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Spatiotemporal Analysis of Functional Dynamic Imaging Data

Cyrus B. Amoozegar

Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy in the Graduate School of Arts and Sciences

COLUMBIA UNIVERSITY 2014

ABSTRACT

Spatiotemporal Analysis of Functional Dynamic Imaging Data

Cyrus B. Amoozegar

Technological advances in image acquisition speeds and new contrast agents, in both clinical and basic research settings, have enabled entirely new approaches to functional imaging in living systems. Analysis of dynamic and multidimensional data requires very different approaches to the classical segmentation and visualization tools developed for purely structural or anatomical imaging. This thesis details the development of two different spatiotemporal analysis approaches for high-speed in-vivo dynamic optical imaging. Optical imaging is a diverse, versatile, and generally inexpensive modality that can take advantage of a wide range of endogenous and exogenous sources of optical contrast within living tissue.

While light scattering can limit resolution and sensitivity of imaging in deeper tissues, optical imaging is well suited for small animal studies where it can be used for studies of physiology and disease processes, for pharmaceutical development and as a test-bed for translation to clinical applications.

In the first part of this work, we present and apply spatiotemporal analysis techniques which we define as

‘dynamic contrast enhancement’ methods. We apply these methods to in-vivo whole body small animal molecular optical imaging to demonstrate that dynamic analysis can be used for longitudinal assessment of organ function. We then demonstrate the equivalence of our approach to dynamic contrast enhanced magnetic resonance imaging. This optical technique could allow for better informed drug development and longitudinal toxicity evaluation. This technique could also serve as a platform for the development of functional imaging methods using dynamic MRI.

We then apply spatiotemporal analysis techniques to high speed optical hemodynamic imaging data acquired on the exposed rodent cortex. The purpose of this work is to develop a mechanistically-based spatiotemporal model of neurovascular coupling, in order to better understand the basis of functional magnetic resonance imaging data in the human brain. Our results also provide new insights into potential links between neurovascular disruption and disease pathophysiology in the brain.

Contents

List of Figures ...... iii List of Tables ...... vii Acknowledgements ...... viii Definitions and List of Acronyms ...... ix Chapter 1 ...... 1 1.1 Reflection and Transmission ...... 4 1.2 Scattering ...... 7 1.3 Absorption ...... 11 1.4 Fluorescence ...... 15 Chapter 2 ...... 19 2.1 In vivo Small Animal Imaging Technologies ...... 22 2.1.1 Fluorescence and Bioluminescence imaging ...... 22 2.1.2 Micro-CT and Small Animal MRI ...... 25 2.2 Liver ...... 27 2.2.1 Liver Physiology ...... 27 2.2.2 Assessing Liver Function ...... 30 2.3 Development of DyCE system and imaging protocol ...... 31 2.3.1 Experimental Set-up ...... 31 2.3.2 Data Preprocessing ...... 33 2.4 Establishment of Repeatability of DyCE Measurements ...... 36 2.4.1 Determining Repeatability ...... 36 2.4.2 Determining the Effect of Organ Dysfunction ...... 38 2.5 Assessing Liver Function ...... 41 2.5.1 Liver function trials ...... 41

2.5.2 Liver function metrics ...... 42 2.5.3 Difficulties in These Experiments ...... 45 2.6 Comparison of DyCE and DCE-MRI ...... 47 2.6.1 DCE-MRI ...... 47 2.6.2 DyCE and DCE-MRI: Healthy mice ...... 49 2.6.3 DyCE and DCE-MRI: Liver tumor mice ...... 53 2.7 Clinical Relevancy ...... 57 Chapter 3 Development of dynamic analysis techniques applied to rodent functional neuroimaging data ...... 58 3.1. Cerebral vasculature, imaging the hemodynamic response, and the importance of modeling ..... 61 3.1.1 Review of Cerebral Vasculature ...... 61 3.1.2 Imaging the Hemodynamic Response ...... 63 3.1.3 Modeling of Neurovascular Coupling ...... 67 3.2 Characterization of the Experimental Data ...... 70 3.3 The Two-component Hemodynamic Response Function ...... 79 3.4 The Smooth Muscle Cell Point Spread Function ...... 83 3.5 The Endothelial Propagation Hemodynamic Response Model and Data Simulation ...... 94 3.5.1 The Endothelial Propagation Hemodynamic Response Model ...... 94 3.5.2 Full Response Prediction ...... 97 3.5.3 Simulating Full Spatiotemporal Data Sets with the EP-HR Model ...... 107 3.6 Conclusions and further work ...... 113 Bibliography ...... 115 Appendix: Publications and Presentations Related to the Thesis ...... 121

List of Figures

1-1. Snell’s Law ...... 5

1-2. Polarization ...... 6

1-3. Point Spread Functions...... 9

1-4. Resolution and Image Formation ...... 10

1-5. Absorption...... 11

1-6. The Optical Window...... 13

1-7. Jablonski diagram...... 15

1-8. Absorption and Emission Spectra...... 16

2-1. Anatomical map generated non-invasively ...... 20

2-2. Fluorescence is zero background...... 23

2-3. Bioluminescence Imaging...... 24

2-4. A reconstruction of a mouse abdomen using µCT...... 25

2-5. Coagulation cascade...... 28

2-6. DyCE Imaging System...... 32

2-7. Time course of ICG fluorescence from a region of interest selected at the border of the lung ...... 34

iii

2-8. Excitation spectrum of ICG in plasma for multiple concentrations ...... 37

2-9. DyCE analysis in mice before and after CCl4 induced liver damage...... 40

2-10. Quantification of the changes seen after CCl4 injection ...... 43

2-11. Comparison of DyCE measurements to liver enzyme concentration during transient liver damage...... 45

2-12. Comparison between DyCE and DCE-MRI with Magnevist in a healthy mouse ...... 51

2-13. Comparison between DyCE and DCE-MRI with Eovist in the liver of a healthy mouse ...... 53

2-14. Comparison between DyCE and DCE-MRI with Eovist in the liver of a mouse with a large liver tumor...... 55

3-1. Diagram of the cortical vasculature...... 62

3-2. The Absorption spectra for HbO, HbR, and H2O, and the wavelength dependence of optical scattering...... 63

3-3. Diagram of the optical intrinsic signal imaging system...... 64

3-4. An example of OISI data...... 66

3-5. Typical representation of electrical activity...... 67

3-6. The goal of determining a mathematical model ...... 69

3-7. Time courses from the surround and responding regions ...... 71

3-8. The hemodynamic response with 12 second stimulus ...... 73

3-9. Minimum Threshold of Data...... 74

3-10. Maximum Threshold...... 75

3-11. Hook response...... 76

3-12.Linear convolution model...... 77

3-13. Amplitude of the linear model predictions as a function of stimulus length...... 78

3-14. Backwards model results...... 82

3-15. Two components of hemodynamic response ...... 84

3-16. Mechanism of smooth muscle cell relaxation...... 86

3-17. Two measured smooth muscle cell point spread functions ...... 87

3-18. ΔHbT time course taken from over skull bone. This time course shows an unexplained global trend...... 88

3-19. A possible mechanism for the ringing effect seen in the smooth muscle cell point spread function ...... 90

3-20. Field of view showing propagation of the hyperpolarization and calcium induced dilation waves...... 91

3-21. Two hypothetical models for how repeated stimuli add together...... 93

3-22. Maximum amplitude of response for a single rat under different stimulus lengths...... 95

3-23. Simulated calcium-mediated dilation wave ...... 96

3-24. Determining the scaling factor ...... 97

3-25. Measured (blue) and predicted changes (green) in ΔHbT for 0.5 – 3 second stimuli for the responding region based on endothelium propagating hemodynamic response model ...... 98

3-26. Measured (blue) and predicted (green) changes in ΔHbT for 4 - 9 second stimuli for the responding region based on the endothelial propagating hemodynamic response model ...... 99

3-27. Measured (blue) and predicted (green) changes in ΔHbT in the responding region for 10 - 14 second stimuli based on the endothelial propagating hemodynamic response model ...... 100

3-28. Simulated data using the full endothelial propagation hemodynamic response model for the responding region ...... 101

3-29. The ringing in the smooth muscle cell point spread function ...... 102

3-30. The time courses of bad fits...... 105

3-31. Determining a(x,y) and b(x,y) spatial maps for the endothelial propagating hemodynamic response model for a rat with 12 second stimulus ...... 108

3-32. Comparison of the experimental response to stimulus and the modeled response...... 110

3-33. Comparison of the experimental response to 14 second stimulus and the modeled response using spatial maps derived from a data of a 12 second stimulus...... 112

3-34. A schematic outline of an artery, capillary, and vein in series ...... 114

List of Tables

Table 1. R2 values for a linear fit between the predicted and measured hemodynamic response lengths for a wide variety of stimulus lengths in a rat………………………………………………………………………………………103

vii

Acknowledgements

I would like to thank everyone who helped make this thesis possible

viii

Definitions and List of Acronyms

ALT Alanine aminotransferase

AST Aspartate aminotransferase

DCE-MRI Dynamic Contrast Enhanced Magnetic Resonance Imaging

DyCE Dynamic Contrast Enhanced Optical Imaging fMRI Functional Magnetic Resonance Imaging

FOV Field of View

Gd Gadolinium

GGT Gamma glutamy transpeptidase

HbO Oxygenated Hemoglobin

HbR Deoxygenated Hemoglobin

HbT Total Hemoglobin

ICG Indocyanine Green

MRI Magnetic Resonance Imaging

PSF Point Spread Function

RGB Red Green Blue

µCT Microcomputed Tomography

Chapter 1

Introduction and Background

In the past both clinical and research imaging methods have focused on anatomical imaging and much work has been done on spatial analysis techniques. Technological advancements are now allowing for high speed in-vivo imaging to be possible and for data to be acquired over time. These advances allow for investigation of dynamic and functional processes, in addition to the acquisition of structural information.

In order to exploit these new imaging capabilities, we must develop a new set of techniques that can extract meaningful functional information from these dynamic data sets. The spatial techniques available for anatomical imaging must be expanded upon to allow for spatiotemporal analysis.

This thesis is focused on functional optical imaging and the development of optical imaging spatiotemporal analysis techniques. Optical imaging is an incredibly versatile modality. Optical imaging methods are inexpensive, generally fast, and allow for significant control over experimental conditions.

Optical imaging is well suited for animal studies due to the wide variety of available contrast agents and the recent progress made in genetic engineering relating gene expression and cellular function to optical fluorescence.

In this thesis we develop and demonstrate spatiotemporal analysis of in-vivo optical imaging data in two settings. The first applies dynamic contrast enhancement methods to small animal molecular imaging. The

1 technique presented allows for whole body imaging of mice and assessment of organ function. With this technique we can impact the pharmaceutical industry by allowing for better informed drug development, longitudinal assessment of treatment efficacy and toxicity evaluation. The second application relates to understanding the spatiotemporal dynamics of blood flow modulations in the living brain. We use spatiotemporal analysis techniques to develop a physiologically based mathematical model of neurovascular coupling to provide insights into the underlying cellular basis of this phenomenon, thus providing improved interpretation of functional magnetic resonance imaging (fMRI) data and possible insight into disease pathologies relating to neurovascular coupling.

The techniques developed here can, in some cases, be translated to clinical dynamic imaging modalities based on CT, MRI, and US. In other cases, these methods provide new insights into physiology and disease that are not available with anatomical imaging. Overall, the development of quality spatiotemporal analysis techniques in small animal imaging provides a method to develop a better measurement and understanding of function and gives insight on how to develop these functional imaging techniques clinically.

This thesis is divided into three chapters:

Chapter 1 introduces in-vivo optical imaging and presents the ways in which photons interact with biological tissues. It provides a context of how these interactions can be exploited to obtain organ function

(Chapter 2) and obtain hemodynamic information (Chapter 3).

Chapter 2 describes the application of dynamic analysis techniques to the problem of small animal molecular imaging. This chapter details the expansion of a whole body small animal imaging modality, termed dynamic contrast enhanced (DyCE) optical imaging, from a tool for developing anatomical maps into a method for assessing organ function. This chapter begins by demonstrating the repeatability of

DyCE measurements and then discusses how DyCE was used to assess liver function in mice. The chapter

2 ends with a comparison of DyCE to the clinically used method dynamic contrast enhanced magnetic resonance imaging (DCE-MRI).

Chapter 3 shows optical hemodynamic imaging in the rodent brain used to explore neurovascular coupling, which forms the basis for fMRI, and establishes a spatiotemporal dynamic model based on this high speed, high resolution data to explain the hemodynamic response and provide insight into a potential underlying cellular mechanism.

1.1 Reflection and Transmission

This section introduces the photon-tissue interactions that form the basis of the optical techniques presented in this thesis. Transmission and reflectance of photons moving between different media, optical scattering, absorbance and fluorescence are presented and discussed in the context of their applications to chapter 2 and chapter 3.

The refractive index of a material is a measure of how quickly light propagates through that particular material. Light travels at a constant speed in a vacuum, but slows when propagating through matter. The refractive index of an object, 푛, describes this change in speed and is defined as:

푐 푛 = 푣 where 푐 is the speed of light in a vacuum and 푣 is the speed of light in the material.

As light moves from between materials with different refractive indices it will change directions. This directional change is referred to as refraction and can be described using Snell’s law. Snell’s law, as shown in Figure 1-1, states

푣1 푛2 sin(휃1) = = 푣2 푛1 sin(휃2)

where 푣1 and 푣2 are the speeds of light in materials 1 and 2, 푛1 and 푛2 are the refractive indices of those materials, and 휃1 and 휃2 are the angles the light forms with a vector normal to the surface.

Figure 1-1. Snell’s Law. As light moves between materials of different refractive indices, the direction and speed of light will change at the interface.

When light is incident on a surface, not all of the light will necessarily be transmitted. At the interface between the two materials, light can also be reflected. The proportion of the incident power that enters the material is referred to as transmittance and the proportion that remains in the original material is referred to as reflectance. Together, transmittance and reflectance sum to one. The transmittance and reflectance are functions of the angle of incidence, the refractive indices of the materials, and the orientation of the light’s electric field to the plane of incidence.

Photons have an electric field and the orientation of this field to the plane of incidence determines how light reflects from the surface. When the electric field of an incident photon is parallel to plane of incidence on a material, the light is said to have parallel polarization and when the electric field is perpendicular to the plane of polarization the light has perpendicular polarization [1]. Figure 1-2 illustrates these polarizations.

Figure 1-2. Polarization. Parallel and perpendicular polarizations are based on the orientation of the light’s electric field to the plane of incidence. When the electric field is perpendicular to the plane, the light has perpendicular polarization. When the electric field is parallel to the plane, the light has parallel polarization

A series of equations called the Fresnel equations can be used to determine the reflectance coefficients of the interface [1]. As light propagates through material i and is incidence on material t, the reflectance coefficient of perpendicular polarized light, 푅⊥, is [1]

2 푛푖 cos(휃푖) − 푛푡 cos(휃푡) 푅⊥ = ( ) 푛푖 cos(휃푖) + 푛푡 cos(휃푡)

and the reflectance coefficient of parallel polarized light, 푅∥, is

2 푛푖 cos(휃푡) − 푛푡 cos(휃푖) 푅∥ = ( ) 푛푖 cos(휃푡) + 푛푡 cos(휃푖)

Unpolarized light can be thought of as having half parallel polarization and half perpendicular polarization.

Therefore, when considering unpolarized light the reflectance coefficient of an interface is [1]

푅⊥ + 푅∥ . 2

1.2 Scattering

Scattering is a form of light-matter interaction that occurs due to refractive index mismatches in materials and causes photons to change directions. Reflection and refraction as discussed here can be considered macroscopic effects of light propagation. Biological tissues are often composed of several materials with different refractive indices. As light moves through the tissue, refraction and reflection effects within the sample will cause photons to change directions and will contribute to the bulk scattering.

Scattering can also be considered in terms of individual scattering events. Scattering is divided into elastic and inelastic forms. Elastic optical scattering conserves the energy of the photon, while in inelastic scattering the energy of the photon changes. Most optical imaging techniques for biologic tissues, particular those that image samples deep in tissue, are affected by elastic scattering. Notably, certain optical imaging techniques for biologic tissues, such as Raman spectroscopy, are designed to exploit inelastic scattering. However, in other optical techniques the effects of inelastic scattering are negligible.

Elastic scattering in biological tissues is divided into Rayleigh scattering or Mie scattering depending on the size of the scatterer. Rayleigh scattering occurs when the scattering particle is significantly smaller than the wavelength of light, while Mie scattering occurs with particles that are approximately the same size as the wavelength of light. Light-tissue interactions with submicron cellular components such as the cellular membrane, collagen fibers, or the golgi apparatus involve Rayleigh scattering and scattering from larger organelles, such as mitochondria (~1µm) or the nucleus (5-10µm) are dominated by Mie scattering

[2, 3].

Rayleigh scattering occurs because the electric field of a photon interacts with a particle. The oscillating electric field of a photon is given by the equation:

2휋푐푡 퐸 = 퐸 cos ( ) 0 휆

7 where 퐸0 is the maximum amplitude of the electric field, 푐 is the speed of light, 푡 is time, and 휆 is the wavelength of the light. When a photon interacts with a small, polarizable particle, the electric field of the photon induces an oscillating dipole moment in the particle. The size of this dipole moment, p, is dependent on the magnitude of the photon’s electric field and the polarizability of the particle, 훼.

2휋푐푡 푝 = 훼퐸 = 훼퐸 cos ( ) 0 휆

This oscillating dipole will radiate a photon of the same energy as the photon that induced the dipole. The occurrence of this Rayleigh scattering phenomenon is proportional to the inverse of the fourth power of the wavelength of light.

Mie scattering theory is based off an exact solution to Maxwell’s equations for spherical particles. In Mie scattering, the size, shape, and index of refraction of the scattering particle will affect the wavelength dependency, but overall Mie theory is significantly less dependent on the wavelength of the light being scattered [4].

