data_med{1}.shift = wavelength_shift(data_med{1}.det); laser_med{1}.shift = wavelength_shift(data_med{1}.det); for i = 1:8 data_med{i}.shift = wavelength_shift(data_med{i}.det); laser_med{i}.shift = wavelength_shift(data_med{i}.det); for j = 1:7 data_med{i}.wavelength_shift(:,j)= data_med{i}.wavelength(:,j)... + data_med{i}.shift(j); data_med{i}.wavenumber_shift(:,j) = (1./laserline - 1./... data_med{i}.wavelength_shift(:,j)).*10^7; laser_med{i}.wavelength_shift(:,j)= laser_med{i}.wavelength(:,j)... + laser_med{i}.shift(j); laser_med{i}.wavenumber_shift(:,j) = (1./laserline - 1./... laser_med{i}.wavelength_shift(:,j)).*10^7; end end %% Filtering and smoothing of measured data to remove high frequency noise for j = 1:size(data_med,2) for i = 1:size(data_med{1}.data,2) temp1 = conv(data_med{1,j}.data(:,i),hamming(16),'same')/... sum(hamming(16));
filt{1,j}.data(:,i) = temp1(15:end-15); filt{1,j}.wavenumber(:,i) =... data_med{1,j}.wavenumber(15:end-15,i); filt{1,j}.wavenumber_shift(:,i) =... data_med{1,j}.wavenumber_shift(15:end-15,i); filt{1,j}.orig_data(:,i) = data_med{1,j}.data(15:end-15,i); filt{1,j}.wavelength_shift(:,i) =... data_med{1,j}.wavelength_shift(15:end-15,i); filt{1,j}.src = data_med{1,j}.src; filt{1,j}.det = data_med{1,j}.det; filt{1,j}.time = data_med{1,j}.time; end end %% Plotting results for each fiber figure for i = 1:8 subplot(4,2,i), plot(filt{1,i}.wavenumber_shift, filt{1,i}.data) xlim([min(filt{1,i}.wavenumber_shift(:,1)),... max(filt{1,i}.wavenumber_shift(:,1))]) end %% Scale data by length of acquisition (to get per sec counts) for i = 1:8
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for j = 1:7 filt{1,i}.data_time(:,j) = filt{1,i}.data(:,j)./... filt{1,i}.time(j); laser_med{i}.data_time(:,j) = laser_med{i}.data(:,j)./... laser_med{i}.time(j); end end %% Plotting per second results dat = zeros(size(filt{1,1}.data(:,1),1),8,8); figure; for i = 1:8 for j = 1:7 num = filt{i}.det(j)/2; % subplot(2,4,num),plot(filt{1,i}.wavenumber_shift(:,j),... % filt{1,i}.data(:,j)) % counts per second % subplot(2,4,num),plot(filt{1,i}.wavenumber_shift(:,j),... % filt{1,i}.data_time(:,j)) % normalized subplot(2,4,num),plot(filt{1,i}.wavenumber_shift(:,j),... filt{1,i}.data_time(:,j)./max(filt{1,i}.data_time(:,j))) hold on dat(:,i,num) = filt{1,i}.data_time(:,j);... %./max(filt{1,i}.data(:,j)); end pause() end mdat = mean(dat,3); med_dat = median(dat,3); figure; plot(med_dat) figure; plot(mdat) %% writing back to file % cd('/Users/jennifer-lynn_h_demers/Desktop/Research/MRI System/2013') % % name = ['mouse',num2str(mouse_num),'_',num2str(mouse_hr),'hr_']; % src = [2,4,6,8,10,12,14,16]; % for i = 1:8 % % filename = [files,'CalSpec/',name,'src',num2str(src(i)),... % '_trans.calspec']; % foo = [laser_med{i}.det; laser_med{i}.data_time]; % save(filename, 'foo','-ascii') % % filename = [files,'CalSpec/',name,'src',num2str(src(i)),... % '_fl.calspec']; % foo = [filt{i}.det; filt{i}.data_time]; % save(filename, 'foo','-ascii') % % filename = [files,'CalSpec/',name,'src',num2str(src(i)),... % '_wavenumber.calspec']; % foo = [filt{i}.det; filt{i}.wavenumber_shift]; % save(filename, 'foo','-ascii') % end end
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11.2 Matlab Code referenced in Chapter 4
