A SMALL ANIMAL TIME-RESOLVED OPTICAL TOMOGRAPHY PLATFORM USING WIDE-FIELD EXCITATION

Transcription

1 A SMALL ANIMAL TIME-RESOLVED OPTICAL TOMOGRAPHY PLATFORM USING WIDE-FIELD EXCITATION By Vivek Venugopal A Thesis Submitted to the Graduate Faculty of Rensselaer Polytechnic Institute in Partial Fulfillment of the Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: BIOMEDICAL ENGINEERING Approved by the Examining Committee: Xavier Intes, Thesis Adviser George Xu, Member Shiva Prasad Kotha, Member Frédéric Lesage, Member Siavash Yazdanfar, Member Rensselaer Polytechnic Institute Troy, New York November 2011 (For Graduation December 2011)

2 c Copyright 2011 by Vivek Venugopal All Rights Reserved ii

3 Contents List of Tables List of Figures v vi ACKNOWLEDGMENT xiii ABSTRACT xv 1. Introduction Pre-clinical imaging: Optical Planar imaging Optical Tomography Source of optical contrast in tissue Small animal optical tomography Imaging geometry Imaging domain Multispectral sampling Wide-field excitation schemes in optical tomography Thesis overview System description and characterization System design Source components Detector components Temporal characteristics Temporal parameters for accuracy Temporal stability Impact of system components on IRF Spectral characteristics Noise characteristics Sources of noise in an ICCD camera Impact of ICCD parameters on noise level Characterizing quantitative accuracy of the system Mathematical model for time-resolved spectroscopy iii

4 2.5.2 Impact of MCP voltage on accuracy Impact of gate-width on accuracy Functional spectroscopy Preliminary optical tomography studies Experiment protocol Pre-experiment calibration Source selection and implementation Data processing and data type selection Reconstruction Functional Tomography studies Reconstructing a complex distribution of absorptive perturbations Simultaneous reconstruction of absorption and scattering coefficients Fluorescence Molecular Tomography studies Resolving fluorescent inclusions at different depths Feasibility of reconstruction in vivo Separating fluorophores based on lifetime contrast Summary Techniques for robust reconstruction performance using time-gated measurements Noise in time-gated measurements Intensity noise Temporal noise Normalization methods In silico investigation of noise characteristics Synthetic model Measurement generation and noise simulation Effect of noise on measurement data type Temporal noise errors Gate-wise error analysis Tomographic reconstruction performance Early gate reconstruction Late gate reconstruction iv

5 4.4 Spatio-temporal noise filtering Experimental validation Experiment design Results Early gate reconstruction Late gate reconstruction Discussion Adaptive full-field optical tomography Measurement-guided pattern optimization Iterative optimization algorithm In silico validation Transmittance optimized patterns In vitro validation Experiment design Pattern optimization results Improvement in tomographic information content Reconstruction results Discussion Near-Infrared FRET Tomography FRET imaging in small animals NIR FRET pair Hierarchical reconstruction scheme In vitro validation Phantom design Results Validation in animal model Animal preparation Results Discussion Conclusions BIBLIOGRAPHY v

6 List of Tables 1.1 Optical properties of small animal organs at 720nm Commercial small animal imaging platforms using epi-illumination configuration Limits of operational power across the NIR window Concentration of mixture components estimated using time-resolved spectroscopy Comparing accuracy in 3D reconstructions Comparison of the relative quantification and resolution using CW and TG data types Optical properties of murine organs used for noise model simulation Errors in the estimation of shorter lifetime component - in silico Optical properties of the phantom Errors in the estimation of relative concentration of the FRETing donor component - in vitro Optical properties of murine organs at 730nm used for simulation Comparing improvement in reconstruction with transmission optimization105 vi

7 List of Figures 1.1 (a) Planar imaging (b) Optical Tomography Absorption coefficients of tissue chromophores System schematic Power control assembly Pico Projector implementation ICCD camera operation principle Data Acquisition Timing Diagram The Instrument Response Function Impact of mis-estimation of IRF FWHM on quantification. The green shaded area marks the region of target accuracy of 10% Impact of mis-estimation of IRF t 0 on quantification. The green shaded area marks the region of target accuracy of 10% Characterizing the drift and jitter in IRF parameters IRF measured for various wavelength of excitation Effect on power control operation on IRF Impact of pattern generation optics on IRF characteristics (a) FWHM, (b) t Effect of MCP voltage on IRF characteristics. The statistics are calculated on a set of 10 measurements at each MCP Voltage Effect of gate-width settings on IRF Spectral Characteristics of source and detector components Pattern projection at the NIR wavelengths Signal level and noise characteristics of MCP gain voltage Signal level and noise characteristics of CCD integration time Variations in estimated optical properties with change in MCP voltage. 39 vii

8 2.20 Comparing the effect of gate-width on quantitative accuracy of timegated measurements Mixture separation using Functional Time-Resolved Spectroscopy. (a) Spectra of India Ink and bovine hemoglobin. (b) Estimated absorption coefficient with estimation errors at each wavelength. (c) Estimated scattering coefficient with estimation errors at each wavelength Subset of wide-field patterns employed. The first 6 patterns are defined on the basis along x-axis and the next 6 are translated along the y-axis The time-gate data type Time-gated Jacobians for wide-field excitation source(at z = 20mm)and a point detector (at z = 0mm) Block-diagram for fluorescence reconstruction Phantom simulating optically heterogeneous model with optical contrast measures Optical reconstructions of the phantom in Figure 3.5(a) The iso-volume was set at 50% of the maximum reconstructed value. The ray-sum projections are provided on the sides of the reconstructed volume Reconstruction of µ a and µ s in vitro:(a) Phantom design. (b) Area of pattern illumination. (c)-(d) TPSF measured at the Green and Cyan detectors respectively. (e)-(g) Normalized Born contrast measures at TG1, TG2 and TG3 respectively % iso-volumes of reconstructed perturbations in optical properties Depth resolution experiment design and contrast measures D reconstruction of effective fluorescence quantum yield. The reconstructions shown are 50% iso-volumes of the effective quantum yield Euthanized animal model for validation of wide-field scheme in murine geometry (Left) 3D reconstruction showing the 50% iso-volume of reconstructed object. (Right) Coronal slice of the reconstructed volume at z = 6.5mm and transverse slice of the volume at y = 21.5mm Phantom design to study the 3D localization and separability of fluorescent markers based on lifetime contrast % iso-volumes of reconstructed concentrations at two different lifetimes viii

9 4.1 (a) Measurement with added poisson noise, (b) Measurement with timing error of 20ps, (c) Relative measurement error due to poisson noise shown in (a). (d) Relative measurement error due to temporal noise shown in (b) (a) Type I normalization scheme (TG 1 ems/cw exc ), (b) Type II normalization (TG 1 ems/tg 2 exc) and (c) Type III Normalization (TG 1 ems/tg 1 exc). The light green marker represents the excitation data type and the dark green marker identifies the fluorescence measurement Mouse model employed in in silico investigation of error propagation in FMT reconstruction. The red inclusion has a single exponential lifetime of 1100ps while the blue inclusion has 50% 290ps fluorescence component and a 50% 1100ps component Measurement error for different values of timing jitter when using (a) early gate at 20%, (b) maximum gate and (c) late gate at 20% (a) Measurement error due to temporal errors only, (b) Measurement errorduetointensityerrorsonlyand(c)measurementerrorduetoboth temporal and intensity errors Total reconstructed fluorescence yield from both components at the central axial slice thresholded at 50%. Reconstruction employed (a)-(c) pure measurement vector, (d)-(f) added temporal noise, (g)-(i) added intensity noise and (j)-(l) added temporal and intensity noise Reconstructed fluorescence yield for shorter and longer lifetime component at the central axial slice thresholded at 50%. Reconstruction employed (a)-(b) pure measurement vector, (c)-(d) added temporal noise, (e)-(f) added intensity noise and (g)-(h) added temporal and intensity noise (a) Filtering scheme showing 3D arrangement of measurements. (b) Example of TPSF with both temporal and poisson errors. (c) Filtered TPSF. (d) Measurement errors when using filtered signals (a) MRI image of phantom used for validation of reconstruction. (b) Phantom design identifying the fluorescent inclusions and the perturbative optical property distribution. (c) Example of raw temporal measurement recorded exhibiting intensity noise. (d) Filtered TPSF which shows a significant reduction in the intensity noise level in these measurements Total reconstructed fluorescence yield from both components at the central axial slice thresholded at 50%. Reconstruction employed (a)-(c) noisy raw signal, (d)-(f) filtered signal ix

10 4.11 Reconstructed fluorescence yield for shorter and longer lifetime component at the central axial slice thresholded at 50%.Reconstruction employed (a)-(b) noisy raw signal, (c)-(d) filtered signal (a) Small animal model imaged in wide-field optical tomography using full-field pattern marked by the red boundary. (b) Dynamic range of measured photon counts for the pattern shown in (a) at the excitation wavelength (a) Optimization scheme. (b) Algorithm flowchart for single pattern optimization Synthetic mouse model used for in silico validation. Three 2 2 2mm 3 fluorescent inclusions are shown in red. The profiles marked in red represent the uniform excitation pattern and the discrete detectors spanning the torso are shown in blue (a) Uniform excitation pattern,(b)-(e) Pattern at each iteration showing correction with transmitted signal. (f) Log-scale transmitted excitation field using the uniform base pattern. (g)-(h) Difference of transmitted excitation signal at maximum gate for patterns (b)-(e) respectively, representing increase in detected photon intensity (in log scale) (a) Increase in maximum photon fluence at each fluorophore inclusion, (b)-(c) Fluorescence signal when using the uniform pattern at early gate at 10% and maximum gate respectively. (d)-(e) Difference of detected fluorescence signal using optimized and baseline pattern at early gate at 10% and maximum gate respectively (in log scale) Tissue-mimicking phantom used for in vitro validation. The uniform full field pattern (recorded during the experiment) projected on the phantom is shown on the xy-plane at z = 0. The green tubes represent the fluorophores contained in glass capillaries located in the center of the phantom. The red tube shows the position of an absorbing perturbation occluding the central fluorescent inclusion (a) Uniform bar pattern used for imaging phantom, (b) Transmittance optimized pattern obtained after 4 iterations, (c)-(d) Recorded excitation signal at 50% time-gate on the rising portion of TPSF, (e)- (f) Recorded fluorescence signal at 50% time-gate on rising portion of TPSF. (g)-(h) Normalized born contrast measure at the 50% time-gate on rising portion of TPSF (a)-(b) Increase in number of source-detector pairs with signal above 200 counts after pattern optimization at excitation and emission wavelengths respectively. (c) Increase in non-redundant information with increase in s-d pairs x

11 5.9 (a) Reconstructed effective quantum yield at z = 12mm using single gates. First row shows the reconstructions using uniform patterns and second row employs transmittance optimized patterns. (b)-(c) 50% isovolume of reconstructed effective quantum yield when using uniform patterns and transmittance optimized patterns respectively. The 50% iso-contours across x = 28mm and z = 12mm are projected along the corresponding planes AbsorptionandemissionspectraofAlexaFluor R 700andAlexaFluor R 750. For all studies described herein, the donor was excited at 695nm and signals were measured at 720nm (a)histogram of estimated lifetime components in the first step of the biexponential fitting process. (b) Examples of fitted temporal point spread functions in the second step of fitting procedure. (c) Estimate of relative abundance of shorter (FRETing) lifetime component Flowchart of hierarchical reconstruction of fluorophore concentrations using time-gates (a) Design of murine phantom with four inclusions carrying mixtures with different acceptor to donor ratios (Red- 1:4, Green-1:2, Cyan-2:1 and Blue-4:1). (b) Normalized born contrast measures of time-gates measured for a single pattern. (c) TPSFs derived from point detectors directly above each of the four inclusions (a) 50% iso-volumes of total reconstructed donor quantum yield. Dotted orange bounding box indicates the reconstructed volume. (b)-(c) Iso-plane images of the reconstructed quantum yield of the shorter component with threshold at 50% of maximum value. (d) Quantitative comparison of tomographic estimates of FRETing donor fraction from above reconstructions (a) MicroCT image of animal model showing two capillaries localized in the abdomen with acceptor-to-donor ratios of 1:4(green) and 4:1(blue). (b) TPSFs derived from point detectors directly above each of the two inclusions. (c)-(e) Time-gated measurements for a single pattern at three time-gates showing the measurement at (c) early gate at 40%, (d) maximum gate and (e) late gate at 15% (a) 50% iso-volumes of total reconstructed donor quantum yield. (b)-(c) Iso-plane images of reconstructed shorter lifetime component at slices shown in (a). (d) Quantitative comparison of tomographic estimates of FRETing donor fraction from above reconstruction xi

12 To my family... This would not have been possible without your support. xii

13 ACKNOWLEDGMENT First and foremost, I want to thank my advisor Dr. Xavier Intes. His constant support and guidance has played an integral role in the successful completion of this dissertation. I am grateful that I never had to worry about financial aid and was able to devote my full attention to research and academics. I owe him a debt of gratitude for the time spent working with him over the past five years as I have learnt not only the do s and don ts and rights and wrongs of good research practices but perhaps, more importantly, how to grow in the academia. I would also like to thank him for being patient with my innumerable procrastinations and for trusting me with thousands of dollars worth of equipment. My experience in setting up the lab was at once both exciting and illuminating. It has been a pleasure. I would also like to extend my gratitude to my committee members. Prof. Lesage, thank you very much for your collaboration and help in getting the wide-field instrumentation off the ground. Dr. Yazdanfar, thank you for all the discussions over the past couple of years. It has always given me a new perspective on my research. Prof. Xu and Prof. Kotha, thank you for your insightful comments and suggestions. Your input has been most invaluable. I would also like to thank the faculty at the BME department at RPI who over the course of my stay at RPI have always given me good advice and guidance. I would especially like to thank everyone one at the department office, Kristen Bryk, Mary Foti and Pam Zepf, for always lending a helping hand over the past years. You made my life so much simpler. I would be remiss if I did not thank James Schatz at the Research Machine Shop at RPI. Jim has played an important role in this project starting with the initial fabrication of the platform to helping me out with the trivial machining jobs over the course of this research. Thank you. I would like to thank Dr. Scott McCallum and Dr. Chris Bjornsson at the Center for Biotechnology and Interdisciplinary Studies at RPI for patiently teaching me the ways of the MRI and the CT. Also, many thanks to Dr. Robert Waniewski at the Bioresearch Core at RPI for all his help with the animal models. I would xiii

14 also like to extend my gratitude to our collaborators at Albany Medical Center, Dr. Margarida Barosso and Dr. Ken Abe. Working with your group at AMC over the past year has been an incredible experience. I am especially grateful for the time spent working with Jin Chen. Jin and I started in our lab around the same time and from the beginning our research has been inextricably linked. Most of the work in this thesis would not have been possible without her help and I wish her all the best for her future endeavours. An endeavour as rigorous as a Ph.D. would never have been successful without the company of great friends. Thank you Ameya, Shreya, Varun and Ruchira for making the past five years so much more bearable. We did indeed manage to turn this little fish bowl of ours into a happening place. One of the good (or bad things) aboutdoingaph.d.isthatyoumakenewfriendsastheycomeandgoaswecontinue with our seemingly never-ending schedules. I have had the pleasure of knowing some awesome people over the past years. All dear friends, near and far and old and new - Jaskaran, Dhanannjay, Swapnil, Iti, Suhas, Anna, Colleen, Shruti and so many more. These have been fun times. A big thanks to my brother Vinu and bhabhi. Thank you for always being there and being the role model that I can always aspire to be. And last but not the least, I would like to thank my parents. Achhan and Amma, thank you for having faith in me and letting me follow my dreams. This work would never have been possible without your support. xiv

15 ABSTRACT Small animal imaging plays a critical role in present day biomedical research by filling an important gap in the translation of research from the bench to the bedside. Optical techniques constitute an emerging imaging modality which have tremendous potential in preclinical applications. Optical imaging methods are capable of non-invasive assessment of the functional and molecular characteristics of biological tissue. The three-dimensional optical imaging technique, referred to as diffuse optical tomography, provides an approach for the whole-body imaging of small animal models and can provide volumetric maps of tissue functional parameters (e.g. blood volume, oxygen saturation etc.) and/or provide 3D localization and quantification of fluorescence-based molecular markers in vivo. However, the complex mathematical reconstruction problem associated with optical tomography and the cumbersome instrumental designs limits its adoption as a high-throughput quantitative whole-body imaging modality in current biomedical research. The development of new optical imaging paradigms is thus necessary for a wide-acceptance of this new technology. In this thesis, the design, development, characterization and optimization of a small animal optical tomography system is discussed. Specifically, the platform combines a highly sensitive time-resolved imaging paradigm with multi-spectral excitation capability and CCD-based detection to provide a system capable of generating spatially, spectrally and temporally dense measurement datasets. The acquisition of such data sets however can take long and translate to often unrealistic acquisition times when using the classical point source based excitation scheme. The novel approach in the design of this platform is the adoption of a wide-field excitation scheme which employs extended excitation sources and in the process allows an estimated ten-fold reduction in the acquisition time. The work described herein details the design of the imaging platform employing DLP-based excitation and time-gated intensified CCD detection and the optimal system operation parameters are determined. The feasibility this imaging approach and accuracy of the system in reconstructing functional parameters and fluorescence xv

16 markers based on lifetime contrast is established through phantom studies. As a part of the system characterization, the effect of noise in time-resolved optical tomography is investigated and propagation of system noise in optical reconstructions is established. Furthermore, data processing and measurement calibration techniques aimed at reducing the effect of noise in reconstructions are defined. The optimization of excitation pattern selection is established through a novel measurement-guided iterative pattern correction scheme. This technique referred to as Adaptive Full- Field Optical Tomography was shown to improve reconstruction performances in murine models by reducing the dynamic range in photon flux measurements on the surface. Lastly, the application of the unique attributes of this platform to a biologically relevant imaging application, referred to as Förster Resonance Energy Transfer is described. The tomographic imaging of FRET interaction in vivo on a whole-body scale is achieved using the wide-field imaging approach based on lifetime contrast. This technique represents the first demonstration of tomographic FRET imaging in small animals and has significant potential in the development of optical imaging techniques in varied applications ranging from drug discovery to in vivo study of protein-protein interaction. xvi

17 Chapter 1 Introduction Over the past decade, small animal models have attained a central role in preclinical research owing to the developments in transgenic mouse models coupled with the advances in molecular medicine [1, 2, 3]. Animal model based pre-clinical testing realises a critical step in the translation of lab-based discoveries to clinical applications. With the increasing role of small animal models in pre-clinical research, the availability of small animal imaging technologies becomes more relevant [4]. In this regard, established clinical imaging modalities like Magnetic Resonance Imaging (MRI), X-ray Computed Tomography (CT), Positron Emission Tomography (PET), have been adapted to pre-clinical settings [5, 6, 7]. Optical methods provide an alternate imaging technique which compares favourably to the established modalities owing to its high sensitivity, low-cost and non-ionizing characteristics [8]. 1.1 Pre-clinical imaging: Optical Optical methods have been well established in microscopic techniques where thin samples are imaged. The high attenuation of light upon propagation through tissue however limits the application of these methods in macroscopic imaging. The developments in optical instrumentation technology combined with advances in the mathematical modelling of light propagation in tissues have allowed the development of novel imaging techniques which permit the optical imaging of thick tissue. In this section, the optical methods used in small animal imaging are described Planar imaging Planar imaging (or photographic imaging) is the simplest optical technique applied to macroscopic imaging. It involves the illumination of the subject and measuring the light emitted/reflected from the surface [9]. In its simplest form, planar imaging systems may be implemented by integrating a CCD camera with a broad-field light source. Several animal imaging studies have utilized planar imag- 1

18 2 ing to detect fluorescent targets under the surface [10]. Advanced implementations of planar imaging technologies have employed multi-spectral excitation and multispectral detection using band-pass filters to perform multiplexed fluorescence imaging studies in small animal models. Despite the ease of implementation of planar techniques, the photographic methods are limited to probing a few millimetres under the surface due to the exponential attenuation of light with depth. Similarly, the non-linear effects of depth and optical properties do not allow the quantification of fluorescent targets. And lastly, the single view imaging scheme does not allow the three-dimensional localization of fluorescence target in vivo. Figure 1.1(a) shows an example of fluorescence detected using planar imaging [11]. Figure 1.1: (a) Planar imaging (b) Optical Tomography Optical Tomography Optical tomography is an alternate approach to volumetric imaging of thick tissue. It is based on the principle that photons in the near-infrared (NIR) wavelengths, 700nm - 900nm, are transmitted deeper into the tissue compared to visible wavelengths [12]. Based on the fundamental principle behind tomographic imaging techniques (like X-ray CT), contrast in measurements of photons transmitted through the tissue are used in the reconstruction of structural and functional parameters. The high scattering of photons upon propagation through the tissue however results in a lower resolution reconstruction when using optical tomographic techniques. This also necessitates the use of a complex mathematical model describing

19 3 the propagation of photons in the tissue to accurately quantify the source of optical contrast in 3D [13]. The contrast in optical tomography typically arises from the heterogeneous distribution of optical properties in the tissue. Classical approaches to optical tomography focus on the reconstruction of these optical parameters. This technique is referred to as Diffuse Optical Tomography (DOT) [14]. In the case of fluorescence imaging in thick tissue, the signal from a fluorophore within the tissue is used as the optical contrast. The model of light propagation employed in DOT can be extended to simulate a secondary light source within the tissue, and the location and concentration of the fluorescent source can be reconstructed by following the same general principles of of optical tomography. Applications of fluorescence imaging techniques currently involve the localization of target specific fluorescent markers (molecular markers). This technique, which allows the visualization of interactions on a molecular level, is referred to as Fluorescence Molecular Tomography (FMT) [15](c.f. Figure 1.1(b) [16]). The parallel developments in imaging technology, transgenic animal models and molecular markers over the past decade combined with the potential of optical tomography in imaging small animal models makes optical imaging one of the most promising tools in preclinical research Source of optical contrast in tissue The interaction of photons with tissue is governed by the physical phenomena of absorption and scattering. These interactions are a characteristic of the tissue and are quantified in terms of their representative coefficients: absorption coefficient and scattering coefficient[17]. These parameters are reconstructed in Diffuse Optical Tomography to identify different types of tissue in the volume imaged [13]. In this section, these tissue parameters are defined and their characteristics are discussed. Absorption coefficient The absorption coefficient (µ a ) quantifies the absorption of photons by the tissue. µ a is defined as the inverse of the distance travelled by a photon in the tissue before it is absorbed [18]. In this thesis, µ a has the units of (cm 1 ). The absorption

20 4 of photons by the tissue can be attributed to several tissue components but in the NIR wavelength range, the primary absorbers (chromophores) are, oxy-hemoglobin (HbO), deoxy-hemoglobin (Hb), water and lipids. The absorption spectra of these four tissue chromophores are shown in Figure 1.2 [19]. The variation in absorption coefficients of the tissue chromophores suggests the wavelength dependence of the absorption coefficient. Absorption coefficient (cm -1 ) For hemoglobin concentration of 150g/L HbO 2 Hb Fat Water 10-4 NIR Window Wavelength (nm) Figure 1.2: Absorption coefficients of tissue chromophores. The absorption coefficient of tissue at a particular wavelength can be calculated as a linear combination of each of these components weighted by their relative contribution in the tissue composition. Due to the relatively low contribution of water and fat at these wavelengths, their contributions may be ignored and the absorption coefficient of a tissue is defined by the Equation 1.1 [20]. µ a (λ) = c Hb c Hb +c HbO2 µ Hb a (λ)+ c HbO2 µ HbO 2 a (λ) c Hb +c HbO2 where, c HbO2 = Concentration of deoxy-hemoglobin. (1.1) c Hb = Concentration of deoxy-hemoglobin. It is worth noting that the linear relationship given in equation 1.1 can be

21 5 used to estimate the composition the chromophores in a tissue by measuring the absorption coefficients at multiple wavelengths. The estimation of chromophore concentrations provides an estimate of the functional state of the tissue. The tomographic approaches can be extended to mutispectral data sets to directly reconstruct the 3D distribution of the chromophore concentrations. This technique is referred to as Functional Optical Tomography (FOT)[21]. Scattering coefficient Scattering has a more dominant impact on the propagation of the photons through biological tissue [22]. The scattering of photons in the tissue can be attributed to refractive index mismatch at a cellular level. In a manner similar to the absorption coefficient, the scattering coefficient (µ s ) is defined as the inverse of the distance travelled by a photon before it undergoes scattering [18]. Another parameter used in defining the scattering of photons is the anisotropy factor (g) of the tissue which represents the measure of scatter in the forward direction after a scattering event [18]. The anisotropy factor represents the direction of photon propagation after scattering and for biological tissues is between 0.69 and 0.99 [22]. The combined effect of both these parameters is defined as the reduced scattering coefficient which is given by, µ s = µ s (1 g) (1.2) Scattering will be defined in terms of µ s in the rest of this proposal and has units of cm 1. The reduced scattering coefficient also has a dependence on wavelength although it is not as significant as the absorption coefficient. The dependence of µ s on the wavelength is given by the relation [20], µ s = Aλ b (1.3) where A is referred to as the scattering amplitude and b is called the scattering power. Table 1.1 gives the values of the optical properties of the major organs in the small animal model (values calculated using [20]).

