A SYSTEMATIC CHARACTERIZATION OF FIBER PHOTOMETRY … · Abduraham Siddiqi, Kyle Sheller. I would...
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A SYSTEMATIC CHARACTERIZATION OF FIBER PHOTOMETRY FOR OPTICAL
INTERROGATION OF NEURAL CIRCUIT DYNAMICS
By
MAY MANSY
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2019
© 2019 May Mansy
To my mother, for empowering me
To my father, for supporting me
To my daughter, for bringing out the best in me
To my husband, for always being by my side
To my family, who fill me with pride
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ACKNOWLEDGMENTS
The true treasures of life are in the people, who stand by us through thick and thin, and
who never cease to believe in us. I have been tremendously blessed to have the most wonderful
people in my life, who have contributed directly and indirectly to the completion of this
dissertation. I would like to start by giving huge thanks to my academic advisor, Dr. Karim
Oweiss, for granting me the opportunity to pursue a Ph.D. in his lab and for his unwavering
efforts to support and guide me over the past six years. I’m immensely grateful for all the
valuable pieces of advice and teachable lessons that improved my critical and analytical thinking
as well as the guidance Dr. Oweiss endowed me throughout the years of my research.
Additionally, I would like to thank Dr. Oweiss for always giving me the opportunity to attend
various scientific research conferences and for encouraging me to engage in activities that
nurtured my personal and professional development. Sincere gratitude also goes to the members
of my committee, Dr. Kevin Otto, Dr. Thomas Foster, Dr. Minghzou Ding and Dr. Brandi
Ormerod for their valuable feedback, advice and continuous support.
Furthermore, I would like to express my genuine appreciation to the graduate advisor of
my Ph.D. program, Dr. Cherie Stabler, who has always been there for me and who never ceased
to believe in me. I would like to thank Dr. Stabler for all the eye-opening, enlightening and very
up-lifting discussions we had. Next, I would like to express my thanks to Dr. Brandi Ormerod
not just for always empowering me and for the many valuable pieces of advice, but also for
being the first to help me discover my teaching talent.
A token of appreciation also goes to Dr. Marwan Abdellah for the opportunity to
collaborate with the Blue Brain Project at EPFL, which made a major part of this dissertation
possible.
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I will now turn to the amazing members of the Oweiss lab. It was a real pleasure to work
and interact with each one of the current and former members of the Oweiss lab. Brandey
Andersen, who was more than just a lab colleague and friend, and who always helped me find
my way. Islam Badreldin who never fell short of providing technical advice for any technical
challenge. Dr. Ali Ibrahim who taught me perseverance. Ben Goolsby who always reminded me
to calm down and who always helped review my writing tasks. Joseph Canzano for the fruitful
scientific chats and brainstorming sessions that always helped me critique my thinking and
identify shortcomings of my research. Dr. Narayan Subramanian, for teaching me about
immuno-histochemical techniques, helping me course-correct when I lost track and get up when
I hit rock-bottom. Rebeca Castro for helping me collect my data during the last phase of my
PhD, Naoki Sawahashi for helping resolve some challenging technical issue I faced towards the
end of my degree, and all the other wonderful members who shaped my experience at the Oweiss
lab: Hong-Jae Kim, Phillip Navarro, Mehrdad Hashemi, Joseph Succar, Michael Brodowski,
Abduraham Siddiqi, Kyle Sheller.
I would like to express my sincere gratitude to mentor, Dr. Yifei Dai, for offering me the
opportunity of an internship at Exactech, for being a constant source of support and
empowerment and for the abundant guidance and advice during my job-hunting phase.
I would also like to acknowledge Dr. Erin Patrick for being a great teaching partner and
mentor. I’d like to thank Dr. Patrick for teaching me about teaching, for her valuable feedback on
my performance and for providing the ultimate guide on how to pursue a career in teaching.
Furthermore, I would like to express my deepest appreciation to Professor William
Mcelroy for teaching me things beyond “Engineering Leadership”, providing precious tips and
advice, and for always checking on me.
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I would also like to express my appreciation to all the administrative staff members who
helped me with filing paperwork, placing orders for my research supplies, installing new
equipment, delivering mail and maintaining my workstation: Kathryn Thompson, Jason Kawaja,
Marcy Lee, Ray McClure, Quashawn Durant, Kimberly Depue, Michelle Evern, Myra Edwards,
Amanda Redinger, Victor De La Cruz and Kaitlynn Gravely.
I would like to thank my husband, partner and best friend Islam Badreldin, for being my
safe place, for being by my side and for always taking care of the things that I get on my nerves.
I deeply appreciate his support and back up during my downtimes and during my times of stress.
I would like to thank my daughter, Noor, for teaching me how to value and enjoy every minute
of every day and for bringing out the best in me with the simplest of words. Her endless
questions and curiosity about the world make me learn new things and acquire new ways to teach
her about them.
The final token of sincere gratitude goes to my siblings and my loving parents for their
endless love, care, and support. I can’t thank them enough for instigating high moral standards
and discipline in me, for allowing me to be who I am, and for always having my back.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ........................................................................................................... 4
LIST OF TABLES .................................................................................................................... 10
LIST OF FIGURES .................................................................................................................. 11
LIST OF ABBREVIATIONS.................................................................................................... 13
ABSTRACT ............................................................................................................................. 14
CHAPTER
1 INTRODUCTION ............................................................................................................. 16
Centuries of Choreographed Synergy ................................................................................. 16
Dissertation Overview ........................................................................................................ 24
2 BACKGROUND AND MOTIVATION ............................................................................. 25
Let there be Light ............................................................................................................... 25 … and there was Light ....................................................................................................... 25
The Origin of Light ..................................................................................................... 26 The Light Duality ........................................................................................................ 26
Basics of Illumination ........................................................................................................ 29 Parameters of Light ..................................................................................................... 31
Radiometric Quantities ................................................................................................ 32 Basics of Optics .......................................................................................................... 33
Propagation of Light .......................................................................................................... 37 Propagation in an Optic Fiber ...................................................................................... 37
Propagation in Neural Tissue ....................................................................................... 38 Fundamentals of Fluorescence............................................................................................ 41
Optical Interrogation of Neural Circuity ............................................................................. 46 Optical Actuators ........................................................................................................ 47
Optical Sensors ........................................................................................................... 49 Comparison of Fluorescent Imaging Techniques ................................................................ 52
Two-Photon Imaging ................................................................................................... 52 Single-Photon Micro-endoscopy.................................................................................. 54
Single-Photon Fiber Photometry .................................................................................. 54 Motivation and Research Aims ........................................................................................... 58
Significance ................................................................................................................ 60 Research Aims ............................................................................................................ 60
3 SPATIAL CHARACTERIZATION OF THE DETECTION VOLUME ............................. 61
Background ........................................................................................................................ 61
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Methods ............................................................................................................................. 62 Fiber Photometry Signal Acquisition ........................................................................... 62
Phantom Brain Preparation .......................................................................................... 63 Acute Brain Slice Preparation ...................................................................................... 63
Fiber Photometry Recording Procedure ....................................................................... 63 Results ............................................................................................................................... 66
Volume of Detection from Phantom Slices .................................................................. 67 Volume of Detection from Acute Brain Slices ............................................................. 69
Discussion .......................................................................................................................... 73
4 VALIDATION OF THE SPATIAL CHARACTERIZATION ............................................ 77
Premise and Hypothesis ..................................................................................................... 77 Methods ............................................................................................................................. 80
Surgical Procedure ...................................................................................................... 80 Fiber Photometry Recording ........................................................................................ 81
Data Acquisition ......................................................................................................... 81 Visual Stimulation ....................................................................................................... 81
Epi-fluorescent Volumetric Scanning .......................................................................... 82 Results ............................................................................................................................... 84
Discussion .......................................................................................................................... 91
5 EMPIRICAL MODELING AND PREDICTION OF THE DETECTION VOLUME ......... 93
Monte-Carlo Simulation ..................................................................................................... 94 Optical Properties of Neural Tissue ............................................................................. 95
Results ........................................................................................................................ 96 A Novel Prediction Tool .................................................................................................. 100
Artificial Neural Network .......................................................................................... 100 Results ...................................................................................................................... 102
Discussion ........................................................................................................................ 106
6 CONCLUSION AND FUTURE WORK .......................................................................... 108
Summary .......................................................................................................................... 108 Future Work ..................................................................................................................... 110
Conclusion ....................................................................................................................... 111
APPENDIX
A SYSTEM DESCRIPTION ................................................................................................... 113
B PILOT EXPERIMENTS ...................................................................................................... 120
C SUPPLEMENTARY MATERIAL ...................................................................................... 130
LIST OF REFERENCES ........................................................................................................ 135
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BIOGRAPHICAL SKETCH ................................................................................................... 150
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LIST OF TABLES
Table page
2-1 Comparison of the three main fluorescent imaging techniques. ...................................... 57
3-1 Detection volume for different optical fibers. ................................................................. 72
3-2 Summary of recent FP studies. ....................................................................................... 75
4-1 Summary of anatomical locations .................................................................................. 91
5-1 Summary of reported optical properties of the rodent brain. ......................................... 107
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LIST OF FIGURES
Figure page
1-1 The first historical report about single cells. ................................................................... 18
1-2 The first description of a single neuron. ......................................................................... 18
1-3 The first published graph of an action current. ............................................................... 20
2-1 Newton’s observation on refraction. .............................................................................. 28
2-2 Electromagnetic spectrum.. ............................................................................................ 30
2-3 Electromagnetic wave. ................................................................................................... 32
2-4 Illustration of Specular and diffuse reflection. ................................................................ 34
2-5 Refraction and reflection................................................................................................ 36
2-6 Cone of acceptance. ....................................................................................................... 36
2-7 The properties of an optical fiber. .................................................................................. 38
2-8 Jablonski diagram. ......................................................................................................... 43
2-9 Example excitation and emission spectrum of a green fluorescent fluorophore. ............. 45
2-10 Different configurations of fluorescent microscopy. ....................................................... 46
2-11 All-optical interrogation of neural circuit dynamics. ...................................................... 47
2-12 Commonly used optogenetic actuators and their excitation spectra. ............................... 48
2-13 Single vs. Two-photon excitation. .................................................................................. 53
2-14 Comparison of fluorescent imaging techniques. ............................................................. 55
2-15 Qualitative comparison chart. ........................................................................................ 57
2-16 Neurometric curve as a function of stimulus intensity. ................................................... 59
3-1 Experimental setup. ....................................................................................................... 65
3-2 Agar-bead setup. ............................................................................................................ 66
3-3 Spatial detection extent in brain phantom. ...................................................................... 68
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3-4 Spatial characterization of detection volume as a function of fiber geometry in acute
brain slices..................................................................................................................... 71
3-5 3D Volume of detection for each optical fiber. ............................................................... 72
4-1 Epifluorescent volumetric scanning setup and LMM...................................................... 83
4-2 In-vivo validation of the directly measured detection profile and volume, location E.. ... 87
4-3 In-vivo validation of the directly measured detection profile and volume, location B. .... 88
4-4 In-vivo validation of the directly measured detection profile and volume, location C. .... 89
4-5 In-vivo validation of the directly measured detection profile and volume, location D ..... 90
5-1 Detection maps simulated with the developed FPMCS. ................................................. 98
5-2 Simulated and directly measured detection boundaries and axial detection profiles. ....... 99
5-3 Empirical model of the detection volume. .................................................................... 105
A-1 GCaMP6f excitation spectrum. .................................................................................... 114
A-2 Diagram of the Fiber Photometry system. .................................................................... 115
A-3 Sample Ca2+ trace recorded with FP. ............................................................................ 118
B-1 Setup of the experiment. .............................................................................................. 123
B-2 Results of Experiment 1. .............................................................................................. 124
B-3 Methods and results of the experiment. ........................................................................ 129
C-1 Surgical procedure and evaluation. .............................................................................. 133
C-2 Quantification of the visually evoked responses. .......................................................... 134
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LIST OF ABBREVIATIONS
1p Single-photon
2p Two-photon
ANN Artificial neural network
AP Anterior-posterior
Ca2+ Calcium
CCD Charged coupled device
Det. Detection
DV Dorso-ventral
Em. Emission
ephys Electrophysiology
Ex. Excitation
FP Fiber Photometry
FPMCS Fiber Photometry Monte Carlo Simulation
GECI Genetically encoded calcium indicator
GEVI Genetically encoded voltage indicator
MCS Monte Carlo Simulation
ML Medio-lateral
OS Optically scanned
TIR Total internal reflection
TPI Two-photon imaging
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Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
A SYSTEMATIC CHARACTERIZATION OF FIBER PHOTOMETRY FOR OPTICAL
INTERROGATION OF NEURAL CIRCUIT DYNAMICS
By
May Mansy
August 2019
Chair: Karim Oweiss
Major: Biomedical Engineering
Identification of the neural signature of behavior is the ultimate goal of neuroscience.
Recent efforts have been devoted to developing all-optical tools for cell-type-specific
interrogation of Ca2+ dynamics in awake behaving subjects. Fiber Photometry (FP) is one such
tool that allows recording and manipulating the aggregate activity of many fluorescing neurons
in vivo. While FP has a good temporal resolution, it has poor spatial resolution compared to
other widely used tools such as microelectrode arrays, single-photon micro-endoscopy, and
multi-photon laser-scanning microscopy.
This dissertation aims to fill a knowledge gap regarding the temporal and spatial
characteristics of the fluorescing tissue volume that the optical fiber can record from as a
function of the fiber geometry. First, the spatial extent of the detected fluorescence in phantom
brain tissue as well in acute brain slices is quantified. The results suggest that two critical device
parameters, namely the numerical aperture and the fiber diameter, affect the possible detection
volume. Second, we demonstrate experimentally that FP can be used to record sufficiently
sensitive signals to characterize the orientation tuning of neurons in the mouse visual cortex.
Validation of the FP signal is achieved in this setting by axial scanning of the hypothesized
detection volume using epi-fluorescent CCD imaging, permitting the weighted reconstruction of
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the FP signal from the CCD-derived fluorescing sources. Third, an empirical model consisting of
an artificial neural network (ANN), which is trained to predict the FP detection volume for
different combinations of fiber diameters and numerical apertures, is developed. The model is
trained using a biophysically-plausible Monte Carlo simulation (MCS) of scattering photons in
brain tissue to simulate detection volumes for any fiber geometry. Results suggest a general
agreement between the experimental data (acute and in vivo preparations) and the simulated data
(MCS). In summary, this research contributes knowledge about the use of fiber photometry as a
ubiquitous tool for biological investigations given its ever-increasing use by the scientific
community.
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CHAPTER 1
INTRODUCTION
Centuries of Choreographed Synergy
“It takes two to tango” would perfectly describe the progression of the dynamic and
symbiotic relationship between optical microscopy and neuroscience. Modern microscopic
neuroscience is the field where the development of a new optical instrument enables a
fascinating scientific discovery, and that discovery then demands an upgrade to the instrument to
further the findings and vice versa. The scientists’ constant curiosity-driven demands and the
availability of the device, constrained by manufacturing limits, choreographed this ongoing
dance and created eras of different performances. It would be fair to say that it all began when
the first microscope inspired the emergence of the term ‘cell’.
The word ‘cell’ did not exist until 1665 when Robert Hooke published his
groundbreaking book, Micrographia, which is Latin for little pictures. This is the first report in
history on biological micrographs of small organisms and objects including, insects, the tip of a
needle and the cross-section of plants. In his 18th observation (out of a total of 60 observations)
Hooke describes the hollow structures in thin slices of cork. The discrete nature and unified
shape of the structures reminded him of the cells of a monastery, and he termed “cells” (Figure
1-1). This was the first occurrence for the word cell in conjunction with a biological system. In
his experiments, Hooke used a simple single-lens microscope to achieve high magnification and
a rather unrefined compound microscope to investigate larger fields of view [1].
Decades later, when glass grinding and lens polishing techniques were improved, Antony
van Leeuwenhoek picked up where Hooke left off and made the first description of the bovine
optic nerve using a 10x compound microscope. In the time between 1832 and 1834 Jan Purkyně
(Purkinje) and his student, Gabriel Valentin, used a then state-of-the-art 40x compound
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achromatic microscope made by the Austrian optical instrument maker Simon Plössl to examine
the structure of nerve tissue in animals and humans [2], [3]. In his publication “Über den Verlauf
Und Die Letzten Enden Der Nerven” (German for: on the course and the terminals of nerves)
Valentin makes the first depiction of a cortical neuron that has a “tail-like process” and
postulates that nerve fibers are not hollow as was the consensus then (Figure 1-2) [4]. A
controversial discovery that surely instigated the interest to dig deeper and see more.
Over the course of the years, optical components were further enhanced to boost
magnification and achieve better visualization of the microscopic structure of nerves. As a result,
more refined anatomical observations became possible like Robert Remak’s description of
myelinated and unmyelinated axons and Jan Purkyne’s (Purkinje) report on cerebellar cells. And
so, the dance goes on until advances in tissue preparation, histology and staining allowed Ramon
y Cajal to visualize different compartments of a neuron and pave the way for the neuron doctrine
in 1875 [5]. Anatomical investigation of the brain and the nervous system was -and still is -
fueled by the agile progression in optical manufacturing and the comprehensive exploration of
light properties, which are the essential elements of optical structural visualization. Anatomical
studies, therefore, continued to be at the forefront. Physiological and functional assessment of the
nervous system, on the other hand, took a slow time course.
Functional assessment of the nervous system pivots on two major requisites: 1- sufficient
knowledge of anatomy (structure) and 2- the maturity of the device technology. Observing the
activity of the nervous system requires a device that operates at a speed and a precision
comparable to the temporal dynamics of the neural activity. Hence, the dance between device
technology and functional neural recording is more of a solo dance challenge, where one dancer
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must wait (sometimes for decades) for the other to finish their performance before they get a turn
to perform.
A)
B)
Figure 1-1. The first historical report about single cells. A) Front cover of Robert Hooke’s book
“Micrographia: OR SOME Physiological Descriptions of MINUTE BODIES MADE
BY MAGNIFYING GLASSES WITH OBSERVATIONS AND INQUIRIES
thereupon”. B) Excerpt summarizing pages 112-116 of the book [6]
A)
B)
Figure 1-2. The first description of a single neuron. Top: original drawing and German text.
Bottom: digitally enhanced drawing and English translation of text [7].
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Galvani’s discovery of the electrical properties of nerve fibers in the frog nerves (1791)
was the first solo on nerve electrophysiology inspiring several scientists to use galvanic currents
to electrically stimulate nerves and measure the effect using Galvani’s galvanometer. However,
the limited speed and sensitivity of the electromechanical galvanometer hampered the
progression of electrophysiology and restricted it to stimulation experiments only. Therefore,
electrophysiology recording from nerve fibers was halted for decades. Alternatively, one could
think of it as the waiting phase in the solo dance challenge when the other is performing their
dance.
In this phase (1845-1902), Dubois Reymond and his students made major improvements
on the side of instrumentation development to allow the detection of small physiological currents
and their amplification. Reymond and his team built the “astatic galvanometer”, which was
relatively more sensitive than the regular galvanometer, yet still fell short on size, sensitivity, and
speed, limiting the investigation to large nerve bundles and muscles while fine nerve fibers were
still not recordable. Nevertheless, their novel tool allowed the observation of the extraordinary
phenomena of “nerve current” and “muscle current” and “negative variation” (negative
Schwankungen) which were proven quantitatively later by his student Julius Bernstein [6], [7].
Julius Bernstein’s ingenious invention of the differential rheotome extended the astatic
galvanometer and allowed plotting the time and magnitude course of the nerve impulse. The first
graphical representation of the “action current” (Aktionsstrom), now known as an action
potential, was published in 1868 [8] and marks the dawn of neurophysiological instrumentation.
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Figure 1-3. The first published graph of an action current (action potential)[8]
In 1875 Richard Caton recorded electrical activity from the brain surface of rabbits and
monkeys but his work was only recognized a few decades later in Hans Berger’s study of the
“Elektrenkephalogramm” (electroencephalogram aka EEG) of the human brain. Berger was the
first to describe brain waves of healthy and diseased brains as well as during different
physiological states in 1929. Still limited by the physical size of the recording instrument all
functional recordings, so far, are extracellular and on a rather macroscopic scale, e.g.; nerve
bundles, muscle fibers, and brain surface. Intracellular recordings were not achieved until the
1940s [9] and were done predominantly in in-vitro settings. The first in-vivo intracellular single-
unit recording was achieved by Sir John Eccles, his daughter and student Rosamond Eccles, and
Anders Lundberg when they recorded spikes (intra-cellular action potentials) from motoneurons
in the anesthetized cat in 1957. Their seminal work was enabled only by the arrival of smaller,
sharper electrodes that could penetrate the nervous tissue in vivo, amplifiers with high input
impedance, better current delivery systems, and relatively high-speed display systems to view
and record these minuscule physiological biopotentials [10], [11].
Further advances in microelectrode fabrication and packaging laid the groundwork for
the first multi-electrode bundle (as opposed to a single electrode) used by Marg and Adams to
record activity from many neural cells (multi-unit activity) at the same time from a patient during
brain surgery in 1967 [12]. This milestone can be considered the finale of the solo dance
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challenge of neural electrophysiology and the opening of the modern era of fusion dance - the era
of cellular functional imaging.
Cellular functional imaging is the fusion between microscopic imaging and functional
recording. It is the art of imaging neurons in action, as they fire and as they communicate. The
only impediment is that functional recording instrumentation was designed based on the
electrical and biophysical properties of neurons. Hence, the key was to tie the neural activity to
an imageable physical quantity, like light. And to be more specific, light emanating from the
molecules of a dye imaged by a fluorescent microscope. The first fluorescent dye, fluorescein,
was developed by Adolf von Bayer in 1871 but needed to wait for the introduction of the first
fluorescent microscope by Oskar Heimstadt to be utilized on a microscopic level in the
investigation of the autofluorescence of cells and tissue under ultra-violet (UV) light in 1914.
