NORTHWESTERN UNIVERSITY

Optical Sensing of Tissue Microstructure and Cell Nanostructure

A DISSERTATION SUBMITTED TO THE GRADUATE SCHOOL IN PARTIAL FULFILLMENT OF THE REQUIREMENTS for the degree DOCTOR OF PHILOSOPHY Field of Biomedical Engineering

by Hariharan Subramanian EVANSTON, ILLINOIS June 2009

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© Copyright by Hariharan Subramanian, 2009 All Rights Reserved

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ABSTRACT

Optical Sensing of Tissue Microstructure and Cell Nanostructure

Hariharan Subramanian

Recently there has been a major thrust to understand biological processes at the micro/nanoscale. Elastic light scattering offers us a powerful and non-invasive means of visualizing the biological medium, as the light scattering signals exhibit characteristic structure dependent patterns and hence are extremely sensitive to micro/nano architectural alterations in tissue and cells. However, in most elastic light scattering experiments the photons undergo several scattering events before exiting the medium thus loosing their sensitivity to micro and nanostructures within the tissue. We have developed two novel optical techniques, low coherence enhanced backscattering (LEBS) and partial wave spectroscopy (PWS) that are sensitive to both tissue microstructure and cell nanostructures.

LEBS enables probing the microarchitecture of

biological tissue by tracking the photons that travel very short distances and hence undergo very few scattering events. Here we developed both numerical and analytical models to understand the fundamental mechanisms of LEBS in biological tissue. Single-cell PWS on the contrary provides a practical means of characterizing cell organization at the nanoscale. Coupled with the mesoscopic light transport theory, PWS quantifies the nanoscale refractive index fluctuations within cells in terms of intracellular disorder strength.

We demonstrated the nanoscale

4 sensitivity of PWS using rigorous finite difference time domain (FDTD) simulations and experiments with nanostructured models. We also showed the potential of PWS in experiments with cell lines and an animal model of colon carcinogenesis, which established an increase in the degree-of-disorder in cell nanoarchitecture parallels genetic events in the early stages of carcinogenesis in otherwise microscopically/histologically normal-appearing cells. We demonstrated that this increase in the disorder strength is not only observed in tumor cells but also in the microscopically normal-appearing cells outside of the tumor in the field of carcinogenesis. Our results from three types of cancer: colon, pancreas and lung showed organwide alteration in cell nanoarchitecture, which appears to be a general event in carcinogenesis. These results have important implications in that PWS can be used as a new methodology to identify patients harboring malignant or premalignant tumors by interrogating the easily accessible tissue sites distant from the location of the lesion.

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Acknowledgements I express my sincere gratitude to my research advisor, Prof. Vadim Backman, for his constant encouragement and support. He has been a great inspiration throughout my research work and his scientific excitement has helped to bring out the best within me. His patience and valuable guidance on research and scientific writing have helped my development as a research scientist. I also thank my committee members: Prof. Allen Taflove, Prof. Thomas Foster, Dr. Hemant Roy, Prof. Malcolm MacIver and Prof. Xu Li for their constructive criticisms and suggestions for improving this thesis. My special thanks to Prof. Thomas Foster for taking time to travel from the University of Rochester for all my committee meetings and for providing valuable insights on my research work. Dr. Prabhakar Pradhan, a research associate at the Biomedical Engineering Department, helped me to understand various matters related to theoretical physics, particularly on mesoscopic theory. I am thankful for his patience in trying to educate me on theoretical aspects behind this research. I am grateful to have worked closely with our previous lab members, Young Kim and Yang Liu. Most of the work discussed in this thesis was built on the framework provided by Young and Yang during their graduate work at the Biophotonics lab. I also thank Dr. Jianmin Gong for his advice on the software needed to control the instrumentation used in this research work. I thank the post-doctoral fellows at the Biophotonics laboratory: Jeremy Rogers, Ilker Capoglu and Alexander Heifetz, for their helpful advice and stimulating discussions. Jeremy

6 offered crucial advice on theoretical and experimental issues and his help on the profilometry measurements discussed in Chapter 8 is highly appreciated. Ilker helped me with the finitedifference time-domain simulations which played an important role in understanding the fundamental aspects of this thesis. I thank the staff at Evanston Northwestern Healthcare: Jameel Mohammed, Nahla Hasabou, Andrej Bogajevic, and Jeen-Soo Chang for collecting the biological samples and helping me with the human studies involved in this project. I also appreciate the help of Dhananjay Kunte at Dr. Hemant Roy's lab for providing the human adenocarcinoma cell lines and for conducting the PCNA studies. I thank my fellow lab members at the Biophotonics lab: Vladimir Turzhitsky, Dhwanil Damania, Andrew Gomes, Sarah Ruderman, Valentina Stoyneva, and Lusik Cherkezyan for creating a dynamic research environment and for your valuable comments. My special thanks to Dhwanil for his experiments on the effect of numerical aperture described in Chapter 8. I also thank the undergraduate students for their assistance in providing the data described here on a daily basis. I am grateful to my parents and parents-in-law for their belief in me and their support beyond measure. They constantly encouraged me and guided me to independence, never trying to limit my aspirations. Finally, the power of words may not be sufficient to express my gratitude for my wife, Vidhya, for her support in every stage of this research work and for guiding me in difficult situations. She patiently endured my graduate student life and her emotional support played a major part in maintaining my sanity throughout the completion of this research work.

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To my wife, Vidhya

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Table of Contents Abstract ............................................................................................................................................3 Acknowledgements..........................................................................................................................5 Table of Contents.............................................................................................................................8 List of Figures ................................................................................................................................12 List of Tables .................................................................................................................................17 Chapter 1 Introduction ...................................................................................................................18 Chapter 2 Modeling low coherence enhanced backscattering.......................................................21 2.1 Introduction......................................................................................................................... 21 2.2 Methods............................................................................................................................... 25 2.2.1 Monte Carlo model of LEBS ....................................................................................... 25 2.3 Results and Discussion ....................................................................................................... 29 2.3.1 Effect of exit angle of photons in low orders of scattering.......................................... 29 2.3.2 Importance of proper exit angle in modeling LEBS peaks.......................................... 33 2.3.3 Validation of LEBS Monte Carlo Simulations ............................................................ 39 2.3.4 Comparison of Monte Carlo simulation with experimental results ............................. 42 2.4 Summary ............................................................................................................................. 45 Chapter 3 Penetration depth of low-coherence enhanced backscattered light in the sub-diffusion regime ............................................................................................................................................46 3.1 Introduction......................................................................................................................... 46 3.2 Methods............................................................................................................................... 49

9 3.2.1 Numerical model using Monte Carlo simulation......................................................... 49 3.2.2 Analytical derivation of p(z), and zmp........................................................................... 51 3.3 Results and Discussion ....................................................................................................... 56 3.3.1 Scattering and penetration depth distribution - numerical studies............................... 56 3.3.2 Comparison of the results of numerical simulations and analytical model ................. 61 3.4 Summary ............................................................................................................................. 67 Chapter 4 Partial wave microscopic spectroscopy detects sub-wavelength refractive index fluctuations.....................................................................................................................................69 4.1 Introduction......................................................................................................................... 69 4.2 Methods............................................................................................................................... 71 4.2.1 Partial-Wave Spectroscopy (PWS) Instrument............................................................ 71 4.2.2 Calculation of fluctuating component R (k ) from the backscattering signal.............. 77 4.2.3 Calculation of disorder strength using mesoscopic theory .......................................... 78 4.2.4 Calculation of Ld in biological cells............................................................................ 79 4.3 Results and Discussion ....................................................................................................... 82 4.3.1 Validation of PWS in computational experiments....................................................... 82 4.3.2 Validation of PWS using nanostructured model media............................................... 87 4.3.3 Experimental PWS data confirms the validity of mesoscopic theory-based analysis . 90 4.3.4 PWS detects human pancreatic cancer ........................................................................ 93 4.4 Summary ............................................................................................................................. 97 Chapter 5 Detecting nanoscale consequences of genetic alterations in biological cells using PWS98 5.1 Introduction......................................................................................................................... 98

10 5.2 Methods............................................................................................................................. 100 5.2.1 Cell cultures ............................................................................................................... 100 5.2.2 Animals ...................................................................................................................... 102 5.3 Results and Discussion ..................................................................................................... 103 5.3.1 Experiments with the animal model of colon carcinogenesis.................................... 109 5.3.2 Length scale probed by PWS..................................................................................... 112 5.4 Summary ........................................................................................................................... 113 Chapter 6 Detecting nanoscale cellular changes in field carcinogenesis using PWS..................116 6.1 Introduction....................................................................................................................... 116 6.2 Methods............................................................................................................................. 118 6.2.1 PWS instrumentation ................................................................................................. 118 6.2.2 Sample preparation .................................................................................................... 119 6.3 Results and Discussion ..................................................................................................... 120 6.4 Summary ........................................................................................................................... 130 Chapter 7 Detecting the presence of field carcinogenesis from lung cancer using PWS: an application in lung cancer screening............................................................................................131 7.1 Introduction....................................................................................................................... 131 7.2 Methods............................................................................................................................. 135 7.2.1 Human Studies ........................................................................................................... 135 7.2.2 Partial wave microscopic spectroscopy ..................................................................... 136 7.2.3 Statistical analysis...................................................................................................... 137 7.3 Results and Discussion ..................................................................................................... 137

11 7.4 Summary ........................................................................................................................... 147 Chapter 8 Demystifying Partial wave spectroscopy ....................................................................148 8.1 Introduction....................................................................................................................... 148 8.2 Methods............................................................................................................................. 149 8.2.1 Real time PWS instrumentation................................................................................. 149 8.2.2 1D FDTD simulation ................................................................................................. 151 8.3 Results and Discussion ..................................................................................................... 152 8.3.1 Source of low frequency signal in PWS spectrum..................................................... 152 8.3.2 Effect of intracellular refractive index fluctuations ................................................... 157 8.3.3 Effect of surface roughness of cells on PWS signal .................................................. 163 8.3.4 Effect of numerical aperture on PWS ........................................................................ 169 8.4 Summary ........................................................................................................................... 172 Chapter 9 Conclusion...................................................................................................................174 References....................................................................................................................................178 Curriculum Vitae .........................................................................................................................189

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List of Figures Figure 2:1. Illustration of time reversed paths in EBS................................................................. 22 Figure 2:2. Normalized intensity at different exit angles in the diffusion regime........................ 31 Figure 2:3. Normalized intensity at different exit angles in the low scattering regime................ 33 Figure 2:4. The dependence of the function on (a) θci and (b) Lsc. ........................ 35 Figure 2:5. The dependence of the function on penetration depth z ....................... 38 Figure 2:6. Probability of exit angle Pex(θci) as a function of θci obtained for low order scattering regime. .................................................................................................................................. 39 Figure 2:7. Comparison of the EBS profile from MC simulation and analytical formulation. .... 40 Figure 2:8. Comparison of the LEBS peak from MC simulation to the experimental results from white paint under LSC illumination...................................................................................... 41 Figure 2:9. Comparison of LEBS peak profile from MC simulation to the experiments from aqueous suspensions of polystyrene microspheres under LSC illumination. ....................... 43 Figure 2:10. Comparison of angular width W of the LEBS peaks obtained from MC simulation with that of LEBS peaks from experiment under LSC illumination. ................................... 44 Figure 3:1. A schematic picture of a photon that undergoes double scattering and exits within a very small radial distance r. .................................................................................................. 52 Figure 3:2. The scattering distribution of the photons p(ns) vs number of scattering ns from the numerical simulation............................................................................................................. 58 Figure 3:3. The penetration depth distribution p(z) of the photons vs depth z from numerical simulation.............................................................................................................................. 59

13 Figure 3:4. The penetration depth distribution p(z) of single scattering photons plotted against those from double scattering photons at different depth z. ................................................... 62 Figure 3:5. Comparison of penetration depth distribution p(z) of photons obtained from numerical simulation and analytical expression. .................................................................. 64 Figure 3:6. Comparison between the effective penetration depth zmp of the LEBS photons predicted by the numerical model and analytical expression. .............................................. 65 Figure 3:7. The dependence of zmp on individual optical properties plotted against ls and g. ..... 67 Figure 4:1. Schematic of the partial-wave microscopic spectroscopy (PWS) system.................. 73 Figure 4:2. The backscattering spectrum obtained using PWS from a single isolated biological cell and glass slide. ............................................................................................................... 75 Figure 4:3. Steps involved in PWS signal acquisition and analysis. ........................................... 81 Figure 4:4. FDTD simulations demonstrate the validity of using 1-D model to analyze the backscattered spectra of each pixel in the PWS image......................................................... 85 Figure 4:5. Comparison of the theoretical disorder strength and the one calculated using the 1D FDTD simulation. ................................................................................................................. 86 Figure 4:6. Validation of the nanoscale sensitivity of disorder strength using experimental nanostructured model media. ................................................................................................ 89 Figure 4:7. Effect of thickness on the disorder strength calculated from nanostructure model media..................................................................................................................................... 90 Figure 4:8. A representative probability density function and correlation decay in biological cells. ...................................................................................................................................... 92

14 Figure 4:9. A representative bright field image and the corresponding pseudo-color Ld map recorded from three different cell types................................................................................ 95 Figure 4:10. The relative values of the disorder strength and standard deviation of disorder strength from for three different pancreatic cell types.......................................................... 96 Figure 5:1. Effect of knockdown of CSK and EGFR gene expression on cell proliferation..... 102 Figure 5:2. Representative (a) cytological images and (b) pseudo-color PWS images from three HT29 cell types. .................................................................................................................. 106 Figure 5:3. Cells with a more aggressive malignant behavior have a higher intracellular disorder strength................................................................................................................................ 107 Figure 5:4. The relative values of the disorder strength L(dg ) and standard deviation σ ( g ) for three HT29 cell types. .................................................................................................................. 108 Figure 5:5. Comparison of the average disorder strength L(dg ) and intracellular standard deviation of the disorder strength σ ( g ) in the wild-type and MIN-mice. ........................................... 111 Figure 5:6. Ld and σ Ld averaged over a cell for the cells obtained from the wild-type and the MIN-mice plotted in the L(dc ) , σ ( c ) parameter space. .......................................................... 112 Figure 6:1. Cells at a distance from a colon tumor undergo changes in their internal nanoarchitecture similar to tumor cells............................................................................... 121 Figure 6:2. The relative values of the disorder strength L(dg ) and intracellular standard deviation of the disorder strength σ ( g ) for the three cell types. ......................................................... 122 Figure 6:3. Cells obtained from histologically normal colonic mucosa have increased disorder strength due to the presence of premalignant tumors anywhere else in colon.................... 124

15 Figure 6:4. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal rectal mucosa in patients with premalignant tumors and those with no tumors present. ............. 125 Figure 6:5. Histologically normal duodenal mucosa cells have increased disorder strength due to the presence of pancreatic cancer. ...................................................................................... 127 Figure 6:6. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal duodenal mucosa in patients with and without pancreatic cancer...................................................... 128 Figure 7:1. Histologically normal buccal mucosa cells have increased disorder strength due to the presence of lung cancer................................................................................................. 138 Figure 7:2. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal buccal mucosa in patients with and without lung cancer. .............................................................. 140 Figure 7:3. Representative bright field images and pseudo-color PWS images from buccal mucosa cells from patients with lung cancer and patients with COPD. ............................. 141 Figure 7:4. Comparison of L(dc ) and σ ( c ) of histologically normal buccal mucosa cells from patients with lung cancer and patients with COPD. ........................................................... 142 Figure 7:5. The relative values of (a) disorder strength L(dg ) and standard deviation σ ( g ) for patients with lung cancer and patients with COPD. ........................................................... 143 Figure 8:1. Schematic of the real time partial-wave spectroscopy (rtPWS) system.................. 151 Figure 8:2. The normalized backscattering spectrum obtained from a single pixel of a biological cell and pure glass slide. ..................................................................................................... 153 Figure 8:3. The normalized backscattering spectrum obtained from a single pixel of a spherical microsphere and thin film. .................................................................................................. 156

16 Figure 8:4. The normalized backscattering spectrum obtained from a single pixel of a spherical microsphere embedded in agarose gel................................................................. 156 Figure 8:5. The 1D backscattering spectrum obtained from FDTD numerical simulation. ...... 160 Figure 8:6. Critical Δn and lc obtained using 1D FDTD numerical simulation and a 1D FDTD backscattering spectrum obtained for medium with Δn above the critical value................ 162 Figure 8:7. Relative thickness of the cell calculated using optical profilometer. ...................... 164 Figure 8:8. Surface roughness of a single biological cell obtained using optical profilometer. 166 Figure 8:9. Surface roughness across a one-dimensional cross section of the biological cell calculated using optical profilometer.................................................................................. 167 Figure 8:10. Disorder strength of a single biological cell obtained using PWS. ....................... 168 Figure 8:11. Disorder strength obtained from different nanostructure model media at three different numerical aperture of illumination....................................................................... 170

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List of Tables Table 7:1. Diagnostic performance of PWS is not affected by the patient demographic factors. ............................................................................................................................................. 145 Table 8:1. Correlation coefficient from curves of different dimensions fit to disorder strength as a function of bead sizes....................................................................................................... 171 Table 8:2. Effect of numerical aperture of illumination on the diagnostic performance of PWS. ............................................................................................................................................. 172

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Chapter 1 Introduction Optical sensing of biological tissue microarchitecture and cell nanoarchitecture is crucial to exploit the use of light for both diagnostic and therapeutic purposes. Several biomedical optical techniques such as diffuse reflectance spectroscopy, optical coherence tomography, Raman spectroscopy, fluorescence spectroscopy, and elastic light scattering spectroscopy have shown great potential to probe tissue optical properties and diagnose tissue architectural alterations [1-10]. Elastic light scattering spectroscopy, in particular, provides a cost effective and non-invasive tool to probe tissue structures. The light that is scattered from the structures within the tissue exhibits characteristic patterns in scattering angle and wavelength with the light scattering signature dependent on the properties of the scatterer such as the shape, size, refractive index and the density. Recently Li et al., showed that the elastic light scattering signal in the backward direction is sensitive to alterations in the refractive index [11]. This sensitivity of light scattering to tissue architecture provide a means of probing tissue structure in a wide range of scales without the need for tissue removal, fixation and staining [3, 5, 12-14]. In conventional elastic light scattering experiments, the light is multiple scattered before exiting the biological tissue resulting in decreased sensitivity of light scattering signals to both the micro and nanoscale structures within the tissue and cells. In this thesis we discuss two elastic light scattering techniques: low coherence enhanced backscattering (LEBS) and partial

19 wave spectroscopy (PWS) that are capable of probing tissue microarchitecture and cell nanoarchitecture, respectively. LEBS enables detecting the enhanced backscattering intensity peaks from different layers within the biological sample and thereby probe tissue microarchitecture [12, 15]. PWS on the other hand probes the nanoarchitecture of biological cells and quantifies the statistical properties of nanoscale refractive index fluctuations. The first part of the thesis discusses the LEBS from biological tissue while the second part of the thesis discusses the PWS measurements from biological samples. The thesis is organized as follows. In chapter 2, we discuss modeling the LEBS peak from biological samples using a photon random walk model. This random walk model based on Monte Carlo simulation explains the fundamental reason behind the broadening of enhanced backscattering intensity peaks in biological tissue. In chapter 4, we develop an analytical model of photon penetration depth in the sub diffusion regime and compare its results with the numerical model obtained using Monte Carlo simulation. These analytical models help us in understanding the dependence of optical properties of biological tissue on the depth to which the photon propagates within the tissue. In chapter 4, we discuss the novel optical technique, partial wave spectroscopy, that enables detecting the 1D backscattering partial waves from biological cells.

We show that these 1D backscattering partial waves are extremely sensitive to

nanoarchitectural alterations in biological cells and hence can be used to diagnose patients with pancreatic cancer who are falsely misdiagnosed to be normal by conventional cytopathology. In chapter 5 we demonstrate that genetic alterations in biological cells translate into changes in their nanoarchitecture which in turn can be sensed using PWS. For example, we show that PWS can

20 be used to detect subtle genetic knockdown variants of human colon adenocarcinoma (HT29) cell lines that are otherwise indistinguishable by conventional histopathology. We also show that PWS can be used to detect early changes in cell nanoarchitecture using an animal model of colorectal cancer - MIN (multiple intestinal neoplasia) mouse. Chapters 6 and 7 show that the cells in the field of carcinogenesis in organs such as colon, pancreas and lung exhibit changes in the nanoarchitecture which can potentially be exploited using PWS to develop non-invasive screening techniques for colon, pancreas and lung cancer.

In chapter 8 we discuss the

fundamental mechanism of light propagation in biological cells. We show the effect of the properties of the medium such as its internal refractive index fluctuations, surface roughness as well as the properties of illumination such as the numerical aperture of illumination/collection on the 1D backscattering partial waves. Chapter 9 concludes the thesis.

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Chapter 2 Modeling low coherence enhanced backscattering 2.1 Introduction The constructive self-interference of coherent waves traveling in time-reversed paths in a random medium gives rise to an enhanced scattering intensity in the backward direction. For a plane wave illuminating a semi-infinite random medium, every photon exiting the medium in the backward direction has a time-reversed photon traveling along the same path in the opposite direction (Figure 2:1). These photons, due to the time reversal invariance of light, have the same phase and, hence, interfere constructively to produce an enhanced backscattering intensity. In case of complete diffusion of light, the amplitude of this intensity profile as a function of the backscattering angle can be as high as twice that of the incoherent background [16]. This increase in reflectivity in the backward direction leads to a reduction in the amount of light transported in the forward direction resulting in the weak localization of photons. phenomenon

of

enhanced

backscattering

(EBS,

also

known

backscattering) was first experimentally observed in aqueous suspensions of

as

This

coherent

22

r k in

θ

θ

r k out

Figure 2:1. Illustration of time reversed paths in EBS. EBS is formed due to the constructive interference between a pair of photons traveling in time reversed paths (solid line and dashed line) in the opposite direction as they exit the medium close to the backward direction ( θ ~ 0 o ).

polystyrene microspheres [16-18]. Thereafter, EBS has become a subject of major research interest and has been observed in solids [19, 20], aggregated media [21], cold atoms [22], liquid crystals [23] etc. In these experiments, in order to explain the enhanced backscattering, the light was assumed to be completely spatially coherent [24, 25].

According to the diffusion

approximation, in a homogeneous semi-infinite random medium, the full angular width at halfmaximum (FWHM), ω hm , of the EBS peak is mainly determined by the transport mean free pathlength ls* of the medium [17, 18]:

ω hm = λ /(3πl s* )

(1)

where λ is the wavelength of light. Although EBS enhancement has been widely studied in a variety of non-biological media (with relatively short ls* [21, 22, 26]) using coherent laser light

23 sources, there are only few reports of EBS observation in biological tissue [27-29]. Measurement of light scattering properties in a biological tissue is crucial to exploit the use of light for both diagnostic and therapeutic purposes [1-8]. Accordingly, EBS may be used as one of the potential tools for noninvasive optical characterization of a biological tissue. However, conventional EBS measurements have several limitations for biological tissue applications: a) due to the inverse relationship between the angular width and ls* (in biological tissue, ls* ~ 3002000 μm [30]), observing the narrow EBS peak is experimentally challenging. Only recently, in pioneering experiments, Yodh and Sapienza [23] have achieved detection of such narrow EBS peaks in non-biological media. b) EBS peaks are masked by speckles in solid samples such as a biological tissue, and hence ensemble averaging over thousands of measurements are often required to uncover a EBS peak in the backscattering direction. Recently, we demonstrated the feasibility of observing EBS under low spatial coherence (LSC) illumination ( Lsc << l s* , where Lsc is the spatial coherence length of the light source). LSC illumination behaves as a spatial filter that rejects longer path-lengths with exponentially low probability, thus resulting in a more than 100 times increase in the angular width of low coherence EBS (LEBS) peaks [15, 31]. Furthermore, we showed that not only does LEBS represent a novel enhanced backscattering phenomenon, but it also opens up the feasibility of studying enhanced backscattering in biological tissue and other media with long l s* and enables depth-selective spectroscopic tissue characterization [12, 15, 31, 32].

For example, we

demonstrated that LEBS can be used to diagnose the earliest, previously undetectable stage of colon carcinogenesis that precedes histologically detectable lesions [12, 33]. The LEBS peaks in

24 these experiments were observed by combining EBS measurements with LSC illumination and low temporal coherence detection.

The LSC illumination was achieved by using a

broadband continuous wave xenon lamp. We note that one of the most intriguing properties of LEBS phenomenon is the dramatically increased angular width of the LEBS peaks, which cannot be explained on the basis of conventional diffusion approximation based models. In order to further our understanding of this unprecedented broadening of LEBS peaks and to identify the origin of LEBS, it is necessary to develop rigorous numerical models. In this chapter we present the photon random walk model of low coherence enhanced backscattering using Monte Carlo simulations, which is subsequently compared with the experimentally obtained LEBS peaks. Monte Carlo simulations have been extensively used to simulate light propagation in biological tissue [34-36]. Many groups have used Monte Carlo modeling of EBS peaks in both biological and non-biological samples [22, 37-40]. Kaiser et al. [40] reported the first quantitative comparison between the experimentally observed EBS peaks and Monte Carlo simulation in cold atoms by taking into account the shape of atomic cloud and its internal structure. Delpy and colleagues [37] used a Monte Carlo model of backscattered light from turbid media to simulate weak localization in biological tissues and thereby extracted optical parameters such as scattering and absorption coefficients from angular intensity profiles of EBS peaks. Berrocal et al. [41] recently characterized intermediate scattering in sprays and other industrially relevant turbid media using Monte Carlo simulation.

Specifically, they

explained the influence of the exit angle of photons on the relative intensity of different orders of

25 scattering in the intermediate, single-to-multiple scattering regime and validated their results by Monte Carlo simulation. Here, we model LEBS for the first time using Monte Carlo simulation. We not only show that our model is in excellent agreement with the experimental data, but also explain the origin of LEBS broadening. We demonstrate that the exit angle of the scattered photons, which is typically neglected in modeling conventional EBS peaks, is of critical importance when the

Lsc of the light source is much smaller than l s* (i.e., Lsc << l s* ). We also show that these exit angles of photons plays only a minimal role in the diffusion regime when Lsc is much greater than l s* of the medium (i.e., Lsc >> l s* ).

