Stokes parameter imaging of multi-index of refraction

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Stokes parameter imaging of multi-index of refraction biological phantoms utilizing optically active molecular contrast agents

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IOP PUBLISHING

MEASUREMENT SCIENCE AND TECHNOLOGY

doi:10.1088/0957-0233/20/10/104003

Meas. Sci. Technol. 20 (2009) 104003 (12pp)

Stokes parameter imaging of multi-index of refraction biological phantoms utilizing optically active molecular contrast agents G C Giakos1,2 , K Valluru2 , V Adya2 , K Ambadipudi2 , S Paturi2 , P Bathini2 , M Becker2 , P Farajipour2 , S Marotta2 , J Paxitzis2 , B Mandadi2 , M Zervakis3 and G Livanos3 1

Department of Electrical and Computer Engineering, The University of Akron, Akron, OH 44325, USA Department of Biomedical Engineering, The University of Akron, Akron, OH 44325, USA 3 Department of Electronic and Computer Engineering, Technical University of Crete, Chania 73100, Greece 2

Received 19 February 2009, in final form 27 June 2009 Published 4 September 2009 Online at stacks.iop.org/MST/20/104003 Abstract The purpose of this study is to assess the potential of novel molecular polarimetric imaging techniques utilizing multi-index of refraction targets, i.e. composite targets made from optically different media, immersed into biological fluids doped with optically active molecules and enzymes. The outcome of this study indicates that the application of Stokes parameter detection principles with concominant administration of fluids containing suitable optically active molecular contrast agents and high index of refraction molecules could enhance the detection and imaging process of internal structures by providing enhanced penetration depth, high contrast and high depolarized scatter rejection. Keywords: polarimetric imaging, molecular imaging, optical active molecules, high index of

refraction molecules, enzymes, local field enhancement, enhancement of the degree of polarization (DOP), enhancement of the degree of linear polarization (DOLP), enhanced image contrast, high scatter rejection, medical imaging applications (Some figures in this article are in colour only in the electronic version)

on an x-ray tube that generates a beam of ionizing radiation [1] and slot-beam arrays or a flat panel of high-resolution, director indirect-based ionization of photon electronic detectors, coupled to data acquisition electronics and signal conditioning circuitry. Typically, high atomic number, high density, high quantum efficiency amorphous silicon (a-silicon), ceramic scintillators, cadmium tungstate (CDWO4 ) or cadmium zinc telluride (CZT) substrates are the detector materials of choice. However, these imaging systems do not offer physiological or metabolic signatures at the diagnostic energy range (18–120 keV), although the deployment of soft x-rays (at energies 12 keV) for backscattering imaging of soft tissue looks promising. On the other hand, PET, SPECT, ultrasound and MRI demonstrate great clinical value for molecular and functional imaging over a wide range of diagnostic applications, although

1. Introduction Imaging systems have provided clinicians and researchers non-invasive methods for observation of internal bodily structures, determination of functional tissue characteristics and identification of diseases and conditions. As technology advances, short data acquisition time, reduced cost, high spatial resolution, high contrast resolution and high-specificity images at a decreased radiation dose are realized, offering patients efficient diagnosis and decreased morbidity. Human anatomical and geometrical information can be displayed by digital radiography and computed tomography (CT) imaging systems. Here, the transmission of ionizing radiation through the body and calculation of its subsequent attenuation by tissues and organs comprise the basis for which these systems operate. Both digital radiography and CT rely 0957-0233/09/104003+12$30.00

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© 2009 IOP Publishing Ltd Printed in the UK

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the true potential of each system within the clinical arena is still largely unexplored. The roots of molecular imaging are with nuclear medicine, as it relies on the emission of radiation by radiotracers from within the body. SPECT for molecular imaging requires the injection of gamma-ray emitting isotopes, such as 99 Tc, 111 In, 123 I or 131 I. Molecular imaging using PET can be achieved by labeling a natural biological molecule with a positron-emitting isotope, such as 14 O, 13 N, 11 C or 18 F, providing accurate chemical classification. These labeled molecules are injected into the patient who is subsequently imaged. The sensitivity of PET, being 10−11 –10−12 mol L−1 , is an order higher than that of SPECT, and is also independent of the depth of the probe in the tissue. Magnetic resonance (MR) imaging generates tomographic images by exploiting the nuclear magnetic resonance properties of tissues, stimulated by applying fixed magnetic and varying radiofrequency (RF) fields. MR highlights anatomical structures, but functional MR is becoming more common. MR is becoming a very important non-invasive imaging modality since it provides unique contrast between soft tissues and very high spatial resolution. Yet the chief advantage of MR over other imaging modalities is the fact that it does not employ ionizing radiation. The clinical applications of each modality differ considering that each system highlights different physical parameters and functions of the human body, and hosts different resolution and sensitivity characteristics. Coupled with contrast-enhancing, radio-labeled and magnetically active imaging agents, these modalities provide clinicians with molecular information and insight into biological and pathological disease processes, resolving limitations introduced by traditional in vitro and histopathological methods [2, 3]. Ultrasound, MR and CT imaging fundamentally rely on the ability to differentiate the target against the surrounding tissue and inherent background noise. As a result, they can produce signals with little sensitivity or specificity. Interestingly enough, other limitations of these techniques are as follows: computed tomography (CT) offers adequate contrast resolution at the expense of the spatial resolution; widespread diffusion of PET is limited mainly by cost, especially when considering the deployment of accelerators in situ for the fabrication of short-lived radioisotopes; MR provides high spatial resolution with excellent tissue discrimination, yet has limited ability to monitor hemoglobin dynamics and contrast agent capabilities; optical tomography is inherently a low spatial resolution imaging modality due to diffuse nature of light photons. Optical imaging [1–22] provides a detailed description of biological tissues [4, 8–20], and offers the potential for noninvasive exploration of molecular targets inside the human body. It allows the characterization of a variety of diseases, such as breast cancer, skin cancer, lung cancer and cancer of the bladder; the study of drug effects on the target pathology and drug treatment effects; the development of biomarkers and molecular contrast agents indicative of disease and treatment outcomes; and the analysis of molecular pathways leading to diseases. Image formation through detection of the polarization states of light offers distinct advantages for a wide