Going beyond the study of UV based autofluorescence seemed farfetched to Heimstadt as he
ended his paper stating: “If and to what degree fluorescence microscopy will widen the
possibilities of microscopic imaging only the future will show” [13], [14]. Nevertheless, the
major challenges of delivering external light, suppressing autofluorescence, eliminating
reflections, and capturing only the desired wavelength were overcome by a team of scientists
including Max Haitinger, who developed fluorochromes to enable secondary fluorescence,
Phillip Ellinger, who built the first prototype of an epifluorescence microscope in 1929, and
Johan Ploem who built dichromatic mirrors and beam-splitters in 1967. After that, fluorescent
imaging was used in various anatomical and immunological applications. However, correlating
fluorescence with function in live cells, i.e.: fluorescence correlation spectroscopy, was first
introduced by Magde et al. [15] when the orange fluorescence of DNA binding with ethidium
bromide was imaged. In the same vein arises the concept of fluorescently tagging calcium
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molecules in actively firing neurons. Since it was known by then that neural activity relied
causally and proportionally on intracellular calcium concentration [16]–[27], Roger Tsien set
forth on developing synthetic fluorescent calcium (Ca2+) indicators that would reliably report the
underlying neural dynamics [28]–[31].
Over the past few decades and till this very day, microbiological advances in the genetic
engineering of Ca2+ indicators and fluorescence microscopy have constantly pushed the limits of
optics to enhance the quality of the functional image (spatial resolution) and to convey more
information about the captured neural dynamics (temporal resolution). In stark contrast to
Heimstadt’s doubts and combining the best of the two worlds, this fusion dance granted
neurophysiology an exquisite technique, as neural activity can be precisely pinned, in time and
space, to neural anatomy. It is needless to state how fluorescence microscopy has revolutionized
our understanding of various neurological processes, disorders, and diseases and will continue to
shed more light on the mysteries of the human brain [32]–[45].
The long-standing synergy between fluorescent microscopy and neurophysiology laid the
foundation for more recent advances in microscopic technology, fabrication of miniaturized
optics and the genetic engineering of fluorescent indicators. Hence, further propelling the optical
approach to the functional and structural interrogation of neural circuits. The result was the
emergence of various optical methods, which makes the selection process quite intricate and the
comprehensive awareness of the technical underpinning indispensable, to guarantee proper
interpretation of the recorded dynamics. Furthermore, the inevitable compromise between cost,
resolution, focality, targetability, flexibility in behavioral paradigms and complexity is shared by
all-optical methods of in-vivo neural interrogation. Determining the optical method of choice for
an experiment can thus be a quite arduous task.
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Among the many optical methods is Fiber Photometry. Fiber Photometry stands out for
the exceptional flexibility in awake behaving experiments, the ability to reach very deep brain
areas, the ease of operation and the low cost. The Fiber Photometry is a versatile, cost-effective
optical method that records bulk fluorescent Ca2+ dynamics from the brain and reports it as an
aggregate one-dimensional signal, making its interpretation an unsolved challenge. This
dissertation, therefore, pivots on systematically characterizing the Fiber Photometry system to
appraise its underlying mechanisms of action and to offer new means of interpreting the
information acquired during in-vivo interrogation of neural circuit dynamics.
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Dissertation Overview
The focus of this dissertation is the systematic characterization of the single-photon Fiber
Photometry (FP), a fluorescence-based recording device of neural activity. The dissertation is
designed to be a self-contained document for both, the general as well as the proficient reader.
Chapter 2 presents background on the fundamental principles of optics as they apply to
fluorescence-based imaging devices. After a brief review of the properties of light and the basics
of single-photon light propagation in biological tissue, a framework for optically interrogating
neurons using fluorescent actuators and sensors will be provided. The experienced reader may
choose to skip to the end of Chapter 2. At the end of Chapter 2, the central problem will be
defined, and the specific research aims of this dissertation will be listed. These aims will then be
addressed one by one in Chapters 3 through 5. The experiments carried out in these chapters are
separate but complement one another to achieve the overall goal. Each chapter will reiterate the
aim of the experiment, provide some experiment-specific background, describe the methods used
and finally present the results and discuss their relevance. Chapter 6 will recapitulate the
findings, put them in perspective to the current state of the field, and discuss the potential
limitations of the experimental approach and provide an outlook on possible future directions.
Additional information is provided in the appendices.
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CHAPTER 2
BACKGROUND AND MOTIVATION
Let there be Light
Light, the visible spectrum of electromagnetic radiation, is one of the most intriguing
elements of life. It has fascinated the early human mind and became a chief consideration to
almost all ancient mythologies. Apollo, Eos, Baldr, Horus, Ao, and many other light deities were
conceived to impersonate the unexplained yet mighty phenomena of light. Scientific endeavors
to examine and investigate the nature of light are as old as mankind and have just come to
fruition in the early 20th century. Before that, the postulation that light could be used to record
and control the activity of individual as well as ensembles of nerve cells inside the living brain
would have been immediately convicted for heresy.
Fortunately, the physical and mathematical formulation for light is now well established
and permits the design of devices that precisely control light delivery, manipulation, and
collection. Moreover, recent advances in light-based technology, do indeed allow us to read
(record) and write (control or modulate) the activity of brain cells. The upcoming sections will
expound the technical details behind this de·Light·ful dialogue (read/write) with the brain.
… and there was Light
For thousands of years, mankind witnessed the bedazzling effects of light as it shimmers
in reddish hues on the water at sunset, as it softly spreads a radiant morning glow and as it
manifests in an iridescent rainbow during a rainy day. Puzzled by its mysterious and impalpable
nature early philosophers and scientists asked two very natural questions: “Where does light
come from?” and “What is light?”
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The Origin of Light
In answer to the first question came the following philosophy: “It is bright, and we can
see things when our eyes are open, and it is dark, and we can’t see when we close them.
Therefore, light must be emanating from our eyes”. The proper term for this theory is the
‘extramission theory’, which was founded by Plato (428 BC–328 BC) and advocated for by his
followers for almost a thousand years. Like Plato, Euclid (330-275 B.C.), Hero (10–70) believed
that light propagates from our eyes as rays that travel to objects in our field of view. Upon
striking an object, those rays interact with it, allowing the eye (or rather the brain) to perceive
size, shape, and color [46].
Over the span of another thousand years, some scientists argued against the extramission
theory, yet no one was able to provide evidence except for Al-Hazen. Al-Hazen laid down the
foundation to our current understanding of optics, light, and vision with his book, Kitab Al-
Manazir (Alhazen's Book of Optics 1027), that constitutes a cornerstone in the field of optics.
Al-Hazen placed two lanterns at different heights outside of a dark room and made a small hole
in the wall. He then stepped into the room and found that when both lanterns are on, their light
passed through the hole and created two bright spots on the opposite wall of the room. When he
turned one of the lanterns off and stepped back into the darkroom, the bright spot corresponding
to that lantern disappeared. Thereby, he provided the experimental evidence to prove that light
emanates from light sources like lanterns and candles and not from the eye. Al-Hazen’s simple
yet elegant experiment marked the fall of the long-standing extramission theory and set the stage
for the next question: “What is light”?
The Light Duality
“What IS light?” - A simple question if light was palpable or would take on one of the
three physical forms of matter: gas, liquid or solid. But, it doesn’t. Light has a dual nature, called
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the wave-particle or wave-corpuscular duality. In other words, light can manifest as a wave
and/or like an energized particle depending on the experimental setup1. It left scientists baffled
until the 1600s when two European scientists tried to explain refraction. Johannes Snell and
René Descartes took different experimental approaches to quantitively describe the phenomenon
of refraction, which is the change in direction of an incident light ray when it passes from one
medium to another, and eventually arrived at the same mathematical formulation, which is now
known as the Snell-Descartes law of refraction [47].
In the 1700s, Francesco Maria Grimaldi and Christiaan Huygens investigated the
diffraction phenomena and could only explain it by attributing a wave-like nature to the light
beam, and drew a one-to-one analogy between sound waves and light waves [48]. Sir Isaac
Newton was Huygens’ contemporary rival and adamantly opposed the wave-theory in favor of
his proposed corpuscular theory, which postulates that light is a beam of minuscule particles that
move at high speed through the ether and hence comply to the laws of gravity and inertia. Based
on Newton’s corpuscular theory, reflection occurs as particles bounce off the surface of a
medium and refraction is the result of the medium’s higher density that creates a stronger
gravitational pull on the particles. However, the corpuscular theory did not lend itself directly to
Newton’s observations on refraction. In one of the pioneering experiments described in his book
“Opticks: or a treatise of the reflections, refractions, inflections, and colours of light” [49],
Newton decomposed a sunbeam into different colors using two prisms and noticed that “Lights
which differ in colour, differ also in degrees of refrangibility” [Part I, page 13]. While his
discovery could give credence to the wave-theory, Newton insisted on the corpuscular nature of
light and argued that the different colors are different types of particles (Figure 2-1).
1 I wonder if the ancient deities could have done that!
28
Figure 2-1. Newton’s observation on refraction. Excerpt from The First Book of Opticks, Part I,
Page 30, by Sir Isaac Newton (1704).
The wave-particle dispute continued throughout the 17th century, with some experiments
showing the clear wave-like behavior of light, while others could only be rationalized by a
stream of particles traveling in a straight line. Since further delving into the history of the wave-
particle debate would be beyond the scope of this chapter, I will rudely ignore the efforts of
Young, Malus, Fresnel, Poisson, and Arago, and fast forward to the 19th century, the time of
James Clerk Maxwell. Maxwell is credited for the classical theory of electromagnetism and his
mathematical formulation ingeniously integrated the results of several other physicists
(Coulomb, Volta, Ampère, Faraday, and others) to demonstrate that electricity, magnetism, and
light are different manifestations of the same phenomena, namely the electromagnetic wave.
Maxwell postulated that since electromagnetic waves, akin to light, propagated through the ether
by undulations and undergo refraction and interference when passing through different media or
small gratings, then light must be an electromagnetic wave. He further asserted his proposition
by proving that light and electromagnetic waves travel through matter at the same speed [50].
29
Maxwell revealed the electromagnetic nature of light and by that also ingrained the wave-theory,
which ruled the roost until the rise of quantum mechanics in the early 1900s. Max Planck’s
quantum theory on the quantization of energy was the tacit precursor to the recovery of the
corpuscular theory.
Albert Einstein appreciated Planck’s idea of energy packets and used it to explain the
photoelectric effect, further argued that “According to the assumption considered here, when a
light ray starting from a point is propagated, the energy is not continuously distributed over an
ever-increasing volume, but it consists of a finite number of energy quanta, localised in space,
which move without being divided and which can be absorbed or emitted only as a whole” [51].
Einstein’s revered stature at the time gave his argument immense credence. However, the
wave specific phenomena like interference were still observed and were only explained with the
wave theory. The conundrum was solved in 1927, when Clinton Davisson and Lester Germer
finally proved the dual nature of light by hitting the surface of a nickel target with a beam of
accelerated electrons (a beam of particles) and observed a diffractive pattern (constructive and
destructive interference) on the detector, reminiscent of wave-behavior [52]. The experiment was
repeated by others to confirm that the Davisson-Germer experiment was not a fluke. The dispute
was once and for all resolved: Light is an electromagnetic wave that consists of minuscule
particles, called photons.
The previous section succinctly chronicled centuries of protracted scientific debates that
revealed the nature of light. The next section will present the common terminology that describes
the different physical qualities and quantities of light.
Basics of Illumination
The Electromagnetic (EM) spectrum is the range of all electromagnetic radiation, from
long, low energy radio waves all the way to very short, highly energetic gamma-rays. Optical
30
radiation is the portion that includes ultraviolet (UV), visible and infrared (IR) radiation. Light is
the very narrow band within the optical radiation spectrum, that is visible to the human eye
depicted by the ROYGBIV in Figure 2-2. ROYGBIV is the acronym that describes the colors
that compose the visible spectrum: Red, Orange, Yellow, Green, Blue, Indigo and Violet. In
contrast to the rest of the optical radiation spectrum, only the visible portion (light) can be
detected by the photoreceptors in the eye and elicits a ‘photometric’ response in the visual
system.
Figure 2-2. Electromagnetic spectrum. Diagram of the electromagnetic spectrum illustrating the
parameters of wavelength and frequency. Depicted are also the range of visible light
as well as that of ionizing and non-ionizing radiation.
There are three approaches to measure the emission and transmission of EM radiation.
The first is Radiometry, which is the most common and general measurement EM radiation.
Radiometry applies to the entire EM spectrum and reports radiative quantities using the SI-
derived units. For instance, the energy of an EM wave is reported in joules [J] and the power in
watts [W=1J/s]. However, those radiative quantities, as well as other quantities, also have a
quantum nature that can be expressed in terms of photons and photon flux to provide a physically
31
meaningful interpretation of the result in certain experiments. Actinometry, the second approach
to the measurement of EM radiation, emphasizes the quantum effect of light and is, therefore,
more suitable for photobiological, photophysical and photochemical applications that rely on the
particle-behavior of light. In other words, actinometry is the quantized version of radiometry.
The third measurement approach is Photometry. Photometry differs from actinometry and
radiometry in that it uses the human eye as the optical detector. The photoreceptors of the human
eye are sensitive to some colors more than others and our visual perception depends on the eye’s
adaptation to darkness or dimness. Photometry, therefore, measures only the visible portion of
the EM spectrum based on its ability to elicit a specific visual response. For that, it uses the CIE2
standard observer conversion function to convert radiant energy to luminous energy reported by
with units of lumens or candela [53]–[55].
The central concern of this dissertation is the characterization of the Fiber Photometry, an
optical device that uses visible light to elicit a photobiological effect and measures the response
with a silicon-based photodetector. Since the response of the device is captured using a
photodetector and not human visual perception, radiometry would provide a more suitable
measurement system. This section will, therefore, provide a brief overview of the most important
parameters of light and some of its radiometric quantities with no mention of their photometric
counterparts to avoid confusion3.
Parameters of Light
Speed of light: In a vacuum, the speed of an EM wave, and hence light, is measured to be
C = 3x108 m/s.
2 Commission Internationale de l'Éclairage: International comission on illumination
3 It should be noted here that the term photometry in the name of the device may be misleading, as it is not
associated with human visual perception
32
Wavelength: The wavelength λ is the distance between two successive crests (or hills) of
the EM wave. It’s measured in units of distance. The wavelength is inversely proportional to the
frequency of the EM wave (Figure 2-2 and Figure 2-3). The visible spectrum extends from
450nm to 650nm. Symbol: λ. Unit: nanometers [nm]
Frequency: The frequency is the number of full cycles (1 cycle = 1 wavelength) the EM
wave completes in one second. It’s measured in units of s-1 or Hz. The frequency is related to the
wavelength through the speed of light υ. The energy of the EM wave is directly proportional to
its frequency (Figure 2-2 and Figure 2-3). Symbol: f. Unit: Hertz or time-1 [Hz or s-1]
Photon: The photon is a single light particle that carries the Energy Ep [J]
𝐸𝑝 = ℎ 𝑓 (2-1)
where h is Planck’s constant = 6.63x10-34 [Js] and f is the frequency of the light in [Hz].
As such, the energy E of a light beam can be only an integer multiple of the energy Ep of a single
photon.
Figure 2-3. Electromagnetic wave. Diagrammatic illustration of frequency f, wavelength λ and
Energy E of an EM wave.
Radiometric Quantities
Radiant energy: The radiant energy is the amount of EM energy emitted, transmitted or
absorbed by a medium or object and is measured in units of Joules [J] or Watt-second. Symbol:
E. Unit: Joules [J]
33
Radiant power: The radiant power is the amount of radiant energy flowing per unit time.
It is measured in units of Watts [W]. Radiant power is also called radiant flux. Symbol: P. Unit:
Watts [W]
Radiant intensity: The radiant intensity is the radiant power per unit solid angle emitted
by a source. Symbol: I. Unit: Watt/steradian [W/sr]
Irradiance and radiant emittance: The irradiance and emittance are both radiant power per
unit area. However, irradiance is the power per unit area received by an object or medium and
while emittance is the power per unit area emitted by a source. Symbol: R. Unit: Watt/meter2
[W/m2]
Basics of Optics
Light can travel undisturbed for miles, if the medium does not change, with some
attenuation possibly caused by the medium’s absorptivity. Once light passes through an optical
interface, optical phenomena, like reflection and refraction, are observed. The following section
summarizes the basic behavior of light at boundaries as it is relevant for the propagation of light
in the FP system and in neural tissue.
Refractive index: Light travels at slower speeds in media of different densities. The ratio
between the speed of light in vacuum, 𝐶, and the speed of light in a material, υ, is called the
refractive index, n. The refractive index n is dimensionless and material specific. The refractive
index of the rodent brain is 1.36.
34
𝑛 = 𝐶
υ (2-2)
𝐸𝑝 = hυ
λ, since 𝑓 =
υ
λ (2-3)
Reflection: Reflection happens when light bounces off a surface. If the surface is polished
(like a mirror) the reflection is called specular reflection. In specular reflection, the light beam is
reflected at an angle equal to its angle of incidence only in the opposite direction. If the surface is
rough (or matte) it is called diffuse reflection and the light is reflected in many directions.
Diffuse reflection is also known as Lambertian scattering (Figure 2-4).
Figure 2-4. Illustration of Specular and diffuse reflection.
Refraction: A light beam bends (or refracts) when it passes through an interface between
media of dissimilar refractive indices. Refraction is how the light beam manifests the change in
velocity and wavelength as it passes from one medium to the other. The frequency of the light
beam, however, is unchanged. It’s imperative to point out here that since the refractive index of a
medium is wavelength dependent, refraction is wavelength-dependent as well. This means
different colors will bend with different angles. The amount of bending in the light beam
depends on the angle of incidence and the refractive indices of the two media. Refraction is fully
described by Snell-Descartes law of refraction:
𝑛1𝑠𝑖𝑛𝜃1 = 𝑛2𝑠𝑖𝑛𝜃2 (2-4)
35
Where n1 and n2 are the refractive indices of medium 1 and 2, respectively. θ1 is the
incident angle and θ2 is the refracted angle with respect to the normal to the surface (Figure 2-5).
Diffraction: The diffraction phenomena is the bending of a light beam after it passes
through a narrow aperture or slit. Diffraction is strongly wavelength-dependent and follows the
following formula:
𝜃𝑑 = 𝜆
𝑑 (2-5)
Where d is the width of the aperture and λ is the wavelength of the light (Figure 2-6B).
Cone of acceptance: The cone of acceptance defines the angular range from which light
can pass through an aperture and be collected by a detector (Figure 2-6C). The cone of
acceptance is measured given by the solid angle Ω of the aperture in [stereo radians or
steradians, sr]. In simple terms, the solid angle Ω is the 3-Dcounterpart of a 2-D angle [radians,
r] that spans a cone rather than a sector. The only catch is that it needs a reference sphere. In
more technical terms, 1 sr solid angle is the angle, which, while its vertex is at the center of a
sphere with radius r, would cut out a spherical surface area equal to the square of the radius of
the circle (Figure 2-6A-B). This means that 4π sr will cover a full sphere. The importance of the
cone of acceptance will become clear in the next section as it relates to the properties of the
optical fiber used in the FP system. Symbol: Ω. Unit: steradians [sr]
36
A)
B)
Figure 2-5. Refraction and reflection. Diagram illustrating the concepts of A) Refraction of an
incident beam on the surface and B) Diffraction of an incident beam on a slit.
A)
B)
C)
Figure 2-6. Cone of acceptance. A) 2D illustration of an angle. B) Description of the solid angle
(3D). C) Illustration of the cone of acceptance.
37
Propagation of Light
The FP system is an optical device that manipulates light with the final goal of collecting
Ca2+ fluorescence from neural tissue. The system relies on an optic fiber that delivers and
collects light to and from the brain. This section will describe basic principles that govern the
propagation of light in the optic fiber as well as in the neural tissue.
Propagation in an Optic Fiber
An optic fiber is a light guide made of glass or plastic and transmits light from one end to
the other by total internal reflection (TIR). An optic fiber is illustrated in Figure 2-7. Commonly
optic fibers are defined by the following set of parameters:
Diameter: Diameter d of the core of the optic fiber. The diameter of the cladding, the
protective layer around the fiber is also given sometimes.
Angle of acceptance: The angle of acceptance, θacc, is the 2D equivalent of the cone of
acceptance described previously (Figure 2-4C). It defines the width of the cone that can collect
light and is defined by the refractive indices of the core and the cladding.
sin(𝜃𝑎𝑐𝑐) = 1
𝑛0 √𝑛1
2 − 𝑛22 (2-6)
Numerical aperture: The NA is a unitless number that is indicative of the size of the cone
of acceptance of the fiber. The NA is defined by the angle of acceptance θacc and hence also
depends on the refractive indices of the core and the cladding:
𝑁𝐴 = 𝑛0 sin(𝜃𝑎𝑐𝑐) = √𝑛12 − 𝑛2
2 (2-7)
38
Total internal reflection: Light propagation through an optic fiber is governed by total
internal reflection (TIR), which relies on the basic optical phenomena of refraction and reflection
described in the previous section. The added constraint is that the incident light beam must arrive
at an angle smaller than θacc to be transmitted to the other end of the fiber via successive total
reflections at the core-cladding interface, i.e.: TIR. A beam of light with an incident angle that is
larger than θacc will be lost due to refraction at the core-cladding interface. Figure 2-7 shows the
concept of TIR as well as the acceptance angle of the fiber.
Figure 2-7. The properties of an optical fiber. Diagram showing the diameter d and the
acceptance angle θacc of an optical fiber. The refractive indices of the medium, core,
and cladding are n0, n1, and n2 respectively. θ1 is the angle of the incident light beam
and θ2 is the angle of refraction at the medium-core interface. The blue dotted line
shows a beam of light propagating through the fiber via TIR at the core-cladding
interface. The orange dotted line shows a beam of light that arrives outside the cone
of acceptance and is lost due to refraction (not transmitted by the fiber).
Propagation in Neural Tissue
For all-optical applications, it is important to differentiate between two kinds of media:
homogenous and inhomogeneous. As the name implies, a homogenous medium has optical
properties that are constant throughout the volume of the medium and is described with optical
parameters that take on constant values. On the other hand, an inhomogeneous (turbid) medium
exhibits optical properties that can change throughout the volume. Neural tissue is one of the
39
most turbid media due to the differential cellular structures, extracellular matrix density,
myelination intensity, and protein and lipid distribution that changes throughout the entirety of
the brain. The propagation of light in the brain is, therefore, less straightforward and requires the
assumption of homogeneity over infinitesimal volumes where the basic geometric descriptions
can hold. Integrating over all infinitesimal volumes then gives rise to an overall description of
the behavior of light in the brain as dictated by its optical properties.