Forward scatter refers to scattered light that continues in the direction of the original propagation and back scatter refers to scattered light that travels towards the direction of its origin. Rayleigh scattering tends to occur as a mix of forward and back scattering, while Mie scattering is mostly in the forward direction [1, 4, 5]. The anisotropy factor, g, is a quantity that describes the directionality of scattering in a tissue. This factor is the mean cosine of the scattering angles. A value of g=0 indicates that the scattering is isotropic, g=1 indicates that only forward scattering occurs, and g=-1 indicates that only backscattering occurs.

The general scattering properties of a biological tissue can also be described by using the scattering coefficient µs. The value µs is the probability that a photon will be scattered per unit length. The inverse of this quantity is referred to as the mean free path and is the average distance a photon travels between

8 scattering events. The anisotropy factor and the scattering coefficient can be combined to determine the reduced scattering coefficient, µs’ by

′ 휇푠 = 휇푠(1 − 푔).

Scattering can also affect an imaging systems resolution. If a target is located deep in tissue, light from the target will scatter before leaving the tissue and reaching the detector, causing the image on the detector to blur. The point spread function of an optical imaging system is a function that describes the image formed from a point source. The image of a more complex object will be the point spread function convolved with that object. Figure 1-3 shows a point source object, a point spread function and the resulting image.

Figure 1-3. Point Spread Functions. The point spread function of an imaging system describes the image formed when imaging a point source. In optical imaging, scattering within the system can lead to blurring. The more scattering that occurs, the wider the point spread function will be.

The greater the amount of scattering that occurs, the wider the point spread function will be and the greater the amount of blurring that will appear in the image. Too many light scattering events can result in objects being difficult to resolve because they will blur together. Figure 1-4 shows two objects that are close together. Optical scattering will cause blurring in the image and this can cause the two objects to blur together.

Figure 1-4. Resolution and Image Formation. Two objects close together will not be able to be resolved in an image if too much scattering occurs.

The point spread function can also be considered the minimal response that the imaging system can make.

Chapter 3 will apply a similar concept to hemodynamic imaging to find the minimum dilation response a vessel can make in response to an external stimulus. Similar to an optical imaging system’s point spread function being used to determine the image of a complex object, the function determined in Chapter 3 will be used to determine other, larger hemodynamic responses.

Scattering in biologic tissues can be considered a combination of Rayleigh scattering and Mie scattering.

1 Overall the wavelength dependence scattering in tissues is dominated by Rayleigh scattering’s 휆4 dependence. As a result, for imaging objects that will have a significant amount of scattering, longer wavelength light is preferred. The whole animal imaging system in chapter 2 uses near infrared (NIR) light so as to minimize the effects of scattering and retain image resolution. Scattering in tissue will also have an effect on the amount of signal lost to absorption.

1.3 Absorption

As light propagates through a material, the material will act as an absorber and some of the photons will be converted into internal energy of that absorber. The macroscopic effect of absorption is that the intensity of light is attenuated as it is transmitted through matter. This attenuation can be described using the Beer-Lambert law. This law states:

−휇훼퐿 퐼 = 퐼0푒

where 퐼0 is the intensity light incident on the matter, 퐼 is the light transmitted, L is the distance the light travels through the matter, and 휇훼 is a tissue-dependent quantity called the attenuation coefficient that is the absorption counterpart of to the scattering coefficient µs. Figure 1-5 illustrates this process. Light of intensity I0 is incident on the material and a lower intensity of light, I, emerges from the other side of the material.

Figure 1-5. Absorption. The incident light intensity I0 is attenuated as the light is transmitted through the material over distance L. The absorption coefficient of the absorber is 휇훼. Light of intensity I is transmitted through the material.

Blurring in images is not the only consequence of scattering. One consequence of the Beer-Lambert law is that increasing L increases the amount of signal attenuation that occurs. Scattering increases the total distance a photon must travel before reaching a detector, thus allowing for more absorption events to

11 occur. The increased absorption attenuates the amount of light available for detection. This stresses the importance of selecting an appropriate light source with optical imaging techniques that require light to propagate through tissue, such as whole body animal imaging.

The attenuation coefficient is often wavelength dependent. On a microscopic level, the electrons in a molecule will have quantized energy levels. A molecule will only absorb a particular photon if the energy of that photon matches the difference energy levels of the electron. The incident photon will excite the electron to its higher energy state. One way this electron can then return to its ground state by converting the energy from the photon into vibrational energy. This conversion of photons into vibrational energy also explains why most materials increase in temperature as they absorb light.

Absorption spectroscopy is a technique to measure the absorption of a sample as a function of wavelength. Biological tissues, such as lipid, oxygenated blood, deoxygenated blood, and water all have different absorption spectra. Figure 1-6, adapted and reproduced from [6], shows the absorption spectra of water, oxygenated, and deoxygenated hemoglobin between 400 and 1000nm. For biologic tissues there is an “optical window” that exists for light with wavelengths between 600nm and 900nm [6-8]. Below

600nm, hemoglobin shows strong absorbance [9, 10]. Above 900nm water the absorption from water increases [11, 12]. This leaves a 300nm band where absorption can be minimized. For techniques such as fluorescence imaging, this optical window is critically important as improper wavelength selection can limit depth of imaging. The optical contrast agents and the light sources used in Chapter 2 were specifically selected because they were in this window, thus minimizing the limitations caused by absorption. In the case of whole body animal imaging, absorption is a limitation, but in Chapter 3 absorption characteristics are exploited in order to obtain functional information.

Figure 1-6. The Optical Window. Also referred to as the near-infrared (NIR) window for imaging biological tissues. Below 600nm there is significant hemoglobin absorption. Above 900nm there is significant water absorption. Adapted and reproduced from [6].

Beer’s law relates the attenuation coefficient of a tissue to the concentration of the different compounds that compose that tissue.

휇푎 = ∑ 휖푛푐푛 푛

where 휖푛 is the molar absorptivity of compound n, another wavelength dependent constant, and 푐푛 is concentration of compound n. The optical imaging system in Chapter 3 takes advantage of this relationship to assess changes in oxygenated and deoxygenated hemoglobin. The technique in chapter 3 is based on a modified Beer-Lambert law approach, which states [13]:

−휇푎,휆(푡)휒휆+퐺 퐼휆(푡) = 퐼휆(0)푒 where the additional G term is a geometry-dependent factor that is difficult to quantify. Only changes in

휇푎 are considered in order to eliminate the G term and Beer’s law is applied.

퐼휆(푡) ln ( ) = −[휇푎,휆(푡) − 휇푎,휆(0)]휒휆 퐼0(0)

퐼휆(푡) ln ( ) = −[휖퐻푏푂2,휆Δ푐퐻푏푂2 + 휖퐻푏푅,휆Δ푐퐻푏푅]휒휆 퐼0(0)

By imaging with two wavelengths, the absorption properties of oxygenated and deoxygenated

hemoglobin can be used to determine the unknowns Δ푐퐻푏푂2 and Δ푐퐻푏푅.

1.4 Fluorescence

Fluorescence is the phenomenon that occurs when a photon is able to excite an electron in a molecule to a higher energy state and then when that electron relaxes to its ground state, a photon of less energy is emitted. Figure 1-7 shows a Jablonski diagram that illustrates the excitation of an electron from its ground state to a higher energy level by absorbing a high energy blue photon. While in the higher energy state, some of the energy is converted to vibrational energy. The electron then relaxes back down to ground state and emits a lower energy red photon.

Figure 1-7. Jablonski diagram. A higher energy photon excites an electron to a higher energy level. When the electron returns to ground state it emits a lower energy photon.

In order for a molecule to fluoresce, the energy of the incident photon must exactly match the difference in the energy levels of the electron. Molecules that can undergo fluorescence are called fluorophores.

When these molecules occur naturally in vivo, it is called intrinsic fluorescence. NADH and FAD are two examples of intrinsically fluorescent molecules of particular importance [14]. Other fluorophores, called exogenous fluorophores can be added to a tissue sample as well. Fluorophore molecules are usually characterized based on their excitation and emission spectra. Excitation spectra are plots of fluorescence intensity as a function of excitation wavelength. Emission spectra are plots of the intensity of emitted light

15 as a function of wavelength. Figure 1-8 provides an example of a typical absorption and emission spectrum for a theoretical fluorophore.

Figure 1-8. Absorption and Emission Spectra. An example of a typical absorption and emission spectrum for a fluorophore.

In biological samples, it is particularly important to consider other possible photon-tissue interactions when selecting a fluorophore. A fluorophore should be selected such that the necessary excitation and emission wavelengths are not excessively absorbed by the surrounding tissue. For whole body animal imaging, fluorophores that excite and emit in the red/NIR portion of the spectrum are preferred to minimize scattering and absorption.

One of the biggest advantages of optical imaging over other modalities is the availability of a wide assortment of both targeted and non-targeted contrast agents [15-18]. For instance, fluorophores can be attached to antibodies that will bind to specific targets on cancerous cells [19, 20]. Reporter dyes are available that are calcium and voltage sensitive [21, 22]. Fluorescent molecules can be genetically encoded into cells or transgenic mice to identify specific cell types or serve as reporter proteins [23]. Fluorophores

16 are available over a wide spectrum of wavelengths and multiple fluorophores can be used simultaneously with proper experimental setup [24].

With optical imaging there is often a tradeoff between depth of imaging and spatial resolution. In biological tissues, this tradeoff is a consequence of photon-tissue interactions. The theoretical maximum lateral resolution any optical imaging system can obtain is called the diffraction limit. According to this limit, the minimum resolvable distance between two points is directly proportional to the wavelength used for imaging. That is, the theoretical maximum lateral resolution of a system can be increased by using lower wavelength of light used. However, this would result in increased scattering and absorption as the light propagated through tissue.

The width of an imaging system’s point spread function affects resolution. Increased scattering will widen a point spread function, resulting in blurring. Microscopy is a high resolution optical imaging technique.

Certain microscopy techniques such as, confocal or two-photon, offer some depth resolution, but are limited to a few hundred microns [25, 26]. These depth limits occur because scattering and absorption increase as the focal plane moves deeper in a tissue sample, resulting in a decreased spatial resolution.

Additionally there is increased absorption as depth increases, reducing the number of photons that can be detected from the sample. In the case of fluorescence, scattering and absorption also lower the number of excitatory photons reaching the target sample. Other optical techniques such as optical tomography have lower spatial resolution but can be used to acquire information about larger samples.

Optical tomography is a technique that involves using information about how light is absorbed and scattered in tissue to reconstruct the internal composition of that tissue [27, 28]. Increased absorption reduces the number of photons that can be detected and increased scattering widens the point spread function, reducing the amount of information available for reconstruction.

Modern cameras are highly sensitive to photon counts and can operate at high speeds. As a result, the time scales of acquisition for optical imaging can be very fast. Many optical imaging techniques can be performed with sub-second acquisition speeds, making them particularly well suited for dynamic imaging

[29]. Development of dynamic analysis techniques with these high speed systems can provide insights which could inform development of similar techniques on systems slower acquisition speeds, such as MRI.

Chapter 2

Dynamic Contrast Enhanced Optical Imaging

Dynamic Contrast Enhanced (DyCE) Optical Imaging is a molecular imaging technique that was born out of the need for inexpensive, fast, non-invasive techniques for small animal imaging. In a 2007 Nature

Photonics paper Dr. Elizabeth Hillman showed that when a fluorescent dye is injected into the vascular compartment of a small animal and a time series of images is acquired, differences in the biodistribution dynamics between organs could be isolated and used to generate anatomical maps [30]. The idea works because each organ in the body has its own vascular signature. As the fluorescent bolus travels through the vascular compartment where the dye washes in and out of each organ’s vasculature at a rate unique to the particular organ system. Organ systems can also exhibit a contrast agent-parenchymal cell interactions. In the original paper, after a time series of images was acquired, two techniques were used to generate anatomical maps. First, principal component analysis (PCA) was applied to the data sets and the first few components were used to make RGB merged images. The second method involved manually selecting nine separate regions of interest from the data set corresponding to different organ systems and then using these as basis functions in a non-negative least squares fit. Figure 2-1 shows an anatomic map generated non-invasively with DyCE. Time courses from bone, kidney, brain, small intestine, spleen, lungs, eyes/lymph nodes, adipose tissue were used with a non-negative least squares fit to develop this map.

Figure 2-1. Anatomical map generated non-invasively from time courses of manually selected regions of interest. Adapted and Reproduced from [30]

Disease states can change the vascular dynamics of an organ and alter cellular activity. Building off this original idea, we postulated that DyCE could be used as a tool to measure the changes caused by different pathologies. This chapter focuses on the development of DyCE as a non-invasive tool for assessing organ function by exploiting changes in the vascular function and parenchymal changes in disease states. The liver was chosen as the organ of interest. This chapter is organized into the following sections:

Section 2.1 provides background on common small animal imaging modalities and discusses their applications and limitations.

Section 2.2 explains the choice of the liver as the organ of interest, providing a description of liver physiology and the current methods for assessing liver function.

Section 2.3 describes the development of DyCE system and imaging protocol. This section discusses the creation of the imaging system and its advantages over commercially available systems. The development of the DyCE preprocessing algorithm is also discussed.

Section 2.4 demonstrates the capability of DyCE to acquire repeatable data sets. This section shows that

DyCE measurements are similar across cohorts and change when organ function is altered.

Section 2.5 demonstrates that DyCE can quantitatively assess organ function. Metrics of assessment for

DyCE measurements of liver function are developed and compared to gold standard tests that are commonly used in hospitals.

Section 2.6 compares DyCE with its magnetic resonance imaging counterpart, DCE-MRI. Similar studies are shown using both DyCE and DCE-MRI in mice with liver tumors. The similarities and differences in the determined dynamics are discussed.

Section 2.7 concludes this chapter and discusses the clinical relevance of the findings of this chapter.

2.1 In vivo Small Animal Imaging Technologies

Small animals, such as rodents, can provide excellent models for studying disease [31-34]. They are relatively inexpensive, reproduce quickly, have relatively short life cycles, and their biology is similar enough to humans that disease models can be developed that mimic human disease pathologies. Insights from the study of small animals are vital to medical research and the development of medical products, such as pharmaceuticals. A number of techniques are available for imaging small animals and each has its benefits and drawbacks.

2.1.1 Fluorescence and Bioluminescence imaging

Fluorescent imaging in small animals is a vast field with a variety of applications ranging from imaging whole bodies of rodents to identifying specific molecular pathways. The fluorescence can come from many sources including intrinsic contrast, genetically transfected fluorescent proteins, exogenous fluorophores [35, 36]. These dyes can be targeted to have higher affinities to particular cellular structures or substances, such as via conjugation to an antibody. This dyes

One particular application well suited for fluorescence imaging is in vivo imaging of tumors. The tumors can either be genetically engineered to express a particular fluorophore or a targeted fluorescent antibody could be used. Figure 2-2, adapted and reproduced from [37], shows an example from such a study. This figure depicts a mouse that was injected with uMUC-1-negative and uMUC-1-positive tumor cells that were allowed to grow. A fluorescent probe designed to recognize the uMUC-1 antigen was injected after the tumors reached approximately 0.5cm in diameter [37].

Fluorescent signals have a much lower intensity than the excitation light, requiring strong emission filters to block out excitation light. These filters allow the fluorescence signal to be revealed but all other light is

22 filtered out, resulting in a zero background signal. This prevents any surrounding structures from being visible, making it challenging to determine the anatomical context of the image.

Figure 2-2. Fluorescence is zero background. This figure shows a white light image (left) and a fluorescence image (right) using a Cy5.5 near infrared probe targeted to uMUC-1. This figure is adapted and reproduced from [37]

Bioluminescence imaging is an imaging modality similar to fluorescence. In bioluminescence imaging luciferase expression is typically induced in the target cell line and then implanted in the animal. The animal is then injected with luciferin, which is oxidized upon encountering luciferase. This reaction releases a photon which can then be detected by a camera system. Bioluminescence imaging is also a zero background technique and requires genetic manipulation of cell lines [38].

Bioluminescence is used a wide range of studies including biodistribution studies, tracking cell mass, assessing cancer treatments [38-40]. Figure 2-3, adapted and reproduced from [40], depicts a typical bioluminescence imaging image. In this study a transgenic mouse was engineered that expressed luciferase on the insulin I promoter

Figure 2-3. Bioluminescence Imaging. A transgenic mouse that expressed luciferase in pancreatic cells was injected with a lucifrerin solution. Adapted and reproduced from [40].

According to the paper, the light is indicating the presence of β cells in the pancreas. However, no surrounding structures can be assessed.

Both fluorescence imaging and bioluminescence imaging are applicable to a wide range of studies. The in vivo nature of both of these techniques makes them well suited for longitudinal studies. Both methods have been used longitudinally to track changes in response to treatment [41-43]. Both of these modalities have also been used for theranostics [44, 45]. The targeted nature of these probes lends itself well to use for targeted treatment.

However, these techniques are incapable establishing any information regarding the surroundings of the target in a non-invasive in-vivo manner. Anatomical localization is critical for some types of studies.

Tumors can cause mass effects and induce changes in other organs that are not necessarily visible in a white light image. Signal from one organ could be mistaken for another organ in close proximity.

2.1.2 Micro-CT and Small Animal MRI

Micro-computed tomography (µCT) is a small animal imaging technique that involves taking a series of x- rays around an axis of rotation, which are then used to create a 3D reconstruction of the object. This technique offers high spatial and temporal resolution and, unlike fluorescence and bioluminescence, is particularly well suited for anatomical localization. By itself µCT provides poor soft tissue contrast.

However, a number of contrast agents are commercially available for soft tissue imaging with µCT [46].

These scanners are different from clinical CT scanner because the user is usually less concerned about radiation use. As a result, the spatial resolution from µCT is can be significantly better than a clinical scanner. This modality is often used in studies that require bone assessment [47, 48].