22 6 Table 1.1: Optical properties of small animal organs at 720nm Tissue type µ a (cm 1 ) µ s (cm 1 ) Adipose Bone Bowel Heart wall Kidneys Liver and spleen Lung Muscle Skin Stomach wall Small animal optical tomography As stated earlier, optical tomography has two main applications in small animal imaging - namely the reconstruction of functional parameters in vivo using Functional Optical Tomography (FOT) and the localization and quantification of molecular markers using Fluorescence Molecular Tomography (FMT). While both tomographic techniques require an accurate photon propagation model for accuracy, the scattering dominant interaction of photons in the NIR window, as discussed previously, results in an ill-posed inverse problem in FOT and FMT [23]. This ill-posedness manifests as a poor spatial resolution in optical tomographic techniques [24]. Furthermore, whole-body optical tomography of small animals presents a particularly challenging problem due to the complex distribution of a wide-range of optical properties in the small volumes encountered in murine models [20]. The ill-posedness of the inverse problem may be mitigated to an extent by selection of instrumentation design and imaging methodology which maximize the tomographic information acquired by the platform. In this section the various design parameters relevant for quantitative reconstructions in FMT and FOT are discussed.

23 Imaging geometry Tomographic reconstruction in optical methods is done by recording the photon flux at multiple points (detectors) on the surface of the animal for different points of injection of light (source). The tomographic imaging geometry refers to the relative arrangement of source and detector positions. The selection of the optimal imaging geometry has a significant impact on the quality of reconstructions obtained due to the highly non-linear light propagation of light in tissue. The different imaging geometries implemented in small animal imaging can be broadly classified into two categories: epi-illumination and trans-illumination. Epi-illumination configuration The epi-illumination refers to the case where the source and detector are on the same side of the animal model. The light reflected/emitted off the surface of the animal is detected at a fixed interval and recorded as a measurement. Thus this imaging configuration is often referred to as reflectance imaging geometry. The source and detector in this configuration are raster scanned across the surface to generate the full set of tomographic measurements. The depth of detection in the reflectance geometry is dependent on the source-detector separation. The primary drawback of this approach is the limited depth resolution provided by this sourcedetector configuration. Specifically, in the reflectance scheme the whole volume is not imaged due to the limited propagation of photons deep into the tissue in case of high absorption and scattering. The limited information thus obtained does not allow the resolution of deep-seated inclusions in fluorescence tomography [25]. However, in conjunction with a mathematical model, this configuration can be used for mapping biological activity in sub-surface tissue (especially in cases with low attenuation e.g. brain imaging). In order to distinguish this approach from a fully tomographic imaging scheme, techniques employing a reflectance geometry are referred to as Diffuse Optical Topography [26]. Despite the limitations of the epi-illumination configuration most commercially available small animal optical imaging systems employ this geometry owing to the ease of implementation and the high-throughput afforded by this configuration (c.f.

24 8 Table 1.2: Commercial small animal imaging platforms using epiillumination configuration System (Company) Imaging method References Multispectral FX Prp (Kodak Carestream) Planar [27] Maestro (Caliper Life Sciences) Planar [28] IVIS 200 (Caliper Life Sciences) Planar [29] ibox Scientia 500 (UVP LLC) Planar [30] Pearl Imager (LiCOR Biosciences) Planar [31] Optix MX3 (ART Advanced Research Technologies) Topographic [32] Table 1.2). Among academic research groups the epi-illumination configuration is usually adopted in research focused on improving the information content provided by these commercial systems by implementing time-resolved or frequency modulated data types [33, 34]. Trans-illumination configuration Trans-illumination geometry refers to the arrangement where the source and detector are positioned on opposite sides of the model being imaged. Here, the detection of the photons transmitted through the entire volume provide a larger amount of tomographic information when compared to reflectance schemes. The collection of tomographic information in this configuration entails the sequential scanning of the source and detector points across the surface to sample the entire volume being imaged leading to a long acquisition times. However, owing to the improved depth sensitivity afforded by trans-illumination schemes there are a few commercially available imaging systems employing this imaging geometry. Among these the IVIS Spectrum series (Caliper Life Sciences, USA) and the FMT2500 (Perkin Elmer, USA) are the most commonly used systems [35]. Among academic research groups, most of the systems employ a trans-illuminations scheme [36, 37, 38]. One of the drawbacks of the trans-illumination geometry is the high dynamic range in detected photons due to variations in optical properties and mouse thickness. In order to offset the effect of geometry some systems designs include the use of a chamber filled with scattering fluid having optical properties similar to the tissue

25 9 wherein the animal is submerged. This reduces the effect of variations in thickness and reduces dynamic range [36] Imaging domain Imaging domain refers to the nature of illumination-detection technology used in the instrumentation which determines the type of data set that is acquired by the system. Data type refers to the measurement derived from the acquired reading that is used for reconstruction. The information content in the data type is related to the imaging domain and it plays a critical role in optical tomography performances. Instrumentation for optical tomography can be classified into three modes based on the characteristics of the source and detector used namely, Continuous Wave (CW), intensity modulated (Frequency Domain - FD) and pulsed (Time Domain - TD). In this section the pros and cons of different imaging modes are discussed. Continuous wave imaging systems Continuous-wave systems as the name suggests, refers to the use of a constant intensity illumination source with the detector measuring the change in absolute intensity to generate the contrast function. CW systems are the most commonly used systems owing to the ease of implementation and the relatively robust measurements with high signal-to-noise ratio (SNR) [39]. The CW systems can employ a wide variety of source-detector technology, including LEDs, laser diodes and solid state lasers as the source and detection devices ranging from high resolution CCD cameras to high sensitivity Avalanche Photodiodes and Photon-multiplier tubes (PMT)[40, 41, 42, 43]. The low-cost of implementation is however offset by the relatively low information content in the CW data type. In the case of FOT, CW systems are unable to distinguish between the attenuation due to scattering and absorption coefficients [23]. In the case of Fluorescence imaging, CW data types are unable to determine lifetime, which precludes lifetime-multiplexed studies. Frequency-domain imaging systems Frequency domain systems employ intensity modulated sources and the changes in amplitude and phase of the photons transmitted through the tissue are used to

26 10 reconstruct the functional parameters or fluorescent yield and lifetime. The collection of phase information in FD datasets allow the separation of contributions from absorbing and scattering inclusions in the medium for FOT studies and can also provide an estimate of lifetime in FMT studies. FD platforms are limited in their application in small animal imaging due to the small volumes encountered in murine models which necessitates the modulation of the source in the GHz range for robust contrast in the phase function for high resolution reconstruction [44]. However, small animal imaging platforms employing lower modulation frequency have (100M Hz) been demonstrated [45, 46, 47] Time-domain imaging systems Optical tomography systems employing a time domain approach inject an ultra-fast laser pulse into the medium and record temporally resolved measurements of photon flux on the tissue surface. These measurements are referred to as the temporal point spread function (TPSF). The time-domain data set provides the highest information content among the three imaging modes. The TPSF measurements can be easily transformed to generate data types generated by CW and FD system (by integration [48] and Fourier transform of the TPSF respectively [49]). Other approaches to data type generation from time resolved measurements rely on the first, second and third order moments derived from the TPSF [50]. It is noteworthy that as the time-domain data sets represent photons exiting the surface as a function of time, it is possible to isolate the early arriving photons which have undergone minimal scattering to provide high-resolution reconstructions [51]. The minimally diffuse photons (referred to as early gates in gated time domain acquisition systems) also provide the advantage of efficiently separating the contrast in scattering coefficient. The drawback of time-resolved system is the relatively high cost of implementation due to the specialized instrumentation. These include ultra-short pulsed laser as the source, sensitive photon counting systems like the Time Correlated Single Photon Counting (TCSPC) device, intensified cameras etc. for detection. Moreover, the measurement of high SNR datasets in time-domain measurements requires

27 11 a relatively long integration time to obtain sufficient signal statistics. This is due to the time domain detection mechanism where only the photons arriving within a specific time window are collected leading to lower SNR. Therefore, the acquisition time-domain measurements tend to have a long acquisition time due to the low level of signal collected at each time point. Moreover, the time-resolved datasets are extremely sensitive to system noise and thus TD DOT platforms demand a careful calibration of the system parameters to obtain accurate reconstructions [52] Multispectral sampling The use of constraints derived from the known spectral behaviors of the chromophores in the NIR window (c.f. Figure 1.2) is an approach used to overcome the non-uniqueness of the inverse problem in FOT and have shown an improvement in quantitative accuracy when used with the CW and FD data types [53, 54]. The use of multispectral datasets have also been shown to improve quantitative accuracy in FOT studies by improved separation of absorption and scattering coefficients when using the CW data type [55]. Multispectral FOT platforms classically employ multiplexed laser diodes to probe the tissue at select wavelengths. The use of a tunable laser source allows the use of a wide range of wavelengths while improving the reconfigurability of the system apropos the selection of optimal wavelengths. Alternatively, time-multiplexed multiple source system have been demonstrated in commercially available small animal imager BioFLECT (Bioscan, USA)[56]. In the case of FMT studies, imaging platforms capable of multispectral excitation allow multiplexing of fluorescent biomarkers based on spectral contrast [57] Wide-field excitation schemes in optical tomography Finally, the resolution of the reconstruction of a complex 3D volume can be improved by increasing the number of point source-detector pairs employed by the system in the solution to the inverse problem [58]. The application of this strategy to whole-body FOT and FMT however requires a prohibitively long acquisition time making it impractical for live animal imaging studies. Wide-field illumination in optical tomography is a relatively new imaging paradigm where the point source excitation schemes are replaced by a wide-field

28 12 illumination patterns and tomographic information is collected by modifying the pattern characteristics [59]. Over a short period of time, a number of wide-field excitation schemes have been implemented and verified in different optical tomography applications. Wide-field excitation strategies One of the earliest wide-field excitation scheme was based on spatially sinusoidal patterns [59]. In this technique, the wide-field sources have a spatially sinusoidal structure and tomographic datasets are acquired by modulating the spatial frequency and by applying a phase shift on the modulation frequency. These patterns were applied in a reflectance configuration with measurements acquired on a CCD camera to reconstruct absorptive inclusions in embedded at different depths in a turbid medium using a CW and FD data types [60]. This technique is referred to as Modulated Imaging. In fluorescence imaging, spatially sinusoidal illumination patterns (modulated imaging) have been used to improve lateral resolution in optical sectioning applications [61]. However, the application of spatially modulated patterns becomes more complex when used with irregular boundaries, such as those encountered in murine models, and requires a correction based on the surface profile [62]. Sinusoidal patterns were also used in the trans-illumination geometry with the time-resolved data type to reconstruct absorptive inclusions [63]. An alternate approach in wide-field imaging employed uniform intensity bar shaped patterns. The bar patterns have been used in a novel pattern-pattern detection scheme where, patterns are applied in the illumination and detection channel allowing high-speed acquisition of tomographic data. This patterned excitation - patterned detection scheme was used to localise an absorptive inclusion in a diffused medium [64]. The bar patterns were also applied in a trans-illumination geometry using time-resolved data types [65]. FOT applications of the bar patterns were shown to successfully separate absorption and scattering coefficients [66]. In FMT, the bar patterns demonstrated the feasibility of wide-field approach to in vivo FMT [67]. These results constitute the work presented in this thesis and are detailed in the following chapters.

29 13 Another method of selecting the excitation scheme was by determining the set of optimal excitation patterns for maximizing the information content in the acquired data [68]. In this case, the set of optimal patterns were defined on a basis comprising of the eigenfunctions of the Laplace-Beltrami operator. The dependence of the optimal patterns on the surface geometry and the distribution of optical properties demanded a subject specific computation of the optimal excitation patterns. The computationally intensive optimization procedure employed in this work makes it unsuitable for adoption into the imaging protocol. Most recently, a new scheme based on wavelet-based patterns which were used in conjunction with a wavelet transform based data-processing scheme to simultaneously reduce acquisition time and reconstruction time have been reported [69]. 1.3 Thesis overview This thesis will describe the development and characterization of a whole-body 3D reconstruction platform for small animal optical tomography for applications in Functional Optical Tomography and Fluorescence Molecular Tomography. The system will operate in the Time-Domain to allow the acquisition of a comprehensive information rich data-set. The time-resolved datasets will be acquired using an Intensified CCD camera providing a dense detector sampling. The temporal datasets will simultaneously provide improved resolution and better quantification in tomographic studies. The system has been designed to function in the trans-illumination mode to achieve a full 3D reconstruction of the animal model. A tunable pulsed laser operating in the NIR range has been selected as the source for the generation of time-domain data sets. This will lend the system design flexibility by not limiting its operation to fixed wavelengths. Furthermore, the tunable characteristic of the source will allow the use of this system with multiple fluorophores in FMT studies and will allow the collection of spectrally dense data sets for functional tomography studies. And lastly, a wide-field excitation scheme has been adopted as the excitation scheme permitting the fast acquisition of whole body data-sets. The scalable nature of wide-field excitation schemes will improve the flexibility of this system by easily

30 14 adapting it to a wide range of imaging models. The combination of these three design principles will allow the fast acquisition of spectrally, temporally and spatially dense data sets which can provide high-resolution 3D parameter maps in functional and fluorescence studies. The following thesis consists of 6 chapters. In Chapter 1, the field of Optical Tomography was introduced and the primary design objectives for the system were defined. Chapter 2 focuses on the development of the imaging platform and a characterization of its operational parameters including their impact on the quantitative accuracy of the system. Chapter 3 details the validation experiments conducted in vitro establishing the performance of this platform in tomographic applications in functional tomography and fluorescence molecular tomography. In Chapter 4, the effect of system noise on resolution and quantitative accuracy of time-resolved imaging is presented. Moreover, data processing and calibration schemes for the robust reconstruction performance are discussed. In Chapter 5 a measurement guided pattern optimization scheme allowing the run-time iterative correction of excitation patterns for improved information content is discussed. And lastly in Chapter 6, the application of the this platform in the tomographic reconstruction of Förster Resonance Energy Transfer (FRET) in vivo is described.

31 Chapter 2 System description and characterization In this chapter, the imaging system is described and its operational parameters are characterized. In Section 2.1, an overview of the system is provided and the different components are detailed. In Sections 2.2 and 2.3, the temporal and spectral characteristics of the system are discussed followed by an analysis of the noise characteristics of the platform in Section 2.4. In Section 2.5 the quantitative accuracy of the system is investigated using time-resolved spectroscopy System design As stated in chapter 1, the objective of this project is to develop an imaging platform that will allow the 3D reconstruction of functional tissue parameters and localise molecular targets in vivo in small animals. Furthermore, the system should allow the acquisition of a comprehensive, information-rich dataset that will help mitigate the limitations posed by the ill-posed inverse problem associated with optical tomographic methods. The system described herein uses a tunable ultra-fast laser which allows the use of multiple excitation wavelengths across the NIR window for Functional Tomography studies, as well as, allows the use of multiple commercially available molecular markers for in vivo Fluorescence Molecular Tomography studies. A gated Intensified CCD camera is used in conjunction with a projector employing wide-field patterns to acquire spatially dense time-resolved datasets. Figure 2.1 shows a schematic of the system Source components Laser A tunable Ti-Sapphire pulsed laser, Mai Tai HP R (Spectra-Physics, Newport Corporation, CA) is used as the source. The laser operates in the NIR window 1 Portions of this chapter previously appeared as: V. Venugopal, J. Chen and X. Intes, Development of an optical imaging platform for functional imaging of small animals using wide-field excitation, Biomedical Optics Express, vol. 1, no. 1, pp ,

32 16 Figure 2.1: System schematic (tunable from 690nm nm) with a repetition rate of 80MHz and pulse-width of 100fs. This refers to a 100fs pulse width during mode-locked operation at an interval of 12.5ns. The laser provides a maximum power of 3W at 800nm and 500mW at 690nm (dynamic range of 2.5W across the tunable range). The wide dynamic range coupled with the high power output (above the Maximum Permissible Exposure (MPE) limit 2mW/mm 2 [70]) necessitates the use of power control mechanism. Power control The power control mechanism (Application Note 30, Newport Corporation, CA) is a polarizer-based power attenuator which allows the computer control and stabilization of laser power. Figure 2.2 shows a schematic of the power control assembly [71]. The Glan-Laser polarizer and the half-wave plate form the central components of the assembly wherein rotation of the half-wave plate controls the direction of polarization of the input beam. The power transmitted through the polarizer which is dependent on the relative orientation of the plane of polarization and the axis of the polarizer (Malus Law) can therefore be controlled by rotating

33 17 Figure 2.2: Power control assembly the half-wave plate. A closed loop control of the orientation of the half-wave plate is achieved using feedback received from the power meter (which measures the power exiting the assembly) maintaining the specified output power with an error less than 10%. The spectrophotometer is incorporated into the assembly to account for the variation in sensitivity of the power meter across the tunable range. The power control assembly has a transmission efficiency of 80% and allows an accurate control of source power spanning three orders of magnitude across the operational tuning range (c.f. Table 2.1). This provides a safe and efficient control of signal level during imaging protocols (e.g. in FMT studies where fluorescence signals can be more than two orders of magnitude smaller than excitation signals). Furthermore, as discussed in the following sections, the wide-field excitation patterns allows the use of a higher power as the laser energy is distributed over a larger area and the maximum power values provided in Table 2.1 are within the above prescribed MPE limit. The beam exiting the power control assembly is injected into a 400µm multimode optical fiber (N.A. 0.22) using a Fiber-beam coupler (F-91-C1-T, Newport Corporation, CA) with a coupling efficiency of 88%. The optical fiber guides the beam to the spatial light modulator at the imaging stage. Spatial light modulator (SLM) A spatial light modulator based on digital micro-mirror device technology is used in this system to generate the excitation source patterns. A commercially

34 18 Table 2.1: Limits of operational power across the NIR window Wavelength (nm) Laser Output (W) Maximum Power (mw) Minimum Power (mw) available hand-held projector(pico Projector, PK101, Optoma USA) was integrated into the system as the full-field pattern generation device. In order to integrate the device into the system, the projector module was disassembled and the light source was replaced with the laser beam from the optical fiber. Figure 2.3(a) shows the internal structure of the optical module [72]. It should be noted that the laser beam was injected into the red channel in the optical module to reduce attenuation by the dichroic mirrors used for beam recombination in normal projector operation. The device was positioned under the imaging stage to provide a full-field excitation pattern3.4cmlongand2.5cmwidewhichiscomparabletoasmallanimaltorso. The patterns used in tomographic studies are controlled and supplied to the projector and using Microsoft Powerpoint R via a USB connection. Figure 2.3b shows an example of the full field pattern and the spatial distribution of light intensity. In order to establish the grayscale level that can be implemented and detected on this system, a test patten shown in Figure 2.3c was imaged. The detected pattern(figure 2.3d) normalized to the full-field intensity map (Figure 2.3b) shows that grayscale levels upto 0.2 can be detected on this system.