The previous section described the different phenomena that occur when a beam of
photons (light) traverses a boundary, where the boundary can be any optical interface between
two media of dissimilar refractive indices. Neural tissue4 is a very turbid medium with various
types and sizes of objects that have different refractive indices, like extracellular matrix, blood
vessels, cell membranes, and organelles and other biological structures. Consequently, each
structure that makes up the tissue is an optical interface (boundary), through which the beam of
photons must propagate. At every boundary-crossing, the beam of photons will undergo
reflection, refraction and/or diffraction, as mentioned earlier. However, particle behavior will
now play an important role and has to be considered. As the beam of photons propagates through
the tissue, it will be subject to a lot of collisions and friction against the constituent biological
structures, resulting in either loss of energy, transfer of energy and/or change in direction. The
amount by which a beam of photon loses energy or changes direction as it travels through any
biological tissue is defined by the optical properties of that tissue. In the following, the main
optical properties of neural tissue will be explained.
4 All biological tissue presents a highly scattering medium, but the focus will be kept on neural tissue here.
40
Transmittance: Transmittance or transmission (T) is a measure of how much energy
remains in the beam of photons (or light beam) after it traverses a medium. It is the ratio between
the initial and final light intensity and can be given in % if multiplied by 100.
𝑇 = 𝐼
𝐼0 (2-8)
Absorption: The energy of a propagating light beam can be lost to the medium as it is
absorbed by the molecules or structures of that medium. The medium’s ability to steal the light
beam’s energy is called absorption coefficient µa and has units of mm-1. Absorption is related to
transmission by Equation 2-7. More on the different types of absorption (radiative and non-
radiative) in later sections.
𝐴 = 𝐼0
𝐼= 𝑙𝑜𝑔10 (
1
𝑇) = 2 − 𝑙𝑜𝑔10(%𝑇) (2-9)
Scattering: Turbid media, like neural tissue, exhibit variations in refractive index as a
function of space, i.e.: n (x, y, z) as opposed to a fixed value for homogenous media.
Consequently, the light beam will be deflected every time it encounters a change in refractive
index. This interaction is called scattering and is measured in terms of the scattering coefficient
µs [mm-1] or its inverse, the mean free path ls [mm]. As such the mean free path ls is the distance
a beam of photons can travel, on average, before it is deflected due to optical non-uniformities
and interfaces in the medium. Therefore, all the microscopic structures that constitute the tissue
are called scattering objects.
Attenuation: Attenuation is the compound effect of scattering and absorption in a
medium. It is characterized by the attenuation coefficient µa [mm-1]. Together, scattering and
absorption exponentially attenuate a light beam according to Beer-Lambert’s law:
41
𝐼(𝑧)
𝐼0= 𝑒−𝜇𝑧 = 𝑒−(𝜇𝑎+𝜇𝑠)𝑧 (2-10)
Where z is the penetration depth [mm] and I is the intensity of the light beam.
Anisotropy: The Anisotropy of a medium describes its preference for the direction of
scattering. Small objects, like cells, that are of a size comparable to that of the wavelength of the
light tend to scatter in a forward direction. The anisotropy factor 𝑔, therefore, is the average of
the cosine of the scattering angle 𝜃 and takes values from 0 to 1, with 1 being strictly forward
while 0 indicates isotropic scattering.
𝑔 = 𝐸𝑐𝑜𝑠𝜃 (2-11)
Fundamentals of Fluorescence
As mentioned earlier, the energy of a beam of photons can be absorbed by the medium or
tissue it is propagating through. The absorbed energy is transferred to the molecules of the
medium causing them to transition from a low energy level to a higher energy level. After a very
short period of time, the molecule returns to its original energy level and emits the absorbed
energy via radiative and non-radiative processes. The latter process is mainly thermal, i.e.: the
energy is released in the form of heat to the surrounding medium. The former process involves
the emission of another photon and is, therefore, called radiative, as it results in the emission of
one or more photons (the basic unit of an EM wave). While both processes, radiative and non-
radiative, occur upon the absorption of a photon (an energy packet), this section will focus
mainly on radiative emission. Specifically, fluorescent radiative emission.
Radiative emission is the process of emitting a photon (or photons) when transitioning
from a higher energy state (electronically excited) to a lower energy state (ground) and can be
categorized based on how the molecule was brought to the excited state. If a chemical reaction
42
was used it’s called chemiluminescence. If extreme heat was used it’s called incandescence. And
if UV or visible light is used it’s called photoluminescence. Photoluminescence includes
fluorescence and phosphorescence, which differ in the configuration of the electronic state and
the emission pathway. These processes are best described using a Jablonski diagram which
illustrates the different vibrational energy levels and the possible excitation and emission
pathways in a hypothetical molecule. Figure 2-8 shows a simplified Jablonski diagram that
would serve the scope of this dissertation. Due to the specific configuration of the electronic
states as well as the vibrational and rotational energy levels that allow for fluorescence, some
molecules are more predisposed for fluorescence than others. This kind of molecules is called
fluorophores, fluorescent probes, fluorochromes or fluorescent dyes.
In the Jablonski diagram shown in Figure 2-8, the different energy levels of a molecule
are marked with the letter S. The least energetic state is the singlet ground state S0 while S1 and
S2 are singlet excited states. Within each energy level, there are multiple vibrational energy
levels, which are represented by the thin horizontal lines. When a photon strikes a molecule, the
molecule can react in one of two ways: 1- absorb the entire energy packet, if it is sufficient to
reach an excited state, 2- not absorb the packet, if it does not fit any possible transition. In other
words, the energy packet must be absorbed in its entirety or not at all. Based on Planck’s
quantum theory, no partial absorption of a photon is possible, and the absorption of a photon is
hence an ‘all or none’ process. In some cases, however, the absorption of an energy packet may
simply bump the molecule to a higher vibrational energy level within the same state because a
transition to an excited state requires a larger energy packet. Or the absorbed energy may be
more than what is needed to transition to an excited state, in which case the remainder is
expended as vibrational and/or rotational relaxation (orange wavy lines in Figure 2-8).
43
Figure 2-8. Jablonski diagram. Showcased is the process of fluorescence through electronic
transitions between the ground state and excited states.
A more efficient way to describe this process is by considering an example. Assuming a
molecule absorbs a photon packet that is sufficient for a transition to an excited state, the
Jablonski diagram in Figure 2-8 depicts two (out of many) possible excitation (absorption)
transitions. The first blue arrow shows a transition from the lowest vibrational level of the
ground state S0 to the third vibrational level of the excited state S2 (S0(0) → S2(3)). The second
blue arrow presents a different excitation path from (S0(1) → S1(5)). In either case, the
absorption process is immediate and takes only ~1x10-15s (1 femtosecond). Also, regardless of
the final excited state and vibrational level, the molecule will release some energy in form of
vibrational relaxation or internal conversion to heat, without the emission of a photon, until it
reaches the first vibrational level of the first excited state S1(0). This non-radiative emission
usually takes ~1x10-12s (1 picosecond). Only a transition from the first vibrational level of the
44
first excited state (S1(0)) to any of the vibrational levels in the ground state will be accompanied
with the emission of a photon and results in fluorescence, which is relatively slow and takes
~1x10-9s (1 nanosecond). Suffice it to say the fluorescence pathway competes with other possible
relaxation pathways like intersystem crossing, quenching, and non-radiative relaxation (not
shown). The absorption and emission of photons is a cyclic process and fluorophores can repeat
this cycle thousands of times. However, excessive exposure to light can harm the fluorophore
and prevent it from fluorescing. This process is called photobleaching.
There are two important things to note in the fluorescence relaxation process: First, the
possibility of transitioning from any vibrational level within one state to any vibrational level
within another state means that the quantal size of the absorbed (S0(y)→Sx(y)) or emitted
(S1(0)→ S0(y)) energy packet can vary. Subsequently, excitation and emission are described by
spectra of variable width, where the width of the spectra corresponds to the range of possible
energy packets. As stated in Equation 2-3, the energy of a photon is a function of its frequency
and hence its wavelength. Excitation and emission spectra can, therefore, be regarded as the
probability density function for a photon with a specific wavelength to be absorbed and to trigger
the fluorescent emission of another photon. Second, the energy of the emitted photon is always
less than the energy of the absorbed photon as some of the energy is lost in internal conversion or
vibrational relaxation. Hence the emitted photon has a wavelength (red-shifted) that is longer
than the absorbed one (see Figure 2-2). This phenomenon is called Stoke’s shift, in honor of Sir
George G. Stokes, who discovered it and is the reason why the emission spectrum is always
shifted to longer wavelengths (lower energy) with respect to the excitation spectrum (Figure 2-
8). Excitation and emission spectra are usually expressed as the central wavelength λ [nm] at
which excitation/emission is most likely, λex & λem, and a number indicative of the width of the
45
spectrum on either side of λex and λem. The spectra illustrated in Figure 2-9 would be represented
as λex = 475/45 and λem = 530/45nm.
Figure 2-9. Example excitation and emission spectrum of a green fluorescent fluorophore. The
spectrum was generated using the publicly available Fluorescence SpectraViewer by
ThermoFisher Scientific Inc.
As discussed earlier, fluorescence-based microscopy originated as a spin-off from UV-
instrumentation used to investigate autofluorescence in small organisms. It was not until the late
1960’s that the first successful fluorescent microscope was reported. Joan S. Ploem, built the first
multiwavelength fluorescent microscope with vertical epi-illumination using 4 dichroic mirrors
mounted on a sliding tray to change the excitation wavelength between UV, violet, blue and
green. His design was based on dichroic mirrors that allowed the excitation beam to reflected
towards the specimen and the emission beam to be transmitted to the observer (Figure 2-10).
Needless to say, the advent of fluorescent-based microscopy revolutionized the field of cell
biology, as the power of live imaging of cellular and subcellular structures was combined with
the highly specific fluorescent labeling of molecular elements achieved with synthetic as well as
genetically encoded fluorophores.
46
A)
B)
C)
Figure 2-10. Different configurations of fluorescent microscopy. A) Trans-illumination,
Observer and light source are on opposing sides of the objective. B) Epifluorescence,
observer and light source are on the same side of the objective. C) Epifluorescence
with dichroic mirror.
Optical Interrogation of Neural Circuity
In an interrogation, the superior party conducts an interview with a suspect to elicit useful
information. Drawing the analogy, the suspect is the neural circuitry in the brain and the scientist
is the interrogator. And as the name implies, an ‘optical’ interrogation will use fluorescence to
elicit useful information. Now the interview part is when the scientist tells the neurons what to
do (stimulation or write) and then listens to what the same or other neurons have to say (record
or read). Figure 2-11 illustrates the concept of all-optical interrogation of neural circuits.
Optical interrogation of neural circuitry is an extremely powerful concept that emerged
with the turn of the century and was catapulted with the extraordinary advances in fluorescent
reporter and actuator probes. The basic idea is to probe the intertwined neural dynamics of a
brain region by switching cell-type-specific neurons on or off and observe the effect of the
perturbation by recording or imaging the resulting neural dynamics. This can be done in
technically any brain region that may play a relevant role in a cognitive modality like learning,
47
skill acquisition, habit formation or in neurological diseases, like Parkinson’s, depression,
epileptic seizures … etc. As such, a more time- and space-specific the optical interrogation will
provide more insight about the underpinning of neural disorders and potentially yield to
scientific findings that could pave the way to viable bed-side solutions. This is the aspiration of
the current tour de force in the development and technical refinement of fluorescent probes as we
as optical device technology [56]–[59].
Fluorescent probes can be broadly categorized, based on the mode of action, into
actuators and sensors. The following sections will provide a quick overview and list the most
commonly used fluorescent probes.
Figure 2-11. All-optical interrogation of neural circuit dynamics. Adapted from [60]
Optical Actuators
An optical actuator probe is a molecule that elicits a secondary effect once illuminated
with a certain wavelength. The most common and naturally occurring is rhodopsin, a light-gated
protein that serves as a sensory photoreceptor in algae and controls phototaxis (movement in
response to light). Other light-sensitive proteins, derived from rhodopsin, have been engineered
to control ion flux, cell excitability, and other cellular processes and constitute what is now
called the optogenetic toolkit. Optogenetics is the field concerned with the design of light-
48
sensitive proteins that express in the membrane of neurons to control the cell’s excitability in
response to the light delivered to the target area via an optical fiber. The two major subtypes are
inhibitory and excitatory optogenetic actuators, where the former pumps ions to hyperpolarize
the cell and the latter pumps ions to depolarize the cell and cause it to fire. As such, optogenetic
actuator probes are tools that allow us to ‘write’ to neurons, telling them when to fire and when
not to.
Optogenetic actuators can be delivered to any target region (deep or superficial) in the
brain via a viral construct that carries the genetic sequence of the light-sensitive protein. Once
inside the cell, it gets transcribed and expresses in the cell’s membrane. This viral construct can
be engineered to target a very specific subtype of neurons and allows for cell-type-specific
targeting. A long array of optogenetic actuators has emerged over the past decade with a spectral
variety that can serve many applications [56]. Figure 2-12 summarizes the most commonly used
optogenetic actuators.
Figure 2-12. Commonly used optogenetic actuators and their excitation spectra. Adapted from
[61]
49
As illustrated in Figure 2-12, optogenetic actuators require light of a certain wavelength
to operate. Not illustrated, however, is the fact that the light also needs to be of a minimum
strength (>1mW/mm2) [57]. The previous discussion about light propagation in turbid media
described the strongly scattering and attenuating properties of neural tissue that result in an
exponential loss in the magnitude of the traversing light beam as a function of depth. Since
optogenetic actuators require a minimum amount of irradiance (Rmin) then it is pivotal to estimate
the required initial irradiance that would compensate for the attenuation occurring in the tissue
and still be sufficient (above Rmin) to activate the optogenetic actuator at the target region.
Several studies sought to answer this question [57], [62], [63] by using optical fibers to
illuminate brain slices of varying thickness with light of different wavelengths and measure the
amount of light transmitted on the other side of the slice. They concluded that a light beam loses
more than 50% of its initial strength within the first few tens of microns after leaving the
illuminating fiber. This is a very significant conclusion given the fact that a particular amount of
irradiance is necessary to turn on the optogenetic actuator and it means that one needs to start
with a relatively high initial irradiance to make up for the expected loss.
Optical Sensors
While optical actuators initiate a process in response to light, optical sensors report an
ongoing process in response to light. In other words, optical sensors are probes that when
illuminated with light will provide a ‘readout’ on the current state of a neuron or a group of
neurons. That readout is in the form of light as well, an optical readout. Reminiscent of
fluorescent probes, optical sensors rely exclusively on fluorescence and differ only in their
coupling mechanism.
Fluorescent sensors can be coupled to 1- synaptic vesicles to report exocytosis and
endocytosis events occurring during synaptic transmissions, like FM dyes; 2- pH and indicate
50
changes in pH of synaptic vesicles, like synapto-pHluorins; 3- the membrane of neurons and
report changes in membrane potential, like fluorescent voltage-sensitive dyes (VSDs); and 4-
intracellular calcium to report changes in intracellular calcium concentration, like fluorescent
calcium-indicator dyes. The last two optical sensors have seen immense progress during the past
decade including the ability to become genetically encoded instead of being washed out after a
few hours, as is the case with dyes. Fluorescent genetically encoded voltage indicators (GEVIs)
and calcium indicators (GECIs) have been widely used in conjunction with fluorescent
microscopy to study various aspect of the brain in an all-optical neurophysiological approach
(Figure 2-15) [64]–[74], [74]–[100]. Transmembrane voltage changes can happen over different
timescales and report a rich repertoire of neuronal behavior. Thus, designing a voltage indicator
that can meet all performance requirements is a challenge. Nevertheless, there is a large variety
of voltage indicators that satisfy a subset of the requirements and meet the needs of certain
scientific questions [101]–[106]. Calcium indicators, on the other hand, have grown a lot swifter
and rendered fluorescent calcium imagining the most mature modality for recording neural
activity [107]–[114]. A brief digression will detail the mechanism of calcium indicators as it is
central to the work presented in this dissertation.
Calcium (Ca2+) is a unique metal ion that serves as the second messenger for
neurotransmitter release and is intimately involved in signaling the arrival of an action potential
and the subsequent generation of other cellular processes. It possesses a uniquely large
concentration gradient across the plasma membrane with an extracellular concentration that
ranges from 1.5 to 2.0mM and intracellular level of 50 to 100nM. The result is in an outside-to-
inside chemical gradient of 15,000–40,000:1 in addition to the electrical gradient that points in
51
the same direction (outside to inside at rest). The opening of a calcium channel thus exposes
calcium ions to an unusually large driving force from the outside to the inside [66], [115]–[117].
There are numerous pathways that allow the influx of Ca2+, through the various types of
Ca2+ channels. However, Ca2+ influx during the conduction of an action potential is
predominately mediated by voltage-gated Ca2+ channels that are present on the neuronal
membrane. Intracellular Ca2+ levels can rise 10-100-fold during the propagation of an action
potential within ~10ms and persists for a few tens of milliseconds.
Ca2+ indicators are fluorescent molecules that increase their fluorescent brightness when
bound to Ca2+. Hence, if they are designed to express in the cytosol, an increase in fluorescence
will be indicative of an increase in intracellular Ca2+ and hence the propagation of an action
potential. Many efforts have been devoted to improving the brightness and kinetics of GECIs
where brightness implies easier detection (higher SNR) and kinetics means faster binding to and
release from Ca2+ to avoid buffering. For instance, a single action potential lasts 3-5 ms at most.
In contrast, it took early GECIs, like GCamP3, ~130 msec to reach the peak of the transient and
a half decay time of ~600 msec, which is orders of magnitude slower than an action potential.
GECIs have evolved over the span of the years providing faster, more robust and sensitive
variants like the widely used GCamp6(f, s) and the recently proposed jGCamp7 series[64],
[110]–[113], [118].
It is essential to reiterate the bidirectional light-based nature of fluorescent Ca2+ imaging
as there are two separate but dependent light paths that play an instrumental role in the imaging
process: 1- the delivery of the excitation light to the region expressing the fluorescent calcium
indicator (GCaMP) and 2- the collection of the fluorescence emission light reported by the
GCaMP. While the basic concept of fluorescent microscopy is at the heart of calcium imaging,
52
different modalities have been proposed to allow fluorescent microscopy to reach various regions
in the brain and to perform in-vivo recording of neuronal activity. The next section will briefly
compare the most common modalities of fluorescent Ca2+ imaging.
Comparison of Fluorescent Imaging Techniques
Fluorescent microscopy endowed neuroscience with the transformational feature of
imaging or recording neurons in action. The ability to record and/or image electrophysiological
markers and to link them to behavior, cognition, memory formation or disease enabled a wide
range of unique experiments and can be considered a groundbreaking advance in neuroscience.
With neural electrophysiology taking a purely optical approach that relies on light-sensitive
actuator and reporter proteins, more and more scientists were inspired to design and build “all-
optical” device technology. Common among all-optical device technology are two main
functions: 1- the delivery of light with specific wavelength and magnitude to a target region 2-
the collection of light with a specific wavelength and of minuscule magnitude from a target
region. The difference among most optical device technology, on the other hand, allows them to
be loosely categorized into three major groups based on their fluorescence excitation technique
and focality: two-photon imaging (TPI), single-photon micro-endoscopy and single-photon fiber
photometry. The next section will portray and compare these fluorescence-based optical tools.
Two-Photon Imaging
As the name implies, two-photon imaging (TPI) entails the use of two photons, as
opposed to a single photon, to elicit a fluorescent response. Given the quantized nature of
fluorescence, this means that the total energy of the two photons together must be equal to the
energy carried by the single photon. In other words, each of the two photons will carry ½ of the
energy of the single-photon and hence have a longer wavelength. This also means that the low
energy two photons must hit the fluorescent molecule simultaneously (within 1 femtosecond) to
53
be absorbed. The probability of this quantum event to occur is infinitesimally low. Therefore,
two-photon imaging circumvents this by using exorbitant light powers (5 - 8 Watts) to focus very
fast pulses (femto-trains) of light on an infinitesimally small volume (point-like region) as seen
in Figure 2-13. This non-linear process increases the likelihood of fluorescent excitation if the
sum of the two photons is greater than the energy required to move the molecule from a ground
state to an excited state. The light beam is then scanned across the field of view (x and y-
direction) at very high speeds to sample the entire plane resulting in a 2D image. The recorded
2D image is at the focal plane of the objective and represents a very fine section in the neural
tissue. Changing the height of the objective then allows taking optical sections at different depths
in the z-direction.
While TPI features unprecedented resolving powers and sub-micron spatial resolution,
the major setback is the limited penetration depth, which is bounded to 300-400µm from cortex
due to the severe attenuation of longer wavelengths. Another limitation is the fact that the subject
must be head-fixed under the TPI microscope, which confines the range of behavioral paradigms
that can be investigated.
Figure 2-13. Single vs. Two-photon excitation. Cartoon comparison of single and two-photon
excitation mechanisms as well as the resulting excitation volume.
54
Single-Photon Micro-endoscopy
Unlike two-photon imaging, single-photon micro-endoscopy confers single energy
quanta (single photons) to elicit fluorescent excitation in a linear process as illustrated in Figure
2-13. This results in a less focused 2D image of coplanar neurons, but the penetration depth
limitation is overcome since shorter wavelengths are used. Single-photon endoscopy relies on
gradient index (GRIN) lenses that collect fluorescent neural activity from a focal plane and can
reach deep brain structures that are not readily accessible using the TPI setup. Usually, GRIN
lenses of 0.5mm - 1.8mm are implanted into the brain and are later connected to a miniaturized
fluorescent microscope and CCD camera. The entire setup is miniaturized and secured to the
subject’s head allowing it to move freely with no head-restraint. Hence, a wider range of
behavioral paradigms can be achieved. One could claim that single-photon endoscopy trades off
resolution for flexibility in the experimental setup and in recording depth, yet on the expense of
introducing reasonable tissue damage due to the large size of the GRIN lens.