function [indata, polY]=BGminmax(indata,Porder) % Based on "A robust method for automated background subtraction of tissue % fluorescence." Alex Cao, 2007, JRS. % % usage: [indata]=BGminmax(indata,Porder) % % where: % indata is a [n x m] matrix with n being the wavelength/wavenumber % axis and m being the number of spectra (m >= 1). % Porder is the polynomial order for background correction, % default == 3, two polynomial orders are actually used, % Porder and Porder+1. Both are optimized and also pinned at % the edges during optimization using the minmax method. % % Written by Francis Esmonde-White, Aug. 22, 2009 % updated June 22, 2010 % updated January 201 if ~exist('Porder','var') Porder = 3; end for i=1:size(indata,2) data = indata(:,i); ndata = numel(data); numbins = floor(ndata/30); noise = min(std(reshape(data(1:numbins*30),[30,numbins]))); all_points = 1:numel(data); selected_points = true(size(data)); prev_err = inf; curr_err = realmax; while (prev_err > curr_err) & (sum(selected_points) > (Porder*5)) % get the polynomial fits for the two selected orders with end % without the endpoitns fixed. local_SP = find(selected_points); % [P,S,MU] = POLYFIT(X,Y,N) % [Y,DELTA] = POLYVAL(P,X,S,MU) [P,S,MU] = polyfit(local_SP,data(local_SP),Porder); [Y(:,1)] = polyval(P,all_points,S,MU); [P,S,MU] = polyfit(local_SP,data(local_SP),Porder+1); [Y(:,2)] = polyval(P,all_points,S,MU); local_SP = selected_points; local_SP([1,end]) = true; % always select the ends local_SP = find(local_SP); [P,S,MU] = polyfit(local_SP,data(local_SP),Porder); [Y(:,3)] = polyval(P,all_points,S,MU); [P,S,MU] = polyfit(local_SP,data(local_SP),Porder+1);
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[Y(:,4)] = polyval(P,all_points,S,MU); % hold off; % plot(data); % hold on; % plot(Y); Y = max(Y,[],2); % plot(Y,'k'); selected_points = selected_points & ((Y + noise) > data); prev_err = curr_err; curr_err = sum((data(selected_points)-Y(selected_points)).^2)... /sum(selected_points); % pause(0.25); end indata(:,i) = data - Y; polY(:,i)=Y; % figure; % plot(data-Y) end
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function [modpoly, wv] = ImodPoly_new(raw,porder) % This function mimics the alogrithm from the University of British % Columbia % Inputs: % raw - is a structure containing both the wavenumber and data axis for % a single measurement % porder - is the polynomial order to be used for fitting % Outputs: % modpoly - is the final polynomial - not the difference obs = raw.data; wv = raw.wavenumber; i = 1; dev_pre = 0; figure(100); hold on % plotting the original spectra here % plot(wv,obs,'r'), hold on while i < 100 % 100 maximum iterations [poly_val, s, mu] = polyfit(wv,obs,porder); poly = polyval(poly_val,wv,s,mu); if i == 1 % Peak Removal res = obs - poly; dev = std(res,1); % type 2 standard deviation peaks = poly + dev - obs; % dev accounts for noise obs(peaks < 0) = []; % remove raman values wv(peaks < 0) = []; % remove corresponding wv values bg = peaks > 0;
poly(peaks < 0) = []; end % plot(wv, poly,'b:') res = obs - poly; %residual dev = std(res,1); % type 2 standard deviation % reconstruction model input diff = poly + dev - obs; new = obs; new(diff < 0) = poly(diff < 0) + dev;
obs = new; criteria = abs(dev - dev_pre)/abs(dev);
if criteria < .003 % this tolerance level can be changed i = 100; end dev_pre = dev; i = i + 1; end modpoly = polyval(poly_val,raw.wavenumber,s,mu); plot(raw.wavenumber,raw.data - modpoly) % plotting the detrended spectra end %function
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function [spec, u] = LLS_specfit(A,data,flag,src,det) % Performs least squares fitting between measured spectrum (data), and % measured basis spectra (in matrix A). % input basis spectra in matrix A with columns denoting spectra. % input data as column vector % set flag to 1 to plot results when the fitting is done % output data is matrix A with each column scaled by its minimization % coefficient [npix,m] = size(A); H = A'*A; b = A'*data; u = H\b; % Constrain negative fits for i = 1:m if u(i) < 0 u(i) = 0; act(i) = 0; else act(i) = 1; end end % Collect unmixed spectra spec=[]; for i = 1:m spec = [spec, u(i)*A(:,i)]; end % Plot flag if flag == 1 figure fit = spec(:,1)+spec(:,2); x_axis = [1:npix]'; plot(x_axis,data, '-k' ,...
