University of Florida Thesis Or Dissertation Formatting Template

A SYSTEMATIC CHARACTERIZATION OF FIBER PHOTOMETRY FOR OPTICAL INTERROGATION OF NEURAL CIRCUIT DYNAMICS

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

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

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.

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.

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.

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

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

BIOGRAPHICAL SKETCH ...... 150

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

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

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

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

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

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

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.

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

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

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]

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].

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.

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

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

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.

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.

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.

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?”

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

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!

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].

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

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

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

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]

퐸푝 = ℎ 푓 (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]

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, 퐶, 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.

퐶 푛 = (2-2) υ hυ υ 퐸 = , since 푓 = (2-3) 푝 λ λ 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:

푛1푠𝑖푛휃1 = 푛2푠𝑖푛휃2 (2-4)

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:

휆 휃 = (2-5) 푑 푑

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]

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.

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.

1 2 2 sin(휃푎푐푐) = √푛1 − 푛2 (2-6) 푛0

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:

2 2 푁퐴 = 푛0 sin(휃푎푐푐) = √푛1 − 푛2 (2-7)

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

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.

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.

퐼 푇 = (2-8) 퐼0 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

-1 beam’s energy is called absorption coefficient µa and has units of mm . Absorption is related to transmission by Equation 2-7. More on the different types of absorption (radiative and non- radiative) in later sections.

퐼 1 퐴 = 0 = 푙표푔 ( ) = 2 − 푙표푔 (%푇) (2-9) 퐼 10 푇 10

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

-1 µs [mm ] 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

-1 medium. It is characterized by the attenuation coefficient µa [mm ]. Together, scattering and absorption exponentially attenuate a light beam according to Beer-Lambert’s law:

퐼(푧) = 푒−휇푧 = 푒−(휇푎+휇푠)푧 (2-10) 퐼0 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 푔, therefore, is the average of the cosine of the scattering angle 휃 and takes values from 0 to 1, with 1 being strictly forward while 0 indicates isotropic scattering.

푔 = 퐸{푐표푠휃} (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

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).

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

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

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.

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,

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-

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]

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

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

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,

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

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.

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

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)

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.

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.

Table 2-1. Comparison of the three main fluorescent imaging techniques. Two-photon imaging Single-photon Single-photon fiber (TPI) endoscopy 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.

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,

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]

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.

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

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

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

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

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

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.

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,

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.

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.

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.

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.

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.

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

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.

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 Target Region(s) Investigation Optical Fiber Power Ref Model PFC, CA1, BLA, LH, Real-time activity relationship Mouse VTA, NAc & BNST among many brain regions during 400/0.48 2.5-50 µW [131] simultaneously social behavior 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 spontaneous activity and early Temporal lobe 200/0.48 250 µW [136] Mouse network oscillations (ENOs) Mouse vS1 Sensory exploration 440/0.22 --- [65] Auditory network calcium Mouse Auditory cortex 200/0.48 10-100 µW [66] transients’ (NCaTs) Hybrid fiber setup exc. Mouse Dorsal STR Voluntary action initiation fiber 3.5 µW and det. fiber 100-120 µW [67] 105 µm, NA not reported V1 and dLGN thalamus Corticothalamic slow oscillations Mouse 200/0.48 <0.1mW/mm2 [137] and VPM of non-Rem sleep Mouse V1 Sensory integration 200/0.48 30 µW [138] Non-human M1 Motor movement mapping 200/0.48 --- [68] primate

Table 3-2 Continued Animal Target Region(s) Investigation Optical Fiber Power Ref Model Hybrid fiber setup exc Mouse striatal projection neurons Operant conditioning fiber 3.5µW and det fiber 100 µW [69] 105µm no NA reported Mouse VTA-Nac projections Social behavior 400/0.48 10-50 µW [70] Locomotion initiation and Mouse CA1 200/0.37 0.6-1.2 mW [71] velocity ARC of the hypothalamus and Mouse Feeding circuits and behavior 400/0.48 70 µW [139] PVH Neural networks activation due Rat S1FL to sensory stimulus neuronal 200/-- 1.3µW/mm2 [140] response Relationship between blood Rat (S1FL) oxygen level–dependent 200/0.48 <1 mW [72] (Bold)and neural activity 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] gonadotropin hormone (GnRH) Mouse ARN 400/0.48 50 µW [142] release 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.