Single-Photon Fiber Photometry
Similar to single-photon endoscopy, single-photon fiber photometry (FP) relies on a
linear fluorescent excitation (single photon) scheme. However, the GRIN lens is replaced with a
sleeker optical fiber (core diameter = 50-400 µm). While this reduces the insult to the tissue, the
major consequence is the complete loss of focality. There are two repercussions for the loss of
focality: 1- the readout is a 1D signal instead of a 2D image, and 2- the 1D signal is collected
from the volume beneath the fiber and represents the aggregate fluorescent activity of neurons
residing in that volume (Figure 2-13). Favorably, since the collected information is collapsed
into a 1D analog signal there is no need for any miniaturized instrumentation on the subject’s
55
head. Instead, the signal can be transmitted via an optical cable to a distant5 single-cell detector
leaving a relatively small footprint on the subject’s cranium. This is very convenient as it allows
simultaneous targeting of other brain regions in the same subject, which can be extremely
challenging with the microendoscope and rather impossible with TPI.
A)
B)
C)
Figure 2-14. Comparison of fluorescent imaging techniques. Comparison of sample data
recordings from different fluorescent imaging modalities. A) Two-photon image of
the mouse visual cortex (V1). B) microendoscope image of the rat’s prefrontal cortex
(PFC). C) fiber photometry signal from the rat’s vibrissal sensory cortex (vS1).
5 A distance within the boundaries of an average lab room.
56
Data collected with the three imaging techniques is shown in Figure 2-13. The high
resolution of the TPI stands out as individual neurons as well as neuronal processes can be easily
discerned (Figure 2-14A). Despite the loss in spatial resolution, single neurons can still be seen
with the single-photon micro-endoscopy image in Figure 2-14B, yet less defined and neuronal
processes are no longer visible. Data recorded with the FP shows as a single trace as seen in
Figure 2-14C, which echoes the lumped activity of a neural population without any spatial
resolution.
Table 2-1 summarizes the main advantages and disadvantages of the three optical tools
qualitatively. These tools represent the parent nodes from which several other modalities were
derived and developed. Yet, the same trade-off between, fluorescent excitation mechanism,
resolution, focality, cost and ease of operation persists, making the selection process an arduous
task that pivots on the scope of the scientific question. For instance, a study of cell-type-specific
interactions in a small cortical region would probably be best addressed using TPI’s high
resolving capabilities. Mechanisms of coplanar neuronal ensembles in deeper brain areas can be
captured by single-photon micro-endoscopes. However, listening to large, cell-type-specific
neuronal populations and inferring average ensemble activity can only be achieved by Fiber
Photometry or classical multielectrode array-based electrophysiology.
57
Table 2-1. Comparison of the three main fluorescent imaging techniques.
Two-photon imaging
(TPI)
Single-photon
endoscopy
Single-photon fiber
photometry (FP)
Fluorescence excitation Two-photon Epifluorescence Epifluorescence
Linearity Non-linear Linear Linear
Readout 2D image 2D image 1D aggregate signal
Resolving power +++ + 0
Field of view +++ ++ ++
Light power +++ -- ---
Focality +++ + 0
Penetration depth --- ++ +++
Tissue insult --- +++ +
Surgical footprint +++ ++ +
Cost +++ ++ +
Ease of operation --- + +++
Figure 2-15. Qualitative comparison chart. Comparison of the three fluorescent imaging
techniques in terms of cost, experimental flexibility, tissue damage, and penetration
depth.
58
Motivation and Research Aims
Fiber photometry offers many features that may not be obvious at first glance or when
contrasted with other fluorescent-based optical tools. The reason being that FP operates on a
different spatial scale, which despite its coarseness can address very significant basic science
questions when coupled to the right experiment design. Appendix A provides an exhaustive
technical description of the FP system.
When I learned about the Fiber Photometry and implemented it, it was the first optical
readout modality used in our lab. Our lab specialized in electrophysiological (ephys) recording of
neural activity using a variety of recording devices like, Michigan Probes, multi-channel
microwire arrays, and tetrodes. Therefore, the most reasonable way to confirm that my
implementation is working as desired was to compare the optical readout to ephys readouts,
which I did in two experiments. For the sake of brevity, I’ll succinctly present only one of the
experiments here. Both experiments are detailed in Appendix B.
The rodent whisker system lent itself as a very apt model to corroborate the viability of
the FP device by virtue of its clear somato-topical organization that allows a one to one mapping
of a single vibrissa (whisker) to a specific cortical column (barrel) in the vibrissal representation
of the somatosensory cortex (vS1). This means that mechanical deflections, which present the
sensory stimulus, of a particular whisker will result in a response in a well-defined cortical area.
Cortical sensory coding of stimulus parameters is abundantly studied, and it has been shown that
changes in sensory stimulus strength are represented as changes in cortical response probability
when multi-unit activity is recorded electro-physiologically [119]–[121]. I was curious to know
how the aggregate FP signal will compare to the multi-unit ephys recoding and whether it will be
sensitive enough to detect changes in sensory stimulus strength. Since this section serves as
motivation and not as experimental results, I’ll present the short answer. The answer was: Yes,
59
the FP signal was able to detect changes in sensory stimulus strength and, like in the ephys case,
coded this change as variation in cortical response probability. Figure 2-16 shows the
neurometric curve of the FP signal and the previously reported ephys recording. The neurometric
curves show strong agreement and similar saturation to high whisker deflection velocities.
This was a very surprising and intriguing result given the aggregate nature of the FP
signal and the complete absence of spatial resolution, which would suggest the loss of
information or reduced sensitivity compared to a multi-unit ephys recording. While this result
was significant in that it 1- validated my implementation of the FP system and 2- provided
evidence of reliable optically recorded sensory coding, it also instigated the core question of my
research: What IS the FP signal? And what is it made of?
A)
B)
Figure 2-16. Neurometric curve as a function of stimulus intensity. A) Fluorescence-based
neurometric data collected with FP from the rat vS1 showing the average (mean ±
s.e.m., n = 4) for a total of 16 recording sessions over 175 days. B) Neurometric
ephys data reported in [120]
60
Significance
Unlike, the other optical readouts the FP signal is not a 2D image that represents a well-
defined plane or a section within a volume of neuronal tissue with spatially identifiable neurons.
On the contrary, the FP is a one-dimensional signal that corresponds to the lumped neural
activity of a volume of neural tissue that lies underneath the optical fiber (Figure 2-14C).
Characterizing the volume from which the FP system can detect emitted fluorescence is thus
crucial for the correct interpretation of the information carried by the FP signal about the neural
circuits being investigated. Hence, the question is: How big is this volume, what defines it, and
how is the activity of individual neurons, that reside within this volume, compounded into the 1-
D FP signal.
Research Aims
The overarching goal of this dissertation is to construe the aggregate 1D FP signal by
conducting a systematic characterization of the FP device. This is achieved via three main aims:
• Aim1: Spatial characterization of the detection volume of the FP system in-vitro.
• Aim2: Validation of the in-vitro spatial characterization by reconstructing the ensemble
statistic of the 1D FP signal from its contributing sources in-vivo.
• Aim3: Empirical modeling of the detection extent of the FP system and development of a
tool to predict the detection volume of arbitrary optical fibers.
Each specific research aim will be thoroughly addressed in the next three chapters.
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CHAPTER 3
SPATIAL CHARACTERIZATION OF THE DETECTION VOLUME
In this chapter, the work done to fulfill the first Aim will be presented. The intention of
this Aim is to characterize the detection volume of the FP signal by performing direct
measurements of static fluorescing sources with known locations, first in phantom brain slices
then in acute brain slices. The detection volume represents the spatial extent, with respect to the
tip of the fiber, from which the fiber can detect fluorescence. The change in the detection
strength as a function of distance from the fiber tip is the spatial detection profile. The detection
volume and the spatial detection profile of four optical fibers are experimentally measured using
green fluorescent beads.
Background
As described in previously, the FP device relies on an optic fiber to deliver excitation
light and collect fluorescent emission light. Thus, the extent (breadth and depth) from which the
FP system can detect emitted fluorescence relies on three factors: 1) how much of the initial
excitation light power (Pex) propagates from the fiber through the tissue, which is called the
volume of influence, 2) the probability that Pex is sufficient to excite the GCamP6 molecule and
cause it to fluoresce at a certain point (x, y, z) with respect to the fiber tip, which is referred to as
the volume of emission, and 3) how much of the emitted fluorescence arrives back to the face of
the fiber within its angle of acceptance, θacc, without being scattered or absorbed by the tissue,
defined as the volume of detection (Figure 4-1A).
Factor #1 involves characterizing properties of light propagation from the fiber through
biological tissue and has been measured at different wavelengths in fixed brain slices of mice
and rats within the framework of optogenetic actuators [57], [62], [63] as described in Chapter
2.5.1 (Optical actuators). Factors #2 and #3 are concerned with the propagation of the light
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emitted by the GCamP6 and its detectability by the fiber. It is important to note that not all
GCamP6 molecules that are influenced (i.e. receive light) are being excited and that not all
fluorescing molecules are being detected. Hence, it is the intersection of these two sets (excited
fluorophores whose emission is detected) that constitute the detection volume.
To quantify the detection volume of the FP system via direct measurements of its extent,
green fluorescent protein (GFP) beads were used as point sources in phantom brain slices, which
presented the turbid media, to demonstrate the principle. In a subsequent experiment, the brain
phantom slices were replaced with live (acute) brain slices to better match the optical properties
of the rodent brain. The thickness of the slices was varied to simulate different depths of the
recorded volume of tissue. Furthermore, four optical fibers of different geometries were used to
investigate possible effects of diameter and numerical aperture (NA) on the detected volume
(Figure 3-1).
Methods
Fiber Photometry Signal Acquisition
A high-power LED (λex = 475 nm, Thorlabs, Newton, NJ) was used to deliver the blue
excitation light to the GFP beads. After exiting the current-controlled LED the light was
collimated, passed through the dichroic mirrors as described previously and transmitted to the tip
of the optical fiber with a patch cord (Figure 3-1). The power of the excitation light coming out
of the fiber was measured with an optical power meter (Thorlabs, Newton, NJ) at the free end of
the fiber. Green fluorescence was collected by the same optical fiber and routed to the femto-
watt photodetector consisting of a single photo-cell (1 mm2) (#2151, Newport, Corporation,
Irvine CA) through a green emission filter (λem = 535 nm) and a convex lens. The photodetector
transduced the detected optical signal to an electric analog signal which is then acquired by the
TDT data acquisition system (Tucker Davis Technologies Inc., FL). The four multimode optical
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fibers that were used had the following core diameter [µm] /NA combination of 400/0.50,
400/0.22, 200/0.5, 200/0.22. The recorded signals were analyzed using custom-written
MATLAB® (MathWorks Inc.) scripts.
Phantom Brain Preparation
To resemble the optical properties of the rat brain, a brain phantom was prepared as
described in [122], [123]. A 6.4% v/v skim milk (Millipore Sigma) solution was added to a 1%
Agarose (Sigma-Aldrich) solution and mixed until uniform. Once the solution is set, an agar-
milk block was affixed to the stage of a vibratome using glue. The block was then sliced into
different thicknesses starting at 50 µm until 750 µm thick slices were achieved.
Acute Brain Slice Preparation
All animal care and experimental procedures were approved by the University of Florida
Institutional Animal Care and Use Committee. Long-Evans rats received a large dose of
pentobarbital while deeply anesthetized. When confirmed areflexia, transcardial perfusion with
ice-cold ACSF was performed. Brains were extracted promptly after decapitation and were
placed in ice-cold ACSF for 5 minutes to settle before being transferred to the vibratome. The
slicing tub of the vibratome, as well as the slicing solution (ACSF), were maintained at 0-2 °C.
Two to three sets of 100 µm to 700 µm thick transverse slices (100µm step size) were collected
serially and the slices were maintained viable in a temperature-controlled (0-2°) ACSF bath
which was continuously perfused with O2.
Fiber Photometry Recording Procedure
The same procedure was followed for recording from phantom slices and live (acute)
brain slices (Figure 3-1C). Polystyrene GFP beads (F8844, ThermoFisher) had a diameter of
15µm which in on a scale similar to that of neuronal bodies with a diameter of 10 - 20 µm. The
beads were then placed on a glass microscope slide using a camel-hair brush. Appropriate bead
64
separation, i.e.: no overlapping beads was assessed under a fluorescent widefield microscope
equipped with a GFP filter. This was done to ensure that the beads are sufficiently separated,
avoiding the possibility to record from overlapping beads. Also, the beads had to be apart from
each other by a distance that is greater than twice the diameter of the used optical fiber to avoid
superposition from multiple sources and to ensure the detected signal comes from a single bead
An acute brain slice was then gently placed on top of the beads and the microscope slide. The
optical fiber was held vertically, as is the case in real-life FP recordings, using a digital
stereotaxic manipulator arm and manipulated in the horizontal plane using micrometer precision.
The micro-manipulator was used to move the fiber along the surface of the slice and to center it
over a fluorescent GFP bead. Fluorescence signals emitted by the beads were then acquired
while the fiber was stereotaxically translated horizontally along the x and y-axis with respect to
the GFP bead. The setup is depicted in Figure 3-2 only using clear for better visualization of the
beads.
A single scan is defined as the process of moving the optical fiber a distance of -500 µm
to +500 µm relative to the GFP bead when the bead is centered at 0 mm. For every slice
thickness, which presents a certain depth, six scans were collected from two non-overlapping
GFP beads. This was repeated twice for each depth using two slices of the same thickness.
Accordingly, there were six scans for every bead, and a total of four beads were recorded for
every depth. Therefore, every recorded data point was repeated 24 times, n = 24 trials. The
instantaneous spatial position (x, y, z) of the optical fiber was displayed on the stereotaxic LED
display and was simultaneously recorded by the data acquisition system to synchronize fiber
position with the detected fluorescent signal. This was achieved by a custom-built interface
board that allowed serial communication between the LED display and the TDT data acquisition
65
system. Two embedded hardware boards (sbRIO-9216 and NI-9263, National Instruments) were
programmed in LabVIEW software. The built-in serial communication port (RS-232) of the
stereotaxic display provided the current x, y, and z coordinates every 10 ms and sent it to the
sbRIO, which read the coordinates via its RS-232 port. The received coordinates (string data
type) were cast to three analog outputs (integer data type) by an embedded code implemented in
LabVIEW on the sbRIO. The analog output was then mapped using the NI-9263 that conformed
to TDT’s analog input range. This was an indispensable step that ensured firm knowledge of the
exact location of the tip of the optical fiber with respect to the recorded GFP bead at every
instance in time, which is essential for accurate characterization of the detection volume.
Figure 3-1. Experimental setup. A) Enlarged view of the red box in B showing the hypothetical
volume of influence (blue) and emission (green). Notice θacc, axial and off-axial axes.
B) Fiber Photometry system. C) Data collection procedure
66
A)
B)
C)
Figure 3-2. Agar-bead setup. A) Widefield fluorescent microscope picture of clear agar mixed
with 15µm GFP beads. B) same as A but showing reference grid placed under petri-
dish. C) Full setup, showing the optical fiber held by the stereotaxic arm and shining
blue light. [Photo courtesy of author]
Results
Moving the fiber towards or away from the fluorescent bead and increasing the thickness
of the tissue (brain phantom or acute slice) mimicked the effect of scanning the volume beneath
the tip of the fiber horizontally and vertically to determine the dimensions of the detection
boundary. The quantification of this boundary using a particular optical fiber and 15 µm beads
was associated with a few technical challenges. For example, extreme care had to be taken
during the manipulation of thin acute slices as they tend to fold and unfolding them can’t be
achieved without damaging the tissue. Placing the acute slices over the fluorescent beads also
required very gentle maneuvers to avoid tissue folding or beads to float over the surface of the
slice, which can compromise the accuracy of the localization process. Last but not least, speed of
data collection was critical to ensure the integrity of the acute brain slice remains the same once
removed from the bath, which can compromise the viability of the optical properties of the tissue
over time.
67
Volume of Detection from Phantom Slices
Brain phantoms can simulate various properties of the brain, like mechanical, optical,
thermal, electrical or magnetic properties. The agar-milk mix mimics the optical properties of the
brain only in a homogenous manner, i.e.: it does not exhibit the small optical inconsistencies
observed in actual biological tissue [122], [123]. The mechanical properties of the agar-milk,
however, are quite different from a rodent brain, especially in terms of texture, consistency and
tensile strength. As such, it provided a good testbed to practice the dexterous manipulations
needed with acute brain slices while eliminating the need for live brains. At each slice thickness,
which represents a different depth, a single fluorescent source (bead) had to be located before the
optical fiber could be centered around it. After localizing the fluorescent bead, the optical fiber
was centered over it by finding the peak in the detected fluorescent signal. The stereotaxic
coordinates of the manipulator's arm were then zeroed, and the optical fiber is positioned -500
µm away from the source center, horizontally, in the x or y-direction. The scanning process
started by translating the optical fiber at ~10 µm/s towards the source center, eventually bringing
it over the source center and passing it by +500 µm. During the scanning process, the volume
beneath the optical fiber is constantly illuminated and any detected fluorescence is recorded with
the TDT system. Hence, the detected FP signal increased monotonically as the optical fiber
approached the source, eventually reached a maximum when the fiber is exactly centered over
the fluorescent source, then started to decline as the fiber was moved away from the source.
Therefore, every scan followed a bell-shaped curve, whose y-abscissa is indicative of the
detection strength as a function of lateral distance, the x-abscissa (Figure 3-1, bottom right).
Characterization of the entire volume from which the optical fiber can detect fluorescent signals
required stacking the recorded curves vertically, along the z-axis, to generate a meridional
section of the fiber’s detection map (Figure 3-3A). Due to the cylindrical nature of optical fibers,
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revolving the meridional section for 360° around the z-axis fully describes the volume of
detection for a given fiber.
This scanning process was performed to measure the detection volume in phantom as
well as in the acute slice preparation described in the next section. The process was repeated for
all depths (slice thicknesses) and the detection map of the 400/0.5 optical fiber from the phantom
brain was generated as shown in Figure 3-3A. It was notable that the detection volume extended
relatively further away from the fiber tip compared to optogenetics studies that quantified light
propagation in highly scattering media in fixed brain slices. These studies focused on measuring
the volume of influence (forward light propagation) and did not consider the emission volume
(backward light propagation). The final results of those studies demonstrated more than 50%
reduction in the initial light intensity within 50-100 µm from the tip of the optical fiber [57],
[62], [63]. This rather exponential decay in the profile of influence is predominantly governed by
Beer-Lambert’s law and is depicted by the blue trace in Figure 3-3 B.
Figure 3-3. Spatial detection extent in brain phantom. A) Spatial detection map for a 400/0.5
optical fiber in agar/milk brain phantom slices in the meridional plane of the fiber (x-
z plane). B) Measured axial detection profile and axial influence profile as computed
using Beer-Lambert’s law and the optical properties of neural tissue.
69
The rapidly declining volume of influence reported by [57], [62], [63] contrasts with that
of the volume of detection measured in our experiment. A substantially different profile was
observed in the gradient of the detection volume along the fiber axis. We found that, while the
influencing light intensity (excitation) is reduced to 50% of its initial value at about 100 µm from
the fiber tip (and even about 50 µm according to [63]), the fluorescent source still received
enough excitation light to fluoresce and be detected with more than 50% probability at depths as
far as ~350 µm below the tip of the optical fiber (Figure 3-3B). This means that the spatial
gradients exhibited by the volumes of influence and detection are significantly different as can be
seen from the overlay of the axial detection profile and the axial influence profile reported
previously (Figure 3-3B).
Volume of Detection from Acute Brain Slices
The discrepancy observed between the detection and influencing profiles could be
explained by the difference in optical properties between the phantom slices and the acute brain
slices. Therefore, we asked whether the detection profile obtained in phantom brains are
similarly observed in acute brain slices that have more biological inhomogeneity and scattering
effects compared to the phantom brain preparation. We also asked whether the detection volume
is a function of the optical fiber geometry, expressed hereafter as the diameter[µm]/ NA
combination. Four optical fiber geometries were compared by varying the core diameter (large =
400 µm and small = 200 µm) and the NA (high = 0.50 and low = 0.22). After collecting six scans
per bead, two beads per slice thickness and two slices per thickness, the resulting 24 trials were
stacked vertically to create a meridional section, which was then revolved around the z-axis. We
found that both the diameter and NA of the optical fiber had differential effects on the size, shape
and spatial gradient of the detection volume (Figure 3-4). In particular, the x-axis represents the
lateral distance from the center of the optical fiber and is normalized to each fiber’s radius, rf.
70
The y-axis represents the depth from the tip of the fiber, which is usually referred to as the z-axis
during an actual recording. The geometry of the optical fiber (diameter[µm]/ NA) is indicated in
the bottom right corner and the graphed iso-contours indicate the 90%, 75%, 50% and 25% of
the maximum detection strength (red, orange, green and blue respectively).
In particular, it was noticeable that the axial boundary of the detection volume was
significantly larger for low NA fibers compared to high NA fibers, where the 50% and 25% is-
contours were approximately 100-150 µm deeper for the latter (t-test, p < 0.002, α = 0.05, n =
24). We also found that the axial detection profile of low NA fibers was associated with slow
decline compared to high NA fibers that exhibited much faster decay as a function of distance
from the fiber tip. The difference in axial detection profile plays a very important role in how
fluorescent sources along the axial direction contribute differentially to the over-all FP signal. In
other words, it defines the share of each source towards the final lumped 1D FP signal.
Detection depth was not the only parameter that was influenced by the geometry of the
optical fiber. The detection from the periphery or the breadth of the detection volume was
impacted by the diameter of the optical fiber rather than the NA. The detection from the
periphery occurs along the off-axial direction defined by the acceptance angle, θacc, of the fiber
as illustrated in Figure 3-1 and previously described in Chapter 2. Specifically, optical fibers that
have a small diameter fiber detected off-axis fluorescent sources with about 50% more detection
strength compared to large diameter optical fibers as seen in the right panel of Figure 3-4.
In addition to the depth and breadth of the detection volume, its shape also varied
significantly depending on the NA of the used optical fiber. Figure 3-5 shows the 3D shape of
the detection volume that results from revolving the meridional section 360° around the z-axis.
71
While high NA (0.50) optical fibers detected a rather conic volume, low NA (0.22) fibers
collected fluorescence from a frustum-shaped volume (Figure 3-5).