Figure 2-4. A reconstruction of a mouse abdomen using µCT. Fat deposits and some organs are visible. Adapted and reproduced from [49]

Small animal magnetic resonance imaging (MRI) is another imaging technique that is well suited for anatomical localization. This technique relies on magnetic field gradients and radio waves to form images based on detection of hydrogen atoms, making it particularly useful for imaging soft tissues.

Similar to µCT, small animal MRI provides high spatial resolution. However, this technique is significantly slower than µCT. Clinical MRI scanners often rely on magnets in the 1-3T range. Small animal scanners, however, can be found in the 9T+ range [50]. Targeted and non-targeted MRI contrast agents are available with varying specificities.

There are several issues with both of these modalities. Both of these systems are expensive and can involve complicated set ups. It is also difficult to manipulate the animal while in these systems. Micro CT involves ionizing radiation and is often limited to bone studies due to bone’s high attenuation of X-rays.

MRI acquisition speeds are often too slow to perform whole body dynamic imaging.

2.2 Liver

The studies in this chapter rely on liver disease models. This section discusses the vital functions of the liver and provides background on the types of symptoms that occur when the liver fails.

2.2.1 Liver Physiology

The liver is a vitally important organ that performs a large number of functions, including serving as the primary metabolic center of the body. The liver is the primary site of glycogenesis, gluconeogenesis, and glycogenolysis in carbohydrate metabolism. In lipid metabolism, cholesterol and fatty acid synthesis both occur in the liver. Hepatocytes are the liver’s functional cell. They produce bile for fat emulsification in digestion, as well as a number of key proteins, including serum albumin, the majority of the clotting factors, and the proteins of the complement system. These necessary functions all underscore the importance of the liver and explain why diseases of the liver can have such drastic effects on patients.

Liver pathologies, such as cirrhosis or hepatocellular carcinonoma, affect hepatocyte function, which in turn can lead to several serious issues, including impaired wound healing and immune system dysfunction.

Serum albumin is a protein found in blood plasma that can serve as a carrier for other compounds.

Albumin is responsible for maintaining fluid balance between the vascular and tissue compartments.

Disruption of liver function can lead to hypoalbuminemia. However, this is not necessarily caused by a decreased functional capacity of the hepatocytes, but by rather the liver down regulating albumin production in factor of increased production of acute phase reactants, the proteins that are involved in the immune system [51-53]. In this state, the lowered oncotic pressure of the vasculature will cause fluid movement into extravascular sites, creating interstitial edema. This edema may delay wound healing and cause tissue damage [51].

The coagulation cascade is the series of biological reactions responsible for the generation of blood clots.

Figure 2-5 depicts this cascade and identifies which precursor compounds are produced exclusively by the liver and which are produced by the liver and extrahepatic sites. Damage to blood vessels exposes the subendothelial tissue where tissue factor can then come into contact with factor VII, initiating this cascade

[54]. Disruption of the production of these factors and the clearance of activated factors can occur in patients with acute liver failure [54, 55].

Figure 2-5. Coagulation cascade. Nearly every precursor is produced by the liver. Many of these are not produced at any extrahepatic sites. Disruption of liver function can affect this cascade and lead to coagulation disorders [54].

The complement system is the innate immune system of the body. This system involves a number of protein cascades that result in the production of cytokines and the membrane-attack complex, a complex of proteins that aides with pathogen cell lysis. Patients with alcoholic liver injury have been shown to have

28 lowered serum levels of the complement system proteins and are at higher risk for bacterial and fungal infections [56, 57]

The liver is also responsible the primary site for drug metabolism and detoxification. This is achieved through the cytochrome p450 system. The system consists of a superfamily of enzymes that are responsible for oxidation of compounds in the liver [58, 59]. Not only do these enzymes affect drug levels in the body, but certain compounds lead to cytochrome up regulation or down regulation, which in turn can lead to massive changes in drug levels in the body [60]. This up/down regulation is responsible for many of the drug-drug interactions seen in pharmacology [61, 62]. Thus, knowledge of liver function is key when it comes to understanding drug function. These cytochrome reactions can also lead to the development of harmful compounds, including reactive oxygen species, which damage the liver [63, 64].

Drug-induced hepatotoxicity is the primary cause of acute liver failure in the United States [65, 66].

Furthermore, hepatotoxicity is the leading cause of FDA-approved drugs being withdrawn from the market. These two facts underscore the importance of having a clear assessment of liver function during the drug development process. The alternative in small animals is to sacrifice animals for histological examination of the liver. This, however, increases the cost and time of study as well as increases animal numbers. Animal sacrifice also precludes the ability to do longitudinal experiments on the same animal.

Non-invasive imaging of hepatic function in small animals could allow for earlier determination of the effects of therapies and pharmacologic agents, thus reducing time and cost of preclinical studies.

2.2.2 Assessing Liver Function

In humans, liver function is most commonly assessed with liver function tests (LFTs), a blood assay. This battery of tests assesses a number of facets of liver function. Levels of alanine aminotransferase (ALT), aspartate aminotransferase (AST), and gamma glutamyl transpeptidase (GGT) are evaluated to identify liver injury [67]. Conjugated and unconjugated levels are bilirubin are measured to provide an assessment of the liver’s metabolic and secretory functions [67]. Serum albumin levels and prothrombin times are used to test the liver’s synthetic ability [67]. Clearance rate tests for exogenous compounds such as galactose or hyaluronan are used to provide insight on the liver’s ability to clear compounds from the blood [68, 69]. Allopurinol or testosterone challenges are stress tests for identifying problems with metabolism and synthesis [67]. Serum levels of certain fibrogenic peptides provide an estimate of the degree of liver fibrosis [67]. This wide variety of tests is necessary because no individual test of liver function has full diagnostic and prognostic value. Furthermore, certain liver functions, such as protein synthesis can still function in disease states. Focal diseases may also not be detected because the remaining portions of the liver will retain full function.

One measurement of particular importance to the experiments in this chapter is the test for ALT levels.

ALT is an enzyme found in high concentration in hepatocytes and is responsible for the transamination reaction that converts L-glutamate and pyruvate into α-ketoglutarate and L-alanine. Lysis of hepatocytes results in release of ALT into the blood. Thus, elevated ALT levels are an indicator of hepatocellular injury.

While these tests indicate the liver’s total function, they cannot be used to localize areas of damage. Also, longitudinal application of these tests requires repeated blood draws, which can cause problems in small animals such as mice.

2.3 Development of DyCE system and imaging protocol

This section describes the development of the DyCE imaging protocol. We begin with the creation of the imaging system and the establishment of the imaging methods that was used in subsequent experiments.

2.3.1 Experimental Set-up

In the time between the original 2007 DyCE paper and these DyCE experiments, the DyCE technology was licensed to CRi Inc (now part of PerkinElmer). The technique has been integrated into CRi’s Maestro system. The Maestro is a self-contained imaging system with an adjustable imaging platform, a built in camera, a light source, and excitation and emission filter sets. The imaging system connects to a computer that runs proprietary CRi Inc Maestro software. We were able to perform DyCE with this system but the workable space on the imaging platform was small. The imaging platform is contained in a box to block outside light, but our DyCE technique involves tail vein injections which require easy access to the mouse at the beginning of imaging. The filter system of the commercial system is not designed to eliminate signal from ambient room lights, so these experiments had to be performed with the room lights out.

Additionally, the proprietary data format limits our acquisition speeds and the types of analysis we can perform.

We found it better to develop our own imaging system that was not reliant on the Maestro system’s light- shielding box and software and could be customized to our specific needs. Figure 2-6 shows this system design. The rodent is positioned on top of a homeothermic heating pad under two laser diodes and a

Dalsa 1M60 CCD camera controlled by custom written software [29]. Two gold surfaced mirrors are positioned at 45° angles on either side of the rodent to provide imaging of orthogonal angles.

Figure 2-6. DyCE Imaging System. System configuration for dynamic ICG imaging. A Dalsa 1M60 CCD camera controlled by custom software is used to image a fluorescent bolus as it is injected into a mouse. Adapted and reproduced from [70]

This open air set up allows for freer movement and easier access to the animal. This set up also allows for constant monitoring of the mouse during imaging to ensure proper levels of anesthesia and that the mouse does not shift positions during imaging. For reasons to be discussed in later sections, the experiments in this chapter used indocyanine green (ICG) as the main contrast agent. Based on ICG’s excitation spectrum, 785nm laser diodes were selected to illuminate the injected bolus. An 850/40 filter was positioned before the camera to isolate the emitted light from the excitation light. The design of the system allows for the laser diodes and emission filter to be easily changed as necessary for different

32 experiments. Owing to the wavelengths used in these experiments and the room only being lit by fluorescent-style lamps, this system can be used without turning off the room lights and without needing any optical shielding. However, using a different fluorophore with different excitation and emission spectra could potentially require additional steps to be taken to eliminate room lights and to image properly.

2.3.2 Data Preprocessing

The DyCE camera acquires a series of images and the custom camera control software stores these images on a hard drive. These images are then converted to a Matlab stack so that the data can be viewed as a movie and further analyzed. In the majority of these experiments, mice were imaged while under isoflurane anesthesia. These anesthetized mice took large breathes sporadically, causing movement artifacts. These movements cause shifts in organ locations in the field of view. A region of interest selected from one frame of the data would not be applicable to all the other frames, making it difficult to obtain accurate time courses of signal intensity. Figure 2-7 shows an example of a time course of a region of interest at the edge of a mouse’s lungs. The sharp spikes are due to breathing. A breathing motion correction scheme, described below, was implemented to remove any movement artifacts.

Figure 2-7. Time course of ICG fluorescence from a region of interest selected at the border of the lung. The spiking seen is due to movement from breathing. The preprocessing algorithm removes the frames that contain breathing artifacts and interpolates over these missing frames.

The first step of breathing correction involves selecting regions of interest in areas with significant, consistent organ movement. Immediately following the tail-vein injection, the fluorescent bolus moves to the lungs for several seconds, making lung movement is visible. The first portion of the video is corrected by selecting a region over the inferior border of the lungs such that the quick breath would increase the mean signal intensity of the region. As the ICG dye bolus distributes, hepatocytes sequester ICG from the blood stream, increasing the signal intensity from the liver and making liver movement visible instead of the lungs. The later portions of the data are corrected by selecting a region of interest along the border of the liver that also increases in mean signal intensity during breaths.

The time courses for these regions are smoothed using a moving average. Only the frames in which the original time courses have a lower intensity value than the smoothed time courses are kept. With this, the frames with breathing movements are essentially removed. The data is then reinterpolated over these missing frames to make it the size of the original data set. After this correction is made, specific regions

34 of interest selected over organs in one frame can be applied to all other frames, yielding smooth time courses of signal intensity and allowing for analysis. The organ biodistribution dynamics are significantly slower than the breathing frequency and therefore this algorithm serves as a low pass filter and does not alter the bolus dynamics of interest.

2.4 Establishment of Repeatability of DyCE Measurements

The original DyCE paper involved imaging mice at a single time point. This is sufficient for developing anatomical maps [30]. However, the establishment of DyCE as a tool for assessing organ function required longitudinal experiments where disease progress could be tracked. In order to properly perform these experiments, we first needed to show that DyCE data could be repeatedly acquired across animals and over time.

2.4.1 Determining Repeatability

In order to determine repeatability, three healthy SKH1 male nude mice were imaged using a 0.06 ml bolus of 260 μM indocyanine green (ICG) (Sigma-Aldrich Fluka Analytical Cardiogreen 21980). Nude mice were specifically chosen because their lack of hair allows for more excitation light to reach the fluorophore and more emission light to be detected from inside the animal’s body due to less absorption. The lack of hair and skin pigment also allowed easier visualization of the tail veins. ICG is an optical dye that excites in the near infrared and is FDA approved for assessing liver function [71]. In humans, an ICG bolus is injected intravenously and then repeated blood draws are taken to determine the rate at which the ICG is removed from the blood stream by the liver [72]. ICG has also been used in rabbit studies of hepatic dynamics in which ICG was imaged via a fiber-probe placed directly onto the exposed liver [73]. The excitation spectrum of ICG is concentration dependent. However, the excitation spectrum in plasma, shown in Figure 2-8, contains a large peak at 800 nm for a wide variety of concentrations [74].

Figure 2-8. Excitation spectrum of ICG in plasma for multiple concentrations. Based on data from [74]. There is a large excitation peak at approximately 800 nm that increases as the concentration of ICG decreases.

The 260 μM concentration of the bolus is diluted as it enters the vascular compartment, strengthening the 800nm excitation peak. As discussed in the previous chapter, the incidence of Rayleigh scattering is

1 proportional to . The long wavelength of ICG excitation allows for non-invasive imaging because the 휆4 excitation light undergoes less scattering events, resulting is less absorption, and can penetrate further into the animal’s body. The emission light also undergoes less scattering events before reaching the camera. The ICG is transported in the blood stream by binding albumin. In a healthy state, ICG from the blood stream is taken up by hepatocytes and sequestered in the liver with bile salts. It is then excreted via the biliary pathway into the gut for excretion. Liver disease states affect hepatocyte function and therefore affect the rate at which ICG is removed from the bloodstream. ICG’s spectra and pharmacodynamics pathway make it a suitable contrast agent for developing DyCE for assessing organ function.

In these experiments, images were acquired with the DyCE system at 10 Hz with 2 x 2 binning (512 x 512 pixels) and a 90 ms integration time. The mice were initially anesthetized with isoflurane in an induction chamber and then transferred to the heat pad on the DyCE imaging platform where they were placed in the prone position and adjusted to be in the camera’s field of view. The mice were continuously anesthetized throughout the experiment using isoflurane (2.5% to 3% in a 1:3 oxygen:air mix) through a nose cone. This level of anesthesia allows for the mice to quickly wake upon removal of the isoflurane at the end of the imaging session. The laser diodes were adjusted to provide uniform illumination over the whole body of the mouse and then a latex glove filled with water was heated and then placed onto the tail for 1-2 minutes in order to dilate the tail veins. Once the veins were engorged, image acquisition started. A bolus of approximately 0.06ml of the ICG solution was injected smoothly into the tail vein over a 1-2 second period. DyCE data sets were acquired in 180s sets. The imaging runs were divided into these smaller sections to assure that the ICG was injected properly. The fluorescence is not visible to the naked eye and the software does not display images as they are acquired. After the first 180s period, the mice were checked to determine if the ICG bolus was injected correctly. If the tail vein injection was correctly placed and the bolus was successfully injected more imaging sessions were performed. If the bolus did not reach the vascular compartment additional tail vein injections were attempted. For longitudinal experiments a single batch of 260 μM ICG was prepared before the first imaging session and used for each subsequent imaging session. Between imaging sessions the ICG batch was stored in the dark at 4°C.

2.4.2 Determining the Effect of Organ Dysfunction

After the first imaging session, we wanted to test if the acquired time courses in healthy mice remained similar over time and if organ damage would result in changes to the acquired time courses. To accomplish this, two of the mice from the previous session each received a single IP injection of carbon tetrachloride

(CCl4) solution (as 0.05ml in corn oil) at a dose of 0.5 µl/g body weight. CCl4 is a well-established hepatotoxic compound that was previously used in the dry cleaning industry but was later banned for its toxicity. Carbon tetrachloride is broken down by the liver’s cytochrome p450 system into a free radical

[75, 76]. Given chronically, these free radicals can induce liver cirrhosis [77]. However, a single dose will

“shock” the liver, temporarily impairing function, but allow it to recover [77]. This damage causes lysis of hepatocytes, resulting in the release of the enzymes that are used in liver function tests.

The two mice given CCl4 and the remaining healthy mouse were imaged again with another 0.06 ml bolus of ICG after 28 hours. Sufficient time was needed for the prior ICG bolus to be removed from the body.

The data was analyzed by first generating simple anatomical maps by creating RGB merges from frames at 2.4, 5.2, and 35 seconds after injection. These frames correspond to the approximate times in which the dye is in the lungs, kidney and brain, and liver, respectively. Each image series was preprocessed as described previously and then time courses were extracted by manually selecting regions of interest over

8 major organs from these anatomical maps. Figure 2-9a shows these merged frames and selected regions of interest.

Figure 2-9b shows the time courses from all three healthy mice during the first imaging session. The plot on the right shows the mean times courses of these three data sets normalized to maximum kidney intensity and the standard error. These time courses shows low variance between mice. This confirms that the underlying mechanisms that determine dye kinetics are similar between mice and indicates that DyCE can be used longitudinally with cohorts of mice without concerns about significant baseline changes. The time courses for all of the organs increase after bolus injection. The time courses for every organ system except the liver peak early and then begin to slowly decay. The liver signal, however, increases as ICG is removed from the blood stream by hepatocytes. This contrast agent-hepatocyte interaction causes the liver to have different dynamics than the other organs. In these trials the signal from the liver became the strongest signal in the field of view within 15 seconds of injection.

Figure 2-9c shows these time courses from the same regions, but 28 hours after the CCl4 injection. The plot on the right shows the normalized mean and standard error of the two mice that received the CCl4.

Again, these time courses show an increase after injection. However, the liver has much slower kinetics resulting from an altered contrast agent-hepatocyte interaction due to the CCl4 injection temporarily decreasing the functional capacity of the liver. The signal from the liver does not increase beyond the kidney signal in the first 40 seconds of this imaging session.

Figure 2-9. DyCE analysis in mice before and after CCl4 induced liver damage (a) Pseudo-colored simple anatomical map images generated using merged frames at 2.4s (green), 5.2s (blue), and 35s (red) after ICG injection with manually selected ROIs overlaid. (b) Time courses of selected regions in healthy mice demonstrating good repeatability. Right: Averages with standard error, normalized to the maximum kidney intensity. (c) Liver and kidney time courses 28 hours after mice 1 and 2 received an IP injection of

CCl4 to induce acute liver damage. Right: averages of treated mice with standard error, normalized to maximum kidney intensity. Arrows indicate crossover point of liver and kidney signal. Traces in treated animals no longer cross within 40s. Adapted and reproduced from [70].