35 Detector components Trigger generator The acquisition of time-resolved datasets requires absolute synchronization between the pulse-generation mechanism and the recording instrumentation. In this regard, the trigger generator performs the task of generating an electric trigger in sync with the emission of a laser pulse. In this system an optical constant fraction discriminator (OCF-401, Becker-Hickl GmbH) is used as the trigger generator. A 1% optical channel split from the laser output is incident on the photo-cathode in the trigger generator, which in turn outputs a 1.5V electrical trigger. The constant (a) Optical module of the Pico Projector. (b) Intensity distribution across a full-field excitation pattern. (c) Grayscale test pattern. (d) Projected grayscale pattern normalized to the full-field pattern. Figure 2.3: Pico Projector implementation

36 20 fraction trigger generation mechanism ensures that the trigger point is independent of the signal amplitude which can vary with the wavelength employed thus allowing seamless multi-spectral studies. Trigger delay unit The trigger delay unit is a programmable delay scan device which receives the electrical trigger from the trigger generator and outputs a TTL signal at a fixed temporal increment or delay. The TTL pulse acts as the trigger for the electronic shutterintheintensifiedccdcamera. Thedelayunitmaybeprogrammedforupto 255 time delays spanning a maximum of 50ns with a minimum temporal resolution of 1ps. Intensified CCD camera The intensified CCD (ICCD) camera employed in this system (Picostar HR, LaVision GmbH) is a high-speed high-resolution gated photon counting device. The ICCD comprises of an intensifier with a dedicated controller, High Rate Imager (HRI, Kentech Instruments, U.K.), and a CCD camera. The gating intensifier is based on the principle of photoelectronic conversion and electron multiplication as outlined in Figure 2.4. The operation of an ICCD camera is briefly described below. The intensifier is made of three components, a photo-cathode for conversion of incident photons to electrons, a micro-channel plate (MCP) which multiplies the generated photoelectrons and a phosphor screen which converts the amplified electrons back to photons. In the inactive state referred to as the gate-off state, the photo-cathode has a positive potential (+50V) and electrons generated in the photo-cathode by impinging photons are pulled back. When the intensifier receives a TTL pulse (from the delay unit), the photo-cathode potential is switched to -180V for a fixed duration, referred to as the gate-width (in the order of a few hundred picoseconds). In the gate-on state the generated electrons are pushed towards the MCP due to the negative potential across the photo-cathode. The MCP is a thin glass plate comprising of millions of channels 10µm in diameter. When the electron ejected from the photo-cathode enters the MCP, it collides with the channel wall producing secondary electrons. The electrons are

37 21 Figure 2.4: ICCD camera operation principle. propagated forward due to a voltage gradient across the MCP, U MCP. Each electron entering the MCP produces 500 electrons with the gain increasing exponentially with MCP voltage (c.f. section 2.4). The MCP voltage for this system has a range of 260V to 800V. After exiting the MCP channels the electrons strike a phosphor screen resulting in the generation of photons. The phosphor screen is a glass or fiber optical base covered with a coating of phosphor at a high potental difference (6kV) relative the MCP. Due to the high potential difference, each impinging electron results in 180 photons. The photons generated by the screen are transmitted to the CCD camera by fiber-coupled relay optics. The CCD camera records the photons arriving within the exposure time and writes the image to file. The CCD camera used in this system, Imager QE, has a 12-bit readout resolution (allowing the measurement of a maximum of 4096 photons) and spatial resolution of The modes of operation of the HRI can be classified into four groups: 1. COMB modes: This refers to the gating of the photo-cathode for set durations ranging from 200ps to 1000ps at 100ps steps. In this implementation, the HRI is operated in this mode.

38 22 Figure 2.5: Data Acquisition Timing Diagram 2. Logical modes: The gating of the photo-cathode is controlled by an external trigger. 3. RF mode: This mode allows the RF modulation of the photo-cathode voltage. This mode is typically used in frequency domain systems. 4. DC mode: In this mode the gate is always open acquiring continuous signals. This mode is used as a test mode. Data acquisition timing The synchronous operation of the various detector components is achieved through electrical signal communications between the devices mediated by the computer. Figure 2.5 shows the timing diagram for data acquisition in this system and each step is described below. 1. The laser pulses are used to trigger the constant fraction discriminator which generates a 1.5V electric trigger.

39 23 2. The trigger delay unit which is programmed to shift the trigger by a fixed increment, applies the requisite time-delay and outputs a 5V TTL pulse. For the first measurement this is 0ps. 3. When the HRI receives the TTL pulse, it switches potential on the photocathode, opening the gate for a fixed gate-width. 4. The amplified signal is integrated by the CCD camera over the exposure time (or integration time) for several laser pulses. For instance, for an integration time of 50ms, the gate is opened at the same time point for each laser pulse repeating every 12.5ns resulting in the integration of 4 million pulses. 5. At the end of the exposure time, the CCD signal is read-out. The intensifier is in gate-off state during CCD read-out and does not open upon the arrival of the pulse. 6. The integrated signal is recorded as the first time-gate. 7. For the second measurement, the delay unit shifts the trigger by a unit delay increment and the process is repeated to record the second gate. 8. This process is repeated for all the delays programmed into the delay unit allowing the measurement of a complete temporal signal. 2.2 Temporal characteristics As mentioned in Chapter 1, time-resolved optical methods provide a robust technique to perform quantitative assessment of tissue optical parameters. The quantitative accuracy of the system is however highly dependent on the temporal accuracy of the system. In case of small animal imaging studies, the temporal accuracy becomes more critical due to the short diffusion distances and wide-range of optical properties, resulting in significant variation in temporal characteristics across the animal torso. In this section, the temporal characteristics of the system are detailed. Typically, the temporal characteristics of a time-domain system are parameterized by

40 24 the properties of its impulse response function, referred to as the Instrument Response Function (IRF). The IRF is the temporal signal measured on the system in the absence of any diffusing medium and is representative of the collective temporal attributes of the system. Imaging protocols therefore employ a pre-imaging calibration step wherein the IRF is recorded for use in data processing and reconstruction. Figure 2.6 gives an example of the IRF obtained on this system for a 100fs laser Figure 2.6: The Instrument Response Function pulse. As noted in Figure 2.6, the two parameters defining the IRF are the peak position t 0 which defines the effective time of pulse arrival and the full-width at half maximum (FWHM). The former characterizes the temporal delay due to the various system components while the latter is representative of the temporal dispersion of the laser pulse upon propagation through the system. In this section, the temporal characteristics of the system will be defined using these two parameters Temporal parameters for accuracy In order to establish the optimal IRF parameters necessary for the quantitative accuracy of the system with less than 10% error, an investigative study based on time-resolved spectroscopy was employed. Time-resolved spectroscopy refers to the estimation of functional parameters by fitting the temporal signals to an analytical model of light propagation in a turbid medium and is a well-established optical technique. The analytical model is described in detail in Section 2.5.

41 25 In this simulation, time-resolved curves in transmittance through a 2cm thick slab (representative of the approximate thickness of a murine model) were simulated for the range of optical properties expected in small animals (µ a = 0.04cm 1 to 0.6cm 1 ; µ s = 4cm 1 to 25cm 1 ; c.f. Table 1.1). This curve is convolved with an experimentally acquired IRF to generate a time-gated temporal point spread function(tpsf). In this study the broadening of the IRF was simulated by convolution of the IRF by a pulse to investigate the effect of underestimation of IRF FWHM by 5ps, 10ps, 15ps and 20ps. The change in t 0 was simulated by shifting the baseline IRF by 5ps, 10ps, 15ps and 20ps. The modified IRFs were then convolved with the theoretical TPSF calculated above to generate the compromised measurements and the optical properties were estimated for each case using the original IRF. The estimation errors for each set of temporal data is consolidated in Figure 2.7. Figure 2.7(a) shows that µ a was estimated within 10% error over the entire range of optical properties for an increase of 5ps in the FWHM. Conversely, Figure 2.7(b) shows an increased sensitivity of µ s estimation to broadening of the IRF with errors in the estimation of µ s with the estimation error rising over 15% for low values (a) Percentage error in estimated µ a. (b) Percentage error in estimated µ s. Figure 2.7: Impact of mis-estimation of IRF FWHM on quantification. The green shaded area marks the region of target accuracy of 10%.

42 26 (a) Percentage error in estimated µ a due to underestimation of t 0. (b) Percentage error in estimated µ s due to underestimation of t 0. Figure 2.8: Impact of mis-estimation of IRF t 0 on quantification. The green shaded area marks the region of target accuracy of 10%. ofµ s. Figures2.8(a)and2.8(b)showthattheshiftint 0 of5psresultsin 10%error in the estimation µ a for the entire range of optical properties considered. However, more than 10% error was observed in the estimation of µ s for small values of µ s. It can therefore be concluded that estimation of µ a is more robust than the estimation of µ s for less than 5ps variation in IRF characteristics. Moreover, broadening of the IRF increases µ s estimation error for tissues with higher absorption coefficients (e.g. heart and liver) while the uncertainty in t 0 has a more severe impact µ s estimation for tissues with smaller values of µ s (bladder). The simulations show for a system performing whole body small animal DOT, the uncertainty in t 0 and FWHM must be less than 10ps for an estimation error less than 10% Temporal stability As the Instrument Response Function is recorded during the pre-imaging calibration, the stability of the IRF for the duration of the experiment becomes a critical factor influencing the accuracy of the platform. Furthermore, the electronic and op-

43 27 tical components in the system need a warm-up time for stable system operation. In this experiment, the temporal stability was characterized by measuring the IRF at 30s interval for 90minutes after turning on the system. The laser was set to emit at 700nm with the ICCD camera acquiring 30 time-gates at 20ps intervals with an integration time of 50ms. The acquired IRF were interpolated to 1ps temporal resolution and the t 0 and FWHM were measured. Figure 2.9 shows the variation the the IRF parameters over the 90 minute period. As seen in Figure 2.9, the system begins stable operation after 40 minutes of warm- (a) Variation in t 0. (b) Variation in FWHM. Figure 2.9: Characterizing the drift and jitter in IRF parameters. up. After the warm-up time, the drift in t 0 over the 50minute acquisition window was found to be 2ps/hr. Also, the jitter in t 0 was found to be 2ps. The variation in IRF FWHM over the same time window was also found to have a variation of 2ps Impact of system components on IRF In this section, the variations in IRF parameters upon the modification of various system parameters are characterized to identify the optimal operational parameters of the system.

44 28 Laser The impact of the laser on the IRF was observed during the tuning operation. Figure 2.10 shows the IRF recorded for 7 wavelengths spanning the operational tuning range employed in functional/fluorescence tomography studies. The IRF t 0 is seen to shift by 700ps upon tuning from 700nm - 880nm. Similarly, the FWHM broadensfrom 200psat 700nmto300psat 880nm. Thisvariation canbeascribedto the tuning mechanism in the Mai Tai. Moreover, this necessitates the measurement of the IRF at each wavelength employed during the imaging session. Power Control In this experiment, the effect of change in power output from the control assembly on the IRF was investigated by making 10 IRF measurements at 7 power setting ranging from 10mW - 150mW. Figure 2.11 shows the changes in IRF t 0 and FWHM to be less than 10ps. The invariance of IRF characteristics with power settings can therefore be concluded. Pico projector The projection mechanism can have a significant impact on the IRF characteristics due to potential non-linearities in the optical modules. The objective of Figure 2.10: IRF measured for various wavelength of excitation.

45 29 (a) Variation in t 0 with increase in signal power. (b) Variation in FWHM with increase in signal power. Figure 2.11: Effect on power control operation on IRF. this investigation was to determine the modification in the IRF parameters across the generated pattern. Furthermore, as stated in Section 2.1, the gray levels are generated by the DLP chip using pulse-width modulation. Therefore a second objective of this investigation was to establish the effect of the light modulation by the micro-mirror on IRF parameters. Figure 2.12 shows the t 0 and FWHM measurements for a uniform excitation field shown in Figure 2.3(b) and the gray-scale test pattern shown in Figure2.3(c). It should be noted that the IRF parameters were estimated for gray-levels greater than 100 counts to avoid any bias in measurements due to poor statistics. The full-field excitation pattern was found to have a t 0 variation of 30ps across the pattern and the IRF broadens by 45ps towards the edge of the pattern. The shift in t 0 is equivalent to a change in pathlength of 9mm which is comparable to the dimensions of the optical module. The broadening of FWHM can be attributed to the integration of photons done by the Fly-eye lens to homogenize the field. Both of these effects are taken into account in the pre-experiment calibration. Furthermore, comparing the IRF parameters for the grayscale pattern with the uniform pattern (as evidenced in the the profile plots in Figure 2.12), the modulation of micro-mirror

46 30 (a) Left: FWHM for uniform full field pattern, (Center) FWHM for grayscale pattern, (right) Comparing FWHM profiles along the center of the pattern (b) Left: t 0 position for uniform full field pattern, (Center) t 0 position for grayscale pattern, (right) Comparing t 0 profiles along the center of the pattern Figure 2.12: Impact of pattern generation optics on IRF characteristics (a) FWHM, (b) t 0 vibration does not have a significant impact on the IRF characteristics. ICCD Camera Among the control parameters on the ICCD camera, the MCP voltage and the gate-width setting were identified as parameters that can potentially affect the IRF of the system. In order to test the impact of these parameters the IRF was measured for different setting of the two parameters. First, the IRF was consecutively measured 10 times for 5 MCP voltage settings spanning from 400V - 800V at 50V steps. Figure 2.13 shows the variation in IRF parameters with MCP voltage and it can be concluded that increasing the gain voltage will result in less than 10ps variation in t 0 position and less than 5ps variation in the IRF FWHM for voltages less than 700V. The 20ps shift in t 0 position for higher MCP voltages can be attributed to high noise levels when employing these gain parameters.

47 31 As stated in Section 2.2 the ICCD camera used in the system is operated in the COMB mode with available gate-width settings ranging from 200ps ps at 100ps intervals. In this test, the IRF was acquired for each above gate-width settings. Figure 2.14 shows that the gate-width has a significant impact on the FWHM of the IRF with minimal impact on the t 0. As shown in Figure 2.5, the gate-width is the the duration of time for which the ICCD camera shutter is open which is then translated across the measurement time window. The impact of gatewidth on the IRF can therefore be defined as a temporal convolution of the laser pulse with a pulse having width equal to the gate-width. This effect is evident in Figure 2.14, where the system IRF has a triangular waveform for shorter gate-widths (less than 300ps) with the IRF approximating a square pulse for gate-widths longer than 400ps. 2.3 Spectral characteristics The spectral response of the system characterizes the non-linear behaviour of the system system components across the operational wavelengths employed in functional and fluorescence tomography studies. (a) Variation in t 0 (b) Variation in FWHM Figure 2.13: Effect of MCP voltage on IRF characteristics. The statistics are calculated on a set of 10 measurements at each MCP Voltage.

48 32 Figure 2.14: Effect of gate-width settings on IRF. In the first test, the efficiency of source pattern generation and detection were characterized. Figure 2.15(a) shows the power incident on the imaging stage for varying levels of power set at the power control output. The power at the imaging stage was measured by focusing the projector output on power meter head using a biconvex lens. By computing the slope of the curves, the transmission efficiency of the pico projector can be estimated. The drop in transmission efficiency with wavelengths can be attributed to the optics used in the projector optics which are optimized for use in the visible wavelengths as opposed to the NIR wavelengths tested here. The spectral efficiency of the ICCD camera is dependent on the sensitivity of the photo-cathode at the intensifier entrance which converts the photons to electrons. The quantum efficiency of the photo-cathode as provided by the manufacturer is shown in Figure 2.15(b). The second set characterization tests focussed on the performance of the projection optics with change in wavelength. As mentioned in Section 2.2, the spatial modulation of the light is achieved by switching the orientation of the micro-mirrors. As the wavelengths employed here are comparable to the distances between the mirrors, image formation by DmD devices are governed by the diffraction at the slits between adjacent micro-mirrors [73]. This implies a dependence of the position of

49 33 (a) Transmission efficiency of the pico projector. (b) Quantum efficiency of the ICCD camera. Figure 2.15: Spectral Characteristics of source and detector components. Figure 2.16: Pattern projection at the NIR wavelengths the projected pattern on the wavelength of light. Commercial projection devices include corrective optical mechanisms to correct for this behaviour. In order to test the pattern generation using the pico projector at wavelengths employed in this system, an arbitrary pattern was projected and measured at multiple wavelengths. Figure 2.16 shows the recorded images and the invariance of pattern position with wavelength can be concluded.

50 Noise characteristics Signal intensity noise plays an important role in time-domain imaging systems due to the sensitivity of the photon-counting detector mechanisms. Noise characteristics of the system in this section therefore refer to the source of error in measured photon intensity using the ICCD camera. As noted in the previous section, the quantum efficiency of the detector significantly drops with increasing excitation wavelength. In this section the ICCD parameters that are used to improve the signal level and their effect on the signal to noise ratio (SNR) is discussed Sources of noise in an ICCD camera Photon statistical noise (also known as shot noise) is a common form of signal noise encountered in photon counting devices. It arises due to the variation in the number of photoelectrons generated by the photo-cathode which follows a Poisson distribution. This noise is amplified by the electron multiplication process in the MCP and represents the most significant source of noise at high gain levels. Intensifier dark noise is the noise generated due to the random emission of electrons from the photo-cathode due to the thermal distribution in the photocathode. This noise is usually significant only for low signal levels and long integration times. CCD dark current is the noise generated in the CCD camera (similar to the intensifier dark noise) due to the thermal distribution of electrons in the silicon substrate. This is reduced by cooling the camera to 11 C. A subtraction of the dark image during pre-experiment calibration reduces this noise component. A dark noise of 30 counts is observed in this system after warm-up. Read-out noise is the noise generated due to the uncertainty in the conversion of CCD charge to pixel values in the amplifier of the camera. This noise can be reduced by hardware binning of the pixels as the signal at multiple pixels are integrated before amplification.

51 Impact of ICCD parameters on noise level The gain voltage across the MCP and the integration time are two commonly used parameters to increase the recorded signal level. Here we consider the signal amplification achieved by each parameter and its effect on the SNR. MCP Voltage The first test focused on the dependence of detected signal on the gain voltage applied. In this study the number of photons detected at different MCP voltages for different levels of input power after transmission through a 2.0cm thick polyurethane phantom was measured. This was done to ensure the recorded signal did not saturate at high input power and high gain voltages. Figure 2.17(a) shows the behaviour of recorded signal with change in MCP voltage. The linearity of the log-log plot suggests a power law relation between the incident photons and recorded signal. By fitting a line to the measured signal values, the amplification factor for each MCP voltage (χ MCP ) was calculated. Figure 2.17(b) shows an exponential increase in the amplification factor with gain voltage. The estimated values of χ MCP can be used to normalize signals recorded at different MCP voltages in the data-processing step. However, the advantages of significant amplification of signal by using the gain voltage parameter is offset by its adverse effect on the noise level in the recorded signal. To compute the SNR for different MCP voltages, 50 temporal measurements of a uniform full-field pattern were made with MCP voltages ranging from 400V - 800V. The signal at each detector on the pattern was defined as the mean signal level (µ) across the 50 frames and the standard deviation (σ) was defined as the noise. The signal to noise ratio was therefore given by SNR = µ/σ. The peak signal level at each MCP voltage was maintained at 3500 counts by modifying the incident power. Figure 2.17(c) shows the change in signal-to-noise ratio with CCD counts for different MCP voltage demonstrating a four-fold drop in SNR when MCP voltage is increased to 800V from 400V. Integration time Integration time refers to the CCD exposure time over which the CCD integrated the incoming photons from the intensifier. It is therefore understood that

52 36 (a) Relationship between incident power and detected signal. (b) Relationship between χ MCP and gain voltage. (c) Impact of MCP voltage on the SNR. Figure 2.17: Signal level and noise characteristics of MCP gain voltage. increasing the integration time proportionately increases the signal level. The objective of these set of test was to establish the linearity of increase in signal level with incident power and thereby establish the signal amplification factors for different integration times. Figure 2.18(a)-(b) demonstrate the linear relationship of the signal amplification factor (χ int ) with integration time.