2.2 Methods 2.2.1 Monte Carlo model of LEBS In order to model the LEBS peak, we used a photon random walk model based Monte Carlo (MC) simulation. As it is challenging to simulate the time-reversal of photons and its interference effects explicitly using MC, the EBS angular profile, I EBS (θ ) , is generally calculated indirectly by using the fundamental relationship between I EBS (θ ) and the probability of radial intensity distribution P(r) of EBS photons with r being the radial vector pointing from the first to last points on the conjugated time reversed light path. The intensity of the EBS peak thus obtained in the backward direction, IEBS, can be written as [18, 42],

r I EBS (q ⊥ ) = ∫∫ P(r ) exp(iq ⊥ .r )d 2 r ,

(2)

26 where q ⊥ is the projection of wave vector onto the orthogonal plane in the backward direction. In an isotropic disordered medium, the two dimensional Fourier integral in Eq. (2) can be further simplified to [31], r I EBS (q ⊥ ) ∝ ∫ rP(r ) exp(iq ⊥ .r )d r ,

(3)

where rP(r) is the radial intensity distribution of the conjugated time-reversed paths around a point-like light source illuminating a sample and the projection of wave vector, q ⊥ = 2π sin θ / λ . MC simulation is used to simulate the rP(r) around a point like light source illuminating the sample. This method of indirectly modeling EBS angular profiles has been successfully used in both biological and non-biological samples [24, 37, 39]. In this chapter, to model the effect of LSC illumination on EBS, we incorporated an additional coherence length dependent weighting factor to the numerical MC simulation. We used the readily derived form of the degree of spatial coherence C Lsc (r ) as follows [43]: C Lsc ( r ) = 2 J 1 ( r / L sc ) /( r / L sc ) ,

(4)

where J 1 is the first order Bessel function, and Lsc is the spatial coherence length corresponding to the 88th percentile of the ideal value of unity. Thus, the LEBS intensity in the presence of a low coherence source can be written as

I LEBS (θ ) ∝ ∫ rP ( r ).C Lsc ( r ) exp(i

2π sin θ

λ

r )d r .

(5)

Similar to the EBS model, the first term in the above equation, rP(r) (≡ I(r)), (i.e., the radial intensity distribution) of the point like source illuminating the sample is obtained using the MC simulation.

27 A detailed description of the MC simulation is given elsewhere [34, 44]. Here we only briefly describe the essential aspects of this method.

In our simulations, we launch

approximately 1010 photon packets into the sample. The optical parameters of the sample are assigned based on the sample size used in the LEBS experiment [15]. The samples are slabs with infinite lateral extents and have optical parameters relevant to biological tissue ( l s* ~ 500 μm -- 2000 μm, g ~ 0.6 -- 0.9, λ = 520 nm). The direction of photon incidence is normal to the sample’s surface (xy-plane) with an initial weight w. As the specular reflectance is completely avoided in the experiment, we allow the photon packets to propagate within the sample with its initial weight of w and random step size s, given by s = − ln(ξ ) / μ t , where μ t is the total interaction coefficient of the medium and ξ is the pseudorandom number uniformly distributed between 0 and 1. Once the photon packet reaches the interaction site, a scattering direction is then defined by the deflection angle θ ( 0 < θ < π ) and azimuthal angle ϕ ( 0 < ϕ < 2π ) which are statistically sampled. We chose the probability distribution of the cosine of the deflection angle according to the Henyey-Greenstein anisotropic phase function [45] given as PHG (cosθ ) = (1 − g 2 ) /( 2(1 + g 2 − 2 g cos θ ) 3 / 2 ) ,

(6)

where < cos(θ ) >= g . We assume the angular distribution to be azimuthally symmetrical, i.e. uniform distribution for ϕ ( = 2πξ ) , such that, Pϕ (ϕ ) = 1 / 2π . The photon packet is terminated using a Russian roulette technique [46] after it undergoes a series of scattering events. The weight of the photon packets escaping from the medium in the forward or backward direction is then recorded in a user defined grid system.

28 Our study is focused on the radial intensity distribution of photons in the backward direction from low order scattering events. Hence the spatial resolution of the grid system used in the MC simulation to collect these low order scattering photons is kept at 1μm. Similarly, we collect the photons exiting at small exit angles (exit angle is defined as the angle at which the photon packets exit the medium in the backward direction) using the grid system with the angular resolution of ~0.3˚. Once the radial intensity distribution P(r ) is calculated from the MC simulation, Eq. (5) is then used to obtain the LEBS peak using the Fourier transform of the radial intensity distribution. The LEBS peak obtained is then convolved with the angular response of the instrument (~ 0.04˚ – 0.3˚) to compensate for the finite point-spread function of the detection system and the slight divergence of the incident beam. The width of the convolved LEBS peak W is defined as follows [47], 2

⎛∞ r r ⎞ r r W = ⎜⎜ ∫ I LEBS (q ⊥ )dq ⊥ ⎟⎟ /( ∫ I 2 LEBS (q ⊥ )dq ⊥ ) . ⎝0 ⎠

(7)

According to our simulations, W provides a better metric to characterize LEBS peak width compared to FWHM. The width obtained from the simulation is then compared with those obtained from the LEBS experiment.

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2.3 Results and Discussion 2.3.1 Effect of exit angle of photons in low orders of scattering In a diffusive multiple scattering regime, the EBS peak is obtained directly from the Fourier transform of the radial intensity distribution rP(r) of the point source illuminating the sample. However, in these EBS models, the angle at which the photons exit the medium in the backward (i.e., exit angle) is often neglected in the rP(r) calculation. Here we study the effect of exit angles in determining the shape of rP(r) in both the diffusion regime and the low order scattering regime. We calculate rP(r) on the surface of the medium with the following optical properties: l s* = 2 mm, the absorption coefficient μa = 0.0001 mm-1 and scattering coefficient μs = 5 mm-1(at λ = 520 nm) respectively. Unlike the grid system used to collect low order scattering photons (Section 1.2), the radial and angular resolutions of the grid system used to collect the diffusive multiple scattering photons are 10μm and 0.3˚ respectively. The rP(r) is calculated using the MC simulation at different exit angles between 0.3˚ and 90˚ as follows, ∞ π /2

∫ ∫ p(r ,θ )drdθ = N ,

(8)

r =0 θ =0

(for μ a ~ 0 and transmission ~ 0 ), where N is the total number of photon packets injected into the medium, r is the distance at which the photons exit the medium and θ is the angle at which the photons exit the medium. We redefine the above probability integral for any finite exit angle as follows:

30 ∞ θci



∫ θ∫ p(r,θ )drdθ = ∫ pθ

r =0 =0

r =0

ci

(r )dr = N ∞,ci .

(9)

We normalize the above probability along the radial direction keeping the maximum exit angles θci (i=1,2, 3,..) constant. Let, p θ ( r ) / N ∞ ,ci = Pθ ( r ) , thus, ci

ci



∫ Pθ

ci

(r )dr = 1 .

(10)

0

We consider three different exit angles, θc1 = 1.5˚, θc2 = 20˚, and θc3 =80˚. As seen in Figure 2:2, in the diffusion regime, the shape of r Pθ ci (r ) , (i =1,2, and 3) is less sensitive to the change in exit angles explaining the reason for neglecting the effect of exit angles in modeling an EBS peak. That is, in the diffusion regime, the slight changes in rP(r) obtained from MC simulation at different exit angles are translated over a radial distance of over 50 mm and hence the small changes in rP(r) do not translate into peak width when the Fourier transform of rP(r) is performed.

Therefore, the exit angles are less sensitive in the multiple scattering regime

providing similar EBS peaks for different exit angles. However, a different picture emerges in the low order scattering regime when the number of scattering events is restricted by the LSC illumination. That is, the r Pθ ci (r ) curves become broader as θci increases from 1.5˚ to 80˚, as shown in Figure 2:3

31

-3

Normalized Intensity rP(r) (A.U)

x 10

θci = 1.5° θci = 20°

6

θci = 80°

4

2

0 0

5

10

15

Radial distance r (mm)

2

25

Figure 2:2. Normalized intensity at different exit angles in the diffusion regime. The intensities are calculated using MC simulation from a medium with l s* = 2 mm, g = 0.9 (at λ = 520 nm) and Lsc = 50 mm. The intensity profiles for different exit angles remains constant in the diffusive multiple scattering regime.

In case of LSC illumination, Eq. (8) can be written as, Lsc π / 2

∫ ∫ p(r,θ )drdθ = N

Lsc

,

(11)

r =0 θ =0

where NLsc is the number of photons restricted by finite spatial area using LSC illumination, and, Lscθci

Lsc

∫ ∫ p(r,θ )drdθ = ∫ p θ 0 0

ci

(r )dr = N Lsc,ci .

(12)

0

Let, p θ (r )dr / N Lsc ,ci = Pθ (r ) , thus, ci

ci

Lsc

∫ Pθ 0

ci

(r )dr =1 .

(13)

32 As pointed out earlier, contrary to the diffusion regime the shapes of r Pθ ci (r ) in the low order scattering regime are different and the shape of r Pθc1 (r ) is much narrower than that of r Pθ c 2 (r ) . For small radial distances corresponding to only few scattering events, this can be

written as, Lsc / 10

∫ Pθ 0

Lsc / 10 c1

(r )dr >>

∫ Pθ 0

c2

(r )dr .

(14)

Normalized Intensity

rP(r) (a.u.)

33

θci = 1.5°

0.06

θci = 20° θci = 80° 0.04

0.02

0 0

200

400

Radial distance r (μm)

600

800

Figure 2:3. Normalized intensity at different exit angles in the low scattering regime. The intensities are calculated using MC simulation (ls* = 2 mm, g = 0.9, at λ = 520 nm) with Lsc = 600 μm. When the number of scattering events is restricted due to the LSC illumination, the intensity profile over r becomes broad as θci increases from 1.5˚ to 80˚.

2.3.2 Importance of proper exit angle in modeling LEBS peaks The above results show that, in the low order scattering regime, the shape of rP(r) is determined by the exit angle of the photons. We asked the following questions: a) what does these exit angles relate to within the medium and b) what exit angles should be chosen to accurately model LEBS angular profiles? In this section we first show that the exit angles are related to the penetration depth of the photons propagating within the medium. This is because the trajectories of the photons are clustered into a compact locus to exit at small angles for low orders of scattering, while the trajectories are less compact for multiple scattering. This is illustrated in Figure 2:4 (a) and (b), which show the quantity < r (θ ci , Lsc ) > calculated for different

34 exit angles and different Lsc. which relates the function < r (θ ci , Lsc ) > with z, where z is the penetration depth of a photon . That is, Lscj

< r (θ ci , Lsc ) >=

∫ rPθ

ci

(r )dr ,

0

where i = 0 to 90 degrees and j = 20 to 140 μm.

(15)

Normalized Amplitude (a.u.)

35 300

(a)

Lsc = 50 μ m Lsc = 75 μ m Lsc = 115 μ m 200

100

0

Normalized Amplitude (a.u.)

Lsc = 35 μ m

300

20

40

60

80

Angle θci (Degree)

θci = 1.5°

(b)

θci = 30° θci = 45° 200

θci = 90°

100

20

60

100

Spatial coherence length Lsc (μm)

140

Figure 2:4. The dependence of the function on (a) θci and (b) Lsc. < r (θ ci , Lsc ) > is calculated using MC simulation from a medium with ls* = 2 mm, and g = 0.9 (at λ = 520 nm). θci is varied from 1˚ to 90˚ and Lsc is varied between 35 μm and 140 μm. < r (θ ci , Lsc ) > is proportional to both θci and Lsc.

36 As seen in Figure 2:4(a), for a given Lsc, the function < r (θ ci , Lsc ) > increases with the increase of the exit angle from 0 to 90 degrees. Similarly, for a fixed exit angle, increase in Lsc from 20 to 140 μm leads to an increase in < r (θ ci , Lsc ) > (Figure 2:4(b)). The relationship between < r (θ ci , Lsc ) > and z is obtained using MC simulation by tracking the propagation of photons along the axial z-direction (the grid size in the z-direction ~ 1 μm). Figure 2:5 shows this relationship from MC, which indicates that < r (θ ci , Lsc ) > is indeed proportional to z. These results not only confirm that the exit angle θci is proportional to the penetration depth of photons, but also indicates the necessity of accurately choosing a particular θci for modeling LEBS peaks. In theory, an exit angle close to the backscattering direction (i.e., θci~0°) will be chosen to model LEBS angular profiles. However, it is impossible to collect the

photons that exit at the exact backward direction using MC simulation. Hence an optimum exit angle close to the backward direction is required to accurately model the LEBS peak. The probability of photon exit angle Pex (θ ci ) under LSC illumination (Lsc = 200 μm) obtained by varying the θci between 1˚ and 90˚is shown in Figure 2:6. As seen, Pex (θ ci ) remains almost identical at small angles between 0.3˚-3˚. Hence we take the mid-point of this distribution (~1.5˚) as the optimum exit angle at which rP(r) is calculated. It is important to note that the LEBS peak width obtained from the exit angle θci ~1.5˚ deviates less than 5% when compared to the photons collected at extremely low exit angles (< 0.3˚). However, any change in the θci beyond this would significantly change the depth from which the time reversed photons are obtained leading to erroneous modeling of LEBS. Thus, the LEBS peak is modeled using MC simulation as follows: a) we obtain P(r) at 1.5˚ using MC simulation and then multiply it by the

37 spatial coherence function (Eq. 4). The coherence function is obtained using the Lsc used in the experiment. b) The Fourier transform of this product is then taken to obtain the LEBS peak. In subsequent sections, we present detailed validation of the LEBS peak obtained using MC simulation.

38

200

2.8

Radial distance r ( μm)

2.6 2.4

400

2.2 2

600

1.8 1.6

800

1.4 1.2

1000

200

400

600

Depth z (μm)

800

1000

1

Figure 2:5. The dependence of the function on penetration depth z is calculated from a medium with ls* = 2 mm, and g = 0.9 (at λ = 520 nm) using MC simulation for a constant θci = 45˚ and Lsc = 600 μm. is proportional to the penetration depth z.

39

Pex ( θci ) (a.u.)

1

0.8

0.6

0.4

0.2

0

0

20

40

60

Angle θ (Degree) ci

80

Figure 2:6. Probability of exit angle Pex(θci) as a function of θci obtained for low order scattering regime. Pex(θci) is calculated using MC simulation (ls* = 2 mm, g = 0.9 at λ = 520 nm) for a fixed Lsc = 200 μm by varying θci between 1˚ and 90˚. Pex(θci) converges at small angles of around 1˚-3˚ when Lsc<
2.3.3 Validation of LEBS Monte Carlo Simulations In order to verify the accuracy of the MC simulation, we first compare the profile of the EBS peak obtained from numerical simulation with the profile of the EBS peak calculated by Akkermans et al. [48] for an isotropic scattering medium. The simulation is performed with l s* = 2 mm and infinite Lsc (Lsc = 50 mm), with the exit angle, θci ≈ 1.5˚. Figure 2:7 shows this agreement between the MC simulation and analytical results. In order to verify the insignificant role played by exit angles in modeling EBS peaks, the results from θci ≈ 1.5˚ are compared with θci=80˚. As shown in Figure 2:7, the MC simulations from small exit angle (circles) agree well

with the results obtained from large exit angles (asterisks).

40 Theory curve °

MC Simulation (θci = 80 )

Normalized Intensity (a.u.)

1.2

°

MC Simulation (θci = 1.5 )

0.8

0.4

0 -0.03

-0.015

0

0.015

Angle θ (Degree)

0.03

Figure 2:7. Comparison of the EBS profile from MC simulation and analytical formulation. The profile of EBS peak IEBS(θ) is calculated from a medium with ls* = 2 mm, and g = 0.9 (at λ = 520 nm) for Lsc = 50 mm. The results from simulation are in excellent agreement with the analytical results. Also, the EBS simulation for θci = 1.5˚ agrees well with the results obtained from θci = 80˚ as the width of the EBS peak is insensitive to the θci in the diffusive multiple scattering regime.

We next validate the spatial coherence function (Eq. 4) used in simulating the LEBS peak. This is done by comparing the profiles obtained from the MC simulation with those of the LEBS experiments (discussed later) for a sample with l s* significantly smaller than Lsc . In this regime ( l s* << Lsc ), though Lsc is small, LEBS profiles are primarily determined by l s* as the light scattering paths are not affected by the Lsc . We simulate the LEBS peak with Lsc = 160 μm from a sample with l s* = 4 μm. The peaks were compared with the experiment where the LEBS peaks were obtained from white paint (Benjamin Moore) with l s* = 4 μm under LSC illumination (Xenon lamp).

41 LEBS Experiment (Lsc = 160 μm)

Normalized Intensity (a.u.)

EBS Simulation

(Lsc = 50 mm)

LEBS Simulation (Lsc = 160 μm)

1.2

0.8

0.4

0

-2

-1

0

1

Angle θ (Degree)

2

Figure 2:8. Comparison of the LEBS peak from MC simulation to the experimental results from white paint under LSC illumination. ILEBS(θ), is calculated using MC simulation from a medium with ls* = 4 mm, and g = 0.9 (at λ = 520 nm) for Lsc = 160 μm. The simulation results agrees well with experimentally observed LEBS peak when Lsc = 160 μm. Also, the EBS peak from Lsc = 50 mm and LEBS peak from Lsc = 160 μm are completely indistinguishable as the peak width is completely determined by the small ls* of the medium and Lsc plays an insignificant role in this regime.

As seen, the LEBS peak obtained from MC simulation matches well with the experimentally observed LEBS peak for l s* << Lsc (Figure 2:8).

This validates the spatial

coherence function used in modeling LEBS peak. We further compare the LEBS profile with the EBS peak obtained from infinite spatial coherence length (Lsc = 50 mm). As expected, the EBS and LEBS peaks are completely indistinguishable as the peak width is completely determined by the small ls* of the medium (Figure 2:8). In the next section, we present the experimental verification of the LEBS simulation in the low order scattering regime when Lsc << l s* .

42

2.3.4 Comparison of Monte Carlo simulation with experimental results The LEBS peak obtained using MC simulations are experimentally verified. The detailed description of our experimental setup is given elsewhere [15, 31]. Here we describe the essential parts in brief.

The experimental setup consists of a 500-W Xe lamp (Oriel) to deliver a

continuous wave broadband light which is then collimated using a 4-f lens system.

The

collimated light is polarized and delivered onto a sample at an incident angle of 15° to prevent specular reflection. The Lsc is varied between 30 μm and 220 μm, and was confirmed by a double-slit interference experiment [43]. The backscattered light from the sample is sent through a setup consisting of a Fourier lens and a polarizer oriented along the same direction of the incident light. The co-polarized light is then collected by an imaging spectrograph (Acton Research) positioned in the focal plane of the Fourier lens and coupled to a CCD camera (Coolsnap HQ, Roper Scientific). The angular distribution of the backscattered light from the sample is projected onto the slit of the spectrograph, which disperses the light according to the wavelength in the direction perpendicular to the slit. The CCD camera records a matrix of light scattering intensity as a function of backscattering angle θ at different wavelengths λ. In each CCD pixel, the collected light is integrated within a narrow band of wavelength around λ, with the width of the band determined by the width of the spectrograph slit. The LEBS peaks are normalized by the incoherent baseline measured at large backscattering angles (θ > 4°) . The resulting LEBS signal is compared with the signals predicted by MC simulation.

43 LEBS Experiment ° LEBS Simulation (θci = 80 )

Normalized Intensity (a.u.)

1.2

° LEBS Simulation (θci = 1.5 )

1 0.8 0.6 0.4 0.2 0 -1

-0.5

0

Angle θ (Degree)

0.5

1

Figure 2:9. Comparison of LEBS peak profile from MC simulation to the experiments from aqueous suspensions of polystyrene microspheres under LSC illumination. ILEBS(θ) is simulated for a medium with ls* = 2 mm, g = 0.9 (at λ = 520 nm) and Lsc = 42 μm. LEBS peak simulated by MC simulation at θci = 1.5˚ matches well with the LEBS peak from the experiment. On the contrary, the LEBS peak from θci = 80˚ is three times narrower than that obtained from the experiment and it does not accurately predict the LEBS peak as it is insensitive to low orders of scattering.

44

Angular width W (Degree)

1.4 Experiment Monte Carlo Simulation

1

0.6

0.2 0

50

100

150

200

250

Spatial coherence length, Lsc (μm)

Figure 2:10. Comparison of angular width W of the LEBS peaks obtained from MC simulation with that of LEBS peaks from experiment under LSC illumination. The width of LEBS peak from simulation (ls* = 2 mm, g = 0.9 at λ = 520 nm) is calculated for 8 different Lsc varying between 30 μm and 220 μm at a fixed θci = 1.5˚. The error bars are the standard errors of mean. The widths of the LEBS peaks predicted by MC simulation are in complete agreement with those determined by the experiment.

We record LEBS from aqueous suspensions of polystyrene microspheres (Duke Scientific, Palo Alto, CA) of various diameters from 200 nm to 890 nm. The dimension of the samples are π x 502 mm2 x 100 mm. We vary the transport mean free path l s* from 500 μm to 2000 μm and the spatial coherence lengths from 30 μm to 220 μm. As a representative, we show here the results obtained from the sample of l s* = 2000 μm and bead diameter of 0.89 μm. Figure 2:9 shows the LEBS peaks predicted by MC simulation and those obtained from the experiment ( Lsc =42 μm). As seen, the LEBS peak obtained from higher exit angles (asterisk) does not accurately model the LEBS peak as it is insensitive to the low orders of scattering. On the contrary, the broadening of the LEBS peak can be accurately obtained only at low exit angles

45 (circle) as it is more sensitive to the low orders of scattering. The simulations are further verified for eight different values of Lsc varying between 35 μm and 220 μm (Figure 2:10). The error bars in the curves are the standard errors obtained from 3 different sets of experiments conducted at different spatial coherence lengths. As shown in Figure 2:10, the widths of LEBS peaks predicted by the MC simulations are in excellent agreement with those determined from the experiment.

2.4 Summary We have demonstrated for the first time that the photon random walk model can be used to model low coherence enhanced backscattering from a weakly scattering medium. We have shown that LEBS predicted by the simulations are in excellent agreement with the experimental data. Furthermore, we have demonstrated that the exit angles of the photons, which are typically neglected in modeling of conventional EBS, play a key role in modeling LEBS peaks. As LEBS peaks depend on the Fourier transform of the radial intensity distribution on the surface of the sample, it is extremely important to consider the change in the shape of the probability distribution P(r) due to the exit angle of photons. Our data indicate that P(r) obtained from low order scattering is sensitive to the exit angles of the photons, which in turn depend on the depth from which the photons are collected.

46

Chapter 3 Penetration depth of low-coherence enhanced backscattered light in the sub-diffusion regime 3.1 Introduction Most biological tissues are multilayered systems that require depth-selective measurements to obtain clinically useful information [2, 3, 9, 10, 49, 50]. Currently, a number of optical techniques based on backscattered light are under development for such depth-selective tissue characterization or imaging. In order to exploit an optical technique in a biomedical setting, a proper knowledge of the photon trajectories within the sample before being backscattered is essential. This information can be characterized by the distribution of photons at different depths, herein called penetration depth distribution, which provides information about the probability that a photon penetrates a certain depth before being detected. The penetration depth distribution, in turn, can be conveniently characterized by the effective penetration depth (depth corresponding to the peak of the probability distribution curve). Several groups have used numerical and analytical models to study the penetration depth of backscattering photons in a multiple scattering medium [51-54]. In particular, Weiss et al. used lattice random walk models to obtain the statistical properties of the penetration depth of photons emitted from a bulk tissue [51, 52]. The depth distribution of photons in a random scattering medium with the thickness of

47 approximately 10 transport mean free paths ( l s* ) was calculated by Durian [53]. Recently, Zaccanti et al. [54] derived analytical expressions for the time resolved probability of photons penetrating a certain depth in a diffusive medium, before being re-emitted.

Although the

penetration depth of photons has been well studied in a diffusive multiple scattering regime, similar understanding in the low-order scattering regime is not complete. This is in part due to the difficulties in collecting photons that undergo only a few scattering events. As explained in the previous chapter, the low-coherence enhanced backscattering (LEBS), spatially filters long traveling photons and collects only photons that travel very short distances and undergo very few orders of scattering. This opened up the feasibility of studying tissue optical properties at a selected depth: LEBS selectively probes short traveling photons from the top tissue layer (50-100 μm, e.g. mucosa and epithelium,) by rejecting long traveling photons from the underlying (stromal/connective) tissue [15, 31]. In this chapter, we use the numerical Monte Carlo (MC) simulation to study the propagation of photons that contribute to LEBS and also report development of a corresponding analytical model to describe the penetration depth distribution and effective penetration depth of these photons. As discussed above, in LEBS, low-spatial coherence illumination (spatial coherence length Lsc < l s << l s* ) behaves as a spatial filter that dephases the conjugated time-reversed paths outside the spatial coherence area and thus rejects longer path lengths. Therefore, the penetration depth of LEBS photons can be controlled externally by changing the spatial coherence length of illumination, Lsc . In order to increase the sensitivity of LEBS measurements to specific tissue depths it is important to know the relationship between Lsc and the depth of penetration of LEBS

48 photons. The penetration depth in turn is characterized by studying the penetration depth distribution of the short traveling LEBS photons p(z) (where p(z) is the probability of photons to penetrate a certain depth z before being detected) and their effective penetration depths (zmp). Unlike the long traveling photons, the short traveling LEBS photons ( r < l s << l s* , where r is the radial distance at which photons emerge) typically undergo very few scattering events; hence, the numerical model and analytical expressions addressed within the diffusion approximation for r >> l s* > l s cannot be used to study the mechanisms of photon propagation in LEBS. Therefore,

we used numerical MC simulations to model low-order scattered photons in order to study the mechanisms of photon propagation as a function of coherence length Lsc, anisotropy coefficient g and scattering mean free path length ls. We also developed an analytical model for p(z) and zmp of LEBS photons, i.e. photons exiting at radial distances r < l s << l s* with Lsc < l s << l s* . In order to study the penetration depth of LEBS photons, we perform the following: First, we use the numerical MC simulation to calculate the penetration depth distribution p(z) and the effective penetration depth (zmp) of the photons that form the LEBS peak. We study this for different coherence lengths (Lsc) of illumination and for media with different scattering mean free paths (ls) and anisotropies (g). Second, we use a double scattering analytical model to develop analytical expressions for p(z) and zmp and show that the analytical expressions of p(z) and zmp compare well with the corresponding numerical results for the parameter regime when Lsc < l s << l s* . Finally, we demonstrate that both p(z) and zmp of the exiting photons in this

regime ( Lsc < l s << l s* ) exhibit a priori surprising behavior, that is, only weak dependence on

49 optical properties (ls and g) and strong dependence on Lsc relative to the diffusive regime. This result is in contrary to the general understanding of the properties of p(z) and zmp observed in the diffusive multiple scattering regime.