2.5 Assessing Liver Function

Once repeatability was established and we had determined that altering organ function results in changes that are measurable by DyCE, we wanted to develop a quantitative method of analysis to use DyCE for assessing organ function.

2.5.1 Liver function trials

To achieve this goal we designed a longitudinal study which expanded upon the previous study, aimed at establishing a method to use DyCE to quantify liver function. For this set of experiments, the same CCl4 model was used at the same dosage (0.5 µl/g) to induce liver damage, but the mice were repeatedly imaged over a longer period of time and additional tests were performed.

Four new 6-week old healthy SKH1 male nude mice were imaged over a 9 day period. The first imaging session was performed on the mice when they were all healthy to establish baseline values. After this imaging session, three of the mice were given the IP injections of CCl4, while the fourth mouse served as a control. All four mice were subsequently imaged after 54, 120, and 217 hours. The DyCE data sets were acquired with the same parameters as in the previous session and then each mouse was imaged for 10 to

14 minutes per session. The data sets were preprocessed and time courses for each organ were manually selected in the same fashion as described previously.

As mentioned above, ALT can serve as a biomarker of hepatocyte injury. When hepatocytes are damaged, this enzyme is released into the blood stream and blood analysis will reveal elevated levels. ALT measurements are a component of liver function tests and serve as a gold standard indicator of liver function, particularly liver injury [67]. For each of these imaging session, we obtained ALT measurements for all the mice in order to provide a metric to compare with the DyCE results.

In order to assess ALT levels, after each imaging session for each mouse, 40-60 μL of blood was collected from the tail vein and immediately put on ice. Once all four animals had been imaged that day, the samples were centrifuged in a refrigerated centrifuge to separate the serum from non-serum components. The serum was stored at -80°C until all imaging sessions were complete and then ALT assays were performed using a Genzyme Diagnostics ALT Aminotransferase-SL Assay. The ALT measurements showed a large spike after 54 hours in the three mice treated with CCl4. The control mouse showed a small increase, but stayed within the normal range. By 120 hours ALT levels had returned to healthy levels in every mouse.

When the initial IP injection of CCl4 “shocks” the liver, some of the hepatocytes are damaged. These damaged cells release ALT, causing an increase in ALT levels in the blood serum. However, since there is not continuous damage to the liver, once the liver begins to heal and the ALT is cleared from the blood stream, the measurements return to normal levels.

2.5.2 Liver function metrics

The changes seen in the organ-specific time courses extracted from these mice after CCl4 were similar to changes seen in the repeatability study. The damage to the liver affects the contrast agent-hepatocyte interaction, slowing ICG uptake, while the maximum signal from the kidney remains higher compared to other organs. Figure 2-10a shows frames from 180 seconds into the imaging session for the same mouse before and 54 hours after CCl4 injection. At 180 seconds there is a clear difference in the relative signal intensity from ICG in the liver and the kidneys before and after CCl4 injection. In the healthy mouse only the liver is visible, while after CCl4 the kidneys are also visible. Figure 2-10b shows the time course from the liver and kidney before and after CCl4. As the mice recovered, the differences in the dynamics between the experimental mice and the control became similar. In this analysis, time courses were manually selected. A non-negative least squares fit using these time courses was applied to the data to determine

42 which organs were found in which pixels. The liver and kidney maps from this fit were then thresholded to identify the pixel clusters that corresponded to these organs. These maps were used to select ROIs on the data from which to collect time courses. A number of simple metrics were explored for the DyCE measurements to assess correlations with the ALT measurements. These metrics were all physiologically reasonable based on ICG’s excretion pathway. These metrics included time necessary for the liver signal to cross the kidney signal, trends in the GI compartment, and the liver signal rate of decay.

Figure 2-10. Quantification of the changes seen after CCl4 injection. (a) DyCE data following ICG bolus injection in a mouse before (left) and 54 hours after CCl4 injection (right), after removal of breathing artifacts. The post-CCl4 mouse has decreased signal in the liver and increased signal in the kidneys after 180s. (b) The average time courses from the liver and kidney (using organ specific ROIs) before and 54 hours after CCl4 injection in the same mouse (normalized to maximum kidney intensity in each case). Dotted line shows the 180s time point. (c) The liver signal to kidney signal ratio before and 54 hours after

CCl4 injection. Adapted and reproduced from [70].

The trends seen in the kidney and liver occur because these organs are the two main methods by which compounds are excreted from the body. In healthy mice ICG is excreted solely by the liver and some albumin is endocytosed by the proximal tubule cells in the kidney [78]. However when hepatocytes are damaged, there is increased pressure to excrete ICG through the kidneys. This could result in a greater amount of albumin bound ICG being temporarily taken in by these renal cells. This observation led to the idea of using the ratio of liver and kidney signals. As shown in Figure 2-10c this ratio was found to have a distinctive gradient over time that differs between treated and untreated mice. We defined the inverse of this gradient to be the Dynamic coefficient:

Δ푡 퐷푐 = 퐿푖푣푒푟 푆푖푔푛푎푙 Δ ( ) 퐾푖푑푛푒푦 푆푖푔푛푎푙

Figure 2-11 shows the dynamic coefficient values for each imaging session and each mouse compared to corresponding ALT measurements. Mouse 7 showed the greatest increase in ALT levels and also had the highest Dc value. Mouse 4 had the lowest apparent response of the CCl4 treated mice and the values for the control mouse remained lower than all treated mice. Excellent correlation between these two measurements is found. A linear regression of ALT and Dc values yielded an R2 value of 0.91.

Figure 2-11. Comparison of DyCE measurements to liver enzyme concentration during transient liver damage. (a) DyCE-derived coefficient (Dc). (b) Alanine aminotransferase (ALT) measurements from blood samples taken during each imaging session. IP injections of CCl4 to induce liver damage were given immediately following the first imaging session, Mice were then imaged 3 more times over each of the following 217 hours. (c) Larger Dc values correlate with higher levels of plasma ALT. The third time point for mouse 4 was not obtains owing to failed ICG injection. A linear fit applied to the Dc and ALT data gives an r2 value of 0.91. Adapted and reproduced from [70].

This ratiometric approach was compared to, and found to be superior to, other metrics including liver and kidney time to peak, rate of increase, rate of decay, and rate of increase in the GI tract. Metrics based on the initial increase in signal, such as time to peak of the kidney signal or rate of increase in the GI tract can be influenced by the rate of injection. Metrics such as the time to peak in the liver are influenced by the size of the bolus. Our ratiometric approach proved far more robust, since the liver and kidneys both see the same input function, which cancels out many of these effects in each mouse.

2.5.3 Difficulties in These Experiments

There were several difficulties that occurred during this set of experiments, but five major ones occurred repeatedly. First, there were initially difficulties with tail vein injection accuracy. Tail vein injections are a skill that, with practice, can be done repeatedly and reliably. They are commonly done in pharmaceutical research. However, when learning this skill, the accuracy of the injections can be quite low. Second,

45 missed injections will lead to tail vein collapse. Injection trials began distally and were moved up the tail if the previous injections failed. After 4-6 attempts the vein collapses and is no longer be suitable for injection. Incorrect injections lead to the bolus being injected into the tail, but outside of the vascular compartment. Third, partial injections or ICG leakage into the vascular compartment from the extravascular space due to a missed injection can lead to unusable data sets. In order to develop a metric for liver function, we required that all the mice start at the same baseline state. The liver would sequester

ICG from partial injections or leakage, leading to the liver time course after a proper injection to start from a non-zero value. Fourth, as discussed previously, many proteins associated with wound healing are synthesized in the liver. Disrupting liver function in mice leads to impaired clotting and wound healing.

Damage to the tail from the tail vein injections and blood collection had to be carefully monitored for infection or necrosis. The third DyCE measurement from mouse 4 is missing because of these four issues.

Tail vein injections were attempted for this mouse, but failed. Additional attempts could not be performed without risking the health of the tail. Fifth, ALT levels become elevated if there is red blood cell lysis. Red blood cells contain less ALT than hepatocytes, but RBC lysis during blood draws would still elevate ALT levels. These sets of experiments were repeated a few times due to these five issues.

2.6 Comparison of DyCE and DCE-MRI

The previous sections were about the development of DyCE as a tool for assessing organ function. This section expands on that work to discuss the similarities between DyCE and Dynamic Contrast Enhanced

MRI (DCE-MRI), a clinically used imaging procedure.

2.6.1 DCE-MRI

Magnetic resonance imaging is traditionally used for anatomical imaging of soft tissue. Contrast agents for MRI are gadolinium (Gd) chelated compounds that are designed to remain in the vascular compartment. More recently, functional imaging methods based on MRI are being developed. The most famous of these is the neuroimaging procedure functional magnetic resonance imaging (fMRI). This technique measures the blood-oxygen-level dependent (BOLD) signal, an indicator of deoxygenated blood. This technique is thought to be useful in imaging neuronal activity by studying changes in blood flow. The next chapter is focused applying many of the same techniques spatiotemporal techniques from this chapter to optical data of changes in oxygenated and deoxygenated blood flow in the brain.

Dynamic contrast enhanced MRI (DCE-MRI) is another, lesser known, functional clinical MRI technique that is similar to DyCE. In DCE-MRI a Gd-based contrast agent is injected into a patient as a series of MRI images are obtained, capturing the flow of the contrast agent. MRI machines obtain images in slices, which can be rendered in three dimensions. However, since MRI acquisition speeds are relatively slow, data in

DCE-MRI is usually acquired in just a few slices, with varying resolution depending on whether structural or dynamic information is sought. MRI contrast agents are not as diverse as those available for optical imaging. In addition to Gd-based contrast agents being designed to remain in the vascular compartment,

47 almost all exclusively eliminated through the renal system. DCE-MRI has found use in imaging tumors, but is not used widely [59-61].

Excessive scattering and absorption makes it almost impossible to consider applying optical DyCE to image the liver of humans. However, because the signal in MRI is based on radio waves, it does not suffer from same penetration-depth issues, making DCE-MRI a potential DyCE counterpart that can be applied clinically. We hypothesized that insights gained with DyCE studies in small animals would carry over to

DCE-MRI in humans. For example, the DyCE liver function studies above demonstrated that ICG allows for quantification of liver function. The majority of DCE-MRI studies currently rely on perfusion only contrast agents. Prior perfusion-CT studies that solely evaluated organ blood flow parameters in a liver tumors concluded that quantitative evaluation of liver function was not possible, finding no correlation with ALT levels in unhealthy livers [79]. The strict use of perfusion only contrast agents may be limiting DCE-MRI development. Using ICG, the dynamics in the previous DyCE experiments were influenced by hepatocyte uptake and excretion rates, thereby providing a signal dependent on the function of organs rather than just perfusion. This section explores the relationship between DyCE with a dye that takes advantage of the contrast agent-parenchyma relationship and DCE-MRI with two contrast agents: one that is perfusion only and one that has a similar contrast agent-parenchyma interaction as DyCE.

While most Gd-based MRI contrast agents are excreted solely through the renal system, one particular agent, Eovist, has been shown to be excreted approximately half through the kidneys and half through the liver in a similar fashion to ICG [62-64]. Therefore, based on the presence of a similar contrast agent- parenchymal interaction, we hypothesized that DCE-MRI performed with Eovist could provide a clinical equivalent to DyCE performed with ICG in the laboratory. Magnevist is a conventional Gd-based MRI contrast agent that is excreted solely through renal system that we used as a control.

2.6.2 DyCE and DCE-MRI: Healthy mice

The first step in comparing DyCE with DCE-MRI was to image healthy mice with both modalities. Two SKH1 male nude mice were first imaged using DyCE using ICG. These experiments were performed with the same imaging set up as described in the previous sections. Images were acquired at 10 Hz with a 90ms acquisition time and using 2 x 2 binning (512 x 512 pixels). The animals were first imaged for 3 minutes and then an image was viewed in real time to verify that the dye was correctly injected. Once this was verified, 9 more minutes of imaging data was acquired. ICG and Eovist share a hepatic excretion pathway, so after the DyCE imaging session the mice were given 48 hours to recover to prevent interference [80-

83].

After this time, the mice were placed in the DyCE system to confirm that no ICG signal was present. Then, the mice were transferred to the MRI imaging facility. The DCE-MRI experiments were performed on a

Phillips 3T clinical scanner using a small animal imaging coil. With DCE-MRI there is a trade off between spatial resolution and temporal resolution. In order to ensure adequate speed of imaging the region of interest must be selected before the DCE-MRI time series is required. Any movement of the mouse after the region of interest selection will affect the data. In DyCE, Direct tail vein injections would occasionally result in movement of the mouse’s body and were therefore not an appropriate method of bolus delivery in DCE-MRI. Tail vein cannulations were attempted but given the size of the tail vein these cannulations proved unstable. To properly ensure that the cannulation was stable and the bolus delivery was successful a jugular cannulation preparation was used. This procedure involved first anesthetizing the mice with a ketamine/xylazine mixture at a dosage of 115 mg/kg ketamine and 5 mg/kg xylazine. The skin around the neck vessels was then dissected and the jugular vein was isolated. The vessel was tied off downstream and then cannulated with a P10 catheter filled with heparinized saline. The catheter was secured and the

49 skin around it was sutured back together. Prior to imaging another half dose of ketamine was given to the mouse.

The cannulated mouse was placed in the scanner in a small animal imaging coil and an anatomical scan was used in order to properly select a region of interest. The scanner was set to scan 4 slices across the liver at a rate of 1.825s/slice. Once the mouse was in place the imaging started. The scan time was set for

30 minutes. After approximately one minute the contrast agent bolus was injected through the cannulation system. The first mouse was imaged using Magnevist, the contrast agent that was cleared through only the renal system. Figure 2-12 shows the results of this imaging session and corresponding

DyCE time courses. Figure 2-12a shows the field over view of the DyCE time series. A region of interest over the liver is shown in green and a region of interest over the brain is shown in blue. Because ICG does not cross the blood-brain barrier, the brain ROI is indicative of perfusion only. Figure 2-12b shows the time courses from these two regions of interest normalized to their individual maximum values. These time courses are similar to the ones from the previous sections, with the brain ROI showing a rapid increase followed by a smooth decay and the liver ROI showing sequestration by hepatocytes. Figure 2-12c shows an image from the DCE-MRI scan and a corresponding region of interest from which a time course was selected. Figure 2-12d shows the first 12 minutes of the time course from this ROI.

The acquisition speed of the DCE-MRI is significantly slower than the acquisition speed of DyCE. As a result, the breathing movement artifact correction that was applied to the DyCE data is not suitable for the DCE-

MRI data. Breathing motions in the DCE-MRI causes shifts in the location of the liver. To correct for this, the DCE-MRI data was separated by slice and all of the images for each slice were coregistered to the first frame in that slice’s series. A region of interest was selected on each slice and the average time course for that region was measured.

Figure 2-12. Comparison between DyCE and DCE-MRI with Magnevist in a healthy mouse (a) DyCE Image and ROIs from brain and liver. The brain time course from this region represents perfusion only. (b) The corresponding time course for these regions. In the brain time course there is an initial spike and an exponential decay to baseline over time. The liver time course has a gradual build up over time as ICG is sequestered by hepatocytes followed by a decrease as ICG moved into the biliary system (c). DCE-MRI Image of the Liver and ROI. (d) The corresponding time course with Magnevist from the liver. Similar to DyCE, there is an initial spike followed by decay to baseline.

The time course from DCE-MRI with Magnevist in the liver shows a large increase in signal after the injection followed by a gradual exponential decay. This time course makes physiologic sense because there is no hepatocyte interaction with the Magnevist, resulting in a perfusion only time course. The rate of decay in the DCE-MRI time course appears to be less than that of the perfusion-only DyCE time course.

After the first mouse was imaged with DCE-MRI, the second mouse was given the same surgical preparation. For this mouse, Eovist was used instead of Magnevist as the contrast agent. Figure 2-13a shows an image from the DyCE time series with an overlay of a liver region of interest. Figure 2-13b shows the time course from this ROI normalized to its maximum intensity. This time course has the same form as the previous DyCE time courses in healthy mice livers. Figure 2-13c is a DCE-MRI image with corresponding region of interest and Figure 2-13d is the time course from this region. These image sets underwent the same registration process that the DCE-MRI data set did in the previous section. The DCE-

MRI time course with Eovist shows similar dynamics to the liver time course with DyCE, with some small differences. The Eovist time course peaks at 2-3 minutes and the DyCE time course peaks at approximately

4 minutes. As with the previous comparison to DCE-MRI with Magnevist, the DyCE time course also shows a faster decay rate than the DCE-MRI time course with Eovist. It is likely that the distribution dynamics with Gd-based MRI contrast agents are slower than those of ICG. After the imaging sessions were complete, the mice were euthanized using a sodium pentobarbital injection.

Figure 2-13. Comparison between DyCE and DCE-MRI with Eovist in the liver of a healthy mouse (a) DyCE Image and ROI from the liver. (b) The corresponding time course for this region. There is an initial spike and then a slower increase followed by a gradual decay over time. (c). DCE-MRI Image with Eovist of the Liver and ROI. (d) The corresponding time course with Eovist from the liver. Similar to DyCE, there is an initial spike followed by gradual decay.

2.6.3 DyCE and DCE-MRI: Liver tumor mice

In addition to examining healthy mice, we wanted to perform these same comparisons in a disease model.

We obtained several black mice that had received a fast growing liver tumor from Dr. Robert Schwabe, an

Assistant Professor of Medicine at Columbia University who studies liver fibrosis and cancer. This liver cancer model was designed so that cancerous cells would seed the liver and would grow to encompass

53 the whole liver over a few weeks. This model was designed for black haired mice, so nude mice were not used. Once the tumors had grown sufficiently large the mice were anesthetized using isoflurance. In order to image, the mouse was first shaven and a hair removal cream was used to remove any remaining fur.

