cpb-us-e1.wpmucdn.com · quantifying optical tomography methods for biomolecular sensing a thesis...

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�

��

��

��

��

��

2� Introduction to Light Interaction with Tissue ......................................................... 8�

�� !�

��

��

��

�� !��"�

�� #��$��%�!��&��'�

��"� ��(�)�� *�

�� " �� #�

�� $& ��+��%��%��)��,��-�

ix

�� !�% � ��.��

�� / �� #�0 �$��.��

�� 1��1$�%��"�

�� 2 ##�� $��&�1�%��3�

��"� 1�%��#��*�

��3� �� #�� #�� -�

3� System Overview ....................................................................................................... 33�

�� $�%&��

�� &�� # ��

�� 2��

�� $�%&"%��!�

�� &�� # �� '�

�� 2�� -�

�� '��(��"��)��

4� Data Processing ......................................................................................................... 44�

)�� %�� ))�

�� ,��&��

�� )�,��&��

�� '�

)�� *��( ��+#�

5� Spatially Offset Raman Spectroscopy Imaging ...................................................... 51�

+�� +��

�� 2��.� � ��#��45�!��

+�� ,��- ��.�� +)�

x

+�� ,��++�

+�� /�'��(0� ��++�

+��)� %��/��(0� ��+��

+��+� *�� ,�� +1�

�� 2��.� � ��#��1!�45�!��'�

+�� 23 �� +!�

+�� (0� ��+4�

+�� *��(� ��#�

�� !�� "��

�� /�� !��#��45�!��"��

+��)�� *�� +�

�� /�� !��#��1!�45�!��""�

+��+�� *�� !�

��"� �� 3-�

+�� $�5��,��- ��*��1#�

�� $��6��%��2� ��3��

�� 0��+ �$ ��3"�

�� $�� 3*�

�� /�� !��3*�

+��)�� (0� ��"��!#�

+��)�� /��"��!��

+��)�� .�� "��5�0��0��%��6�� !1�

+�� %��!4�

+�)� ��*�� !4�

6� Surface-Enhanced Raman Imaging ........................................................................ 91�

xi

�� 2%��$� ��4��

"�� ,$��1��*��

"�� 1��*��

"�� !�� #�� 1�%��*3�

�� %��44�

�� *�� 44�

7� Cerenkov Excited Fluorescence Tomography Using External Beam Radiation Treatment ...................................................................................................................... 101�

1�� #��

1�� "�0 ��#��

1�� %��#+�

1�)� *�� #��

1�+� �� %��#1�

1�� *�� #!�

8� Fluorescence Imaging ............................................................................................. 109�

!�� #�

!�� 23 ��*��

!�� 23 ��%��

'�� ,$��1��

'�� 1��

!�)� ��5�0��*�23&.�� *��#�

!�+� � ��

!�� %��)�

!�1� ��*�� )�

xii

9� Comparison of Imaging Methods .......................................................................... 125�

4�� "�� +�

4�� 0�'��1�

4�� 23 �� !�

*�� #��%��

4�)� ��*�� +�

References: ..................................................................................................................... 137�

10� Appendix A ............................................................................................................ 159�

11� Appendix B ............................................................................................................ 161�

�� "��,�� 0� ��

�� "��,�� 0� ��)��4�

�� "��,�� 0� ��1��11�

xiii

List of Figures

��7�*��0 5��0�� 0� ��0��,��,� �� 0�� 0�� 0��0�� 5�� 58��5��0�� 3�� 0�� 0� ��#�

��7�9/��:�*�� ,� � � �� 0�� ,� � � �� 9%��0:��0�� 0 5��0��'�� 0��5 ��,��3 �� 0�� 6��

��7��0� � 0 ��,� � � �� 8� � �� 0��5�0�� 0��,��$�%�5��0�8��0 5�� ;+1&�#<��

��)7�9/��:�(0 �� %��0��"��0 5��0�� ,�,�� ,��0��6�� 0�� 5�9%��0:�� 0��,�� "��%��0�� 5��0��)�

��+�9/��:�2��0 5��0��,� � � 8�� &��9�� 5:8�,�� 0�� 0 ��5�0��0��5��0��9%��0:��0�� 0 5��0��,� � � ��8��,��8�� 0 ��5�0�0�� =��,� �,��5�0�0�� 0 5��0�� 8��8�� 0�� 0�50��0��,��8�5�0�0�� =�� 0�� 0��+�

��7�9� :�2�� 0�� 0 �� 5�� =��&� =��%��8�5�0�0�� 0 8��8�0��0��,��0��0�� 9� �:��0�� 0 5��0�� %��0��5�0�� &� =�� =��0�� 0��&� =�� =�� 5�� 0�� 5�� ,��0�� 6��,�� 1�

��17�9/��:�*��3 ��0�� 0�� 5�0�%�� 0��3�� 0�� 9%��0:��0 5��0 5�0�� 0 �5��08��0 5��,��8�� 0�� 0�� 0� ��0�0��/�(%��4�

��!7�9/��:��0 5��0��0� �� 0��= �� 0 �5��5�0�� 0�� 05�� 0��0�� 8�� 3��θ�>�)��9%��0:�%� �� 0�� 0�0��,��0��= ��5�0�0��&�3��,��0��,�� 0 ��0�5��08�5�0��0��0��,��0��,�� 5��0��$�%�� 0�� ,��α��?@��#�

xiv

��47�9/��:��0��=��0� �0�,�5�� 9%��0:��0�� 0�� 0� �0�� A0��0��,�� 0 ��=�� 3��0�� 0��

��#7��9/��:�23�� 0��0��0 58�5�0�+�� #�� 5�0�� 0��9%��0:�%�� 0 � �� ,B��5�0��#C� ��

��7�� %��0�� ,�� 0��0��0�� 0�� 0��0��,��0��*��,�� 0��3�� 0��5�0�0�� 0��1!+�� !�#��+�

��7�*��,��0��,�� 0��'�� 0��$�%&��,�� 3��%��

��7�23�� *�� %�� 0��$�%&��%�� 3��0��0��,�� 0 ��,��=��,�� 50�� =��0 ��6 ��,��,��,��

��)7�9/��:�23�� $� �� 0��5��0��0� �3��9��:�� 5��08��0 5��0�� 5�� %�� =��9%��0:��0��*� ��50��0� ��0��,��5��'��5�0�50��08��0 5��0�� ,�� 0��,��0�� 0��*� �3��1�

��+7�� 0�� ,��,��8�5�0��,�� 3�� 0�� ,�� 0�� 4�

��7�*��,��0��,�� 0��"%�&$�%��'��,�� 3�� %�� =��)#�

��17��23�� 0�� 0� �8��0 5��0�� '�� )��

��)��7�9/��:�/ ��0��,��#� ��0�� 0� �8��0 5��0�� 0��,��9%��0:��0�� 0� ��0��,��8�� 0�0�� 8� � ��5�0�� 0��5��,��)+�

��)��7�*�� 0�� 0 ��,��,��D0� ��;��#<8�50��0� � ��,��=�� ,��=�� 0��3 �� 5�0��0��'��)1�

xv

��)��7�9/��:�%�� ,��5�0�� 0 �8��0 5��0�� 8�5�0�0��0��0��0�� ,�� 9%��0:�� %�� =8��0 5��0��,�5��0�� 50��0�� =�� )!�

��)�)7�23�� 3 �� 5�0��= ��3�� 0��5��0� ��0�� =��=��'��0�� 0�� 8��'��= 5�� 0��3 �� 0�� 0 ��,��=�� )4�

��+��7�� ,��5�0��)��,�� 0�� 8�, 0�0�� ,��,�� 0��0� ��0�0�� 5�� 0��+)�

��+��7�� ,��5�0�0�� ,�� ,�� 0��'�� 0� ��'�� 0��,��0 �� '��,�0��++�

��+��7��0�� 0�� ,�� 0�� 0��,��0 �� 0��'�� 0� ��3 ��0 5�5�0�0��,�� +��50��0�5�� &�� '�� 0� ��5�0��)��5�� +��

��+�)7�0�� 0�� ,��50�� 0� ��0�� , ��5�0��0�� 0��%�� 0�� +1�

��+�+7�23�� ,�� )��'�� 0� ��'�� $ ��0�� 0��,��0��5�� ,�� 0�� 0�� 0��(� � ��0 5��+� ��0��#�� ,��0��+!�

��+��7�9�:�E�� 0� ��5�0�� ,��0 ��5�0��0 5��0�� 0�� 9,:�"�� 5�0 ��,��=�� ,�� #�

��+�17��9�:�"�� 1� �� 0��8��0 5�� 5�� =�� ,�� 9,:�( �� ,��=�� 50��0 � �� 0� ��9�:��5�0�� %�� =�F�0�� 0��,��=�� 0��,�5��0��8�0��0��0��0�� 0�� 0�� 0��%��

��+�!7�/ ��0�� 0�� ,�5��0�� ,��0 5�� 3 �� , 0�0��+��)��'�� 0� ��3 ��+�

xvi

��+�47�9�:�(� � ��0�� %��23�� 0�� !�� 1�� 0��9,:�� 0�� 5�0�0��, �� 0��

��+��#7�9��G�,:�23 �� %�� &,�� 0� ��5�0�� 0�� ,��0 � �� 0��5 �� 9��G��:�23 �� %�� 0� ��50�� 0�� 0��1�

��+��7��,��0 ��,��0��H�� "��0��9/��:��0�� 0�� 0��=�� 0 �� F�0�� 0��)�� ,��9%��0:�� 0� �� 0��0 ��9� �� (��I=��,��8�J�I8��#��8;��<:��1��

��+��7�9/��:��*��5�� 0��,��8��0 5��0��0�� 8�50��0�� 5��0�� 0��,��=�� 5�0�0��9%��0:��0�� 0 ��5�0��0�� ,��0�� 0�� 1��

��+��7�$�� 0 5��0�� 6��J�� ,��8�50��0�� 0�� 0�� 0�� 0 5��0�� ,��,�� 0��0� � ��0 5��0�� ,�� 0��, �� 0��8��0 � �� 0�� 0��8�50��0��, �� 1)�

��+��)7�*�� 0�� 0�� ,��0 �� 5 �=��9*�� 5 �=�� A��0��8�"�8�H��:�5�0�� ,��8��I*��0�� 5�� +�� ,��,�� 0��8��0��0��0��0�� 0��0��0��,��0�� '��=�� 0�� 1+�

��+��+7�*�� 0�� 0�� ,�� 5 �=��9*�� 5 �=�� A��0��8�"�8�H��:� ��0��8�� 1+�

��+��7�9/��:�*�� 0�� 0 5��0�� 0�� 0��9%��0:�(0 � ��0��, ��5�0�0��3�� ,��0�� 0�� 0��,��5��0� �0��, ��1!�

��+��17�"�� 0�� ,��5�0��5�0 ��0�� 0�� =�!)��1!�

��+��!7�9/��:�*�� 0�� ,��8�5�0��0��8��0�� 0��,��9��:�� 5 ��,��0 5��0�� 0�� 0��9%��0:�-�� 5� ��0��,��0 5��0�� 0��+��,��0��,�� 0�� 0��14�

xvii

��+��47�(0 �� 0�� 0��%�� 0� ��5�0�0�� 0�� 3�� 50��0�� 0��!#�

��+��#7��0 5��0�� 8��0��0�� 0��%�� 0��0�� !#�

��+��7�9/��:��5�0��,�� 0��9%��0:��0�� &�� 5�� !��

��+��7�� '�� 0�� '�� 8��0 5��0��0�� %��5�0��0��,��=�3� �0��%��8�� 0��0��'�� 0��,��%��, ��!��

��+��7��5�0�0��,�� 9�� 5:� �� 9��:8��0��,�� 0��5�� 3 �� 0��0 5��0�� 0��0 � �� ,�� 0��0��0��0 5��0�� 0��B �� !��

��+��)7�*��0 5��0�� 0�� ,��9��:��0�� 9��:�� 0��,�� 3 ��!)�

��+��+7�9/��:�� 0��=��,�0�� 9��:�� 0��0 5��0 5�0��0 5�0�� ,��0��9%��0:��0 5��0��, �� ,��8�5�0�0��5 � �0��5�0�� 0�� 8��0��5 � �0��0�5�0� �� 0��0��0��0��0�� 5�� ,�5��0�� 0��0 ��8�� 0��!+�

��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)�

xviii

��+: (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!�

��L��M�N�� O��O��O�� ,��0��&�� 9�:��0�� 5� ��0�� 0� ��0��50��&��0�� 0��3 �� 5�0�0�� 0� ��3�� 0��0��0��5�0��#��

��1��7�/��'�� 0��,��=�� 5�� 0�� 0 5��9�:��9�:�23�� #��?�/�� 9,:�23�� #�!��?�/�� 9�:�� 0��0�� 0 ��0�� #+�

��1��7�MN�� O�O�� O��M�N��0�� 0 5�50�� 0� ��0�� =��9�:��0�� 0� �,�5��0�� 0�� 0�� 0 5��0�� 0��#��

��!��7��,� � � �� /�&�I%��%*��!##�A�5�0�0�� 0��3�� 9� ��:�� 9��0��:�;�1!<��

��!��7�� 0�� 0�� ,�� 0�� 0�� &�B��

xix

��!��7�� 0� ��5�0��,�� C�� %!##�� 5�0�0�� 0�� 0�� =��)�

��!�)7�(� ��0�� 0�� 0�� 0�� 0�� 0��,��0�� 8�5�� 0�� 0��*�� 0�� 0 ��0�� 50�� ,�� 0��5�� 0�� +#�"��)�

��!�+7��0��"%��5 �=�� 5�5�0�� 0�� #��,�5��0��B�� 0��E�� 0�� "%�� 5�� 0��0��0�� 0�� 0�� 0��0��0��0�� '�� 0��+�

��!��7�*�� 0�� 0�� 5��'�� 0��B�� 0 ��8��0�� ,��0�� 0��5��0�� 0��0�� "%��

��!�17�� 0�� *�� 0�� 0��2��0�� 6��,��3�� 8� �� 0��6�� 0�� 0��,�� 5��0�� 0��,��=�� ,��0��)�0 ��8�,�� 0��0 ��!�

��!�!7��0�� 0 ��0��B�� 0�� 0��%E�� 0��0�� 0�� 0��0�� 0 ��E��0��E�(8�%��0��%!##��0��,��0��0��1##��0��0��0 5��0��0��,�� 0��0��0��0�� 0��,��5�0�0��0��,�� 0��0��0��E�(��0��0�� ,��0��,��

��!�47�� 0�� 0��E�(�� 0��0� ��0�� 0��!##&�0�� 0��0 �� B�� /�� ,��6��5�0��0��,��

��!��#7��0�� )�0 �� B�� 0�� E��0��E�(8�%��0��%!##��0��,��0��0��1##��0��0��0 5��0��0��,�� 0��0��0��0��0�� 0��,��0��0�� 8��0��0��E�(��0��0�� ,��0��,��

��!��7�� 0�� 0��E�(�� 0��0� ��0�� 0��!##&�0�� 0��)�0 �� B�� 0�� 0 5�� 5�� 5�0�0�� 0�� 0��,��

xx

��4��7�� 0� ��0��30�,�� 0�� 0�� 0�� 0��3�� 0�� 0��0��,� � ��0�'��

��4��7��&�� 5�0�� 0��0�� 0��%�� 5��,�� 0��0��0��3��

��#��7�� 0� ��0��30�,�� 0��,��0�� 8�� = 5��0�� 0�� 0��0��,� � ��0�'��#�

xxi

List of Tables

��,��&�7��0�� 0� ��0�� 0� ��0��5��,��0��5 �=��

��,��+&�7��,�� ,��5��0�� /� ��"��6��0�� =8� �� 8�5��0�� 11�

��,��+&�7��0 5��0�� 0�� 0��,�� 50��0�� 0��,��5��0��*��0 5�� =�� J��48��#�)��11�

��,��+&�7�� ,��=�� 9��%:�� %��9��:� �� 5�0��,�� 8��0�� %��!��

��,��+&)7�� ,��=�� 9��%:�� %��9��:� �� 5�0�0��=��,�� 0�� %��!��

��,��+&+7�� ,��=�� 9��%:�� '�� 0��5�0�0��6�� #�#�� #��!!�

��,��+&�7�� ,��=�� 9��%:�� '�� 5�0�0��6�� #�#�� #��!!�

��,��!&�7��0�� ,��=�� 9��%:�� 0��5 �� 0�� ,��50�� 0�� 0��0��0�� ,��0��0��0��,�� 0��,��=�� !�

��,��!&�7��0�� ,��=�� 9��%:�� 0�� 0 5�0��5�0��0��0��6�� 0�� 5�� 0��0�� 4�

��,��4&�7�/��5� ��0��,� � �� , ��3��%��K��;��)<8�� =�;�!�<8�/��;�!1<8�"��;)�<8��;�!!<8�/ ��;�!4<��% 5��;�4#<��

��,��4&�7�/��5� ��0��,� � �� &�� &�� 3 �� %��2�&��;�!�<8�*��;�!�<8�K��;��4<8�D��;�)�<8��(��&��=�;�4�<��

xxii

��,��4&�7�/��5� ��0��,� � �� , ��3��%��D��=�;�!+<8�E��=��;�!)<8�$6��0�� ;�14<8�K �� ;�4�<8�K ��;�4�<��)�

xxiii

Table of Acronyms

�� !��"�� #�� $ �� %�� #�� &'��#�� &'��#�� %�� "�� (��$��"�� $ �� $�� )*�� $�� $��+��+�� (��,��+�� -�� (��$ ��*�� .��%� �� .��%�� .�� #�� .�� (��$��"��/�� +��*� �� (�� +�� 0�� 0��*�� 0�� +��* ��"�� +�� "�� "�� +�.� �� +�� *� �� ( �� *��

xxiv

�� *��&�� "��(�� +��"�� -++��"�� *�� 1 ��2��

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

S1

S2 Excited States

Ground State

S0,0�S1,0 S0,0�S1,1

S0,0�S1,2

S0,0�S1,3

S0,0�S2,1

Frequency

Inte

nsity

��

��

��

��

��

��

��

��

��

��

��

��

�

��!"# !"# $�� %��' *��+�

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

��

�

�

��

��

��

��

��

�

��

��

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

��

��

'�4)��G�"#��

��&%-��+

2��-��!��

�%��%��!%��+

�+��

��

7 5+55�

5H

D+� 7 5+5�5H

�5��

��5+�

�+��

�!D� 7

5+5�

�5

�H

�+��

��

�5� !�� 7 5+��5 �H

��B��

��5+�

��

�555��5

�555��5

��

��

� �+��

� �

�

�

�D

�

��+��5+�

�+��5+�

�+�

�!�

�� 7

5+5�

�5

�H

�� !�� 7 5+��5 �H

�5555��55

�� +��

��

40

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

Inte

nsity

(arb

uni

ts)

Wavenumber (cm-1)

Teflon

a b

61

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

Inte

nsity

(a

rb u

nits

)

Wavenumber (cm-1)

Inte

nsity

(arb

uni

ts)

Wavenumber (cm-1)

Inte

nsity

(arb

uni

ts)

Wavenumber (cm-1)

63

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

Log

Inte

nsity

(arb

uni

ts)

Source Detector Pair

Log

Inte

nsity

(arb

uni

ts)

S D t t P i

a b

67

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

5e-5

0

2.5e-5

0

2.2e-5

0

4.2e-5 a b

c d

68

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.

��

�� !��"� ��

��!��"� ��

��

��

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.

��

��

81

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.

82

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.

84

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].

85

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.

86

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

��

��

��

��

87

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

88

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

��

��

89

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

90

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.

91

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

92

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.

94

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.

95

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

96

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

97

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

98

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.

99


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.


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

100

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.

101

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

102

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,

103

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

104

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

105

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)

Rec

on V

alue

(a.u

.) c 0.2

0.4

0.1

0.8

�

��

��

��

��

��

b a

Cerenkov Radiation Beam �

��

��

��

��

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.


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.


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 biologically 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.

109

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

Source 90°

135°

180°

��

��

Fluo

resc

ence

/Tra

nsm

issi

on

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

120

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.

122

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.

123

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.

124


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.


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


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


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


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:

�� *��A��E� � 8�P�� =�� 7� �� 5 �=8P��(0�� 0�� 8�!4&4+�9�##�:��

�� J��0,��J��"�� 8��$�� $&� ��#��% �� 9/� �� A��G�A��=��8��#��:��

�� E��K ��8�P��& 0 �� 0�8P�(� �� 0��222��8��#&��4�9�4!�:��

)�� /��%��= 5��=8�P( �� 0�8P��5��,� ��8��+&��4�9�4!):��

+�� /��J��'��8�P/��&�� 8P��7�80��9'*:��4�-�;��:�0��8�9�� I ��(0 ��8��4!4:8��1&��

�� J��.�� 8�PQ��R�� Q?�R��&�� 8P�� 0��,� � ��8��&��)�9�##�:��

1�� "��*��" ��8��8��"�0��&J��8�P��%�� 8P�J�� I ��8�#��#��9�##+:��

!�� "��A ��8�"��8��.��8�P(� �� &�� 0�� ,�� 8P�J �� ,� �� 8�#��#)&#��#)&#��)�9�##1:��

4�� K��8�E��8��8��%��6��8�P*�� ,��%�� 8P�J�� 0 ��8��&�!�9�##4:��

�#�� 2��"��=&"��8�J��(��- �� 8��"��E��=��8�P�� &�0��8�� 5�0�� 8P�� 0��,� � ��8��)�&�+#�9�##�:��

138

�� 2��8��J��8��'��8�$��0�08�*��J�=�, 5�=�8�J��8�%��- �� ,�8��J�� ,��8�P� �� ,� � � �� &�� 0�8P�� 8��&��!�9�##�:��

�� E��"��=�8�P�0��I3��8�� "�� 0��I3�� "�8P�%��5� ��8�)�)&)))�9�4)�:��

�� K��K�� 8�P(�� 3��8P��-2��J ��8�1��&1�+�9�4!4:��

�)�� -��J��"��, ��8�"��" ��8�%��A��8�"��*��8��0 ��8��/��J��'��8�P�&.�� -��=�� 8P�/��"��8��4�&�#��9�44):��

�+�� .��0��8�P$ &�� 0��,�� 8P��$�� 8��)&��+�9�441:��

�� "��*��E��J��.�� 8�P�� &�� 8P��0 ��%��8�++�&+��9�##�:��

�1�� "��K��0��8�H��"�0� �8�%��K��8�%��A��8��/��J �� 0� 8�P�� ,�� 8P��%��0��8�!��&!��+�9�##�:��

�!�� /�� 8�.��K��6��8��/��E�,,�&��8��E� �38��"��8�%��I=� = �8�/��$� 8��K0��8��6��8��J��.�� 8�P�0��/�%2S�� &�� 7��&�&0��,�� 0� �� 8P��I� ��8��4)�&�4+��9�##4:��

�4�� .��K��0��5��8��"��/��0��8�K��*��(��8��A��( ��8�P*��=&�� ,� ��,�� 8P�I ��/��8��4��&�4��9�#��:��

139

�#�� 0� �� 8�I��$��E ��8�E��(�6 �8�J��K�� 0�8��J��"��8�P%��" ��7��$ �� 0�'�� *�� H�� 8P�2�� H� � ��8��#�&��9�#��:��

�� 2�� 8�E��J��8�� 8��$��$��0� =�8�P-��0&�� 0��0�� 0�� 0�� 0�� 0�8P�E�� 2� ��8�)�1&)1)�9�###:��

�� .��K��0��5��8�(��J��- ��8�K��= �8�J��IT-��8��-��8��A��( ��8�P�� 0�� 5�0�� 0�� 8�� 8��,� �� 8P�J �� I ��9�##4:��

�� "��I��2��"��&K��8�%$8��$8�P2�� G�*�� "��8�$��8�G��-��0�&�%��%� ��8P��9��8��##+:��

�)�� "�0��&J��8�"��"��0��8�$��%��B��8��"�� 8��0 ��8�H��H6��8��%��%��0��&K ��8�P$��&��%�� 8P�(0 �0��(0 ,� ��8��&��9�44!:��

�+�� $�� 8�%��=��8�K��% ��8��A��(��=��8��(��"� ��=8�P��,�� ,�� 5�0�� %�� 9�I%�:7�� ,�� 0�� ,��8P��8�!44&4#+�9�##1:��

�� 8��&-��(��8�*��I��8��&E �8�E��D��0�8�*��"��0�8�/��8��$�� 8�"��*��A��8��$��8�P�� 5�0��&�0��%�� 8P�$��,� ��0 � ��8�!�&4#�CU��#!1&#�+��9�##1:��

�1�� /��E�,,�&��8�5�� )�� )�#�� #��#�� #�� 9*�� 0�� 8��##!:��

�!�� $��8��K��8�*��-��8�$��/��8�"��"�B�8�"��(��8�%��*�� 8��"��B�8�P�� &�� 0�� 0�� 7�� 8P�� 3 ��8��1!&�4��9�#��:��

140

�4�� -��/�� 8�"��$ ��0�8��"��8��"��=�8�2��K ,��0�8�-��=�8��=��8�P�� 0�� & ��+&�� &��&�� , ��,�� 8P�"��8�1+)&1��9�#��:��

�#�� A�� 8�2��"��=8�"��(�� 8��0��8�P��&�� ,� �� 8P�(� �� 0��222��8�4�!&4�#�9�44�:��

�� 2��8�*��J�=�, 5�=�8�$��0�08��'��8�%��/��8��J��8�*��-��8�J��8�%��- �� ,�8��J�� ,��8�P� �� 0��0�� 0�8P�J �� I ��8��#&1��CU��#!�&��!�9�##�:��

�� *��"��6��8�E��,��8�/��%��(� ��68�%��/��0��8��"��A��*�50��8�P�� 0� 3��0�� 0��0��=8P�� J �� %�� I� � ��V�� V�(0��8��!+&�!4�9�441:��

�� 8�*��-��8�$��0�08�%��"�0�8��*��=�8�J��8��J�� ,��8�P(�� ,�� B��0�� 0�� 8P�(� �� 0��$�� 8�)#�)&)#�4�9�##1:��

�)�� /��K��8�E��(��IT$��8�(��J��.��=��8�J��2��8�J��"��8��J 0�8�P23 �� E?-��0��&��&�� 0�� 8P��%��0�8��++�&�++4�9�44+:��

�+�� "��8��% B 8��I��W�8�J�� 8�"��E�6��8�J�� 8��*�� 8��"��&E��8��%��B��8��J��,��8�P23 �� 4+-2%�8�� 0��-2%�� 8�� &-2%��0�� ,��8P�J �� 0��$�� 8��!&��!�9�##1:��

�� /��%��8�%��5��8��*X� �6�8�2��(�6��8�(��/��Y8�A��*��/��8�/��E�� 8�*��%��05��68�K��%��0 8��(��J��" ��8�P��0�B�� &��&)��'�� 3 �� ,�� 8P��%��0�8��+�1&�+1+�9�##�:��

141

�1�� K�8��A�8�"��E��=��8��0��B8��A��8�2��"��=&"��8��/�8�P$��&�� 50�� ,��3� ��8P��%��0��8�1!1#&1!1+�9�##�:��

�!�� E��"��*��8�E��0��8�/��"��8�$��J��-��8�%��E��(��B0��8�A��K��8�� 8�J��J �8�-��J��E��8��E��J��D��8�P�� &� �� ,�� &;�� 0�<��7��&0��8P�$��"��8��+&��4�9�#��:��

�4�� K��3 8�K��0��8�K��= �8�J��E�8�(��J��- ��8��A��( ��8�P�� , �� , ��8P�(� ��I��8��#�4#�9�#��:��

)#�� /��/� �8�(��8��A��E��&�� 8�P�� 7��,�� 8P��8��1&��9�44�:��

)�� E� 8��8�%��"��/�� 8�/��A��K��0��8��$��8�P�� 5�0�� '�� 8P�$��,� ��0 � ��8�4�4&41��9�##):��

)�� A��0�8�P"�� 8P�J �� $��"��8��&��!��9�##!:��

)�� J��J 0� ��*�5� &-��0��8�P(�� ,�� &��&��,� � � ��8P��8��1)&�1!�9�44�:��

))�� 2��(��"��% ��8�2��"��A ��8�J��"��0�� 8��A��J��"��=8�K��(0��8�2��J��%��.��=8��-��J��8�A��"��$��8��2��(��%��8�P� �� 0�� 5�0�, �� *�� 5�0��0� �� ,�� 8P�� 0��0� �� ,�� 8�+1�9�#�):��

)+�� $��J��8�"��/��=��8��"��2��8�P�� 0�� B ��, �� ,��‐��‐��,� � � ��9*2��:8�5�0�� ,��8P��(0�� 8��+�&��9�44�:��

142

)�� %��"��8�"��*��" ��8��0�8�*��0�=��%� 8�A��8�2��A��B�B�8��E ��8�P� �� 5 ��5�0��5�0 �� 8P�� 8��4#&��4+�9�##�:��

)1�� J��%��"�0��8�"��=�0��8�-��5��8��J��8�P%�� ,� ��0�� , �� &�� 0�� 0��8P�J �� ,� �� 8�#!1#��&#!1#��&#!1#��9�#��:��

)!�� "��*��" ��E��"��8�P%�� 8P��I�0 �%��%��8��#&��4�9�#��:��

)4�� 2��(��(��0��8�2��*�� 8��8�(��0��8�%��"�� 08��/�� =��8�P��%�� 0�� , �8P��8�)!#&)!1�9�44�:��

+#�� D�0��8�%��2��/�=��=�8��"�0� �8��E��J ��8�/��8��J��.�� 8�P�� &�� ,��8P�$��,� ��0 � ��8��)!&��+)�9�##�:��

+�� K��"��K 6� ��8�%��A��8��H��"�0� �8�P$ �� , ��8P�J �� "��%��0��8��#!&��9�##1:��

+�� "��8�%��E��8��"��8�P�!�&�� , ��8P��$��"��8��&�1�9�41�:��

+�� E��"��=�8��&J��(��=&- � 0�8�E��J��%�� =8�� 8�P�� , ��5�0�0�� !�&�� 44��&��0�� 0 � 0 ��8P��$��"��8��!&)4�9�##�:��

+)�� %�� 2��% ��8�P/��&�� 8P�� /��" �,�7�(0�� 0��8�(��9�44):��

++�� %�� 8��#��4�$��%�) �� &�9A�� 8��##�:��

+�� J�� 38��J��*�A��8��J��/��8�P��3 �� "��%��0� �� 8P��J �� (0��8��#�9�##�:��

143

+1�� (��0�8�PI ��,� � � � ��0�� ,�8P��9�444:��

+!�� J��'��8�PI ��,� � � � ��8P�I�� "��/��8�http://omlc�� ?� ��?��?��0��9�##�:��

+4�� %��/��(��.��8�-��, ��8��(��8�� 8��%��,��8�P*�� .��&$�%��,� � � �� 8�5�0��&�� 8P�� % �� 1 ��8�9I �� 8��##):8��)��

�#�� E��"��-��"��%��8�PI �� 5��0��##&�� ##&Z��5��0�� 8P�� I ��8�+++&+��9�41�:��

�� J�� ,��8��8�$��0�08�"�� 8��*��=�8�*��-��8�J��8��%��"�0�8�P��,��7�� ,��7�� &�� 5 �� B��0�� 0�� 8P��%��0��8��14�9�##+:��

�� I��"��8��A��( ��8��J��8�H��/��I��,��8��K��*��(��8�P�� &�� '��&� ��&�� 0�� 0�� ,�� 0��,�� 8P�%��5� ��8��!�1&�!�)�9�##�:��

�� -��/��8�*�� 8��D0��8��E�� 08��0��8�P*�� ,� �� 3�� $�%��08P�(0��"�� 8��4!��9�44+:��

�)�� J��%��" ��8�J��(��8��-��-��0��8��2��=8�*��0�8��"��J 0� 8�P"��0�� /��0�� %�� $ ��I ��&��*�� 8P�� I ��8��+!�&�+4��9�44!:��

�+�� J��%��A�,��8�*��J��8��J��*��=�8��J�� ,��8�P$ � �� ,� � � �� 08P�J �� (0��8��#�#�!&�#�#�!&�#�#�4�9�##4:��

144

�� E��A��8�A��"��8��A�� 8�P�� 8P�(0 �0��(0 ,� ��8��#�&��CU��1+�&�#41�9�44!:��

�1�� "��" ��8�P�� 0�� 8P�� 0 � ��5��8��1&�+��CU��!1&��+��9�##+:��

�!�� 2��[ ��8��J��%��8�J��"��K��8��"��08�(��2=��8�"��K��8��J��-��8�P$��&�� 0 ��&� �� 0 � 0�� 0��,��8P�� 8��#1+&�#!)�CU��4��&#!+��9�##!:��

�4�� J��%��8��8�"��.��"��0��8��2��8��2��"��=&"��8�P/�� 0��0��5�0��&�� 8P�� ,� ��0 � ��8�1)&!��CU�#4+!&��4�9�##4:��

1#�� D�0��8�%��2��/�=��=�8��"�0� �8��E��J ��8�/��8��J��.�� 8�P�� &�� ,��8P�$��,� ��0 � ��8��)!&��+)�CU��#!1&#�+��9�##�:��

1�� A��8�K��0�8�D�&��/�8��E��,0��8��0�8�P*��&�� ,�� (2��&�� 8P�J �� $��"��8��!��&�!1#�CU�#��&++#+�9�##1:��

1�� (�� 5�=�8�"��6�8��"��*��" ��8�P"��6�� ,��%�� 8P�J �� "��%��0��8��!&��CU��+��&)�!��9�##�:��

1�� "��I��5�8��-��8�� =�8�K��B��8�-��=�8��=��8�P/�,��&��,� �0�� 0��5�0�0��0&� �� %�� 8P�� 0��,� 0��0�� 8��1#&�1)�CU�###�&#�4��9�##4:��

1)�� J��A��0�8�*�� 8��"��/��8��D5��8�J�� 8��-��8�P$ �� =��,�� %�� 8P��0��8��!#&��!1�CU�###�&�1##�9�##!:��

145

1+�� K��0��8�2��H��,8��J��%��E� ��8�P��&�� ,��,��%�� 7�� 0��0�� 0��0�� 8P�J �� ,� � ��0 ��8��4&�!�CU�#��1&1#��9�###:��

1�� 2��A��B�B�8�$��8��&��0�8�"��*��" ��8�"��6�8��%��"��8�P��&�� 6�� 9��2":�� 0� �� %��8P�� 8��+�&��9�##�:��

11�� (��J��08�"��"��-��8��A��8��/��"��0��8��(��%�� 8�P�� "�0 �� =�� ,�� %�� 8P�� 7��#��)�+��9�#��:��

1!�� 8��K��(��8�E��K��0�=��8�%��2��A�,��8�-��*��8�J��0�=��8�.��"��$��=8�%��$��=8�E��A��8��%��%�,�08�P�� ,��0 �� ,��=�� ,�� 8P�J �� %�� 8��44&��#+�CU��#41&)+++�9�##1:��

14�� J��K�� 8�-��K�� 8��K��K�� 8�P�2%�&&��&� �� ,� ��8P��0�� 5��8��#+�&�#�#�9�##!:��

!#�� . &*�08�(��K��8��"��A�,��8�P$� � ,�� ,� �� 8P�$� ��7�� 0 � ��8�,� � ��8��8��&�#�9�##�:��

!�� "��K��0��8��D��8�J��.��J =��8��/��D��8�(��J��K�� 8�2��"��8�K��(��8�%��-��8�� 8��-�,�8�%��8��A��8��K��"��0 ��8�2��- ��8��E��,0��8�P��,�� 5�� &� ��"%�& 0 �� &%�� 8P�$��"��8�!�4&!�)�9�#��:��

!�� (��= �8�P.��,�� ,�� 5�0�� 3��0�� 08P�(0��%��8�#�1!&#�14�9�4�1:��

!�� %��D0��8��J�� 38��K��E��8�*��J��E�� 8��A��( ��8�P�� = �� ,�� 0�� 0� ��8P�(0��"�� 8�+)11�CU�##��&4�++�9�#��:��

146

!)�� -��/��8��"�� 8�-��J��8�E��(��38��8�"��(��0�8��E��,0��8�/��8��D��0��8�P�� = �� 7��,��3 ��8P�J �� $��"��8��+14&�+!)�CU�#��&++#+�9�#��:��

!+�� -��*�0�0��8�"��2��2��8�(��K��0�8��*��8��8��"�� 8��A��( ��8��K��*��(��8�P$�� 0��$�%��7�� 0�� 8P�� $��"�0�2��8�1��&1��9�##4:��

!�� A�&��0� �8��(��0�8��J��A��08�P��5� ��0�� ,� � ��8P��222�B �� '�� 8��&��!+�9�44#:��

!1�� K��"��D��8�(��=8�0 ��$��&�9�� &A��8�%��8�"�8��4�1:8� ��+��

!!�� %��8�"�� 8��*��*�� 8�P�0��0� ��,�� 0�� 0��0��7�� '��8P�(0��"�� 8��+��&�+�#�9�44�:��

!4�� 2��*��8��%��I��8��J��E ��8�P�� ,�5�� &� 0��0�� 0 �8P�"��(0��8��#��&�#��9�##�:��

4#�� (��0�8�K��B6��8�"�8�J��'��8��/�8�G�A��08��J�8�P��" �� 0� � �� 8P�* �� ,� � ��8��#�&��9�4!4:��

4�� "��J��8�-��E0��8�"��"�� 8�A��8��*��8�-��*�0�0��8��A��( ��8�P�� 0��0&'��0��&�� 0�� 0�8P�J �� I ��8�#!�##1&#!�##1�CU�#!�#!�&#!��!�9�#��:��

4�� %��/��8�P*�� &%��8P��9E ��(��8��41+:��

4�� E�� 0�8�K�� 8��H�60��8�-��8��$��(��=8��-��"�� 08�P�� '�� )&

147

��5�0�6&�� 8P�"�� 0��8��+��&�+)1�9�##+:��

4)�� K��"��8�P"�� ,�� 0�8P��0�B �� 8�)#4&)��9�44�:��

4+�� *��%8�P� ��0 �� 8P��9E ��(��8��41):��

4�� %��*��8�/��"�= ��8�"��E ��08�"�� 8��J��K ��0��8�P�� 9�I$�%:7��6�� 8P��8��)�#&�)��9�41�:��

41�� -��E�� 8�E��I68�$��K��8��(��8�P"%��&�� &�� 8P�"��%�� 8�)�1&))��9�##�:��

4!�� (��8�J��J��2�� 8��J��"�"��8��%��/��8�PE�� 9��:��0��"%�� 7��8��8�� 8P��0��5��8��4�&��+��9�444:��

44�� (��I=��,��8�*��8�"��=��,��8��5 ��8��E ��8��"��*��" ��8�P$ ��%�� ,��7�� 0� �� , ��'��8P�J �� I ��8�#4#+#��&#4#+#��CU�#4#�#!�&#4#��!�9�#��:��

�##�� J�&/��*��8��( ��8��/�,� �8��2�� &A0��8�(��I=��,��8��"��" ��8�P��'�� %�� 8P��9�� I ��(0 ��8��#��:8�1!4��&1!4��&1!4��

�#�� "��E��0��8��A�� 8�2��"�� 8��"��A��08�P�� ,��& �� ,�� %�� 8P�� 8��4&��1�9�444:��

�#�� /�� 8�P��H�� /��8P��5��%��%:��9�##1:��

�#�� J��%��J��=8�� # ��$��4��%�%) ��9�(�2�(��8��0��8�A��0�8��##�:8� ��3��8�4#��

148

�#)�� 8�P��E�� %��0��8P��1��%��%�9A�� 0 0 �=�8�(�8��##1:��

�#+�� A��/��2�� &A0��8�K��2�� &A0��8��"��*��" ��8�P"� ��*�� 5�0�"�B �� '��7�� *�� 0�8P�� 8�!+&4!�9�#��:��

�#�� *��8��A��( ��8�%�� 8��/��8�(��"�6��=�5�68��8��/��E�,,�&��8��J��8�-��*�0�0��8��K��*��(��8�P"�� &� � �� 0�� 8P�%��8�#�)�#��9�##!:��

�#1�� /��/��8��$��0 ��8�$��%�B��8��J��A��8�P(� ,�� 0��=�� 8P�J �� ,� �� 8�#��#��&#��#��&#��#�4�9�#��:��

�#!�� *��J��8�P"�0 �� ,��=�� ,�� %�� = 5�� 8P��8��4!&��#��9�##4:��

�#4�� J��8��A��8�%��%��*��8��"��8�P$��&��%�� 0��8P�� 8��#�&�#!�9�441:��

��#�� J��D0� 8�-��/��8�*��"�/��8��-��D��8�P�� ,��=�� ,�� 0�� ,� ��%�� 8P�� 8��+&��9�##1:��

�� "��8��-��% ,�� 8��A��8��-��J��-�� 8�P� ��7��0��3�� 8P�"�� 8��1+&��!#�CU��+��&�+4)�9�##�:��

�� J�&"��-�� 8�P/��3�� I�� 7��8P��0��J �� 0�� 0��8��)#��9�44�:��

149

�� J��8��A 8��J��8��(��A��0 � � 8�P( �&�� 0�� 0�� 0��8P�� 0�� 0��%�� 8�!#�&!#+�9�44�:��

��)�� 2��(��(��0��8�2��0��8�E��/��8�E��=�� 8�%��"�� 08��/�� =��8�P� �� &��=�8P�J�� "��%��8��###&�##)�9�##):��

��+�� $��J��8�.��( ��8�"��*��" ��8�(��0��8��"��6�8�P%�� 0 � 0�� 0�� ,�� 6�� 8P�� 8�)�)&))��9�##�:��

�� (��"� ��=��$�� 8�P2�� %�� ,� � ��8P��8��#+!&�#��9�##4:��

��1�� "��*��" ��8�A��8�%��"��%�B��0��8��*��-��K 08�P� �� ,��,��%�� 8P��*��8��+4&��!F�� 4&�!��9�##):��

��!�� 2��%��*�� 8�"��*��" ��8�$��(��0 8�(��"� ��=8�"�� 5��8��A��(��=��8��2��E ��0� 8�P$ �� , ��&�� %�� 8P�J�� "��%��8��4�!&�41��9�##+:��

��4�� "��.��0��08�K��* ��8�"��*��" ��8��"��.��8��E ��8�P�� ,�� %�� , �� ,��8P�J�� I ��8�#�#+#��9�##�:��

��#�� "��.��0��08�J��-�� 8�K��* ��8�"��*��" ��8�J��"��K��8��E ��8��8��A��( ��8�P$ ��%�� 0�� , ��8P�J�� I ��8�#�#+#��9�##!:��

�� 8�"��0��08�J��-�� 8�K��* ��8�J��"��K��8��A��( ��8�"��*��" ��8��E ��8�P��&��%�� , �� 8P�I �23 ��8��4#&��##�9�##!:��

150

�� "��*��K��8��K��"�B��8��"�0��&J��8�P� �� %�� 8P�I �/��8�4��&4�!�9�##4:��

�� (��"� ��=8�2��%��*�� 8��2��E ��0� 8��(��=8�K��/��% ��8��A��(��=��8�P$ ��%�� -��Q��R��.�� Q?�R8P�� 8�1+!&1��9�##�:��

��)�� *��K� �0��8��*��8�-��*�0�0��8�K��*��(��8��A��( ��8�P��,�� 0�� 6��,� �,�� ,B��,�� 5�0�� 08P�� I ��8��4&��1!�9�##1:��

��+�� A��/��2�� &A0��8�K��2�� &A0��8�"��%��K ��8��E ��8��J��% ��8��"��*��" ��8�P�� 0� ��5�0�� %�� 0�8P��8�))�1&)))��9�#��:��

�� J��"��8�"��(�� 8��A�� 8�P�0�� =�� ,� �,��&�� 0� ��8P�(0��,� � ��8�4!+�9�44�:��

��1�� /��,��"�0��&J��8�P�� 0 �� ,�� ,� � ��%�� 8P�� 8��&��1�9�##�:��

��!�� *��8�-��*�0�0��8�J��A��8��J��8��A��( ��8��K��*��(��8�P��&�� 0�� 5�0�/� ��&� ��6�� 8P�I �23 ��8�)#��&)#!��9�##1:��

��4�� ,��8�J��%� ��8��.��$6��0�� 8�P�� 0��0�� 0�� 7�� 0�� 6�� 8P��222��"��8��11&��!��9�##+:��

��#�� "��.��0��08�J��-�� 8�J��"��K��8��2�� &A0��8�K��* ��8��E ��8��"��*��" ��8�P�� %�� , �� 8P�� 8��!�&�4+�9�##4:��

�� "��.��0��08�K��* ��8��"��.��8��E ��8��"��*��" ��8�P��,�� %��

151

�� 5�0��,��& ��8P�� 8��1�&�1!�9�##1:��

�� (��I=��,��8�*��8�"��=��,��8��5 ��8��E ��8��"��*��" ��8�P$ ��%�� ,��7�� 0� �� , ��'��8P�J �� I ��9�#��:��

�� E��D0� 8�A��K��/�8��"�8��K��8��- 8��J��"��=�8�P( ��5�� 5��5��0�� 0�� 8P�� (0��/��8��4��&�4��9�###:��

��)�� A��K��8�*��,��8�-��K��E��8�"��0��8�J��*�'��=��8��J��%��8�P�0��2�� (0� ��\�� 6�� '�� , ��,��*��8P�2�� J �� %�� 8�!�&4��9�44+:��

��+�� J��6��8�J��%��"�0��8�"��=�0��8�2��"��05��68��J��8��-��5��8�P� ��,�� 0��7�%�� 0�� 0�� 0��8P�J �� ,� ��0��8�1��&1�#�9�#��:��

�� E��.��8�2��K��0�8�J��K�� 8�-��E��%��8��J��A��08�PH�� =�8P�/��"��8��&�)��9�444:��

��1�� "��J��8��( ��8�-��%��E0��8��*��8�"��"�� 8��-��*�0�0��8�P��&��,��5 �=�� 5�� &��0�� 8P�� % ��7� ��8�9I �� 8��#��:8��A��1��

��!�� "��J��% ,��8�"��*��8��J��"��-��8�P�0�� (2E�� 8P��5��CU�#��4&)#4��9�#��:��

��4�� K��8��D��8�D��0��8��/��D��8�I��E0��8��E��,0��8�P$ �� ,B��%�� 8P�(� �� 0��$�� 8�+!))&+!)4�CU�##�1&!)�)�9�##!:��

152

�)#�� K��"��0��8�%��A��- �8��2�&E0��8��*��8�K��= �8�J��%��E�8��/�,� �8��A��( ��8�P*��&��,��=�� ,�� 0�� 0�8P�J�� I ��8��##��9�#��:��

�)�� /��D��8��%��08��A�� 8�A��* ��8�E��*��8��0 B��8�"��J��$��8��E��,0��8�P"�� 3�� 0��%�� %�� 8P�(� �� 0��$�� 8��+��&��+��9�##4:��

�)�� "��K��0��8��D��8�J��.��J =��8��/��D��8�(��J��K�� 8�2��"��8�K��(��8�%��"��-��8�� 8��-�,�8�%��8��A��8��K��"��0 ��8�2��- ��8��E��,0��8�P��,�� 5�� &� ��"%�& 0 �� &%�� 8P�$��"��8�!�4&H��+�9�#��:��

�)�� 2��$ ��8��/��0��8�"��%�� 58�*��%��(��8��2�&J�5�0��8��6�=�8�J��/ ��8�"��%��8��0�=��8�P��0 � �� 8P�� 8��14&�!��9�##4:��

�))�� J��3�� 8��*��8�*��J��E�� 8��A��( ��8�P��= �� ,��3��,�� 8P�"��(0��8�)��1�9�#��:��

�)+�� K��E��8�%��D0��8��*��8�*��J��E�� 8��A��( ��8�P��&��0��= �� 0� ��8P�I ��/��8��4�&��4+�9�#��:��

�)�� %��* 0��8�%��J��E �� 8�2��J��=� 8��-�� 8��*��(�5��&A ��8�P��= ��%�� 2��9�%2�:��7��$ ��"�0 �� I �� (2�� 8P�(� ��I��8��##�9�#�#:��

�)1�� %��D0��8��E��8��.��2�� 8��K��=8��*��8��.� �� 8�*��E�� 8��A��( ��8�P��= �� 3��9�%2/:��3��,�� 0�� 7�" �� 3�� 0� ��8P�� 3 ��8��!�&��4)�9�#��:��

153

�)!�� *��8��A��( ��8��8�-��*�0�0��8��K��*��(��8�P� �� 0��,��8P�J �� (0��8�&�9�##4:��

�)4�� *��8�K��= �8�J��IT-��8��/��E�,,�&��8�K��*��(��8��A��( ��8�P� � �� &�� &�� 0�� ,�� 8P�J�� I ��8�#+��#��9�#�#:��

�+#�� 8�J�� 8�K��= 8�J�� =��8�-��B 8�(��8�"��8�*��3�8��B��8��E��8�PE2�$�)\�� =�8P�$��"�0 ��(0��%��0�� 7�� 8�� 8�*�� 2'�� 8��+#&�#��9�##�:��

�+�� (��8�(��%� 8�"��W��8��J��/��8�PE�"I�7��3�,��5 �=�� E��)�� 8P��--'�5�� &�� :�1% �� #��%��"$�!�� %��2��<��(�$��:�2��%:�=��&8��##!:8��4&�+��

�+�� $��*�� 8�J��*�0��8��A��8�J��/�� 8�� 8��.��$6��0�� 8�P�&�� &�� B�� 0�8P�J �� I ��8�#�#+#4�9�##4:��

�+�� *��%�6��=��.��$6��0�� 8�P-�,�� 0 �� 0��&��&,�� 8P�"��(0��8�)�4��9�##1:��

�+)�� A�� 8�E��A��8�*��K��8��/��8�"��J��8�/��.��A��8�2��- ��8�E��"�/��8�(��"��8��J��D�,��8�P(�� 0 �� ,� �� 0�8P�I ��23 ��8��1+�&�11��9�##+:��

�++�� -��*�0�0��8��*��8��*��J��8��A��( ��8�K��*��(��8��"��(�� 8�P� �� ,� �� 0�8P�I ��/��8��+&��1�9�##�:��

�+�� /�8�E��"��0��8��%��0��8�P��= �� 0�� &��8P�I ��/��8��#4&��9�#�#:��

154

�+1�� /�8��D0��8��* ��0�8�*�� 8�J��8��0�8��0�6�� 8�P� �� &�� ,� �� 0��5�0�� 8P�I ��3 ��8�!#��&!#!#�9�##4:��

�+!�� J��%��I��8��(��A��8�(��0��8��*�3��8��/��J��-��8�P�0� � �� 5�0��0��,�� *$��T�� 0��8P��0��/��8��1�&�1)�9�##�:��

�+4�� K��2��8�J��%��8��*��8��8�"��08�"��.��"��0��8��2��8�2��"��8�/��08��%��E�� 8�P*�� 0�� 0��8P�� 3 ��8��)&��+�9�#�#:��

��#�� /��E�,,�8�P$�� &��8P��8��11&�!1�9�#��:��

�� A��*��8��J�� 8��8�J�� 8��E��"��0��8�P�� 0��,�� 0�6��,�� 8P��0��B �� 8��)�&�)+�9�##�:��

�� (��.��0��8��" ��8��,��&%�0��8��=,��8�J��E�� 8��6��8��A��8��%�� 8�P"�0��,�� ,��&�� 0�'�� 0� �� ,��8P�2�� J �� I� � ��92J�I:��8��)1&�+��9�##1:��

�� (��.��]�8��/�,� �8��K��8��-��8��A�� 8��8��*�� 8��-�� 8��J�8��K��2�=��8�P�� 7�� /�&��( �� ,� ��=��8P�J �� 8��9�#��:��

��)�� *��K��8�(��0 � � 8�K�� 8��K��*��$�5�8�P�� 6�� 0 ��6�� ,�� 0�� 0��8P�(0 �0��(0 ,� ��8�1!1&14#�9�4!1:��

��+�� 2��%��E��%��/��8�P�� ,�� 0��,� �&,��,�� 0�� 0�� ,�� 7��,��0�� 8P�J��I� ��8��#�&��9�##1:��

155

�� E��2��" ��8�A��(�� 8�/��08��A��A��A��=��8�P�0��H�� $�� 7��0�� 6�� ,�� V8P�J �� 8��4�&�4!�9�4)!:��

��1�� (��5��8�K��-��=�5�8��/��8��%��*��"�� 8�P�� 0�� ,��7�� ,� �&,��,��8P�J �� 8��41&1#+�9�4!1:��

��!�� "��.��"��0��8�J��%��8��8�"��08�K��2��8��A��8��2��8�2��"��8�/��08��2��"��=&"��8�P$��&�� 0��5�0�� 7��5�� 8P�I �� B ��9I��:��8��

��4�� *��8�J��"��*�� 8��" �� 8�P�� (� ��"��, �� E��9��E:��%�� 0�8P�� I 00�� 8��+&�1�9�###:��

�1#�� %�� -��K��8�P�� 0�8P�(0��,� � ��8��+4�9�41!:��

�1�� 2��$ ��,��8�"��8�/��E^��8�E��(��8�-��8��$�� 8��_0�8��E��8��J�� 8�P�� ,��8��6�� ,��2E�%&,��, �� 8P�$��,� � ��8��#4&��!�9�##1:��

�1�� /��8�"��-��8�%��0��8�I��0�� 8�.��0�� =8�E��K��&"��=8��E��B,�=0�0�8��J�� 8�P��, �� 0��6�� -2%�& �� ,��&��8P��%��0��8��!)#&�!)4�9�##!:��

�1�� /��E^��8�"��0�58��I�� 8��-^��]&E�0�,��8��A�, ��8�J�� 8��B�8�P�� 6�� 2E�%&,��, �� 7�"�0 � � �� 8P��J�I� ��8�1+1&1��9�#�#:��

�1)�� J��/^�,� �8�J��5��08�.�� 0��8�J�� 8��_0�8��B�8�P��, �� 7�� 0�� 8�� ,� ��0 � �� 8P��,��/��8��1#&��!#�9�#�#:��

156

�1+�� *��8�K��= �8�J��IT-��8��/��E�,,�&��8�-��/��(��8�(��J��- ��8�K��*��(��8��A��( ��8�P"%�&� � �� 0��'��2E�%��,�� 8P�� 8��1�&�1��9�#�#:��

�1�� %��K��8�"��8��K �� 8��8�A��A��A��8��(��K��8�PE�� 3 �� 6�� 8P�� 0�'��8��+#�9�44+:��

�11�� *��"��0��= �8��/�=�� 8��K��/�=�� 8�P�� =�� Q��R�� Q?�R��8P��,� ��0 � ��8��#+&��9�##+:��

�1!�� /�&�� 8�P�%*��!##�AP�9�#�):8��http://www.licor.com/clinical_translation/irdye_800CW_NHS_ester_optical_properties_and_structure.html��

�14�� .��$6��0�� 8��&-��8��8��%��A��8�P�� 0�� 8P�$��"��8�1+1&1��9�##�:��

�!#�� %��-��8�/��- �8��.��8�J��"��E��8�-��. ��8�.��8��0�8�P�� &�� 0 �� ,�� 8P�" �� 8��+&��9�##�:��

�!�� .��$6��0�� 8��8��%��A��8�P�� 5�0��&��07��5��0 � ��0��,�� 8P�2�� 8��4+&�#!�9�##�:��

�!�� J��*��.��/�,0��5��8�P�0��6�� =��,�� 0��8P�� B �� 0��8�+�&+4�9�##�:��

�!�� -��2�&��8��-��8��"��2�&��8�P�� ,� � � � ��&2E�%��, �� B�� 7�� 8P�$� ��8�!�4&!�)�9�##+:��

�!)�� "��E��=��8��K�8�2��"��=&"��8�A��A��8��/�8�P�� &�� 5�0�

157

�� 8P�J �� ,� �� 8�#�)#�4&#�)#�44�9�##+:��

�!+�� *��D��=8�*��,��8�-�� 8��A��8�%��8�(��0��8�"��,��8�%��K`�0��8�"��K��8��- ��8�P�H�$��I$�I��+&�"�$I/2.H/�$��*��$*H�2*��/HI%2��2$�2��"(%I.2��-2��(2��I��/�**2%��$�2%�*2�2��I$8P��0��J �� H� � ��8��+&��4�9�##�:��

�!�� J��2�� =8�%��08��E��8�(��8��2��8��-��K��E��8�P" �� ,��, �� ,��'�� 0�8P�J �� "��%��0��8��)4&�+1�9�4!4:��

�!1�� /��8�J��-��K��=8�"��A��-��68�(��8��/�8��"�0��8��-��K��E��8�P. ��'�� 0�� 0�� 3��7�(�� , ��08P�� 8��#�&�#!�9�441:��

�!!�� 8��(��8��/��08�E��"��(0��8��"�0��&J��8��J��$��8�P%��0�� 50 ��, �&��&�� 8P�J �� ,� ��0��8��41&�#��9�#��:��

�!4�� I��/ ��8�� =��8�J��A��=��8�(��.��A�=��8��"��I��38�P� �� , �� 0��7�� 0�� 0�8P�� 8�)�1&)1��9�44�:��

�4#�� %��2��% 5��8�J��J 5��8��J��-��"��0��8�P"�� , �� , �7��"�� 0�� 8P�%�� %��0��8��)&�)��9�4+4:��

�4�� (��&��=8�"��0��8�/��J��&J��8��8��-��- ��8�P*�� 6�� 3�� 5�0�0��8P�� 8��!+&��4)�9�##+:��

�4�� K �� 8�"��(��=��=�8��&��/�8��E�� 8�%��E�� 8�� 8�E��- 8��6�B8�E�� 8��J��D0��8�P*�� '�� &�� &��

158

� �� 0��9�"�:8P�" �� 8�)!!&)44�9�#�#:��

�4�� J��/��K ��8�A��"��. ��0��=8�J��0�8��"�� 8�P(�� 0 �� 50�� &� � �� 8P��,� �0��8�)1&+)�9�##1:��

�4)�� 8��&-��(��8�*��I��8��&E �8�E��D��0�8�*��"��0�8�/��8��$�� 8�"��*��A��8��$��8�P�� 5�0��&�0��%�� 8P�$��,� ��0 � ��8�!�&4#�9�##!:��

�4+�� J�&-��K��8�J�&��K��8�-��0 �8��&"��/��8��&-��J�8�K�&$��8�2��K�=8��&K��K��8�*��-��J� �8��"�&-��0 8�P$� �� ,��5�0��0��%�� 8P��0��8��4�1&�41��9�##�:��

�4�� K��"��0��8�K��= �8�K��J��3 8�J��%��E�8��-��8��A��( ��8�P�� 0��,�� &�� 8P�J �� ,� �� 8�#��##��&#��##��#�9�#��:��

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;

166

%% 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);

167

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

168

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

169


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);

170

[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

171

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

172

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;

173

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

174

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

175

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

176

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

177


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;

178

%% 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

179

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')

180

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;

181

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

182

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';

183

% 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;

184

% 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));

185

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) = ...

186

(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,...

187

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

188

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));

189

[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

cpb-us-e1.wpmucdn.com · quantifying optical tomography methods for biomolecular sensing a thesis...

Documents