53 37 (a) Relationship between incident power and detected signal. (b) Relationship between signal amplification factor χ int and integration time. (c) Impact of integration time on the SNR. Figure 2.18: Signal level and noise characteristics of CCD integration time. To compute the impact of integration time on the SNR, 50 temporal measurements of a uniform full-field pattern were made with integration times ranging from 25ms - 400ms. The SNR was computed by calculating the ratio of the mean signal to the standard deviation across the 50 frames (c.f. 2.18(c)). As expected, the SNR was found to increase with integration time, however, the SNR values were comparable

54 38 for integration times greater than 50ms. 2.5 Characterizing quantitative accuracy of the system In this section the quantitative accuracy of this system is established using Time-Resolved Spectroscopy. Time-Resolved Spectroscopy (TRS) is the most accurate technique to estimate the optical properties of thick, highly scattering tissue [74]. TRS fits the experimentally acquired TPSF to the analytical expression describing the temporal propagation of photons through the medium to estimate the optical properties of the medium [75]. While TRS can be performed using a widefield or a point-source, the analytical expression used in TRS is prone to error in the case of a model with irregular surface geometry when using a pattern excitation scheme as the source. Therefore, to mitigate the associated source of inaccuracy, a point excitation scheme is employed to spectroscopically estimate the average optical properties of the medium by measuring the TPSF at finite points on the model Mathematical model for time-resolved spectroscopy For a homogeneous slab of thickness d and absorption coefficient, µ a and reduced scattering coefficient µ s, the temporal point spread function measured at a distance ρ from the axis of excitation is given by Eq ( T(ρ,d,t) =(4πDc) 3 5 ρ 2 2 t 2 exp( µa ct)exp 4Dct n= { z 1,n exp ( z 2 ) 1,n 4Dct ) z 2,n exp ( z 2 )} (2.1) 2,n 4Dct In Eq. 2.1, z 1,n and z 2,n are the positions of the n th image sources used to model the extrapolated boundary conditions, D = 1/3(µ a +µ s) and c is the speed of light in the medium [76]. The infinite series of source images are used to force the fluence rate to zero at the two boundaries. In our implementation only the first 4 pairs of image sources were considered. The analytical function from Eq. 2.1 is convolved by the instrument response function (IRF) representative of the impulse response of the system to obtain the theoretical TPSF for this system. The experimental

55 39 TPSF (10% of the peak value on the rising edge to 1% of peak value on the falling edge) is fit to the above computed theoretical TPSF using a sequential quadratic programming method (fmincon, MATLAB) Impact of MCP voltage on accuracy Figure 2.19: Variations in estimated optical properties with change in MCP voltage. In this experiment, the impact of the deterioration of SNR due to increase in gain voltage on the accuracy of estimated optical properties was investigated. TPSF were recorded in transmittance through a 3.44 cm thick resin phantom having homogeneous optical properties (µ a = 0.06cm 1 and µ s = 11.3cm 1 ) at multiple MCP voltages (400V-800V) with the ICCD employing 200ps gates at 20ps intervals. The incident power of the source was kept constant through the experiment at 30mW. The optical properties in a 1.2cm radius area around the axis of excitation ( 450 detectors) were estimated by TRS. The coefficient of variation (c v ) given by the ratio of the standard deviation of the estimated optical properties to the mean value of the estimated optical properties was used as the figure of merit used to evaluate the impact of SNR. Figure 2.19 shows that the estimated absorption coefficient is more sensitive than the scattering coefficient to the reduced SNR with the c v of both coefficients increasing by more than 50% for MCP gain voltages above

56 40 600V. Therefore the ICCD camera should be operated below 600V for accurate estimation of optical properties Impact of gate-width on accuracy As described in Section2.2, the gate-width is the length of temporal window over which photons are collected at each time point. Therefore, the total number of photons detected at each gate are increased by using longer gates, thereby improving the SNR of the measurements. Conversely, the gate-width has a pronounced effect on the system IRF with the FWHM of the IRF being comparable to the gate-width at longer gates. Increasing the gate-width therefore limits the range of optical properties that can be accurately estimated on this platform as the width of the IRF becomes comparable to the width of the TPSF. For instance, in case of tissues having high absorption coefficient and/or low scattering coefficient. The broad range of optical properties encountered in small animals therefore makes the selection of gate-width a critical factor affecting the accuracy of the estimated optical properties. The effect of gate-width on estimation of physiologically relevant optical properties by time-resolved spectroscopy was investigated by using a 2cm thick liquid phantom. The liquid phantom was constructed by a mixture of Intralipid-20% (Sigma Aldrich, MO, USA) as the scattering agent and Black India ink (Higgins-Sanford) as the absorber diluted in water. TPSF were measured at a resolution of 20ps using different gate-width settings (200ps, 300ps, 400ps, 600ps and 800ps) for an MCP gain voltage of 400V and integration time of 100ms. Two separate experiments were conducted to estimate the absolute optical properties for the above detector settings; first, with increasing absorption coefficient (0.05cm 1 to 0.37cm 1 ) and constant scattering coefficient (8cm 1 ) by increasing the volume of India ink and second, with increasing scattering coefficient (6cm 1 to 16cm 1 ) for a constant absorption coefficient (0.07cm 1 ) by increasing the volume of Intralipid-20%. Figures 2.20(a)-(b) shows the estimated absorption and scattering coefficients obtained for various values of absorption coefficient. It may be noted that the broadening of the IRF for gate-widths has minimal effect on the estimation of absorption

57 41 (a) Estimated absorption with increasing volume of ink. (b) Estimated scattering coefficient with increasing volume of ink. (c) Estimated absorption coefficient with increasing volume of Intralipid-20%. (d) Estimated scattering coefficient with increasing volume of Intralipid-20%. Figure 2.20: Comparing the effect of gate-width on quantitative accuracy of time-gated measurements. coefficient below 600ps. However, gate-widths less than 300ps should be preferred for the accurate estimation of the scattering coefficient with an estimation error less than 10%. Figures 2.20(c)-(d) show the estimated absorption and scattering coefficients with increasing scattering coefficient. The gate-width has a less pronounced

58 42 effect on the estimation of scattering coefficient. It is expected as the FWHM of the TPSF increases with increasing scattering coefficient and is not significantly biased by the broadening of the IRF. In this case, the maximum error of estimation 8% was obtained when using 800ps gates for the lower values of scattering. Nevertheless, the broadening of the IRF affects the estimation of absorption coefficient, with estimation error greater than 20% when using 800ps gates. The increase in the estimated absorption coefficient with the volume of Intralipid may be attributed to the cross talk between absorption and scattering coefficients. It is therefore determined that gate-widths shorter than or equal to 300ps must be used for the accurate estimation of optical properties in small animal imaging for estimation errors less than 10% Functional spectroscopy In this experiment, performance of the platform in the estimation of the concentration of multiple chromophores in a homogenous mixture is investigated. The accurate estimation of the mixture composition is dependent on the accuracy of estimated optical properties at multiple wavelengths in the NIR window. India ink and Bovine Hemoglobin (Sigma Aldrich, MO, US) were selected as the two chromophores for this experiment. The absorption spectra of the two chromophores were calibrated before the experiment using a spectrophotometer (USB2000, Ocean Optics, FL) (Figure 2.21). A 2cm thick liquid phantom was constructed using a polycarbonate tank carrying a mixture of, 5.7% hemoglobin and 0.1% ink and water to provide µ a of 0.18cm 1 and µ s of 7cm 1 at 740nm. Wavelengths of nm were selected for this experiment based on the spectral behaviour of the chromophores (Figure 2.21). TPSF were measured using 300ps gates at 20ps interval over a 1.8ns time window for a single source-detector pair. Figures 2.21(b)-(c) show the comparison of the estimated absorption and scattering coefficient at each wavelength. It may be noted that the absorption coefficient was estimated with less than 3% error while the scattering coefficient had a maximum estimation error of 6%. The linear relationship between the absorption

59 43 Extinction coefficient of ink, (cm -1 ink /ml) (a) India Ink Bovine Hemoglobin Wavelength nm) Extinction coefficient of hemoglobin, (cm -1 hem /ml) Absorption coefficient, a (cm -1 ) (b) Estimated a Expected a Scattering Coefficient, s ' (cm -1 ) (c) Expected s ' Estimated s ' Wavelength (nm) Wavelength (nm) Figure 2.21: Mixture separation using Functional Time-Resolved Spectroscopy. (a) Spectra of India Ink and bovine hemoglobin. (b) Estimated absorption coefficient with estimation errors at each wavelength. (c) Estimated scattering coefficient with estimation errors at each wavelength. Table 2.2: Concentration of mixture components estimated using timeresolved spectroscopy. Component Expected (µl/ml) Estimated (µl/ml) Error (%) India Ink Bovine hemoglobin Water

60 44 coefficient and the concentration of each chromophore weighted by its extinction coefficient at each wavelength is used to estimate the composition of the mixture. The results tabulated in Table 2.2 show that the error estimated concentration of ink and haemoglobin was 6.4% and 4.2% respectively. These results validate the quantitative accuracy of the platform when using multi-spectral time-gated datasets for functional imaging.

61 Chapter 3 Preliminary optical tomography studies After the detailed description of the system and a characterization of its operational parameters, in this chapter, the performance of the system in optical tomography studies is investigated. Following the objectives laid out in Chapter 1, two parallel evaluation studies were undertaken. The first group of experiments focused on the performances of the system in Functional Optical Tomography (FOT) studies, i.e. the reconstruction of absolute tissue optical properties. The second set of experiments tested the system performance for Fluorescence Molecular Tomography (FMT) applications. In Section 3.1, the experiment protocol for this system is provided including the details regarding source selection, data-processing and the mathematical model used for reconstruction. Section 3.2 describes the experiments validation system performance for FOT studies and lastly, Section 3.3 discusses FMT studies establishing the feasibility of the system for molecular imaging applications Experiment protocol In this section, the tomographic data acquisition procedure is described. 2 Portions of this chapter previously appeared as: V. Venugopal, J. Chen and X. Intes, Development of an optical imaging platform for functional imaging of small animals using wide-field excitation, Biomedical Optics Express, vol. 1, no. 1, pp , J. Chen, V. Venugopal, F. Lesage and X. Intes, Time-resolved diffuse optical tomography with patterned-light illumination and detection, Optics Letters, vol. 35, no. 13, pp , V. Venugopal, J. Chen, F. Lesage and X. Intes, Full-field time-resolved fluorescence tomography of small animals, Optics Letters, vol. 35, no. 19, pp , J. Chen, V. Venugopal, and X. Intes, Monte Carlo based method for fluorescence tomographic imaging with lifetime multiplexing using time gates, Biomedical Optics Express, vol. 2, no. 4, pp ,

62 Pre-experiment calibration As inferred from the characterization studies, the variations in the temporal, spectral and signal characteristics with the experiment settings necessitate an instrument calibration procedure which comprises of the following steps. Prior to an experiment, the system is set to acquire (but not record) complete TPSFs to achieve operational stability in the temporal characteristics. Based on the drift characterization done in Section 2.2, the ICCD camera acquires dark signals (with the lens-cap on) for a duration of 1hour. After warm up the IRF for each pattern used in the experiment are recorded. Acquisition of the IRF allows the characterization of pre-experiment system settings and also provides an estimate of spatial variations across patterns being imaged. The IRFs are once again recorded at the end of the imaging session to estimate the drift in temporal characteristics over the experiment time. In the next step, the subject being imaged is placed on the imaging stage and TPSFs are measured to optimize the various recording parameters, specifically, the input power, MCP voltage, integration time, span of the temporal window and the gate-interval and gate-width. The optimization refers to a peak recorded signal count greater than 3500 counts. With the experiment settings determined, the CCD dark image is recorded with the laser turned off. 16 frames of dark images are recorded and averaged to find the mean CCD dark current. This is a baseline noise level subtracted from every recorded image through out the imaging session. A white-field image of the subject being imaged is acquired with the ICCD camerainthedcmode(andthelaserturnedoff). Asthefield-of-viewofCCD camera spans the entire imaging stage, the white field image is used to identify the region of interest during data processing. The system is then returned to the experiment parameters identified previously and imaging session is started.

63 47 Figure 3.1: Subset of wide-field patterns employed. The first 6 patterns are defined on the basis along x-axis and the next 6 are translated along the y-axis Source selection and implementation A broad range of excitation patterns are available when using wide-field strategies, varying from structured patterns with sinusoidally varying intensity to information optimized patterns derived from theoretical models. In the studies described herein, a set of arbitrary bar-shaped patterns (c.f. Figure 3.1) are selected. The patterns are defined such that for any pattern, half of the imaging area along the x-axis or the y-axis is uniformly illuminated. These patterns are then shifted along the corresponding axis at fixed separation providing the set of excitation patterns. Typically, in these studies a total of 36 patterns are employed, with 18 patterns derived from the basis along each axis. The use of such broad patterns provides two advantages. First, as biological tissue acts as a low-pass filter of the spatial information due to photon scattering, the low spatial frequency content in these patterns ensures maximum transmission of photons through the tissue. Second, such patterns inject significantly more photons into the medium resulting in larger number of source-detector measurements with high signal-to-noise ratio (SNR) while maintaining low incident power per surface

64 48 area. The pattern images are compiled in Powerpoint and directly displayed on the Pico Projector. TPSFs are consecutively recorded for all patterns at each excitation wavelength (and emission wavelengths in Fluorescence studies) Data processing and data type selection The TPSF s are recorded by the ICCD control software as 16-bit grayscale images with each image representing one time-gate. The data processing step refers to the extraction of TPSFs for each detector from the CCD images. The first step in data processing, the selection of region-of-interest (ROI) as determined from the white-field images. Each recorded pixel corresponds to 62.5µm 62.5µm (without hardware binning) and the pixels within the ROI in the recorded images are binned during post-processing to generate 1mm 1mm detectors. For each pattern, a fixed number of pixels spanning the ROI are selected (to be used for image reconstruction) and TPSFs are constructed for each detector position. It should be noted that each time-gate is processed independently and the temporal information is not affected. Figure 3.2: The time-gate data type A typical TPSF recorded on the system is shown in Figure 3.2. The TPSF is an information rich data-set which can be processed to lend several useful data (measurements) types in all optical imaging paradigms. For instance, an integration of the TPSF over time provides the continuous-wave (CW) data type obtained using

65 49 steady-state systems. Moreover, by taking a Fast Fourier Transform (FFT) of the TPSF, the amplitude and phase functions at multiple modulation frequencies may be derived. It should be noted that that FFT of the TPSF can provide information at modulation frequencies higher than those achieved by source intensity modulation in frequency-domain systems. And within the time-domain paradigm, the time-gates, the temporal moments of the TPSF and transforms applied to the TPSF (namely normalized Laplace transform, Mellin transform) constitute useful data types. In this work, we use the time-gates (TG) as the data-type. As shown in Figure 3.2, the time-gate data type is the intensity of photons at each time-point in the measured TPSF. Time-gates can be broadly classified into two groups around the maximum - early gates and late gates, and are referred to by the percentage intensityofthepeakcountinthetpsf(maximumgate). Forinstance, thefirstgate in Figure 3.2 is referred to as the early gate at 25%, the second gate is the early gate at 50% etc. The calculated data types for each source (pattern) and detector pair are then used to solve the inverse problem in tomographic reconstruction Reconstruction The anatomical complexity of the imaged volume in pre-clinical DOT necessitates the use of a rigorous model of light propagation in tissues for quantitative accuracy, especially when considering time-resolved data types such as early gates. In this work, a Monte Carlo (MC) based forward model (developed for use with the time-gated datasets generated by this system) is used for modelling the photon propagation in murine models [77]. The flexibility of the MC model allows the accurate modelling of complex boundary conditions and remains valid for the wide range of optical properties encountered in small animal models. We provide below a brief description of this model apropos the reconstruction schemes used in Functional Optical Tomography and Fluorescence Molecular Tomography. Functional Optical Tomography The Monte Carlo method for light propagation is a photon tracing method. In the forward model a large number (typically 10 9 ) of photons are injected into the medium one at a time where the model geometry and bulk optical properties

66 50 µ a and µ s are provided a priori. The path of photon propagation from a point source to a point detector, referred to as the s-d pair, is numerically calculated and the path length of each photon through the voxelized model and the number of scattering events along the path of propagation are recorded. The final measurement of the photon packet at the detector, W referred to as the photon weight, can be then calculated. The MC model described here is based on perturbation theory, wherein conversely to the absolute optical properties, the localized perturbations in the coefficients is reconstructed. In the perturbation MC model, a perturbation in the average optical properties (δµ a and δµ s ), results in a perturbed detector reading Ŵ(t) at the time-gate t and is given by Eq Ŵ(t) = W(t) n j=1 ( ) p(rj,t)( ) p(rj,t) ˆµs (r j )/ ˆµ t (r j ) ˆµt (r j ) µ s (r j )/µ t (r j ) µ t (r j ) exp( (ˆµ t (r j ) µ t (r j ))L(r j,t)) (3.1) In Eq. 3.1, W(t) is the unperturbed detector reading, p(r j,t) is the number of collisions and L(r j,t) is the path length of the photon detected at time-gate t in voxel r j and n is the total number of photons. Theˆ. symbol identifies the perturbed optical properties and the attenuation coefficient is defined as µ t = µ a + µ s. Ŵ(t) computed in Eq. 3.1 is extended to an arbitrary wide-field excitation scheme by assigning a uniform probability of photon injection across the area of excitation with initial photon weights on source plane simulating the intensity profile of the pattern. The unperturbed detector reading is used to compute the Jacobian matrix for a specific time-gate. Areconstructionprobleminvolvingthereconstructionofµ s andµ a forj voxels using I s d pairs can be linearized using the Born formulation and is expressed as shown in Eqn In Equation 3.2, W i (t) is the difference between the perturbed andunperturbeddetectormeasurementsfor thei th source-detectorpair at time-gate t. It should be noted that Equation 3.2 can be extended to multiple gates.

67 51 δµ a (r 1 ) W 1 (t) J1,1(t) a J1,J a. = (t) Js 1,1(t) J1,J s (t) δµ a (r J ) W I (t) JI,1 a (t) Ja I,J (t) Js I,1 (t) Js I,J (t) δµ s (r 1 ). δµ s (r J ) where, J a i,j(t) = Ŵi(t) δµ a (r j ) J s i,j(t) = Ŵi(t) δµ s (r j ) (3.2) Figure 3.3 shows the time-resolved Jacobians computed using this model for a wide-field source and a point detector. The increasing width of the Jacobian with an increase in time suggests the accurate modelling of time-resolved photon propagation. Also noteworthy, is the reduced sensitivity of the Jacobian along the source plane contrary to the detector plane. This is a characteristic feature of widefield excitation strategies. Figure 3.3: Time-gated Jacobians for wide-field excitation source (at z = 20mm)and a point detector (at z = 0mm). When using this model for reconstructing experimental data, the baseline (bulk) optical properties are obtained by TRS and are used to compute the unperturbed detector measurements W(t) and in turn the Jacobian matrix J. Specifically, in case of planar/slab geometry, the measurements at excitation wavelength are directly used to estimate the optical properties via an extension of Eq. 2.1 to wide-field excitation patterns. In the case of complex boundary conditions wherein Eq. 2.1 cannot be directly applied, a separate slab phantom is constructed from the same material to estimate the bulk optical properties. In order to solve the

68 52 inverse problem, the experimental measurements obtained at time-gate t are used to solve the inverse problem in Eq. 3.2 using a least-squares minimization function (lsqr, MATLAB) to simultaneously compute the perturbation in µ a and µ s in the 3D volume. Fluorescence Molecular Tomography The photon propagation model used for FMT closely follows the MC model described for FOT described above [78]. Here we define the total absorption coefficients due to the background tissue and fluorophores as µ x a and µ m a at the excitation wavelength (λ x ) and emission wavelength (λ m ), respectively. Then the effective quantum yield η(r) is defined as the probability of a photon to be emitted upon absorption of a photon by the total absorption coefficient, η(r) = µx af (r)φ µ x a(r) (3.3) whereφisthequantumyieldandµ x af istheabsorptioncoefficientcontributedbythe fluorophore, which is linearly related to the concentration of the fluorophore by the extinction coefficient. For a fluorophore in the medium that has a mono-exponential decay with lifetime τ, under the assumption of equal absorption and scattering coefficients at λ x and λ m, the fluorescence signals can be simulated by convolving the temporal signals generated at the excitation wavelength by the exponential timedecay of the fluorophore given by, e t/τ. The spatial and temporal Jacobians for FMT can therefore be calculated using the following, J fluo (t) = t 0 dt J a (t )e (t t )τ, (3.4) To cast the inverse problem, we employed a Born formulation in which the emission field is normalized by the excitation field [79] by normalizing the experimental time-domain emission measurements to the CW excitation flux at the same position. We therefore have Φ = Mm i (t) M x i = α U x i K k=1 d 3 rj k i,j(t)η k j, (3.5)

69 53 where α incorporates gain and attenuation factors employed during measurement acquisition (change in power, integration time etc.), M m i (t) is the total signal from all fluorophores with different lifetimes at the emission wavelength for the i th s d pair at time-gate t, M x i and U x i are the measured and simulated, respectively, total excitation flux measured at the detector for the i th s d pair. This normalization efficiently mitigates the dependence of the detected fluorescent signal on the optical properties of the examined tissue [80, 79], thus the absorptive heterogeneities associated with the different organs in the small animal model are not modelled. Note also that this formulation employs the CW excitation flux at the same position to alleviate the unavoidable time errors associated with drift and jitter in time-resolved studies (See Chapter 4). For a reconstruction problem involving I s d pairs and a model discretized into J voxels, Eqn. 3.5 can be written as the linear system given by Eqn Φ 1. Φ I = β 1 J fluo 1,1... β 1 J fluo 1,J..... β I J fluo I,1... β I J fluo I,J η fluo 1. η fluo J, (3.6) where J fluo i,j is the weight function for the i th (s = 1,...,I) measurement, and β i = α i /U x i is the normalization factor for the i th measurement and the corresponding weight function. The above equation has a general form Ax = b, then x = [η fluo1 1,...,η fluok J ] T and is computed by solving the above system using a leastsquares solver (lsqr, MATLAB). In summary, our approach to reconstruct the effective quantum yield is schematically depicted in Fig Functional Tomography studies In this section we describe the in vitro experiments undertaken to test the feasibility of this system for reconstructing the optical properties in small animal models. As stated in Chapter 1, the size and distribution of organs in vivo and the wide-range of their optical properties present a significant challenge in the quantitative reconstruction of functional parameters. The first study therefore focuses on the feasibility of reconstructing multiple absorptive inclusions at close proximity to

70 54 Figure 3.4: Block-diagram for fluorescence reconstruction. each other using the wide-field strategies described earlier. In the second study, the objective was to investigate the potential of the time-gate data types in separating the contribution of the absorption and scattering coefficients thereby improving the accuracy of the estimates of functional parameters Reconstructing a complex distribution of absorptive perturbations Figure 3.5(a) shows the design of the phantom employed in this study. The phantom was a polycarbonate tank of dimensions 80mm 50mm 20mm filled with a mixture of Intralipid-20% (Sigma-Aldrich, USA) and India Ink to simulate tissue-like optical parameters (µ a = 0.05cm 1 and µ s = 11.6cm 1 ). 3 cylindrical glass inclusions having a maximum diameter of 7mm distributed over the volume as depicted in Figure 3.5(a) to simulate the distribution of optical properties due to the heart and lungs in the thoracic cavity. The inclusions were filled with the same mixture as the background with additional absorber to create a contrast of

71 55 8x for objects II and III, and 4x for object I. The phantom was illuminated over a 45mm 35mm using 36 bar patterns. The acquisition parameters of the camera were set to 300ps gates at 40ps intervals with a high voltage of 510V. The overall time of acquisition for 36 excitation patterns was less than 12 minutes. (a) Phantom design. (b) Comparing time-gated and CW contrast measures. Figure 3.5: Phantom simulating optically heterogeneous model with optical contrast measures. Figure 3.5(b) shows the normalized Born contrast functions for a single pattern. A comparison of the contrast information provided by the CW and time-gate data type shows the higher resolution provided by the early time-gates. Measurement vectors were constructed for the 5 time-gates shown in Figure 3.5(b) and the Jacobians were constructed for the volume shown in Figure 3.5(a) (white dotted boundary). It should be noted that the volumes represent the 50% iso-volume for each inclusion. The mean absorption coefficient of the reconstructed volume and its diameter are used as metrics to compare the accuracy of the two data types and are provided in Table 3.1 [65] Simultaneous reconstruction of absorption and scattering coefficients. In this experiment we investigated the performance of this system for tomographic reconstruction of absorption and scattering coefficients using the time-gate

72 56 (a) CW reconstruction. (b) Time-gated reconstruction. Figure 3.6: Optical reconstructions of the phantom in Figure 3.5(a) The iso-volume was set at 50% of the maximum reconstructed value. The ray-sum projections are provided on the sides of the reconstructed volume. data type on a murine model phantom. The phantom (Figure 3.7) consisted of a 2cm thick polycarbonate tank carrying a mixture of Intralipid-20% and India ink in (µ a0 = 0.05cm 1 ; µ s0 = 9cm 1 ). Two tubes with 10mm inner diameter were suspended in the tank with India ink and Intralipid-20% solutions added to tubes 1 and 2 to simulate localized contrast in absorption (µ a = 0.4cm 1 ; µ s = 9cm 1 ) and scattering (µ a = 0.05cm 1 ; µ s = 18cm 1 ) respectively. The inclusions were selected to simulate perturbations comparable to the size of large organs (e.g. liver, lungs) in murine models. The intensifier was operated with a gate-width of 300ps at 20ps intervals spanning a 2.2ns time window and two sets of measurements were acquired; first, with Table 3.1: Comparing accuracy in 3D reconstructions Data type Estimation Error (%) Diameter (mm) Incl I Incl II Incl III Incl I Incl II Incl III TG CW

73 57 8, a0 a0 s0, 2 s0 32mm (b) Photon counts (a.u.) 3000 TG TG TG1 500 (c) Photon counts (a.u.) TG TG TG1 500 (d) Gate # (a.u.) Gate # (a.u.) 20mm 35mm (a) (e) (f) (g) Figure 3.7: Reconstruction of µ a and µ s in vitro:(a) Phantom design. (b) Area of pattern illumination. (c)-(d) TPSF measured at the Green and Cyan detectors respectively. (e)-(g) Normalized Born contrast measures at TG1, TG2 and TG3 respectively. the tube containing the background mixture (homogeneous) and second, with the added India ink and Intralipid solutions (heterogeneous). The optimum signal was obtained using 560V across the MCP and an integration time of 50ms per gate on the CCD. The entire acquisition protocol was completed in 9minutes. Figure 3.7(b) shows the comparison of the homogeneous and heterogeneous TPSFs at two point detectors located over the absorption and scattering perturbation. It may be noted that the absorptive perturbation produces higher contrast for later gates while the scattering perturbation has predominant contrast in the early gates with minimal contrast observed in later gates. The normalized born contrast function at three time-gates (TG1 20% of peak intensity on the rising edge, TG2 peak intensity and TG3 50% of peak intensity on the falling edge) across the excited volume shows a distinct separation of the contrast due to the two perturbations with predominant contrast due to the scattering object during the early gate while the scattering perturbation showed minimal contrast during the late gates (Figure 3.7(c)). To solve the inverse problem, the measurement vector was constructed by heuristically selecting 6 time-gates for each detector (8%, 12% and 17% of the peak

74 58 on the rising edge; peak; 80% and 60% of the peak on the falling edge). It should be noted that the time-gates were selected based on the homogeneous measurement. The phantom volume was modelled as a slab discretized into 2mm 2mm 2mm voxels and the Jacobians for perturbations in the scattering and absorption coefficients were computed using the average optical properties photons were launched during the MC simulations. The Jacobians calculated were scaled by their mean-column value to reduce the inter-parameter cross talk. A spatially varying regularization was applied while solving the inverse problem. The regularization parameter was empirically determined to have a value of 10 3 on the source detector layers and on the penultimate layers. (a) Reconstructed absorption coefficient. (b) Reconstructed scattering coefficient. Figure 3.8: 50% iso-volumes of reconstructed perturbations in optical properties. The 3D visualization of the reconstructed optical properties is shown in Figure 3.8. The mean value of the 50% isovolume for both parameters was found to have an error less than 5% (Absorption coefficient, inclusion 1: Expected value = 0.35cm 1, Reconstructed mean value = 0.33cm 1 ; Scattering coefficient, inclusion 2: Expected value = 9.0cm 1, Reconstructed mean value = 8.92cm 1 ) [66].