Once a large enough region was cleared to view the liver the mouse was imaged with DyCE using ICG. The mouse was given 48 hours to recover and then taken to the MRI for imaging. The same jugular cannulation and imaging procedures were performed as in the healthy mice studies. Only one mouse was fully imaged with Eovist. A second mouse was attempted but died when given anesthesia. Mice with liver tumors are in a poor state of health.

Figure 2-14a shows an image from the DyCE time series and the selected region of interest over the liver.

Figure 2-14b is the time course for this region normalized to its maximum value. The signal increases with the initial bolus injection at a fast rate. This rate slows down between 30 seconds to 1 minute and then continues to increase through the 12 minute imaging session. This time course agrees with the finding in the previous session. Figure 2-14c shows a slice from the DCE-MRI scan and Figure 2-14d shows the time course from this region. There is a slower initial increase that peaks at approximately 3 minutes and then begins to decrease. At 12 minutes the maximum signal intensity is approximately 25% of its peak value.

Unlike the healthy mice trials, this DyCE with ICG shows a markedly different time course than DyCE with

Eovist in the liver of mice with liver tumors.

Figure 2-14. Comparison between DyCE and DCE-MRI with Eovist in the liver of a mouse with a large liver tumor (a) DyCE Image and ROI from the liver. (b) The corresponding time course for this region. There is an initial spike and then a slower increase over time. (c). DCE-MRI Image with Eovist of the Liver and ROI. (d) The corresponding time course with Eovist from the liver. There is an initial spike that is more gradual than seen in the healthy mouse followed by a more rapid decay.

We believe that the excretion pathway differences between ICG and Eovist might explain the similarities between in the DyCE with ICG and DCE-MRI with Eovist time courses seen in the healthy mice and the differences seen between them in the mice with liver tumors. In the case of DyCE, ICG is normally excreted

55 solely through the liver. Therefore if a liver tumor decreases the functional capacity of the liver to remove

ICG, it will increase the time necessary for the liver to remove the ICG from the blood stream. This will result in a more gradual build-up of liver signal over time, which is what is seen in the DyCE time course in Figure 2-14b.

Decreased functional capacity of the liver, as seen in pathologies such as liver cirrhosis, can affect kidney function. Hepatorenal syndrome refers to kidney failure that occurs secondary to liver failure. Both the

CCl4 model and the liver tumor model involve rapid decreases in hepatic function which may put excessive strain on the kidneys. With a sufficient amount of liver function compromised the kidney may excrete some amount ICG, but the majority is still excreted through the liver. This increased pressure on the kidneys to serve as an excretion pathway would explain the increase in kidney signal seen in the CCl4 mice and the decreased hepatocyte function would explain the slower rate of ICG extravasation from the vascular compartment. In the case of DCE-MRI and Eovist, the liver and kidney both have sufficient systems for Eovist excretion. When liver function is compromised, the kidney can take over for the liver and excrete a greater share of Eovist without the limits seen with ICG. The decreased function in hepatocytes would result is that there is less overall uptake of the Eovist by the liver instead of taking a greater time because there would be faster excretion of the agent from the bloodstream by an alternate pathway. This idea is supported by the DCE-MRI time course which shows a slight increase at the beginning, but lacks the build up seen with ICG. While these modalities do not yield exactly equivalent results in the case of liver tumors, an understanding of the underlying pharmacokinetics differences between ICG and Eovist can be used to explain the differences.

2.7 Clinical Relevancy

The results shown in this chapter indicate that dynamic contrast enhanced optical imaging holds clinical relevance. Establishing DyCE as a tool capable of assessing organ function in longitudinal experiments could help expedite pharmaceutical development in the preclinical phase and decrease the time necessary from drug inception to phase I clinical trials. The results of section 2.6 show that DyCE and DCE-

MRI data are not equivalent in disease settings, but the differences can be explained by the known excretion pathways of each contrast agent. Based on our DyCE results, we posit that DCE-MRI techniques could be enhanced by acquiring signals in multiple organs in parallel, which could allow extraction of normalized or comparative dynamics, as were found to be highly useful for the quantification of liver function via our dynamic coefficient Dc. We also posit that MRI contrast agents designed to interact more strongly with particular organ systems could potentially provide highly specific measures of organ function compared to measurements of perfusion alone. Based on conversations with clinical radiologists, we believe that agents such as Eovist are not regularly used because of its altered excretion dynamics.

However, we believe that these differences are not limitations and allow for agents with organ specificity to be used for functional assessment. DyCE is an inexpensive imaging platform, particularly when compared to MRI. Our results suggest that DyCE could provide a simple test-bed for the development of novel clinical dynamic contrast agents and techniques. Furthermore, in the case of liver, our results also suggest that the function of specific regions of the liver could be spatially mapped and quantified, which would prove useful for diagnosis of liver disease, cancer or metastasis, or surgical planning for resection of specific lobes of the liver.

Chapter 3

Development of dynamic analysis techniques applied to rodent functional neuroimaging data

In response to external stimuli, regions of the brain will have increased neuronal activity. In most cases, this increased activity will be accompanied by a corresponding increase in blood flow to those regions, referred to as the hemodynamic response. Functional magnetic resonance imaging (fMRI) is a technique commonly used for studying brain function. The fMRI blood-oxygen-dependent (BOLD) signal is sensitive to paramagnetic deoxyhemoglobin [84], with an increase in BOLD signal indicating a decrease in the deoxygenated hemoglobin concentration.

The BOLD signal is often misinterpreted as a direct indicator of neural activity. However, the increase in

BOLD signal usually detected comes from increased perfusion of oxygenated blood to the region, which in turn decreases the concentration of deoxygenated hemoglobin [85]. This means that BOLD detects an active blood flow response to stimulation, as opposed to being a simple measure of oxygen consumption or neuronal firing. The mechanism linking these blood flow changes to neuronal activity is referred to as neurovascular coupling and has not been fully determined. Elucidating this mechanism would provide a fuller understanding of fMRI BOLD data.

The temporal point spread function that mathematically translates neuronal activity to the vascular response is referred to as the hemodynamic response function. One widely held theory is that a stimulus

58 leads to perivascular astrocytes releasing vasoactive arachidonic acid derivatives onto the smooth muscle cells surrounding diving arterioles [86-90]. However, such theories fail to fully explain the spatiotemporal vascular response seen with stimulus. Elucidating the proper mechanism may allow for a better understanding of the neuronal underpinnings of fMRI signals and may yield information regarding how particular disease pathologies affect neurovascular coupling.

This chapter is focused on the development of a dynamic mathematical model of the hemodynamic response to stimulation. Since it is not possible to measure in parallel every parameter and cell type involved in neurovascular coupling, we hypothesize that the development of such a model, and comparison of this model to dynamic, multiscale optical imaging data acquired on the exposed rodent brain will permit the underlying mechanisms driving the response to be elucidated.

Section 3.1 provides a review of the cerebral vasculature and optical imaging methods for visualizing the hemodynamic response. It then discusses the goals of modeling the hemodynamic response and gives a brief background on previous attempts at modeling the neurovascular response to stimulus.

Section 3.2 presents the characterization of the data sets used and introduces the two component hemodynamic response function. Within the data, four strong patterns are identified that a proper model must be able to describe.

Section 3.3 describes the two component hemodynamic response function and sets the framework on which this chapter’s model is based. This section also discusses our initial efforts at developing a backwards model for the stimulus induced hemodynamic response.

Section 3.4 introduces the forward model and the smooth muscle cell point spread function. This section discusses smooth muscle cell physiology and the dilation signal propagation along pial vessels. The implications of this point spread function are also discussed.

Section 3.5 establishes the endothelial propagation hemodynamic response model (EP-HRM) and analyzes the applications of this model for prediction of the hemodynamic response and simulation of data. This model is used to simulate full data sets under a variety of stimulus parameters.

Section 3.6 concludes this chapter by discusses the clinical implications of the findings and how these findings can be applied to future studies on the nature of neurovascular coupling.

3.1. Cerebral vasculature, imaging the hemodynamic response, and the importance of modeling

The optical imaging system presented in this chapter allows for arterial, parenchymal, and venous responses to stimulus to be studied simultaneously, as well other parameters such as vessel diameter. An understanding of the relationship of these vessel compartments is vital to understanding the spatiotemporal characteristics of blood flow in the brain.

3.1.1 Review of Cerebral Vasculature

The brain is supplied blood from the heart through the internal carotid arteries, which are branches of the common carotid arteries which originate from the arch of the aorta. The internal carotid arteries branch in a number of vessels which supply the brain, the most important of which are the anterior cerebral artery, the middle cerebral artery, and the posterior communicating artery. Figure 3-1 (adapted and reproduced from [91]) shows the organization of the cortical vasculature within the brain. The pial arteries are located on the surface of the brain. These branch and become diving arterioles, which travel perpendicular to the surface, into the cerebral cortex. Beneath the surface these arterioles branch into the capillary beds where the majority of oxygen exchange takes place. These capillaries then feed into the ascending venules which return to the surface to join the pial veins. The veins of the surface of the brain collect blood into a series of sinuses which join to form the interior petrosal sinus and the sigmoid sinus.

These sinuses further condense to form the internal jugular veins which leave the head.

Figure 3-1. Diagram of the cortical vasculature. Pial arteries and veins are visible on the surface of the cortex. These pial arteries branch and dive into the cortex as arterioles, which give rise to capillary beds. Ascending venules collect blood from the capillary beds and return to the surface and join pial veins. Adapted and reproduced from [91].

Since the arterial, capillary, and venous compartments are connected in series, a change in one compartment will affect the other two. Some of these changes will be simply as a result of physical changes in another compartment. Poiseuille’s law indicates that vessel resistance is generally considered a function of diameter [92, 93]. If arteries in a particular region dilate, the decrease in resistance will result in an increase in flow, which may result in a passive dilation of the vessels that are immediately downstream (arteries/capillaries). However, these vascular compartments may also communicate via signaling with one another and coordinate active dilations. Vessel dilation in the arteries is achieved by the relaxation of vascular smooth muscle cells. Capillaries lack these smooth muscle cells, but are instead surrounded by a similar cell type called pericytes. The major difference between smooth muscle cells and pericytes is that the smooth muscle cells form their own layer of the vascular wall, while pericytes are embedded within the basement membrane of the capillary endothelial cells [94]. The exact role of these pericyte cells is still unknown, but they may play a smooth muscle cell type function on the capillaries, indicating that there may be active dilation and constriction in the capillary beds [86, 95, 96].

3.1.2 Imaging the Hemodynamic Response

Optical intrinsic signal imaging (OISI) of the exposed cortex allows for wide-field imaging of the hemodynamic response, meaning this system is able to image the full exposed region in the camera’s field of view [29]. Oxygenated and deoxygenated hemoglobin (HbO, HbR) have different absorption spectra.

Figure 3-2 shows the absorption spectra for HbO, HbR, H2O, and the wavelength dependence of optical scattering over the visible range.

Figure 3-2. The Absorption spectra for HbO, HbR, and H2O, and the wavelength dependence of optical scattering. Adapted and reproduced from [13].

Figure 3-3 shows a diagram of our OISI system. A Dalsa 1M60 CCD camera is placed above where the rodent is placed and positioned so that the cortex will be in the camera’s field of view [29]. Depending on the experiment, either two or three LEDs are used to illuminate the surface of the animal’s brain. In earlier experiments, a green and a blue light emitting diode (LED) were used to illuminate the exposed cortex.

The green 530nm LED was fit with a 530±5nm filter and the blue 470nm LED was fit with a 460±30nm filter. Later experiments introduced a third, red 630±5nm LED. The camera and LEDs are controlled by custom written software that acquires frames and strobes the LEDs in synchrony [29, 97]. The camera measures the signal 퐼휆(푟, 푡).

Figure 3-3. Diagram of the optical intrinsic signal imaging system. Experiments either involve strobing blue and green LEDs or blue, green, and red LEDs while imaging.

A 530nm green LED was used because a 530nm is an isobestic point for hemoglobin absorption (Figure

3-2). At this wavelength, the absorptions of HbO and HbR are equal, so measurements at this wavelength are only functions of HbT. A 470nm blue LED was used because the HbR and HbO have significantly different absorption values at this point. Scattering from biological tissues significantly increases as the wavelength of light decreasing. Using a low wavelength light source enhances the signal from the pial vessels on the surface compared to the subsurface vessels.

Chapter 1 introduced the modified Beer-Lambert law and discussed how changes in 휇푎 could be used to measure concentration changes in HbO and HbR. Extending this relationship spatially yields:

퐼 (푟, 푡) 휆 [ ]( ) [ ] ln ( ) = −[휖퐻푏푂2,휆Δ 퐻푏푂2 푟, 푡 + 휖퐻푏푅,휆Δ 퐻푏푅 (푟, 푡)]휒휆 퐼 휆(푟, 0)

where 퐼휆(푟, 푡) is the intensity detected at time t, 휖퐻푏푂2,휆 and 휖퐻푏푅,휆 are the molar absorptivity of HbO and

HbR for light with wavelength 휆, and 휒휆 is the average pathlength of a photon with wavelength 휆. The values 휒470 and 휒530 are determined by Monte Carlo simulations [13, 98]. Using this equation for 휆 =

470 and 휆 = 530, the quantities Δ[퐻푏푂2] and Δ[퐻푏푅] can be determined. Applying simultaneous equations yields

퐼 (푟, 푡) 휆 [ ]( ) [ ] ln ( ) = −[휖퐻푏푂2,휆Δ 퐻푏푂2 푟, 푡 + 휖퐻푏푅,휆Δ 퐻푏푅 (푟, 푡)]휒휆 퐼 휆(푟, 0)

1 퐼470(푟, 푡) ∆휇푎,470(푟, 푡) = 휇푎,470(푟, 푡) − 휇푎,470(푟, 0) = − ln ( ) 휒470 퐼470(푟, 0)

1 퐼530(푟, 푡) ∆휇푎,530(푟, 푡) = ∆휇푎,530(푟, 푡) − ∆휇푎,530(푟, 0) = − ln ( ) 휒530 퐼530(푟, 0)

ϵHbO,470Δμa,530(r, t) − ϵHbO,530Δμa,470(푟, 푡) Δ[HbR](r, t) = 휖퐻푏푂,530휖퐻푏푅,470 − 휖퐻푏푂,470휖퐻푏푅,530

ϵHbR,470Δμ푎,530(r, t) − ϵHbR,530Δμ푎,470(푟, 푡) Δ[HbO](r, t) = 휖퐻푏푂,530휖퐻푏푅,470 − 휖퐻푏푂,470휖퐻푏푅,530

Total hemoglobin is determined by

Δ[HbT](푟, 푡) = Δ[HbR](푟, 푡) + Δ[HbO](푟, 푡)

Depending on the experiment, either a mouse or a rat is anesthetized and then a ~3x3 mm area of the cerebral cortex is exposed through either a craniotomy or thinning of the skull. In this chapter the early modeling attempts relied on data sets from mice that were genetically engineered to express GCaMP3 in neurons. This is a calcium sensitive reporter protein that indicates when neurons fire. These mice were anesthetized using a 1.5mg/kg dose of urethane and imaged using a thinned skull preparation. Neuronal activity in these mice lead to increases in intracellular calcium levels in the neurons, causing green

65 fluorescence. Later modeling developments were based on data sets from imaging the exposed cortex of several rats while under intravenous alphachloralose anesthesia. The external stimulus was an electrical

3 Hz hindpaw stimulation and the exposed rodent cortex was imaged using the OISI technique previously described.

Once acquired, the data sets are all normalized by the baseline values in the second before receiving stimulation. An example of the type of data obtains with the OISI system is shown in Figure 3-4 (adapted and reproduced from [29]). This figure demonstrates HbO, HbR, and HbT maps and typical time courses associated with the hemodynamic response. The dynamics of Δ[HbO], Δ[HbR], and Δ[HbT] in arterioles, capillary beds (parenchyma), and venules can be extracted from a single widefield optical imaging data set.

Figure 3-4. An example of OISI data. Left: A gray scale image of the exposed cortex of a rat. Color images show the response maps for HbO, HbR, and HbT at 11 seconds (dotted line) in response to a hindpaw stimulus. The plot shows the average time courses over the field of view. Adapted and reproduced from [29].

Studies have approached deducing the mechanism of neurovascular coupling by looking at cellular activation, vascular activation, and biochemical pathways [87, 99-104]. A s imaging technologies advance, experimental measurements have moved from coarse, low-resolution or ex-vivo techniques to high-speed, high-resolution, in-vivo techniques.

3.1.3 Modeling of Neurovascular Coupling

The basic goal of modeling any system to provide an understanding of the patterns the system shows in response to different inputs. Modeling a system can provide insight into how that system works and can also inform future development of experiments for deducing the specific mechanics of the system. Several attempts have been made to model the hemodynamic response.

One of the first models was Heegan’s linear model [105]. This model attempted to model the fMRI response to a stimulus as a convolution of a temporal impulse response function and the time course of neural activity. Figure 3-5, adapted from [91], shows the typical electrical response seen in response to 12 second, 3 Hz electrical hindpaw stimulus. With the onset of stimuli there is a large increase in electrical activity. Subsequent pulses fall in magnitude to a steady state over the next few seconds. The electrical activity returns to zero at the end of the stimulus.

Figure 3-5. Typical representation of electrical activity seen in response to a 12 second, 3 Hz hindpaw stimulus. Adapted and reproduced from [91]

To a first approximation, this response can be modeled as a box function. The point spread functions of these models are solved for using experimental data and usually take the form of a gamma distribution

[106, 107].