3.2 Methods 3.2.1 Numerical model using Monte Carlo simulation In order to explore the depth of penetration of LEBS photons and its dependence on the optical properties of a medium, we use the MC simulation discussed in Chapter 2. In this chapter we use MC simulation to study the propagation of photons and its dependence of optical properties in the low order scattering regime, particularly when the photons undergo minimum of double scattering events and then exit within a narrow radial distance ( r < l s << l s* ). The double scattering is of significance because in EBS the minimum number of scattering events is two. The single scattering events contribute only to the incoherent baseline and not to the EBS peak formation. We recently demonstrated a direct experimental evidence that double scattering is the minimal scattering event necessary to generate an EBS peak in a discrete random medium [55]. We also showed that the LEBS isolates double scattering from higher order scattering when Lsc *

is on the order of the scattering mean free path l s of light in the medium ( l s = l s (1 − g ) ). Description of the MC simulation is given in detail in the previous chapter and in references [34, 44, 56]. For this study, we launch an infinitely narrow photon beam consisting of 1010 photon packets into a homogeneous disordered single layered medium with thickness much

50 greater than the spatial extent of the photon distribution (thickness of the medium = 50mm). We vary the scattering mean free path ls between 50-500 μm and the anisotropy factor g between 0.7-0.9. We assume absorption to be negligible (absorption length, la = 1000 cm). We record the trajectories of all photons that undergo two and higher order scattering events, and exit the sample at an angle < 3˚ from the direction of backscattering. We obtain the penetration depth distribution of photons in the axial ‘z’ direction (p(z)) using a two-dimensional grid system whose grid separations in the r and z directions are δr = 2 μm and δz = 5 μm, respectively, with the total number of grid points Nr = Nz = 1000. Furthermore, to account for the number of scattering events ( n s ), we set up a separate two-dimensional grid system with δr = 2 μm interval between scattering events δ ns = 1 , total number of grid points Nr = 1000 and the total number of scattering events N ns = 500 , respectively. Therefore, we can obtain the scattering distribution p(ns), penetration depth distribution p(z) and the effective penetration depth zmp as a function of

radial distance r. We also calculate p(ns), p(z), and zmp as a function of spatial coherence length Lsc by incorporating the effect of low spatial coherence illumination on EBS in the numerical model. The LSC illumination is incorporated by using the spatial coherence function C (r ) (Eq. (4)) discussed in Chapter 2. As C (r ) is a decay function of r, it acts as a spatial filter allowing only photons emerging within its effective coherence area (~ L2sc ) to contribute to p(r). Therefore, we can obtain p(z) and zmp as a function of r or Lsc.

51 The following section discusses in detail the derivation of the analytical expressions of p(z) and zmp from a double scattering analytical model and its comparison with the results of our

numerical MC simulations.

3.2.2 Analytical derivation of p(z), and zmp We derive the expressions for p(z) and zmp of photons that contribute to LEBS peak on the basis of a double-scattering analytical model of backscattering photons.

Previous

experimental studies [55] and the numerical results of the Monte Carlo simulations, which will be discussed in detail below (Section 2.3.1), demonstrate that LEBS peaks from a low spatial coherence illumination are mainly generated by the photons that predominantly undergo double scattering events. Hence, we use the double scattering analytical model to derive the expressions for p(z) and zmp and to verify our results from the numerical simulations.

p(z) and zmp as a function of radial distance r:

The probability of radial distribution of photons exiting a medium p(r ) due to double scattering events can be expressed as [57], ∞

p( r ) = ∫ 0



∫r 0

2

dz' dz' ' exp[−μ s ( r 2 + ( z ' '− z' ) 2 + z '+ z' ' )]μ s F (θ )μ s F (π − θ ) , 2 + ( z' '− z' )

(16)

where r is the radial distance at which photons emerge, z ' and z ' ' are the vertical distances from the surface to the scatterers, F (θ ) is the phase function of single scattering with

θ = tan −1 (r /( z ' '− z ' )) , and μ s (≡ 1 / l s ) is the scattering coefficient. A schematic picture of the

52 scattering geometry is shown in Figure 3:1. In our study, we use the Henyey-Greenstein scattering phase function, F (θ ) =

1 1− g 2 4π 1 + g 2 − 2 g cos θ

(

)

3/ 2

.

(17)

r

z'

dz ' θ

z' '

θ

dz ' '

Figure 3:1. A schematic picture of a photon that undergoes double scattering and exits within a very small radial distance r. z ' is the vertical distance of the first scatterer from the surface of the medium, z ' ' is the vertical distance of the second scatter and θ is the scattering angle. In order for the photon to undergo double scattering and exit within the narrow radial distance ( r < l s << l s* ), one of the scattering event occurs closer to the surface of the medium. That is z ' << z ' ' or z ' ' << z ' .

To obtain the expressions of p(z) and zmp of a double scattering photon from Eq. (16), we perform the following: we define a new variable z = z ' '− z ' and z ' ' ' = z ' '+ z ' . The coordinate system, in the above double scattering model, can be transformed to a zz ' ' ' coordinate system, using a Jacobian transformation. We then approximate the penetration depth of the double scattering events as ~ z, as one of the scattering events occurs much closer to the surface of the

53 medium than the other scattering event when the exit distances r of the majority of photons are restricted due to the finite value of Lsc ( r , Lsc < l s << l s* ). Indeed, Figure 3:1 illustrates that in order for the photons to undergo double scattering events within a small r, one of the scattering events must occur very close to the surface of the medium ( z ' ≈ 0 ) (approximation validated in Section 2.3.2). Therefore, the double scattering expression can be rewritten as, ∞



0

0

p(r ) = ∫

2dzdz ' ' ' exp[ − μ s ( r 2 + z 2 + z ' ' ' )]μ s F (θ ) μ s F (π − θ ) . 2 2 +z

∫r

(18)

Integrating over z ' ' ' in Eq. (18) we obtain, ∞



p ( r ) = ∫ p (r , z )dz = ∫ 0

0

2

dz exp[ − μ s ( r 2 + z 2 )]μ s F (θ ) μ s F (π − θ ) . μs r + z2 2

(19)

From Eq. (19) it follows that for a given r, the penetration depth distribution p(z ) can be written as, p( z | r ) =

2

1 exp[− μ s ( r 2 + z 2 )]μ s F (θ ) μ s F (π − θ ) . 2 μs r + z 2

(20)

Substituting θ = tan −1 (r / z ) , the phase function Eq. (17) can be rewritten as, F (θ ) =

1− g 2 1 4π ⎛ z ⎜1 + g 2 − 2 g ⎜ r2 + z2 ⎝

. ⎞ ⎟ ⎟ ⎠

(21)

3/ 2

Because the phase function F is mostly uniform around the backward direction, i.e. θ ~ π , we approximate, F (π − θ , λ ) ≈ 1 . Then the penetration depth distribution at a given r, becomes,

p(z|r)

54

μ 1 p( z | r ) = s 2 exp[− μ s ( r 2 + z 2 )] 2 2π r + z ⎛

1− g 2

⎞ ⎜1 + g 2 − 2 g ⎟ ⎜ ⎟ r2 + z2 ⎠ ⎝ z

3/ 2

.

(22)

Eq. (22) is the depth distribution of photons that undergo double scattering events and exit the medium in the backward direction at radial distances r < l s << l s* . The effective penetration depth z = zmp is the solution of the following equation dp ( z ) dz

=0.

(23)

z = z mp

From the Eqs. (22) and (23) we obtain,

⎡r2 ⎤ ⎡2⎤ 2 ⎡ ⎤ r2g r2g 3 z mp + ⎢ ⎥ z mp + ⎢r 2 + z + − ⎥=0 ⎥ mp ⎢ 2 2 1 + g − 2g ⎦ ⎣ ⎣ μs ⎦ ⎣ μ s μ s (1 + g − 2 g ) ⎦

(24)

Solving the above cubic equation (Eq. (24)) for zmp , we obtain the exact solution for the effective penetration depth zmp of double scattering photons:

[

]

⎡ B(r, g, μ ) + B 2 (r, g, μ ) + 4 A3 (r, g, μ ) 1 / 3 ⎤ s s s ⎢ ⎥ + ⎥ 2 , 2 1 ⎢ 24 / 3 z mp (r | g, μ s ) = ⎥− 2 ⎢ A(r, g, μ s ) 3μ s (1 − g ) ⎢ ⎥ 3μ s − ⎢ 2 2 / 3 × B(r, g, μ ) + B 2 (r, g, μ ) + 4 A3 (r, g, μ ) 1 / 3 ⎥ s s s ⎣ ⎦

[

where 2 ⎡ 3gr 2 μ s ⎤ A(r , g , μ s ) = (1 − g ) 4 ⎢− 4 + ⎥ , and (1 − g ) 2 ⎥⎦ ⎢⎣ 2 ⎡ 45gr 2 μ s ⎤ B(r , g , μ s ) = (1 − g ) ⎢− 16 + ⎥. (1 − g ) 2 ⎦⎥ ⎣⎢ 6

]

(25)

55 The dependence of z mp on r (from Eq. (25) ) for μ s r ≈ 0 is approximately linear. Here we are interested in z mp in the regime relevant for LEBS: r / l s < 1 ,

(1 − g ) 2 ( μr ) 2 → 0 ,

and ( g ) 2 ( μr ) 2 ~ 1 . To see the leading behavior of z mp in this regime, we expand the right side of

Eq.

(25)

(

in

terms

of

)

A

and

B,

(i.e.,

when

A / B << 1 )

and

obtain

z mp ∝ 2 (3μ s (1 − g ) 2 ) [2 B(r , g , μ s )] . This can be re-written as: 1/ 3

z mp (r | g , l s ) ∝

[

g 1/ 3 l π r2 2/3 s (1 − g )

]

1/ 3

.

(26)

The above equation implies that the effective penetration depth of a LEBS photon is proportional to the (1/3) power of the volume of a virtual cylinder whose area is formed by a circle of radius r and height l s . In the case of biological tissue (i.e., g ~ 1 ), Eq. (26) can be

rewritten as,

z mp ls

⎡r ⎤ ∝ ⎢ ** ⎥ ⎣ ls ⎦

2/3

, where l s** = l s (1 − g ) . This provides a critical value of r in the

units of l s for the double scattering regime; i.e., for r < l s** when double scattering events dominate compared to higher order scattering events.

p(z) and zmp as a function of spatial coherence length Lsc

To calculate the dependence of p(z ) and z mp on coherence length Lsc , we first weight the Eqs. (9) and (12) by the coherence function C (r , Lsc ) , and integrate over r : ∞

p ( z | Lsc ) =

∫ p( z | r )C

r =0

Lsc

(r )dr ,

(27)

56 ∞

z mp ( Lsc | g , μ s ) =

∫z

mp

(r | g , μ s )C Lsc (r )dr .

(28)

r =0

Eqs. (27) and (28) represent the analytical expressions for the penetration depth distribution, and effective penetration depth of photons that predominantly undergo double scattering events in LEBS. Under low-coherence illumination with spatial coherence length Lsc < l s << l s* : μ s r < 1 and C (r , Lsc )dr ~ dr Lsc .

In this low-coherence regime, integration in Eq. (28) can be

performed analytically. l sc

z mp ( Lsc | g , l s ) ~

∫ z mp (r | g, Ls )C(r, Lsc )dr 0



[

g 1/ 3 l s π L2sc (1 − g ) 2 / 3

]

1/ 3

.

(29)

Eq. (29) implies that the effective penetration depth of a LEBS photon is proportional to the 1/3 power of an effective coherence volume in a large parameter space. For example, at g = 0.7 and ls = 100 µm, the plot of log( z mp ) versus log(πl s L2sc ) has a slope of 0.28 (~1/3).

3.3 Results and Discussion 3.3.1 Scattering and penetration depth distribution - numerical studies The probability with which a photon scatters, p(ns), and the depth to which it penetrates, p(z), before it exits the medium at radial distances r < l s << l s* is discussed in this section. As stated throughout this paper, we consider a low-coherence regime: Lsc < l s << l s* . We performed numerical simulations using MC (Section 2.2.1) for media with different optical properties (ls =

57 50-500 μm and g = 0.7-0.9) in order to obtain p(ns) and p(z). As an illustration, here we discuss the results obtained for a medium with ls = 100 μm and g = 0.9 and 0.7. Figure 3:2(a) and Figure 3:2(b) show p(ns) for photons that exit at r < l s << l s* for g = 0.9 and 0.7. For r = 5 μm (r/ls = 0.05), it can be clearly seen that the photons predominantly undergo double scattering events (Figure 3:2(a)). This can be seen from a sharp peak in p(ns) for ns = 2. However, as r increases (r>25 μm) the probability of collected photons to undergo higher order scattering (ns > 2) increases. Typically in a medium consisting of small particles (g << 1), photons undergo isotropic scattering and hence penetrate shallower distances than in the medium with a large anisotropy factor (g ~ 0.9). As a result, the photons propagating in a sample with small g undergo relatively few scattering events before exiting the sample. This effect can be seen in Figure 3:2(b), where the scattering distribution p(ns) is obtained for a medium with g = 0.7. In this case, the shape of p(ns) as a function of n s is considerably sharper than p(ns) for g = 0.9 (r = 5 μm), illustrating that the photons have higher probability of exiting the medium after undergoing double scattering events. It is also interesting to note that for small particles, the probability of two and three scattering events of photons are comparable at r = 50 μm.

58

(a)

(b)

(c)

(d)

Figure 3:2. The scattering distribution of the photons p(ns) vs number of scattering ns from the numerical simulation. The numerical simulation is performed for r < l s << l s* and Lsc < l s << l s* ( Lsc - spatial coherence length of illumination) for two different media with anisotropy factors g = 0.9 and 0.7 at constant ls = 100 µm. The photons predominantly undergo double scattering at small ‘r’ and ‘Lsc’. However, the contribution from the double scattering photons decreases with increase in r and Lsc.

59

(a)

(c)

(b)

(d)

Figure 3:3. The penetration depth distribution p(z) of the photons vs depth z from numerical simulation. The numerical simulation is performed for r < l s << l s* and Lsc < l s << l s* from two different media with anisotropy factors g = 0.9 and 0.7 at constant ls = 100 µm. The p(z) of the photons predicted by the numerical simulations suggests a strong dependence on r and Lsc and relatively weak dependence on the optical properties ls and g.

In the case of LEBS, the coherence area within which a photon exits a medium is controlled by the Lsc of the light source. The plots of p(ns) for three different values of Lsc for samples with g = 0.9 and 0.7 are shown in Figure 3:2(c) and Figure 3:2(d). Within a narrow coherence area defined by Lsc < l s << l s* (e.g., Lsc = 5 μm) , it can be seen that the majority of the

60 photons experience double scattering while the probability of photons undergoing higher orders of scattering is exponentially low. However, for Lsc = 50 μm the probabilities of 3 and 4 scattering events are comparable to that of double scattering. These results are critical to the following discussion as they validate our use of the double scattering model to derive the analytical expressions for p(z) and zmp in the low-coherence regime ( Lsc < l s << l s* ). Figure 3:3 shows numerical simulations of p(z) for two sets of optical properties (ls=100 μm, g =0.9 and ls =100 μm, g=0.7) at different radial distances r ( r = 5 μm, 25 μm, 50 μm ) and spatial coherence lengths Lsc ( Lsc = 5 μm, 25 μm, 50 μm). For r = 5 μm << ls, the photons typically penetrate a shallow distance into the medium, which is, importantly, less than the scattering mean free path of the medium ls. Also, for a constant g and ls the penetration depth of the photon increases with increase in the radial distance r at which photons exit the medium. However, when the results of p(z) are compared to the medium with a different optical property (g = 0.7, ls = 100 μm), the change in p(z) is less significant ( < 5%). This indicates that p(z) is only weakly dependent on the optical properties of the medium for small radial distances r < l s << l s* . On the contrary, p(z) shows a strong dependence on r, and the shape of p(z) vary significantly (> 50 %) for different r. Similarly, the penetration depth distributions at different Lsc also show a relatively weak dependence on optical properties, and strong dependence on Lsc (Figure 3:3(c) and Figure 3:3(d)). This weak dependence of penetration depth on optical properties for photons exiting at r , Lsc < l s << l s* was further verified by our numerical simulation for other values of ls and g of the medium (data not shown). It is interesting to note that within a narrow coherence area

61 defined by Lsc < l s << l s* (e.g., Lsc = 5 µm), the majority of photons penetrate only to a shallow depth ( ~ 25 µm < ls). However, as Lsc increases, the photons have a higher probability of penetrating deeper into the medium. From these results, we conclude that the tissue depths that are predominantly sampled by the LEBS photons can be controlled by varying the spatial coherence length of illumination Lsc, and the resulting penetration depth of the photons is essentially insensitive to the specifics of the tissue optical properties. Also, the LEBS photons typically penetrate a shallow distance which is less than the scattering mean free path ls of the medium.

3.3.2 Comparison of the results of numerical simulations and analytical model Here we compare the analytical expressions of p(z) and zmp as a function of r (Eq. (22) and Eq. (25)) and Lsc (Eq. (27) and Eq. (28)) with the corresponding numerical simulations in the low-coherence regime: Lsc < l s << l s* .

As a representative illustration, the analytical and

numerical results are shown for a medium with ls = 100 μm and g = 0.9. First we validate our hypothesis stated in (Section 2.2.2) that in the double scattering regime when r , Lsc < l s << l s* , the distance from the surface of the medium to one of the scatterers is negligibly small relative to that of the other scatterer, i.e. the vertical distance to the deeper scatterer is several orders greater than the other scatterer (either z ' << z ' ' or z ' ' << z ' ). To validate this hypothesis, we used MC simulations analogous to the one discussed in Section 2.1. This time, however, we followed photons that undergo only single scattering.

62 0.6

Single scattering Double scattering

p (z)

0.4

0.2

0 0

50

z (μm)

100

150

Figure 3:4. The penetration depth distribution p(z) of single scattering photons plotted against those from double scattering photons at different depth z. At r < l s << l s* , the first scatterer is located close to the surface of the medium while the second scatterer is located several orders deeper than the first scatterer. Hence, the difference in vertical distances of the two scatters can be taken as the penetration depth of the photon.

Figure 3:4 shows the plots of p(z) of photons that undergo both single scattering and double scattering events for r = 5 µm. It is seen that the shape of p(z) of a single scattering photon is several times sharper than that of double scattering photons. The average depth of a single scattering photon is ~ 8 µm while those of double scattering photon is ~ 70 µm. This confirms that for r < l s << l s* , the distance to the first scatterer is negligibly smaller than the distance of the second scatterer which is located much deeper within the medium. That is, in order for the photons to undergo double scattering and exit within a narrow radial distance r < l s << l s* (e.g., restricted by Lsc < l s << l s* ), one of the scattering events must occur close to the surface of the medium. Hence, for a photon undergoing double scattering, the difference in

63 vertical distances between the two scatters can be taken as the penetration depth of this photon. The validation of this assumption will be important for the validation of the p(z) obtained using the analytical model with the predictions of numerical simulations. Figure 3:5(a) compares p(z) given by Eq. (22) and the one obtained by the numerical model for r = 5 μm, 25 μm and 50 μm.

As seen in the double scattering regime (i.e.,

r , Lsc < l s << l s* ), the predictions of the analytical model are in good agreement with those of the numerical simulations with root mean square error (RMSE) of less than 0.5 %. Similarly, p(z) obtained for Lsc = 5 μm, 25 μm and 50 μm indicates that the analytical expression derived from the double scattering model (Eq. (27)) can aptly describe the distributions obtained from the numerical model (RMSE < 0.4 %) (Figure 3:5 (b)). Even though the numerical model takes into account higher order scattering events, Figure 3:5(a) and Figure 3:5(b) clearly show that for r , Lsc < l s << l s* , the analytical and numerical results are in good agreement. This result further confirms that for r , Lsc < l s << l s* , the photons predominantly undergo double scattering events, and Eq. (22) and Eq. (27) can accurately model the penetration depth distribution of the photons.

64

(a)

(b)

Figure 3:5. Comparison of penetration depth distribution p(z) of photons obtained from numerical simulation and analytical expression. (a) The distributions are obtained for a medium with g = 0.9 and ls = 100 µm for a radial distance r = 5 µm and 25 µm. (b) The distributions are obtained for a medium with g = 0.9 and ls = 100 µm for a spatial coherence length, Lsc = 5 µm and 25 µm.

Figure 3:6 compares zmp of LEBS photons predicted by the numerical model and analytical expression (Eq. (28)). Here, zmp is obtained as a function of Lsc for two different media with g = 0.7, g = 0.9, and ls = 100 μm. It is seen from this plot that in the low-coherence regime ( Lsc < l s << l s* ), the predictions of zmp by the analytical double-scattering model are in good agreement with those of the numerical simulations for all Lsc < l s (RMSE < 5 μm). This good agreement is due to the fact that, as discussed above, double scattering dominates in this regime. Furthermore, even if a photon undergoes a higher order scattering, the condition Lsc < l s << l s* and backscattering light collection restrict the majority of the backscattered photons to go through only one backscattering event. Therefore, higher order scattering events only broaden the probability depth distribution p(z) compared to the purely double scattering events whereas the value of zmp. remains approximately unchanged. However, for larger coherence lengths (Lsc ~

65 ls; e.g. Lsc = 90 μm), zmp obtained by the analytical model deviates from the one obtained by the numerical simulations due to the emergent effect of higher order scattering events (ns > 5) and fails for Lsc >> l s > l s* . We conclude that in the low-coherence regime, which is the subject of our current investigation, the analytical model enables accurate prediction of both p(z) and zmp, and, thus, can be used to model p(z) and zmp of LEBS photons.

[

z mp ∝ ( g 1 / 3 (1 − g ) 2 / 3 ) l s π L2sc

100

]

1/ 3

50 ls = 100 μm, g = 0.9, Analytical

z

mp

(μm)

75

ls = 100 μm, g = 0.9, Numerical 25

ls = 100 μm, g = 0.7, Analytical ls = 100 μm, g = 0.7, Numerical

0

0

25

50

L

sc

(μm)

75

100

Figure 3:6. Comparison between the effective penetration depth zmp of the LEBS photons predicted by the numerical model and analytical expression. zmp is obtained as a function of Lsc for two different media with anisotropy factors, g = 0.7 and g = 0.9 and a constant ls (ls = 100 μm). The agreement between the numerical model and analytical expression decreases with the increase in Lsc as the photons undergo higher order scattering events.

Figure 3:7 shows the dependence of zmp on the optical properties of a medium (ls and g) and the spatial coherence length of illumination Lsc using the analytical model (Eq. (28)). The figures are plotted for different values of g (0.7 – 0.9) and ls (80 μm – 500 μm) for a constant Lsc

66 (Lsc = 5 μm). As seen, zmp shows a relatively weak dependence on the optical properties of the medium when Lsc < l s << l s* (Figure 3:7 (a) Figure 3:7 and (b)). However, as shown in Figure 3:6, zmp depends primarily on Lsc. This property of zmp is critical for LEBS measurements in biomedical applications as it enables probing a given physical depth of a biological tissue. That is, by adjusting the Lsc of a light source, it should be possible to collect photons propagating into a tissue up to the depth of interest regardless of specific optical properties of a given tissue sample. It is also noticed that for a given Lsc ,

z mp ( g , l s ) ∝

g 1/ 3 [l s ]1 / 3 which is a much (1 − g ) 2 / 3

slower varying function of g and ls than another length scale frequently used to describe light transport in tissue, l s∗ =

ls . (1 − g )

67 (a)

(b)

Figure 3:7. The dependence of zmp on individual optical properties plotted against ls and g. (a) zmp increases slowly between the anisotropy values of 0.7 and 0.9 after which zmp increases sharply. (b) zmp depends on ls only slightly over the range 100 µm and 500 µm that is relevant to the biological systems.

Experimental realizations to obtain the information about the depth of penetration of LEBS photons can be implemented in different ways as follows. a) The depth to which a photon penetrates can be experimentally estimated by varying the thickness of the sample. Varying the thickness provides a simple method for quantifying the contribution of different depths to the LEBS signal [58]. b) Time resolved measurements can also be used to assess the penetration depth by measuring short light pulses backscattered from the sample without any sample preparation. The depth of a photon inside the sample can then be experimentally gated based on the time of flight of such short light pulses [59].

3.4 Summary We have derived an analytical model of the penetration depth distribution p(z) and effective penetration depth zmp of photons that generate an LEBS peak (spatial coherence length

68 Lsc < l s << l s* ), in the sub-diffusive scattering regime. We have performed numerical Monte Carlo simulations to support our analytical results. The results from the analytical model are in good agreement with those obtained from the Monte Carlo simulations. Our results demonstrate that z mp ∝ ( g 1 / 3 (1 − g ) 2 / 3 )[l s π L2sc ] , i.e. zmp of the LEBS photon is approximately proportional 1/ 3

to the 1/3 power of an effective coherence volume [l s π L2sc ]

1/ 3

in an experimentally relevant

parameter regime. More importantly, LEBS photons typically penetrate less than the scattering mean free path of the medium ls (i.e., z mp < l s ) when Lsc < l s << l s* . Furthermore, the analytical calculation and numerical simulation show strong dependence of zmp on Lsc (that can be controlled externally) and relatively weak dependence to tissue optical properties (l s , g ) , which suggests the possibility of using LEBS for depth-selective analysis of weakly scattering media such as biological tissue.

69

Chapter 4 Partial wave microscopic spectroscopy detects sub-wavelength refractive index fluctuations 4.1 Introduction Spectroscopy of elastic light scattering is commonly used to probe tissue morphology [5, 10]. This premise of elastic scattering is based on the fact that the spatial variation of the concentration of intracellular solids (e.g., proteins, DNA, RNA, lipids) gives rise to spatial fluctuations in the refractive index of the tissue. However, the sensitivity of light scattering signal to refractive index fluctuations is significantly reduced when the size of the scattering structures falls below the wavelength (~500 nm). Recently, there has been significant interest in understanding biological systems at the nanoscale, which requires measurement of subwavelength refractive index fluctuations. According to mesoscopic light transport theory [60-62] it is indeed possible to probe refractive index fluctuations of any length scale including those well below the wavelength [61, 62] if a) the object is weakly disordered and weakly scattering and

b)

one

analyzes

a

signal

generated

by

the

multiple

interference

of

1D-

propagating waves reflected from weak refractive index fluctuations within the object. (Enhanced sensitivity of 1D-propagating waves to sub-wavelength correlation length of refractive index fluctuations lc (i.e., l c < wavelength λ ) can be understood from the following

70 consideration: while in 3D the scattering coefficient ~ (l c / λ ) 3 , and, thus, a contribution from small length scales is weighted down as l c2 , for 1D-propagating waves the scattering coefficient is ~ (l c / λ ) [43, 63].) 1D-propagating waves are one of many ‘partial waves’ propagating within a scattering particle. (Hereafter we define partial waves as any subset of waves propagating within a scattering object.) The mesoscopic light transport theory [60-62, 64-66] states that the reflected signal in 1D, which is the result of the multiple interference of light waves reflected from refractive index fluctuations, is non-self-averaging for all length scales for weak refractive index fluctuations [64-67]. In a self-averaging system the standard deviation of a parameter relative to its mean decreases with increase in system size, typically as the square root of the system size.