x_axis,spec(:,1),x_axis,spec(:,2),x_axis,fit,':'); ylabel('counts/s'); xlabel('pixel number'); title(['Src ',num2str(src), ' Det ',num2str(det)]) end % error = data - fit; % error_sum = sum(error); % n = size(spec); % spec(1,n+1) = error_sum;
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function [spec,mid] = LLS_specfit_3_circshift(A,data,flag,src,det,begin,stop,pixel_step) % Performs least squares fitting between measured spectrum (data), and % measured basis spectra (in matrix A). % input basis spectra in matrix A with columns denoting spectra. % input data as column vector % set flag to 1 to plot results when the fitting is done % output data is matrix A with each column scaled by its minimization % coefficient % src, det are used when plotting in the Title % pixel_step relates to the number of pixels to be circshifted % CIRCSHIFT IS APPLIED TO THE FIRST COLUMN OF A if nargin == 7 pixel_step = 5; end val = 0.008; val2 = -0.0075; val3 = -1.0006; nums = [-5:1:15]; %number of different fits to test (~10nm lower and 30nm higher) [npix,m] = size(A); % find the lowest sum squared error for the different fits foo = abs(nums)*pixel_step; for ii = 1:size(nums,2) replace = repmat(val,foo(ii),1); zer = find(foo == 0); clear temp; A_new = A; if ii < zer % A(:,1) = [replace; A(foo+1:end,1)]; replace2 = repmat(val2,foo(ii),1); temp(:,1) = [A(foo(ii)+1:end,1);replace]; temp(:,2) = [A(foo(ii)+1:end,3);replace2]; elseif ii == zer temp(:,1) = A(:,1); temp(:,2) = A(:,3); else replace2 = repmat(val3,foo(ii),1); % A(:,1) = [A(1:(end-foo-1));replace]; temp(:,1) = [replace; A(1:(end-foo(ii)),1)]; temp(:,2) = [replace2; A(1:(end-foo(ii)),3)]; end A_new(:,1) = temp(:,1); A_new(:,3) = temp(:,2); A_new = A_new(begin:stop,:); data_new = data(begin:stop,1); % least squares fitting H = A_new'*A_new; b = A_new'*data_new; u = H\b; % Constrain negative fits for i = 1:m
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if u(i) < 0 u(i) = 0; % else % act(i) = 1; end end % Collect unmixed spectra spec1=[]; for i = 1:m spec1 = [spec1, u(i)*A_new(:,i)]; end fitted = spec1(:,1)+spec1(:,2)+spec1(:,3); error(1,ii) = sum((fitted - data_new).^2); end [low, ind_s] = sort(error); ind = find(error == low(1)); % find the values of spec for the lowest error if find(ind == zer) == 1 ii = find(ind == zer); else ii = ind(1); end k = 2; tr = 1; while tr == 1 mid = foo(ii); % tells us how much the shift was A_new = A; replace = repmat(val,foo(ii),1); zer = find(foo == 0); clear temp; if ii < zer replace2 = repmat(val2,foo(ii),1); temp(:,1) = [A(foo(ii)+1:end,1);replace]; temp(:,2) = [A(foo(ii)+1:end,3);replace2]; elseif ii == zer temp(:,1) = A(:,1); temp(:,2) = A(:,3); else replace2 = repmat(val3,foo(ii),1); temp(:,1) = [replace; A(1:(end-foo(ii)),1)]; temp(:,2) = [replace2; A(1:(end-foo(ii)),3)]; end A_new(:,1) = temp(:,1); A_new(:,3) = temp(:,2); A_new = A_new(begin:stop,:); data_new = data(begin:stop); % least squares fitting H = A_new'*A_new; b = A_new'*data_new; u = H\b; % Constrain negative fits for i = 1:m
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if u(i) < 0 u(i) = 0; % else % act(i) = 1; end end % Collect unmixed spectra spec=[]; for i = 1:m spec = [spec, u(i)*A_new(:,i)]; end if spec(1,1) == 0; tr = 1; k = k + 1; ii = ind_s(k-1); if k == 17 tr = 0; end else tr = 0; end end fitted = spec(:,1)+spec(:,2)+spec(:,3); n = size(spec,2); spec(1, n+1) = sum((fitted-data_new).^2); if flag == 1 figure x_axis = [1:npix]'; x_axis = x_axis(begin:stop); plot(x_axis,data_new, '-m', x_axis,spec(:,1),'r',x_axis,spec(:,2),'b',x_axis,spec(:,3),'k',x_axis,fitted,'k:'); ylabel('counts/s'); xlabel('pixel number'); title(['Src ',num2str(src), ' Det ',num2str(det)]) legend('data','fluor em','b/g','fluor ab') end
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function I = integrate_spec(xvalues, yvalues, start, stop, detnum) % load wavelngth list from txt file to convert from pixel number to nm. % xvalues and y values; start and stop are the numbered locations of % the xvalues at which you want to integrate over; detnum is the number % of detector (and data rows) that need to be integrated. % the VALUES put into START and STOP should be a few (3) pixels to the % side of the expected Raman peak I=[]; integrated_intensity = []; for i=1:detnum wave_lengths = xvalues; % determine wavelength intervals A = wave_lengths(start:(stop-1)); B = wave_lengths((start+1):stop); wv_interv = B-A; %clear A B values = yvalues(i,start:stop); % min_wv = min(wv_interv); max_wv = max(wv_interv); %calculate average intesity for pixel n and n+1 foo = values(2:end); foo2 = values(1:(end-1)); avg_intens = 0.5*(foo+foo2); spec_element_area = wv_interv.*avg_intens; % integrated_intensity = ...