Another early model was Buxton, Wong, and Frank’s “balloon” model [108]. This model attempted to relate electrical activity in the brain with the BOLD signal seen with fMRI. A central assumption in this model was that the changes in blood volume only occurred in the venous compartment. A series of other assumptions were then made regarding in-flow and out-flow in the venous compartment as well as with oxygen extraction in the capillary bed [108]. Only modeling the venous compartment proved to be insufficient to accurately describe the events seen with fMRI and several additions to the balloon model have been published to address non-linearities of the BOLD response that are not predicted by the balloon model [109, 110].

These models were very general. They did not address the underlying cellular mechanisms that were at play leading to these responses. Other models were then developed and over time became more complex and expanded to include the arterial and capillary compartments [109, 111-113]. Other approaches developed methodologies to view and model individual capillaries and study the dynamics of red blood cell movement in these capillaries [95, 114, 115]. Some models have also introduced branching between the compartments to attempt to explain the spatial characteristics seen in the neurovascular response

[92]. The vascular anatomical network model considered vessel branching and was able to predict a passive surround negative vascular response by focusing on the relationship between non-neuronal parameters, such as vessel diameter, flow speed, and blood pressure [92]. These models provide some explanation for spatiotemporal relationships seen in fMRI data, but many have failed to link these properties to neuronal firing and provide an understanding of the underlying physiological mechanisms

68 of neurovascular coupling. Other studies have identified mechanisms that could potentially explains some aspects of the hemodynamic response, but not applied these mechanisms to predict spatial chacteristics.

One of the ultimate goals of developing a mathematical model of neurovascular coupling is to use the implications of the model to identify the cascade of cellular events that take electrical neuronal activity as an input and result in changes in blood flow in the brain (Figure 3-6). However, many of the published models do not. Establishing a cellular mechanism to explain why a particular mathematical model holds predictive value may be able to inform how failures in this process may ultimately lead to pathologies.

Figure 3-6. The goal of determining a mathematical model of neurovascular coupling is to transition that knowledge into developing an understanding of the underlying cellular mechanisms of the mechanism

Prediction of all the components of a cellular mechanism may not be feasible with a mathematical model alone, but a model can also inform the design of further experiments because it can eliminate potential pathways with physiological parameters that do not fit the model. Experiments that rely on pharmacology or genetic engineering can also be used to isolate specific cellular pathways in this process. This chapter aims to provide a mathematically based model that is tied to the potential cellular mechanisms. This model could potentially help elucidate more of the underlying cellular mechanisms that translate electrical activity seen in the rodent brain from an external stimulus to the observed changes in HbT, HbO, and HbR.

3.2 Characterization of the Experimental Data

Our lab has performed a number of studies that involve imaging exposed rodent cortices in order to better understand the nature of neurovascular coupling. The goal of this section was to characterize the changes in HbT in the hemodynamic response of healthy rats as a function of stimulus length. The patterns found were then used to develop a model that could accurately describe these changes and, given a particular stimulus length, be used to predict the hemodynamic response.

This assessment was performed on two rats that were imaged using a wide variety of stimulus lengths.

Data from several other animals was used to test these theories, but the vast majority of the findings were from the two. In these experiments one rat were imaged at an effective frame rate of 25 Hz and the other was imaged at 37.5 Hz, with a 5ms exposure time, and at either 256x256 or 512x512 pixels. Data was collected in runs, which are the averages of five trials of data acquired in sequence. That is, to collect a 2 second stimulus run, five trials were performed. Data from the optical imaging system was converted to hemodynamic data using an established protocol in Matlab [100]. This data was then viewed as a movie in order to determine regions of interest over arteries in the center of the responding region and in the periphery of the field of view. Our previous studies have indicated that, with stimulus, there are two characteristic responses. The first is a localized area with high activity, referred to as the responding region, and the second is in the area just beyond this first region, called the surround region.

Average time courses of the changes in hemodynamics over the responding region and the surround on the exposed cortex of rats receiving 3 Hz hindpaw stimuli ranging from 0.5 seconds to 14 seconds were analyzed and a number of patterns emerged across the data. Four common patterns were identified as key in developing an understanding of what form the HbT hemodynamic response to stimulus should take.

1. Responding region vs. Surround Round

The first element, as shown in Figure 3-7, was that there is a different characteristic hemodynamic response in the responding region compared to the surround. Our lab’s previous work has shown that the hemodynamic response seen in the responding region is a function of stimulus length, while the response in the surround region requires a stimulus, but is independent of stimulus length. Figure 3-7 shows this pattern with time courses from these regions with a short 0.5 second stimulus, a medium 7 second stimulus, and a long 14 second stimulus.

Figure 3-7. Time courses from the surround and responding regions. The surround response is small and nearly constant, while the responding region shows large responses and stimulus length dependence.

Any predictive model would need to be able to accurately explain this spatial characteristic mathematically and provide insight into potential cellular mechanisms. Figure 3-8a and 8b show examples of the typical fields of views from two different rats with selected regions of interest in the responding and surround regions. The rat in Figure 3-8a was imaged at 512 x 512 pixels and the rat in Figure 3-8b was imaged at 256 x 256 pixels. Data from these rats were converted to ΔHbT to create the hemodynamic maps seen in Figure 3-8c and d. These images show a large increase in ΔHbT over responding region. This

71 is the area that dilates most in response to a hindpaw stimulus. Additionally the arteries in the surround region show some dilation.

Figure 3-8e shows the time courses over the regions of interest shown in Figure 3-8a and Figure 3-8f shows the average time courses over five trials in the regions of interest shown in Figure 3-8b for a 12 second stimulus . The solid gray line shows the onset of stimulus and the dotted gray line shows the time point where the maps in Figure 3-8c and d are from. These time courses show that there is a large response in the responding region and a smaller, shorter response in the surround. The time courses in Figure 3-8e shows a global trend underlying the data, but the response to stimulus still occurs.

Figure 3-8. The hemodynamic response with 12 second stimulus (a-b) The field of view for two rats showing two regions of interest each. The blue region of interest is over an artery in the responding region. The green region of interest is over an artery in the surrounding region. (c-d) Hemodynamic maps showing ΔHbT over the baseline 2 seconds after stimulus. There cyan regions are the responding regions and the arteries outside of this region that show a response indicate the surround region. (e-f) Time courses from the regions of interest shown in (a-b) for a 12 second stimulus. The responding region has a large response while the surround has a smaller response.

2. Minimum Threshold

Figure 3-9. Minimum Threshold of Data. Experimental measurements of HbT in the responding region for stimulus lengths up to 1 second. Shorter stimulus lengths result in the same hemodynamic HbT response.

The second element is that the hemodynamic response has a minimum threshold in terms of amplitude and duration. As the duration of the stimulus decreases, the amplitude of response also tends to decrease.

However, the amplitude of the response does not trend to zero. Instead, for a range of extremely short stimuli (0.5, 0.75, 1 second stimuli), there is a near constant, non-zero hemodynamic response in the responding region. Figure 3-9 shows time courses from single runs using these stimulus lengths for one rat. The vertical line on Figure 3-9 represents the onset of the stimulus. The frequency of the stimulus was

3 Hz. This means that 0.5, 0.75, and 1 second stimulus actually correspond to 1 pulse, 2 pulses, and 3 pulses of stimuli, respectively. This constant hemodynamic response involves a rapid vessel dilation, shown as an increase in HbT, at the onset of stimulus, which peaks and then constricts. The hemodynamic signal returns to baseline approximately 7 seconds later. The vessel continues to constrict before undergoing a second smaller dilation.

3. Maximum Threshold

Figure 3-10. Maximum Threshold. Experimental measurements of HbT for different stimulus lengths. Longer stimulus lengths reach a maximum amplitude threshold. (a) A hemodynamic map of the responding region (b) Time courses from the selected region of interest (black box) for 0.5, 2, 8, and 11 seconds. Each of these runs is an average of five trials.

The third element is that amplitude of response reaches a maximum threshold. For longer stimuli, regardless of stimulus length, there was a maximum ΔHbT that the hemodynamic response would never go beyond. Figure 3-10 shows hemodynamic responses to longer stimulus lengths reaching this maximum threshold. Figure 3-10a shows the hemodynamic map with the selected ROI in black. Figure 3-10b shows the average ΔHbT time course for the selected region for multiple stimulus lengths. This figure shows that for shorter stimuli, such as 0.5s and 2s, as the duration of stimulus increases, the vessel dilation increases, but the 8s and 11s stimuli have nearly identical maximum values. Relating to the first element, this analysis also shows that increases in stimulus duration beyond 1 second, the duration of the response was directly proportional to the stimulus length.

4. Long stimulus “hooking”

Figure 3-11. Hook response. The hemodynamic response resulting from 8 seconds and 12 second stimuli. The 12 second stimuli results in a “hook” towards the end of the main response. This “hook” is only present in longer stimulus runs.

The fourth element is a “hook” towards the later part of the response with long duration stimuli. For stimuli less than 11 seconds in length, the response involves a large increase followed by a large decrease.

For longer stimuli there is a second smaller dilation on top of the large initial dilation at approximately 11 seconds into the response. Figure 3-11 shows two time courses from the same region of interest seen in

Figure 3-10a. The 12 second stimulus time course shows the described hook, indicated by a *. This hook is not present for the 8 second stimulus hemodynamic response. An accurate model must be able to describe all four of these elements.

To conclude, these four patterns are:

1. Responding region vs. Surround region

2. Minimum Threshold

3. Maximum Threshold

4. Long stimulus “hooking”

The typical linear convolution model is incapable of explaining all of these patterns. An example of one of the hemodynamic response functions from a linear model is shown in the left portion Figure 3-12. There is a large increase in signal at the onset of stimulus and then a gradual decline after the peak. The right portion of Figure 3-12 shows this point spread function convolved with a box function, representing neuronal activity.

Figure 3-12.Linear convolution model. An example of a hemodynamic response function that takes the form of a gamma distribution (left) and a series of predictions based on convolving the hemodynamic response function with a box function of the length of a stimulus, representing neuronal activity.

These models do not predict patterns 1, 2, and 4. These models only use a single term and are therefore unable to explain both the surround response and the responding region response. Figure 3-13 shows the maximum predicted amplitudes from Figure 3-12.

Figure 3-13. Amplitude of the linear model predictions as a function of stimulus length. This model reaches a maximum amplitude, but goes to zero as the stimulus length approaches zero.

This shows that there is no minimum threshold. As the length of stimulus approaches zero, so does the magnitude of response. However, this does show that there is a maximum amplitude threshold. This is a consequence of using a convolution based model. Therefore the model does not describe the second pattern, but does accurately describe the third. Lastly, these linear models with simple gamma function point spread function are unable to predict pattern 4, the hook seen with longer stimuli. Functional MRI does not necessarily have the spatiotemporal resolution or sensitivity to identify all of these patterns and therefore these linear models have been applied.

3.3 The Two-component Hemodynamic Response Function

Studies of the peripheral vasculature along with our lab’s previous work have led us to the hypothesis that two main components compose the hemodynamic response, and the signals for these response components are transmitted along the arterial endothelium [91]. The first response is thought to be a fast electrical response transmitted through endothelial gap junctions and the second is a slower calcium based response [116]. The fast electrical response travels a greater distance than the slower calcium response. Our first approach to developing a two component model to describe Δ퐻푏푇 was to develop a backwards model that began with experimental data and determined the appropriate hemodynamic response functions. This model was assumed to take the general form:

Δ퐻푏푇(푥, 푦, 푡) = (푆1(푥, 푦, 푡) ⊗ 퐻푅퐹1(푡)) + (푆2(푥, 푦, 푡) ⊗ 퐻푅퐹2(푡))

where HRF1(t) and HRF2(t) corresponded to the initially unknown hemodynamic response functions of the electrical and calcium waves, respectively, and ⊗ indicates a convolution. S1 and S2 correspond to the respective triggers functions of these waves. In this case, these functions describe the signals driving the dilation of the pial arterioles. These triggering functions initiate the hemodynamic response and by performing this convolution will estimate the output, which is the Δ퐻푏푇 time course. In linear models that involve convolving a point spread function with electrical activity, the electrical activity signal is this trigger function. The trigger functions account for the spatial characteristics of the data. This model makes no assumptions regarding the forms of HRF1(t) and HRF2(t).

The theoretical hemodynamic response functions can be solved for as follows by assuming forms for the trigger functions S1 and S2:

By using Fourier transforms, we can solve for the second HRF as follows

ℱ(푆1(푥, 푦, 푡) ⊗ Δ퐻푅퐹1(푡)) + ℱ(푆2(푥, 푦, 푡) ⊗ Δ퐻푅퐹2(푡)) = ℱ(Δ퐻푏푇(푥, 푦, 푡))

ℱ(푆1(푥, 푦, 푡)) = 푆̂1(푥, 푦, 푓)

ℱ(Δ퐻푅퐹1(푡)) = Δ̂퐻푅퐹1(푓)

ℱ(푆2(푥, 푦, 푡)) = 푆̂2(푥, 푦, 푓)

ℱ(Δ퐻푅퐹2(푡)) = Δ̂퐻푅퐹2(푓)

ℱ(Δ퐻푏푇(푥, 푦, 푡)) = Δ̂퐻푏푇(푥, 푦, 푓)

푆̂1(푥, 푦, 푓)Δ퐻푅̂퐹1(푓) + 푆̂2(푥, 푦, 푓)Δ퐻푅̂퐹2(푓) = Δ̂퐻푏푇(푥, 푦, 푓)

Let a and b correspond to two different stimulus regimes.

푆̂1푎(푥, 푦, 푓)Δ̂퐻푅퐹1(푓) + 푆̂2푎(푥, 푦, 푓)Δ̂퐻푅퐹2(푓) = Δ̂퐻푏푇푎(푥, 푦, 푓)

푆̂1푏(푥, 푦, 푓)Δ̂퐻푅퐹1(푓) + 푆̂2푏(푥, 푦, 푓)Δ퐻푅̂퐹2(푓) = Δ̂퐻푏푇푏(푥, 푦, 푓)

Δ̂퐻푏푇푎(푥, 푦, 푓) − 푆̂2푎(푥, 푦, 푓)Δ퐻푅̂퐹2(푓) Δ̂퐻푅퐹1(푓) = 푆̂1푎(푥, 푦, 푓)

Δ̂퐻푏푇푎(푥, 푦, 푓) − 푆̂2푎(푥, 푦, 푓)Δ퐻푅̂퐹2(푓) 푆̂1푏(푥, 푦, 푓) ( ) + 푆̂2푏(푥, 푦, 푓)Δ퐻푅̂퐹2(푓) = Δ̂퐻푏푇푏(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓)

푆̂ (푥, 푦, 푓) 푆̂ (푥, 푦, 푓) 1푏 ̂ 1푏 ̂ 푆̂2푏(푥, 푦, 푓)Δ̂퐻푅퐹2(푓) − 푆̂2푎(푥, 푦, 푓)Δ̂퐻푅퐹2(푓) = Δ퐻푏푇푏(푥, 푦, 푓) − Δ퐻푏푇푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓)

푆̂1푏(푥, 푦, 푓) 푆̂1푏(푥, 푦, 푓) Δ̂퐻푅퐹2(푓) (푆̂2푏(푥, 푦, 푓) − 푆̂2푎(푓)) = Δ̂퐻푏푇푏(푥, 푦, 푓) − Δ̂퐻푏푇푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓)

푆̂1푏(푥, 푦, 푓) Δ̂퐻푏푇푏(푥, 푦, 푓) − Δ̂퐻푏푇푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓) Δ̂퐻푅퐹2(푓) = 푆̂1푏(푥, 푦, 푓) 푆̂2푏(푥, 푦, 푓) − 푆̂2푎(푥, 푦, 푓) 푆̂1푎(푥, 푦, 푓)

푆̂ (푥, 푦, 푓) Δ̂퐻푏푇 (푓) − 1푏 Δ̂퐻푏푇 (푓) 푏 푆̂ (푥, 푦, 푓) 푎 Δ퐻푅퐹 (푓) = ℱ−1 1푎 2 푆̂ (푥, 푦, 푓) ̂ ( ) 1푏 ̂ ( ) 푆2푏 푥, 푦, 푓 − ̂ 푆2푎 푥, 푦, 푓 ( 푆1푎(푥, 푦, 푓) )

This method theoretically can take measured hemodynamic responses and assumed trigger functions and output hemodynamic response functions for the two components of the response. This method was applied to the GCaMP3 mice data discussed previously to attempt to determine the hemodynamic response functions. This data was selected because these mice had an optical signal that was characteristic of the underlying neuronal activity. Several sets of trigger functions were tested, including impulse functions, box functions, and functions based on the fluorescence signal from GCaMP3 mice.

However, this backwards model is highly dependent on Fourier transform based deconvolutions and, as a result, highly amplifies noise in data. Figure 3-14a shows examples of the trigger functions tested. The left shows an impulse function, the middle shows a box function, and the right shows the portion of the calcium fluorescence signal that occurred during the stimulus period. Figure 3-14b shows the an example of an unfiltered hemodynamic response function that can be derived from this method and Figure 3-14c shows the filtered version of Figure 3-14b. A physiologically reasonable hemodynamic response should start at zero, show a change in HbT, and then return to zero. However, Figure 3-14c starts at approximately

3 µM and is thus not particularly physiologically reasonable.

Figure 3-14. Backwards model results. Purely analytical method for determining the hemodynamic response function (a) Examples of the trigger functions used. (Left) Impulse response, (Center) Box function (Right) Calcium signal from the GCaMP3 mouse. (b) An example of an unfiltered HRF derived from this method using the calcium signal. It contains significant noise. (c) A filtered version of the determined hemodynamic response function. This HRF does not start at zero and is thus not physiologically reasonable.

The application of a backwards model resulting in unreasonable hemodynamic response functions. We therefore decided to apply another method to identify the hemodynamic response functions of this two component hemodynamic response function model. We noticed that the surround response resembles the typical point spread function with some extra features. We then decided attempt a forward model using the surround response as the hemodynamic response function.