75 59 (a) Phantom design. (b) Normalized-born contrast measures for the dual-view measurements. Figure 3.9: Depth resolution experiment design and contrast measures. 3.3 Fluorescence Molecular Tomography studies The objective of the Fluorescence Molecular Tomography studies was to establish the performance of this system in resolving the effective quantum yield of a fluorophore embedded in murine models. Specifically, the advantages of time-gate data type in providing improved resolution and allowing the separation of multiplexed molecular markers in vivo are investigated Resolving fluorescent inclusions at different depths. The first test in testing the feasibility of the system in FMT applications, was to determine the effectiveness of this system in resolving fluorescent inclusions lo-

76 60 (a) Using CW data type. (b) Using time-gated data type. Figure 3.10: 3D reconstruction of effective fluorescence quantum yield. The reconstructions shown are 50% iso-volumes of the effective quantum yield. cated at different depths in the tissue. A liquid phantom (shown in Figure 3.9(a)) containing 3 inclusions situated at depths of 3mm, 7.5mm and 11mm from the detector plane was constructed to determine the depth resolution using wide-field excitation strategies. The phantom comprised of a 14mm thick polycarbonate tank holding a mixture of Intralipid-20% (Sigma-Aldrich) and a water-soluble NIR Dye (Epolight 2717, Epolin) diluted in water to simulate the average optical properties of murine models (µ a = 0.16cm 1 and µ s = 17cm 1 ). The fluorescent targets consisted of 3 tubes having an inner diameter of 1.5mm each filled with 2.5nmol of IRDye800CW R (LiCOR Biosciences, USA) in 180µL ethanol (13µM concentration). The experiment protocol employed 36 patterns and 112 detectors evenly spaced over the imaged surface. As shown in Figure 3.3, the asymmetric distribution the sensitivity function is a characteristic of wide-field excitation strategies. In this experiment any bias arising from the asymmetry was mitigated by acquiring a dual-

77 61 view dataset. a second set of excitation and fluorescence measurements were acquired by rotating the phantom by 180 degrees. The acquisition of 115 gates at the excitation and fluorescence wavelengths for 36 patterns in both views was completed in less than 24 minutes ( 6 min per view, per wavelength). The time-gate at 50% of the maximum value of the TPSF was empirically selected as the TG data type based on SNR considerations. Figure 3.9(b) show the normalized-born contrast when using the TG and CW data respectively. It may be noted that contrary to the CW contrast images, all 3 objects are resolved using the TG data type, irrespective of their distance from the surface. A 1cm wide region of the imaged volume (shown in dark red) along the x-axis was reconstructed with 1mm 3 voxel resolution. Figure 3.10 shows the 50% iso-volume of the reconstructed quantum yield. The average effective quantum yield of each object normalized to the maximum value and the mean diameter of the inclusions are used as the figures of merit for relative quantification and resolution (3.2). The time-gate data type provided improved quantification especially for the inclusions closer to the surface with 3% quantification error while the CW data type resulted in 18% error. The TG data type (early gate) also improved resolution, particularly in the central inclusion with the CW reconstruction resulting in a 66% increase in mean diameter [67]. Table 3.2: Comparison of the relative quantification and resolution using CW and TG data types. Data type Relative quantification (a.u.) Mean Diameter (mm) I (Red) II (Green) III (Blue) I (Red) II (Green) III (Blue) TG CW Feasibility of reconstruction in vivo In the second experiment, we investigated the applicability of the wide-field patterned strategy in a small animal model with complex boundaries. Typical approaches to FMT in animal models rely on the use of a matching fluid in which

78 62 the animal is submerged in a scattering medium having optical properties similar to the average optical properties of a murine model. This is done to ensure uniform boundary conditions and known baseline optical properties for an accurate forward model in reconstruction. In the design of this system, a free-space imaging approach was favoured in the interest of its ease-of-use and animal-friendly imaging protocols. This experiment was performed to test the feasibility of this free-space approach when using the wide-field strategies. (a) CT image of the animal model. (b) White-field image showing the span of excitation. (c) Excitation field (d) Normalized born contrast. Figure 3.11: Euthanized animal model for validation of wide-field scheme in murine geometry. In order to simulate an accurate small animal geometry with heterogeneous optical properties, a 13mm long tube(1mm diameter) was placed in the thoracic cavity of a freshly euthanized mouse. The tube contained 14pmol of IRDye 800CW R (LiCOR Biosciences, USA) in 1µL ethanol (Concentration: 14µM. The animal was restrained in the imaging chamber (Figure 3.11(b)) and consecutively imaged on the optical tomography system and a µct scanner (Scanco Viva CT40). The CT scans were used to extract the surface geometry and pinpoint the location of the implanted capillary (Figure 3.11(a)). Fiducial markers placed on the imaging chamber were used to register the CT measurements with the white-field images acquired on the optical platform. It may be noted that no anatomical a priori information was used in the reconstruction. The tomographic imaging protocol used 64 bar

79 63 patterns projected over a 33mm 18mm area across the upper torso of the animal (Figure 3.11(a)). 97 point detectors measured the excitation and fluorescence photons transmitted through the animal (Figure 3.11(c)-(d)). It should be noted that the excitation field shows a localized high intensity spot due to the channelling of light through the chest cavity due to a collapsed lung. A similar channelling of fluorescence photons was observed but cancelled out in the normalized Born scheme. As in the previous experiment, the early gate at 25% of the maximum value was Figure 3.12: (Left) 3D reconstruction showing the 50% iso-volume of reconstructed object. (Right) Coronal slice of the reconstructed volume at z = 6.5mm and transverse slice of the volume at y = 21.5mm. empirically selected as the data type and the corresponding weight functions were computed using the average background properties of the small animal thoracic cavity (µ a = 0.3cm 1 and µ s = 25cm 1 ) [81]. Figure 3.12 shows the 50% iso-volume of the reconstructed effective quantum yield. Moreover, the transverse and coronal cross-sections of the reconstructed volume overlaid on the corresponding CT slices validate the accurate localization of the inclusion in the chest cavity. The 50% isovolume of the reconstructed inclusion had a maximum length of 10.8mm and mean diameter of 3mm across the length of the tube.

80 Separating fluorophores based on lifetime contrast The final experiment in this set of FMT studies focused on the advantages of using time-gated datasets to separate and localize multiple fluorophores in the medium based on a contrast in their lifetime. The design of the phantom used for this test consisted of two tubes having an inner diameter of 1.5mm positioned in the center of a liquid phantom in a 14mm thick polycarbonate tank(c.f. Figure 3.13(a)). To achieve lifetime contrast, tube I, II were filled with 2.5nmol of Indocyanine Green (τ 1 = 0.45ns) and IRDye 800CW (τ 2 = 0.8ns) dissolved in 180µL ethanol, respectively. The effective quantum yield of the two tubes was externally calibrated and tube I was found to have 1.5 times the yield of tube II (Concentration of 14µM each). The tank was filled with a mixture of Intralipid-20% (Sigma-Aldrich) and a water-soluble NIR Dye (Epolight 2717, Epolin) diluted in water to simulate the average optical properties (µ a = 0.16cm 1 and µ s = 17cm 1 ) of murine models. (a) Phantom design. (b) Normalized-born contrast measures for timegated measurements. Figure 3.13: Phantom design to study the 3D localization and separability of fluorescent markers based on lifetime contrast. The normalized Born contrast functions for the late time-gates are shown in Figure 3.13(b). It is worth noting that as the time-gate progresses from the

81 65 maximumgatetothelategateat20%, thereducedlifetimeoficg(lefttube)results in a change in the contrast function profile with Tube II providing the maximum contrast due to its longer lifetime. To achieve better separation between the two fluorophores while maintaining resolution, the early gate at 50%, the maximum and the late gate at 75%, 50%, 25% were chosen as the data type for reconstruction. Furthermore, gates with less than 400 photons were discarded in the reconstruction process to maintain an appropriate signal-to-noise ratio (SNR). (a) τ 1 = 450ps (b) τ 1 = 800ps Figure 3.14: 50% iso-volumes of reconstructed concentrations at two different lifetimes. The reconstruction results are shown in Figure In order to quantify the quality of fluorophore separation, the crosstalk was defined as X 1 = max[η 2(Ω 1 )] max[η 1 (Ω1)] X 2 = max[η 1(Ω 2 )] max[η 2 (Ω2)] (3.7) where, Ω k is the reconstructed volume for the k th fluorophore. The two objects are separated with crosstalk X 1 = 31.23% and X 2 = 28.77%. The ratio of the mean reconstructed yields within the 50% iso-volume of tube I and II was found to be The average dimension of the reconstructed tubes was 37.5% larger along the x axis and 87.5% larger along the z axis (depth). This result is consistent with the reconstructed dimensions of the central tube in Section

82 Summary In conclusion, the protocol for the application of this platform to functional and fluorescence imaging studies in murine models was outlined. The accuracy and applicability of this platform for the range of applications of optical imaging. Specifically, the studies investigated efficacy of the system for 3D reconstruction of perturbations in absorption and scattering coefficients, reconstruction of effective quantum yield of fluorescent inclusions and lifetime multiplexed fluorescence tomography applications based on lifetime contrast. The results of the above studies establish the feasibility of the wide-field excitation scheme as a effective substitute for the point source imaging paradigm. More importantly, the adoption of the wide-field schemes has provided a ten-fold improvement in the acquisition time. A second outcome of these studies has been the successful demonstration of the use of time-gates in wide-field illumination scheme as a viable measurement data type. The complementary information provided by the early gate (resolution) and late gates (lifetime contrast) provide an information-rich data set for the accurate reconstruction of the fluorescence and functional parameters in small animal models.

83 Chapter 4 Techniques for robust reconstruction performance using time-gated measurements As demonstrated in Chapter 3, time-gate data types derived from temporal measurements provide a very powerful measurement in optical tomography. However, the sensitivity of the instrumentation used in the collection of time-resolved measurements makes them significantly more susceptible to noise. The addition of noise to the signal can have a severe influence on the accuracy of the technique especially when using the time-gates directly as a data type [50]. In this chapter, the effect of noise on FMT studies will be discussed exclusively as the lower intensity of fluorescence signals transmitted through an animal model results in a measurement vector with low SNR. The most common forms of noise in time-resolved measurement can have either a temporal nature or intensity/amplitude based characteristics. The effect of noise can be potentially exacerbated when using the normalized born reconstruction scheme, wherein, the fluorescence signal is normalized by the excitation signal. In this chapter, the effect of these types of noise in time-resolved measurements on the accuracy of tomographic reconstruction when using different normalization schemes is investigated. Specifically, the effect of noise on the measurement vector and correspondingly on the reconstruction is first investigated through an in silico study. Next, a spatio-temporal filtering scheme is described and its impact on the noise level in time-gated measurement errors is demonstrated. Lastly, the efficacy of the filtering scheme is investigated in the reconstruction of experimental data. 4.1 Noise in time-gated measurements The sources of noise in time-resolved instrumentation can be classified into two categories: a) intensity noise or photon noise and, b) temporal noise or timing errors. Both of these forms of noise are uncorrelated signal variations which result in an error in the photon counts recorded at each of the time-gates. In this section, each of 67

84 68 the above sources of noise are detailed and their impact on different sections of the temporal point spread function (TPSF) are discussed. For the purposes of analysis in this section and the rest of this chapter, the TPSF has been broadly classified into the early portion (rising part) or the late portion (decaying part). As stated in the earlier chapters, the early portions correspond to minimally scattered photons while the late gates represent photons on the decaying portion of the TPSF which retain the lifetime characteristics of the fluorophore. The early gates typically reject a significant number of the arriving photons and have low signal levels. Furthermore, the high rate of change of photon intensity in the early portion of the TPSF can lead to significant variations in the recorded photon counts in the early gates due to noise Intensity noise Intensity noise or photon noise is defined as the deviation in the number of recorded photons at each time-gate due to errors in photon counting. Variations in recorded photon counts can arise due to source power drift and/or amplification errors introduced in the detector system. Typically, the detector components are more susceptible to intensity noise errors as the image formation process in photon counting technologies (Intensified CCD cameras, Time Correlated Single Photon Counting modules etc.) used for time-resolved imaging relies on the photoelectronic conversion of photons and the amplification of signal intensity based on electron amplification. In this chapter, the focus will be on the sources of intensity errors in ICCD based camera systems. As discussed in Chapter 2, the detector shot noise, CCD and intensifier dark noise and CCD read out noise are the primary sources of intensity noise in the Intensified CCD camera system used in this platform. Several of these sources of noise can be mitigated by selection of appropriate protocol measures. For instance, the dark noise errors in CCD and intensifier systems are dependent on temperature and can be controlled by employing cooling systems which ensure operation of these components at a lower temperature ( 11 C for the ICCD system employed herein). Furthermore, reducing variations in room temperature can improve the

85 Relative error in photon counts (%) Relative error in photon counts (%) 69 Normalized photon counts (a.u.) Normalized photon counts (a.u.) Pure signal 10 Noisy signal 10-1 Time (ps) (a) Pure signal Photon count error Time (ps) (c) Normalized photon counts (a.u.) Normalized photon counts (a.u.) Time (ps) (b) Time (ps) (d) Pure signal Noisy signal Pure signal Photon count error Figure 4.1: (a) Measurement with added poisson noise, (b) Measurement with timing error of 20ps, (c) Relative measurement error due to poisson noise shown in (a). (d) Relative measurement error due to temporal noise shown in (b). noise performance of these systems and reduce dark noise errors. Moreover, sufficient warm-up time and subsequent background subtraction mitigates errors due to dark noise. CCD read-out noise arise from errors in incorrect electron read-outs from the CCD chip. This form of noise can be minimized by employing appropriate hardware binning strategies. In case of CCD based detector systems, the high spatial density of detectors allows for the possibility of an appropriate pixel binning to be applied on the recorded images without affecting the resolution of the time-gated measurements. The last form of noise, shot noise, refers to uncertainties in the recorded photon counts arising from the photon-electronic conversion process at different stages of the image formation mechanism of the ICCD system. Specifically, at the photo-cathode (photons to electrons), the phosphor screen (electrons to photons) and lastly on the CCD chip (photons to electrons). The shot noise is an unavoidable form of noise

86 70 and is the most common source of error in time-resolved measurements. It has a poisson distribution with the standard deviation dependent on the N, where N is the number of detected photons. Figure 4.1(a) shows an example of temporal measurement with added poisson noise. The relative errors in measured photons given in Figure 4.1(c) identify the maximal effect of shot noise on the gates with low photon counts on the early and late portion of the TPSF. These gates play an important role in the two unique aspects of the time-resolved measurements (high resolution and lifetime contrast) and can introduce significant errors in reconstruction Temporal noise Temporal errors comprise of variations in recorded photon counts due to timing drift and jitter. These error can also arise from timing uncertainties on both the source and detector subsystems. The variations in pulse generation times in the pulsed laser module is the prime cause of timing errors in the source subsystem and errors in trigger generation mechanism (due to variations in temperature etc.) lead to drift and jitter in the recorded temporal signals. Typical approaches towards alleviating timing errors rely on the use of an independent reference channel which can recalibrate the measurements in time. While this approach can reduce errors due to source drift and jitter, the uncorrelated timing errors between the detector system and the reference channel can retain and even exacerbate the effect of temporal errors on the measurements. The effect of temporal errors are further amplified in the case of systems employing discrete TCSPC detector modules as each channel can have an uncorrelated timing error. Conversely, ICCD systems while susceptible to timing jitter are more robust as the temporal errors are correlated for all detectors (or pixels) in the camera. While this does not preclude the possibility of timing non-linearities across the CCD, the correlated nature of these errors makes it easier to apply a correction on recorded measurements. Figure 4.1(b) shows an example of a temporal measurement with a 20ps offset in the recorded signal. Note that the temporal resolution of the pure signal is twice the jitter (at 40ps), however, the temporal error results in over 500% error in the recorded photon counts on the early portion of the TPSF due to the high rate of change in counts in this portion of the

87 71 TPSF. It is therefore understood that while both these sources of error in timeresolved imaging systems can be reduced by appropriate protocol measures, they may not be completely avoided and can have a significant impact on the early and late gate sections of the TPSF. Furthermore, both sources of error exist simultaneously in time resolved systems and appropriate data type processing and calibration techniques are necessary to reduce their effect on reconstruction performance. 4.2 Normalization methods As noted in Chapter 3, measurement data types derived from the time-gated measurements typically implement a normalized Born form. Specifically, this refers to the normalization of the fluorescence time-gate measurement by the excitation signal which allows for the minimization of the effect of optical properties on the accuracy of the forward model. While the generation of the normalized Born data type is relatively simple in the case of CW measurements, the selection of an appropriate normalization scheme becomes important when using time-gated measurements. This is especially critical in light of the sources of noise detailed in Section 4.1 as uncorrelated variations in the excitation and fluorescence signals can introduce significant errors in to measurement data type. Normalized photon counts (a.u.) Fluorescence signal Excitation signal Normalized photon counts (a.u.) Fluorescence signal Excitation signal Normalized photon counts (a.u.) Fluorescence signal Excitation signal Time (ps) Time (ps) Time (ps) (a) (b) (c) Figure 4.2: (a) Type I normalization scheme (TG 1 ems/cw exc ), (b) Type II normalization (TG 1 ems/tg 2 exc) and (c) Type III Normalization (TG 1 ems/tg 1 exc). The light green marker represents the excitation data type and the dark green marker identifies the fluorescence measurement. In this section, three normalization schemes which can be considered for gener-

88 72 ation of the normalized Born data type in time-resolved measurements are outlined. Type I normalization (Figure 4.2(a)) refers to the normalization of the time-gate fluorescence measurement by the CW (integrated) excitation signal measurement. Type II normalization (Figure 4.2(b)) is the normalization of the time-gate fluorescence measurement by the equivalent time-gate in the excitation channel. e.g. a measurement at 50% of the decaying portion in the fluorescence signal is normalized by the time-gate at the 50% of the decaying portion of the excitation TPSF for the same detector. And lastly, Type III normalization refers to the normalization of the fluorescence time-gate by the excitation time-gate at the same time point. However, due to the longer temporal span of fluorescence measurements, this normalization scheme is limited for use in early gate reconstruction. Among the three schemes, Type I normalization has been employed extensively in this thesis and also more recently investigations on multiple time-gate based FMT reconstruction [78, 82]. The application of the Type III normalization has been demonstrated in early photon tomography studies and Type II normalization is a new scheme devised to avoid the limitation of the type III normalization scheme owing to differences in temporal span. In this chapter, the effect of these three schemes on measurement fidelity will be investigated in silico and in vitro. It is expected that uncorrelated temporal and intensity noise in the excitation and fluorescence channel will introduce significantly larger errors when using time-gate based Type II and Type III normalization, while Type I normalization will only be susceptible to errors due to noise in the fluorescence channel. 4.3 In silico investigation of noise characteristics A simulation based study was undertaken in order to assess the impact of the intensity and temporal errors on the measurement data types used for reconstruction using each of the above normalization schemes. Furthermore, the subsequent effect of the measurement errors on reconstruction using the early gates and late gates was investigated by performing the tomographic reconstruction of two fluorescent inclusions in a synthetic mouse model.