On the contrary, in a non self-averaging system the standard deviation of a

parameter relative to its mean increases with increase in system size. In other words, the reflected signal is sensitive to any length scale of refractive index fluctuations including those below the wavelength [63, 68-70].

This presents an opportunity to characterize cell

nanoarchitecture by detecting waves propagating in 1D. This, however, has not been feasible using conventional far-field microscopy or light scattering techniques. Here, we present a new type of microscopic spectroscopy, referred to as partial-wave spectroscopy (PWS). PWS detects 1D-propagating backscattered photons in the far-field. In this chapter we demonstrate that the mesoscopic theory-based analysis of the spectra of partial waves propagating within a weakly disordered medium such as biological cells quantifies refractive index fluctuations at subdiffractional length scales.

We validate this nanoscale

sensitivity of PWS using rigorous finite difference time domain (FDTD) simulations and

71 experiments with nanostructured models. We also demonstrate the potential of this technique to detect nanoscale alterations in cells from patients with pancreatic cancer who are otherwise classified as normal by conventional microscopic histopathology. In particular, we show that the disorder strength of refractive index fluctuations is increased in cancer cells.

4.2 Methods 4.2.1 Partial-Wave Spectroscopy (PWS) Instrument The design of the PWS instrument is shown in Figure 4:1. A broadband, spatially lowcoherent white light (spatial coherence length <1 μm) is focused onto the sample by a lownumerical aperture (NA) objective (Edmund Optics, NA~0.35). The illumination beam diameter (~200 μm) is much larger than the micrometer sized biological cells and is well collimated with respect to the size of a cell (~8 μm). The resulting backscattered image is projected in the farfield (magnification = 60x) onto the slit of an imaging spectrograph (slit width = 10 μm) coupled with the CCD camera (Coolsnap HQ, Roperscientific, 1392 x 1040 pixels, CCD pixel size = 6.2 μm) and mounted on a motorized one-dimensional linear scanning stage (Zaber Technologies).

The backscattering image (~200 μm) is acquired by linearly scanning the slit (step size = 10 μm) of the spectrograph (size of pixel in image plane (image pixel) = 6.2 μm x 10 μm, size of pixel in the object plane (cell pixel) = 100 nm x 165 nm). At each scanning step x, the CCD camera records a matrix with one axis corresponding to the wavelength of light λ and the other to the spatial position of the image (y) resulting in a 3D data cube (x,y, λ ). In order to ensure that the image of the entire cell was sampled, the system contains a flipper mirror that directs the image

72 into a digital camera for quick realization. Hence, unlike conventional microscopy where an image is obtained by integrating the light intensity over a broad range of spectrum, in PWS the backscattering spectrum I (λ ; x, y ) (λ=390-750nm, spectral resolution ~3nm, spectral sampling ~ 0.25nm; only signal from λ1 = 500 nm to λ 2 = 670 nm is analyzed, due to the low illumination and transmission efficacy of the instrument) is recorded for each cell pixel (x,y). All spectra obtained from each cell pixel are normalized by the spectra of the incident light using mirror reflection. The normalized intensity spectra I (λ , x, y ) are further analyzed (discussed in the following section) to calculate the fluctuating component of these backscattering spectra,

R(λ , x, y ) ( λ is the wavelength of light) that arises from the interference of photons reflected from refractive index fluctuations within a scattering object. It is important to realize that unlike traditional light scattering experiments where a scattering signal is formed by all waves propagating within a scattering particle and interfering in the far-field, the backscattering spectrum analyzed in PWS is formed by the subset of waves, in particular 1D propagating waves. Both the properties of the object and instrumentation facilitate detection of these 1D partial waves: low spatial coherence, high spectral resolution, weak refractive index fluctuations within the object, and small radius of curvature of the cell spread on the slide. Under these conditions, light propagation through a complex 3D weakly disordered medium can be approximated as a combination of several spatially independent parallel 1D channels with

R(λ ) generated by the multiple interference of photons propagating in these 1D channels. In a weakly scattering object, the interference among different 1D channels is negligible and is

73 further prevented by the low-coherence illumination.

Although the diffraction limit

determines the lateral size of each channel, the information about refractive index fluctuations at sub-wavelength scale is embedded into R(λ ) .

M

TL

D

BS Lamp C

L

A

L

O S

Figure 4:1. Schematic of the partial-wave microscopic spectroscopy (PWS) system. (a) C: condenser; L: lens (f = 150 mm); A: aperture; BS: beam splitter; O: objective lens; TL: tube lens (f = 450 mm); S: sample; D: detector (including the imaging spectrograph (slit width = 10 microns, spectral resolution ~2 nm, Acton Research) and CCD camera (CoolSnap HQ, Roper Scientific).

A typical spectrum R(λ ) obtained from a particular cell pixel (in this case, a cell was isolated from human pancreatic epithelium) spread on a glass slide is shown in Figure 4:2(a). Figure 4:2(b) shows the normalized backscattering spectrum I (λ ) along with the polynomial fit I p (λ ) ( I p (λ ) is discussed below). In order to show the noise level, the spectrum is compared with the one obtained from a pure glass slide. As seen, the spectrum from the biological cell contains spectral fluctuations that are otherwise absent in the signal from the pure glass slide, confirming that the fluctuations seen in biological cells are well above the noise floor (absorption does not play a significant role as the absorption coefficient μa ~ 1.5 cm-1 [71] and the thickness

74 of cell is ~ 4 μm). This brings us to the question about the possible methods of relating R(λ ) and the following properties of the object: thickness (L), average refractive index (n0), the variance and the correlation length of refractive index fluctuations ( < Δn 2 > and lc). In the regime where the approximation of 1D independent channels is valid, R (k ) ( k = 2π λ ) can be characterized using 1D mesoscopic light transport theory [60-62]. Accordingly, the root mean square average of R(k ) can be written as: < R >≡ Lξ −1 , where ξ −1 is the scattering coefficient of a 1D channel. Generally a complicated function of < Δn 2 > and lc, ξ −1 can be simplified for klc<1: ξ −1 ∝ 2k 2 Ld n02 with Ld =< Δn 2 > l c . Following terminology used in condensed matter physics, the statistical parameter Ld is referred to as the disorder strength.

75 5

x 10-3

(a)

R(λ)

4 3 2 1 0 500

540

580

620

660

Wavelength, λ (nm) x 10-3

(b)

65

I(λ)

60 55 50 45 500

540

580

620

660

Wavelength, λ (nm) Figure 4:2. The backscattering spectrum obtained using PWS from a single isolated biological cell and glass slide. (a) The spectrum of R(λ) obtained from a single cell pixel of a biological cell (blue) and from a pure glass slide (red). (b) The corresponding I(λ) with the I p (λ ) (black).

Thus the disorder strength Ld ( x, y ) =< Δn 2 > lc can be calculated for each cell pixel (x,y) from the spectral fluctuations R(k ) . Therefore, a two-dimensional map of the disorder strength

76

Ld (x, y) depicts the spatial distribution of the degree of disorder in the cell under analysis. In practice, it is convenient to quantify a particular cell or a group of cells by a finite number of parameters, rather than an entire 2D image. For example, a cell can be characterized by two convenient statistics: the mean intracellular disorder strength L(cd ) (i.e. Ld ( x, y ) averaged over x and y) and the intracellular standard deviation σ ( c ) of Ld ( x, y ) . The averages of L(dc ) , σ ( c ) over a group of cells, such as all cells from a particular cell line or a particular patient, are termed the group means L(dg ) and σ ( g ) . The disorder strength quantifies the spatial variability of refractive index and, thus, the local concentration of intracellular material. At a given point in a cell, Δn is proportional to the local concentration of intracellular solids [72, 73] while l c can be viewed as the characteristic size of the intracellular ultrastructure of a cell (e.g., macromolecular “building blocks” of a cell). We have confirmed the dependence of Ld , as measured by PWS, on nanoscale refractive index fluctuations by conducting rigorous numerical experiments using FDTD simulations (lc from 5 to 45 nm) and experiments with deterministic nanostructured model media (lc from 20 to 125 nm). (Both sets of experiments are discussed in Results.) Importantly, these studies demonstrated that, in principle, there is no limitation on the minimum lc that can be assessed by PWS, in contrast to conventional microscopy which is limited by the diffraction limit of the system. (In practice, of course, the limit of sensitivity to lc is determined by the signal-to-noise ratio.)

77

4.2.2 Calculation of fluctuating component R (k ) from the backscattering signal R(k ) is computed from I (k ) for each pixel in a cell image. This is accomplished in four steps. First, we filter out the high frequency noise by using a 6th-order low-pass Butterworth filter with a normalized cut off frequency of 0.08. We estimated the amplitude of the noise and the normalized cutoff frequency (normalized to the sampling frequency - data is sampled every 0.25 nm) from our previous experiments using polystyrene microspheres with known sizes [74]. The polystyrene microsphere has no disorder and the backscattering spectrum is known analytically via Mie theory, thus the noise level was easily distinguishable from the signal. This normalized cutoff for noise filtering also corresponded to the spectral resolution of the instrument and has the following practical implication. The spectral resolution of the instrument is 3 nm. The CCD oversamples a spectrum into 1392 pixels with a single pixel corresponding to, on average, 0.25 nm band (In our experiment, we did not bin the adjacent pixels in the CCD camera to reduce the over sampling. However, we removed all spectral oscillations less than the resolution of the spectrometer by using a low pass filter). Because spectral fluctuations with spectral frequencies higher than that of the point spread function can only be attributed to instrument noise, a low-pass filter with normalized cutoff frequency of 0.08 (cutoff frequency/sampling frequency) filters out these spectral fluctuations.

Also, varying the

normalized cutoff frequency below the spectral resolution does not significantly affect the disorder strength. For example, change in the normalized cutoff frequency from 0.08 to 0.03 (i.e., filters all oscillations less than 9nm instead of 3nm) results in a change in disorder strength

78 of ~ 5% which is much smaller than the difference between different cohorts of cells/patients. On the other hand, if the normalized cutoff frequency is above the spectral resolution, the filter does not completely remove the spectral noise, which may affect the disorder strength. For example, an increase in the normalized cutoff frequency from 0.08 to 0.25 (i.e., filters out oscillations under 1nm instead of 3nm) results in a change in disorder strength of ~ 65%. The result of is a noise-filtered spectrum I (k ) . Second, a sixth-order polynomial ( I p (k ) ) is fit to

I (k ) . Third, R(k ) is obtained as R(k ) = I (k ) − I p (k ) .

4.2.3 Calculation of disorder strength using mesoscopic theory Since R(k) is formed primarily by 1D backscattered photons, R(k) can be analyzed by means of the 1D mesoscopic light transport theory in disordered media [60-62, 64-66]. This theory has been well studied and used for electron transport in conductors and light transport in dielectric media. The mesoscopic theory enables quantification of the statistical properties of the spatial refractive index variations within a 1D scattering medium, e.g. a 1D channel within a cell. A corresponding measurable statistical parameter obtained for each channel is the disorder strength Ld = α < Δn 2 > l c (following terminology used in the condensed matter physics), where < Δn 2 > is the variance of refractive index fluctuations Δn within a channel, l c is the spatial

correlation length of these refractive index fluctuations, and α is a numerical factor ~1. One can determine Ld for each pixel in a cell image from two experimentally acquired quantities: R(k ) and its autocorrelation function:

79 C (Δk ) = < R(k ) R(k + Δk ) > < R(k ) R(k ) > [60-62, 64-66]. In a weakly disordered medium

(i.e., R << 1 ), the probability density distribution of R is log-normal for all length scales of the disordered scattering medium [62, 66, 67]. The ensemble average of the R-distribution over the ensemble of 1D independent parallel disordered channels < R >≅

[

]

1 2 exp(4k 2 Ld L / n0 ) − 1) , 2

where n0 is the average refractive index of the medium and L is the longitudinal (i.e. along the direction of incident light propagation) dimension of the medium.

If klc << 1 and

2

4k 2 Ld L / n0 << 1 [62, 66, 67],

< R >≅ 2k 2 Ld L n02 .

(30)

Furthermore, C (Δk ) ≅ exp[−(Δk ) 2 f (Ld )AL] , where f (Ld ) is a slowly varying function for realistic values of the disorder strength and is neglected in the following analysis. Thus, ln(C (Δk ) = −(Δk ) 2 AL ,

(31)

where A is a constant [67, 75]. Therefore, knowing < R > and C (Δk ) for each channel in a cell, one can calculate Ld by eliminating L .

4.2.4 Calculation of Ld in biological cells For each 1D-channel, the mean fluctuating component < R > is calculated by taking the root mean square average of R(k ) over a spectral range from λ m = 500 nm to 660 nm (outside this range the intensity of the spectrum drops below the noise floor and hence was not included in our analysis). Because C (Δk ) is a function of k , C (Δk ) is calculated for k corresponding to

80 the middle of the spectrum 580 nm for a better spectral averaging and for the full use of the spectra in the calculation. Figure 4:3 illustrates the steps involved in obtaining a PWS image of a cell. The instrument measures the total backscattering signal I (λ , x, y ) for each point (x, y). The next step is to extract R(λ , x, y ) from I (λ , x, y ) as discussed above. Then C (Δk , x, y ) is calculated from R (k , x, y ) . For each channel (x, y) , disorder strength Ld ( x, y ) is computed from R (k , x, y ) and

C (Δk , x, y ) using Eqs. (30) and (31).

81 Reflection of 1 cell

Reflection of N channels/pixels



(a) x x

R (λ ) (a.u)

x 10

Reflection Intensity I(λ) of a single channel/pixel (amplified)

-3

1

7

.5

6

0

Fluctuating part of the reflection coefficient : R(λ)

5 4 3 2 1 0 500

550 600 Wavelength λ (nm)

650

Figure 4:3. Steps involved in PWS signal acquisition and analysis. (Inset) A typical backscattering spectrum I(λ) from a single pixel of a biological cell image. (Main panel) The spectrum of a typical reflection coefficient R(λ) obtained after removing the noise and the background reflection. R(λ) is the fine fluctuating component of the backscattering spectrum I(λ) that originates from the interference effect of 1D-propagating photons reflected from refractive index fluctuations within the cell.

82

4.3 Results and Discussion 4.3.1 Validation of PWS in computational experiments In order to validate the nanoscale sensitivity of PWS, we first perform finite-differencetime-domain (FDTD) [76] simulations of light propagation in random 3-D cell-emulating media with controlled refractive index distributions. This is accomplished using the finite-differencetime-domain (FDTD) [76] method which provides an accurate solution for the propagation of light in essentially arbitrary media. The accuracy and robustness of FDTD modeling has been confirmed in previous reports [76]. In our simulations, we consider refractive index fluctuations ranging from 0.01 to 0.05 (which is the biologically relevant regime) and correlation lengths l c ranging from 1 to 100 nm. Figure 4:4(a) and Figure 4:4(d) shows the geometry in the FDTD simulation. Here, an inhomogeneous dielectric cylinder with diameter of 8 microns and height of 5 microns is imported in the FDTD grid with 20 nm resolution. The cylinder has refractive index distributed randomly in 600 nm by 600 nm by 100 nm rectangular blocks (Figure 4:4(a)) and in 60 nm by 60 nm by 60 nm rectangular blocks (Figure 4:4(d)) with the mean refractive index n0 = 1.38 and maximum refractive index fluctuation Δnmax = 0.02.

In the FDTD

simulation, the grid is terminated using a Berenger perfectly matched layer (PML) absorbing boundary condition [77]. The total-field/scattered-field (TF/SF) technique [78] is employed to source an x-polarized plane wave propagating in the FDTD grid. We choose a modulated Gaussian pulse as the time-domain source waveform which accommodates the complete frequency range of visible light. The scattered-field frequency response is extracted via a

83 discrete Fourier transform (DFT) of the time-domain data recorded on the six surfaces of the scattered-field region and normalized by the spectrum of the source pulse. A modified version of 3D near-to-far field transformation in the phasor domain [79] is implemented to calculate the farfield scattered wave in the backward direction. Figure 4:4(b) and Figure 4:4(e) shows the synthesized backscattering intensity image by applying the vector diffraction theory [80] to the far-field scattering fields calculated by FDTD.

Figure 4:4(c) and Figure 4:4(f) shows the

comparison of the FDTD-calculated backscattering spectra at 4 locations in the synthesized microscope image (as shown by the color-coded markers in Figure 4:4(b) and Figure 4:4(e)) with that calculated by 1D slab model. The refractive index distribution in 1D slab model follows the point-spread function averaged vertical refractive-index distributions of pixels centered at the corresponding location in the FDTD geometry (displayed with color-coded markers in Figure 4:4(a) and Figure 4:4(d)). In essence, the results in Figure 4:4 indicate that PWS enables isolating 1D-propagating backscattered waves within the scattering media as seen by the good agreement (r2 ~ 0.81) between PWS spectra calculated by FDTD for any given 1D channel and the spectra calculated for 1D disordered media with the refractive index profile the same as in the given 1D channel (referred to as the 1D-slab model). Having demonstrated the agreement between the full 3-D model and the corresponding 1D model, we then performed extensive FDTD simulations for the latter. We consider a homogeneous dielectric slab with random refractive index fluctuations around the background refractive index n0 = 1.38 (similar to the average refractive index of a biological cell). The standard deviation Δn of the fluctuations is varied from 0.01 to 0.05. The correlation length lc of

84 the fluctuations is defined as < Δn( L)Δn( L' ) >≡< Δn 2 > exp[− | L − L'| / l c ] , and is varied from 5 to 45 nm (klc << 1). The thickness of the sample L is varied from 1.5 to 4 μm. In all cases, Ld is calculated using Eqs. (30)-(31). As shown in Fig. 4, the values of Ld determined based on the spectral analysis are in good agreement with the true value (r2 = 0.91), thus confirming the mesoscopic theory based analysis.

85

Figure 4:4. FDTD simulations demonstrate the validity of using 1-D model to analyze the backscattered spectra of each pixel in the PWS image.

Calculated disorder strength, Ld (μm)

86 20

x 10-6 30nm, LL == 2 2μm, = 0.01 – 0.05 lcc == 30nm, ?m, ?nΔn = 0.01 - 0.05 llcc == 55-45nm, L = 2μm, Δn = 0.02 - 45 nm, L = 2?m, ?n = 0.02 llcc==30 nm,LL==1.5 - 4–?m, ?n = 30nm, 1.5 4μm, Δn0.02 = 0.02

16 12 8 4 0

0

4

8

12

16

20 x 10-6

Theoretical disorder strength, Ld = lc <Δn2> (μm)

Figure 4:5. Comparison of the theoretical disorder strength and the one calculated using the 1D FDTD simulation. The simulations were performed on a homogeneous dielectric slab with random additive refractive index fluctuations around the background refractive index n0 = 1.38. The disorder strength was obtained for the following parameters: a) standard deviation of the refractive index fluctuations Δn between 0.01 to 0.05, b) the correlation length lc between 5 to 45 nm and c) the thickness of the sample L between 1.5 to 4 μm. As can be seen, the calculated and theoretical values of Ld agrees well with each other (r2 = 0.91) thereby confirming its agreement with the mesoscopic theory.

A key result of this study is that Ld is linearly dependent on lc for klc < 1 . Thus, in principle, there is no limitation on the minimum correlation length that can be assessed by means of the spectral analysis of 1D-propagating photons. In practice, of course, the sensitivity to small lc is limited by the signal-to-noise ratio and other technical considerations.

It should be

emphasized, however, that contrary to conventional optical microscopy, the sensitivity of PWS to small length scales is not bound by a fundamental physical limit.

87

4.3.2 Validation of PWS using nanostructured model media We also experimentally verified the sensitivity of PWS by performing experiments on a series of known nanostructured model media comprised of aggregated polystyrene nanospheres. The fabrication protocol is described in detail elsewhere [81]. In brief, the aqueous suspension of monodispersed polystyrene nanospheres (Duke Scientific, Inc.) of volume ~ 50 µl is uniformly smeared on a flat surface of a glass slide. The self-assembled lattice is formed after 15 minutes of evaporation process at room temperature. We use models with thickness L varying from 0.3 to 13 μm and nanosphere sizes 20, 40, 60, 80, 100 and 125 nm (standard deviations of the nanosphere sizes ~10%). PWS measurements are obtained from 30 different combinations of L and nanosphere sizes thereby obtaining R (k ) spectra from ~ 100,000 channels. Since both lc and Δn are known a priori in this model, i.e., lc corresponds to the size of a nanosphere and Δn corresponds to the refractive index of a polystyrene sphere relative to air, we then theoretically estimate the expected Ld of a model and compare it with the Ld found from PWS data (Eq.(30)). As seen in Figure 4:6 there is a good agreement (r2 = 0.97) between the experimentally observed values of Ld and those calculated theoretically. These results confirm that PWS is indeed sensitive to nanoscale refractive index fluctuations. These experiments are also used to calibrate the experimentally measured disorder strength by determining the calibration constant B in Eq. (30). It is important to note that in these experiments on nanostructure model media, the thickness of the samples were not kept constant at different nanosphere sizes. Hence to verify whether the thickness of the nanostructure model media can be a confounding factor for measured Ld , we plot thickness as a function of nanosphere sizes. As seen in Figure 4:7 (a), the

88 experimentally measured Ld using PWS is highly correlated with the nanostructure sizes. However, as seen in Figure 4:7 (b), both Ld and lc are only weakly correlated with the L ( Ld vs L: R2 = 0.38 and lc vs L: R2 = 0.51). Also, the change in L as a function of lc is much smaller than the increase in Ld observed at different lc. These results confirm that the changes in Ld observed in experiments with nanostructure model media cannot be attributed to the thickness of the nanostructure model.

89 x 10-3

x 10

(c)

12

r2 = 0.97

d

Experimental L (μm) Experimental ExperimentaldL(L m)

12 12 R2 =

8

8 8

R2 = 0.97 0.97

4

4 4

0

0 0

0 0

0

4 4

4

8 8 8

Theoretical Ld (μm)

12 12 12

x 10-3

Figure 4:6. Validation of the nanoscale sensitivity of disorder strength using experimental nanostructured model media. The theoretical disorder strength calculated using the bead size and relative refractive index of polystyrene beads agree well with the experimentally observed disorder strength using PWS.

14

x 10-3

(a)

12 10 8 6 4

6 5 4 3 2

2 0

(b)

7

Thickness (μm)

Disorder strength Ld (μm)

90

0

20

40

60

80

100

Correlation length lc (nm)

120

140

1

0

20

40

60

80

100

120

140

Correlation length lc (nm)

Figure 4:7. Effect of thickness on the disorder strength calculated from nanostructure model media (a) The experimental disorder strength observed using PWS at different bead sizes. (b) The thickness of the nanostructure model media observed using optical profilometry at different bead sizes. Both lc and Ld are only weakly correlated to the thickness of nanostructure model media.

4.3.3 Experimental PWS data confirms the validity of mesoscopic theorybased analysis As discussed above, we validated PWS in rigorous computational experiments and studies with deterministic nanostructured models. As a further proof, we wanted to obtain evidence that our mesoscopic theory-based analysis is valid for real biological cells. Luckily, retrospective analysis of the data (R and C) could be used to validate the analysis. Indeed, as discussed above, 1D mesoscopic theory-based analysis is applicable if three conditions are satisfied: 1) < R ><< 1 , 2) the probability distribution function (p.d.f) of < R > is lognormal, and 3) The autocorrelation function C (Δk ) is a Gaussian function.

The PWS spectrum from

biological cells shows that these three conditions are satisfied. 1) The fact < R ><< 1 is clear

91 from Figure 4:3 2) Figure 4:8(a) shows a representative p.d.f of < R > for the ensemble of biological cells. This p.d.f is well approximated by the lognormal function (r2=0.98). 3) Finally, as illustrated in Figure 4:8(b), C (Δk ) is well approximated by a Gaussian function (average r2=0.98 for a linear fit to ln C (Δk ) vs. Δk 2 for the ensemble of biological cells). This indicates that our experimental cell data indeed conforms to the 1D mesoscopic theory.

92

Probability density P()

(a) 30 25 20 15 10 5 0

ln(c(Δk))

(b)

0

5



15 x 10-3

10

0

-0.02 -0.04 -0.06 -0.08

0

1

2

(Δk)2 (μm)2

3

4 x 10-5

Figure 4:8. A representative probability density function and correlation decay in biological cells. (a) A representative probability density function (p.d.f.) P() of the mean fluctuating component in biological cells. The solid lines are the fitted P(R) curve that follows the lognormal distributions (r2 > 0.95). (b) The representative correlation decay C (Δk ) computed from R(k). The logarithm of the autocorrelation function ln( C (Δk ) ) (circles) follows a linear dependence on (Δk)2 (solid line) (r2 = 0.98).

93

4.3.4 PWS detects human pancreatic cancer The nanoscale sensitivity of PWS could be critical to cell microscopy where cells are regularly imaged to understand disease processes. Due to its diffraction limited resolution, conventional cytology is not sensitive to changes involving cell nanoarchitecture (e.g. ribosomes, membranes, nucleosomes, just to name a few cell structures with subdiffractional dimensions). At the same time, these are some of the most fundamental building blocks of the cell. We hypothesize that PWS can be applied to detect nanoarchitectural alterations in cells that are undetectable by cytology. We consider pancreatic cancer as a case in point. Pancreatic cancer is the 4th leading cause of cancer deaths in the US with an overall 5-year survival rate of <5%. For diagnosis, pancreatic cells are extracted using fine needle aspirations and subjected to a cytopathological analysis. However, the sensitivity of cytological diagnosis is low for mass lesions in symptomatic patients (~70%) and much lower for early lesions. These suboptimal sensitivity rates are due in part to the relative rarity of frankly malignant-appearing cells that can be identified by cytology.