range of detection and classification problems, and has been explored by a number of authors, given the intrinsic potential of optical polarimetry to offer high-contrast, high-specificity images under low-light conditions [4–7, 9, 21, 22]. On the clinical side, optical polarimetry [4, 8–22] provides enhanced imaging and spectral polarimetric information regarding the metabolic information of the tissue, as well as the molecular mechanism of a biological function, drug–cell interaction, single-molecule imaging and so on. Absorption and scattering are wavelength and penetrationdepth dependent. Light loss mechanisms such as light absorption by hemoglobin, melanin, lipids and other compounds, and light scattering from tissue are limiting factors for imaging of deep biological structures. As a result, the potential to image contrast of deep structures in tissue and differentiate them in the presence of an interfering background is reduced. On the other hand, interrogation of tissue with NIR wavelengths of light, or optical clearing techniques [24], leads to an enhancement of the penetration depth at the expenses of the imaging contrast; in fact, reduced backscattering at molecular level and reduced refractive mismatch across heterogeneous boundaries at macroscopic scale lead to enhanced penetration depth but reduced contrast. When linearly polarized light is passed through a substance containing optically active molecules (chiral molecules) or nonchiral molecules arranged asymmetrically, a rotation of the polarization vector takes place. This phenomenon is called optical rotation or optical activity. Glucose molecules and most of the biological molecules such as proteins or enzymes are optically active molecules. The level of polarization preservation and the variation of the rotation of linearly polarized light fraction with glucose concentrations, as well as with chiral and nonchiral molecules, in the turbid samples have been reported in a number of studies [27, 28]. However, most of these research efforts have been concentrated toward the development of non-invasive techniques for glucose monitoring based on reflectance spectroscopy, Raman, scattering or fluorescence [26] rather on imaging. The dilemma lies on how to achieve both improved penetration depth and imaging contrast at the same time. An immediate question to address is whether utilizing the optical activity associated with both chiral molecules and amplification of the refraction index of the liquid phase, together with Stokes parameter imaging, can alleviate this problem. Based on this assumption, a novel optical imaging technique has been proposed by Giakos [4, 18–20]; this technique relies on the synergistic efforts of doping the background surrounding the target with optical active molecules or high index of refraction molecules, in conjunction with the application of efficient polarimetric interrogation techniques. As a result, the proposed technique would provide both optical clearing and enhanced contrast capabilities; minimizing refractive index differences between the optically active fluid medium and the target would result to an increase of the degree of polarization (DOP), with increasing the concentration of the optically active 2

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Specifically, the Stokes vector of the incident beam is ⎛ ⎞ S0 ⎜S1 ⎟ ⎟ (2) S=⎜ ⎝S2 ⎠ . S3 The Mueller matrix of a rotating quarter-wave retarder is ⎛ ⎞ 1 0 0 0 ⎜0 sin 2θ cos 2θ sin 2θ ⎟ cos2 2θ ⎟ . (3) MR = ⎜ ⎝0 sin 2θ cos 2θ −cos 2θ ⎠ sin2 2θ 0 sin 2θ cos 2θ 0 The Mueller matrix of the linear horizontal linear polarizer is ⎛ ⎞ 1 1 0 0 ⎜1 1 0 0⎟ ⎟ Mp = ⎜ (4) ⎝0 0 0 0⎠ . 0 0 0 0

Figure 1. Applied geometry of the polarimetric formalism applied in the laser-beam experiments.

molecules, at the expenses of the contrast resolution; on the other hand, enhanced image contrast would result due to local field enhancement as well as using Stokes parameter imaging because of its intrinsic potential to detect weakly backscattered linearly polarized radiation, in the presence of highly backscattered depolarized radiation, while maintaining the original state of polarization of the incident light. Overall, using high refractive index dielectric particles dispersed within fluids would cause the refractive index of the liquid to become a volume-weighted average between refractive indices of optically active molecules and the liquid phase, ultimately giving rise to an amplification of the index of refraction and local field enhancement, yielding an enhanced DOP and DOLP signal-to-background ratio (SBR) [4, 18–20]. In order to assess the potential of the applied methodology, the degree of polarization (DOP) was estimated by measuring the Stokes parameters of the backscattered light by means of the ‘Fourier analysis using a rotating quarter-wave retarder method’ [5, 6].