Finally, the physical volume bounded by each detection iso-contour was quantified
analytically by calculating the volume enclosed by the convex surfaces created by the iso-
contours in 3D. Table 3-1 summarizes the value of the detection volume of each examined
optical fiber and is categorized by iso-contour percentage.
Figure 3-4. Spatial characterization of detection volume as a function of fiber geometry in acute
brain slices. A) Left: Detection extent in the meridional plane the high NA fiber.
Middle: same as A but for the low NA fiber. Right: axial (solid line) and off-axial
(dashed line) detection profiles. B) the same as in A but for small diameter (200µm)
fiber.
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Figure 3-5. 3D Volume of detection for each optical fiber. A) Left: Volumes enclosed in 90, 75,
50 and 25% iso-contours for large/high NA fiber. Right: for low NA fiber. B). same
as A but for small (200µm) fiber
Table 3-1. Detection volume for different optical fibers.
Fiber Detectable Volume (x105 µm3), [µm]
<75% <50% <25%
400/0.50 3.2 [68] 16 [117] 58 [180]
400/0.22 8.7 [95] 47 [168] 156 [250]
200/0.50 1.9 [57] 10 [100] 38 [156]
200/0.22 9.2 [97] 27 [139] 59 [181]
Note: The geometry of each optical fiber is listed in the first column. Each subsequent column
lists the volume enclosed within the 75%, 50%, and 25% detection contours. To develop a better
sense of the physical size of the detection volume, the length of one side of a perfect cube that
would encompass the quantified detection volume is reported in square brackets. In other words,
the values within square brackets denote the cubic root of the detection volume and present the
side of a cube of equivalent volume.
73
Discussion
The detection volume of the optical fibers was measured directly using fluorescing
sources (GFP beads) in brain phantom and in acute brain slices. The phantom preparation served
as a pilot experiment and revealed a stark difference between the previously reported influencing
profile and the detection profile measured in this experiment. Considering the exponentially
decaying profile of influence, one would presume a similarly shaped detection profile. However,
the detection profile showed a rather smooth spatial decline. We, therefore, conducted the same
experiment using acute brain slices to allow for a better comparison with the volume of influence
reported by optogenetics studies that were carried out in acute and fixed slice preparations. The
results from the acute slice preparation confirmed the smooth spatial decline in the detection
profile, which has direct implications on the extent to which individual neurons, neuropil, and
other structures could contribute to the FP signal.
Furthermore, we considered four optical fiber geometries that are commonly used and
offered good contrast in terms of diameter size (400 vs. 200 µm) and NA (0.5 vs 0.22). Our data
suggest that the fiber diameter and NA play critical roles in defining the size and shape of the
detection volume, in accord with a recent study that conducted a similar experiment to measure
the detection extent of optical fibers [124]. The study investigated the detection volume of three
optical fibers (50/0.22, 200/0.39 and 200/0.5) analytically and numerically. The analytical
approach Pisanello et al. presented in their study is a direct implementation of the theory from
[125], which describes the detection volume of an optical fiber-based on the geometry of the
cone of acceptance only, without the consideration of the optical properties the medium. Hence,
the unreasonably large detection volumes (up to 800 µm) were expected. On the other hand, the
numerical modeling of the detection volume in a homogenous medium yielded results that are
comparable to the detection extent we measured using the phantom-brain, which presents a
74
homogenous medium as well. At the end of the study, Pisanello et al. quantified the detection
extent of two optical fibers (200/0.39 and 200/0.5) in acute brain slices and the reported
detection volume for the 200.0.5 fiber is comparable to the volume we measured in this study.
One important contribution compared to the work reported in [124] is that we used a
single photon illumination scheme and the same photodetector to accurately replicate the
conditions under which FP recordings are readily conducted. Pisanello et al., on the other hand,
used a combined confocal/two-photon illumination setup and photomultiplier tubes (PMTs) that
are rarely used during FP recordings, possibly hindering the extension of their results to other
setups. Other attempts to quantify the detection volume were performed as an ancillary to the
main study and were either specific to a certain brain region of the mouse brain [126] or used an
unrealistic fluorescent source [127].
Furthermore, the findings illustrated in the previous section instigate a very significant
observation considering the ramping number of recent studies that utilize the FP system to record
neural ensemble activity from various brain regions (Table 3-2). Many FP studies rely on the FP
system for its low cost, versatility, ease of operation and flexibility in awake behavioral
experiments. However, it is often the case that the same optical fiber, that was used in a cited
study, is chosen with little consideration for its suitability [128]–[130]. The previous findings, on
the other hand, suggest that deliberate selection of the geometry of the optical fiber is crucial to
determine the specifications of the detection volume. In other words, the type of study and the
targeted brain region should guide the selection of the diameter and NA combination of the
optical fiber that will be used for an FP-based experiment.
75
Table 3-2 Summary of recent FP studies listing used animal model, target region(s), type of investigation and geometry
(diameter[µm]/NA) of the optical fiber utilized in the study.
Animal
Model Target Region(s) Investigation Optical Fiber Power Ref
Mouse
PFC, CA1, BLA, LH,
VTA, NAc & BNST
simultaneously
Real-time activity relationship
among many brain regions during
social behavior
400/0.48 2.5-50 µW [131]
Mouse DRN Acute social isolation 400/0.48 10-50 µW [132]
Mouse SON of the hypothalamus Ingestive behavior 200/0.39 100-200 µW [133]
Mouse Lateral hypothalamus Eating behavior 200/0.37 100 µW [127]
Mouse NAc Drug seeking addiction 400/0.48 30-75 µW [134]
Mouse vS1 and OFC Sensory integration 200/0.39 --- [135]
Neonatal
Mouse Temporal lobe
spontaneous activity and early
network oscillations (ENOs) 200/0.48 250 µW [136]
Mouse vS1 Sensory exploration 440/0.22 --- [65]
Mouse Auditory cortex Auditory network calcium
transients’ (NCaTs) 200/0.48 10-100 µW [66]
Mouse Dorsal STR Voluntary action initiation
Hybrid fiber setup exc.
fiber 3.5 µW and det. fiber
105 µm, NA not reported
100-120 µW [67]
Mouse V1 and dLGN thalamus
and VPM
Corticothalamic slow oscillations
of non-Rem sleep 200/0.48 <0.1mW/mm2 [137]
Mouse V1 Sensory integration 200/0.48 30 µW [138]
Non-human
primate M1 Motor movement mapping 200/0.48 --- [68]
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Table 3-2 Continued
Animal
Model Target Region(s) Investigation Optical Fiber Power Ref
Mouse striatal projection neurons Operant conditioning
Hybrid fiber setup exc
fiber 3.5µW and det fiber
105µm no NA reported
100 µW [69]
Mouse VTA-Nac projections Social behavior 400/0.48 10-50 µW [70]
Mouse CA1 Locomotion initiation and
velocity 200/0.37 0.6-1.2 mW [71]
Mouse ARC of the hypothalamus and
PVH Feeding circuits and behavior 400/0.48 70 µW [139]
Rat S1FL
Neural networks activation due
to sensory stimulus neuronal
response
200/-- 1.3µW/mm2 [140]
Rat (S1FL)
Relationship between blood
oxygen level–dependent
(Bold)and neural activity
200/0.48 <1 mW [72]
Mouse mPFC and M1 Motor Skill learning 105/0.22 100 µW [126]
Mouse NAc Stress Susceptibility 400/0.4 --- [73]
Mouse PBN–projecting neurons Itch sensation --/0.37 --- [141]
Mouse ARN gonadotropin hormone (GnRH)
release 400/0.48 50 µW [142]
Abbreviations: PFC: Prefrontal cortex. CA1: hippocampal area CA1. BLA: Basolateral amygdala. VTA: Ventral tegmental area. NAc:
Nucleus accumbens, LH: Lateral hypothalamus, BNST: Bed nucleus of stria terminalis, DRN: Dorsal raphe nucleus, SON: Supraoptic
nucleus, OFC: orbitofrontal cortex, vS1: vibrissal primary somatosensory cortex, STR: striatum, V1: Primary visual cortex, dlGN:
dorsal lateral geniculate nucleus, VPM: ventral posteromedial nucleus, M1: Primary motor cortex, ARC: arcuate nucleus, PVH:
paraventricular hypothalamus, S1FL: primary somatosensory cortex, forelimb region, PBN: parabrachial nucleus, ARN: arcuate
nucleus kisspeptin, exc: excitation, det: detection.
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CHAPTER 4
VALIDATION OF THE SPATIAL CHARACTERIZATION
The preceding chapter showed how the shape and size of the detection volume depend
heavily on the geometric specification of the optical fiber, specifically the combination of
diameter and numerical aperture (NA). Due to the arduous nature of conducting direct
measurements using 15 µm fluorescent beads, the investigation was carried out in an in-vitro
preparation and was limited to quantifying the detection volume of four optical fibers1. There are
two main limitations of this investigation. First, it was performed in-vitro in acute brain slices
and second, only four optical fibers were considered. This chapter will focus on the first
limitation while the second limitation will be addressed in the next chapter.
The in-vitro acute brain slice preparation offered a good approximation regarding the
inhomogeneous optical properties of the rodent brain, but it cannot be claimed that the optical
properties are identical to their in-vivo counterpart as tissue integrity may be compromised
during the recording process. Therefore, validation of the direct measurements in an in-vivo
setup is the second Aim of this research.
Premise and Hypothesis
The goal of Aim2 is to validate the direct measurements of the detection volume in the
mouse visual cortex (V1) during the presentation of drifting orientation gratings. V1 is a well-
characterized cortical area where sensory-evoked responses from single neurons are referred to
as tuning curves. Turning curves define which visual stimulus, in this case, which orientation of
the drifting gratings a certain neuron is most selective to [143], [144]. Neurons that are selective
to a particular orientation are grouped in a columnar organization in highly visual mammals like
1 Likely the reason why Pisanello et al. only examined two fibers in their in-vitro preparation too.
78
the cats, ferrets, tree shrews and the non-human primate [145], [146]. In the rodent, however, this
columnar organization is not evident. Recent studies in the mouse visual cortex showed that
neurons that respond to the same orientation have a topographical organization of fuzzy patches
rather than columns [107], [147]–[149].
The difference in the topographical organization doesn’t have a consequence on the
tuning or selectivity when single cells are considered. However, when considering a group of
cells or an ensemble, as is the case with the FP, then the topographical organization of patches
will have a unique effect on the recorded signal. The proportion of differently tuned neurons that
compose a patch and where the optical fiber falls relative to the different patches will result in
different FP signals. Simply stated, the recorded signal will represent the combined ensemble
tuning of the neurons within the detection volume of the optical fiber. The ensemble tuning
recorded by the optical fiber differs from one location to another throughout V1 as each location
falls within a different patch and has a different composition of tuned neurons. This is a desired
feature, which allowed the validation of the direct measurements of the detection volume in
different regions.
The premise is that the combined tuning of the constituent sources will give rise to the
overall ensemble tuning, where the tuning of the sources and the ensemble is defined by the
tuning statistic 𝑇𝑛,𝑑(𝜃𝑘), and 𝑇𝐹𝑃(𝜃𝑘), respectively. Therefore, volumetric optical scanning (OS)
of the detection volume using epi-fluorescent CCD-imaging was performed to record from single
sources and to reconstruct the overall ensemble statistic using a linear mixture model (LMM)
(Figure 4-1A). Optical sectioning was one of the possibilities but was ruled out as it relies on
two-photon illumination, which is nonlinear and fundamentally different from the single-photon
illumination scheme used in FP.
79
The LMM derives a pseudo-population2 statistic, 𝑂𝑆(𝜃𝑘) from the constituting single
sources’ statistic. Taking advantage of the linearity of the problem, the LMM assigns a weight
wd(x, y) to each source statistic 𝑇𝑛,𝑑(𝜃𝑘), that falls within the boundary of the detection volume,
at every depth d, based on its spatial location x ,y with respect to the fiber. Accounting for all
depths then yields a composite pseudo-population statistic 𝑂𝑆(𝜃𝑘) that corresponds to the
recorded population FP statistic 𝑇𝐹𝑃(𝜃𝑘), (Equation 4-1 and Figure 4-1E). The pseudo-
population statistic, 𝑂𝑆(𝜃𝑘) was contrasted to the observed population statistic, 𝑇𝐹𝑃(𝜃𝑘),
recorded with the FP (Equation 4-2), where 𝜃𝑘represents the eight different visual stimuli (k
=1,..8 corresponding to 8 orientations 0° ,45°, …, 315°). The values of the weights and
boundaries are adapted from the direct measurements reported previously [150] (see Figure 3-3).
A more detailed mathematical formulation of the tuning statistic, as derived from the recorded
calcium trace, and of the LMM can be found in Appendix C.
Figure 4-1E illustrates a hypothetical volume of tissue, where neuronal sources are
distributed within the 90, 75, 50 and 25 % detection contours of a fiber. Taking an optical scan at
depth d = 1 will result in circular shaped boundaries in the x-y plane as opposed to the parabolic
contours in the y-z plane. Accordingly, sources within the red boundary will be weighted by 0.9
while sources inside the blue boundary will contribute by 0.25. The LMM directly implements
the detection boundaries of the in-vitro study. As such, if the in-vitro direct measurements are
valid in-vivo, then the pseudo-population statistic, 𝑂𝑆(𝜃𝑘) should approximate the FP- recorded
population statistic 𝐹𝑃(𝜃).
2 The terms ensemble and population will be used interchangeably.
80
𝑂𝑆(𝜃𝑘) = ∑
𝐷
𝑑=1
∑ 𝑤𝑛,𝑑(𝑥, 𝑦)𝑇𝑛,𝑑(𝜃𝑘)
𝑁
𝑛=1
(4-1)
𝑇𝐹𝑃(𝜃𝑘) ≈ 𝑂𝑆 (𝜃𝑘) (4-2)
The proposed hypothesis mandates that the FP and OS responses must be recorded from
the exact same location in V1. To achieve this, a coordinate system, whose zero is centered at a
reference point marked on the subject’s head plate, was implemented (Figure 4-1C). Figures 4-
1D-E summarizes the proposed hypothesis and illustrates the experimental setup.
Methods
Surgical Procedure
All animal care and experimental procedures were approved by the University of Florida
Institutional Animal Care and Use Committee. Wild type C57B6/J mice (n = 2) received bilateral
craniotomies of 5mm radius centered over V1 (ML: +/-2.5 mm, AP: -3.5 mm, DV: -0.3 - -0.5
mm). 1 µL of AAV1.Syn.GCaMP6f.WPRE.SV40 (titer: ~ 2.5x1012 genomes/mL) was injected
in each hemisphere at a rate of 75 nl/min. Half of the volume was infused at -0.5 mm before the
tip of the needle was retracted to -0.3 mm to inject the rest of the volume. The needle was fully
retracted after a 10-15 minute wait period. Finally, each craniotomy was covered with an
optically clear cranial window (#1943 5 mm, Bellco Glass, Inc.), which was secured to the skull
and the metal head plate with dental cement. The metal head plate was designed in house using
SolidWorks®. The design was fabricated with stainless steel 304 (304SS) material using
professional laser cutting (https://www.lasercuttinginc.com/). Subjects were monitored post-
operatively to ensure a healthy recovery. Expression spread was monitored weekly and after the
third week, a reference point was marked on the metal head plate (Figure 4-1B-C and Figure C-
1). Coordinates to different locations in V1 were measured with respect to this reference point
which allowed the exact spot to be revisited between sessions of FP and OS data collection.
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Fiber Photometry Recording
A current-controlled blue LED (λex = 475 nm, Thorlabs, Newton, NJ) was used for GFP
excitation. The light was collimated and routed through a patch cord to the tip of an optical fiber
(Figure 1B). The power of the light emanating from the fiber was measured with an optical
power meter (Thorlabs, Newton, NJ) and set to 80 µW before every recording session. Emitted
green fluorescence (λem = 535 nm) was collected by the same optical fiber and routed to a single
cell (1 mm2) femto-watt photodetector (Newport, Corporation, Irvine CA) via a green emission
filter and a convex lens. The photodetector converted the optical signal to an analog signal that is
then acquired by a TDT data acquisition system (Tucker Davis Technologies Inc., FL) for
storage and later analysis. Custom MATLAB (MathWorks Inc.) scripts were written to analyze
the recorded signal.
Data Acquisition
The recording setup involved three separate components:1- Ca2+ signal acquisition in
form of an FP signal or a CCD camera image, 2- Visual stimuli display and 3- Delivery of the
stimuli by switching the screen on and off. These three components had to be precisely
synchronized and could not be controlled by different PCs. The TDT system was therefore
programmed to send control signals to trigger each one of those components and to receive
acknowledgment signals in response. All data were collected on the computer that runs the TDT
system. The subjects were head-fixed under the imaging modality (FP, 1p or 2p) by clamping the
head posts.
Visual Stimulation
Drifting sinusoidal orientation gratings were displayed on a presented on a 9.7-inch LCD
screen (LG LP097QX1, Adafruit) that was positioned at eye-level about 15-20cm away from the
eye to ensure coverage of the entire visual field. The screen contrast was set to 100% and the
82
spatial frequency was set to 0.4 cycles per degree. The gratings were presented at eight
orientations with a 45° step. The eight stimuli were presented randomly for 4 seconds and
repeated ten times. The inter-stimulus-interval was 4 seconds. The screen was programmed using
the Psychophysics Toolbox in Python and was controlled to turn on and off with a TTL signal
generated by the TDT system.
Epi-fluorescent Volumetric Scanning
White light from a high-power mercury lamp (X-Cite 120Q Excelitas Technologies
Corp.) was used for the epi-florescent imaging. The light was first passed through an excitation
to filter out all wavelength except blue (λex = 475 nm) to excite GCamP6f. The blue light was
then attenuated from ~8mW to ~80µW with an optical density filter (NE20A-A, OD:2, Thorlabs
Inc.) to match the power used during FP recording. A 16x/0.8NA objective (Nikon) was used to
focus the light on the brain. The focal plane was then adjusted to different depths by moving the
objective along the z-axis. Emitted fluorescence was collected by the same objective and filtered
by an emission filter (λem = 535 nm) before it was collected by a CCD camera (Electro Retiga,
QImaging Inc.). Images captured were acquired by the CCD camera’s proprietary software
Ocular at an exposure of 60 ms and 2x2bining. Image acquisition was triggered via a TTL signal
from the TDT and every frame acquisition henceforth was reported via another TTL signal to the
TDT system.
83
A)
B)
C)
D)
E)
Figure 4-1. Epifluorescent volumetric scanning setup and LMM. A) Illustration of the theory of
volumetric optical scanning. Left: initial position of the objective with maximum
fluorescence collection occurring from the focal plane. Right: Displacement of the
objective in the +/z-direction causes the focal plane, and thus the plane from which
fluorescence is maximally collected, to move up/down. B) Viral injection of
GCaMP6f in V1 followed by placement of a cranial window and the metal head-
plate. 2p, 1p Epifluorescence, and FP data are recorded through the cranial window at
the same anatomical location. C) Anatomical locations of the recorded data within V1
with respect to the reference point. Blue and red dots correspond to the subject1 and 2
(n = 2). Scale bar = 1 mm. D) Visual stimulation setup. Moving orientation gratings
are displayed on the LCD screen while FP or 1p Epifluorescence responses are
recorded. E) Hypothetical decomposition of the aggregate FP signal. Left: Sources
that contribute to the FP response and their spatial location with respect to the fiber’s
detection volume and contours in the y-z plane (red, orange, green, blue correspond to
the 90,75, 50 and 25% detection boundary respectively). Middle: optical planes
corresponding to sections d=1 and d=D in the left panel. Circles are x-y sections of
the contours shown in the left panel. Right: Mathematical formulation of the LMM
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Results
As described before, V1 recordings usually show tuning of single cells to one orientation
while the aggregate signal recorded by the FP results in a tuning curve that is representative of
all neurons within the boundary of the detection volume. The tuning curve of this aggregate
signal was called ‘ensemble tuning’, 𝑇𝐹𝑃(𝜃𝑘). In an ensemble tuning curve, the tuning of the
loudest sources, i.e.: the ones closest to the fiber, will dominate the tuning curve while the other
sources will still contribute to the rest of the curve. Given the topographic organization of
patches and the lack of clear columns in the mouse V1 [149], two scenarios are possible during
the recording of the ensemble tuning. One such scenario would be if the optical fiber landed in
the center of an orientation patch, where a group of neurons is selective to the same stimulus,
resulting in a peak in the ensemble tuning at the orientation of this stimulus. The other scenario is
if the optical fiber landed rather at the periphery of one patch or where one or more patches
intersect. In that case, the ensemble tuning curve would be less likely to show prominent tuning
to one orientation and will rather show uniform responsiveness to most stimuli.
In Figure 4-1C five locations (A, B, C, D, and E) in V1 are shown (Table 4-1). These are
the locations from which FP and OS signals were recorded. As described in the Methods section
recording the ensemble tuning curve of a certain location is rather straight forward using the FP.
To recap, the fiber was positioned at the desired location, the eight visual stimuli were presented
randomly and repeated ten times and the visually evoked responses (VER) were collected
simultaneously, with no further manipulation needed. Recording the VERs while optically
scanning the detection volume, on the other hand, is a quite elaborate process, which we’ll refer
to as the OS (optically scanned) signals from now on.
During the OS recording session, each of the eight visual stimuli was presented randomly
and repeated ten times at every depth, starting from the pia at depth = 0 and at every 20 µm steps
85
until a depth of 250 µm was reached. VERs are recorded simultaneously in the form of a series
of images, a video. At every transition, the objective was moved down to position its focal plane
at the desired depth. This results in a stack of video files that correspond to every depth and that
shows the visually evoked fluorescent sources. These sources were considered regions of interest
(ROIs) and were extracted using the publicly available CaImAn toolbox [151], [152]. Since the
CaImAn was developed to handle high resolution, two-photon images some customization was
needed to adapt it to the less defined, low-resolution images acquired with OS. In OS-ed images,
individual neurons can only be seen if their soma falls exactly within the objective’s focal plane.