To test our hypothesis, we perform a pilot study on archival

pancreatic cells (fixed with alcohol) obtained from 16 patients (7 normal and 9 malignant). 6 cases from these 9 adenocarcinomas are cytologically diagnosed as benign (cytologically normal). PWS measurements are obtained from three different cohorts of cells: cytologically normal cells from normal patients (N), cytologically malignant cells from cancer patients (C) and cytologically normal cells from cancer patients (CN). For each patient, ~ 40 cells are chosen at random. A typical bright field image and its corresponding PWS image obtained from these

94 three cell types are shown in Figure 4:9. As seen, the Ld map constructed by plotting the Ld values for all the pixels (x,y) corresponding to the cell shows a clear difference between normal and malignant cells. More importantly, Ld maps are different between cytologically normal cells obtained from normal and cancer patients. Further statistical analysis is performed using the two parameters that are obtained from the Ld maps: the average disorder strength of a cell ( L(cd ) ) and its standard deviation ( σ (c ) ). As shown in Figure 4:10(a) and Figure 4:10(b), both the L(cd ) and

σ (c )

(where,

is the average taken over all the cells within a patient cohort) are highly

significantly elevated in cancer patients compared to the control group (P < 0.001). A prediction rule developed using a linear regression model yielded 100% sensitivity and 100% specificity for cytologically normal patients vs cancer patients. Interestingly, the cytologically normal cells from cancer patients also had significantly elevated L(cd ) and σ (c )

(P < 0.001) with 83%

sensitivity and 100% specificity. These results indicate that the sub-cellular alterations and heterogeneity which are otherwise undetectable by conventional histopathology can be detected using PWS implying the promise of this technique to better characterize the nanoscale abnormalities of a biological cell. The progressive increase in L(cd ) and σ (c ) between the three different cell types (N, CN and C) imply that as cancer develops, there is progressively higher disorder strength of the cell architecture. The higher Ld may be due to the increase in the refractive index fluctuation < Δn 2 > and/or longer correlation length lc. Higher < Δn 2 > can be associated with the increased density of intracellular macromolecular complexes [82] while the change in lc may be due to the macromolecular aggregation such as chromatin clumping.

95

(a)

CN

N

C

5μm 5 ?m

(b)

Glass

5μm 5 ?m

5

10

15

20

Disorder strength, Ld (μm)

25 x 10-6

Figure 4:9. A representative bright field image and the corresponding pseudo-color Ld map recorded from three different cell types. (a) Bright field image and (b) PWS image from cytologically normal cell from normal patient (N), cytologically malignant cell from cancer patient (C) and cytologically normal cell from cancer patient (CN). The color-bar shows the magnitude of the Ld in a cell. We have also shown the Ld of a pure glass slide in order to show the noise level.

96

(a) Disorder strength, Ld (μm)

-6 30 x 10

25

* p-value < 0.001

20

*

*

15 10 5

N

CN

C

Standard deviation of Ld, σLd (μm)

(b) 21 16

x 10-6

* p-value < 0.001

*

*

11 6 1

N

CN

C

Figure 4:10. The relative values of the disorder strength and standard deviation of disorder strength from for three different pancreatic cell types. N - cytologically normal cell from normal patient, C - cytologically malignant cell from cancer patient and CN - cytologically normal cell from cancer patient. The error bars are the standard errors of the mean.

97

4.4 Summary In summary, the backscattering spectrum from a weakly disordered medium contains spectral fluctuations that can be used to measure the disorder strength of the refractive index fluctuations within the scattering object.

We confirmed using numerical simulations and

experiments with model media that the disorder strength is indeed sensitive to nanoscale refractive index fluctuations that are much smaller than those that can be observed using diffraction limited microscopy. As an illustration of the potential capabilities of PWS, we showed that this technique may identify cancer cells by sensing microscopically undetectable alterations in cell architecture. Though many questions remain such as the origin of the changes in intracellular disorder, we believe that PWS could bring a new dimension in our understanding of cell biology and disease processes.

98

Chapter 5 Detecting nanoscale consequences of genetic alterations in biological cells using PWS 5.1 Introduction Existing knowledge of changes in cell architecture in disease processes is based to a large degree on the histological examination of cells and tissue. On the other hand, it is well accepted that histological and, thus, microarchitectural, aberrations are preceded by molecular, genetic or epigenetic changes. One may pose a question if these events are still accompanied by alterations in cell architecture that are histologically undetectable. Indeed, the diffraction limit restricts the resolution of conventional light microscopy to, at best, 200 nm. This is larger than the sizes of the fundamental building blocks of the cell, such as membranes, cytoskeleton, ribosomes, and nucleosomes. Thus, conventional light microscopy is insensitive to changes in nanoarchitecture, which is the fundamental basis of cell organization. It is clear that the fact that a cell is histologically normal may not necessarily be equated with the cell not having nanoscale structural alterations. Cellular alterations in carcinogenesis provide an illustrative and practically important example. The process of carcinoma formation involves stepwise accumulation of genetic and epigenetic alterations in epithelial cells over a time period of many years.

Dysplasia, or

99 structural alterations detectable by microscopy, is a relatively late event in this process. From a cancer research perspective, it is important to recognize the earlier stages of carcinogenesis that precede histological changes.

One can hypothesize that although these genetic/epigenetic

aberrations have not yet resulted in histologically-apparent changes, they may still be accompanied by architectural consequences that occur at the nanoscale. Therefore, it is of major importance to design optical techniques for inspecting cell nanoarchitecture. One approach to probe cell architecture has been through the use of spectral analysis of light scattering [5, 6, 10, 50]. However, light scattered by cells and tissues is typically recorded after its three dimensional (3D) propagation within tissue.

As a result,

although light scattering does depend on a wide range of length scales of refractive index fluctuations including those smaller than the wavelength of light, the sensitivity to subwavelength length scales decreases fast with size due to the Fourier transform relationship between the scattering signal and the scattering potential [43]. On the other hand, as discussed in the previous chapter, if photons propagating in one dimension (1D) are recorded, a completely different scenario emerges. That is, the reflected signal in 1D is sensitive to any length scale of refractive index fluctuations including those below the wavelength [63, 68-70]. We have shown in the previous chapter that PWS detects 1D propagating waves from a biological cell thereby characterizing its sub-cellular nanoarchitecture. This sensitivity to nanoarchitecture has not been feasible using conventional far-field microscopy or light scattering techniques. In this chapter we use PWS to study nanoarchitectural alterations in the process of colon carcinogenesis that precede histological changes. Our approach is to assess alterations in colon

100 cells undergoing defined genetic modulations that are biologically significant but failing to result in abnormalities detectable by conventional microscopy.

Specifically, we use RNA

interference (RNAi) in the human colorectal cancer cell line (HT-29) to test the effect of a modest (~30-50%) suppressor of the gene c-terminus src kinase (CSK) and a proto-oncogene, epidermal growth factor receptor (EGFR), proteins implicated in early colon carcinogenesis. Following this, we use a mouse model in which the adenomatous polyposis coli (APC) gene underwent a germline mutation, the initiating genetic event in ~80% of human colon carcinomas. We report that, although these molecular events do not result in histologically-detectable changes in cells, PWS imaging demonstrates profound alterations in the statistical properties of cell nanoarchitecture. This has future applications in early diagnosis of cancer.

5.2 Methods 5.2.1 Cell cultures We developed EGFR and CSK gene knockdown stable constructs following a conventional protocol.

The HuSH EGFR-shRNA vector and the control vector (Origene,

Rockville, MD) and the CSK shRNA vector (BD Biosciences- Clontech San Jose, CA) are transfected in colon cancer cell line HT29 by using Lipofectamine 2000 (Invitrogen, Carlsbad, CA) according to manufacturer’s instructions. After transfection, cells are incubated at 37°C in a humidified 5% CO2 incubator. Stable clones for EGFR shRNA and control vector are selected by puromycin (0.5µg/ml) and the stable clones for CSK shRNA vector are selected by

101 hygromycin (600 µg/ml). The stable clones are confirmed for gene knock-down by RT-PCR and western blotting by standard methods. Proliferation of the CSK shRNA and EGFR constructs is determined as follows. Proteins from the stable constructs for CSK shRNA, control vector and the EGFR shRNA are isolated and subjected to western blotting using standard methods and probed with antibodies for or against CSK (BD Biosciences), EGFR and PCNA (Both from Santa Cruz Biotechnology) and beta actin (Sigma). We found that stable transfection of the shRNA vectors resulted in 50% decrease in the expression of CSK and EGFR. We have previously shown that CSK down-regulation leads to increased epithelial cellular proliferation. This is evidenced by a significant increase in the proliferation specific marker PCNA in the CSK shRNA construct. EGFR plays an important role in signaling pathways (including cell proliferation) which are implicated in various cancers. Down-regulation of this gene imparts a less proliferating phenotype to the cells. This is confirmed by the dramatic decrease in the proliferation marker PCNA in the EGFR shRNA construct as compared to the control vector (Figure 5:1).

102 Control

CSK

EGFR

PCNA β Actin

Figure 5:1. Effect of knockdown of CSK and EGFR gene expression on cell proliferation. Knockdown of CSK and EGFR gene expression is achieved in human colon cancer cell line HT29 by stable transfection of the CSK-specific and EGFR specific shRNA vectors. HT-29 cells transfected with empty vector (control vector) is used as control. Total cellular proteins are extracted in 2X Lammeli Sample buffer. Equal amount (40µg) of protein samples are separated by polyacrylamide gel electrophoresis and transferred on PVDF membrane and probed with an antibody against the proliferation specific marker – proliferating cell nuclear antigen (PCNA). Consistency in protein loading is assessed by probing membranes with anti-β-actin. Compared to the control vector, the CSK shRNA construct show a 30% increase in the levels of PCNA (p<0.05, indicating increased cell proliferation) whereas the EGFR shRNA construct show a 27% decrease in PCNA (p<0.05, indicating decrease in cell proliferation).

5.2.2 Animals We performed all animal studies in accordance with the institutional Animal Care and Use Committee of Evanston-Northwestern Healthcare. Four male C57Bl mice (APC wildtype) and 4 C57Bl APCmin are euthanized at 15 weeks of age. Intestines are removed, opened longitudinally, and flushed with phosphate buffered saline. Following this, the intestines are placed on dry ice for 5 minutes to optimize detection of adenomas. Areas of non-dysplastic epithelium are identified using a dissecting microscope and are subjected to gentle treatment with a cytology brush. Cells from the cytology brush are immediately smeared onto a glass microscope slide and the slide is placed in 95% ethanol. The measurements by PWS are taken on isolated colonic cells obtained at random from the colonic mucosa (~30 cells per animal). We

103 also perform cytological analysis on 10 randomly collected and H&E-stained colonic cells at each time points. The analysis performed by a board-certified pathologist specializing in gastrointestinal cytology confirmed that all cells are histologically normal.

5.3 Results and Discussion To demonstrate the ability of PWS to identify nanoarchitectural changes in cells that are otherwise histologically indistinguishable, we performed our first set of experiments on the HT29 human colonic adenocarcinoma cell line. We focus on colorectal cancer given that it is a major public health problem (second leading cause of cancer deaths in Western countries). The choice of this model is based also on the fact that the malignant behavior of the HT29 cells can be controlled by genetic modification of these cells [83-85]. We select the tumor suppressor gene, C-terminus Src kinase (CSK) and the proto-oncogene, epidermal growth factor receptor (EGFR). We construct stable Sh-RNA in HT-29. Thus, we use three variants of HT29 cells: original HT29 cell line transfected with empty vector, HT29 cells after CSK knockdown, which leads to increased malignant aggressiveness, and the cells after EGFR knockdown, which partially suppresses the malignant aggressiveness of the cell line We noted, as expected, that CSK knockdowns behave more aggressively whereas EGFR was less aggressive using proliferation (proliferating cell nuclear antigen) as a surrogate marker (Figure 5:1). Importantly, as

demonstrated

in

previous

literature

[83-85],

the

three

cell

lines

are

microscopically/histologically indistinguishable, which was further corroborated by a pathologist examining the stained cytological preparations of these cells. This is related, at least partly, to the relatively modest knockdown achieved (~30-50%), meaning that the magnitude of genetic

104 alterations is insufficient to cause microscopic alterations but did result in the modulation of cellular physiology such as proliferation (CSK ShRNA > HT-29 empty vector >

EGFR

ShRNA). PWS measurements are conducted on ~50 cells randomly selected from each of the three cell types (~500 1D-channels per cell). The protocols for PWS measurements and signal analysis are discussed in the previous chapter. Two major conclusions are made from the inspection of Figure 5:2, Figure 5:3, and Figure 5:4. The first conclusion is that PWS enables sensing architectural changes in otherwise histologically indistinguishable but genetically and physiologically different cells.

Figure 5:2(a,b) compares H&E and PWS images of three

representative cells from the three cell lines: control HT29, EGFR knockdown, and CSK knockdown cells.

As can be seen from the images, the three representative cells appear

cytologically similar. This was also confirmed by the analysis of at least 10 cells from each of the cell lines. For comparison, PWS images are clearly different. Overall, a cell from the most aggressive cell line (CSK-knockdown) has the highest intracellular disorder strength, while the least aggressive cell line (EGFR-knockdown) exhibits the least disorder. This suggests that higher disorder strength is associated with an increased malignant behavior. Figure 5:2(b) also shows a PWS image of a glass slide with no cells to illustrate the noise level in Ld -images: the disorder strength of the pure glass is negligible compared to Ld of cells and is spatially uniform, as expected.

This further validates that PWS is sensitive to nanoscale refractive index

fluctuations given the current signal-to-noise ratio. Figure 5:3 plots intracellular averages of disorder strength vs. its intracellular standard deviation L(cd ) vs. σ (c ) for all cells for the three cell

105 lines with each cell being represented by a single point : (L(dc ) ,σ ( c ) ) . Clearly, L(cd ) and σ (c ) parallel increased malignant potential of the cell lines. This is further illustrated by Figure 5:4 (a,b) that show that L(dg ) and σ ( g ) are progressively and highly statistically significantly increased from EGRF-knockdown to control HT-29 and to CSK-knockdown cell lines (ANOVA p-value < 0.001).

We also point out that, intriguingly, there is a certain degree of intercellular

heterogeneity among cells belonging to the same cell line as illustrated by a spread of data points in the L(dc ) versus σ ( c ) -plot. The intercellular heterogeneity appears to be the highest for the most aggressive CSK-knockdown cells. We note that despite partial overlap among cells from different groups, it was still possible to differentiate the three cell lines by analyzing a group of cells. For example, in order to achieve a statistical power of 90%, the data set shown in this study required 23 cells to differentiate EGFR vs. control HT29 cells and 15 cells to differentiate CSK vs. control HT29 cells. It is also important to note that this increase in disorder strength of the cells might not be completely explained by the cell division rate of the cells. For example, the flow cytometry measurements on propedium iodide stained HT29 and CSK cells indicate that ~ 11% HT29 cells are in proliferative 's' phase compared to ~ 20% in CSK cells [83]. However, our PWS experiments reveal that more than 50% of CSK cells have higher disorder strength compared to control HT29 cells, thus indicating that the increased disorder strength might not necessarily be due only to the increased cell division rate.

106 Control

EGFR

(a)

CSK Cytoplasm Nucleus

5 μm

Control

EGFR

(b)

CSK

Glass

5 μm

0

2

4

6

Disorder strength Ld (μm)

8

10 x 10-4

Figure 5:2. Representative (a) cytological images and (b) pseudo-color PWS images from three HT29 cell types. The color in the PWS image shows the magnitude of the disorder strength Ld in a cell. Although the cytology images shown in panel (a) appear similar, the PWS images are distinctly different from each other. In order to see the noise level, we also provide an Ld image of a pure glass which shows very low Ld relative to those of the cells.

107 x 10-3

x 10-3 5

CSK Control EGFR

4

σLd (μm)

Standard deviation of Disorder strength σLd (μm)

6 4 2 0

0

2

4

Ld (μm)

6

x 10-3

3 2 1 0

0

1

2

3

Disorder strength Ld (μm)

4 x 10-3

Figure 5:3. Cells with a more aggressive malignant behavior have a higher intracellular disorder strength. (Main panel) The values of Ld and its intracellular standard deviation σ Ld averaged over a cell

(average over ~400 channels per each cell), that is L(cd ) and σ (c ) , for the EGFR- knockdown HT29 cells, control HT29 cells, and CSK-knockdown cells are plotted in L(dc ) ,σ ( c ) parameter space. Each point in this diagram corresponds to a single cell. As can be seen, for each cell type there is a separate regime in the parameter space which only slightly overlaps with the regimes of the other cell types. (Inset). The part of the parameter space for the EGFR and control HT29 cells with small Ld and σ Ld values is amplified in order to show their separation in the parameter space.

108 (a)

Disorder strength Ld (μm)

x 10-3

1.6 1.2

p-value < <0.001 p-value 0.001

0.8 0.4 0.0 EGFR

(b)

Standard deviation of Disorder strength σLd (μm)

p-value <0.001 0.001 p-value <

2.0

1.6

Control

CSK

p-value < 0.001

x 10-3

1.2

0.8

p-value p-value<< 0.001 0.001

0.4

0.0 EGFR

Control

CSK

Figure 5:4. The relative values of the disorder strength L(dg ) and standard deviation σ ( g ) for three HT29 cell types. L(dg ) is obtained by averaging L(cd ) from randomly chosen ~50 cells for each of the three cell

types. The error bar represents the standard error of the mean. Both L(dg ) and σ ( g ) are significantly decreased for the least-aggressive EGFR-knockdown cells compared to that of HT29 cells (Student t-test p-value <0.001) and significantly increased for the most-aggressive CSK-knockdown cells (p-value < 0.001).

109

5.3.1 Experiments with the animal model of colon carcinogenesis Based on our cell line studies, we hypothesize that the degree of disorder of cell nanoarchitecture correlates with the neoplastic behavior and can be used as a marker of carcinogenesis. We test this hypothesis in animal studies. We employ one of the best-validated models of intestinal carcinogenesis, the MIN-mouse. In this model, there is a truncation in the APC tumor suppressor gene (codon 850) which results in spontaneous development of intestinal adenomas. Importantly, given the germline nature of the mutation, all intestinal epithelial cells (including those that were histologically normal) contained the mutation in this tumor suppressor gene. The relevance of this mutation is underscored by the observation that ~80% of sporadic colorectal cancers are believed to be initiated by APC truncation. We asked the following question: Although appearing normal by the criteria of microscopic histopathology, do precancerous intestinal cells possess alterations in their nanoarchitecture that are detectable by PWS? In our studies, we used four C57 Bl male wildtype mice (negative control) and 4 age-matched male C57Bl APCmin animals. The mice were euthanized at age of 15 weeks and intestines were washed. Samples were taken from visually normal mucosa using a cytology brush. Care was taken to avoid any possibility of contamination with adenomas through examination with a dissecting microscope of dry ice treated epithelium. The wildtype animal intestines were treated identically. Cells from the cytology brush were smeared onto a glass slide and alcohol fixed according to a standard protocol (discussed in SI). For each mouse, ~30 cells were randomly chosen for PWS analysis. All cells were obtained from the macroscopically and histologically normal mucosa outside any neoplastic lesion. The

110 cytology specimens were then examined by a surgical pathologist, who confirmed that all cells were histologically normal. Figure 5:5(a,b) and Figure 5:6 show that both L(dg ) and σ ( g ) are highly significantly (p<0.001) increased in the cells from the MIN mice compared to those from wild type mice, in agreement with the findings of the cell line study. Thus, we conclude that the germline mutation in otherwise microscopically normal-appearing cells results in the increase in the disorder of cell nanoarchitecture. It has to be pointed out that although cells obtained from the same animal exhibit a certain degree of intercellular variability in their L(cd ) and σ (c ) , these parameters are quite well conserved among cells from different parts of the intestine and even different mice.

The

intercellular standard deviation of L(dc ) for control animals is less than 15% of its mean, L(dg ) . For comparison, this intercellular variability of L(cd ) increases in MIN-mice up to ~50%. This suggests that the population of precancerous cells is significantly more heterogeneous compared to the cells from control animals. The biological significance of this finding remains to be explored.

111 (a)

Disorder strength Ld (μm)

9

x 10-5

p-value p-value<<0.001 0.001

7 5 3 1

Wild type

Min mice

Standard deviation of Disorder strength σLd (μm)

(b)

6

x 10-5 p-value < <0.001 p-value 0.001

5 4 3 2 1 Wild type

Min mice

Figure 5:5. Comparison of the average disorder strength L(dg ) and intracellular standard deviation of the disorder strength σ ( g ) in the wild-type and MIN-mice. There is a significant increase in both L(dg ) and σ ( g ) (p-value < 0.001) for the MIN-mice compared to the control wild-type animals. We emphasize that all MIN-mice cells were deemed to be histologically normal by conventional histopathology.

112

Standard deviation of Disorder strengthσLd (μm)

x 10-4 2.5

Min mice Wild type

2.0 1.5 1.0 5.0 0.0

0

1

2

3

Disorder strengthLd (μm)

4 x 10-4

Figure 5:6. Ld and σ Ld averaged over a cell for the cells obtained from the wild-type and the MIN-mice plotted in the L(cd ) , σ (c ) parameter space. Each point in this diagram corresponds to a single cell. Both the wild-type and MIN-mice cells have a separate regime in the parameter space with slight overlaps.

5.3.2 Length scale probed by PWS. Because Ld is a product of Δn and lc, it is impossible to determine lc explicitly. However, an approximate value of lc can be estimated. For Δn ranging between 0.02 - 0.10, which is typical for a biological tissue [82], the experimentally measured values of Ld for the cell lines and mice cells correspond to l c less than or around 100 nm. This is the length scale of the fundamental “building blocks” of the cell, such as protein complexes, cytoskeleton, intracellular membranes, and nucleosomes. It needs to be emphasized that lc is not a mere size of a particular cell structure, but instead characterizes the statistical properties of the entire complexity of the intracellular refractive index fluctuations.

113

5.4 Summary PWS provides a unique way of isolating 1D backscattering photons, which are sensitive to minute changes in the refractive index fluctuations at sub-diffractional length scales. Combined with mesoscopic light transport theory for statistical analysis of the backscattered photons, PWS provides a unique statistical view of subcellular architecture at nanoscale beyond what conventional microscopy reveals. In particular, PWS measures the disorder strength, a statistical parameter of the complex refractive index fluctuations at a single-cell level. We demonstrate, for the first time, that PWS has the ability to provide unprecedented detail about the nanoscale architecture of a cell. This was validated in studies where defined genetic alterations were introduced both in vitro and in vivo and the disorder consequences were assessed in histologically-normal cells. In the in vitro study, PWS was used to image cells from three genetic variants of HT29 colon human tumor cell line (original HT29 cell line and EGFR and CSK-knockdowns). Although microscopically indistinguishable, these three types of cells exhibit different degree of malignant behavior, from less aggressive (EGFR-knockdown) to more aggressive (CSK-knockdown). Our results demonstrate that PWS was able to differentiate cells from these lines by quantifying the disorder of cell nanoarchitecture. In particular, the increase in malignant aggressive behavior was associated with the increase in the disorder strength of intracellular organization. The increase in the disorder of cell architecture was further confirmed in the study with the MIN-mouse model of intestinal carcinogenesis. Again, the same trend was observed: a germline mutation in intestinal epithelial cells in the MIN-mice that were normalappearing by conventional histologic standards resulted in a profound increase in the disorder

114 strength compared to the control mice.

This suggests that early carcinogenesis is

accompanied by increasing disorder and progressively higher heterogeneity of the intracellular nanoarchitecture. These results may have profound biological and medical implications. From the cancer biology perspective, PWS may be used to better understand early cellular events in carcinogenesis. Cell architecture may be much more “in tune” with the molecular events than previously thought. Although it may not be possible at this point to identify which specific structures are responsible for the increase in the disorder and associated molecular mechanisms, we can get some insights into the kinds of nanoscale changes developing in preneoplastic cells. As Ld =< Δn 2 > lc , a higher disorder strength is due to the increase in the refractive index fluctuations Δn 2 , or refractive index correlation length l c . A higher Δn 2 may be associated with the increased spatial variation of the density of intracellular material (e.g., DNA, RNA, proteins and lipids) [72, 73]. As discussed in Results, lc~100 nm. Thus, a change in l c may represent aggregation or “packing” of some of the basic “building blocks” of the cell. Similarly, the increase in l c can be related to the increase in fractal dimension reported by other groups [10] and also to the lognormal size distribution of particles [86, 87], where the increase in lc would indicate the increase in the average and standard deviation of the lognormal distribution. Furthermore, our data also suggest that the increase in the disorder strength is not limited to a specific organelle or a type of molecule.

Instead, it represents the progression of global

intracellular organization towards a more disordered state.

115 From the clinical perspective, our data indicate that PWS has the potential to detect cell changes that would otherwise be missed by conventional histopathology. PWS may potentially provide another dimension to histopathology and complement and expand its use. Moreover, PWS could be useful to detect field carcinogenesis in organs such as the colon providing a potential means of using easily accessible normal-appearing mucosa to determine the risk of neoplasia throughout the colon without the need for interrogation of a formed dysplastic lesion. This may also be applicable to other cancer sites where field carcinogenesis is known to be important (e.g. lung, breast etc). If the results are confirmed in humans, we may have to redefine our understanding of the significance of cell architecture and what we consider to be a “histologically-normal” cell.

116

Chapter 6 Detecting nanoscale cellular changes in field carcinogenesis using PWS 6.1 Introduction Neoplastic transformation is a protracted process of stepwise accumulation of molecular abnormalities which eventually lead to microscopic abnormalities (dysplasia).

Prior to

histological abnormalities, there are profound genetic, epigenetic (e.g. methylation and histone acetylation) and cellular function changes (decreased apoptosis and increased proliferation). Many of the gene products dysregulated early in carcinogenesis would be predicted to have structural consequences via, for example, interactions with cytoskeleton (e.g. adenomatous polyposis coli or E-cadherin in colon carcinogenesis). However, these cells appear histologically normal largely because the diffraction limited resolution renders conventional microscopy insensitive to structures less than ~200 nm.

As a result, microscopy is unable to detect

alterations in cell nanoarchitecture (e.g. the fundemental cellular “building blocks” with sizes <200 nm including ribosomes, nucleosomes, membranes, macromolecular complexes, etc.) that could potentially be affected by genetic/epigenetic changes in early carcinogenesis. We pose a question if in early carcinogenesis microscopically normal appearing cells do have alterations in their architecture, although these changes occur at length scales not accessible by conventional

117 microscopy, i.e. nanoarchitecture. In order to assess the nanoscale we have utilized the fundamental principle of PWS that the signal in 1-dimension arising due to multiple interferences of light waves reflected from weak refractive index fluctuations is sensitive to any length scale of refractive index fluctuations. One of the most important applications of PWS is in the study of field carcinogenesis [88], a well established phenomenon that the genetic/epigenetic alterations that result in a neoplastic lesion in one area of an organ should be detectable throughout the organ. For example, this is the theoretical underpinning behind the widely used clinical test, flexible sigmoidoscopy, in which the endoscopic examination of the distal colonic mucosa is able to predict risk for the entire colon. The field effect may occur during neoplastic transformation in many organs (liver, esophagus, breast, etc).