[sum(spec_element_area(1,min_pix:max_pix))]; integrated_intensity = [sum(spec_element_area)]; I = [I; integrated_intensity']; end % fluorescence background of the biological fingerprint region % of the Raman spectra (450-1850cm-1) end
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11.3 Matlab Code referenced in Chapter 7
function interp_field %% This function takes the output of GAMOS, a monte carlo program, % and interpolates the location of the modeled Cerenkov field, % into the mesh generated to mimic the phantom. % % cd('/Users/jennifer-lynn_h_demers/Desktop/JENN/voxilised_off_center') off_center = 1; load('/Users/jennifer-lynn_h_demers/Desktop/JENN/voxilised_off_center/off_center_data'); % cd('/Users/jennifer-lynn_h_demers/Desktop/JENN/voxilised_centered') % off_center = 0; % load('/Users/jennifer-lynn_h_demers/Desktop/JENN/voxilised_centered/center_data'); Im = GPReduce(data); % Im = data; % Im = GPReduce(Im); % decreases the image sise by 2 - 0.5mm steps to 1.0mm steps %% i_t =[]; k_t =[]; j_t=[]; val_t=[]; for ii = 1:size(Im,3); %slice where detectors are vals = Im(:,:,ii); [i,j] = find(vals); x_temp = ((43*2 - i)/2 + 0.5); y_temp = ((43*2 - j)/2 + 0.5); in = sqrt(x_temp.^2 + y_temp.^2) < 42.8; [foo,foo2,val] = find(vals); val_t = [val_t; val(in)]; i_t = [i_t; x_temp(in)]; j_t = [j_t; y_temp(in)]; k_t = [k_t; repmat(ii,size(i(in),1),1)]; end % %% % x_t = 2*((43/2 - i_t)) + 0.5; % y_t = 2*((43/2 - j_t)) + 0.5; % z_t = 2*((164/2 - k_t) + 0.5); %% mesh = load_mesh('1L_anom_prop'); if off_center == 1 j_t = -j_t; end mesh.source.coord = [i_t,j_t,k_t]; mesh.source.fixed = 0; mesh.source.distributed = 1; mesh.source.num = (1:size(i_t,1))'; % mesh.source.fwhm = ones(1:size(i_t,1))'; mesh.source.val = val_t;
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%% tic [ind, int_func] = mytsearchn(mesh,mesh.source.coord); toc %% mesh.phix(1:size(mesh.nodes,1),1) = 0.1; for ii = 1:size(int_func,1) na = isnan(int_func); if ii ~= find(na) el = ind(ii); ns = mesh.elements(el,:); for i = 1:4 mesh.phix(ns(i),:) = mesh.phix(ns(i),:) + mesh.source.val(ii).*int_func(ii,i); end end end %% meshplot(mesh,mesh.phix) end
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function [fwd_mesh,pj_error] = reconstruct_cerenkov_fl(fwd_mesh,... recon_basis,... phix,... data_fn,... iteration,... lambda,... output_fn,... filter_n) % [fwd_mesh,pj_error] = reconstruct_fl(fwd_mesh,... % recon_basis,... % frequency,... % data_fn,... % iteration,... % lambda,... % output_fn,... % filter_n) % % reconstruction program for fluorescence meshes % % fwd_mesh is the input mesh (variable or filename) % recon_basis is the reconstruction basis (pixel basis or mesh filename) % frequency is the modulation frequency (MHz) % data_fn is the boundary data (variable or filename) % iteration is the max number of iterations % lambda is the initial regularization value % output_fn is the root output filename % filter_n is the number of mean filters % always CW for fluor frequency = 0; %******************************************************* % Read data data = load_data(data_fn); if ~isfield(data,'amplitudefl') errordlg('Data not found or not properly formatted','NIRFAST Error'); error('Data not found or not properly formatted'); end % remove zeroed data ind = data.link(:,3)==0; data.amplitudefl(ind,:) = []; clear ind scale = 1; anom = log(data.amplitudefl./scale); % Only reconstructs fluorescence yield! %******************************************************* % load fine mesh for fwd solve: can input mesh structured variable % or load from file if ischar(fwd_mesh)==1 fwd_mesh = load_mesh(fwd_mesh); end if ~strcmp(fwd_mesh.type,'fluor')