3.4 The Smooth Muscle Cell Point Spread Function

Developing a backwards model involves determining hemodynamic response functions from experimental data sets. However, the development of a forward model involves creating a hemodynamic response function and determining the proper trigger functions and comparing the resulting model to the experimental data. Our lab’s recent work suggests that endothelial signaling driven arterial dilation is key to understanding the hemodynamic response seen in the arterial compartment with wide-field imaging.

In the peripheral vasculature, it has been demonstrated that two types of dilation propagations occur

[116]. Following a stimulus there is a fast, gap-junction mediated dilation wave that begins in the capillary bed or diving arterioles and then back propagates along the arterioles for distances in excess of 1mm

[116]. This initial dilation wave achieves maximum ΔHbT between 3-6 seconds following the onset of stimulus. There then is a second dilation wave that is not gap junction mediated, but may be mediated by

2+ a wave in Ca levels in the endothelial cells that evokes an NO and prostacyclin-dependent dilation over distances of around 500 microns [116]. This is a shorter distance of travel than the first wave and does not reach the more distal pial arterial vessels. This cellular mechanism model could explain the spatial characteristics seen in the exposed cortex in response to stimulus. The faster and further traveling initial dilation wave would be responsible for the stimulus-independent response seen in the surround region and the slower, secondary dilation wave would be the stimulus-dependent response in the responding region. In the peripheral vasculature, these waves are initiated by increases in the intracellular calcium levels of the endothelial cells lining the vessel, with the fast component requiring a higher (340 nM) change compared to the slower component (220 nM) [116]. Researchers of neurovascular coupling have tended to view the brain’s vasculature as distinct from the peripheral vasculature. Chen et. al. showed that, in the brain, this first wave was endothelium-dependent by using a light-sensitive dye to disrupt electrical signaling in the endothelial cells [91]. This eliminated the surround response, but a stimulus-

83 dependent response remained in the responding region. We postulate that the brain does indeed follow a similar mechanism to the peripheral vasculature. That is, these two dilation waves are trigged based on the endothelial intracellular calcium levels and reaching different thresholds of endothelium intracellular calcium will lead to different forms of arterial dilation [116]. Figure 3-15 depicts the two components of the response and their associated endothelium intracellular calcium levels.

Figure 3-15. Two components of hemodynamic response. The left shows a depiction of the 2 component hemodynamic response function with assumed “fast” and “slow components”. Both may originate from endothelial signaling. The right shows the assumed intracellular endothelial calcium increases required to evoke each response.

Based on this hypothesis, we developed a two component model based on the two dilation waves. These components both used the average surround response as a hemodynamic response function. The first, further traveling components used an impulse response as the trigger and the second component used a box function.

The theory of two responses with different propagation distances can describe the spatial characteristics seen with stimuli. The responding region appears to be the area that experiences both the electrically mediated and the calcium-mediated dilation waves. The calcium-mediated wave does not propagate as far and thus the surround region appears to only experience the electrically mediated dilation wave.

The endothelial cells may transmit the signal that leads arterial dilation, but it is the smooth muscle cells along the vasculature that are responsible for the dilation itself. There are multiple mechanisms which lead to smooth muscle relaxation and vasodilation, including hyper-polarization mediated, cAMP- mediated, and cGMP-mediated. These three mechanisms are initiated differently, but share the fact that they all lead to a decrease in the cytoplasmic levels of calcium and an increase in MLC phosphatase [117].

MLC phosphatase dephosphorylates the myosin light chain phosphate, allowing for smooth muscle cell relaxation and vessel dilation. Figure 3-16, adapted and reproduced from [117], shows these different pathways. Vascular smooth muscle cells are normally in a state of slight contraction because intracellular calcium levels. A decrease in cytoplasmic calcium causes deactivation of MLC kinase. MLC phosphatase can then dephosphorylate the myosin light chain, leading to vascular smooth muscle cell relaxation and vasodilation. Since these pathways all share the same end steps and the actual mechanism of relaxation is the same throughout, it indicates that there may be a universal smooth muscle cell response that could be described with a point spread function.

Figure 3-16. Mechanism of smooth muscle cell relaxation. There are a number of ways to trigger vessel dilation through smooth muscle cell relaxation, but each of these mechanisms share the same end steps of lower cytosolic calcium levels in order to induce myosin light chain relaxation. Figure from [117]

We postulated that this abbreviated response occurred due to the onset of the stimulus and was indicative of the minimal response to stimulation that a smooth muscle cell can make. Because the electrically mediated wave occurs due to the onset of stimulus and not the duration of stimulus, this cellular model explains the first two patterns of the observed data sets: the spatial characteristics of the responding region and surround response and the non-zero minimum hemodynamic response.

Because the vascular smooth muscle cells were directly responsible for the vasodilation and the surround region response was constant, the HbT time courses for the arteries in the surround region were used as the smooth muscle cell point spread function and thought to represent the minimum response possible to stimulus. The electrically-mediated dilation wave was assumed to occur in response to stimulus onset and thus should only represent a single trigger for smooth muscle cell action. This idea is also supported

86 by the observation that this surround response resembles the minimum response seen in the responding region that was shown in Figure 3-9 for 1, 2, and 3 stimulus pulses.

The surround response was measured for every experimental run over the regions of interest shown in green in Figure 3-8a and b. For each experiment, these time courses were averaged and filtered to determine the smooth muscle cell point spread function for each rodent. Figure 3-17 shows two examples of these smooth muscle cell hemodynamic response functions from different rats. Even though these are different rats in separate experiments the point spread functions share many similar characteristics. They both have a large initial increase in ΔHbT at the onset of the stimulus at 6 seconds that then returns to baseline. After the first wave is at least one smaller wave that peaks at approximately 20 seconds (14 seconds after stimulus onset).

Figure 3-17. Two measured smooth muscle cell point spread functions. These were determined by averaging time courses taken from arterial vessels from the surround region to determine the constant surround response. (a) The smooth muscle cell point spread function for one rat (b) The smooth muscle cell point spread function for another rat.

A physiologically reasonable hemodynamic response function should start and end at zero. Because these functions are based on experimental data, global trends in the data can cause this to not be the case. The period before the stimulus is not be affected by the stimulus. We therefore set all prestimulus values to zero for the measured response functions. Experimental runs with abnormal responses that deviated significantly from the other responses in that experiment were excluded from analysis. These tended to be runs that contained significant global trends that were not from changes in the hemodynamics. Figure

3-18 contains an example of such a time course. This time course was obtained by selecting a region of interest over the skull. The theoretical ΔHbT time course over the skull should be zero. The small response seen at the onset of the stimulus is likely due to photons reflected from the adjacent brain region.

However, these photons are not enough to explain the large increase in signal seen over the imaging period.

Figure 3-18. ΔHbT time course taken from over skull bone. This time course shows an unexplained global trend.

These smooth muscle cell point spread functions shared a number of strikingly similar characteristics across different rats, indicating that these time courses are likely accurate representations of an underlying biological process. One important aspect of these point spread functions is that they contain ringing. Hemodynamic response functions are typically shown as starting at zero, increasing at the onset of stimulus, peaking and then returning the baseline, resembling a gamma distribution. These smooth muscle cell point spread functions have this first wave, but then are followed by lower amplitude dilations.

One possible explanation that can be derived from studies of peripheral vasculature is that this ringing is the result of a latency period in which the relaxation mechanism of smooth muscle cells cannot be triggered again. This type of ringing effect has been seen in the context of vasomotion. In smooth muscle cells a number of pathways exist that serve to either increase or decrease cytoplasmic levels of Ca2+. In the peripheral vasculature Ca2+ gradients have been found to spread within and between vascular smooth

2+ muscle cells. These Ca gradients are thought to trigger IP3 dependent increase in intracellular calcium.

Once this pathway is triggered, there is a refractory period in which this mechanism is no longer active, even if the trigger is still present [118]. After the cytoplasmic Ca2+ levels decrease leading to vascular smooth muscle cell relaxation, one of the mechanisms of this relaxation may also have a refractory period.

Continued stimulus for vascular smooth muscle cell relaxation may be present, but in this period, the cytosolic levels of calcium in the smooth muscle cells would increase, causing vessel contraction. After this period is over there may be sufficient signal either from the endothelial cells or still on the smooth muscle cell to cause some smooth muscle cells to remove their cytosolic calcium again, leading to relaxation from some muscle fibers. Figure 3-19 illustrates this idea. Initially there is no stimulus, so the smooth muscle cell cytoplasmic Ca2+ levels are normal. Upon receiving the stimulus, the endothelial cells communicate with the smooth muscle cells, leading to a drop in smooth muscle cell cytoplasmic Ca2+ levels, causing vessel dilation. This dilation seizes and the vessel constricts. This may occur because the

89 dilation mechanism enters a latency phase. Once this latency phase is over, continued dilation signal may initiate the smaller, secondary dilation response.

Figure 3-19. A possible mechanism for the ringing effect seen in the smooth muscle cell point spread function. Certain vascular smooth muscle cell contraction mechanisms are believed to contain latency periods. This same phenomenon may occur with dilation mechanisms and would explain the second, smaller dilation seen on the time course at approximately 16 seconds. The endothelial cells provide a dilation signal to the smooth muscle cells, but the mechanism of action in the smooth muscle cells undergoes a latency period, affecting cytoplasmic calcium levels which affect the state of muscle fiber contraction.

The arterial dilation resulting from the fast electric wave and the slow calcium wave are both dependent on smooth muscle relaxation, therefore this smooth muscle cell point spread function was assumed to apply to both waves. The first stimulus pulse received by the animal was assumed to lead to an increase in endothelial cell calcium levels, inducing the electric and calcium-based dilation waves. The electric wave quickly propagates, inducing the smooth muscle cell point spread function as a response. In the full form of the model, this wave is modeled as the smooth muscle cell point spread function convolved with a delta

90 function at the onset of the stimulus. The calcium wave travels over the responding region, inducing more smooth muscle cell fibers to relax and the vessels to dilate. The dilation caused by the calcium wave is delivered on top of the dilation from the electric wave. Figure 3-20 illustrates the propagation of these two waves with the initial hyperpolarization wave traveling from the center of the responding region along to distant pial vessels and the calcium wave starting from the center and traveling a shorter distance.

Figure 3-20. Field of view showing propagation of the hyperpolarization and calcium induced dilation waves. The fast, hyperpolarization wave propagates a longer distance and reaches distant vessels (left). The calcium wave propagates a shorter distance, creating the responding region (right).

The initial response of the vessels is from the hyperpolarization wave. The subsequent calcium wave was assumed to involve repeated stimulus for the duration of the stimulus. Repeatedly adding together the smooth muscle cell point spread function for each stimulus results in a predicted response of a much greater magnitude than the observed responses. Two possible reasons were hypothesized for this observation. One hypothesis is that the calcium wave induces a decrease in the vascular smooth muscle cell cytoplasmic calcium levels through a different mechanism that leads to a smaller magnitude response.

The other hypothesis is that with the initial dilation wave there are many myosin fibers that are able to relax. With subsequent stimulus pulses there were less that were able to relax, causing a smaller amplitude response. Individually the responses are smaller, but enough of these lower magnitude

91 responses will add up. Eventually the rate of myosin fibers recovering and reconstricting equals the number being relaxed with the stimulus, reaching a steady state until the end of stimulus. These two possible mechanisms are not mutually exclusive. Figure 3-21 illustrates these hypothetical mechanisms.

The top gives an example of the first hypothesis. The first wave from the hyperpolarization signal causes

35% of the myosin fibers to contract, and subsequent waves from the calcium wave signal cause 9% of fibers to contract. The bottom of Figure 3-21 gives the example of the second hypothesis. With each stimulus, 20% of the constricted fibers relax and 20% of the relaxed fibers enter a refractory period. Based on the observations regarding the magnitude of the experimental response and the hypothesized mechanisms, the calcium wave dilation is modeled as the smooth muscle cell point spread function convolved with a box function multiplied by a rat-dependent scaling factor. This scaling factor adjusts for experimental differences between runs and the statistical distribution of myosin fiber rephosphylation times.

Figure 3-21. Two hypothetical models for how repeated stimuli add together. Hypothesis 1: The initial hyperpolarization wave dilation response has a larger magnitude response than the subsequent calcium waves owing to a separate dilation mechanism. The 35% and 9% values are simply to give an example of how these stimuli add together. Hypothesis 2: The initial hyperpolarization response has more available myosin fibers to relax. Some of the relaxed fibers enter a refractory period in which they reconstrict, but are unable to relax again. In this example, each stimulus causes 20% of constricted fibers to relax and 20% of the already relaxed fibers enter the refractory period.

3.5 The Endothelial Propagation Hemodynamic Response Model and Data Simulation

The previous section shows how the point spread function of a smooth muscle cell was determined and introduces the assumptions made to model each dilation wave. This point spread function is the basis of the response in both the responding and the surround regions. This section expands on these previous findings to introduce the full endothelial propagation hemodynamic response model (EP-HRM) and then shows the ability of this model to explain the observed stimulus-induced hemodynamic response.

3.5.1 The Endothelial Propagation Hemodynamic Response Model

Based on the previous section, the total hemodynamic response in the area around the responding region takes the form

Δ퐻푏푇 = (푃푆퐹(푡) ⊗ 훿(푥, 푦, 푡)) + (푃푆퐹(푡) ⊗ 퐵(푥, 푦, 푡))푆퐹푅퐷 and in the surround region takes the form

Δ퐻푏푇 = 푃푆퐹(푡) ⊗ 훿(푥, 푦, 푡) where PSF(t) is the measured smooth muscle cell point spread function, 훿(푥, 푦, 푡) is a delta function at the onset of stimulus, 퐵(푥, 푦, 푡) is a box function starting at stimulus onset and running the duration of the stimulus, and 푆퐹푅퐷 is the rat-dependent scaling factor. The measured ΔHbT responses reach a maximum amplitude of the first peak approximately 4 seconds after stimulus onset. The maximum amplitude depends factors such as the experimental set up, the animal’s temperature, and the brains microenvironment. Therefore for each experiment and each new rat a new SFRD scaling factor must be determined.

Figure 3-22a shows the maximum amplitudes of the first peak of the experimental time courses with lines of best fit for the data between 0.5 second and 4 seconds stimuli and for between 4 seconds and 14 seconds. As explained earlier the amplitude of the experimental data approaches a non-zero value as the length of stimulus approaches zero. Figure 3-22b shows the maximum amplitudes of the first peak of the experimental time courses minus the smooth muscle cell point spread function. This represents the second component of the endothelial propagated hemodynamic response model.

Figure 3-22. Maximum amplitude of response for a single rat under different stimulus lengths. The blue x’s represent experimental runs. The green lines are lines of best fit for the stimuli of 0.5 to 4s and from 4s to 14s. (a) The maximum amplitude of the measured data (b) the maximum amplitude of the measured data minus the smooth muscle cell point spread function

Figure 3-23a shows the unscaled simulated second dilation wave responses. These were developed by convolving the smooth muscle cell point spread function with a box function of stimulus length. Figure

3-23b is a plot of the amplitude of the initial peak of these predicted time courses with the same best fit lines as in Figure 3-22b.

Figure 3-23. Simulated calcium-mediated dilation wave (a) The unscaled predicted calcium-mediated dilation wave responses determined by convolving the smooth muscle cell point spread function with a box function (b) The maximum ΔHbT of the simulated calcium-mediated dilation wave responses.

The first step in determining value for SFRD was to subtract the smooth muscle cell point spread function from the measured time courses. This result represents the calcium-mediated dilation wave response.

Each experimental calcium-mediated dilation wave response was then fit to the appropriate predicted response to determine a scaling factor. Figure 3-24 shows this process for an experimental run of 5 trials with a 12 second stimulus. Figure 3-24a shows the values of the experimental ΔHbT time course minus the smooth muscle cell point spread function versus the unscaled predicted calcium wave ΔHbT time course. The linear regression between these two has a 0.418 term. This term is the scaling factor for this particular experimental run. This same progress was repeated for every run and the average of these scaling factors was the rat dependent scaling factor, SFRD.

Figure 3-24. Determining the scaling factor (a) A plot of the experimental ΔHbT and the unscaled predicted ΔHbT for a 12 second stimulus. The green line is a linear regression. The 0.0418 value is the scaling factor for this run. The scaling factors for each of the runs of a rat were averaged together to determine SFRD. (b) A plot of the experimental ΔHbT in blue and the scaled predicted ΔHbT in green.

3.5.2 Full Response Prediction

Once the proper scaling factor was determined, the endothelial propagating hemodynamic response model was used to estimate the full response in the main responding region for a series of stimulus lengths ranging from 0.5 to 14 seconds. Along an artery in the responding region the full model simplifies to:

Δ퐻푏푇 = 푃푆퐹(푡) + (푃푆퐹(푡) ⊗ 푠푡푖푚(푡))푆퐹푅퐷 where stim(t) is a box function of value one during the stimulus and zero at all other times. The particular stimuli used varied from experiment to experiment depending on the particular needs of that experiment.

Figure 3-25, Figure 3-26, and Figure 3-27 show examples of the estimated and actual time courses from experimental runs of a single rat in the responding region for stimuli from 0.5 to 14 sec.