Moreover, several authorities have made the

observation that the “field” may extend outside the organ undergoing carcinogenesis [89-96]. For instance there is compelling evidence of buccal mucosal alteration in patients with lung cancer (from shared exposure to cigarette smoke) or hair follicles in prostate cancer (representing altered androgen levels) [88]. This leads to a question if microscopically normal cells in the field undergo alterations in their internal nanoarchitecture and if so, how far away from the tumor this field extends? We, therefore, performed studies to assess whether nanoarchitectural alterations in easily accessible mucosa could sense the presence of major malignancies.

118

6.2 Methods 6.2.1 PWS instrumentation The design of the PWS instrument is discussed in detail in Chapter 4. In brief, a nearly plane wave of white, low-spatially coherent light illuminates the sample, and an image formed by the backscattered photons is acquired. The spectra of the backscattered light within the wavelength range from 400 to 700 nm are acquired from each pixel, normalized by the spectrum of the incident light, and filtered to remove spectral noise (see chapter 4). This yields a data cube

R(λ , x, y ) (λ is the wavelength, x and y are pixel coordinates), which is referred to as the fluctuating part of the reflection coefficient. Hence, unlike conventional microscopy, in which an image is formed by integrating the reflected or transmitted intensity over a broad spectrum, PWS measures spectral fluctuations in the backscattering spectra. In essence, PWS decomposes a complex 3D weakly disordered medium such as a biological cell into many spatially independent parallel 1D channels each with diffraction-limited transverse size and acquires 1Dreflection spectra R(λ ; x, y ) . These spectral fluctuations are then analyzed by means of 1D mesoscopic light transport theory. The statistical parameter determined from the analysis is the disorder strength Ld =< Δn 2 > l c , where < Δn 2 > and lc are the variance and the spatial correlation length of the refractive index fluctuations.

At a given point in a cell, Δn is

proportional to the fluctuation in the local concentration of intracellular solids and l c is related to the size of the intracellular structures within a cell. We have demonstrated using numerical simulations and model experiments (see SI) that there is no limitation to the minimum lc that can

119 be probed by PWS. Using PWS, a two-dimensional map depicting the distribution of disorder strength Ld (x, y) can be obtained for a particular cell. From these 2D images several statistical parameters can be extracted, such as the mean intracellular disorder strength L(cd ) (the average Ld ( x, y ) over x and y) and the standard deviation of intracellular disorder strength, σ (c ) . The averages of L(dc ) , σ (c ) over a group of cells, such as cells sampled from a particular patient category, are termed the group means L(dg ) and σ ( g ) .

6.2.2 Sample preparation All samples were obtained with the approval of the institutional review board at Evanston Northwestern Healthcare. Colon: An Olympus 180 series pediatric variable stiffness video-colonoscope was inserted to

the cecum under direct visualization. Upon withdrawal to the rectum, a cytology brush was passed through the endoscope and gently applied to the visually normal rectum. Pancreas: An Olympus 180 series upper endoscope was inserted under direct visualization to

the second portion of the duodenum. The ampulla was identified and then an endoscopically compatible cytology brush was used to gently sample the endoscopically-normal peri-ampullary mucosa. The cytology brush was then applied to a sterile glass slide. The slides were then fixed in an alcohol bath containing 80% ethylalcohol.

120

6.3 Results and Discussion We first confirmed that PWS could distinguish morphologically normal and abnormal cells by examining cytological preparations of brushings from colorectal cancer samples (n=20) and normal patients (n=15). First, we noted that both L(dc ) and σ (c ) showed no significant difference (P > 0.2, ANOVA) among cancer cells obtained from tumors located at different parts of the colon. Figure 6:1 plots L(cd ) vs. σ (c ) for all cells for the normal and cancer groups with each cell being represented by a point: (L(dc ) ,σ ( c ) ) . Clearly, both L(cd ) and σ (c ) are increased in cancer cells. This is further illustrated by Figure 6:2(a,b). These results agree well with the conventional cytology in that cancer cells show a significant difference in their morphology compared to the normal cells.

121 x 10-4

Standard deviation of Ld (σLd) (μm)

10

Tumor 4cm away from tumor

8

Control

6 4 2 0 0

1

2

3

Disorder strength Ld (μm)

4 x 10-4

Figure 6:1. Cells at a distance from a colon tumor undergo changes in their internal nanoarchitecture similar to tumor cells. The values of Ld and its intracellular standard deviation σ Ld averaged over a cell, that is L(cd ) and

σ ( c ) , for control cells, tumor cells, and cells at a 4 cm distance from tumor plotted in L(dc ) ,σ ( c ) parameter space. Each point in this diagram corresponds to a single cell. As can be seen, the histologically normal cells at a distance from a tumor have an increased disorder strength due to field carcinogenesis.

122

(a) Disorder strength Ld (μm)

5 4

x 10-5

* p-value < 0.0001

*

*

3 2 1 0 Control

(b)

x 10-5

4cm away tumor

Tumor

Standard deviation of Ld (σLd) (μm)

10 8

* p-value < 0.0001

*

*

6 4 2 0 Control

4cm away tumor

Tumor

Figure 6:2. The relative values of the disorder strength L(dg ) and intracellular standard deviation of the disorder strength σ ( g ) for the three cell types. Both L(dg ) and σ ( g ) is obtained from ~30 cells for each cell type. The error bars represent the

standard error of the mean. L(dg ) and σ ( g ) is significantly increased in the tumor cells compare to control cells (Student t-test p-value <0.0001). We next study the changes in the internal architecture of the cells outside of the spatial extent of tumors in the field of carcinogenesis. The cells were obtained from the patients with

123 colorectal cancers (n = 20), this time from locations greater than 4cm away from the tumor. All cells were verified to be cytologically normal by a surgical pathologist. The question we asked was as follows: although appearing normal by the criteria of microscopic histopathology, do these colonocytes possess alterations in their nanoarchitecture? Figure 6:2(a,b) show that both L(dg ) and σ ( g ) are highly significantly (p-value<0.001) increased in the cells obtained from outside the tumor boundary compared to those from normal patients. Interestingly, these cells only have a slightly decreased L(dg ) and σ ( g ) compared to cancer cells leading us to speculate that the nano-architectural alterations are very early events in carcinogenesis. These alterations seem to occur at lc~50 nm (Δn~0.1 [97]). This length scale corresponds to the size of some of the most fundamental building blocks of the cell, such as ribosomes, cytoskeleton, membranes, etc. It is also well below the diffraction limited resolution of the conventional microscopy, which explains why these cellular changes have not previously identified by conventional histopathology.

124 x 10-5

Standard deviation of Ld (σLd) (μm)

6 5 4 3 2 Adenoma Advanced Adenoma No dysplasia

1 0

0

1

2

3

x 10-5

Disorder strength Ld (μm)

Figure 6:3. Cells obtained from histologically normal colonic mucosa have increased disorder strength due to the presence of premalignant tumors anywhere else in colon. The values L(cd ) and σ (c ) obtained from histologically normal rectal mucosa from control patients and those with adenomatous polyp elsewhere in the colon. Though histologically normal, the rectal cells from patients with premalignant tumors occupy a separate regime in the parameter space with only slight overlap with the normal cells.

125

(a) Disorder strength Ld (μm)

9

7

x 10-6

*

* p-value < 0.0001

5

*

3

1 Control

(b)

Standard deviation of Ld (σLd) (μm)

14

Adenoma

Advanced adenoma

x 10-6

* p-value < 0.0001

*

10

* 6

2

Control

Adenoma

Advanced adenoma

Figure 6:4. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal rectal mucosa in patients with premalignant tumors and those with no tumors present. (a) The average disorder strength L(dg ) is significantly elevated in cells from patients with presence of adenomatous polyps elsewhere in the colon compared to controls (p-value <0.0001). Similar to L(dg ) , the σ ( g ) is significantly elevated in patients with the presence of premalignant tumors elsewhere in colon (p-values < 0.0001).

126 The next step is to assess the extent of the field carcinogenesis and to study whether the cells from the easily accessible sites could serve as markers for field carcinogenesis. The rectum is the easiest accessible part of the colon that is commonly probed for digital rectal exam, rectal temperature, etc. It has been validated earlier from studies on epithelial proliferation [98], alterations in gene expression [99] and protein profiles [100] that molecular alterations in the rectal mucosa are associated with neoplasia elsewhere in the colon. However it has not been understood whether these genetic and molecular changes translate into nanoarchitectural alterations. To answer this question, we performed PWS on rectal histologically normal cells collected using cytological brushings from 35 patients (21 with no neoplasia, 10 with nonadvanced and 4 with advanced adenomas) during routine colonoscopy procedures. Figure 6:3 and Figure 6:4 show that both L(dg ) and σ ( g ) are highly significantly elevated in patients with adenoma compared to the control group (P < 0.001). Interestingly, the patients with advanced adenoma (adenoma >10 mm) had the highest L(dg ) and σ ( g ) . Thus a gradient in the increase of L(dg ) and σ ( g ) in microscopically normal rectal cells parallels the significance of neoplasia. These results confirmed the alteration of cell nanoarchitecture in field carcinogenesis in the colon. We then wondered whether this phenomenon applies to other organs. As an illustration, we performed PWS on patients with pancreatic cancer.

Standard deviation of Ld (σLd) (μm)

127 40

x 10-5 Cancer No dysplasia

30

20

10

0 0

4

8

Disorder strength Ld (μm)

12

x 10-5

Figure 6:5. Histologically normal duodenal mucosa cells have increased disorder strength due to the presence of pancreatic cancer. The L(cd ) and σ (c ) obtained from histologically normal duodenal mucosa from patients with pancreatic cancer and with no cancer. Though histologically normal, the duodenal cells from pancreatic cancer patients only slightly overlap with the normal cells.

128 x 10-5 4

Disorder strength Ld (μm)

(a)

3

2

1 Control

(b)

Cancer

x 10-5

Standard deviation of Ld (σLd) (μm)

7

* p-value < 0.0001

*

5

3

1 Control

Cancer

Figure 6:6. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal duodenal mucosa in patients with and without pancreatic cancer. The average disorder strength L(dg ) is significantly elevated in cells from patients with presence

of pancreatic cancer compared to normal (p-value <0.0001). Similarly, σ ( g ) is significantly elevated in patients with the presence of pancreatic cancer (p-values < 0.0001). Pancreatic cancer is one of the most lethal common malignancies.

The cells were

obtained from the cytologically normal periampullary duodenal mucosa (epigenetic alterations

129 were observed in previous studies from duodenal mucosa of pancreatic cancer patients [93]) of 35 patients (controls = 26, cancer = 9) who undergo endoscopic ultrasound (EUS) or endoscopic retrograde cholangiopancreatography (ERCP) procedures. Figure 6:5 and Figure 6:6 show that the disorder strength is significantly elevated in duodenal mucosa cells of patients with pancreatic cancer compared to controls (P < 0.001). These results not only show that the cytologically normal cells undergo changes in their nanoarchitecture due to field carcinogenesis but also the potential of applying field carcinogenesis clinically wherein patients can potentially be screened for the presence of premalignant/malignant tumors by looking at cells from easily accessible surrogate anatomical locations. For example, this method of diagnosing the cells in the field carcinogenesis would significantly help screening patients with early colon carcinogenesis.

Current screening

modalities such as colonoscopy and flexible sigmoidoscopy have shown to be effective in reducing colorectal cancer mortality by direct visualization of colon. Though it is recommended that all patients over 50 years of age undergo colonoscopy, the majority of the population does not undergo any screening technique due to the reluctance from both patients and physicians. Also, it is estimated that around 70% of all patients who undergo colonoscopy do not harbor polyps. This has warranted a robust and cost effective prescreening technique that can classify patients into a high risk group thereby reducing needless colonoscopy procedures. Though various prescreening techniques such as fecal DNA analysis and CT colography have been proposed they have often yielded sub-optimal sensitivities. Field carcinogenesis presents an attractive alternate approach wherein the easily accessible surrogate site can be interrogated for

130 the presence of polyps in the difficult to reach target organ. Results presented in this paper show that rectal cells undergo alterations in their internal nanoarchitecture due to the presence of adenomatous polyps elsewhere in the colon thereby providing an optimum methodology that can be tapped for prescreening patients before being sent to the painful colonoscopy. Unlike colon cancer, at the present time, no effective screening technique for pancreatic cancer is available. This is in part because the interrogation of the pancreatic duct is associated with an unacceptably high rate of significant complications. On the other hand, due to its accessibility, interrogating the adjacent duodenal mucosa presents a wonderful opportunity to screen asymptomatic patients with high risk of pancreatic cancer. Since the duodenal cells undergo increased alterations in their nano-architecture in patients with pancreatic cancer compared to normal patients, by using PWS it may be possible to screen for asymptomatic patients.

6.4 Summary In summary, our study provides powerful evidence that the microscopically-normal mucosa in field carcinogenesis has undergone profound nanoscale alterations with increased disorder in their nanoarchitecture detectable by PWS.

These changes can potentially be

exploited to develop novel screening strategies by providing a minimally intrusive means of identifying field carcinogenesis and, thus, patients at increased risk for cancer. Future studies should elucidate the molecular mechanisms through which intracellular disorder increases in early carcinogenesis.

131

Chapter 7 Detecting the presence of field carcinogenesis from lung cancer using PWS: an application in lung cancer screening 7.1 Introduction Lung cancer is the leading cause of cancer related deaths among Americans with an estimated 215,020 new cases in 2008 [101] and 161,840 deaths [101]. The lifetime risk of an American to develop lung cancer is 1 in 12 in men and 1in 16 in women. As with any major cancer, the detection of lung cancer at an early stage is often curable through surgical resection. The survival of lung cancer is mainly dictated by the stage of diagnosis with 49% survival for localized, 16% for regional and 2% for distal lung cancers. However, early diagnosis of lung cancer is uncommon with only 16% of cancers being diagnosed at a localized stage, whereas 37% and 39% of cancers are being diagnosed at regional and distant stage respectively. This is largely because the symptoms tend to be a harbinger of more advanced disease. There are 4 major histological subtypes of lung cancer with 35% of cases being adenocarcinoma, 29% squamous cell carcinoma, 18% small cell and 9% large cell (anaplastic) carcinomas.

132 While all these carcinomas vary in location, radiographic manifestation etc., all are believed to have been increased by smoking. Smoking is the single most important risk factor of lung cancer accounting for ~90% of lesions. Given that worldwide ~1.3 billion people smoke, cigarette smoking contribute to almost 5 million preventable deaths per year. Dosage of cigarette smoking appears to be an important factor of lung cancer. For example, tripling the number of cigarettes smoked per day increases the risk of lung cancer by three fold. However, increasing the duration of smoking by 3 times resulted in a 100 fold increase in risk of lung cancer. Although quitting has a beneficial effect with a direct relationship between period of abstinence and decrease in risk, the risk of lung cancer does not ever go back to that of a non-smoker. For instance, even after abstaining for more than 40 years, the risk of lung cancer remains significantly elevated. The presence of emphysema is an increased risk factor, increasing the risk three fold when compared to the subjects with same tobacco exposure but without chronic obstructive pulmonary disease (COPD). Passive smoking, also known as environmental tobacco smoke (ETS), provides a significant risk, although it is more weakly associated with lung cancer risk. Estimates suggest that passive smoke accounts for 3000 deaths per year in the United States. Gender and race may also play some role in augmenting tobacco sensitivity. While more males smoke and hence get lung cancer, the gender gap appears to be narrowing as the females appear to be more sensitive to tobacco smoke compared to males. Similarly, from a racial perspective, African Americans males are 45% more likely to develop lung cancer than white males, which is believed to be due

133 to the increased sensitivity to the carcinogenic effects of tobacco smoke.

Further

compounding this is that the disease appears to be more aggressive in African American males. As mentioned earlier, if caught at an early stage lung cancer is eminently curable through surgical resection. However, symptom development is generally a harbinger of advanced and hence incurable disease. Indeed, since only 16% of patients are diagnosed at the localized stage, in aggregate, the five year survival for lung cancer patients is only ~15%. Lung cancer would represent an ideal malignancy to be screened as the risk factor is well established and potent and hence the screening techniques could be targeted towards the at-risk population. For instance, the potency of smoking is underscored by the observation that ~10-15% of smokers will develop lung cancer [101]. There have been a number of screening approaches that have been proposed including chest X-ray, sputum cytology etc., all of which have been shown to lack the sensitivity to lung cancer [102]. Computed tomography (CT) has the combination of accuracy and minimal intrusiveness making it a potentially ideal screening test for lung cancer. In particular, there has been an interest in the use of low dose computed tomography (LDCT) for primary screening of lung cancer [103]. The sensitivity of LDCT over chest X-ray is clear, with LDCT detecting 3 times as many lung nodules as chest X-rays. While initial reports were positive, the survival benefit has not been replicated [104, 105]. Importantly, low dose CT has issues with cost, detecting clinically insignificant lesions etc.

This has led the American College of Chest

Physicians to recommend against the routine use of low dose CT scans for lung cancer screening [102].

134 The ideal lung cancer screening test would need to be accurate, inexpensive and minimally intrusive.

One potentially attractive means is through the exploitation of field

carcinogenesis, the concept that the genetic/environmental milieu that results in a lesion in one area of the lung should be detectable throughout the aerodigestive mucosa [106]. Evidence supporting the field carcinogenesis is the relatively common occurrence of multiple primary lung tumors, sharing of chromosomal loss of heterozygosity between tumors and uninvolved epithelium (termed allele-specific mutations), shared gene methylation signatures or EGFR mutations between resected tumors and adjacent non-neoplastic epithelium [107, 108]. Recently there is emerging evidence of extended field carcinogenesis in lung cancer that encompasses the buccal (cheek) epithelium [88, 109-111].

For example, the reports suggest that genetic

techniques such as loss of heterozygosity in buccal cells can differentiate smokers with and without lung cancer [112]. Similarly, morphometric studies have shown that the buccal mucosa is different between patients with and without lung cancer [111, 113]. While these studies underscore the biological plausibility for assessing buccal mucosa for lung cancer detection, the current approaches have woefully inadequate performance characteristics (sensitivity and specificity) [112, 114]. Conventionally, biomedical optics have been used as a means for detecting dysplasia in lung [1, 14]. For instance, laser-induced fluorescence endoscopy (LIFE) has been shown to outperform white light endoscopy for detection of preneoplastic lesions (squamous metaplasia etc.) [115].

Other groups are also developing approaches such as endoscopic reflectance

spectroscopy [116], optical coherence tomography (OCT) [117] and Raman spectroscopy [118].

135 However, these approaches are at an earlier phase of development awaiting clinical confirmation of utility. In this chapter we utilize the novel light scattering technique, partial wave microscopic spectroscopy, to probe the nanoscale architecture of the histologically normal buccal cells. We show that the nanoscale refractive index fluctuations are present in the buccal cells due to extended field carcinogenesis in lung. We also show the feasibility of predicting lung cancer through the PWS assessment of normal-appearing buccal mucosa cells without the need for the direct imaging of lung.

7.2 Methods 7.2.1 Human Studies The human studies were approved and done in accordance with the institutional review board at Evanston Northwestern Healthcare. After informed consent, the visually normal buccal mucosa was brushed gently with a cytological brush from 22 normal patients and 52 cancer patients. The normal group consisted of those patients without any personal history of lung cancer or a significant family history of lung cancer. The normal group also had no current history of smoking. The cancer group was defined as patients with histologically confirmed lung cancer including non-small cell carcinoma, small cell carcinoma, squamous cell carcinoma etc. The cytological brush was then applied to a sterile glass slide. The cytological slides were then immediately fixed in an alcohol bath containing 80% ethyl alcohol. Since smoking is the most important risk factor for lung cancer and may alter the oral epithelium, we also obtained buccal brushings from 29 patients who were cancer free but had smoked an equivalent amount and thus

136 developed chronic obstructive pulmonary disease, COPD. All the buccal mucosa cells were confirmed to be cytologically normal by an expert cytologist. The PWS measurements were then performed on ~ 25-30 randomly taken cells from each patient.

7.2.2 Partial wave microscopic spectroscopy The design of the PWS instrument is discussed in detail in Chapter 4. In brief, a focused wave of broadband, low-spatially coherent light of ~700 nm illuminated the sample, and an image formed by the backscattered photons was acquired in the far-field. The spectrum of the backscattered light intensity from 390 to 750 nm was recorded for each pixel of the image with 3 nm resolution. As discussed earlier, PWS combines certain aspects of microscopy and the spectroscopy of light elastically scattered by cells. However, unlike conventional microscopy, in which an image is formed by integrating the reflected or transmitted intensity over a broad spectrum, PWS measures spectral fluctuations in the backscattering spectra. That is, PWS virtually divides a cell into a collection of parallel channels each with a diffraction-limited transverse size, detects backscattered waves propagating along 1D-trajectories within these channels, and quantifies the statistical properties of the nano-architecture of a cell by the analysis of the fluctuating part of the (normalized) reflected intensity R (λ ; x, y ) , where λ is the wavelength of light and x and y are the spatial coordinates of a particular channel. The spectral fluctuations were then analyzed by means of 1D mesoscopic light transport theory to yield the statistical parameter disorder strength: Ld =< Δn 2 > l c , where < Δn 2 > and lc are the variance and the spatial correlation length of the refractive index fluctuations. Using PWS, a two-

137 dimensional map depicting the distribution of disorder strength Ld (x, y) was obtained for a particular buccal mucosa cell.

From these 2D images several statistical parameters were

extracted, such as the mean intracellular disorder strength L(cd ) (the average Ld ( x, y ) over x and y) and the standard deviation of intracellular disorder strength, σ (c ) . The averages of L(dc ) , σ (c )

over a group of cells from a particular patient category yielded the group means L(dg ) and σ ( g ) .

7.2.3 Statistical analysis All statistical analysis were done using Microsoft Excel and STATA data analysis and statistical software package (Statacorp LP, College station, TX). The mean intracellular disorder strength and standard deviation of intracellular disorder strength were compared between different patient groups using the Student's t test. The effects of different demographic factors were analyzed using two-way ANOVA. Two sided P values were used for all analyses. A twosided P value less than 0.05 was considered as statistically significant.

The performance

characteristics such as the sensitivity and specificity were calculated using logistic regression.

7.3 Results and Discussion We first performed PWS experiments on buccal cells obtained from 22 normal patients and compared them with 52 cancer patients. These PWS measurements were obtained to ascertain whether nanoarchitectural alterations are present in the cytologically normal buccal cells due to extended field carcinogenesis in lungs. The age was 64 ± 12 years (mean ± standard deviation) for the 22 normal patients and 69 ± 11 years for the 52 cancer patients.

138 Approximately 60% of patients were females in both the normal and cancer group. The cancer patients also had a smoking history of 55 ± 39 median pack-years. As discussed in methods, PWS measurements were obtained from ~ 25 cells from each patient and the L(cd ) and

σ ( c ) were calculated for each cell.

Standard deviation of Ld (σLd) (μm)

x 10-5

12.5

8.5

Cancer Normal

4.5

0.5 1

6

11

16

21 x 10-5

Disorder strength Ld (μm) Figure 7:1. Histologically normal buccal mucosa cells have increased disorder strength due to the presence of lung cancer. The L(cd ) and σ (c ) are obtained from histologically normal buccal mucosa from patients with lung cancer and with no cancer.

Figure 7:1 plots L(dc ) vs. σ ( c ) for all cells for the normal and cancer groups with each cell being represented by a point: (L(dc ) ,σ ( c ) ) . Clearly, both L(cd ) and σ (c ) are increased in cancer cells. This is further illustrated by Figure 7:2 which show that both L(dg ) and σ ( g ) are highly

139 statistically significantly increased in cytologically normal cells from patients with lung cancer than when compared to normal patients (P < 0.001). We also point out that, intriguingly, there is a certain degree of intercellular heterogeneity among cells belonging to the same patient group with the intercellular heterogeneity being highest for patients with lung cancer. These results confirmed the presence of nanoarchitectural alterations in buccal cells due to field carcinogenesis in the lung. However, we wondered whether this increase in disorder strength might be due to the difference in smoking history between the normal and cancer patients as cigarette smoking is known to alter the oral epithelium. Hence to control for the cigarette exposure we performed PWS measurements on 29 COPD patients who were cancer free but had smoked an amount similar to cancer patients. The age of the COPD patients was 70 ± 9 years and approximately 50% were females. The COPD patients had a smoking history of 61 ± 39 median pack-years. Similar to cancer patients, PWS measurements were obtained from ~ 25 cells from each COPD patient and the L(cd ) and σ (c ) were calculated for each cell. Figure 7:3 compares the bright field image and PWS images of three representative cells from the COPD and cancer groups. As seen from the images, the three representative cells from patients with lung cancer and COPD appear to be cytologically similar. This was also confirmed by the analysis of at least 20 cells from each patient group. For comparison, PWS images are clearly different between COPD and cancer cells. That is, the cells from cancer patients have a higher intracellular disorder strength compared to the cells from COPD patients.

This is further

illustrated in Figure 7:4 which plots L(cd ) vs. σ (c ) for all cells for the COPD and cancer groups.

140

Disorder strength Ld (μm)

(a) 8

x 10-5

* * P < 0.0001

6

4

2 Normal

Cancer

(b) Standard deviation of Ld (σLd) (μm)

x 10-5

*

5

* P < 0.0001 3

1 Normal

Cancer

Figure 7:2. The relative values of the L(dg ) and σ ( g ) for cells from histologically normal buccal mucosa in patients with and without lung cancer. The average disorder strength L(dg ) is significantly elevated in cells from patients with presence

of lung cancer compared to normal (p-value <0.0001). Similarly, σ ( g ) is significantly elevated in patients with the presence of lung cancer (p-values < 0.0001).

141 (a)

(b)

x 10 11

--5

10 9

(c)

7 6 5 4

(d)

3

Disorder strength Ld (μm)

8

2 1

Figure 7:3. Representative bright field images and pseudo-color PWS images from buccal mucosa cells from patients with lung cancer and patients with COPD. Panels (a) and (b) are the bright field and PWS images of buccal cells from a COPD patient while panels (c) and (d) are those from a cancer patient. The color in the PWS image shows the magnitude of the disorder strength Ld in a cell. Although the bright images shown in panel (a) and (c) appear similar, the PWS images are distinctly different from each other. This shows that the disorder strength is significantly elevated in buccal cells due to field carcinogenesis.

142

Standard deviation of Ld (σLd) (μm)

x 10-5

12.5

8.5 Cancer COPD 4.5

0.5

1

6

11

16

21 x 10-5

Disorder strength Ld (μm)

Figure 7:4. Comparison of L(cd ) and σ (c ) of histologically normal buccal mucosa cells from patients with lung cancer and patients with COPD. The COPD patients are considered to compensate for cigarette smoke exposure. Both L(cd ) and

σ ( c ) are highly elevated in patients with lung cancer.