89 Synthetic model The small animal volume was accurately simulated using the Digimouse animal model (c.f. Figure 4.3) [83]. In this study, two fluorescent inclusions 3 3 3mm 3 in dimension were placed in the chest cavity surrounded by the highly absorbing and scattering lungs and heart. The optical properties for the different organs in this volume was assigned based on values in the literature and have been tabulated in Table 4.1. The two inclusions were assigned fluorescence parameters exhibiting contrast in lifetime. Specifically, co localized fluorescence condition was simulated by assigning Inclusion I (Blue inclusion in Figure 4.3) two lifetime components with lifetimes of 290ps and 1100ps in equal proportion. Inclusion II had only a single component with lifetime of 1100ps. Heart Lungs Fluorophore 1 Fluorophore 2 Liver Figure 4.3: Mouse model employed in in silico investigation of error propagation in FMT reconstruction. The red inclusion has a single exponential lifetime of 1100ps while the blue inclusion has 50% 290ps fluorescence component and a 50% 1100ps component Measurement generation and noise simulation The time-resolved measurements for this model were simulated using the perturbation Monte Carlo model for excitation and the Monte Carlo fluorescence forward model described by Chen et al for fluorescence measurements [78]. In com-

90 74 Table 4.1: Optical properties of murine organs used for noise model simulation Tissue type µ a (cm 1 ) µ s (cm 1 ) Heart Lungs Liver Bone Muscle puting the solution to the forward model, the organs in the model were assumed to have equal optical properties at excitation and emission wavelengths to reduce the computational burden. This assumption has limited effect on the accuracy of the model and does not affect the effect of noise investigated herein [78]. The separate simulation of fluorescence measurements ensured that the inverse crime problem was avoided. The fluorescence measurements were computed for 36 bar patterns as the excitation source and 88 point detectors spanning the imaging volume (thoracic cavity) at a separation of 2mm. An experimentally recorded Instrument Response Function (IRF) was convolved with simulated measurements to implement the effect of 300ps gate integration and generate temporal signals with a temporal resolution of 40ps (comparable to time intervals employed in all studies described in this work). The temporal noise was added by applying a uniformly random jitter over a range of ±dps on the IRF before convolution. The values of d were selected as 5ps, 10ps and 20ps. While the first two values simulate the jitter encountered in TCSPC modules [84], the 20ps jitter was based upon the maximum jitter in the ICCD system (as provided by the manufacturer). The intensity noise was simulated using a poisson noise model. As the shot noise is encountered during image formation at each gate, the imnoise function in MATLAB (MathWorks, Natick, MA) was used to generate intensity based shot noise for an image derived from the detector reading at each gate. The lower signal levels in the case of fluorescence measurements results in higher intensity noise (c.f Figure 2.18(c)) in the measured TPSF (especially when employing high MCP voltage for

91 75 optimal signal level. Conversely, the excitation signal which has a higher signal intensity has much lower intensity noise. Therefore, the poisson noise was added only to the fluorescence measurements which are more susceptible to shot noise errors Effect of noise on measurement data type The effect of the noise on measurement errors was quantified using the metric given in Equation 4.1. ɛ = mean( Un i U p i U p i ) (4.1) In Equation 4.1, U n and U p refer to the noisy and noiseless measurements respectively and i (1...sd) where, sd is the number of source detector pairs employed. In order to estimate statistically significant measurement errors (due to random nature of noise added to the measurements), 50 measurement sets were simulated. The results from the error analysis are given below Temporal noise errors Measurement error (%) Type I Normalization Type II Normalization Type III Normalization Measurement error (%) Type I Normalization Type II Normalization Measurement error (%) Type I Normalization Type II Normalization Timing jitter (ps) Timing jitter (ps) Timing jitter (ps) (a) (b) (c) Figure 4.4: Measurement error for different values of timing jitter when using (a) early gate at 20%, (b) maximum gate and (c) late gate at 20%. In the first study, the effect on temporal noise was investigated for three gates representative of the early gate (20%), maximum gate and late gate (20%) respectively. It should be noted that Type III normalization was not considered for the investigations on the effect of temporal errors on maximum gate and late gate due

92 76 to the absence of a corresponding excitation time-gate at these time points. As expected, Figure 4.5(a)-(c) show the increasing measurement error with temporal drift. It should be noted that the early gate is more sensitive to temporal errors as observed in Figure 4.1(d) with a maximum error of 25% for drift of 20ps. Upon comparing the two time-gate normalization schemes, the Type II normalization was found to be most sensitive to the temporal errors. This can be attributed to the fact that normalization by the corresponding excitation time-gate for early gates results in selection of measurements from early portion of the excitation signal which is itself prone to temporal errors due to high rate of change in photon count. On the other hand, Type III normalization results in the selection of excitation gate closer to the peak intensity value resulting in lower measurement errors. Similar comparison of the Type I and Type II normalization scheme for the maximum and late gates shows a significantly lower measurement error as expected Gate-wise error analysis In the next study, the effect of temporal and intensity noise when using the three normalization schemes were investigated. Specifically, three cases were considered, temporal noise only, intensity noise only and both intensity and temporal noise. The analysis of the resulting measurement errors was done for multiple timegates equally spaced over the range from 10% on the early portion to 10% on the late portion. It should be noted that the Type III normalization was restricted to the early portion of the TPSF due to the limitations of the scheme described previously. Moreover, a maximum temporal jitter of 20ps was assigned to all temporal noise simulated herein. It is observed that Type I normalization results in lowest errors for all cases considered. Figure 4.5(a) shows the errors arising from temporal noise only and similar to the analysis shown in Section , Type II normalization is more sensitive to temporal errors for early gates. However, the error drops rapidly as later gates are considered. Conversely, Type III normalization is highly unstable in the case of intensity errors as observed in Figures 4.5(b) and(c). It is worth noting that in the case of intensity errors, Type I and Type II schemes have similar errors.

93 77 Measurement error (%) Type I Normalization Type II Normalization Type III Normalization Measurement error (%) Type I Normalization Type II Normalization Type III Normalization Measurement Error (%) Gate position (% of peak count) (a) Type I Normalization Type II Normalization Type III Normalization Gate position (% of peak count) (b) Gate position (% of peak count) (c) Figure 4.5: (a) Measurement error due to temporal errors only, (b) Measurement error due to intensity errors only and (c) Measurement error due to both temporal and intensity errors. However, the sensitivity of Type II scheme to temporal errors results in a higher error than Type I scheme when both temporal and intensity errors are considered. And lastly, it can be concluded that all three normalization schemes are more sensitive to intensity errors which result in higher measurement errors Tomographic reconstruction performance In this section, the propagation of the errors observed in each of the cases considered in Section in tomographic reconstruction is investigated. The time-gate measurements are divided into two groups. The first comprising of a single time-gate measurement at 20% on the rising portion for each of the 88 detectors for

94 78 the 36 excitation patterns. The second set includes the maximum time-gate and the 25% time-gate on the decaying portion of the curve Early gate reconstruction Type I Normalization Type II Normalization Type III Normalization Noiseless signal With temporal noise With intensity noise With temporal and intensity noise (a) (b) (c) (d) (e) (f) (g) (h) (i) (j) (k) (l) Figure 4.6: Total reconstructed fluorescence yield from both components at the central axial slice thresholded at 50%. Reconstruction employed (a)-(c) pure measurement vector, (d)-(f) added temporal noise, (g)-(i) added intensity noise and (j)-(l) added temporal and intensity noise. Figure 4.6(a)-(c) shows the reconstruction using the early gate set for the pure signal to determine the best quality benchmark. All reconstructions for this data set were performed using 20 iterations of the lsqr algorithm. It is worth noting that the resolution is not affected by the different normalization schemes. The effect of temporal noise on reconstruction performance as shown in Figure 4.6(d)-(e) follows

95 79 the trend observed in Figure 4.5(a), wherein, Type II normalization scheme has the poorest reconstruction performance. While Type III normalization scheme is also sensitive to temporal errors (albeit to a lesser degree), the Type I normalization scheme is shown to be more robust to temporal errors. When considering the case with intensity errors (c.f. 4.6(d)-(f)), the reconstruction performance improved with better reconstruction of both objects when using Type I and Type III normalization schemes with both schemes resulting in comparable reconstructions. Type II normalization displays poor performance with fragmentation of the reconstructed object. And finally when considering the case with both temporal and intensity errors (c.f. 4.6(d)-(f)), the Type I normalization scheme is shown to be the most robust resulting in localized results comparable to ground truth. The time-gate based normalization schemes (Type II and Type III) result in poor reconstruction with severe fragmentation of reconstructed objects. It can be concluded that, when using early gates for reconstruction, temporal noise has a dominant effect on the reconstruction performance. The use of time-gate based normalization schemes results in poor resolution which is characterized by the breakdown of the object and increase in surface artifacts. It is worth noting that in agreement with the trend observed in Figure 4.5(a), Type I normalization scheme provides the best reconstruction for all noise models considered Late gate reconstruction The reconstruction of the two fluorescent inclusion using the late gate sets focussed on the quantitative separation of the two objects based on lifetime contrast. In this regard, the absolute error in the estimation of the shorter lifetime component (290ps) was selected as the performance metric. The reconstruction for all gate sets was done using 30 iterations of the lsqr algorithm. It should be noted that Type III normalization scheme was not included in this analysis due to the absence of corresponding excitation gates at these time points. Figure 4.7(a)-(b) and 4.7(c)-(d) show the reconstruction of the two lifetime components at 290ps and 1100ps respectively for Type I and Type II normalization schemes. It should be noted that in both normalization schemes provide compa-

96 80 Type I Normalization Type II Normalization = 290ps = 1100ps = 290ps = 1100ps Noiseless signal (a) (b) With temporal noise (c) (d) With intensity noise With temporal and intensity noise (e) (f) (g) (h) 0.0 Figure 4.7: Reconstructed fluorescence yield for shorter and longer lifetime component at the central axial slice thresholded at 50%. Reconstruction employed (a)-(b) pure measurement vector, (c)-(d) added temporal noise, (e)-(f) added intensity noise and (g)-(h) added temporal and intensity noise. rable localization and quantification with neither scheme outperforming the other. However, in the presence of temporal errors, the Type II normalization scheme results in poorer resolution and boundary artifacts indicating instability in the fitting procedure due to the noise. Type I normalization however is minimally affected and provides quantification and localization comparable to the noiseless case (c.f. Figure 4.7(e)-(h)). Upon the addition of intensity errors to the signal, both normalization schemes are affected with poorer resolution and object fragmentation. This effect is visible in the case when considering signals with temporal and intensity errors. The performance metrics derived from the above reconstructions are compiled in Table

97 Table 4.2: Errors in the estimation of shorter lifetime component - in silico Measurement Pure signal With temporal errors With intensity errors With temporal and intensity errors Absolute estimation error (%) Normalization scheme Inclusion 1 Inclusion It should be noted that the estimation errors are less than 5% when only temporal and intensity errors are added to the signal. Furthermore, in all cases the errors when using Type II normalization scheme are larger, although by a very small margin. The higher errors observed for the quantification of Inclusion II may be attributed to the use of limited number of sub-optimal time-gates. It can be argued that the selection of optimal time-gates for reconstruction will significantly reduce the cross talk observed in Inclusion II. In such cases Type I normalization scheme will provide better quantitative performance. 4.4 Spatio-temporal noise filtering The results of the analysis of the in silico investigation establish that both temporal and intensity errors have a significant impact on the quality of reconstruction when using early gate data types and minimal impact when using late gate data types. While the temporal errors can be mitigated by the use of a reference channel, it can never be completely avoided and will always present a source of error. It can however be minimized by selection of appropriate system operation protocols ensuring sufficient warm up of the electronics and an accurate control of ambient

98 82 t y x Gate 1 Gate 2 Gate 3 Gate 4 Gate 5 Gate n-1 Gate n Normalized photon counts (a.u.) Simulated TPSF TPSF with Poisson and Temporal noise (a) Time (ps) (b) Normalized photon counts (a.u.) Simulated TPSF Filtered TPSF Measurement error (%) Type I Normalization Type II Normalization Type III Normalization Time (ps) (c) Gate position (% of peak count) (d) Figure 4.8: (a) Filtering scheme showing 3D arrangement of measurements. (b) Example of TPSF with both temporal and poisson errors. (c) Filtered TPSF. (d) Measurement errors when using filtered signals. temperature. In this section a data filtering method which removes intensity noise errors (and thereby reduces reconstruction artifacts) is discussed. The fundamental principle in this filtering algorithm is the transformation of poisson statistics to a normal distribution when the value of N is large due to the central limit theorem. This is a valid assumption as the poisson statistics are integrated over the time of the gate-width during ICCD operation. As observed in the examples of temporal measurements with poisson noise (c.f. Figure 4.1(a)), the poisson noise manifest as random variations in photon counts at each gate. In order to simultaneously filter the noise from the spatial and temporal domain, the

99 83 temporal measurements are arranged in a three-dimensional matrix (as shown in Figure 4.8(a)) for each excitation source. Next a 3-dimensional filter is applied to this measurement set using the fspecial3 function available from MathWorks File Exchange. The filter performs a block-wise operation on the data set while applying a gaussian filter simultaneously on the temporal and spatial measurements. As the filtering process is applied on measurements acquired from a single excitation pattern at a time, any uncorrelated temporal noise arising from source variations is not corrected. It should be noted that the application of this filtering process on the temporal measurements derived from discrete TCSPC detectors exhibiting uncorrelated temporal errors will allow the smoothing of photon errors between neighbouring detectors due to timing jitter. Figure 4.8(b)-(c) show the comparison of temporal measurements exhibiting temporal and poisson errors before and after filtering respectively. The qualitative assessment of the measurements establish the successful removal of intensity noise. In order to quantitatively analyse the effect of the filtering process on the measurement error the method is applied to the noisy data sets simulated in Section The measurement error in the filtered data shown in Figure 4.8(d) shows a reduction of error when using the Type III normalization scheme by an order of magnitude. The Type I and Type II schemes exhibit a smaller yet significant reduction in the measurement error with error values approaching the errors due to addition of temporal errors. It is thus concluded that the spatio-temporal filtering scheme successfully reduces measurement errors arising from intensity noise. 4.5 Experimental validation In this section, the performance of the filtering method when using experimental data is investigated in vitro. In order to simulate a lifetime multiplexing model similar to the in silico model, a FMT imaging study of FRET effect is considered. Chapter 6 discusses the details of FRET tomography. In this case, the weak fluorescence signals in FRET imaging make it a suitable model for analysing the effect of noise on FMT quantification and also the efficacy of the filtering method described in the previous section.

100 Experiment design The tissue-mimicking phantom with heterogeneous distribution of optical properties carrying a NIR FRET pair Alexa Fluor R 700 and Alexa Fluo R 750. Figures 4.9(a)-(b) show the design of the phantom identifying the locations of absorptive and scattering perturbations. The phantom was constructed using agarose with a water-soluble NIR Dye (Epolight 2717, Epolin) as the absorber and TiO 2 as the scattering agent. The optical properties of the different regions in the phantom were measured using time-resolved spectroscopy and are provided in Table 4.2. Perturbation I Perturbation II Incl. 1: Af700 Incl 2: Af700 +Af750 22mm (a) (b) Normalized photon counts Fluorescence signal Inclusion I Fluorescence signal Inclusion II Excitation signal Time (ps) (c) Normalized photon counts (a.u.) Fluorescence signal Inclusion I Fluorescence signal Inlcusion II Excitation signal Time (ps) (d) Figure 4.9: (a) MRI image of phantom used for validation of reconstruction. (b) Phantom design identifying the fluorescent inclusions and the perturbative optical property distribution. (c) Example of raw temporal measurement recorded exhibiting intensity noise. (d) Filtered TPSF which shows a significant reduction in the intensity noise level in these measurements. The measurement acquisition scheme employed 36 bar patterns as the excitation source and 99 point detectors spanning the imaging volume at a 3mm separation. The temporal measurements were acquired using 400ps time-gates at a

101 85 Table 4.3: Optical properties of the phantom. µ a cm 1 µ s cm 1 Bulk Inclusion Inclusion temporal resolution of 40ps. The fluorescence measurements were acquired at an integration time of 600ms and excitation signals were measured at 50ms exposure time Results A comparison the fluorescence signals recorded at detectors directly above the two inclusions indicates a contrast in lifetime and more importantly, the effect of noise on the excitation at fluorescence signal. As observed in the results of the filtering process applied to the synthetic measurements, the spatio-temporal filtering successfully reduced intensity noise in the temporal measurements. In order to investigate the advantage of this approach in tomographic performance, measurements derived from time-gates at 20% on the rising portion of the TPSF were selected as the early gate set. The late gate set employed 5 time-gates spanning the decaying portion of the TPSF from maximum gate to the gate at 25% Early gate reconstruction Figure 4.10 shows the 50% iso-countour of the reconstructed total fluorescence yield for the central axial slice. Figures 4.10(a)-(c) show the results obtained when using the noisy raw data directly for reconstruction while Figures 4.10(d)-(e) employ measurement data types derived from filtered the dataset. The noise present in the data results primarily in localization errors. It should be noted that Inclusion II is consistently reconstructed with a localization error of 2mm and any deviation from that position, including object fragmentation is considered as localization error. A comparison of figures 4.10(a) and 4.10(d) demonstrates the artifacts resulting from noise in the measurements resulting in

102 86 Using noisy measurements Using filtered measurements 5mm 5mm Type I Normalization 5mm Type II Normalization 5mm Type III Normalization (a) (b) (c) 5mm 5mm (d) (e) (f) Figure 4.10: Total reconstructed fluorescence yield from both components at the central axial slice thresholded at 50%. Reconstruction employed (a)-(c) noisy raw signal, (d)-(f) filtered signal poor resolution of the reconstructed object. Contrary, to the in silico studies, the use of time-gated measurements does not result in a complete breakdown of the reconstruction (e.g. Type II normalization). This can be attributed to lower measurement jitter in the platform (2ps) as opposed to the maximum possible value of 20ps which was simulated in the simulation studies. Figures 4.10(b) and 4.10(c) exhibit a better performance of the Type II normalization compared to the Type III normalization scheme, indicating a predominant effect of intensity errors. While the filtering reduces the artifacts in the reconstructed volume, the localization error is exacerbated when using the Type II and Type III normalization schemes Late gate reconstruction Figure 4.11 shows the results of the reconstructions for the 4 cases comparing the 2 normalization schemes for the filtered and unfiltered signals. The quantification metric is the relative concentration of the shorter lifetime component (donor under FRET) which is derived from the maximum reconstructed concentration for each inclusion. The expected relative concentration for each inclusion was 0% and 40% respectively. A qualitative assessment of the localization accuracy and quan-

103 87 tification indicates identical performance of the two signal data sets. However, while the signal noise level does not affect the reconstruction as significantly as expected, the Type II normalization fails in both cases when using the late gates. This is signified by poor resolution of the shorter lifetime component when using Type II normalization (c.f. Figure 4.11(b) and 4.11(d)). Type I Normalization Type II Normalization Using noisy measurements Using filtered measurements 5mm = 290ps = 1100ps = 290ps = 1100ps 5mm 5mm 5mm 5mm (a) (b) = 290ps = 1100ps = 290ps = 1100ps (c) 5mm 5mm (d) 5mm Figure 4.11: Reconstructed fluorescence yield for shorter and longer lifetime component at the central axial slice thresholded at 50%.Reconstruction employed (a)-(b) noisy raw signal, (c)- (d) filtered signal. For a more quantitative comparison of the quality of reconstruction, absolute errors in the estimation of concentration of are compiled in Table 4.4. Table 4.4: Errors in the estimation of relative concentration of the FRETing donor component - in vitro Measurement Using noisy measurements Using filtered measurements Absolute estimation error (%) Normalization scheme Inclusion 1 Inclusion 2 I 41 9 II I 31 5 II 19 25

104 88 Based upon the performance metric, it can be concluded that the filtering of the signal reduces the estimation error by 10% for the Type I normalization scheme. The relatively higher robustness observed when comparing the reconstructions done using filtered and unfiltered signals can be ascribed to the use of multiple time-gates. In other words, the use of multiple gate (5) measurements spanning the decaying portion of the TPSF results in the model fitting to a trend in the photon counts at the different gates and not the absolute counts themselves. The iterative least-squares solver therefore acts as a low-pass filter with the role of the noise becoming critical only when the iteration number if very high. 4.6 Discussion In conclusion, the effect of system noise on tomographic reconstruction was investigated using in silico and in vitro studies. Two forms of noise were identified as the main source of error when directly using time-gated measurements for reconstruction. The temporal noise referring to noise arising from timing errors and the intensity noise due to the photon-starved operation of the ICCD resulting in high level of shot noise. The comparison of the effect of noise on the various time-gated reconstruction data types was done using a comparison of three normalization schemes. The first employed normalization by CW measurement of the excitation signal, Type II selected the equivalent time-gate and Type III used the corresponding time-gate. Among the three schemes, CW normalization is most robust due to the absence of any temporal influence on the normalizing measurement. In other words, the uncorrelated temporal noise due to drift and jitter (irrespective of magnitude) can result in significant errors in the constructed measurement vector. This effect was confirmed in tomographic reconstruction wherein, both time-gate based normalization schemes were adversely affected by the added noise while the Type I normalization was able to retain fidelity in its measurements. Lastly, a new filtering method, based on the simultaneous filtering of noise from temporal measurements in both spatial and temporal domains was developed to reduce the effect of intensity errors on quantification in lifetime multiplexing

105 89 studies. The application of this technique to synthetically simulated data resulted in a 50% reduction in average errors for all three normalization schemes. It should be noted that the application of such filtering methods can be extended to lifetime estimation studies wherein, the multi-exponential fitting model is highly sensitive to noise in the the temporal measurement. The efficacy of this filtering technique was validated using experimental measurements where the filtering of intensity noise resulted in the robust reconstruction of the two objects when using early gate data type and a 10% improvement in quantitative accuracy when using the late gate data type.