Figure 3-25. Measured (blue) and predicted changes (green) in ΔHbT for 0.5 – 3 second stimuli for the responding region based on endothelium propagating hemodynamic response model

Figure 3-26. Measured (blue) and predicted (green) changes in ΔHbT for 4 - 9 second stimuli for the responding region based on the endothelial propagating hemodynamic response model

Figure 3-27. Measured (blue) and predicted (green) changes in ΔHbT in the responding region for 10 - 14 second stimuli based on the endothelial propagating hemodynamic response model

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The predictions from this model follow the same four patterns seen in the original analysis of the data:

1. Responding region vs. Surround region

2. Minimum Threshold

3. Maximum Threshold

4. Long stimulus “hooking”

This model addresses pattern 1 by having two terms that are applied different spatially. Figure 3-28 shows the predicted time courses and a plot of the maximum amplitude of the initial peak. Since the constant surround response is introduced with any stimulus initiation, a floor is set on the minimum response

(pattern 2). This allows the simulations to have the second pattern in that for short duration stimuli (0.5,

0.75, 1 sec), there is a near constant response. At these low stimulus durations, this hyperpolarization term dominates the model. Figure 3-28b indicates that as the length of stimulus approaches zero, the maximum amplitude of the response approaches a non-zero number.

Figure 3-28. Simulated data using the full endothelial propagation hemodynamic response model for the responding region (a) The scaled predicted full response. (b) The maximum ΔHbT of initial peak of the simulated hemodynamic response. The best fit lines for 0 to 4 second stimulus and for 4 to 14 second stimulus are shown in green. These show that this model meets the 4 criteria outlined earlier as necessary for a proper model

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Figure 3-28b also shows that the model predictions follow pattern 3. The maximum amplitude of the initial peak reaches a constant. The presence of the term SFRD allows this threshold to be approximately the same as seen in the actual experimental data. Pattern 4 of the experimental data can be seen in Figure

3-28a. For stimuli starting at 11 seconds there is a clear “hook” pattern towards the end of the stimulus.

This hook is a function of the ringing found in the smooth muscle cell point spread function. Figure 3-29 shows the results of applying the model algorithm using a smooth muscle cell point spread function. With no ringing, the prediction reaches a constant and remains at that value before returning to baseline.

Figure 3-29. The ringing in the smooth muscle cell point spread function is responsible for the ringing. (a) The smooth muscle cell point spread function modified to contain no ringing (blue) and the original (gray) (b) A prediction of the responding region with a 14 second stimulus using the endothelial propagating hemodynamic response model with no ringing (green) and without ringing (gray). The experimental data (blue) contains a “hook”. The “hook” is only present in the simulations when the smooth muscle cell point spread function contains ringing.

There is a natural variation from run to run, even with the same stimulus duration so not all of the predictions exactly match the measured response. This is particularly evident above with stimuli of 2-6

102 seconds. This variation leads to the maximum amplitude for the 2 second stimuli is greater than the shown

3 second stimuli. The 6 second response amplitude is also less than the amplitude from the 4 and 5 second responses. Within the 2 second stimulus runs, some runs have a greater maximum amplitude than the predicted time course and some had less. A linear fit between the post-stimulus portion of the predicted hemodynamic time courses and the post-stimulus portion of the measured responses was performed for all of the runs of the rat data shown above. Each run consists of five trials performed back to back and then averaged. Table 2 shows the R2 values for each of these fits for stimuli of 0.5 to 14 seconds.

Stimulus Duration (s) Run (Avg of 5 trials) R2 Value 0.5 1 0.9057 0.75 1 0.8498 1 1 0.8674 2 0.8936 1.5 1 0.8623 2 0.8376 2 1 0.8532 2 0.8157 3 0.2334 4 0.2308 5 0.2949 3 1 0.5556 4 1 0.7262 2 0.8863 5 1 0.8143 6 1 0.9345 7 1 0.7190 8 1 0.7987 2 0.8284 9 1 0.9027 10 1 0.9249 11 1 0.9817 12 1 0.9343 2 0.9149 13 1 0.8773 14 1 0.9374

Table 2. R2 values for a linear fit between the predicted and measured hemodynamic response lengths for a wide variety of stimulus lengths in a rat.

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The vast majority of these fits are above 0.8, indicating that the prediction explains at least 80% of the measured experimental response. Four of the 26 runs had an R2 value of less than 0.6. These were three of the 2 second stimulus runs and the 3 second run. There are reasonable explanations for each of these.

Figure 3-30 shows plots with bad fits.

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Figure 3-30. The time courses of bad fits. (a) The modeled and experimental ΔHbT time courses from the responding region with a 2 second stimulus. The experimental time course has a second large dilation beginning at approximately 16 seconds (red region). The endothelial propagation hemodynamic response model has a much smaller dilation/ΔHbT increase at this time. (b) A plot of the predicted ΔHbT and the experimental ΔHbT with a line of best fit. The blue x’s correspond to the blue region in (a) and the red x’s correspond to the red region. The second large oscillation causes the red x’s to have a different trend than the blue x’s. As a result, a single line of best fit does a poor job describing the data. (c) The modeled and experimental ΔHbT time courses from the responding region with a 3 second stimulus. The modeled and experimental measurements are well synchronized in the blue region and then become unsynchronized in the red. (d) ) A plot of the predicted ΔHbT and the experimental ΔHbT with a line of best fit. The red x’s correspond to the unsynchronized time points and have many values that are distant from the line of best fit.

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Figure 3-30a shows the experimental ΔHbT time course for the responding region of a rat with a 2 second stimulus and the corresponding modeled time course using the endothelial propagation hemodynamic response model. The experimental time course shows two large dilation responses. The model fits well with the first dilation response that occurs at the onset of stimulus. This region is indicated on the plot in blue. At approximately 14 seconds the experimental ΔHbT levels off and begins another dilation response at approximately 16 seconds. The time course from the model has a dilation response at this time.

However, it is of a much smaller magnitude. This region is indicated on the plot in red. Figure 3-30b shows a plot of the experimental ΔHbT values and the modelled values and a line of best fit in green. The blue x’s correspond to the blue region in Figure 3-30a and the red x’s correspond to the red region. Because the model and experimental values are initially of similar amplitude and then there is a large difference, the trend of the blue x’s is significantly different than the red x’s. As a result, the line of best fit does not fit well to the data, resulting in a low R2 value.

Figure 3-30c shows the experimental ΔHbT time course for the responding region of a rat with a 3 second stimulus and the corresponding modeled time course. The fit error for this experimental comes from a different source. Here, after stimulus onset, the experimental time course and the predicted model time course are in phase. This region is shown in blue and matches the blue x’s in Figure 3-30d. At approximately 17 seconds, the experimental and modeled time courses become out of phase. This region is indicated in red and corresponds to the red x’s in Figure 3-30d. The red x’s in Figure 3-30d show a greater dispersion than the blue x’s, indicating that this out of phase region has many points distant line of best fit, resulting in a low R2 value.

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3.5.3 Simulating Full Spatiotemporal Data Sets with the EP-HR Model

Thus far the model has been compared to selected time courses from data sets. These fits mainly focused on comparing the predicted response to the response from a region of interest at the center of the responding region. Predictions of the full responding region are made using

Δ퐻푏푇(푥, 푦) = 푎(푥, 푦)(푃푆퐹(푡) ⊗ 훿(푥, 푦, 푡)) + 푏(푥, 푦)(푃푆퐹(푡) ⊗ 퐵(푥, 푦, 푡))푆퐹푅퐷 where 푎(푥, 푦) and 푏(푥, 푦) represent the spatial distributions of the two components of the model. The goal of the model is to be able to explain and predict the response over the entire field of view which contains many time courses. In order to do this, the model was split into its two components, Δ퐻푏푇푒푙푒푐 and Δ퐻푏푇퐶푎2+ , where

Δ퐻푏푇푒푙푒푐 = 푃푆퐹(푡) ⊗ 훿(푥, 푦, 푡)

Δ퐻푏푇퐶푎2+ = (푃푆퐹(푡) ⊗ 퐵(푥, 푦, 푡))푆퐹푅퐷

These are two components are the first and second terms of the model without the corresponding spatiotemporal multiplicative factors 푎(푥, 푦) and 푏(푥, 푦). Thus, the model can be described as:

Δ퐻푏푇 = 푎(푥, 푦)(Δ퐻푏푇푒푙푒푐) + 푏(푥, 푦)Δ퐻푏푇퐶푎2+

Given a set of experimental data, the smooth muscle cell point spread function can be determined as described previously. For any data set as long as this function and the stimulus parameters are known, the time courses of the two components, Δ퐻푏푇푒푙푒푐 and Δ퐻푏푇퐶푎2+ , can be determined. These two time courses can be assumed to be the basis functions for the full data set and can be used to find 푎(푥, 푦) and

푏(푥, 푦). Figure 3-31 shows this process for a data set from a rat with a 12 second stimulus. Figure 3-31a shows the field of view for this data set. There is a large vein in the center and a number of arteries in the bottom right and top left. Each pixel in this field of view has an associated time course with it. In a manner similar to the previous DyCE chapter, the spatial maps 푎(푥, 푦) and 푏(푥, 푦) were found by applying a non-

107 negative least squares fit to each pixel in the data set. Figure 3-31b shows the Δ퐻푏푇푒푙푒푐 and

Δ퐻푏푇퐶푎2+ time courses that are the basis functions in the non-negative least squares fit.

Figure 3-31. Determining a(x,y) and b(x,y) spatial maps for the endothelial propagating hemodynamic response model for a rat with 12 second stimulus. (a) The field of view of the exposed cortex of a rat receiving a 12 second stimulus (b) The 훥HbTCa2+ and 훥HbTelec times courses that are serving as the basis functions for this data set. (c) A map of the fit of 훥HbTelec to the data set. This map is 푎(푥, 푦). The 훥HbTelec response can be seen in many of the surrounding arterial vessels. (d) A map of the fit of 훥HbTCa2+ . This map is 푏(푥, 푦). The 훥HbTCa2+ is only found in the responding region.

Figure 3-31c and d shows the results of the non-negative least squares fit. Figure 3-31c is the fit for the

Δ퐻푏푇푒푙푒푐 component, which is the smooth muscle cell point spread function. This fit shows that this function can describe the time courses in most of the arteries seen in the field of view. These results agree

108 with the theory that this smooth muscle cell point spread function propagates far along the pial vessels.

In the full model, this map corresponds to 푎(푥, 푦). Figure 3-31d is the fit for the Δ퐻푏푇퐶푎2+ component.

This map shows that this component is only seen in the responding region. In the model, this map is 푏(푥, 푦). The value of 푏(푥, 푦) is found to be zero in the surround region. These findings also supports our hypothesized cellular mechanism in that the electrically induced dilation wave propagates far along the arterial vessels while the calcium wave induced dilation only propagates a short distance. These results are particularly significant because it indicates that the arterial vascular dynamics can be explained with two basis functions: the smooth muscle cell point spread function and the predicted responding region time course. The strong fit between the measured and predicted data indicates that the smooth muscle cell point spread function can be used to accurately predict the arterial hemodynamic response.

With this last calculation, the model has been calculated and thus the whole data set can be simulated.

Figure 3-32 shows comparison of the experimental data with the modeled responses based on the

Δ퐻푏푇퐶푎2+ and Δ퐻푏푇푒푙푒푐 basis time courses and the spatial maps a(x, y) and b(x, y). The left column is the experimental response at stimulus and then 2 seconds, 4 seconds, 10 seconds, and 16 seconds after stimulus onset. The middle column shows the modeled response for these same time periods and the right column shows the difference between the experimental and modeled response. The modeled response strongly resembles the experimental response data. The difference maps show consistently low values over the arterial regions. The area with the largest difference is large vein in the center.

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Figure 3-32. Comparison of the experimental response to stimulus and the modeled response. Left column is the experimental response to a 12 second stimulus at stimulus, 2 seconds, 4 seconds, 10 seconds, and 16 seconds after stimulus. The center column is the modeled data based on the basis functions

훥HbTCa2+ and 훥HbTelec and spatial maps 푎(푥, 푦) and 푏(푥, 푦). The right column is the difference the experimental and modeled responses. The difference is small over the arterial regions. There is a larger difference over the large vein in the center.

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These spatial maps from one stimulus duration were also used to attempt to model the response to other stimulus durations. The previously determined maps from the 12 second stimulus data was used to model

14 second stimulus data. This means that the a(x, y) and b(x, y) spatial maps were derived from data that had a 12 second stimulus. The basis functions Δ퐻푏푇푒푙푒푐 is the smooth muscle cell point spread function.

The second basis function Δ퐻푏푇퐶푎2+ was created by convolving the smooth muscle cell point spread function and applying the rat dependent scaling factor. Figure 3-33 shows the results of this comparison.

The left column is the data from a 14 second stimulus at stimulus onset and 2 seconds, 4 seconds, 10 seconds, and 16 seconds after stimulus onset. The middle column shows the modeled responses and the right column shows the difference between the experimental and modeled responses. Comparison of the left and middle columns show that the use of the 12 second stimulus maps for 14 second stimulus data does not yield as good results as modeling 12 second stimulus data using the spatial maps 푎(푥, 푦) and

푏(푥, 푦) derived from the data itself. For instant, at 4 seconds post-stimulus the modeled response shows a greater proportion of the arteries in the responding region having a strong response. The difference maps of Figure 3-32 mainly showed the large vein in the center of the field of view, while in Figure 3-33 some of the arteries in both the responding and surround regions are visible on the difference maps.

There are several possible explanations for these findings. The application of a spatial map to a particular data set requires that the map and the data set share the exact same field of view. Small perturbations of the camera can cause shifts in the field of view which would result in larger differences on the difference map, particularly around the edge of vessels. Also, the physiology of the animal can change over the course of an experiment. The specifics of a vessel dilation are dependent on the microenvironment of that vessel. If a rat is anesthetized for a sufficient period of time, this microenvironment can change and may require a new spatial map.

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Figure 3-33. Comparison of the experimental response to 14 second stimulus and the modeled response using spatial maps derived from a data of a 12 second stimulus. The left column shows the experimental response data at the point of stimulus and 2 seconds, 4 seconds, 10 seconds, and 16 seconds after stimulus onset. The middle column shows the modeled data, created using the spatial maps a(x,y) and b(x,y) from a 12 second data set. The right column shows the difference between the experimental data and modeled data.

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3.6 Conclusions and further work

This chapter introduced a model that is able to accurately represent the observed spatiotemporal changes in total hemoglobin in response to stimulus in the exposed cortex of a rat. By applying some of the same techniques as seen in the previous DyCE chapter, full experimental hemodynamic data sets can be simulated with a high degree of accuracy. Both basis functions used in this model originated from the smooth muscle cell point spread function, supporting the argument that the observed spatiotemporal dilation characteristics are due to an hyperpolarization wave and a calcium based wave along the vessel endothelium that signal the vascular smooth muscle cells to dilate.

There are a few potential developments that would add to the strength of this model. First, the lack of electrophysiology data caused the model not to be designed to have electrical activity as an input.

However, the determined trigger functions were a delta function and a box function. Together these two functions highly resemble the typical electrical activity in response to external stimulus, as shown in Figure

3-5. Second, the BOLD response in fMRI is ultimately a measure of deoxygenated hemoglobin. The

Endothelial Propagating Hemodynamic Response model was developed to explain the changes observed in total hemoglobin. This model could be expanded to address changes in deoxygenated hemoglobin by developing a transform that would take the predicted change in total hemoglobin in the arterial compartment and output the change in deoxygenated hemoglobin in the venous compartment. This transform would have to take into account a number of new elements including oxygen transport in the capillaries, vessel diameter and flow rates, location of the initiation of the dilation waves. Furthermore, because this extension would require expanding to downstream compartments, the effects of changes in one compartment must be account for in the other compartments. For instance, a dilation in the arteries without a corresponding increase in volume input would lead to a decrease in the speed of blood transport in the capillaries, which would in turn affect oxygen transport to the parenchyma.

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Figure 3-34. A schematic outline of an artery, capillary, and vein in series. Oxygenated blood enters the pial artery, which descends and branches into capillaries. Oxygen transport occurs along these capillaries and the deoxygenated blood enters the ascending venules, which lead to the pial veins.

Developing a better understanding has some significant clinical implications. Understanding the driving forces of neurovascular coupling could provide new methods for interpreting fMRI data. The Endothelial

Propagating Hemodynamic Response model is based on the idea that brain vasculature has similar regulatory mechanisms as the peripheral vasculature. A major implication of this idea is that this relationship may explain some of the neurological impacts of diseases that involve peripheral vascular endothelial dysfunction. Diseases such as diabetes, hypertension, and microangiopathy have altered fMRI findings that may be explained by this mechanism [119-121].

There is also increasing evidence that neurovascular coupling may play an important role in certain neurodegenerative diseases, such as Alzheimer’s [122, 123]. Having a mathematical model that implies a cellular mechanism could allow for prediction of how imaging modalities could view specific pathologies in vivo and potentially indicate treatment targets. However, the hemodynamic response is dependent on the vascular microenvironment and cellular functions, applying this model to a vastly different species, such as humans, may introduce some additional challenges.

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Appendix: Publications and Presentations Related to the Thesis

Peer Reviews Publications

Amoozegar CB, Wang T, Bouchard MB, McCaslin AFH, Blaner WS, Levenson RM, Hillman EMC, “Dynamic contrast-enhanced optical imaging of in vivo organ function”, Journal of Biomedical Optics, 17(9) (2012)

Hillman EMC, Amoozegar CB, Wang T, McCaslin AFH, Bouchard MB, Mansfield J, Levenson RM, “In vivo optical imaging and dynamic contrast methods for biomedical research”, Philosophical Transactions of The Royal Society A, 369(1955) 4620-4634 (2011)

Oral Presentations

Amoozegar CB, Persigehl T, Bouchard MB, Schwartz LH, Hillman EMC, “Comparison of Optical and MRI Dynamic Contrast Imaging in Liver Pathologies” RSNA 2011

Amoozegar CB, “Non-Invasive Evaluation of Organ Function using Dynamic Contrast Enhanced Molecular Imaging” ECI: Advances in Optics for Biotechnology, Medicine, and Surgery XI 2009

Conference Abstracts

Hillman EMC, Levenson RM, Amoozegar CB, Bozinovic N, Chen BR, Burgess SA, Bouchard MB, “Dynamic Contrast Enhancement for Molecular Imaging” World Molecular Imaging Congress 2008

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