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.

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 푇푛,푑(휃푘), and 푇퐹푃(휃푘), 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.

2 The LMM derives a pseudo-population statistic, 푇̂푂푆(휃푘) 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 푇푛,푑(휃푘), 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 푇̂푂푆(휃푘) that corresponds to the recorded population FP statistic 푇퐹푃(휃푘), (Equation 4-1 and Figure 4-1E). The pseudo- population statistic, 푇̂푂푆(휃푘) was contrasted to the observed population statistic, 푇퐹푃(휃푘), recorded with the FP (Equation 4-2), where 휃푘represents 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, 푇̂푂푆(휃푘) should approximate the FP- recorded population statistic 푇̂퐹푃(휃).

2 The terms ensemble and population will be used interchangeably.

퐷 푁 (4-1) 푇̂푂푆(휃푘) = ∑ ∑ 푤푛,푑(푥, 푦)푇푛,푑(휃푘) 푑=1 푛=1

푇퐹푃(휃푘) ≈ 푇̂푂푆 (휃푘) (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.

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

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.

A) B)

C) D)

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

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’, 푇퐹푃(휃푘). 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

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,푇̂푂푆(휃푘), 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

exhibited sharp tuning, others seemed unselective to the presented stimulus. The overall ensemble tuning statistic 푇퐹푃(휃푘) observed with the FP is shown in the left panel of Figure 4-2A.

The middle panel demonstrates the pseudo-tuning statistic 푇̂푂푆(휃푘)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.

A) C)

D) E)

Figure 4-2. In-vivo validation of the directly measured detection profile and volume. A) Left: Ensemble tuning statistic, 푇퐹푃(휃푘), recorded through FP from location E. Middle: pseudo-ensemble tuning statistic, 푇̂푂푆(휃푘), 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 푇푛,푑(휃푘). 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).

A) C)

D) E)

Figure 4-3. In-vivo validation of the directly measured detection profile and volume. A) Left: Ensemble tuning statistic, 푇퐹푃(휃푘), recorded through FP from location B. Middle: pseudo-ensemble tuning statistic, 푇̂푂푆(휃푘), 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 푇푛,푑(휃푘). 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).

A) C)

D) E)

Figure 4-4. In-vivo validation of the directly measured detection profile and volume. A) Left: Ensemble tuning statistic, 푇퐹푃(휃푘), recorded through FP from location C. Middle: pseudo-ensemble tuning statistic, 푇̂푂푆(휃푘), 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 푇푛,푑(휃푘). 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).

A) C)

D) E)

Figure 4-5. In-vivo validation of the directly measured detection profile and volume. A) Left: Ensemble tuning statistic, 푇퐹푃(휃푘), recorded through FP from location D. Middle: pseudo-ensemble tuning statistic, 푇̂푂푆(휃푘), 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 푇푛,푑(휃푘). 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).

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

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.

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.

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.

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],

-1 [163]–[166] (Table 5-1). For instance, for blue light, µs values of 8 - 13 mm 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,

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

-1 the size of a neuron (10 - 20 µm) was used. A value of µs = 60 mm for the forward path at 473

-1 nm and µs = 46 mm 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).

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.

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.

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.

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.

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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.

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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 µ µ λ Preparation s a g Illumination Measurement technique Reference Model [mm-1] [cm-1] [nm] 32 0.9 0.9 405 Mouse 23 0.3 0.9 532 1p Simulation based on mouse brain atlas [164] 19 0.1 0.9 635 In-vitro- 17 0.5 -- 480 Rat whole 1p Contact spatially resolved spectroscopy [162] 13 0.9 -- 530 brain 20 -- 0.93 480 1p Mathematical model [165] 12 -- 0.93 530 32 0.9 0.9 405 Double-integrating sphere setup, and Rat 23 0.3 0.9 532 1p [168] optical coherence tomography 19 0.1 0.9 635 In-vitro, Mouse 20 Ignored 0.925 920nm 2p --- [124] slice Mouse In-vivo 13.3 1 0.9 ---- 2p --- [125] 650------8-12 -- 0.9 1p --- [161] 950 Light transmission using optical power- Mouse Slice 21.1 0.62 0.86 473 1p [63] meter Cortical Rat/mouse 10.3/11.2 0.69 0.88 473 1p [62] slice 16.1 453 Slice, Light transmission using optical power- Mouse 16.5 --- >0.9 528 1p [166] Subcortical meter 14.08 940 Double-integrating-sphere to measure diffuse transmittance, diffuse Rat Cortex 17 0.25 0.9 532 1p reflectance, and ballistic transmittance [163] followed by inverse adding doubling method (IAD)