106 Chapter 5 Adaptive full-field optical tomography As demonstrated in Chapter 3, wide-field excitation schemes play a significant role in improving experimental performances in optical tomography applications. The advantages of these schemes include a reduced acquisition time, scalability and improved SNR in fluorescence tomography studies. However as noted previously, the pattern set employed in the preliminary studies are not optimized a priori. In this chapter, the measurement-guided optimization of these patterns for improved reconstruction performance is discussed. The fundamental approach to pattern optimization is discussed in Section 1 and the iterative algorithm is detailed in Section 2. This is followed by in silico and in vitro validation of this approach including a quantification of performance improvement in tomographic studies when using the optimized pattern set in Section Measurement-guided pattern optimization Despite developments in wide-field patterned excitation schemes, the highlyscattering interaction of photons in the near-infrared spectral range coupled with the reduction in sensitivity due to full-field illumination presents a highly ill-posed inverse problem in FMT. An approach towards reducing the ill-posedness in the inverse problem is to maximize the information in the recorded measurements. As in the case of classical optical tomography techniques, this can be achieved by using advanced measurement data types in the frequency-domain (FD) and time-domain (TD). Alternatively, wide-field FMT provides an approach wherein the recorded tomographic information can be maximized by optimizing the excitation pattern employed. In this regard, a recently developed model-based method employs an optimization procedure incorporating the a priori knowledge of animal geometry and distribution of optical properties in vivo [68]. However the intra-species variability of these parameters necessitates a subject-specific optimization protocol. This limits its application in experimental settings due to the extreme computational burden 90

107 91 associated with this approach. Moreover, the model-based optimization of patterns does not ensure the quality of measurements (for instance, high SNR) obtained in experimental settings rendering such an approach impractical for experimental implementation. Figure 5.1: (a) Small animal model imaged in wide-field optical tomography using full-field pattern marked by the red boundary. (b) Dynamic range of measured photon counts for the pattern shown in (a) at the excitation wavelength. In this chapter, we present a new wide-field optical tomography technique, referred to as Adaptive Full-Field Tomography (AFFT), wherein the excitation patterns are iteratively updated during acquisition to maximize the information content in the recorded measurements. Specifically, this approach aims to increase the number of tomographic projections acquired with high SNR by reducing the large dynamic range in photons transmitted through the model. This is achieved by locally controlling the amount of light injected. In whole-body small animal imaging, the dynamic range of transmitted photons can be attributed to two factors, namely, the animal specific geometry exhibiting variations in thickness across the imaged volume (e.g. neck to tail) and the wide range of optical properties of murine organs [20]. The combined effects of these two factors result in significant variations in the degree of signal attenuation across the small animal body. Furthermore, the effects of these factors become more critical for free-space imaging applications in the absence of matching liquid chambers. The large dynamic range in photons transmitted through the small animal model reduces the number of detectors on the surface acquiring signals with adequate signal to noise ratio, especially in photon-starved imaging

108 92 techniques like time-resolved imaging. This, in turn, leads to a reduced number of measurements employed in the reconstruction process. Especially, detectors positioned in the central part of the animal or positioned below highly attenuating organs lead to poor reconstruction performances due to measurements highly affected by noise (as discussed in Chapter 4). Figure 5.1(b) shows an example of the dynamic range observed in an animal model upon illumination by a uniform pattern shown in Fig. 5.1(a). Here the limited transmission of photons through the thoracic cavity due to highly absorbing organs (e.g. heart and lungs) combined with the high signal transmitted through the edge of the model (due to reduced thickness) results in a high dynamic range resulting in limited number of detectors around the edge of the model with sufficient signal levels. In such scenarios, AFFT iteratively adapts the spatial intensity distribution across the excitation pattern and to increase the number of detectors acquired with high signal for each individual pattern across the animal body. The iterative correction of the excitation pattern in AFFT is implemented by a measurement-driven pattern optimization scheme which does not require a priori knowledge of model geometry and optical properties. Thus it provides an experimentally efficient pattern optimization scheme in wide-field optical tomography. It is also worth noting that the optimization of the excitation pattern in AFFT based upon the signal transmitted at the excitation wavelength produces a corresponding improvement in the fluorescence signal measurements (using identical patterns) which improves the performance of wide-field FMT. 5.2 Iterative optimization algorithm As stated in Section 5.1, the iterative correction of excitation pattern in AFFT modifies the spatial distribution of incident power by modulating the gray levels in the illumination pattern. The optimization procedure therefore employs the measurements from the detectors spanning the area of the pattern on the surface of the model. As a part of pre-optimization calibration, the excitation pattern is measured using a white diffusing paper and its spatial characteristics are determined. Next a transformation matrix mapping the image used to define the full field pattern to the measured full field is computed. This is done to account for spatial deformations in

109 93 the projected pattern due to the projector optics. If α < β α = β x,y If α max n = 1 Figure 5.2: (a) Optimization scheme. (b) Algorithm flowchart for single pattern optimization. Consider the animal model shown in Figure 5.2(a) where the white border represents the excitation pattern. The optimization of the patterns described herein is based on time-resolved data and the process begins with the acquisition of temporal measurements for each of the N patterns in the user defined set. It should be noted that this algorithm can also be applied to CW and FD data types without

110 94 loss of generality. As the dynamic range limits the maximum photons recorded in each time-resolved curve, for each pattern P n (n = 1...N), an excitation map (E n ) is constructed from the maximum measured counts (peak counts of the TPSF) at each detector. At each pixel at (x,y) in the n th pattern at the i th iteration the multiplicative update value α is computed and the corresponding pixel is updated using the formulae given in Eqn α = χ K E n (x k,y k ) d k k=1 K d k k=1 P i+1 n (x,y) = α P i n(x,y) (5.1) In 5.1, χ is the maximum desired photon counts, (x k,y k ) is the position of the k th neighbor within a radius r and d k is distance of the k th neighbor from (x,y). The selection of detectors within distance r (resulting in a total of K neighboring detectors) incorporates the effect of photon diffusion when computing the update value for the pattern. Furthermore, we define a parameter β as the maximum power amplification allowed when acquiring the TPSF. This ensures that the algorithm does not exceed the maximum permissible exposure limit of laser power during optimization. The iteration is completed after each pixel in the pattern has been updated. The maximum update value (α nmax ) among all points for pattern P n is the amplification in laser power that must be employed while acquiring the temporal measurements during the next iteration. This process is repeated until α nmax equals 1 (indicating convergence with all detectors reaching χ counts) or the change in the pattern ( P i+1 n P i n 2 ) is less than 5%. The above process is repeated for all patterns in the base pattern set and the final set of patterns is referred to as the transmittance-optimized patterns. The optimization procedure is outlined in Figure 5.2(b). In the studies described in this paper, a neighborhood radius of 4mm was employed during optimization. While the radius of neighborhood was selected heuristically in these validations studies, the

111 95 distance of the pattern from the edge of the model can be used as a metric for the selection of neighborhood radius. Moreover, a gray level represented by a point in the pattern is updated only if it has a value greater than This ensures that the updated pattern will be accurately generated by the pico projector. It should be noted that, by using the above method, each pattern will converge to the optimality condition at a different rate and will require different power amplification. For instance, photons from a pattern probing the thoracic cavity will be highly attenuated due to highly absorbing and scattering organs (e.g. heart and lungs), while the signal from another pattern in the same set probing the abdominal area will encounter a thicker volume with low absorbing tissue (e.g. stomach, intestines etc.). This leads to variation in the signal attenuation profiles recorded on the surface for each pattern and necessitates the individual optimization of each pattern in the set. In this implementation of the above algorithm, all patterns were batch optimized to ensure experimental efficiency. In other words, the temporal measurements for all patterns in the set were acquired consecutively and followed by the optimization of each pattern in the set. Specifically, the optimization algorithm was implemented in two steps. First, the pattern update value was unbounded (β = ) during optimization and the optimal patterns were computed. As stated previously, each pattern will have been assigned different power amplification for the next iteration. In the second step, the minimum power amplification among all patterns in the set is set as the upper bound on the value of α (β = min(α nmax )). This ensured that the laser power employed during the acquisition step will not saturate the ICCD for any pattern in the set. Moreover, the constant source power allowed a rapid acquisition of the complete pattern set with high experimental efficiency. 5.3 In silico validation The efficacy of the optimization algorithm for whole-body imaging of small animals was validated using a synthetic mouse model (Digimouse) [83]. Figure 5.3 shows the model employed, where seven major organs in the animal torso were modeled to simulate the propagation of photons in small animals. The optical properties

112 96 Figure 5.3: Synthetic mouse model used for in silico validation. Three 2 2 2mm 3 fluorescent inclusions are shown in red. The profiles marked in red represent the uniform excitation pattern and the discrete detectors spanning the torso are shown in blue. at730nmgivenintable5.1wereassignedtoeachorgan[85,77]. Furthermore, three 2 2 2mm 3 fluorophore inclusions were positioned as shown in Figure 4 to simulate the effect of optical properties and/or geometry on the fluorescence signal intensity. An area of uniform illumination spanning the whole body (as shown in Figure 5.3) was selected as the base pattern and the excitation field was recorded at discrete detectors at 1mm separation in transmittance mode. The optimization scheme was employed to achieve χ = 4000counts at each detectorwhichisthemaximumnumberofphotoncountsthatcanbedetectedbythe ICCD camera used in the study (12-bits). After convergence, a Monte Carlo based fluorescence forward model was employed for the uniform and optimized pattern sets to determine the corresponding changes in fluorescence signal intensity [78] Transmittance optimized patterns The optimization of photons transmitted through the synthetic animal model using the full field pattern shown in Figure 5.3 was completed in 4 iterations. The optimization was terminated due to less than 5% change in pattern characteristics.

113 97 Table 5.1: Optical properties of murine organs at 730nm used for simulation Tissue type µ a (cm 1 ) µ s (cm 1 ) Heart Lungs Liver Spleen Stomach Kidneys Bladder Bone Muscle Figures 5.4(a)-(e) show the modifications in the pattern spatial intensity distribution over the 4 iterations. It should be noted that the gray levels on the pattern are adjusted to match the geometry and organ distribution in the animal model with the maximum intensity retained in the thickest portion of the body comprising of the highly absorbing organs like the liver and spleen. Figure 5.4(f) shows the transmitted excitation field measured using the original pattern exhibiting a dynamic range of 6 orders of magnitude when using a full-field uniform pattern. Following the characteristics of the optimized patterns described above, the optimization process leads to 4-orders of increase in transmitted light for the central portion of the torso reducing the effective dynamic range in the excitation field to 2 orders of magnitude. In order to test the hypothesis that the optimization of transmitted excitation field improves the fluorescence measurements, we considered the maximum photon fluence at each inclusion shown in Figure 5.3. Figure 5.5(a) shows a 4-order increase in photon fluence at each inclusion in agreement with the increase in transmitted excitation signal. Moreover, at the end of 4 iterations, the photon fluence at Inclusion 2 is 2 orders of magnitude greater than that at Inclusion 1. Figures 5.5(b) and 5.5(d) show the fluorescence signal measured on the surface in transmission at the 10% early time-gate and the maximum gate respectively. It should be noted that the signal from inclusion 2 is smaller than signal from inclusion 3 by approximately 5 orders of magnitude due to its position in the thickest region of the animal body

114 98 (a) (b) (c) (d) (e) (f) (g) (h) (I) (j) Figure 5.4: (a) Uniform excitation pattern, (b)-(e) Pattern at each iteration showing correction with transmitted signal. (f) Log-scale transmitted excitation field using the uniform base pattern. (g)-(h) Difference of transmitted excitation signal at maximum gate for patterns (b)-(e) respectively, representing increase in detected photon intensity (in log scale). and the highly absorbing organs in its neighborhood. The increased photon fluence at each inclusion (c.f. Figure 5.5(a)) due to pattern optimization results in 1.6 order increase in photons at inclusion 2, as observed in Figures 5.5(c) and 5.5(e). Moreover, the signal from inclusion 3 is not modified for both gates considered and retains the high signal level obtained using the original patterns. 5.4 In vitro validation Experiment design The improvement in performance in tomographic reconstruction was investigated using an agarose phantom mimicking a small animal model. The baseline pattern set employed in this tomographic study are binary bar-shaped patterns

115 Photon fluence (a.u.) Incl 1 Incl 2 Incl Iteration # (a) (b) (c) (d) (e) Figure 5.5: (a) Increase in maximum photon fluence at each fluorophore inclusion, (b)-(c) Fluorescence signal when using the uniform pattern at early gate at 10% and maximum gate respectively. (d)-(e) Difference of detected fluorescence signal using optimized and baseline pattern at early gate at 10% and maximum gate respectively (in log scale). described in Chapter 3. The performance of this pattern set in a non-planar geometry is tested using a truncated hemi-cylindrical phantom shown in Figure 5.6 with an absorption coefficient of 0.1cm 1 and reduced scattering coefficient of 13cm 1. Furthermore, a cylindrical absorber with 6 times absorption (0.6cm 1 ) simulating absorbing organs in the small animal torso (e.g. liver) is placed along the central axis of the phantom. The geometry of the phantom coupled with the absorber results in a high dynamic range across the surface in transmittance. Two 10mm long capillary tubes (1.5mm inner diameter) containing 14pmol of Cardiogreen (Sigma Aldrich, MO) in 10µL Phosphate-buffered saline were placed at depths of 11mm and 9mm. Moreover the deeper inclusion was placed below the absorber simulating the occlusion of fluorescent markers by absorbing organs in vivo. The tomographic imaging session employed 36 bar patterns (34mm 24mm) described previously. The temporal measurements at excitation wavelength (λ ex = 780nm) were acquired at 40ps interval spanning 2ns (50 gates) using 300ps gates (MCP Voltage = 570V; integration time = 25ms). The measurements at excitation wavelength for 36 patterns were acquired in 3 minutes. The fluorescence measurements (at λ em = 832nm) were acquired for the optimized pattern set (MCP Voltage = 570V; integration time = 500ms). The acquisition of measurements spanning

116 100 Inclusion 1 Inclusion 2 Figure 5.6: Tissue-mimicking phantom used for in vitro validation. The uniform full field pattern (recorded during the experiment) projected on the phantom is shown on the xy-plane at z = 0. The green tubes represent the fluorophores contained in glass capillaries located in the center of the phantom. The red tube shows the position of an absorbing perturbation occluding the central fluorescent inclusion. 3ns (75 time-gates) was completed in 18 minutes. The fluorescence measurements using the uniform pattern set was also acquired for comparison of reconstruction performance. The tomographic reconstruction of the effective quantum yield of the two inclusions in 3D was performed using measurements at 231 point detectors uniformly sampling the surface of the phantom at 2mm intervals. The time-gate data type derived at each detector was defined by the number of photons measured relative to the peak photon count and was used to construct the time-gated measurement vector. The effective quantum yield was reconstructed by solving the inverse problem with measurements derived from multiple-gates. Furthermore, an X-ray CT image of the phantom was acquired following the optical imaging protocol. The 3D image of the volume was used to generate the model geometry and also for validation of the tomographic performance of the pattern optimization scheme Pattern optimization results The experimental validation of AFFT using the murine model was performed by batch optimization of the 36 patterns in the baseline set. The iterative scheme was

117 101 terminated in 4 iterations with the power amplification factor reaching a value of 1. All patterns were simultaneously optimized in 3minutes (including 1minute of pattern setup time per iteration). The optimization procedure of the entire pattern set (4 iterations) including the acquisition of temporal measurements was completed in 24 minutes. Figures 5.7(a) and 5.7(b) compare the structure of the full-field pattern for the uniform and the transmittance-optimized grayscale patterns. It can be inferred that the optimization procedure removed the sections of pattern beneath the region with smaller thickness to correct for the dynamic range while retaining the high intensity across the central axis to compensate for the absorber. Figures 5.7(c) and 5.7(d) compare the excitation field acquired for the original and optimized patterns for the early gate at 50%. As expected, the original pattern results in a higher signal towards the edges of the phantom (c.f. Figure 5.7(c)) demonstrating the role of model geometry as a source of high dynamic range. Conversely, the transmittance optimized field provides a high signal across the area of the pattern (c.f. Figure 5.7(d)) with maximum of 2000 photons (at the 50% time-gate, 4000 counts at the maximum gate) across the area of the pattern representing the successful optimization of the transmitted signal. Figure 5.7: (a) Uniform bar pattern used for imaging phantom, (b) Transmittance optimized pattern obtained after 4 iterations, (c)-(d) Recorded excitation signal at 50% time-gate on the rising portion of TPSF, (e)-(f) Recorded fluorescence signal at 50% time-gate on rising portion of TPSF. (g)-(h) Normalized born contrast measure at the 50% time-gate on rising portion of TPSF.

118 102 A similar comparison of the fluorescence field shown in Figures 5.7(e) and 5.7(f) demonstrates that the optimization of the excitation field improves the fluorescence signal from Inclusion 1. Lastly, it is worth noting that while the use of normalized Born measures (shown in figures 5.7(g) and 5.7(h)) improves the signal level from the central inclusion to an extent, the contrast measures derived using the optimized patterns clearly distinguish the 2 objects. This demonstrates an improved contrast and higher signal over a larger number of detectors when using AFFT Improvement in tomographic information content The impact of the improvement in the overall signal level demonstrated in the measurements on the quality of the tomographic information recorded is quantified using a two-step process. First the percentage increase in number of source-detector pairs at different gates along the temporal measurement which are above the noise threshold level is used to quantify an increase in the number of usable measurements. The noise threshold for this system was empirically determined to be 200 photon counts. Figures 5.8(a) and 5.8(b) show 200% increase in the number of s-d pairs for excitation signal and 80% in the fluorescence signal at the early gates, with a smaller yet significant improvement for the maximum gate ( 25% for fluorescence field, 15% for excitation field). The improvement in the time-gated signal at the early gates and the late gates establishes the advantages of this imaging technique for high-resolution optical reconstruction and lifetime multiplexing applications respectively [51, 86, 87]. It is also worth noting that the transmittance optimized patterns result in a higher increase for the late gates conversely to the early gates as the optimization procedure corrects for the effects of the highly absorbing local perturbation in the experimental phantom which reduces signal at the late gates. Next, the analysis of tomographic information content in the measurements is extended to the quantification of increase in non-redundant information using a model based analysis. Following the work by Freiberger et al, we define the orthogonality of the different rows in the fluorescence weight matrices J fluo as a measure of the information content [88]. For a set of N patterns, let M be the total number of measurements (s-d pairs) above the set threshold. Consider a set of

119 103 measurements S n for the n th pattern. Then the non-redundant information h n for the n th pattern is defined as the average orthogonality of each measurement in S n with respect to the remaining measurements (M \S n ). h n is computed using Eqn h i = 1 1 M \S i S i n M\S i (j m,j n )2 j m S m 2 jn 2 i (5.2) Here, j m and j n are the m th and n th rows from J fluo. The average nonredundant information content for the entire pattern set is therefore given by, H = 1 N N h i (5.3) i=1 Increase in sd-pairs at excitation wavelength (%) Early gates Late gates Increase in sd-pairs at emission wavelength(%) Early gates Late gates Uniform patterns Transmittance optimized patterns Gate position (% of TPSF maximum) Gate position (% of TPSF maximum) Gate position (% of TPSF maximum) Figure 5.8: (a)-(b) Increase in number of source-detector pairs with signal above 200 counts after pattern optimization at excitation and emission wavelengths respectively. (c) Increase in nonredundant information with increase in s-d pairs. The average information content value of 1 represents maximal non-redundancy in the measurement suggesting maximum information content in the measurements. Figure 5.8(c) shows the comparison of average non-redundant information content for the uniform and the transmittance-optimized pattern set at individual time-gates along the TPSF. It is observed that the optimization of transmittance excitation field leads to 6% increase in the information content at the early gates and 16% increase for gates along the decaying section of the TPSF. This closely follows the trend in increase in number of s-d pairs observed in Figure 5.8(a).

120 104 y Figure 5.9: (a) Reconstructed effective quantum yield at z = 12mm using single gates. First row shows the reconstructions using uniform patterns and second row employs transmittance optimized patterns. (b)-(c) 50% iso-volume of reconstructed effective quantum yield when using uniform patterns and transmittance optimized patterns respectively. The 50% isocontours across x = 28mm and z = 12mm are projected along the corresponding planes Reconstruction results In order to determine the impact of increased information content on the quality of reconstructions in the image space, the effective quantum yield was reconstructed using three time-gates spanning the rising portion of the TPSF (early gates at 20%, 50% and the maximum gate). These gates were selected on the rising part of the TPSF as it correlates to resolution improvement in the reconstruction whereas late gates are critical in lifetime multiplexed studies, which we do not consider herein [78]. Figures 5.9(a) and 5.9(b) show the 50% iso-volumes of the effective quantum yield obtained by solving the inverse problem by least-squares minimization. The lower number of source-detector pairs available when using the uniform pattern set (more than 36% reduction) leads to reduced tomographic information in the measurements as discussed previously. This results in poor discrimination of the two objects in the reconstruction and their incorrect localization (c.f. Figure 5.9(a)). Specifically, both objects are reconstructed 5mm above the expected position along the z-axis. Moreover, the lower resolution of the reconstructed volume is evidenced by the connected reconstructed objects. On the contrary, the reconstructed volume obtained using the transmittance optimized patterns allows to discriminate

121 105 and accurately localize the two inclusions as shown in Figure 5.9(b). The resolution metrics comparing the reconstructed 50% iso-volumes with the ground-truth values obtained from the X-ray CT are compiled in Table 5.2. It is worth noting that the two inclusions are accurately localized with 1mm error. Table 5.2: Comparing improvement in reconstruction with transmission optimization Dimensions (mm) Position of centroid (mm) Inclusion x y z Expec. Recon. Expec. Recon. Expec. Recon Also, the separation between the two objects was found to be 9mm (expected 8.3mm) resulting in less than 1mm localization error. Furthermore, the reconstructed dimension of the inclusions had 1mm and 2mm error along the x-axis and y-axis respectively. The resolution of inclusion 2 along the z-axis also had less than 2mm error, however inclusion 1 had significantly lower z-resolution due to the limited projection angles in the planar imaging configuration. 5.5 Discussion The optimization of excitation patterns for more accurate reconstruction in wide-field optical tomography of small animals is an emerging area of investigation owing to the experimental advantages provided by wide-field imaging techniques. Conversely to model-based optimization techniques, in this work we investigated a novel measurement-guided pattern optimization technique with the objective to reduce the dynamic range in intensity of photons transmitted through the small animal model. The iterative pattern correction scheme described herein was based upon the characteristics of the transmitted excitation field allowing a fast optimization of excitation patterns during acquisition. Furthermore, the associated

122 106 improvement in fluorescence signal by proxy upon the optimization of the transmitted field established AFFT as a useful technique in FMT. It is worth noting that the acquisition-time optimization of patterns in AFFT introduced minimal time cost to the experimental protocol. Hence, it can be readily implemented for in vivo studies to acquire optimal data sets by taking into account at each imaging session the geometry of the specimen imaged (animal and posture specific) and its optical parameter characteristics (e.g. spatial distribution of organs which is dependent on posture, functional state, disease progression). The in silico validation of this approach in a synthetic animal model demonstrated an increase in transmitted photon intensity by four orders of magnitude. Furthermore, the adaptive correction of excitation pattern was simultaneously able to improve the signal from three fluorescent inclusions located in the animal torso. Specifically, the fluorescent signal from Inclusion 2 located in the center of the torso occluded by highly absorbing organs (e.g. liver and spleen) was increased by two orders of magnitude after pattern optimization. The increase in information content with the increase in s-d pairs allows the accurate reconstruction of deep-seated fluorescent inclusions which are poorly localized when using the uniform patterns. The application of this technique in FMT was found to especially improve the signal level at the time-gates on the early rising and late falling portion of the TPSF that correlates with lower photon counts. The corresponding 80% increase in the number of source-detector measurements above the noise threshold acquired in experimental settings demonstrates the advantage of this approach in FMT applications employing early photons for high resolution optical reconstructions [86]. Similarly, the improvement in signal level at the late gates implies more robust measurements in fluorescence lifetime based tomographic imaging where multiple fluorophores can be resolved with lower crosstalk owing to improved signal to noise ratio [89, 90]. Moreover, the advantages of pattern optimization in FMT also extend beyond the improvement in tomographic information content, in that the improved signal level from deep-seated fluorescent markers will allow the robust estimates of fluorescence lifetime due to the higher SNR of the measurements. The application of the pattern optimization technique described in this paper

123 107 is directed towards time-resolved fluorescent tomographic imaging. However, it is worth noting that this approach can be readily translated to other optical tomographic imaging paradigms. For instance, by assuming equivalent characteristics of the continuous-wave data type and the time-gate at maximum intensity, it can be determined that the pattern optimization scheme also provides added information in tomographic systems employing the CW data type. Similarly, the optimization scheme can also be an effective imaging approach in systems implementing a cylindrical imaging geometry or a multi-view setup based on mirrors where dynamic range is a critical issue in experimental implementation [40]. We further hypothesize that the approach described here can also be extended to point source excitation schemes, wherein the optimized pattern derived from a full-field illumination pattern can be used as a template to assign the relative power injected into the model at each source location. Lastly, the optimization scheme described here also has applications in related optical imaging applications. For instance, in the case of Fluorescence Reflectance Imaging which is a commonly used preclinical imaging modality, a measurement guided optimization of excitation field based upon the fluorescence signal detected may improve the depth sensitivity of the technique. In conclusion, we have for the first time described a measurement-guided pattern optimization scheme which increases the tomographic information collected in whole-body small animal imaging applications. The preliminary results presented here establish the feasibility and the applicability of the technique. The future work will focus on the impact of specific parameters of the optimization scheme (e.g. the neighborhood radius) on the convergence of the technique. We next plan to extend the approach to include optimization of patterns based upon the fluorescence field. Pattern optimization based on this criterion will allow the detection of lower concentrations of fluorophores increasing the sensitivity of the technique. We anticipate the use of measurement-guided excitation optimization schemes to further improve the applicability of FMT in molecular imaging applications.