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errordlg('Mesh type is incorrect','NIRFAST Error'); error('Mesh type is incorrect'); end fwd_mesh.link = data.link; % clear data etamuaf_sol=[output_fn '_etamuaf.sol']; %********************************************************** % Initiate log file fid_log = fopen([output_fn '.log'],'w'); fprintf(fid_log,'Forward Mesh = %s\n',fwd_mesh.name); if ischar(recon_basis) fprintf(fid_log,'Basis = %s\n',recon_basis); end fprintf(fid_log,'Frequency = %f MHz\n',frequency); if ischar(data_fn) ~= 0 fprintf(fid_log,'Data File = %s\n',data_fn); end if isstruct(lambda) fprintf(fid_log,'Initial Regularization = %d\n',lambda.value); else fprintf(fid_log,'Initial Regularization = %d\n',lambda); end fprintf(fid_log,'Filtering = %d\n',filter_n); fprintf(fid_log,'Output Files = %s',etamuaf_sol); fprintf(fid_log,'Initial Guess muaf = %d\n',fwd_mesh.muaf(1)); % fprintf(fid_log,'Output Files = %s',tau_sol); fprintf(fid_log,'\n'); %*********************************************************** % get direct excitation field % Flag mesh to not calculate the intrinsic emission and fluorescence % emission fields fwd_mesh.fl = 0; fwd_mesh.mm = 0; if isfield(fwd_mesh,'phix')~=0 fwd_mesh = rmfield(fwd_mesh,'phix'); end % calculate excitation field % data_fwd = femdata(fwd_mesh,frequency); % data_fwd.phi = data_fwd.phix; data_fwd.phi = load(phix); %*********************************************************** % load recon_mesh if ischar(recon_basis) recon_mesh = load_mesh(recon_basis); [fwd_mesh.fine2coarse,... recon_mesh.coarse2fine] = second_mesh_basis(fwd_mesh,recon_mesh); elseif isstruct(recon_basis) == 0 [fwd_mesh.fine2coarse,recon_mesh] = pixel_basis(recon_basis,fwd_mesh); elseif isstruct(recon_basis) == 1 if isfield(recon_basis,'nodes') recon_mesh = recon_basis;
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fwd_mesh.fine2coarse = recon_mesh.fine2coarse; else recon_mesh = recon_basis; [fwd_mesh.fine2coarse,... recon_mesh.coarse2fine] = second_mesh_basis(fwd_mesh,recon_mesh); end end %************************************************************ % initialize projection error pj_error=[]; %************************************************************* % modulation frequency omega = 2*pi*frequency*1e6; % set fluorescence variables fwd_mesh.gamma = (fwd_mesh.eta.*fwd_mesh.muaf)./(1+(omega.*fwd_mesh.tau).^2); % check for input regularization if isstruct(lambda) && ~(strcmp(lambda.type,'JJt') || strcmp(lambda.type,'JtJ')) lambda.type = 'Automatic'; end if ~isstruct(lambda) lambda.value = lambda; lambda.type = 'Automatic'; end % determine regularization type if strcmp(lambda.type, 'Automatic') if size(anom,1)<2*size(recon_mesh.nodes,1) lambda.type = 'JJt'; else lambda.type = 'JtJ'; end end %************************************************************* % Calculate part of Jacobian which does not change at each iteration % (call it "pre-Jacobian") [Jpre,datafl,MASS_m] = prejacobian_fl(fwd_mesh,frequency,data_fwd); %************************************************************* % Iterate for it = 1 : iteration % Update Jacobian with fluroescence field (changes at each iteration) if it == 1 [Jwholem,junk] = update_jacobian_fl(Jpre,fwd_mesh,frequency,data_fwd,MASS_m); clear junk else [Jwholem,datafl] = update_jacobian_fl(Jpre,fwd_mesh,frequency,data_fwd,MASS_m); end