143

Disorder strength Ld (μm)

(a)

x 10-5

* 7

* P < 0.0001

5

3

COPD

Cancer

(b) Standard deviation of Ld (σLd) (μm)

x 10-5 6

* * P < 0.0001

4

2

COPD

Cancer

Figure 7:5. The relative values of (a) disorder strength L(dg ) and standard deviation σ ( g ) for patients with lung cancer and patients with COPD. L(dg ) is obtained by averaging L(cd ) from randomly chosen ~25 cells. The error bar represents the

standard error of the mean. Both L(dg ) and σ ( g ) are significantly increased in buccal cells from patients with lung cancer compared to the patients with COPD (P <0.0001).

144 The average intracellular disorder strength L(dg ) and standard deviation of disorder strength σ ( g ) obtained from the cytologically normal appearing buccal mucosa cells of COPD and cancer patients are shown in Figure 7:5. As seen there is a dramatic increase in both L(dg ) and σ ( g ) in patients with lung cancer when compared to patients with COPD (P < 0.0001 for both L(dg ) and σ ( g ) ).

These results not only confirm that the nanoscale refractive index

alterations are present in buccal cells of lung cancer patients but also validate that the difference in disorder strength between COPD and cancer patients may not be due to the difference in cigarette smoke exposure. Also, these alterations seem to occur at lc~100 nm (Δn~0.1 [97]). As discussed previously, this length scale corresponds to the size of some of the most fundamental building blocks of the cell, such as ribosomes, cytoskeleton, membranes, etc. However, this length scale is well below the diffraction limited resolution of conventional microscopy explaining the reason why these intracellular changes are not identified using conventional cytopathology. To ascertain the performance characteristics of these markers, we obtained the performance of both L(dg ) and σ ( g ) for discriminating COPD patients from cancer patients by logistic regression of the markers L(dg ) and σ ( g ) . The two markers yielded an area under the ROC (AUROC) curve of 80% with the sensitivity of 80% and specificity of 75%. In comparison the two markers yielded an AUROC of 92% for discriminating normal patients from lung cancer patients with a sensitivity of 90% and specificity of 80%. As discussed earlier smoking history is an important risk factor in developing lung cancer. Hence we wanted to ensure that the changes in disorder strength measured using PWS

145 detects carcinogenesis itself rather than a mere difference in smoking history among patients with lung cancer and patients with COPD. To answer this question we investigated how the markers L(dg ) and σ ( g ) vary with patients' smoking history. The effect of patients' smoking history was addressed by using two-way ANOVA to measure the differences between COPD and lung cancer patients as well as between smoking history. As shown in Table 7:1, the twoway ANOVA analysis shows that both L(dg ) and σ ( g ) are not significantly associated with smoking history (P > 0.4).

Similarly, we found that the markers L(dg ) and σ ( g ) have no

significant association with other demographic factors such as age, race and gender (Table 7:1). Hence, the changes in L(dg ) and σ ( g ) are unlikely to be attributed to difference in age, gender, race and smoking history in the patient population.

Table 7:1. Diagnostic performance of PWS is not affected by the patient demographic factors.

Demographic factor

Effect on L(dg ) , P-value

Effect on σ ( g ) , P-value

Age

0.56

0.45

Smoking

0.65

0.48

Race

0.40

0.40

Gender

0.79

0.93

The above results show for the first time that nanoscale architectural alterations are present in buccal cells outside the spatial extent of a lung tumor, i.e. in the field of

146 carcinogenesis.

These alterations are an increased disorder in intracellular nanoscale

architecture. It has long been assumed that the buccal cells in the field of carcinogenesis are morphologically normal. However, we demonstrate here for the first time that the cells do possess morphological alterations, although not at the microscale but at the nanoscale – the length scale of the macromolecular complexes and other fundamental building blocks of the cell. It is to be noted that the genetic/epigenetic alterations have been previously observed in the buccal cells due to field of carcinogenesis [109-111]. However, we show here for the first time that these molecular changes translate into nanoarchitectural alterations thereby suggesting that the molecular events and cell structure are more closely interrelated than previously thought. The results reported in this chapter also show the feasibility of diagnosing lung cancer by means of examining the buccal mucosa without direct visualization of the lung. As discussed previously, PWS is remarkably sensitive to the changes in intracellular nanoarchitecture which are otherwise undetectable using conventional cytology.

Hence, the intracellular disorder

strength quantified in terms of L(dg ) and σ ( g ) are able to distinguish lung cancer patients from COPD patients with an AUROC of 80%. This performance of buccal PWS is exceedingly encouraging from a clinical perspective given that we have demonstrated the capability in the most difficult case, that is, in COPD patients who have a high risk of lung cancer. Interestingly, the AUROC was even greater for distinguishing lung cancer patients from normal controls. Also the diagnostic performance of PWS did not appear to be compromised by confounding factors such as smoking history, age, race and gender. That is, the two way ANOVA statistical analyses

147 showed that the changes in disorder strength between different patient groups is unlikely to be attributed to differences in patient demographic factors.

7.4 Summary We report, for the first time, that the disorder strength obtained from partial wave microscopic spectroscopy is able to accurately predict lung cancer through the assessment of cytologically normal buccal mucosa without the need for any imaging of the lung. Since smoking is the most important risk factor for lung cancer and may alter the oral epithelium the diagnostic performance was compared with patients who were cancer free but had smoked an equivalent amount and thus developed COPD. The results from patients with lung cancer and patients with COPD shows a diagnostic performance of 80% sensitivity and 75% specificity. This diagnostic performance is not compromised by demographic factors such as age, smoking history, gender and race. This approach of probing the nanoarchitectural alterations in field carcinogenesis can potentially revolutionize screening for lung cancer by providing a highly accurate, non-invasive means of risk assessment. Future large scale studies will be done to validate this potentially new paradigm in lung cancer screening.

148

Chapter 8 Demystifying Partial wave spectroscopy 8.1 Introduction Recently there has been a significant interest in understanding biological cells at the nanoscale. To this effect, the novel optical spectroscopy technique, partial wave microscopic spectroscopy has been shown to be exceedingly useful in detecting the nanoscale refractive index alterations within biological cells. For example, we showed that PWS detects nanoarchitectural alterations in HT29 human colon adenocarcinoma cell lines that are induced by gene knockdown. We also demonstrated the ability of PWS to detect nanoarchitectural alterations in cytologically normal buccal mucosa cells and its potential application as a screening technique for lung cancer. Though these studies demonstrated the nanoscale sensitivity of PWS, many questions still remain regarding the working mechanism of PWS. For example, questions such as the origin of PWS signals in a random medium and the role played by the surface roughness of medium have not been addressed. In this chapter we attempt to answer some of these questions of PWS which would further our understanding of PWS.

149

8.2 Methods 8.2.1 Real time PWS instrumentation The PWS instrumentation discussed in Chapter 4 acquires the backscattering image by linearly scanning the entire length of an isolated cell. Hence, it takes an average of 3-4 minutes to acquire the data from a single cell and 60-80 minutes to diagnose a single cytological specimen (20-30 cells) from a patient. Though the PWS system is sensitive to nano-architectural alterations in a cell compared to conventional cytology, this delay in data acquisition will prevent its widespread implementation in clinical settings. The reasons for the delay in acquiring data using the current PWS system include a) the spectrograph that scans 400-700 nm for every pixel of the image and b) the scanning stage that scans the entire image of the cell in steps of 10nm. Hence, we developed an improved PWS instrumentation that acquires PWS images in quasi-real time similar to those in conventional microscopes. In the real time PWS system (rtPWS), to avoid spatial scanning of each pixel in a cell, we replaced the spectrograph-scanning stage combination with a liquid crystal tunable filter (LCTF). The schematic of the real time PWS system is shown in Figure 8:1. The white light from the Xenon lamp (150 W, Oriel Corporation) is collimated by a 4f-lens relay system and focused onto a sample by a low numerical aperture (NA) objective (NA = 0.4, Edmund Optics). The objective lens in the rtPWS system contains a correction collar to compensate for any aberrations that may arise due to the presence of coverslip. This enables us to obtain backscattering images from cytological specimens that are covered with the coverslip. The backscattered image is then

150 projected through the liquid crystal tunable filter (CRI, Inc, spectral resolution = 7 nm) on to a CCD camera. That is, the LCTF collects the backscattering image of a cell at a particular wavelength between 400 nm and 700 nm and projects it onto the CCD camera thereby avoiding the need for spatially scanning each pixel in the cell. Hence similar to the PWS system, rtPWS system generates a three dimensional data cube R(λ ; x, y ) where (x,y) refers to a pixel in the object plane.

The disorder strength and the related parameters are then calculated from

R(λ ; x, y ) using the methods discussed in Chapter 4.

151

BS

CCD LCTF

TL

OBJ

Figure 8:1. Schematic of the real time partial-wave spectroscopy (rtPWS) system. (a) C: condenser; L: lens (f = 150 mm); A: aperture; BS: beam splitter; OBJ: objective lens; TL: tube lens (f = 450 mm); SS: sample stage; LCTF: liquid crystal tunable filter (λ = 400 nm to 700 nm) CCD: detector CCD camera (CoolSnap HQ, Roper Scientific).

8.2.2 1D FDTD simulation A 1D finite difference time domain (FDTD) numerical model, similar to those discussed in Chapter 4, is constructed to study the properties of 1D waves that are propagating within a weak refractive index random medium. We consider a homogeneous dielectric slab with random refractive index fluctuations around the background refractive index n0 = 1.38 (similar to the average refractive index of a biological cell). The Δn of the refractive index fluctuations is varied from 0.01 to 0.1. The correlation length lc of the fluctuations is varied from 5 to 100 nm

152 (klc << 1). The thickness of the sample L is varied from 1 to 5 μm. The 1D spectrum is obtained directly from the FDTD model and the corresponding disorder strength Ld is calculated using Eqns discussed in Chapter 4.

8.3 Results and Discussion 8.3.1 Source of low frequency signal in PWS spectrum The 1D reflection spectrum R(λ ; x, y ) is calculated from the normalized backscattering intensity spectrum I (λ ; x, y )(≡ I (λ )) measured for each pixel inside a biological cell.

As

discussed in chapter 4, R(λ ; x, y ) is calculated from I (λ ; x, y ) as follows: a) first a low pass filter is used to remove all oscillations that are less than the point spread function of the system, as all the oscillations less than the resolution of the system can only be attributed to the system noise. b) second a low order polynomial I p (λ ) is fit to the filtered I (λ ) . The 1D backscattering spectrum R(λ ) is obtained by subtracting I (λ ) with I p (λ ) (i.e., R (λ ) = I (λ ) − I p (λ ) ). The normalized I (λ ) along with the low order polynomial I p (λ ) is shown in Figure 8:2.

153

x 10-3 65

Single isolated cell Glass slide

I(λ)

60

55

50

45 500

540

580

620

Wavelength, λ (nm)

660

Figure 8:2. The normalized backscattering spectrum obtained from a single pixel of a biological cell and pure glass slide. The spectrum from the biological cell exhibits a low frequency slope that is otherwise absent in the spectrum from a glass slide.

We asked the question whether this low frequency slope in the backscattering spectrum of a biological cell could be contributed by structures that are on the order of or below the wavelength of light. In order to answer this question we perform PWS measurements on a thin film of arbitrary thickness. The normalized backscattering spectrum I (λ ) obtained from a single pixel of a thin film is shown in the Figure 8:3. As expected, the backscattering spectrum contains high frequency oscillations that corresponds to the thickness of the thin film. More importantly, the low frequency slope in I (λ ) that is observed in biological cells is absent in the I (λ ) spectrum from a thin film. We then perform similar experiments on a homogeneous

microsphere of size 11 μm. Similar to the thin film, the microsphere has a homogeneous

154 refractive index with no refractive index alterations. However the microsphere exhibits surface curvature that is otherwise absent in the thin films. The backscattering spectrum I (λ ) is shown in Figure 8:3. As seen, the I (λ ) from the spherical microsphere contains the low frequency spectrum similar to those from biological cells. Similar studies were performed on microspheres of different sizes to confirm that these low frequency spectra from microspheres are not the 3D Mie oscillations observed in a Mie sphere. These results confirm that the low frequency spectrum observed in the biological cells might not be contributed from small structures inside the biological cell. We hypothesize that these low frequency spectra that are otherwise absent in a flat thin film might arise due to the surface curvature in microspheres and biological cells. That is, when a plane wave illuminates the sample with a small curvature some of the waves are focused into the medium and get reflected in the backward direction due to the presence of glass substrate below the medium. Hence instead of giving rise to a uniform incoherent background, the surface curvature induces a non uniform background thereby giving rise to a small slope in the backscattering spectrum. To test our hypothesis that these incoherent waves are formed due to the reflection from the substrate, we perform PWS measurements from microspheres that are kept on a refractive index matching solution instead of a glass slide. The

I (λ ) from a microsphere embedded in a refractive index matching liquid (agarose gel, n = 1.45) is shown in Figure 8:4. As expected, the low frequency spectrum observed earlier is no longer present in microspheres embedded in a refractive index matching liquid. These results not only confirm that the low frequency spectrum is due to non uniform reflection from the glass substrate

155 but also validate the reason for removing these low frequency spectra to extract the 1D backscattering partial waves from the medium.

156 1.5

Microsphere Thin film

I(λ)

1.3 1.1 0.9 0.7 0.5 500

540

580

620

660

Wavelength λ (nm) Figure 8:3. The normalized backscattering spectrum obtained from a single pixel of a spherical microsphere and thin film. The spectrum from the microsphere exhibits the low frequency slope that is otherwise absent in the spectrum from flat thin film. 1.5 Microsphere in agarose

I(λ)

1.3 1.1 0.9 0.7 0.5 500

540

580

620

660

Wavelength λ (nm) Figure 8:4. The normalized backscattering spectrum obtained from a single pixel of a spherical microsphere embedded in agarose gel. The spectrum from the microsphere does not exhibit the low frequency slope as it is embedded in the refractive index match agarose gel.

157

8.3.2 Effect of intracellular refractive index fluctuations We first answer the question whether the 1D spectra obtained using PWS are indeed sensitive to nanoarchitectural refractive index fluctuations in the cell.

This is particularly

important given that the refractive index difference at the air-cell interface (herein defined as refractive index contrast) is much higher than the weak refractive index fluctuations (Δn) found within the cell. Hence we asked ourselves the question whether the 1D spectra obtained from the biological cell are sensitive to nanoscale fluctuations within the cell or whether it is merely proportional to the size of the biological cell. To answer this question, we perform 1D FDTD numerical simulations on a homogeneous medium with no refractive index fluctuations inside the sample (Δn = 0). The refractive index contrast ( ni − n0 ) for the top layer is assumed to be 0.38 ( ni = 1.38 for a biological cell and n0 = 1.0 for air) and for the bottom layer is assumed to be 0.14 ( ni = 1.52 for a glass slide and n0 = 1.38 for a biological cell). This numerical setup is similar to a typical PWS experiment wherein a single isolated biological cell is kept on a glass slide and is illuminated by a plane wave. The thickness of the homogeneous medium is assumed to be 3 μm which is the typical thickness of a biological cell. The results obtained from such a medium using a 1D FDTD model is shown in Figure 8:5. The backscattering spectrum from a homogeneous medium with no refractive index fluctuations should resemble the interference patterns from a thin film. As expected, the results from the 1D FDTD simulation resemble a sine wave with its frequency corresponding to the thickness of the sample and the amplitude corresponding to the refractive index contrast (Figure 8:5 (a)). We then incorporate weak refractive index fluctuations into the medium to mimic the intracellular organelles within the

158 biological cell. The refractive index fluctuation Δn is varied between 0.01 - 0.1 and the correlation length of refractive index fluctuation lc is varied between 5 to 100 nm.

A

representative 1D spectrum obtained from a sample with Δn = 0.05, lc = 50 nm and thickness of 3 μm is shown in Figure 8:5(b). As seen, unlike the homogeneous medium with uniform reflection spectrum, the 1D backscattering spectrum from a medium with weak refractive index fluctuations shows random variations in its peak amplitude (r2= 0.21 compared to spectrum from homogeneous medium) with the randomness in the spectrum becoming increasingly significant with the increase in Δn and lc (data not shown). These results not only confirm that the 1D backscattering spectrum is indeed sensitive to weak refractive index fluctuations but also show that the 1D spectrum is not overwhelmed by the reflections due to the refractive index contrast at the top and bottom portion of the cell. Interestingly, averaging the 1D spectrum over a few hundred realizations results in a spectrum similar to those from a homogeneous medium (r2= 0.93) Figure 8:5 (c). Averaging several 1D spectra within a sample is similar to a 3D system where different waves propagating within a medium are averaged in the far field resulting in decreased sensitivity to refractive index fluctuations within the sample. However, as shown in Figure 8:5, detecting the 1D propagating partial waves enables PWS to quantify the weak refractive index fluctuations within the sample. We next derive the critical Δn and lc above which the internal refractive index fluctuations can indeed be quantified by analyzing the 1D backscattering partial waves. In order to calculate the critical Δn and lc we assume that the backscattering reflection arises due to the reflections from internal refractive index fluctuations within the sample (Rint), the reflections

159 from the refractive index mismatch between the air and the sample interface (Rext), the reflections due to imperfect fit of low order polynomial Ip(λ) (Rcurvature) and the reflections due to imperfect removal of noise in the backscattering spectrum (Rnoise). That is, R = Rint + Rext + Rcurvature + Rnoise . Rint is defined as, Rint = 2Δn 2lc Lk 2 / ni2 where k is the wave number ( k = 2πn / λ ), L is the thickness and ni is the refractive index of the medium. Similarly, Rext = ((ni − n0 ) /(ni + n0 )) 2 where n0 is the refractive index of air.

Rcurvature is

numerically derived from a sample with maximum radius of curvature, such as a microsphere. The I(λ) from a microsphere (Figure 8:3) contains a low order slope which is removed by fitting a low order polynomial Ip(λ). Rcurvature, quantified as the root mean square (RMS) value of the imperfections in the fit of Ip(λ), is found to be ~10-5 using the 4th order polynomial. Similarly, Rnoise is numerically calculated from the imperfect removal of high frequency white noise from the 1D FDTD spectrum. Rnoise is found to be ~ 10-4 for a signal that is more than twice the noise portion as is frequently seen in PWS experiments (Figure 4:2) and ~ 10-3 for a signal that is similar to the noise portion. Since both Rnoise and Rcurvature are significantly smaller than Rext (~0.03), the backscattering reflections is rewritten as, R ~ Rint + Rext . Thus, in order for the backscattering spectrum to be sensitive to internal refractive index fluctuations it is necessary that Rint is greater than Rext. Thus the critical Δn necessary to satisfy the above condition can be written as, Δn >

((ni − n0 ) /(ni + n0 )) 2

2l c Lk 2 / ni2

(32)

160

R(λ)

(a)

0.04 0.03 0.02 0.01 450

(b)

0.16

550 650 Wavelength λ (nm) r2 = 0.21

R(λ)

0.12 0.08 0.04 0

450

R(λ)

(c) 0.08

550 650 Wavelength λ (nm) r2 = 0.93

0.06

0.04 450

550

650

Wavelength λ (nm)

Figure 8:5. The 1D backscattering spectrum obtained from FDTD numerical simulation. 1D reflection spectrum obtained from (a) a homogeneous medium with Δn = 0, lc = 0 (b) a weak refractive index medium with Δn = 0.05, lc = 50 nm (c) realization average of 100 1D spectra from a medium with Δn = 0.05, lc = 50 nm.

The critical Δn obtained for a sample with different lc and L is shown in Figure 8:6 (a). As discussed above, the critical Δn is defined as the Δn above which the reflections due to the

161 refractive index contrast between the air and the sample do not overwhelm the reflections from the internal refractive index fluctuations within the sample. In all these cases, the refractive index contrast between the air and the medium is kept constant at 0.38. As seen, the critical value of Δn decreases with the increase in lc. For example, in order to detect an intracellular organelle of refractive index correlation length lc=50nm the critical Δn should be ~ 0.025 which is smaller than the typical refractive index of structures found within a biological cell. The above results were also confirmed using 1D FDTD simulations where the 1D backscattering spectra calculated for Δn above the critical values yielded a correlation coefficient r2 < 0.5 compared to those obtained for the homogeneous medium. A representative 1D spectrum from a medium of thickness 3 μm, lc = 30nm and Δn = 0.04 with r2 < 0.3 is shown in Figure 8:6 (b). In essence, these results indicate that the internal refractive index fluctuations within a biological cell can give rise to oscillations in the 1D backscattering spectra and that these oscillations are not completely overwhelmed by the reflections due to the refractive index contrast at the top and bottom surface of the cell.

162 (a) Standard deviation of refractive index Δn

0.09 ni = 1.38, L = 1μm ni = 1.38, L = 2μm ni = 1.38, L = 3μm

0.07 0.05 0.03 0.01 10

30

50

70

90

Refractive index correlation length lc (nm) (b) 0.16 R(λ)

r2 = 0.3 0.12 0.08 0.04 0 450

500

550

600

650

700

Wavelength λ (nm) Figure 8:6. Critical Δn and lc obtained using 1D FDTD numerical simulation and a 1D FDTD backscattering spectrum obtained for medium with Δn above the critical value. (a) The critical Δn is calculated for a sample with different refractive index correlation length lc and different thickness L. (b) A representative 1D spectrum obtained from a medium with thickness 3 μm, lc = 30 nm and Δn = 0.04 which is slightly greater than the critical value calculated using the analytical equation.

163

8.3.3 Effect of surface roughness of cells on PWS signal The next question we attempt to answer is whether the backscattering spectrum obtained using PWS is due to the internal refractive index fluctuations within the cell or is due to the variations in the cell membrane (i.e., surface roughness of the cell). In order to answer this question we first perform optical profilometry measurements on buccal mucosa cells and then compare the results with the disorder strength obtained using rtPWS.

The profilometry

measurements are obtained using an optical profilometer which calculates the surface profiles of cells under consideration. The diffraction limit of the optical profilometer is around 300nm, which is twice higher than the diffraction limit of the PWS system. The profilometry image of a single buccal mucosa cell on top of a glass slide is shown in Figure 8:7. As seen, the buccal mucosa cells have thicknesses varying between few hundred nanometers to several microns with the highest thickness found near the nucleus.

164 4000

Y – axis (μm)

3000 30 2000 50 1000 70 0

Relative thickness (nm)

10

90 10

20

30

40

50

X – axis (μm) Figure 8:7. Relative thickness of the cell calculated using optical profilometer. The colorbar shows the thickness of the cell relative to the surrounding glass slide.

From these optical profilometry maps, the surface roughness of the cell is calculated by measuring the average difference in height between adjacent pixels within a diffraction limited area. The pixel size in the optical profilometry image is ~ 250 nm while the diffraction limit in the PWS system is ~ 700 nm. Hence a 3 by 3 moving window is considered, and the standard deviation in thickness of all the pixels within this moving window is calculated. Thus we calculate the roughness profile of the biological cell under consideration by measuring the standard deviation within the 3 by 3 pixel for the entire profile map. The roughness profile calculated for a single buccal cell is shown in Figure 8:8. As seen, the surface roughness of the biological cell is on an average ~ 200 nm with the portion of the cytoplasm close to the nucleus exhibiting a higher surface roughness. Interestingly, though the nucleus has a higher thickness compared to the surrounding cytoplasm, all the pixels within the nucleus are relatively smooth

165 compared to those pixels from the cytoplasm. The roughness profile along a cross section of the cell is shown in Figure 8:9. As seen the surface roughness of pixels along the spatial direction of the cell varies anywhere between 50 nm to 500 nm. Considering a maximum roughness of 500 nm, the corresponding interference spectrum obtained from a portion of the cell with such roughness would translate into half a period in the backscattering spectrum. However this half a period in spectrum is not sufficient to cause random variations in the amplitude of the 1D backscattering spectrum. Hence it is safe to assume that the surface roughness of a biological cell is not sufficient to contribute to the disorder strength calculated from the PWS signal. We also compare the roughness profile of the cell with the corresponding disorder strength map obtained from the cell (Figure 8:10). As expected, there is no correlation between the roughness and the disorder strength map (r2< 0.2) further confirming that the surface roughness is not the source of disorder variations in a biological cell. These conclusions were further validated using 10 different cells of varied thicknesses.

166

Y – axis (μm)

800

30

600 50 400 70

200

90 10

20

30

40

50

Surface roughness (nm)

1000

10

0

X – axis (μm)

Figure 8:8. Surface roughness of a single biological cell obtained using optical profilometer. The surface roughness is defined as the standard deviation in thickness between adjacent pixels within a diffraction limited area.

Surface roughness (nm)

167

600

400

200

0

0

20

40

60

80

Y- position of cell (μm) Figure 8:9. Surface roughness across a one-dimensional cross section of the biological cell calculated using optical profilometer. The surface roughness obtained from three different cross sections across the biological cell indicates that the roughness varies between 50 nm and 500 nm.

168 x 10-5 14

10

Y – axis (μm)

12 30

10 8

50

6 4

70

Disorder strength Ld (μm)

(a)

2 90 10

20

30

40

50

X – axis (μm)

(b)

Disorder strength Ld (μm)

x 10-5 12

8

4

0

0

20

40

60

80

100

Y- position of cell (μm) Figure 8:10. Disorder strength of a single biological cell obtained using PWS. (a) disorder strength map of the cell with color bar showing the magnitude of disorder strength. (b) disorder strength obtained from three different cross sections across the biological cell.

169

8.3.4 Effect of numerical aperture on PWS We next study the effect of numerical aperture (NA) of the objective on the 1D backscattering spectrum. As discussed earlier, detecting these 1D backscattering partial waves enables quantifying the nanoarchitectural alterations within a biological cell. Both the properties of the medium as well as the illumination enables PWS to detect the 1D backscattering partial waves. For example, in a weakly scattering refractive index medium the interference among different 1D channel is prevented due to the low NA of the objective. Hence it is important to study the effect of NA of illumination on the disorder strength measurements obtained using PWS. In order to test the effect of NA on PWS measurements we first perform experiments on nanostructure model media similar to those discussed in Chapter 4. The fabrication protocol of the nanostructured model media is discussed elsewhere [81]. In brief, we uniformly smear an aqueous suspension of monodispersed polystyrene nanospheres on a flat surface of a glass slide. The spheres form self-assembled lattices after 15 minutes of evaporation process at room temperature. These nanostructure model media are constructed using nanospheres of sizes 40, 60, 80, 100, 125 and 150 nm. The PWS measurements are obtained from these different nanospheres using different NA of illumination. The NA of illumination is varied by changing the diameter of aperture A2 in Figure 8:1 to 0.38 mm, 3.1 mm, and 10 mm. Given that the focal length of the objective is 9 mm, the corresponding NA of illumination is 0.02, 0.18, and 0.4 respectively.