124 Chapter 6 Near-Infrared FRET Tomography Förster Resonance Energy Transfer (FRET) is a non-radiative transfer of energy between two fluorescence molecules (a donor and an acceptor) in close proximity [91]. This distance dependent interaction on a nanometer scale allows the investigation of biomolecular interactions on a cellular level and provides information well beyond the diffraction limits of standard microscopy techniques [92]. FRET imaging methods have been applied to proteomic studies and drug discovery applications wherein FRET efficiency measurements and stoichiometric measurements of FRET interaction are quantitative parameters of interest [93, 94]. The translation of FRET imaging techniques to small animal models will allow biologists to investigate physiological processes in situ. In this chapter a new method for quantitative reconstruction of FRET in small animals incorporating a full-field tomographic acquisition system with a Monte Carlo based hierarchical reconstruction scheme is described and validated in murine models with the objective of quantitative estimation of the relative concentration of two forms of donor species (FRETing and nonfreting) in the presence of an acceptor. 6.1 FRET imaging in small animals In current biological research, FRET imaging is limited to microscopic techniques focussing on the study of bio-molecular interactions in cell-based assays. The fundamental principles in FRET imaging are based on the detection of reduction in the intensity level and fluorescence lifetime of the signal from the donor or the increase in acceptor signal upon FRET [91]. The prevalent microscopy techniques, e.g. spectral microscopic methods and lifetime-based imaging methods, namely Fluorescence Lifetime Imaging Microscopy (FLIM), are currently used to provide a quantitative measurement of FRET activity. Spectral imaging employs a three channel measurement of donor and acceptor emission for different excitation wavelengths and performs a ratiometric calibration to quantify FRET activity by removing spec- 108

125 109 tral bleedthrough effects between the different channels. Lifetime based methods, rely on the measurement of the fluorescence decay of the donor signal and therefore require only a single spectral channel measurement. Conversely to intensity based techniques FLIM-FRET methods provide a highly robust approach due to the invariance to fluorescence lifetime with concentration, excitation intensity and other experimental parameters. The above mentioned approaches have been translated to small animal FRET imaging. The most commonly used techniques employ intravital microscopy which requires invasive surgery and more importantly are limited to the assessment of superficial tissue [95]. More, recently, lifetime based mesoscopic imaging techniques (life Optical Projection Tomography) allowing the tomographic imaging of thin biological tissues (e.g. developmental models like zebra fish) have been used for FRET imaging [96, 97]. Such techniques, despite the high-resolution performance are not capable of effective assessment in preclinical models and frequently require the optical clearing of the model before imaging. In such scenarios, a macroscopic imaging method based in the diffuse regime, for instance Fluorescence Molecular Tomography (FMT), is necessary and the time-resolved FMT platform described herein provides a robust approach to whole body FRET imaging in small animal models based on lifetime contrast. One of the drawbacks of tomographic imaging methods in the diffuse regime as noted in the previous chapters is the limited resolution due to the highly scattering interactions of photons with biological tissue. Time-resolved FMT provides an approach towards improvement in the low resolution performance through the use of minimally scattered (early) photons. Furthermore, the quantitative detection of FRET is nevertheless dependent on the lifetime information in the decaying portion of the temporal fluorescence measurements and acquisition of measurements with high temporal and spatial resolution will provide sufficient tomographic information to quantitatively localize FRET activity in preclinical models. The feasibility and applicability of time-resolved FMT for tomographic FRET imaging has been demonstrated recently [98]. These studies however have utilized existing FRET pairs in the visible wavelength range and have focussed on small imaging volumes (e.g. the

126 110 limbs etc.). Visible fluorophores are poorly transmitted through biological tissue due to absorption by tissue chromophores making them unsuitable for whole body imaging studies. In the following sections, two critical aspects of whole-body FRET imaging are discussed. First, a Near-Infrared fluorophore (NIR) pair capable of FRET interaction is characterised and its viability for diffuse imaging based on lifetime contrast is established. The next section focuses on the development of new hierarchical reconstruction scheme which allows for a optimal combination of structural information at a higher resolution using minimally scattered early photons and accurate quantitation using photons in the late gates. 6.2 NIR FRET pair As stated previously, the development of a FRET imaging technique in small animal models necessitates the use of a FRET-compatible fluorophore pair in the near-infrared wavelength range (650nm1000nm) owing to the maximum transmission of photons in this spectral window through biological tissue. It is worth noting thattheuseofnirfretpairinsmallanimalmodelsalsomitigatesanyinterference due to tissue autofluorescence eliminating a major source of noise in the visible wavelength range. The optimal FRET-compatible fluorophore pair is defined by three criteria: a) a significant overlap of donor emission and acceptor excitation spectra ensuring successful transfer of energy, b) compatible orientation of fluorophore dipoles and, c) a Förster distance (separation at which energy transfer efficiency is 50%) which will be compatible with intermolecular distances in biological models. AmongcommerciallyavailablefluorophorestwoAlexaFluordyes,AlexaFluor R 700 (Af700) and Alexa Fluor R 750 (Af750), were found to be suitable for FRET imaging in the NIR wavelengths as the donor and acceptor respectively. Figure 6.1 shows the spectra of the two dyes and it is observed that the significant spectral overlap between the two dyes is sufficient for successful energy transfer. Furthermore, the Förster distance (R 0 ) for the two dyes was found to be 7.5nm (provided by manufacturer) is comparable to the R 0 values for commonly used FRET fluorophores. The large R 0 distance ensured that biomolecules tagged by these dyes

127 Af700 absorption Af700 emission Af750 absorption Af750 emission Figure 6.1: Absorption and emission spectra of Alexa Fluor R 700 and Alexa Fluor R 750. For all studies described herein, the donor was excited at 695nm and signals were measured at 720nm. will interact with high probability at intermolecular distances encountered in FRET applications. In all the validation studies described herein, functionalized variants of the dyes Alexa Fluor R 700 (Mouse IgG1) and Alexa R Fluor 750 (goat anti-mouse IgG) which formed an antibody-antigen complex with high affinity provided an optimal model for FRET imaging in the NIR window. The dependence of FRET interaction on the relative concentrations of donor and acceptor molecules was used to establish a model for the assessment of estimation of FRETing and nonfreting components. Specifically, five donor-acceptor mixtures with different acceptor-to-donor (AD) ratios (0.25, 0.5, 1.0, 2.0, 4) representative of the range of donor-acceptor concentrations encountered in biological applications were constructed. The concentration of the donor fluorophore was kept constant at 10µg/ml. The fraction of FRETing donor (f d ) in each sample was expected to linearly increase with the relative concentration of the acceptor. Capillary tubes containing the above samples were directly imaged (in the absence of any diffusing medium) and the resulting temporal profiles were fit to a biexponential decay model.

128 112 Γ(t) =IRF(t) (N +A 1 e t τ 1 +A 2 e t τ 2 ) where, N is an additive noise factor (6.1) # of pixels (a.u.) Shorter lifetime components Longer lifetime components Lifetime (ns) (a) 70 Normalized photon counts (a.u.) A:D = 1:4, χ 2 = 0.83 A:D = 1:2, χ 2 = 1.49 A:D = 1:1, χ 2 = 1.21 A:D = 2:1, χ 2 = 1.96 A:D = 4:1, χ 2 = 0.97 IRF Time (ps) (b) Shorter lifetime component (Quenched donor fraction), f d (%) Acceptor:Donor Ratio (a.u.) (c) Figure 6.2: (a)histogram of estimated lifetime components in the first step of the biexponential fitting process. (b) Examples of fitted temporal point spread functions in the second step of fitting procedure. (c) Estimate of relative abundance of shorter (FRETing) lifetime component. The measured data was fit to the biexponential model given by Eq The fitting process was carried out in two steps to alleviate the inherent instability of biexponential fitting procedure. First, the measurements were fit with unbound lifetime estimates. The lifetime components thus obtained were plotted and the mean values of each component group was selected as the fixed lifetime estimate for

129 113 the second step (c.f. Figure 6.2). The lifetime of the nonfreting and FRETing donor molecules were estimated to be 1.1 ± 0.2ns and 0.29 ± 0.19ns respectively. This represents a significant change in lifetime which can be observed in the diffused TPSFs recorded in transmittance through the animal model. The selection of a FRET pair with a significant change in lifetime (as in this case) is a critical factor affecting fluorophore selection due to the smearing effect of tissue transport on temporal fluorescence signals which may reduce observable lifetime contrast. In the second step, the lifetime was fixed to the previous values and the amplitudes of each of the two components was estimated. Figure 6.2(b) provides an example of the fitting to the measurements from the five capillaries. It should be noted that goodness-of-fit parameter (χ 2 ) for each of the above cases shows a good fit despite the fixed lifetime assumption. Furthermore, as expected, the amplitude of FRETing donor (shorter lifetime component) was found to increase linearly with AD ratio (Figure 6.2(c)). 6.3 Hierarchical reconstruction scheme As discussed in Chapter 3, the mathematical model of photon propagation in tissue plays a very important role in the accurate reconstruction of fluorophore concentration, especially when employing time-resolved datasets. In this method we implement the Monte Carlo based numerical photon propagation model described in Chapter 2 which allows the reconstruction of fluorophore concentration directly using multiple time-gates. The MC-based method retains its accuracy over a wide range of optical properties (observed in small animal models) and can accurately model the temporal response of the tissue across all time points in the typical measurement window (including minimally scattered early photons). And as noted previously, the early gate data types while providing improved resolution are unable to accurately quantify concentration or separate multiple fluorophores based on lifetime contrast. Conversely, the late gates encode the lifetime decay of the fluorophores but result in poor resolution as observed in the results in Chapter 4. An approach for the combination of the complementary information provided by these two data types is the simultaneous reconstruction of the fluorophore con-

130 114 Acquire temporal measurements at excitation and emission wavelengths Estimate average optical properties and compute sensitivity function at excitation wavelength Wexc W exc Estimate fluorescent lifetime of FRETing and nonfreting donor Compute W Fluorescence sensitivity functions W FRET nonfret W W exc exc e e t / FRET t / nonfret Reconstruct and localize the two donor species using early gates Initial estimate Reconstruct volumetric abundance maps of the two donor species using late gates Figure 6.3: Flowchart of hierarchical reconstruction of fluorophore concentrations using time-gates. centration using both data types. In this regard, an alternate scheme was formulated wherein, the early gate data type was used to provide the inital localization of the fluorophores. The result from the first step was used to estimate the total fluorescence yield for each of the two objects and this provided the position of the fluorophores with higher resolution. This estimate of the fluorophore position was used in the second step where multiple time-gates on the decaying portion of the TPSF are selected as the data type. The advantages of this approach are twofold. First, this method allows the use of both lifetime-encoding late gates and the early gates providing higher resolution. Second, the separation of early and late gate measurements allows the selection of more late gates for the second step (without memory constraints) thus improving the quantification. The reconstruction scheme for estimating relative fluorophore concentrations in a FRET complex using the

131 115 inverse problem is schematically depicted in Figure 6.3. As noted in Figure 6.3, one of the aspects of this reconstruction model is the a priori knowledge of the fluorescence lifetime. In this work, the lifetime estimates of the two donor species (FRETing and nonfreting) are used as the lifetimes for the quantification of their respective concentration. Moreover, it is to be noted that the reconstructed concentrations are normalized within each inclusion to obtain the fraction distribution of the FRETing donor in each localised donor population. 6.4 In vitro validation The first study for the validation of the above detailed FRET imaging technique was performed in a tissue-mimicking scattering phantom with donor-acceptor mixtures embedded in capillaries. The objective of this study was to determine the lifetime contrast observed when using this FRET pair for imaging in a diffusing medium and the resulting quantitative accuracy of this model in estimating the fractional distribution of FRETing donor Phantom design The tissue mimicking hydro-gel phantom used for the validation of the tomographic estimation method in a homogeneous slab phantom was constructed using agarose (Fluka 05040, Sigma Aldrich, MO, USA) and had a thickness of 17mm. The scattering and absorption coefficients of the phantom were controlled using Titanium Dioxide (Ti-Pure R-101 Titanium Dioxide, DuPont, USA) as the scattering agent and water soluble NIR dye (Epolight 2735, Epolin, USA) as the absorber. The optical properties of the phantom were estimated using time-resolved spectroscopy and were found to be, µ a = 0.07cm 1 and µ s = 6.17cm 1. Four 10mm long capillary tubes (1mm inner diameter) containing the donor-acceptor mixtures with AD ratios of 0.25, 0.5, 2.0 and 4.0 were embedded in the phantom at a depth of 11mm (c.f. Figure 6.4(a)). The acquisition protocol used the bar pattern set comprising of 36 patterns and acquisition was done used 400ps time-gates at a temporal resolution of 40ps. The excitation signal at 695nm was acquired at an integration time of 50ms and the fluorescence signal was acquired at a 500ms integration time at 720nm (us-

132 116 ing interference filters). The complete acquisition protocol was carried out in 24 minutes. Time: 0.36ns Time: 0.80ns Time: 1.36ns 10mm Time: 1.72ns Time: 2.28ns 7mm 17mm 4mm 34mm (a) Normalized photon counts (a.u.) A:D - 1:4 A:D - 1:2 A:D - 2:1 A:D - 4:1 (b) Time (ns) (c) Figure 6.4: (a) Design of murine phantom with four inclusions carrying mixtures with different acceptor to donor ratios (Red- 1:4, Green-1:2, Cyan-2:1 and Blue-4:1). (b) Normalized born contrast measures of time-gates measured for a single pattern. (c) TPSFs derived from point detectors directly above each of the four inclusions Results The primary observation from the time-gated measurements shown in Figure 6.4(b) is that the lifetime contrast is preserved however the inclusion with highest AD ratio (having the highest FRETing donor component) shows a discernible decay. This observation is confirmed in the TPSF measurements shown in Figure 6.4(c) wherein, as opposed to the lifetime contrast (observed between all four inclusion) upon direct measurements is diluted due to the tissue transfer function (especially for AD ratio of 0.25 and 0.5). Two time-gated measurement vectors were constructed using the early gate at 25% and the late gates at 100%, 80%, 50% and 40%. Figure 6.5(a) shows the 3D visualization(50% iso-volume) of the reconstructed

133 117 (a) 40mm 32mm 17mm (b) (c) Shorter lifetime component (Fraction of quenched donor molecules), f d (%) Baseline estimate (Direct imaging) Tomographic estimate in phantom Acceptor:Donor Ratio (a.u.) (d) Figure 6.5: (a) 50% iso-volumes of total reconstructed donor quantum yield. Dotted orange bounding box indicates the reconstructed volume. (b)-(c) Iso-plane images of the reconstructed quantum yield of the shorter component with threshold at 50% of maximum value. (d) Quantitative comparison of tomographic estimates of FRETing donor fraction from above reconstructions. total fluorescence yield (FRETing and nonfreting donor) obtained following the tomographic reconstruction of the mm 3 volume. The mean diameter of the 50% iso-volumes of the reconstructed tubes was 6mm. Figure 6.5(b)-(c) shows the successful resolution of multiple fluorescent inclusions closely situated in a diffusing medium with less than 1mm error in localization along the x and y axes and less than 2mm error along the z axis. The maximum reconstructed quantum yield for the shorter lifetime component (FRETing donor) was used to calculate the estimate of f d for each object and was used as the performance metric to establish quantitative accuracy. A comparison of the estimated and expected f d (obtained by direct imaging) shown in Figure 6.5(d) shows an absolute error of less than 3% in the tomographic estimate for AD ratios less than 2.0. For AD ratio of 4.0 the estimation error was found to be higher at 9%.

134 Validation in animal model Following the successful reconstruction of the donor populations with less than 10% quantification error, the next study focused on the investigation of the effect of heterogeneous optical property distribution (as observed in animal models) on the quantification and localization of the FRET effect (b) A:D = 4:1 A:D = 1:4 Photon count (a.u.) Time (ps) (a) (c) (d) (e) Figure 6.6: (a) MicroCT image of animal model showing two capillaries localized in the abdomen with acceptor-to-donor ratios of 1:4 (green) and 4:1 (blue). (b) TPSFs derived from point detectors directly above each of the two inclusions. (c)-(e) Time-gated measurements for a single pattern at three timegates showing the measurement at (c) early gate at 40%, (d) maximum gate and (e) late gate at 15% Animal preparation The small animal model employed in the study was euthanized using carbon dioxide inhalation and death was confirmed by cervical dislocation. The animal body (from neck to tail) was shaved on the dorsal and ventral side. The capillary tubes were inserted into the model through a 5mm incision in the lower abdomen

135 119 on the ventral side. Two capillary tubes with an internal diameter of 3.5mm (containing donor-acceptor mixture at AD ratio of 0.25 and 4.0) placed in the abdomen of a euthanized mouse replicated localized FRET activity (c.f. Figure 6.6(a)). The inclusions were attached to the abdominal organs using an optically clear topical tissue adhesive (GLUture, World Precision Instruments, USA). It should be noted that the inclusion with an AD ratio of 0.25 is occluded by highly absorbing abdominal organs, e.g. liver, kidneys etc.. The animal model was then placed in an imaging chamber and restrained by mild compression to a thickness of 15mm. The optical properties of the volume reconstructed were estimated using time-resolved spectroscopy. The average optical properties in the abdominal region of the model was found to be, µ a = 0.05cm 1 and µ s = 4.56cm 1. The acquisition protocol employed in this experiment was exactly identical to the previous study Results The measurements for a single pattern shown in Figure 6.5(c)-(e) reiterate the retention of lifetime contrast in fluorescence signals transmitted through the tissue. The absorptive effects of the organs is evident in the recorded TPSFs shown in Figure 6.5(b) with the signal from object with AD ratio of 0.25 having a lower number of photon counts. The reconstruction of fluorophore concentration was done using the same set of gates as in the previous study. A mm 3 volume was reconstructed and the 3D representation of the total reconstructed fluorescence yield is shown in Figure 6.7(a). The 50% isovolumes of the reconstructed fluorescence inclusions had a mean diameter of 9mm and similar to the tomographic reconstruction of the homogeneous phantom were localized with less than 2mm error in all three dimensions (c.f. Figure 6.7(b)). The quantification metric derived from the relative maximum reconstructed fluorescence estimated for the FRETing donor component is shown in Figure 6.7(c). It should be noted that the quantitative accuracy of the method is retained when imaging optically complex volumes with less than 5% absolute error when the AD ratio is The relatively higher f d estimation error ( 10%) observed in both studies for an AD ratio of 4.0 can be attributed to the limited number of time-gates used in

136 120 (a) (b) Shorter lifetime component (Fraction of quenched donor molecules), f d (%) (c) Baseline estimate (Direct imaging) Tomographic estimate in phantom Tomographic estimate in animal model Acceptor:Donor Ratio (a.u.) Figure 6.7: (a) 50% iso-volumes of total reconstructed donor quantum yield. (b)-(c) Iso-plane images of reconstructed shorter lifetime component at slices shown in (a). (d) Quantitative comparison of tomographic estimates of FRETing donor fraction from above reconstruction. the reconstruction. The higher f d due to the higher acceptor concentration implies a larger shorted lifetime component which reduces the width of the recorded temporal curve. Therefore a larger number of time-gates are required to separate the contributions from either donor species from the temporal response of the tissue. It should however be noted that a 60% FRETing donor component (for AD ratio of 4.0) represents an extreme case in FRET-based studies. 6.6 Discussion Quantitative imaging of FRET activity in preclinical models is a very powerful tool which allows the study of biomolecular interactions in situ. The localization and quantitation of such interactions presents a challenge due to the highly diffusing transport of photons through thick tissue. The time-resolved fluorescence tomographic imaging method presented in this work is able to quantitatively resolve interactions between NIR-FRET probes from depths greater than 10mm which is well beyond the limits of current preclinical FRET imaging techniques. Through the combination of a fast wide-field time-resolved tomographic imaging platform and a Monte Carlo based reconstruction scheme the method described herein was able to accurately localize and quantify volumetric abundances of FRETing and nonfret-