Otherwise, their activity is picked up in out-of-focus ROIs that do not necessarily resemble the
shape of neurons. Therefore, some parameters like the ROI size and the spatial correlation
threshold had to be adjusted. After extraction of the ROIs and the location of their centroids
using the modified version of the CaImAn, a weight wn,d(x, y) (score) is assigned to each ROI
(Equation 5-1). Those weights come from the direct measurements reported in Chapter 3 and
depend on the ROI’s spatial location and depth as seen in Figure 4-1E. As such, ROIs that fall
within the red contour will receive a weight of 0.9 while ROIs inside the blue contour will be
weighted by 0.2. The fidelity of the OS-ROIs was validated by comparing them to ROIs in a
two-photon image taken at the same depth. OS-ROIs that didn’t coincide with a two-photon ROI
and that fell outside of the boundary of the detection volume (i.e.: outside the blue contour) were
not included in the construction of the pseudo-ensemble statistic,𝑂𝑆(𝜃𝑘), recorded with OS.
Figure 4-2 shows the data collected from location E as well as the weight assignment
approach that was taken by the LMM based on the spatial location of the OS-ROI. The visually
evoked response (VER) traces of a few OS-ROIs are presented in Figure 4-2C-E along with their
individual tuning profile. While some OS-ROIS were selective to a certain orientation and
86
exhibited sharp tuning, others seemed unselective to the presented stimulus. The overall
ensemble tuning statistic 𝑇𝐹𝑃(𝜃𝑘) observed with the FP is shown in the left panel of Figure 4-2A.
The middle panel demonstrates the pseudo-tuning statistic 𝑂𝑆(𝜃𝑘)constructed from the OS-
ROIs with the LMM using the weights and boundary constraints from the direct measurements
[150].A visual comparison of the observed and pseudo-tuning statistic makes it clear that both
share common features, with strong ensemble tuning to 90-180° that peaks at 135°, and near
chance tuning to other orientations. This can be explained by the fact that some of the shallower
OS-ROIs were more selective to 90-180°, while deeper and/or more peripheral ROIs were
selective to the other orientations. Furthermore, the statistical evaluation of the observed and
pseudo-tuning statistic proved that they come from the same distribution (two-sample
Kolmogorov-Smirnov test, p = 0.92, α = 0.05). In contrast, the left panel in Figure 4-2A shows
the control-pseudo tuning statistic resulting from the process of eliminating the spatial boundary
and profile. The control-pseudo tuning statistic was constructed without the spatial constraints
and characteristics derived from the direct measurements, i.e.: all OS-ROIs were included with
equal weights regardless of their spatial location. As expected, the result is a near-uniform tuning
statistic that is significantly different from the observed FP statistic and the constructed OS
tuning statistic (two-sample Kolmogorov-Smirnov test, p = 0.0014, α = 0.05). These results
suggest that the direct measurement of the detection volume and the spatial profile are valid and
applicable in-vivo as without them the information coded in the tuning statistic is lost. This
procedure was repeated in three other regions in V1 and similar results were observed for all
locations (Figure 4-3, 4-4 and 4-5) except one where the threshold for statistical significance was
not met.
87
A)
B)
C)
D)
E)
Figure 4-2. In-vivo validation of the directly measured detection profile and volume. A) Left:
Ensemble tuning statistic, 𝑇𝐹𝑃(𝜃𝑘), recorded through FP from location E. Middle:
pseudo-ensemble tuning statistic, 𝑂𝑆(𝜃𝑘), estimated using individual sources
detected from volumetric OS data. Right: control-pseudo tuning statistic estimated
using all sources in volumetric OS data in the absence of the spatial constraints
imposed by the measured detection volume. (p<0.01 = **, ns = not significantly
different) B) FP and OS recorded calcium traces showing average ± s.e.m VERs to
the eight visual stimuli. Scale bars are 0.5s and 1 z-score unit. C) Left: Sample OS
image from a superficial range of depths (0-80µm). Scale bar is 100µm. The overlay
shows detection boundaries used by the LMM. Source 1 corresponds to a weight of
0.25 while sources 2-4 correspond to 0.75. Right: Corresponding 2p image at the
same depth showing the contributing cell bodies. Scale bar is 100µm. Bottom:
calcium traces of the sources during multiple trials of visual stimuli presentation (red
dashed lines indicate stimulus onset) and their individual tuning profiles 𝑇𝑛,𝑑(𝜃𝑘).
Scale bars are 4s and 1 z-score unit. D) same as C but from an intermediate section
(80-150µm). E) same as C but from a deeper section (150-250µm).
88
A)
B)
C)
D)
E)
Figure 4-3. In-vivo validation of the directly measured detection profile and volume. A) Left:
Ensemble tuning statistic, 𝑇𝐹𝑃(𝜃𝑘), recorded through FP from location B. Middle:
pseudo-ensemble tuning statistic, 𝑂𝑆(𝜃𝑘), estimated using individual sources
detected from volumetric OS data. Right: control-pseudo tuning statistic estimated
using all sources in volumetric OS data in the absence of the spatial constraints
imposed by the measured detection volume. (p<0.01 = **, ns = not significantly
different) B) FP and OS recorded calcium showing average ± s.e.m VERs to the eight
visual stimuli. Scale bars are 0.5s and 1 z-score unit. C) Left: Sample OS image from
a superficial range of depths (0-80µm). Scale bar is 100µm. The overlay shows
detection boundaries used by the LMM. Sources 2 and 3 corresponds to a weight of
0.75 while sources 1-4 correspond to 0.5. Right: Corresponding 2p image at the same
depth showing the contributing cell bodies. Scale bar is 100µm. Bottom: calcium
traces of the sources during multiple trials of visual stimuli presentation (red dashed
lines indicate stimulus onset) and their individual tuning profiles 𝑇𝑛,𝑑(𝜃𝑘). Scale bars
are 4s and 1 z-score unit. D) same as C but from an intermediate section (80-150µm).
E) same as C but from a deeper section (150-250µm).
89
A)
B)
C)
D)
E)
Figure 4-4. In-vivo validation of the directly measured detection profile and volume. A) Left:
Ensemble tuning statistic, 𝑇𝐹𝑃(𝜃𝑘), recorded through FP from location C. Middle:
pseudo-ensemble tuning statistic, 𝑂𝑆(𝜃𝑘), estimated using individual sources
detected from volumetric OS data. Right: control-pseudo tuning statistic estimated
using all sources in volumetric OS data in the absence of the spatial constraints
imposed by the measured detection volume. (p<0.01 = **, ns = not significantly
different) B) FP and OS recorded calcium traces showing average ± s.e.m VERs to
the eight visual stimuli. Scale bars are 0.5s and 1 z-score unit. C) Left: Sample OS
image from a superficial range of depths (0-80µm). Scale bar is 100µm. The overlay
shows detection boundaries used by the LMM. Source 2 corresponds to a weight of
0.75 while source 1 corresponds to a weight of 0.5 and sources 3-4 to 0.25. Right:
Corresponding 2p image at the same depth showing the contributing cell bodies.
Scale bar is 100µm. Bottom: calcium traces of the sources during multiple trials of
visual stimuli presentation (red dashed lines indicate stimulus onset) and their
individual tuning profiles 𝑇𝑛,𝑑(𝜃𝑘). Scale bars are 4s and 1 z-score unit. D) same as C
but from an intermediate section (80-150µm). E) same as C but from a deeper section
(150-250µm).
90
A)
B)
C)
D)
E)
Figure 4-5. In-vivo validation of the directly measured detection profile and volume. A) Left:
Ensemble tuning statistic, 𝑇𝐹𝑃(𝜃𝑘), recorded through FP from location D. Middle:
pseudo-ensemble tuning statistic, 𝑂𝑆(𝜃𝑘), estimated using individual sources
detected from volumetric OS data. Right: control-pseudo tuning statistic estimated
using all sources in volumetric OS data in the absence of the spatial constraints
imposed by the measured detection volume. (p<0.01 = **, ns = not significantly
different) B) FP and OS recorded calcium traces showing average ± s.e.m VERs to
the eight visual stimuli. Scale bars are 0.5s and 1 z-score unit. C) Left: Sample OS
image from a superficial range of depths (0-80µm). Scale bar is 100µm. The overlay
shows detection boundaries used by the LMM. Source 1 corresponds to a weight of
0.75 while sources 2-4 correspond to 0.25. Right: Corresponding 2p image at the
same depth showing the contributing cell bodies. Scale bar is 100µm. Bottom:
calcium traces of the sources during multiple trials of visual stimuli presentation (red
dashed lines indicate stimulus onset) and their individual tuning profiles 𝑇𝑛,𝑑(𝜃𝑘).
Scale bars are 4s and 1 z-score unit. D) same as C but from an intermediate section
(80-150µm). E) same as C but from a deeper section (150-250µm).
91
Table 4-1. Summary of anatomical locations
Location AP [mm] ML [mm]
A -3.58 2.28
B -3.17 2.92
C -3.57 2.35
D -3.2 2.93
E -4.04 3.1
Discussion
The goal of Aim2 was the validation of the directly measured volume of detection in an
in-vivo setup as opposed to in-vitro. The hypothesis that the LMM of the individual sources that
constitute the ensemble FP tuning statistic would result in a pseudo-ensemble tuning statistic that
resembles the actual FP statistic is a valid test of the reliability of the spatial characterization and
direct measurements reported in Chapter 3. The reason being that the LMM used the weights and
boundary, which are based on the in-vitro spatial characterization. As such, if the previously
reported direct measurements and spatial profiles were poor then the reconstruction of the
ensemble statistic would not have been possible. However, the results presented in the previous
section show that the weights and boundaries that constrained the LMM were accurate as they
yielded a pseudo-ensemble statistic almost identical to the original ensemble statistic. Omitting
the spatial weights and boundary resulted in the loss of the information conveyed by the
ensemble statistics, implying that the detection volume and the spatial profile that were measured
in-vitro also apply and are valid in-vivo.
Furthermore, the in-vivo investigation threw some light onto the nature of the aggregate
1D FP signal. Few interpretations of the FP signal exist but were not tested experimentally.
Among them is the opinion that describes the FP signal as the bulk fluorescence activity of the
neural ensemble [74], [153] within the volume of detection. The investigation presented here
simplified the time-dependent FP signal as an ensemble statistic that is indicative of the
92
collective neural activity. The findings shown above provide experimental proof that the
ensemble FP statistic is a spatially weighted sum of the sources that fall within the detection
volume. This means that the position of the tip of the fiber with respect to the cells or region of
interest plays a critical role in interpreting the recorded dynamics and in drawing conclusions
about the observed neural activity.
Another opinion states that the FP signal is a measure of synchrony [154] where peaks
are indicative of the simultaneous firing of more than one neuron. The current design of this
experiment, however, doesn’t provide an optimum framework to appraise this opinion.
This chapter addressed the first limitation of the in-vitro investigation of the spatial
detection profile and showed evidence of the validity of the direct measurements in-vivo,
satisfying Aim2. The next chapter will attend to the second limitation, which is the restricted
number of optical fibers, addressing the third and last aim of this dissertation.
93
CHAPTER 5
EMPIRICAL MODELING AND PREDICTION OF THE DETECTION VOLUME
The findings presented in Chapter 3 showed that the geometry of the optical fiber, as
given by the diameter/NA combination, determined the detection boundary and spatial profile
and buttressed the importance of the deliberate selection of the optical fiber geometry to match
the desired target region. The direct measurements of the detection volume and spatial detection
profile were demonstrated for four specific optical fibers. Limiting the investigation to only four
fibers stemmed from the fact the collecting direct measurements is a very arduous and time-
consuming task. However, the selection of these particular fibers was not arbitrary. It resulted
from an exhaustive literature search that showed large variability in the diameter and NA of the
optical fibers used in Fiber Photometry studies[68]–[70], [72], [73], [75], [76], [127], [131]–
[135], [137]–[139], [142], [153], [155]–[157]. Some studies also chose optical fibers similar to
those used in optogenetic stimulation [74] or used the same optical fiber to stimulate
optogenetically and record fluorescent Ca2+ dynamics with an FP system [140]. The four fibers
were therefore selected to be representative of the range of diameters (largest and smallest) and
NAs (highest and lowest) that are most commonly used. Specifically, the diameters and NAs
were selected to create four combinations that encompass large diameter/ high NA, large-
diameter/low NA, small-diameter/ high NA and small diameter/low NA.
Nonetheless, there was still a clear need to extend the direct measurements of the
detection volume to other optical fibers. Therefore, the intent of Aim3 is to generalize the
findings to arbitrary optical fibers. Since conducting direct measurements is very laborious, a
different solution had to be sought.
94
Monte-Carlo Simulation
Computer-based simulations of light propagation is a long-standing technique to predict
the behavior of light as it penetrates biological tissue [158]. Many Monte-Carlo simulations
(MCS) have been proposed in conjunction with different models of light propagation to describe
the interaction of light in scattering media. Therefore, implementing an MCS for the FP system
was the solution of choice.
I was honored to be granted the opportunity to collaborate with Dr. Marwan Abdellah,
the Scientific Visualization Engineer in the Blue Brain Project1, led by Prof. Henry Markram.
This fruitful collaboration resulted in the development of a fluorescent, wavelength-dependent,
bi-directional MCS that precisely replicates the optical conditions under which FP recordings are
conducted, the Fiber Photometry Monte-Carlo Simulation (FPMCS).
The FPMCS simulation relied on the implementation reported in [159], [160]. Briefly, a
forward Monte Carlo simulation was built to shoot rays from the source, here the GFP beads,
towards the detector, which in this case was the facet of the optical fiber. A per-photon event
approach was used to capture the scattering and attenuating effects of the tissue on the
propagating photons, rather than a transmittance-based approach where the light beam
interaction with the tissue is simplified using Beer-Lambert’s law (see Chapter 2.4). The
implementation consisted of two steps: 1- calculating the probability of excitation upon
absorption, and 2- the probability of emission as a function of wavelength to accurately simulate
real-life conditions (see Chapter 2.5). The angle of acceptance of the optical fiber was accounted
for in the transmission and reception paths. Furthermore, the code was parallelized and
1 The Blue Brain Project is a research initiative located in the Brain Mind Institute at the Swiss Federal Institute of Technology (EPFL) and is dedicated to digitally reconstruct the brain anatomy of rodents by reverse-engineering
neural circuitry.
95
distributed on large scale visualization clusters as an extension of [160] to simulate light
propagation in fluorescent tissue models using backward ray tracing.
Optical Properties of Neural Tissue
The FPMCS required prudent selection of the optical properties of the rodent brain
including, the attenuation coefficient µa, the scattering coefficient µs and the anisotropy factor g
(see Chapter 2.4). While µa and g are well documented the scattering coefficient µs is still under
constant investigation. The scattering coefficient, µs, is the inverse of the distance a photon may
travel without disturbance (mean free path), i.e.: it’s the distance the photon travels before being
scattered. The neural tissue of the rodent brain is a very turbid medium with various types and
sizes of scattering objects, like extracellular matrix, blood vessels, cell membranes, and
organelles and other biological structures. Thus, the scattering coefficient is technically varying
at the scale of the smallest structure, making measurements of exact scattering coefficients
impossible. Earlier studies, therefore, resorted to the measurement of absolute scattering
coefficients which report the overall scattering value for a certain type of tissue in-vitro. In-vivo
reports of scattering coeffects are harder due to the complex measuring setups, the manifold of
available calibration techniques, the assumed light propagation model and the used wavelength
[161], [162]. Therefore, the values of in-vivo scattering coefficients reported in the literature,
span a wide range and vary significantly from 8 mm-1 to 32 mm-1 [62], [63], [124], [125], [161],
[163]–[166] (Table 5-1). For instance, for blue light, µs values of 8 - 13 mm-1 correspond to
mean free paths of ~77 - 128 µm, which means a photon can travel through the neural tissue for
77 - 128µm before it interacts with an optical boundary [161]. Knowing that most structures in
neural tissue are smaller than one-tenth this distance, it is clear that these values for the scattering
coefficient are not realistic. One of the smaller reported values for the scattering coefficient at
~475 nm is the value of 21.1 mm-1 indicating a mean free path of 47 µm [63]. This value,
96
although it presents the shortest reported mean free path, is still larger than the average neuronal
structure.
The goal, however, was to build an MCS that resembles a real-life, in-vivo FP recording,
where photons are transmitted and collected from neuronal tissue with structures whose
dimension range from sub- µm to 10-20µm, considering large neuronal cell bodies. Also,
considering the wavelength dependence of the scattering coefficient [54], [161], [167], means the
FPMCS needs to use a different µs for the forward path (blue, 475 nm from the fiber to the
tissue) and the return path (green, 530 nm from the fluorescent sources to the fiber). All reported
values for the scattering coefficient from the literature were harvested and summarized in (Table
5-1).
Results
The goal was to build an MCS that resembles a realistic in-vivo FP recording, where
photons are transmitted and collected from neuronal tissue with structures whose dimension
range from sub- µm to 10 - 20 µm, considering large neuronal cell bodies. Therefore, an iterative
approach was adopted, and multiple scattering coefficients were simulated. The result for each
simulation was contrasted to the direct measurements conducted previously. It was no surprise
that scattering coefficients that corresponded to mean free paths values that are 5 - 10 multiple
times larger than a single neuron resulted in extremely large detection maps, where an optical
fiber could detect fluorescence from depths farther than 700 µm as reported in [124]. After
multiple iterations, a scattering coefficient that would result in a mean free path comparable to
the size of a neuron (10 - 20 µm) was used. A value of µs = 60 mm-1 for the forward path at 473
nm and µs = 46 mm-1 for the return path at 535 nm presented realistic values and resulted in a
simulated detection profile that strongly resembled the detection maps from the direct
measurements previously shown in Chapter 3 (Figure 5-1).
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Figure 5-1 shows the MCS simulated detection maps for the four optical fibers used in
the direct measurement and the directly measured detection maps side-by-side. It is evident that
both simulated and directly measured detection maps are concordant. Furthermore, the 80%,
50% and 20% detection contours depicted in Figure 5-2A show how the shape of the simulated
and directly measured detection boundaries are in strong agreement as indicated by the
significantly positive association measured by Pearson’s correlation (r > 0.96, p < 0.001, α =
0.05) and the failure of a two-sample t-test (t-test, 0.93 < p > 0.12, α = 0.05), confirming the
validity of the developed FPMCS. Another important factor to consider, when comparing
simulated and directly measured data, is the spatial detection profile along the z-axis, as it
determines the weights or shares of the individual sources that constitute the overall FP signal.
Figure 5-2B shows that the axial detection profiles of the FPMCS and those of the direct
measurements are comparable with no significant statistical difference (t-test, p > 0.3, α = 0.05).
These results substantiate the reliability of the developed FPMCS to simulate data that match the
direct measurements and hence can be used to provide actual data in the development of the
prediction tool.
So far, the detection maps were not yet extended to optical fibers other than the one used
in the in-vitro investigation. However, the developed FPMCS paved the way to generalize the
detection maps to arbitrary optical fibers.
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A)
B)
Figure 5-1. Detection maps simulated with the developed FPMCS. A) Directly measured detection maps for the original four optical
fibers. B) FPMCS simulated detection maps the same four optical fibers. Optical fiber geometry is indicated in the lower
right corner of each detection map.
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Figure 5-2. Simulated and directly measured detection boundaries and axial detection profiles.
A) 80, 50 and 20% detection boundary for each optical fiber. Solid: average of the
directly measured boundary. Shaded: standard error of mean (s.e.m.) of the directly
measured boundary. Dashed: detection boundaries simulated with FPMCS.
Diameter/NA of each optical fiber is indicated in the lower left corner. Lateral
distance is normalized by the radius (rf) of the optical fiber. Pearson’s correlation
coefficient r400/0.5(80%) = 0.98, r400/0.5(50%) = 0.97, r400/0.5(20%) = 0.99, r400/0.22(80%)
= 0.96, r400/0.22(50%) = 0.96, r400/0.22(20%) = 0.98, r200/0.5(80%) = 0.98, r200/0.5(50%) =
0.99, r200/0.5(20%) = 0.96, r200/0.22(80%) = 0.99, r200/0.22(50%) = 0.99, r200/0.22(20%) =
0.76, p<0.000, n=24. Two-sample t-test p400/0.5(80%) = 0.34, p400/0.5(50%) = 0.16,
p400/0.5(20%) = 0.27, p400/0.22(80%) = 0.11, p400/0.22(50%) = 0.35, p400/0.22(20%) = 0.68,
p200/0.5(80%) = 0.92, p200/0.5(50%) = 0.36, p200/0.5(20%) = 0.11, p200/0.22(80%) = 0.7,
p200/0.22(50%) = 0.13, p200/0.22(20%) = 0.12, n=24. B) Axial detection profiles along
rf=0. Fiber diameter is indicated in lower left corner. Solid: average of the directly
measured boundary. Shaded: standard error of mean (s.e.m.) of the directly measured
boundary. Dashed: detection boundaries simulated with FPMCS. Two-sample t-test
p400/0.5= 0.57, p400/0.5 = 0.78, p200/0.5= 0.56, p200/0.22= 0.31, n=24.
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A Novel Prediction Tool
The beginning of this chapter discussed the importance of selecting the diameter and the
NA of the optical fiber to match the targeted brain region and to ensure its confinement to the
fiber’s detection volume. So far, only the four original optical fibers that were used for the direct
measurements were considered [150]. Numerous recent FP studies relied on optical fibers similar
to the ones characterized by Mansy et al and Pisanello et al. [124], [150], as well as other optical
fibers (Table 3-2) to record in-vivo neural correlates of social interaction [70], [132], anticipatory
regulation of ingestion [133], sensory and motor skill learning [72], [126], [157], eating-
associated orexin neurons [127], and cocaine addiction [134] from different deep brain areas.
The diameter[um]/NA combination (geometry) of an optical fiber plays a fundamental role in
determining the dimensions of the tissue from which fluorescence will be detected. This implies
that, depending on the shape and size of the target brain region, some optical fiber might be
better suited to record from this region that another fiber. However, to the best of our knowledge,
there is no current means to determine which optical fiber is optimum for a given brain region. In
other words, the detection map of a given optical fiber is not readily available for people to select
the optimum optical fiber. Reporting on the detection boundary for other optical fibers is thus
instrumental.
To fill this gap, the implemented FPMCS was used in conjunction with a machine-
learning algorithm to build a novel tool that would predict the detection boundary for any
arbitrary optical fiber, satisfying the goal of the last Aim (Aim3) of this research.