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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.

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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

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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].

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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.

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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

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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].

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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]

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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

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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).

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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

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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

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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.

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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]

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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 푦푖(푡) (snippet):

휏푖 = {푡 ∶ 푦푖(푡) = max(푦푖 (푡))} 퐴푖 = 푦푖(푡)훿(푡 − 휏푖) ∑푁 |푦(푡) − 푦̅|2 휎 = √ 푡=1 푖 푁 − 1 Where i is the trial number and 𝑖 ∈ (1,2, … ,10), N is the number of samples in the snippet and 푦̅ is the temporal average of the snippet.

퐴푖 푥̅푖 = [휏푖 ] , where 푥̅푖, is the feature vector associated with every trial i 휎푖

2. Decision rule

From a signal detection theory perspective, the problem can be formulated as a binary hypothesis test in which the null hypothesis, 퐻표, expresses the observation when no stimulus is presented, noise, n(t). The alternative hypothesis, 퐻1, is when the observation contains a stimulus-evoked response, ver(t).

퐻표: 푦푖(푡) = 푛(푡) , 푦푖(푡) ~ 풩(0, 휎푖)

퐻1: 푦푖 (푡) = 푣푒푟(푡) + 푛(푡) , 푦푖(푡)~풩(푣푒푟(푡), 휎푖)

However, since we apply the hypothesis test only at time 휏푖 , then

푦푖(푡)~풩(푣푒푟(푡), 휎푖) and 퐻1 can be written as: 퐻1: 푦푖(푡) = 푣푒푟(푡) + 푛(푡) , 푦푖(푡)~풩(퐴푖, 휎푖)

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As such the discriminability index d’ (also known as sensitivity or index of separation) will evaluate to 푑′ = 퐴푖 1 √ 휎2 2 푖

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 푃푦|퐻0 푦 퐻0 and

( | ) 푃푦|퐻1 푦 퐻1 will result in the log-likelihood ratio LLR, which defines the detection threshold, γ.

2 1 퐴푖 퐿퐿푅(푦푖 = 퐴푖) = ( ) ≥ γ (C − 1) 2 휎푖

In the case of the ideal observer, the detection threshold is formally the ratio of the priors

( ) 푃0 퐻0 , equally penalizing missed events and false positives. However, the LLR is also related to 푃1(퐻1) d’ through the parameter c, which is the distance between the actual threshold and the threshold of the ideal observer.

′ 퐿퐿푅(푦푖 = 퐴푖) = 푐 푑 (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 휑(푥푖), 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 휏푖, which is derived from the physiological characteristics of the visually evoked response [107], [144], [144], [149], [177], [197]–[199].

퐴푖 1, ≥ 2 푎푛푑 휏푖 ∈ [0.02,2]푠 휑(푥푖) = { 휎푖 } 0, 표푡ℎ푒푟푤𝑖푠푒 3. Tuning curve derivation:

푇∙(휃푘) = ∑ 휑(푥푖) , 훤 = { 푚: 휃푚 = 휃푘} 푖 ∈ 훤 휃∙ ∶ {1,2, … ,8} → {0°, 45°, … 315°} and 훤 is the set of trials with trial number m such that the orientation of the presented stimulus 휃푚 is equal 휃푘.

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4. The LMM:

푇퐹푃(휃푘) ≈ 푇̂푂푆(휃푘) 퐷 푁

푇̂푂푆(휃푘) = ∑ ∑ 푤푛,푑(푥, 푦)푇푛,푑(휃푘) 푑=1 푛=1

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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.]

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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.

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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

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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.

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