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Jm = Jwholem.completem; clear Jwholem % Extract log amplitude reference data clear ref; ind = datafl.link(:,3)==0; datafl.amplitudem(ind,:) = []; clear ind ref(:,1) = log(datafl.amplitudem); % Calculate projection error data_diff = (anom-ref); pj_error = [pj_error sum(abs(data_diff.^2))]; %*********************** % Screen and Log Info disp('---------------------------------'); disp(['Iteration_fl Number = ' num2str(it)]); disp(['Projection_fl error = ' num2str(pj_error(end))]); fprintf(fid_log,'---------------------------------\n'); fprintf(fid_log,'Iteration_fl Number = %d\n',it); fprintf(fid_log,'Projection_fl error = %f\n',pj_error(end)); if it ~= 1 p = (pj_error(end-1)-pj_error(end))*100/pj_error(end-1); disp(['Projection error change = ' num2str(p) '%']); fprintf(fid_log,'Projection error change = %f %%\n',p); if (p) <= 2 disp('---------------------------------'); disp('STOPPING CRITERIA FOR FLUORESCENCE COMPONENT REACHED'); fprintf(fid_log,'---------------------------------\n'); fprintf(fid_log,'STOPPING CRITERIA FOR FLUORESCENCE COMPONENT REACHED\n'); % set output data_recon.elements = fwd_mesh.elements; data_recon.etamuaf = fwd_mesh.etamuaf; break end end %************************* clear data_recon % Interpolate Jacobian onto recon mesh [Jm,recon_mesh] = interpolatef2r_fl(fwd_mesh,recon_mesh,Jm); Jm = Jm(:, 1:end/2); % take only intensity portion % Normalize Jacobian wrt fl source gamma Jm = Jm*diag([recon_mesh.gamma]); if strcmp(lambda.type, 'JJt') % build Hessian [nrow,ncol]=size(Jm); Hess = zeros(nrow); Hess = Jm*Jm';
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% add regularization reg = lambda.value.*(max(diag(Hess))); disp(['Regularization Fluor = ' num2str(reg)]); fprintf(fid_log,'Regularization Fluor = %f\n',reg); Hess = Hess+(eye(nrow).*reg); % Calculate update u = Jm'*(Hess\data_diff); u = u.*[recon_mesh.gamma]; else % build Hessian [nrow,ncol]=size(Jm); Hess = zeros(ncol); Hess = Jm'*Jm; % add regularization reg = lambda.value.*(max(diag(Hess))); disp(['Regularization Fluor = ' num2str(reg)]); fprintf(fid_log,'Regularization Fluor = %f\n',reg); for i = 1 : ncol Hess(i,i) = Hess(i,i) + reg; end % Calculate update u = Hess\Jm'*data_diff; u = u.*[recon_mesh.gamma]; end % value update: recon_mesh.gamma = recon_mesh.gamma+u; recon_mesh.etamuaf = recon_mesh.gamma.*(1+(omega.*recon_mesh.tau).^2); % Negative constraint neg = find(recon_mesh.etamuaf <= 0); if isempty(neg) ~= 1 recon_mesh.etamuaf(neg) = 10^-20; end % assuming we know eta recon_mesh.muaf = recon_mesh.etamuaf./recon_mesh.eta; clear u Hess Hess_norm tmp data_diff G % interpolate onto fine mesh [fwd_mesh,recon_mesh] = interpolatep2f_fl(fwd_mesh,recon_mesh); % filter if filter_n ~= 0 disp('Filtering'); fwd_mesh = mean_filter(fwd_mesh,filter_n); end %PLOTIMAGE plotimage(fwd_mesh,fwd_mesh.eta.*fwd_mesh.muaf); % figure;
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% meshplot(fwd_mesh,datafl.phim); % semilogy(data.amplitudefl./scale,'bx-'),hold on, semilogy(datafl.paam,'ro-') %********************************************************** % Write solution to file if it == 1 fid = fopen(etamuaf_sol,'w'); else fid = fopen(etamuaf_sol,'a'); end fprintf(fid,'solution %d ',it); fprintf(fid,'-size=%g ',length(fwd_mesh.nodes)); fprintf(fid,'-components=1 '); fprintf(fid,'-type=nodal\n'); fprintf(fid,'%g ',fwd_mesh.etamuaf); fprintf(fid,'\n'); fclose(fid); end fin_it = it-1; fclose(fid_log); % Output recon basis mesh to use in subsequent reconstruction attempts. recon_mesh.fine2coarse = fwd_mesh.fine2coarse; fwd_mesh.recon_mesh = rmfield(recon_mesh,{'gamma','etamuaf','muaf','eta','tau'}); %****************************************************** % Sub functions function [val_int,recon_mesh] = interpolatef2r_fl(fwd_mesh,recon_mesh,val) % This function interpolates fwd_mesh into recon_mesh % For the Jacobian it is an integration! NNC = size(recon_mesh.nodes,1); NNF = size(fwd_mesh.nodes,1); NROW = size(val,1); val_int = zeros(NROW,NNC*2); for i = 1 : NNF if recon_mesh.coarse2fine(i,1) ~= 0 val_int(:,recon_mesh.elements(recon_mesh.coarse2fine(i,1),:)) = ... val_int(:,recon_mesh.elements(recon_mesh.coarse2fine(i,1),:)) + ... val(:,i)*recon_mesh.coarse2fine(i,2:end); %val_int(:,recon_mesh.elements(recon_mesh.coarse2fine(i,1),:)+NNC) = ... % val_int(:,recon_mesh.elements(recon_mesh.coarse2fine(i,1),:)+NNC) + ... % val(:,i+NNF)*recon_mesh.coarse2fine(i,2:end); elseif recon_mesh.coarse2fine(i,1) == 0 dist = distance(fwd_mesh.nodes,fwd_mesh.bndvtx,recon_mesh.nodes(i,:)); mindist = find(dist==min(dist));
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mindist = mindist(1); val_int(:,i) = val(:,mindist); %val_int(:,i+NNC) = val(:,mindist+NNF); end end for i = 1 : NNC if fwd_mesh.fine2coarse(i,1) ~= 0 recon_mesh.region(i,1) = ... median(fwd_mesh.region(fwd_mesh.elements(fwd_mesh.fine2coarse(i,1),:))); recon_mesh.eta(i,1) = (fwd_mesh.fine2coarse(i,2:end) * ... fwd_mesh.eta(fwd_mesh.elements(fwd_mesh.fine2coarse(i,1),:))); recon_mesh.muaf(i,1) = (fwd_mesh.fine2coarse(i,2:end) * ... fwd_mesh.muaf(fwd_mesh.elements(fwd_mesh.fine2coarse(i,1),:))); recon_mesh.gamma(i,1) = (fwd_mesh.fine2coarse(i,2:end) * ... fwd_mesh.gamma(fwd_mesh.elements(fwd_mesh.fine2coarse(i,1),:))); recon_mesh.tau(i,1) = (fwd_mesh.fine2coarse(i,2:end) * ... fwd_mesh.tau(fwd_mesh.elements(fwd_mesh.fine2coarse(i,1),:))); elseif fwd_mesh.fine2coarse(i,1) == 0 dist = distance(fwd_mesh.nodes,... fwd_mesh.bndvtx,... [recon_mesh.nodes(i,1:2) 0]); mindist = find(dist==min(dist)); mindist = mindist(1); recon_mesh.region(i,1) = fwd_mesh.region(mindist); recon_mesh.eta(i,1) = fwd_mesh.eta(mindist); recon_mesh.muaf(i,1) = fwd_mesh.muaf(mindist); recon_mesh.gamma(i,1) = fwd_mesh.gamma(mindist); recon_mesh.tau(i,1) = fwd_mesh.tau(mindist); end end function [fwd_mesh,recon_mesh] = interpolatep2f_fl(fwd_mesh,recon_mesh) for i = 1 : length(fwd_mesh.nodes) fwd_mesh.gamma(i,1) = ... (recon_mesh.coarse2fine(i,2:end) * ... recon_mesh.gamma(recon_mesh.elements(recon_mesh.coarse2fine(i,1),:))); fwd_mesh.muaf(i,1) = ... (recon_mesh.coarse2fine(i,2:end) * ... recon_mesh.muaf(recon_mesh.elements(recon_mesh.coarse2fine(i,1),:))); fwd_mesh.eta(i,1) = ... (recon_mesh.coarse2fine(i,2:end) * ... recon_mesh.eta(recon_mesh.elements(recon_mesh.coarse2fine(i,1),:))); fwd_mesh.etamuaf(i,1) = ...
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(recon_mesh.coarse2fine(i,2:end) * ... recon_mesh.etamuaf(recon_mesh.elements(recon_mesh.coarse2fine(i,1),:))); fwd_mesh.tau(i,1) = ... (recon_mesh.coarse2fine(i,2:end) * ... recon_mesh.tau(recon_mesh.elements(recon_mesh.coarse2fine(i,1),:))); end function [J,data,MASS_m]=prejacobian_fl(mesh,frequency,datax) % [J,data,MASS_m]=jacobian_fl_new_new(fn,frequency,mesh,data) % % Calculats jacobian for fluorescence yield. % Ensure data input is excitation field data!! % % mesh is the input mesh (variable or filename) % frequency is the modulation frequency (MHz) % datax is the excitation field data (variable) % error checking if frequency < 0 errordlg('Frequency must be nonnegative','NIRFAST Error'); error('Frequency must be nonnegative'); end % If not a workspace variable, load mesh if ischar(mesh)== 1 mesh = load_mesh(mesh); end % modulation frequency omega = 2*pi*frequency*1e6; % Create Emission FEM Matrix if mesh.dimension == 2 [i,j,s] = gen_matrices_2d(mesh.nodes(:,1:2),... sort(mesh.elements')', ... mesh.bndvtx,... mesh.muam,... mesh.kappam,... mesh.ksi,... mesh.c,... omega); elseif mesh.dimension ==3 [i,j,s] = gen_matrices_3d(mesh.nodes,... sort(mesh.elements')', ... mesh.bndvtx,... mesh.muam,... mesh.kappam,... mesh.ksi,...