Artificial Neural Network
The deep learning algorithm was based on a feed-forward artificial neural network
(ANN). Simply stated an ANN is an empirical model that tries to learn a relationship between a
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set of inputs and their corresponding output. In machine learning terms, the inputs are usually
called featured and the output is called labels. If the labels take on discrete values from a finite
set (usually 2 or 3) then the ANN is a classification predictive model. If, however, the labels are
continuous values then it is a regression predictive model. Since the goal is to predict the shape
of the detection boundary, which is defined by a set of continuous points, a regression predictive
model was selected.
The ANN consisted of a nine-node input layer, two 64-node hidden layers, and an 11-
node output layer. The detection boundaries of the four optical fibers used in the direct
measurements and their FPMCS simulated peers composed the training dataset of the ANN.
Each node in the input layer corresponded to one out of nine features that were derived from
each optical fiber’s diameter and NA. The 11 nodes in the output layer (the labels) presented 11
points on the 80% detection contour. That is, each detection contour was described with 11
points as illustrated in Figure 5-3A. Thus, nine geometric features of the optical fiber are mapped
to 11 points that defined the fibers 80% detection contour or boundary. As mentioned earlier,
there were 24 trials for each optical fiber in addition to FPMCS simulated trial (i.e. 25 trials per
optical fiber). Since there were 4 optical fibers, then the total number of examples that were used
to train the ANN was 100. The network is built and trained in the TensorFlow platform using the
Keras API and Python programming language. The ANN was optimized by an RMSprop
optimizer with a learning rate of 0.001, which is a variant of stochastic gradient descent (SGD).
Efficient training of the ANN was achieved by making use of the patience parameter to abort the
training if performance is not improving after a set number of training iterations. Following the
convention of the machine learning community, the training dataset (100 samples) was split 80-
20 between the train and test sets. 20% of the training set was used for cross-validation.
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Results
The gold standard in machine learning is the to assess the trained ANN’s performance on
the test set, which is a measure of how well the ANN’s has learned the relationship between the
input features and output labels. A common measure for the ANN’s performance on the test set
is the difference between the actual and predicted output in the form of the mean absolute error
(MAE). Figure 5-3 demonstrates the ANN’s performance on the test set. With an MAE as low as
0.01, the predicted and actual boundaries are almost identical (r > 0.98, p < 0.001, α = 0.05),
providing evidence that the ANN has reliably learned the relationship between the geometrical
features of the optical fiber and the associated 80% detection boundary.
However, a more robust test is to assess the ANN’s ability to extrapolate to new samples.
Said differently, it is desired to measure the ANN’s predictive power on geometrical features it
has not seen in the training dataset. The importance of this lies in the fact, that some FP studies
may choose to use an optical fiber whose geometry was not included in the training data set yet
would like to be informed about the fiber’s detection boundary.
The ANN’s extrapolative prediction power was assessed in two steps and both use the
developed FPMCS. First, the detection maps of four new fibers were simulated using the
FPMCS. The diameter[µm]/NA combination of the new optical fibers was 300/39, 300/0.22,
100/39 and 100/22. The 80% detection contours were extracted from the simulated detection
maps and were considered the ground truth. Next, the ANN was used to predict the 80%
detection contour for the new fibers and the predicted contours were compared against the
simulated ones. In Figure 5-3C, it can be clearly seen that the ANN’s predicted detection
boundaries for the new (un-seen) optical fibers are very similar to the actual detection
boundaries, with an average MAE as low as 0.02 and a significant positive association as
measured by the Pearson’s correlation (r > 0.95, p < 0.0001, α = 0.05).
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The second step that was taken, to further assess ANN’s extrapolation power, relied on an
exhaustive approach that tested the asymptotic performance of the ANN on new geometric
features. The developed FPMCS was used again to simulate the ground truth detection
boundaries. This time, however, the FPMCS simulated the detection maps for a continuous range
of diameter/NA combinations, ranging from 50µm - 700µm / 0.1 - 0.8, which was a very
computationally expensive and time-consuming operation. The trained ANN was used to predict
to detection boundary of the same range of geometric feature combinations. The predicted and
simulated detection contours were then contrasted, and the MAE was calculated for every
combination. In Figure 5-3D the x-axis presents the range of NAs and the y-axis is the range of
diameters. The color-coded value of each pixel in the heatmap is indicative of the amount of
MAE between the predicted and actual 80% detection boundary. As such blue values indicate
low MAE values and high predictive power while orange and red values mean high MAE and
low prediction performance. The asymptotic performance of the ANN is summarized in Figure
5-D which informs when the proposed prediction tool will provide reliable estimates of the
detection boundary. Figure 6-5D provides compelling evidence that the prediction tool operates
with high performance for geometries that coincide with the optical fibers that are commonly
used in neuroscience applications. In neuroscience studies, valid concerns about tissue damage
usually lead to the selection of optical fibers with diameters < 500µm. Regarding the NA, the
ANN’s prediction power seems to roll off at about 0.7. However, since the largest commercially
available NA is ~0.66, with larger NAs possibly subject to fabrication limits, it is safe to
consider the ANN for optical fibers with NA’s up to the largest commercially available NA.
The ANN was developed in the scientific Python environment Spyder using the
TensorFlow/Keras API. These platforms are not commonly used in the neuroscience community
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and could be hard to navigate. Hence, the final element of this dissertation was to package the
ANN in a more common framework, like MATLAB®. For this, the Deep Learning Toolbox™ in
MATLAB® was used to import the ANN’s structure and parameters from TensorFlow/Keras and
to allow predictions to be made in a single MATLAB® script. The MATLAB® script takes the
diameter and NA of an optical fiber as input arguments and returns the predicted 80% detection
boundary associated with the fiber.
105
A)
B)
C)
D)
Figure 5-3 Empirical model of the detection volume. A) ANN architecture. X1-9 are input nodes
that correspond to the geometrical features of the optical fiber. P1-11 are output nodes
that correspond to samples defining the 80% detection contour. B) ANN performance
on the test set. Diameter/NA of each optical fiber is indicated in the lower-left corner.
MAE and Pearson’s correlation coefficient are MAE400/0.5=0.008, r400/0.5=0.99;
MAE400/0.22=0.010, r400/0.22=0.98; MAE200/0.5=0.009, r200/0.5=0.99; MAE200/0.22=0.007,
r200/0.22=0.99. Lateral distance is normalized by the radius (rf) of the optical fiber. C)
ANN prediction performance using a set of four optical fiber parameters that are not
part of the training set. Diameter/NA of each optical fiber is indicated in the lower-
left corner. MAE and Pearson’s correlation coefficient are MAE300/0.39=0.02,
r300/0.39=0.97; MAE300/0.22=0.011, r300/0.22=0.98; MAE100/0.39=0.009, r100/0.39=0.97;
MAE100/0.22=0.052, r100/0.22=0.95. Lateral distance is normalized by the radius (rf) of
the optical fiber. D) Asymptotic performance of the ANN for a continuous range of
diameters and NAs. The color-coded value of each pixel in the heatmap corresponds
to the amount of MAE between the predicted and actual 80% detection boundary.
106
Discussion
Fiber photometry has gained immense popularity by merit of its experimental flexibility,
ease of operation and low cost. However, unlike other methods of optical interrogation, the
nature of the recorded 1D signal and the volume of tissue from which it is detected were unclear.
The findings presented in Chapter 4 shed light on the composite nature of the FP signal
demonstrating its dependency on the spatial detection profile of the used optical fiber. Hence
deliberate selection of the optical fiber is key in interpreting the recorded signal and in ensuring
that the collected fluorescence is confined to the proclaimed region of interest. This means that a
brain region-optical fiber-matching process is necessary for meaningful interpretation of the
recorded signal. As such, a small diameter, high NA fiber may offer detection breadth while a
large diameter, low NA fiber would provide detection depth. The results presented in this chapter
aid this selection process and automate it. The bi-directional, fluorescent FPMCS developed in
collaboration with Dr. Abdellah has been the cornerstone for the success of the novel, ANN-
based prediction tool as it relied on the data generated by the FPMCS. The proposed prediction
tool serves as a powerful resource as it provides an accurate estimate of the detection boundary
associated with a given optical fiber and hence will inform the brain region - optical fiber -
matching process.
This chapter concludes the contributions of this dissertation by proposing a novel
MATLAB®-based tool that predicts the detection boundary of any optical fiber-based on its
geometrical features, the diameter and NA, and was developed using the custom-designed
FPMCS and an ANN.
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Table 5-1. Summary of reported optical properties of the rodent brain.
Animal
Model Preparation
µs
[mm-1]
µa
[cm-1] g
λ
[nm] Illumination Measurement technique Reference
Mouse
32
23
19
0.9
0.3
0.1
0.9
0.9
0.9
405
532
635
1p Simulation based on mouse brain atlas [164]
Rat
In-vitro-
whole
brain
17
13
0.5
0.9
--
--
480
530 1p Contact spatially resolved spectroscopy [162]
20
12
--
--
0.93
0.93
480
530 1p Mathematical model [165]
Rat
32
23
19
0.9
0.3
0.1
0.9
0.9
0.9
405
532
635
1p Double-integrating sphere setup, and
optical coherence tomography [168]
Mouse In-vitro,
slice 20 Ignored 0.925 920nm 2p --- [124]
Mouse In-vivo 13.3 1 0.9 ---- 2p --- [125]
--- --- 8-12 -- 0.9 650-
950 1p --- [161]
Mouse Slice 21.1 0.62 0.86 473 1p Light transmission using optical power-
meter [63]
Rat/mouse Cortical
slice 10.3/11.2 0.69 0.88 473 1p [62]
Mouse Slice,
Subcortical
16.1
16.5
14.08
--- >0.9
453
528
940
1p Light transmission using optical power-
meter [166]
Rat Cortex 17 0.25 0.9 532 1p
Double-integrating-sphere to measure
diffuse transmittance, diffuse
reflectance, and ballistic transmittance
followed by inverse adding doubling
method (IAD)
[163]
108
CHAPTER 6
CONCLUSION AND FUTURE WORK
Summary
Fiber photometry is an optical method for in-vivo interrogation of neural circuit dynamics
that depends on an optical fiber to relay neural dynamics from deep brains structures. Since
optical fibers lack a focal plane, the FP collects aggregate fluorescent Ca2+ dynamics from an
excitable volume of tissue as a one-dimensional signal. The aggregate and surrogate nature of the
FP signal make its interpretation a challenge. Hence, the central aim of this dissertation was to
construe the lumped 1D FP signal by conducting a systematic characterization of the FP
modality through three main steps. The three steps were motivated when the FP’s sensitivity was
assessed and compared to classical electrophysiological multi-unit recordings by applying
mechanical stimuli of varying intensity while recording the evoked responses in the rat’s whisker
system. It was evident that the FP signal reported a neurometric curve that is strongly concordant
to the previously reported electrophysiological curve.
In the first step, the extent from which the FP collects fluorescence was quantified in
brain phantom slices and acute brain slices using GFP beads by means of direct measurements of
the detection volume. Since the collection of fluorescence occurs through the optical fiber, four
optical fibers with different diameter/NA combinations were investigated. It was shown that the
size and shape and of the detection volume pivots on the geometrical features of the optical fiber
in question, with low NA fibers allowing fluorescence to be collected from depths as far as ~300
µm from the tip of the optical fiber and large-diameter fiber permitting increased peripheral
detection along the lateral axis. The diameter/NA combination also affected the spatial detection
profile in the axial direction determining the magnitude by which each source will contribute to
the aggregate FP signal.
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Second, the spatial characterization of the detection volume was validated in-vivo in the
mouse visual cortex utilizing epi-fluorescent volumetric scanning as well as two-photon
microscopy. Optical scanning of the detection volume offered the spatial resolution, inherently
lacking in the FP system, to debrief the individual sources that constitute the aggregate FP signal
and the two-photon images verified the reliability of the sources. Compounding the sources by
applying the directly measured boundary of the detection volume and spatial profile enabled the
construction of a pseudo-FP statistic from its contributing sources in the form of a weighted sum.
In the third and final step, the quantification of the detection volume was generalized to
arbitrary optical fibers other than the four with which the investigation started, and a novel
prediction tool was delivered. This was achieved by developing two separate but interconnected
modules. First, a bi-directional, wavelength-specific and physically-plausible Monte Carlo
Simulation was developed to closely mimic the optical conditions under which the FP collects
neural dynamics. Second, an artificial neural network was trained to learn the relationship
between the geometrical features of an optical fiber and the associated shape of the detection
volume boundary. The FPMCS simulated the detection volume for optical fibers that were used
to train an artificial neural network and for new optical fibers that were needed to test the
network’s predictive power in extrapolating to un-seen geometric features. The artificial neural
network showcased strong prediction power for optical fibers with diameters less than 600 µm
and NAs between 0.15 and 0.66. This novel prediction tool was then translated to a MATLAB
based platform for ease of use and convenience.
110
Future Work
Future work spans two aspects that address the main limitations of the research presented
in this dissertation. The first aspect is regarding the in-vivo validation of the detection volume. It
was shown that the overall ensemble statistic recorded by the FP system can be reconstructed
from the constituent sources. However, this ensemble statistic is a holistic measure that does not
reflect the temporal evolution of the neural activity. The reason, this approach was selected is
because the FP and the OS recordings were performed sequentially rather than simultaneously.
Hence, the temporal correspondence between both recorded signals was lost and a more holistic
measure had to be found. In the future, it’d be very insightful to compare both signals
temporally, which can be achieved if FP and OS signals are collected simultaneously from the
same location. The technical challenge will be how to combine the two optical paths whilst
minimizing interference. However, given the myriad of newly developed optics and abundant
optical tricks, this challenge might come with a possible solution.
The second aspect is related to the contributed novel prediction tool. So far, the tool
showed high performance in predicting the detection volume for optical fibers whose geometry
is close to the geometry of the optical fibers is in the training of the network. As such, having a
larger training set that is representative of more geometrical feature may lead to higher prediction
performance for optical fibers of large diameter and high NA. Furthermore, the tool was trained
on simulated detection volumes for blue excitation and green emission light only. In other words,
the tool is strictly wave-length dependent and is tailored to fluorescent sources that have a GFP-
like spectrum. In order to stay abreast with the quickly emerging spectra of state-of-the-art Ca2+
indicators (and other indicators), it would be highly advantageous to expand the prediction tool
to handle other wavelengths as well.
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Conclusion
Uncovering the neural basis of sensory integration, motor planning, cognition and
learning in the healthy and diseased states of the brain is the ultimate quest of neuroscience. It’s a
quest that has been, and still is, undertaken on multiple fronts with several investigational
approaches that vary in spatiotemporal resolution and hence provide unprecedented amounts of
information. Some approaches even combine the temporal precision of electrophysiology, with
the spatial single-cell resolution of two-photon microscopy and the coarse ensemble dynamics of
ECoG arrays in an attempt to elucidate neural circuit dynamics.
The past few decades have seen a vast expansion in new modalities that rely on light (in
the visible and invisible spectrum) to further our understanding of neural dynamics. Those tools
allow in-vivo reading from (recording or imaging) as well as writing to (modulating) neurons in
a way that simultaneously links structure and function. These agile advances in neural device
technology have been constantly reinforced by unceasing efforts to develop more robust calcium
(Ca2+) indicators, which serve as a proxy to neural activity and aim to relay information from
large ensembles with spatial and temporal resolution.
All these massive strides in microscopic technology, miniaturized optics, microbiology,
and biotechnology have certainly propelled the optical approach to the functional and structural
interrogation of neural circuits. However, technological advances are a double-sided sword
whose unfavorable side can be easily overseen given the extremely beneficial edge that offers
abundant features.
Whilst utilizing a new neural recording device or a novel imaging method to conduct
ground-breaking research, it is mandatory to Know Thy Device. In other words, new recording
and imaging methods shall not be used without a full understanding of their specifications as
112
well as their limitations. This can be troublesome, given the wide array of options that are
currently available and that complicate the selection process.
Nowadays, selecting the recording or imaging method of choice relies heavily on the
scientific question and type of investigation as different methods are more suitable for certain
research endeavors than others. Furthermore, all-optical methods of in-vivo neural interrogation
come at the inevitable trade-off between cost, resolution, focality, targetability, flexibility in
behavioral paradigms and complexity. As such selecting the optimum method for an experiment
can be quite cumbersome. However, among all-optical methods, there is one that stands out for
its exceptional flexibility in paradigms of awake behavior, its ability to target superficial as well
very deep brain structures, its ease of operation, its versatility and low cost. This method is the
Fiber Photometry, which was systematically characterized in this dissertation in hope to inform
about its underlying mechanisms of action and to provide novel metrics of consideration when
utilizing this optical method for in-vivo interrogation of neural circuit dynamics.
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APPENDIX A
SYSTEM DESCRIPTION
In 2015, I was granted the outstanding opportunity to attend a Fiber Photometry
workshop at the Deisseroth lab at Stanford University. The two-and-a-half-day workshop
introduced us to the modern1 FP design reported in Gunaydin et al. 2014 and offered hands-on
experience in the assembly of the system. After a great learning experience at Stanford, I
returned to our lab to establish the new technique. I implemented a modified version of the FP
rig that allowed for simultaneous calcium recording and optogenetic excitation while
maintaining a compact and portable footprint. Since then, the FP system was used in different
experiments to recorded neural activity in our lab.
The goal of FP is to record calcium transients (dynamics) as reported by a genetically
encoded calcium indicator (GECI), like GCamP6, that is expressed in neurons of awake or
anesthetized subjects under single-photon illumination. This assumes that subjects have
undergone a surgical procedure to deliver the GCamP6 to a target region and have been
implanted with an optical fiber in the same region. In the following, the different components of
the FP system will be described in detail.
System components
The FP system components and the different input, output, light path, and system controls
are illustrated in Figure A-2A. Figure A-2B shows a simpler cartoon of the FP system and zooms
into the optical fiber - brain interface.
1 I’m calling it “modern” FP design as the fundamental theory of FP existed long before 2014 [65], [136], [169]
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Light source
Since GCaMP6 relies on a green fluorescent protein (GFP) reporter it requires to be
illuminated with blue light in the range of 450-490 nm. A Light Emitting Diode (LED) with λnom
= 470 nm is thus used to deliver the blue excitation light. A second light source, a violet LED
with λnom = 405 nm, is used as a reference light for control measurements and motion artifact
removal.
Figure A-1. GCaMP6f excitation spectrum. Adapted from [170].
115
A)
B)
Figure A-2. Diagram of the Fiber Photometry system. A) Detailed system components showing control signals (red) from TDT to the
LED driver. The LEDs are the light source and generate the blue and violet lights (forward path). Green fluorescent light
from expressing neurons is detected (return path) and acquired by TDT (green). B) Enlarged view of the red box in A
showing fiber-brain interface.
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Optical path
The optical path can be split into forward and return paths. The forward-path addresses
the delivery of the excitation light (blue) from the source to the GCaMP6 expressing neurons in
the brain while the return path describes the collection of the fluorescence (emission light, green)
emitted from those neurons and its propagation to the photodetector. In the forward path, the
excitation light exits the LED and is collimated onto an excitation filter before it passes through a
dichroic mirror (DMLP425). Likewise, the reference light is collimated on an excitation filter
before it reaches the dichroic mirror. At the same dichroic mirror, the reference light is deflected
and forced to merge in the direction of the excitation light. Obviously, this dichroic mirror
transmits blue light and reflects violet. Both lights continue to propagate until they pass through
a second dichroic mirror (NFD01-532) before they are collimated onto the optical patch cable
that guides both lights to the optical fiber implanted in the brain. The lights will emanate from
the fiber and illuminate a volume of GCaMP6 expressing neurons inside the brain. When
actively firing, those neurons will emit green fluorescence which demarcates the return path. In
the return path, green light emitted by active neurons will be captured at the tip of the fiber and
guided along the patch cable back to the collimator. After the collimator, it will arrive at the
second dichroic mirror. The second dichroic mirror (NFD01-532) serves in the forward and
return paths as it transmits all wavelengths except those falling between 502-562 nm, which
correspond to green light. Once directed upwards by the dichroic mirror, the green fluorescent
light goes through an emission filter and then a convex lens. The convex lens focuses the
collected green light onto a single cell photodetector where it is transduced to an electrical signal
and sent to the data acquisition system.
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Photodetector
The photodetector is a transducer that detects light and converts it to an electric signal
that is proportional to the intensity of the detected light. Photodetectors have a wide range of
specifications that make one design more suitable for a given application. FP relies on the
measurement of minute changes in fluorescent intensity inside a highly scattering medium, like
the brain. Thus, high sensitivity and high gain are an indispensable feature of the FP
photodetector. Miniscule signals, like the one recorded by the FP, also need good shielding from
60Hz interference. While this could be remedied using signal processing techniques and filtering,
it is always better to avoid it during signal acquisition. Battery-operated photodetectors,
therefore, offer an important edge compared to their power-line operated counterparts. A battery-
operated femto-watt photodetector (Newport, Corporation, Irvine CA) that offers extremely high
gain (up to 1x1011) and can detect sub-pico-watts to 0.5 nano-watts optical signals is thus the
right choice.
System controls and data acquisition
A Tucker Davis Technology (TDT) BioAmp processor was used to control the LED
drivers for the excitation and reference lights. While most fluorescence applications use constant
illumination, the FP makes use of a very smart trick. Instead of driving the LEDs with a constant
current resulting in constant illumination, which could lead to tissue heating or photobleaching of
the fluorescent protein, it modulates the excitation and reference lights sinusoidally at different
frequencies, fex and fref respectively. The detected signal (electrical) is then demodulated at those
frequencies to extract physiologically relevant fluorescence emitted due to excitation light at fex
and fluorescence due to motion artifact or other non-physiologically relevant processes occurring
at fref. The modulation frequency can take on any value but must satisfy the following
constraints:
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• It must meet the Nyquist criterion for GCamP6 signals, i.e.: be several times higher than
the fastest GCamP6 event, which could reach up to ~15 Hz. As such it needs to be higher
than 100 Hz.
• It must fall within the bandwidth of the used photodetector.
• It must be spectrally separated from sources of optical and electrical noise. This means it
cannot take on values of 6 0Hz and its harmonics.
Accordingly, 210 Hz was chosen as fex chosen to be fast enough to easily recover the
signal of interest, to be near the peak responsiveness of the detector, and to be 30 Hz away from
harmonics of 60 Hz. Similarly, 530 Hz was chosen for fref.