170 x 10-2

Disorder strength Ld (μm)

8 Numerical Aperture = 0.02 6

Numerical Aperture = 0.18 Numerical Aperture = 0.40

4

2

0 40

60

80

100

120

140

160

Size of nanosphere (nm) Figure 8:11. Disorder strength obtained from different nanostructure model media at three different numerical aperture of illumination. The disorder strength is less sensitive to bead size for NA = 0.4 relative to NA = 0.02. The numerical aperture of collection is kept constant at 0.4 for different numerical aperture of illumination.

The disorder strength obtained using different size nanostructure model media at three different aperture sizes is shown in Figure 8:11. As seen, the disorder strength increases linearly with increase in bead size for NA of 0.02. However, for a constant bead size the disorder strength decreases with the increase in NA of illumination. For example at NA ~ 0.4, the disorder strength is less sensitive to bead size compared to those calculated at NA = 0.02. We also calculate the correlation coefficients obtained by fitting curves of different dimensions to the disorder strength parameter.

As seen in Table 8:1, at low NA of illumination the linear

relationship between the disorder strength and bead size agree well with each other. However,

171 the linearity decreases with the increase in NA of illumination. These results validate the importance of NA of the objective in detecting nanoscale refractive index fluctuations within a weakly scattering medium. That is, at low NA of illumination the photons are focused into the medium with a narrow cone and with an increased degree of collimation. Hence these photons incident with a low NA of illumination have an increased probability of undergoing 1Dpropagation than compared to the photons with large NA of illumination.

Table 8:1. Correlation coefficient from curves of different dimensions fit to disorder strength as a function of bead sizes

Numerical aperture

Dimension of fit,

Dimension of fit,

Dimension of fit,

D=1

D=2

D=3

0.02

R2 =0.91

R2 =0.95

R2 =0.95

0.18

R2 =0.77

R2 =0.76

R2 =0.70

0.40

R2 =0.61

R2 =0.59

R2 =0.52

We next perform clinical studies on buccal mucosa cells to validate the effect of low NA of illumination on the diagnostic performance of PWS. We collect buccal mucosa brushings from 25 patients (patients with COPD = 14, patients with lung cancer = 11) and perform PWS measurements using two different NA of illumination, that is NA = 0.18 and NA = 0.4. As seen in Table 8:2, the diagnostic performance (as indicated by the p-values) of PWS decreases with the increase in NA of illumination implying the importance of the NA of objective in PWS measurements. It is important to note that this increased diagnostic performance at low NA of

172 illumination is unlikely due to the increased pixel size. That is, with increased pixel size there is an increase in the averaging of 1D channels which results in the reduced sensitivity of 1D photons to nanoscale refractive index fluctuations (Figure 8:5)

Table 8:2. Effect of numerical aperture of illumination on the diagnostic performance of PWS.

Effect on L(dg ) , P-value

Effect on σ ( g ) , P-value

NA = 0.18

0.02

0.03

NA = 0.40

0.98

0.60

8.4 Summary In summary, we first we show the possible source of low frequency slope that is observed in the PWS experiments on biological cells and microspheres. We then show using 1D FDTD numerical model that the refractive index variations within the medium give rise to oscillations in the backscattering spectrum that are not overwhelmed by the refractive index contrast between the air-cell interface. We also derive the critical Δn and lc above which these refractive index fluctuations within the cell can be accurately detected. We next study the effect of the surface roughness of the biological cell by comparing the surface roughness profile obtained using the optical profilometer with the disorder strength obtained using PWS. Our results show that there is no correlation between the surface roughness and disorder strength indicating that the surface roughness is not the source of the oscillations in the PWS spectrum. Finally, we demonstrate the

173 important role of the numerical aperture of the objective in PWS. That is, at low NA of illumination the interference between adjacent 1D channel is prevented thereby maintaining the sensitivity to nanoscale refractive index fluctuations. These studies on PWS not only answers several questions regarding PWS but also help us to further our understanding on the novel optical spectroscopy technique, Partial wave spectroscopy.

174

Chapter 9 Conclusion The elastic light scattering signals from cells and tissues are typically recorded after their three dimensional propagation within tissue. As a result, although light scattering signals do depend on a wide range of length scales of refractive index fluctuations, including those smaller than the wavelength of light, the sensitivity to sub-wavelength length scales decreases fast with size due to the Fourier transform relationship between the scattering signal and the scattering potential. On the other hand the reflected signal in 1D is sensitive to any length scale of refractive index fluctuations including those below the wavelength. We have shown that the 1D backscattering spectrum from a weakly disordered medium such as a biological cell contains spectral fluctuations that are sensitive to refractive index fluctuations within the scattering object. We confirmed using nanostructure model media as well as with 1D FDTD numerical simulations that the spectral fluctuations are indeed sensitive to nanoscale refractive index fluctuations that are much smaller than those observed using diffraction limited microscopy. We also showed using numerical models that these spectral fluctuations arising due to refractive index fluctuations within the medium are not overwhelmed by the refractive index contrast between the air-cell interface. We also found no correlation between the surface roughness and the spectral fluctuations indicating that the refractive index fluctuations and not the surface roughness are the source of these 1D backscattering spectral fluctuations. We demonstrated that the low NA of

175 illumination prevents the interference between adjacent 1D channels thereby maintaining the sensitivity to nanoscale refractive index fluctuations. Partial Wave Spectroscopy provides a unique way of isolating these 1D backscattering partial waves that are sensitive to minute changes in the refractive index fluctuations at subdiffractional length scales. Combined with the mesoscopic light transport theory for statistical analysis of the backscattered photons PWS measures the disorder strength, a statistical parameter of the complex refractive index fluctuations at a single-cell level.

We first validated the

nanoscale sensitivity of PWS in HT29 human colon cancer cell line where defined genetic alterations were introduced. Our results demonstrated that PWS was able to differentiate the HT29 cell variants that are otherwise cytologically indistinguishable by quantifying the disorder of cell nanoarchitecture. This increase in the disorder of cell architecture was further confirmed in the study with the MIN-mouse model of intestinal carcinogenesis where a similar trend was observed. That is, a germline mutation in intestinal epithelial cells in the MIN-mice that were normal-appearing by conventional histology resulted in a profound increase in the disorder strength compared to the control mice suggesting that early carcinogenesis is accompanied by increasing disorder and progressively higher heterogeneity of the intracellular nanoarchitecture. From the clinical perspective, these results indicate that PWS has the potential to detect cell changes that would otherwise be missed by conventional histopathology. For example, our studies on field carcinogenesis provided powerful evidence that the cytologically normal mucosa in field carcinogenesis undergoes profound nanoscale alterations with increased disorder in its nanoarchitecture that are detectable by using PWS. These changes can potentially be exploited

176 to develop novel screening strategies by providing a minimally intrusive means of identifying field carcinogenesis and, thus, patients at increased risk for cancer. These results from PWS may have profound biological and medical implications. From the cancer biology perspective, PWS may be used to better understand early cellular events in carcinogenesis. Cell architecture may be much more “in tune” with the molecular events than previously thought. Although it may not be possible at this point to identify which specific structures are responsible for the increase in the disorder and associated molecular mechanisms, we can get some insights into the kinds of nanoscale changes developing in preneoplastic cells. For example a higher refractive index fluctuation may be associated with the increased spatial variation of the density of intracellular material while a higher refractive index correlation length may represent aggregation or “packing” of some of the basic “building blocks” of the cell. Furthermore, our data also suggest that the increase in the disorder strength is not limited to a specific organelle or a type of molecule.

Instead, it represents the progression of global

intracellular organization towards a more disordered state. The results from our studies on LEBS demonstrated that the enhanced backscattering peaks from weakly scattering medium can be accurately modeled using a photon random walk model.

We further showed that the exit angle of photons, that is typically

neglected in modeling conventional EBS plays a key role in modeling LEBS. We also derived an analytical model of the LEBS photon penetration depth and confirmed it using numerical Monte Carlo simulations. Our results showed that the penetration depth of LEBS photons have

177 weak dependence to tissue optical properties, which suggests the possibility of using LEBS for depth-selective analysis of weakly scattering media such as biological tissue.

178

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189

Curriculum Vitae

EDUCATION NORTHWESTERN UNIVERSITY, Chicago, Illinois (12/2008) Doctor of Philosophy in Biomedical Engineering ~ GPA: 3.97/4.00 ~ Coursework in Modern Optical Microscopy and Imaging, Applied mathematics and Differential equations, Advanced Systems Physiology, and Digital image analysis. ~ Dissertation title: Optical Sensing of Tissue Microstructure and Cell Nanostructure. ~ Committee: Prof. Vadim Backman, Prof. Allen Taflove, Prof. Xu Li, Prof. Malcolm MacIver, Prof. Thomas Foster (University of Rochester), and Dr. Hemant Roy (Evanston Northwestern Healthcare). (12/2004) TEXAS A&M UNIVERSITY, College station, Texas Master of Science in Biomedical Engineering ~ GPA: 3.70/4.00 ~ Coursework in Physiology, Optical Engineering, Bio-Optical Imaging, Bio-Optical Sensing and Diagnostics, Physics and Analysis of Images, and Cardiovascular Biomechanics. ~ Thesis title: Real-time Perfusion and Oxygenation Monitoring in an Implantable Optical Sensor. ~ Committee: Prof. Gerard Cote', Prof. Lihong Wang, and Prof. Henry Taylor. (06/2001) UNIVERSITY OF MADRAS, HINDUSTAN COLLEGE OF ENGINEERING, Chennai Bachelor of Engineering in Electronics and Communication ~ Graduated with Distinction ranking 3rd in a class of 75 ~ Coursework in Electric circuits, Electron devices, Digital signal processing, Signals and Systems, and Electro medical instrumentation.

190

PROFESSIONAL EXPERIENCE (09/2005 – present) NORTHWESTERN UNIVERSITY, Chicago, Illinois Research Assistant, Department of Biomedical Engineering • Involved in developing a novel optical imaging technique that is sensitive to nanoarchitectural changes inside a single cell. • Developed a novel optical screening technique for lung, colon and pancreatic cancer. • Advised undergraduate and graduate students in Biophotonics Laboratory. Teaching Assistant, Department of Biomedical Engineering (01/2008 – 03/2008) • Assisted in teaching graduate level course on cardiovascular physiology. Research Technologist, Department of Biomedical Engineering (06/2004 – 09/2005) • Studied the effect of polarization sensitive light scattering spectroscopy in detecting early pre-cancerous epithelial lesions • Developed a Monte Carlo based model on coherent backscattering.

(08/2002 – 05/2004) TEXAS A&M UNIVERSITY, College station, Texas Research Assistant, Department of Biomedical Engineering • Involved in developing an implantable optical sensor system to measure tissue blood perfusion and oxygenation in transplant organs • Created a new signal processing package for separating blood perfusion and tissue oxygenation • Developed a robust algorithm for real time monitoring of tissue blood perfusion in ‘noisy’ conditions Teaching Assistant, Department of Biomedical Engineering (08/2003 – 12/2003) • Assisted in teaching lab course on Biomedical Electronics using PSpice and LabView

(01/2001 – 12/2001) SRI. RAMACHANDRA MEDICAL COLLEGE & RESEARCH INSTITUTE, India Junior Research Fellow, Biomedical Sciences Division • Worked with Dept. of Ophthalmology to analyze the effect of Lasers on cerebral circulation and asymmetry of brain using optical sensors • Carried out projects with Speech and Hearing Sciences Division to analyze the relationship between sound stimuli and brain asymmetries using optical sensors • Designed and developed an optical sensor instrument to investigate the cardiovascular functions of small animals in collaboration with Dept. of Anatomy.

191

HONORS AND AWARDS • • •

Best Student Presentation Award, Frontiers in Optics - 2007, 91st 'Optical Society of America' Annual meeting, San Jose, CA, September 16-20, 2007. Walter P. Murphy Fellowship, Northwestern University, 2005. Best Paper award, Student Research Week, Texas A&M University, 2004.

PROFESSIONAL ACTIVITIES • •

• • • • • •

Review Panelist of National Science Foundation (NSF) Small Business Innovation Research Program (SBIR): September 2008. Co-Founder, SEPOCS-Revolution in Scope Technology. (SEPOCS is a startup company sprung from the collaborative effort between Northwestern's Kellogg School of Management, McCormick School of Engineering, Feinberg School of Medicine, and School of Law. Reviewer, IEEE Potentials (Magazine for up-and-coming engineers), 2003-2004 Reviewer, IEEE Computer Graphics and Applications (2005) Member, Biomedical Engineering Society (BMES) Member, Optical Society of America (OSA) Member, Institute of Electrical and Electronics Engineers (IEEE) Member, International Society for Optical Engineering (SPIE)

PATENTS • •

J. Kes, J. Kason, E. Rouse, H. Subramanian, "Light source and lens cleaner for laparoscopic surgery", pending, 2008. V. Backman, P. Pradhan, H. Subramanian, Y. Liu, Y. Kim, "Method for indentifying refractive index fluctuations of a target", pending, 2007.

PUBLICATIONS Peer-reviewed Journal Publications •

H.Subramanian, H. K. Roy, P.Pradhan, M. J. Goldberg, et. al., “Nanoscale cellular changes in field carcinogenesis detected by partial wave spectroscopy", (submitted for publication).



H.Subramanian, P.Pradhan, Y. Liu, I. R. Capoglu, J. D. Rogers, H. K. Roy, R. E. Brand, and V. Backman,et. al., “Partial wave spectroscopic microscopy detects sub-wavelength

192 refractive index fluctuations: an application to cancer diagnostics", Optics Letters (in press), 2008. •

H.Subramanian, P.Pradhan, Y. Liu, I. R. Capoglu, X. Li, J. D. Rogers, A. Heifetz, D. Kunte, H. K. Roy, A. Taflove, and V. Backman, “Optical methodology for detecting histologically unapparent nanoscale consequences of genetic alterations in biological cells", PNAS, vol. 105, no. 51, pp. 20124-20129, 2008.



H.Subramanian, P.Pradhan, Y.L.Kim, and V.Backman, “Penetration depth of lowcoherence enhanced backscattering of light in sub-diffusion regime”, Physical Review E, vol. 75, 041914, 2007.



H.Subramanian, P.Pradhan, Y.L.Kim, Y.Liu, X.Li and V.Backman, “Modeling lowcoherence enhanced backscattering (LEBS) using Monte Carlo simulation”, Applied Optics, vol. 45, pp. 6292-6300, 2006.



Y.L.Kim, P.Pradhan, H.Subramanian, Y.Liu, M.H.Kim, and V.Backman, “Origin of lowcoherence enhanced backscattering”, Optics Letters, vol. 31, pp. 1459-1461, 2006.



Y.L.Kim, Y.Liu, V.M.Turzhitsky, H.K.Roy, R.K.Wali. H.Subramanian, P.Pradhan, and V.Backman, “Low-coherence enhanced backscattering (LEBS): Principles and applications for colon cancer screening,” Journal of Biomedical Optics, vol. 11, 041125, 2006.



H.Subramanian, B.L.Ibey, S. Lee, W. Xu, M. A. Wilson, M. N. Ericson, and G.L. Cote', “An autocorrelation based time domain analysis technique for monitoring perfusion and oxygenation in transplanted organs”, IEEE Transactions on Biomedical Engineering, vol.52, no.7, pp.1355-1358, 2005.



H.Subramanian, B.L.Ibey, W. Xu, M. A. Wilson, M. N. Ericson, and G.L. Cote', “Real-time separation of perfusion and oxygenation signals for an implantable sensor using adaptive filtering”, IEEE Transactions on Biomedical Engineering, vol.52, no.12, pp.2016-2023, 2005.

Selected Peer-reviewed Conference Abstracts •

R. Brand, H. Subramanian, H.K. Roy, N. Hasabou et. al., “Pilot study examining changes induced in duodenal epithelial cells by different pancreatic diseases as measured by a novel optical imaging modality, single-cell partial wave spectroscopy microscopy”, Gastroenterology, vol. 134, no.4, pp. A93, 2008.

193 •

H.K. Roy, Y. Liu, H. Subramanian, D. Kunte et al., "Detection of colorectal cancer (CRC) field effect through Partial Wave spectroscopic microscopy (PWS) ”, Gastroenterology, vol. 132, no.4, pp. A169, 2007.



H. Subramanian, R. Brand et al., "Pilot study determining the feasibility of diagnosing pancreatic cancer using single cell partial wave spectroscopy of the duodenal mucosa”, Pancreas, vol. 35, pp. 429, 2007.



R. Brand, H. Subramanian, C. Sturgis et al., "A novel highly accurate bio-optical approach for improving the cytologic diagnosis of pancreatic adenocarcinoma", Gastroenterology, vol. 132, no.4, pp. A119, 2007.



H. K. Roy, H. Subramanian, P. Pradhan, H. T. Lynch et. al.,"Identification of inherited predisposition to colonic neoplasia through partial wave spectroscopic analysis of the microscopically normal colonic epithelium," Gastroenterology, vol. 134, no.4, pp. A109, 2008.

Refereed Conference Papers and Proceedings •

H. Subramanian, P. Pradhan et al., "Detection of nanoscale alterations of field carcinogenesis using Partial wave spectroscopic microscopy ", Biomedical Engineering Society (BMES) 2008 Annual Meeting, St. Louis, MO, October 2008.



J. D. Rogers, H. Subramanian, V. Turzhitsky, P. Pradhan, et. al., "Enhanced backscattering for tissue characterization and diagnostics (Invited paper)", International symposium on Antennas and Propagation, SanDiego, CA, July 2008.



T. A. Hensing, H. Subramanian, H. K. Roy, D. Breault et. al., "Identification of malignancy-associated change in buccal mucosa with partial wave spectroscopy (PWS): A potential biomarker for lung cancer risk," American Society of Clinical Oncology Annual Meeting 2008, Chicago, IL, May 2008.



D. Breault, H. Subramanian, D. Ray, N. Deep et. al.,"Bio-Optical assessment of buccal mucosa: A novel risk marker for lung cancer," American Thoracic Society - 2008, Toronto, Canada, May 2008.



R. Brand, H. Subramanian, H.K. Roy, N. Hasabou et. al., “Pilot study examining changes induced in duodenal epithelial cells by different pancreatic diseases as measured by a novel optical imagin modality, single-cell partial wave spectroscopy microscopy,” Digestive Disease Week - 2008, San Diego, CA, May 2008.



H. K. Roy, H. Subramanian, P. Pradhan, H. T. Lynch et. al.,"Identification of inherited predisposition to colonic neoplasia through partial wave spectroscopic analysis of the

194 microscopically normal colonic epithelium," Digestive Disease Week - 2008, San Diego, CA, May 2008. •

H. Subramanian, P. Pradhan, D. Kunte, N. Deep et. al., “Single-cell partial wave spectroscopic microscopy,” Biomedical Optics Topical Meeting, St. Petersburg, FL, March 2008.



P. Pradhan, V. Turzhitsky, A. Heifetz, D. Damania, H. Subramanian, H.K. Roy et. al., “Measurement of optical disorder strength due to the nanoscale refractive index fluctuations of tissues/cells: Inverse participation ratio (IPR) analysis of transmission electron microscopy (TEM) images,” Biomedical Optics Topical Meeting, St. Petersburg, FL, March 2006.



P. Pradhan, V. Turzhitsky, H. Subramanian, A. Heifetz et al., “Inverse participation ratio (IPR) analysis of Transmission Electron Micrsoscopy (TEM) images: Quantification of optical disorder strength due to nanoscale refractive index fluctuations of tissues/cells,” American Physical Society March Meeting, New Orleans, March 2008.



H. Subramanian, P. Pradhan, N. Deep et.al., “Single-cell partial-wave spectroscopic microscopy: early detection of cancer (Invited paper) ,” BiOS 2008, Photonics West, San Jose, January 2008.



H. Subramanian, “Partial wave spectroscopy,” SPIE Chicago/Midwest Conference, Evanston, IL, November 2007.



H.Subramanian, P. Pradhan, et.al.., “Alteration of nano-architecture of cell in early stages of carcinogenesis demonstrated by single cell Partial Wave Spectroscopy: Ultra-early detection of cancer,” SPIE Chicago/Midwest Conference, Evanston, IL, November 2007.



H. Subramanian, R. Brand et al., "Pilot study determining the feasibility of diagnosing pancreatic cancer using single cell partial wave spectroscopy of the duodenal mucosa", American Pancreatic Association 2007 Annual Meeting, Chicago, IL, November 2007.



H. Subramanian, P. Pradhan et al., "Partial wave spectroscopy: Understanding cell nanoarchitecture and its alteration in carcinogenesis", Biomedical Engineering Society (BMES) 2007 Annual Meeting, Los Angeles, CA, September 2007.



H. Subramanian, P. Pradhan, V. Backman, "Understanding cell nano-architecture and its alteration in carcinogenesis via Partial-wave spectroscopy", Frontiers in Optics - 2007, San Jose, CA, September 2007.

195 •

V. Backman, Y. Kim, Y. Liu, V. Turzhitsky, H. Subramanian, P. Pradhan et. al., "Lowcoherence enhanced backscattering and its applications," 29th Annual International conference of the IEEE EMBS, Lyon, France, August 2007.



R. Brand, H. Subramanian, C. Sturgis et al., "A novel highly accurate bio-optical approach for improving the cytologic diagnosis of pancreatic adenocarcinoma", Digestive Disease Week - 2007, Washington D.C., May 2007.



H.K. Roy, Y. Liu, H. Subramanian, D. Kunte et al., "Detection of colorectal cancer (CRC) field effect through Partial Wave spectroscopic microscopy (PWS)", Digestive Disease Week - 2007, Washington D.C., May 2007.



H.Subramanian, P. Pradhan, Y.L. Kim et al., “Penetration depth of low-coherence enhanced backscattering photons”, American Physical Society March Meeting, Baltimore, March 2007.



P. Pradhan, H. Subramanian, Y. Liu et al., “Application of mesoscopic light transport theory to ultra-early detection of cancer in a single biological cell,” American Physical Society March Meeting, Baltimore, March 2007.



H.Subramanian, P. Pradhan, Y.L. Kim et al., “Penetration depth of low-coherence enhanced backscattering photons in the subdiffusion regime”, BiOS 2007, Photonics West, San Jose, January 2007.



Y.L. Kim, P. Pradhan, V. M. Turzhitsky, H. Subramanian et al., “Low-coherence Enhanced Backscattering: characteristics and applications for colon cancer screening (Invited paper)”, BiOS 2007, Photonics West, San Jose, January 2007.



P. Pradhan, H.Subramanian, Y. Liu et al., “Alteration of nanoscale cell architecture in early stages of carcinogenesis demonstrated by single cell partial wave spectroscopy: ultraearly detection of cancer”, BiOS 2007, Photonics West, San Jose, January 2007.



H. Subramanian, P. Pradhan, Y. L. Kim et al., “Penetration depth of low-coherence enhanced backscattering (LEBS) in sub-diffusion regime,” Biomedical Engineering Society (BMES) 2006 Annual Meeting, Chicago, IL, October 2006.



Y. L. Kim, P. Pradhan, H. Subramanian, Y. Liu et al., “Probing minimal scattering events in coherent scattering of light using low-coherence induced dephasing,” Photonic Metamaterials: From Random to Periodic, Grand Island, The Bahamas, June 2006.

196 •

P. Pradhan, Y. L. Kim, H. Subramanian et al., “Effect of the anisotropy factor of scattering and the finite spatial coherence length of light source on enhanced backscattering,” American Physical Society March Meeting, Baltimore, March 2006.



H.Subramanian, P. Pradhan, Y.L. Kim et al., “Monte Carlo model of low-coherence enhanced backscattering (LEBS) from anisotropic disordered media,” Biomedical Optics Topical Meeting, Fort Lauderdale, FL, March 2006.



Y. L. Kim, P. Pradhan, H. Subramanian, Y. Liu et al., “Minimal scattering events in enhanced backscattering (EBS) of light: Origin of low-coherence EBS in discrete tissue models,” Biomedical Optics Topical Meeting, Fort Lauderdale, FL, March 2006.



H.Subramanian, P. Pradhan, Y.L. Kim et al., “Modeling Low-coherence Enhanced Backscattering (LEBS) using Photon random walk model of Light Scattering”, BiOS 2006, Photonics West, San Jose, January 2006.



Y. L. Kim, P. Pradhan, H. Subramanian, Y. Liu et al., "Origin of Low-coherence Enhanced Backscattering (LEBS) of light in discrete tissue models: double scattering", BiOS 2006, Photonics West, San Jose, January 2006.



P. Pradhan, Y.L. Kim, H.Subramanian, V. Backman, “Effects of the anisotropy factor of scattering and the finite spatial coherence length of light source on Enhanced Backscattering”, BiOS 2006, Photonics West, San Jose, January 2006.



Bennett Ibey, H.Subramanian et al., “Processing of pulse oximeter signals using adaptive filtering and autocorrelation to isolate perfusion and oxygenation components”, BiOS 2005, Photonics West, San Jose, January 2005.



M.Rao, H.Subramanian, H.Sundram, “Acquisition, Treatment and Analysis of Biological Signals”, National Seminar on Medical Informatics, Chennai, June 21-22, 2002.



M. Rao, H.Subramanian, V.Venkataramana, “Investigations of Cardiovascular functions of guinea pig with the help of optical sensors”, National conference on Sensors & Instrumentation, Hyderabad, January 5-6, 2002.



H.Subramanian, M.Rao, “Effect of double frequency YAG laser on the cerebral circulation in diabetic retinopathy detected by the use of photoplethysmography technique”, World congress of International Society for Laser Surgery and Medicine, Chennai, August 27-30, 2001.

197 Meeting presentations •

H.Subramanian, P. Pradhan, Y. Liu et.al., “Alteration of nano-architecture of cell in early stages of carcinogenesis demonstrated by single cell Partial Wave Spectroscopy: Ultra-early detection of cancer,” Applied Research Day, Northwestern University, February 2007.



H.Subramanian, “Partial-wave spectroscopic (PWS) microscopy: understanding cell nanoarchitecture and its alteration in carcinogenesis,” Biotechnology Training Seminar, Northwestern University, January 2007.



H.Subramanian, “Single cell partial wave spectroscopy,” Pancreatic Research Meeting, Evanston Northwestern Healthcare, December, 2006.



H.Subramanian, B.L.Ibey, G.L. Cote et al, “An autocorrelation based time domain analysis technique for monitoring perfusion and oxygenation in transplanted organs”, Student Research Week, Texas A&M University, 2004.

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