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mesh.c,... omega); end junk = length(find(i==0)); MASS_m = sparse(i(1:end-junk),j(1:end-junk),s(1:end-junk)); clear junk i j s; % If the fn.ident exists, then we must modify the FEM matrices to % account for refractive index mismatch within internal boundaries if isfield(mesh,'ident') == 1 disp('Modifying for refractive index') M = bound_int(MASS_m,mesh); MASS_m = M; clear M end % Calculate the RHS (the source vectors) for the Emission. source = unique(mesh.link(:,1)); [nnodes,junk]=size(mesh.nodes); %[nsource,junk]=size(source); ind = mesh.link(:,3)==0; foo = mesh.link; foo(ind,:)=[]; clear ind source = unique(foo(:,1)); nsource = length(source); %qvec = zeros(nnodes,nsource); qvec = spalloc(nnodes,nsource,nsource*100); % Simplify the RHS of emission equation beta = mesh.gamma.*(1-(sqrt(-1).*omega.*mesh.tau)); % get rid of any zeros! if frequency == 0 beta(beta==0) = 1e-20; else beta(beta==0) = complex(1e-20,1e-20); end if mesh.dimension == 2 for i = 1 : nsource val = beta.*datax.phi(:,i); qvec(:,i) = gen_source_fl(mesh.nodes(:,1:2),... sort(mesh.elements')',... mesh.dimension,... val); end elseif mesh.dimension == 3 for i = 1 : nsource val = beta.*datax.phi(:,i); qvec(:,i) = gen_source_fl(mesh.nodes,... sort(mesh.elements')',... mesh.dimension,... val); end end
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clear junk i nnodes nsource val beta; % Calculate EMISSION field for all sources [data.phim,mesh.R]=get_field(MASS_m,mesh,qvec); clear qvec; % Calculate Adjoint source vector [qvec] = gen_source_adjoint(mesh); % Calculate adjoint field for all detectors [data.aphim]=get_field(conj(MASS_m),mesh,conj(qvec)); clear qvec R; % Calculate boundary data [data.complexm]=get_boundary_data(mesh,data.phim); data.link = mesh.link; % Map complex data to amplitude and phase data.amplitudem = abs(data.complexm); data.phasem = atan2(imag(data.complexm),... real(data.complexm)); data.phasem(data.phasem<0) = data.phasem(data.phasem<0) + (2*pi); data.phasem = data.phasem*180/pi; data.paam = [data.amplitudem data.phasem]; data.phix = datax.phi; % Build the Emission jacobian data2 = data; ind = data.link(:,3) == 0; data2.complexm(ind,:)=[]; [J] = build_prejacobian_cw_fl(mesh,data2,omega); function [J] = build_prejacobian_cw_fl(mesh,data,omega) % J = build_jacobian_cw_fl(mesh,data,omega) % % Used by jacobian_fl, builds the jacobian matrix % % mesh is the input mesh (variable) % data is the data % omega is frequency ind = mesh.link(:,3)==0; foo = mesh.link; foo(ind,:)=[]; clear ind source = unique(foo(:,1)); meas = unique(foo(:,2)); % source = unique(mesh.link(:,1)); % meas = unique(mesh.link(:,2));
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[ncol,junk] = size(mesh.nodes); [nrow] = length(find(mesh.link(:,3)~=0)); [nsd, msd] = size(mesh.link); J.complexm = zeros(nrow,2*ncol); % define parameters gamma and tau if isfield(mesh,'gamma') == 0 mesh.gamma = (mesh.eta.*mesh.muaf)./(1+(omega.*mesh.tau).^2); end f_gamma = complex(1,-omega.*mesh.tau); f_tau = complex(0,-omega.*mesh.gamma); k = 1; for i = 1 : nsd if mesh.link(i,3) == 1 sn = source == mesh.link(i,1); dn = meas == mesh.link(i,2); if mesh.dimension == 2 % Calculate the gamma part here J.complexm(k,1:end/2) = ... IntFG(mesh.nodes(:,1:2),... sort(mesh.elements')',... mesh.element_area,... conj(data.aphim(:,dn)),... (data.phix(:,sn)).*f_gamma); elseif mesh.dimension == 3 % Calculate the gamma part here J.complexm(k,1:end/2) = ... intfg_tet4(mesh.nodes(:,1:2),... sort(mesh.elements')',... mesh.element_area,... conj(data.aphim(:,dn)),... (data.phix(:,sn)).*f_gamma); end k = k + 1; end end