Once demodulated, the detected signal represents the raw fluorescence emitted by the
GCamP6 expressing neurons. This signal is proportional to the firing activity of these neurons
and represents the aggregate ensemble dynamics. In other words, every time one or more
neurons fire there will be an increase in the detected fluorescent GCamP6 signal. This raw
GCamP6 signal can then be manipulated to calculate the amount of change in form or dF/F or a
Z-score. Figure A-3 shows a sample trace of the GCamP6 signal recorded with the FP from the
rat’s vibrissal sensory cortex during presentation of mechanical whisker deflections.
Figure A-3. Sample Ca2+ trace recorded with FP. Red ticks indicate the presentation of the
sensory stimulus. Top: recorded fluorescent green channel showing Ca2+ transients in
response to stimuli. Bottom: recorded violet channel.
119
The previous section expounded the fundamental mechanics of FP, which can be
summarized by shining blue light onto GCamP6 expressing neurons and recording their
aggregate activity that is reflected as transients in the detected green fluorescent signal. A very
natural thought that follows here is, how does this aggregate (optical) neuronal signal compare to
classical multi-unit electrophysiological recordings? The next appendix will briefly summarize
two experiments I carried out to answer this thought. These two experiments inspired the main
question of my research and serve as the main motivation behind it.
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APPENDIX B
PILOT EXPERIMENTS
Experiment 1
Single-photon fiber photometry is a very simple and economic modality to record Ca2+
dynamics as a surrogate for neural activity. However, validation was necessary for the
implementation of the nascent technique. The system was implemented according to the material
provided in a workshop at Stanford University (Deisseroth lab, 2015) [70]. The rodent whisker
system lends itself as a very apt model to corroborate the viability of the device, by virtue of its
clear somato-topical organization that allows a one to one mapping of a single vibrissa to a
specific cortical column (barrel) in the vibrissal representation of the somatosensory cortex
(vS1). This means that mechanical deflections, which present the sensory stimulus, of a
particular whisker will result in a response in a well-defined cortical area. Cortical sensory
coding of stimulus parameters has been intensely investigated and was shown that changes in
sensory stimulus strength are coded in cortical response probability [119]–[121]. These studies
used classical electrophysiological (ephys) methods to record multi-unit activity. I was curious to
know how the aggregate FP signal will compare to the multi-unit ephys recoding and whether it
will be sensitive enough to detect changes in sensory stimulus strength.
Methods
Surgical Procedure
All animal care and experimental procedures were approved by the University of Florida
Institutional Animal Care and Use Committee. Long Evan rats (n = 4) were injected with ~1 µL
of GCaMP6f (AAV1.CamKII.GCaMP6f.WPRE.SV40) and chronically implanted with an optical
fiber (diameter = 400 µm, 0.5 NA) in vS1 (AP: -3.2, ML: -5, DV: 0.6 mm). After recovery and
121
viral expression (~4 weeks), animals were lightly sedated, and a single whisker was
mechanically deflected by a piezo-electric element at different velocities Figure B-1A.
Whisker deflection
The deflection waveform was carefully designed to accommodate the slow dynamics of
calcium currents and consisted of three epochs: 1. a linear ramp that elicits a distinct cortical
response aligned to the onset of the stimulus; 2. an extended hold time (6 s) which allows
capturing the slow calcium response; 3. A slow return that prevents the masking of the original
response by a stimulus-offset response Figure B-1C. The whisker was deflected at six different
velocities 1500, 1000, 500, 250, 125 and 62 °/s, that were picked to satisfy the minimum criteria
for sensory detection reported in the literature [120], [121], [171]–[176].
Data collection and analysis
The FP system delivered blue light (λ = 475nm), modulated at fex = 210 Hz, for GCamP6f
excitation and violet light (λ = 405 nm), modulated at fref = 530 Hz, for motion artifact removal.
Green fluorescence (λ = 535 nm) emitted by GCamP6f was collected by the optical fiber and
routed to a single cell femto-watt photo-detector. The photo-detector converted the optical signal
into an analog signal that is fed to a Tucker Davis Technologies (TDT) data acquisition system
for storage and analysis. The TDT system controlled the delivery of the mechanical deflections
to the whisker and guaranteed synchrony between stimulus presentation and recorded FP signal.
Custom MATLAB® scripts were used written to demodulate, low pass filter and down-
sample the recorded signal. After correcting for motion artifact, by subtracting the violet channel
from the green channel, dF/F was calculated as the Z-score of the green channel to simplify
cross-animal comparison.
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Results
The aim of this experiment was to compare the optical readout from the FP with the
previously reported ephys readout to draw a conclusion regarding how the FP signal compares to
ephys data. The Ca2+ traces recorded in response to whisker stimulation are shown in Figure B-
2A. Large transients can be seen following the stimulus presentation. Some cases did not elicit a
response, reminiscent of cortical response variability. The cortical response probability was
calculated for each of the different deflection velocities and was summarized in the optical
neurometric curve in Figure B-2B, which strongly reflects the ephys neurometric curve for the
same velocities [119]–[121]. As such it was concluded that the optical signal recorded with the
FP was sensitive enough to detect changes in the sensory stimulus parameter and reliably
encoded the velocity of the stimulus.
Furthermore, the experiment assessed the reliability of the FP signal in a longitudinal
study. Since the brain constantly changes its microstructure on short and long timescales to adapt
to the environment, long term stable recordings are thus crucial to capture the dynamics of
processes like learning and memory consolidation. The major drawback of current
electrophysiological recording modalities is the short signal lifetime. Therefore, the longevity of
the FP signal was appraised. The stability of the signal in the coding of the sensory presentation
was quantified in terms of peak amplitude and latency (Figure B-2C) for up to 200 days.
Transients were classified as stimulus-evoked responses following the criteria in [177]. In Figure
B2-D the sensory-evoked responses recorded on the first and last day are shown with significant
similarity, proving reliable signal detection after five months that potentially outperforms
penetrating microelectrodes [178].
123
A)
B)
C)
D)
Figure B-1. Setup of Experiment 1. Sprague-Dawley rats (n = 4) were injected with GCamP6f in
L4 of vS1 and chronically implanted with a fiber optic. B) Diagram of the FP system.
C) Untrimmed D1 or D2 whisker was inserted in a light-weight polyimide tube
(diameter: 137µm) and deflected 3-5mm from the base with 6 velocities (Vd) under
anesthesia. D) Picture of the implanted subject. [Picture courtesy of the author]
124
Figure B-2. Results of Experiment 1. A) Top: Two-minute trace of stimulus-evoked, time-locked
Ca2+ transients in response to whisker deflection. Notice the absence of some
responses, resembling cortical response probability. Bottom: Control trace. B) Left:
Overlaid single response (blue) and miss (orange) trials (KS-test, p<0.01). Right:
Representative single Ca2+ transient. C) Ca2+ transient peak amplitudes (mean ±
s.e.m.) and latency for n=4 across all recording sessions at Vd=1000 °/s. D) Average
waveforms on first and last day of recording for n=4. The shaded area represents the
standard deviation. ρ is the Pearson’s correlation coefficient
125
Experiment 2
The vagus nerve, the longest nerve in the human body, is the tenth cranial nerve and
predominantly provides parasympathetic innervation to the lungs, heart, and digestive tract.
Nevertheless, vagus also comprises a significant array of sensory afferents that report different
states of the body to the central nervous system (CNS) by means of neuromodulator transmission
[179].
Different techniques, like vagotomies, electrical stimulation, and pharmacological
inactivation, were used to investigate the functional role of the vagus nerve in conveying
modulatory information from the autonomic nervous system to the brain. Many recent studies
showed the various neuromodulator mediated effects of vagus on memory consolidation [180],
[181], learning [182], increased alertness (desynchronized EEG) [183], [184], improved
cognitive functions, targeted cortical plasticity [185]–[190] and accelerated motor rehabilitation
after traumatic brain injury in animal models [185], [191]. This pronounced enhancement of
different cognitive modalities with electrical stimulation of the vagus nerve has been linked to
adequate provision of the neuromodulator Acetylcholine (Ach) [185], [192]–[194].
Nevertheless, further refinement of VNS mechanisms can lead to more accurate control
of neuromodulator release, which governs specific cognitive conditions, and thereby improve or
expedite therapy. The aim experiment is to explore the effect VNS parameters on neuronal
ensembles in the medial prefrontal cortex (mPFC) using the optical readout from the Fiber
Photometry system. Specifically,
Vagus nerve stimulation is a technique that requires mastering fabrication of miniature
stimulating cuff electrodes and a highly precise surgical implantation procedure. I had the
pleasure of receiving hands-on training in two renowned labs at the University of Texas Dallas
(Dr. Kroener and Dr. Kilgard).
126
Subjects were implanted with a vagus nerve cuff, injected with GCaMP6f and implanted
with an optical fiber in mPFC simultaneously. Standard stimulation was delivered 3-4 weeks
after surgery while mPFC Ca2+ dynamics were recorded using the FP. Vagally induced effects
were quantified in mPFC by monitoring changes in the rate of Ca2+ transients when the pulse
width was varied (Figure B-3B).
Methods
Surgical methods
Wild type (WT) Long-Evan rats (n = 3, 250 - 350 g) were anesthetized with 2 - 3 %
isoflurane. About 1 µl of GCamP6f (AAV1.CamKII.GCaMP6f.WPRE.SV40) was injected in
medial prefrontal cortex (mPFC AP: +3.00, ML: 1.00,DV: -3.2 mm) and a multimodal fiber-
optic cannula (NA = 0.5, diameter = 400 µm) was be implanted approximately 100 µm above the
injection site. The bipolar stimulation cuff needs to maintain smooth edges and be fully insulated
on the outside. The electrodes (bare wires on the inside) must provide 1 - 10 kΩ impedance.
Once built, tested for impedance and sterilized, the cuff is ready for implantation. Animals were
implanted with a vagus nerve cuff (built in house, ~3 kΩ impedance) during the same procedure.
Vagus nerve stimulation connector and fiber cannula were secured to the skull using dental
cement and four bone screws. Animals were then left to recover and express the virus for 3
weeks. Afterward, they were tethered to the optical patch cord and the VNS stimulator while
lightly sedated. Recording and stimulation commenced only after the animals regained
consciousness and were fully ambulatory in their home cage.
Vagus nerve cuff implantation
Blunt dissection of the cervical section of the vagus nerve mandates minimal damage to
the surrounding neck muscles and tissue to warrant apt animal recovery. Separation of the vagus
nerve from the carotid artery is followed by removal of all layers of thin connective tissue that
127
constitutes the sheath around vagus. This step is crucial as it guarantees confined electric
stimulation to the nerve of interest and saves the surrounding tissue and other fine sensory nerves
from being influenced, which may pose a confounding factor. Once ~4 - 5 mm of the nerve is
fully exposed, the cuff is passed through a subcutaneous tunnel from the head down to the neck.
The exposed nerve is placed inside the cuff and the integrity of the procedure is tested by
observing a cessation of breathing (COB) or a ~15 % drop in oxygenation upon delivering of a
test stimulus (0.8 mA, 100 µs, 30 Hz, 10 s). It is important at this stage to watch for any adverse
effect to the stimulation, like jaw twitching, whisker deflection, head jerking, which are
indicative of having other fine nerves or tissue caught inside the cuff. In this case, the cuff must
be removed to allow for further cleaning of the nerve (Figure B-3A).
Vagus nerve stimulation
An isolated current stimulator (A-M systems model 4100) was programmed to deliver
standard VNS stimulation parameters (trains of 100 µs pulses at 30 Hz for 500 ms, inter-train-
interval of 5 s, for 2 minutes). The pulse width was varied to 300 and 500 µs to explore pulse
width effects (Figure B3-B).
Data collection and analysis
The FP system delivered blue light (λ = 475 nm), modulated at fex = 210 Hz, for
GCamP6f excitation and violet light (λ = 405 nm), modulated at fref = 530 Hz, for motion artifact
removal. Green fluorescence (λ = 535 nm) emitted by GCamP6f was collected by the optical
fiber and routed to a single cell femto-watt photo-detector. The photo-detector converted the
optical signal into an analog signal that is fed to a Tucker Davis Technologies (TDT) data
acquisition system for storage and analysis. The TDT system and the VNS stimulator are
synched via a ‘gating’ signal generated by TDT. Custom MATLAB® scripts were written to
demodulate, low pass filter and down-sample the recorded signal. After correcting for motion
128
artifact, by subtracting the violet channel from the green, dF/F was calculated as the Z-score of
the green channel to simplify cross-animal comparison.
Results
The aim of this experiment was to explore the neuromodulatory effects on the excitatory
neurons in mPFC under electrical stimulation of the vagus nerve. The effect was quantified in
terms of changes in Ca2+ transients or spike rate. This means the number of Ca2+ peaks were
counted per unit time and compared under different pulse width stimulation. Figure B-3C shows
the recorded Ca2+ traces during epochs of stimulation (orange shading) and epoch where
stimulation was withheld. Visually inspecting the responses, it can be seen that the 300 and 500
µs stimulation pulses caused an increase in spiking rate. The increase in spiking rate was
quantified and is summarized in Figure B-3D, which demonstrates the significant increase in
excitability with 300 µs stimulation. A pulse width of 500 µs also resulted in a higher spiking
rate but not as significant as the 300 µs. It should be noted, that the inter-stimulus-trial of
2minutes may have been too short, possibly not allowing the system to return to baseline. An
observation that could explain the increased spiking rate during the no-stim epochs of the 300
and 500 µs stimulation compared to the 100 µs pulse width stimulation.
The results of this experiment were exciting as they provide evidence that the FP system
is capable of detecting slight changes in neuronal excitability due to modulatory effects mediated
by the electrical stimulation of the vagus nerve.
.
129
Figure B-3 Methods and results of the experiment. A) Surgical procedure. Left: The exposed
vagus nerve. Inset: picture of the fabricated and tested cuff with stimulation
connector. Right: Process of placing the nerve inside the cuff. B) Left: Picture of
vagus nerve cuffed subject tethered to VNS stimulator and FP rig. Head-cap shows
VNS connector and fiber cannula cemented to skull. Right: VNS pattern as described
in [72]. Two-minute stimulation epochs that consisted of 500msec trains of 0.8mA,
30Hz pulses every 5seconds. C) Sample Ca2+ recording from a subject while being
stimulated with 100µs pulse width (top trace), 300µs (middle) and 500µs (bottom).
Asterisks indicate Ca2+ transients (spikes). Orange shading present stimulation
epochs, white intervals are no-stimulation epochs. D) Bar graph illustrating vagally
induced increase in Ca2+ spike rate (orange), compared to no-stimulation epochs
(blue). (t-test, ** p < 0.005; *** p < 0.0005, n = 3) [Pictures courtesy of the author]
130
APPENDIX C
SUPPLEMENTARY MATERIAL
Mathematical Formulation of the Tuning Statistic and the LMM
The calcium trace C(t) (recorded with FP or extracted from OS data) is chopped into 8s
snippets y(t) that are aligned with the onset of the visual stimulus, θ. Eight visual stimuli were
presented randomly in 10 repeated trials.
1. Feature extraction from time series y(t) after the presentation of the stimulus
The following was extracted from every time signal 𝑦𝑖(𝑡) (snippet):
𝜏𝑖 = 𝑡 ∶ 𝑦𝑖(𝑡) = max(𝑦𝑖 (𝑡))
𝐴𝑖 = 𝑦𝑖(𝑡)𝛿(𝑡 − 𝜏𝑖)
𝜎𝑖 = √∑ |𝑦(𝑡) − |2𝑁
𝑡=1
𝑁 − 1
Where i is the trial number and 𝑖 ∈ (1,2, … ,10), N is the number of samples in the
snippet and is the temporal average of the snippet.
𝑖 = [𝐴𝑖
𝜏𝑖
𝜎𝑖
] , where 𝑖, is the feature vector associated with every trial i
2. Decision rule
From a signal detection theory perspective, the problem can be formulated as a binary
hypothesis test in which the null hypothesis, 𝐻𝑜 , expresses the observation when no stimulus is
presented, noise, n(t). The alternative hypothesis, 𝐻1, is when the observation contains a
stimulus-evoked response, ver(t).
𝐻𝑜: 𝑦𝑖(𝑡) = 𝑛(𝑡) , 𝑦𝑖(𝑡) ~ 𝒩(0, 𝜎𝑖)
𝐻1: 𝑦𝑖 (𝑡) = 𝑣𝑒𝑟(𝑡) + 𝑛(𝑡) , 𝑦𝑖(𝑡)~𝒩(𝑣𝑒𝑟(𝑡), 𝜎𝑖)
However, since we apply the hypothesis test only at time 𝜏𝑖 , then
𝑦𝑖(𝑡)~𝒩(𝑣𝑒𝑟(𝑡), 𝜎𝑖) and 𝐻1 can be written as: 𝐻1: 𝑦𝑖(𝑡) = 𝑣𝑒𝑟(𝑡) + 𝑛(𝑡) , 𝑦𝑖(𝑡)~𝒩(𝐴𝑖, 𝜎𝑖)
131
As such the discriminability index d’ (also known as sensitivity or index of separation)
will evaluate to 𝑑′ = 𝐴𝑖
√1
2𝜎𝑖
2
The log-likelihood ratio LLR is a robust strategy for selecting the position of the
detection threshold. Taking the log of the ratio of the conditional probabilities 𝑃𝑦|𝐻0(𝑦|𝐻0) and
𝑃𝑦|𝐻1(𝑦|𝐻1) will result in the log-likelihood ratio LLR, which defines the detection threshold, γ.
𝐿𝐿𝑅(𝑦𝑖 = 𝐴𝑖) = 1
2(
𝐴𝑖
𝜎𝑖)
2
≥ γ (C − 1)
In the case of the ideal observer, the detection threshold is formally the ratio of the priors
𝑃0(𝐻0)
𝑃1(𝐻1), equally penalizing missed events and false positives. However, the LLR is also related to
d’ through the parameter c, which is the distance between the actual threshold and the threshold
of the ideal observer.
𝐿𝐿𝑅(𝑦𝑖 = 𝐴𝑖) = 𝑐 𝑑′ (C - 2)
It’s become custom for the value of c to be chosen empirically and with the aid of visual
inspection [195], [196]. As such, the decision rule 𝜑(𝑥𝑖), decides in favor of one hypothesis over
the other based on 1-the detection threshold derived from combining Equation C-1 and C-2, and
2- the value of 𝜏𝑖, which is derived from the physiological characteristics of the visually evoked
response [107], [144], [144], [149], [177], [197]–[199].
𝜑(𝑥𝑖) = 1,
𝐴𝑖
𝜎𝑖≥ 2 𝑎𝑛𝑑 𝜏𝑖 ∈ [0.02,2]𝑠
0, 𝑜𝑡ℎ𝑒𝑟𝑤𝑖𝑠𝑒
3. Tuning curve derivation:
𝑇∙(𝜃𝑘) = ∑ 𝜑(𝑥𝑖)
𝑖 ∈ 𝛤
, 𝛤 = 𝑚: 𝜃𝑚 = 𝜃𝑘
𝜃∙ ∶ 1,2, … ,8 → 0°, 45°, … 315° and 𝛤 is the set of trials with trial number m such that
the orientation of the presented stimulus 𝜃𝑚 is equal 𝜃𝑘 .
132
4. The LMM:
𝑇𝐹𝑃(𝜃𝑘) ≈ 𝑂𝑆(𝜃𝑘)
𝑂𝑆(𝜃𝑘) = ∑
𝐷
𝑑=1
∑ 𝑤𝑛,𝑑(𝑥, 𝑦)𝑇𝑛,𝑑(𝜃𝑘)
𝑁
𝑛=1
133
Figure C-1. Surgical procedure and evaluation. Monitoring of the viral expression. The top row
corresponds to subject 1 and bottom to subject 2. Left to right: V1 targeting,
placement of optically clear cranial window and head plate. Expression spread 1
week after the day of injection. Expression spread 3 weeks after the day of injection.
[Pictures courtesy of author and Rebeca Castro.]
134
Figure C-2. Quantification of the visually evoked responses (VER). Quantification of the peak
amplitude and latency of the recorded VERs. Each row represents the recording
session from one of the four anatomical locations (A-E). The left column shows
latency and peak amplitude for VERs recorded with OS. Middle column shows
latency and peak amplitude for VERs recorded with FP. Right column compares the
latency of FP and OS VERs.
135
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150
BIOGRAPHICAL SKETCH
May was born in Cairo, Egypt and lived a considerable amount of her childhood in
Dresden, Germany. She finished her primary education in an international German school in
Cairo where she received the Abitur (Germany’s higher education entrance qualification
requirement). After that, she pursued a Bachelor of Science degree in systems and biomedical
engineering at the Cairo University in Egypt, which she graduated with honored distinction. May
worked for three years as a software engineering at two healthcare and medical software solution
companies.
In 2012 May moved to the US to start graduate school. She was admitted to Dr. Karim
Oweiss’ lab at Michigan State University in 2013, where she started her Ph.D. in electrical and
computer engineering. One year later, she moved with Dr. Oweiss to the University of Florida
and transferred to the Department of Biomedical Engineering.
May work in the Oweiss lab was very versatile and spanned numerous neuroscience
techniques like stereotaxic cranial surgery, injections and implants, post-mortem histological
analysis, neural data analysis, neural device design as well as peripheral nerve surgery, cuff
fabrication and electrical stimulation. She also served as the lab manager for three years.
May’s doctoral research focused on recording in-vivo neural ensemble activity as
reported by genetically encoded Ca2+ indicator using the fiber photometry system. She then
concentrated her efforts on deciphering the nature of neural signal recorded by the Fiber
Photometry system and conducted a systematic characterization of the device.
Over the course of her doctoral tenure, May also served as a graduate teaching assistant
for three graduate and undergraduate courses with the biomedical engineering department and
co-instructed the bioelectrical systems class with the Department of Electrical and Computer
Engineering at UF. May had numerous leadership experiences and received a certificate in
151
engineering leadership by the College of Engineering at UF in 2018. In 2017, she was elected
president of the Women in Science and Engineering (WiSE) student organization and has been
an active member since then. Her strong passion to encourage grade school students to learn
about STEM topics keeps her constantly involved in outreach programs and events.