The Stokes parameter in the front of the detector, after passing through the retarder–polarizer configuration, is ⎛ ⎞ 1 ⎜1 ⎟  2 1 ⎟ S = 2 (S0 + S1 cos 2θ + S2 sin 2θ cos 2θ + S3 sin 2θ ) ⎜ ⎝0 ⎠ . 0 (5) But S0 = I (θ ) is given as I (θ ) = 12 (S0 + S1 cos2 2θ + S2 sin 2θ cos 2θ + S3 sin 2θ ). (6) Reducing equation (6) to a truncated Fourier series In (θj ) = 12 [A + B sin 2nθj + C cos 4θj + D sin 4nθj ],

where ωt = nθ j and θ j is the step size of rotation of the analyzer retarder. Carrying out a Fourier analysis, the four Stokes parameters are calculated through the Fourier series coefficients via the relationships [5]

2. Stokes parameter formalism The polarimetric formalism of this study, used for 830 nm light excitation experiments, is conveyed by the analyzer geometry of the detector system, shown in figure 1. This research imaging system operates on active polarimetric detection principles performing a Fourier analysis using a rotating quarter-wavelength retarder. The Stokes vector, S , at the input of the detector, is related to the incident on the polarization state analyzer S = (S0 , S1 , S2 , S3 )T through the Mueller matrix M, where M describes the elements of the analyzer polarization of the phase retarder and the polarizer in front of the detector, including instrumental polarization, and polarization sensitivity of the detector, as M = MR · M p ,

(7)

S0 = A − C,

(7a)

S1 = 2C,

(7b)

S2 = 2D,

(7c)

S3 = B.

(7d)

Once the Stokes parameters are estimated, the degree of polarization (DOP) is estimated in terms of Stokes parameters as  2 1/2 S1 + S22 + S32 DOP = . (8) S0

3. Experimental description

(1)

where MR and Mp are the Mueller matrices of the analyzer retarder and polarizer elements, respectively.

Studies on the impact of the image quality, by doping the background of the target with l-phenylalanine and glucose 3

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Figure 2. Calibration of polarizers P1 and P2.

Figure 3. Calibration of quarter-wave retarders.

molecules, were performed under two different series of experiments, under backscattered geometry, at 830 nm and 655 nm light excitation wavelengths, respectively. In both cases, experiments were performed using biological phantoms immersed in an aqueous solution, doped with l-phenylalanine and glucose molecules. A photometric Sensys (1401E, Roper Scientific Inc.) high-resolution (1317 × 1035 imaging array), 6.8 × 6.8 μm pixel, electro-cooled CCD camera system was used to acquire the images of the phantom. The camera was equipped with a 10× Macro Zoom Lens R (MLH-10×, Computar ) that provides magnification ideally matched to that of an optical microscope. The experiments throughout this study were repeated three times and hence three sets of measurements were obtained for each optical molecular contrast agent used. Several contrast measures and statistical analysis techniques were performed on the acquired measurements.

3.2. Calibration of the quarter-wave retarders Quarter-wave retarders are used to convert the linearly polarized light into circularly polarized light or vice versa. The ‘null intensity method’ was used to calibrate the wavelength retarders. Specifically, polarizers P1 and P2 were oriented in cross-polarized configuration such that minimum light intensity was observed on the oscilloscope. The quarter-wave retarder R1 was then placed in between the two polarizers as shown in figure 3, and rotated around the beam axis and the orientation at which the light beam remained extinct was found and marked as 0◦ . The retarder was then rotated at exactly 45◦ around the beam axis from this position. At this orientation angle, the retarder was expected to convert the polarization form of the light beam from linear to circular. To assess the quality of the circularly polarized light obtained, polarizer P2 was rotated and it was observed that the intensity of the light passing through polarizer P2 was unchanged. This confirmed that the output polarization state of the retarder was circularly polarized and the orientation angle was marked as 45◦ . Since R2 was also a quarter-wave retarder, the same setup as shown in figure 3 was employed and the same procedure was followed for its calibration except that R2 replaced R1.

3.1. Calibration of polarizers The calibration procedure is shown in figure 2. Two highcontrast dichroic polarizers (03 FPC 011, Melles Griot, Rochester, NY) were used in the study one of which was used on the transmission side and the other as an analyzer on the receiver side. By rotating the transmitter polarizer, P1, without the presence of the analyzer polarizer from 0◦ to 360◦ , the corresponding intensity variations were observed on the oscilloscope. The angle at which the maximum intensity was obtained was marked and polarizer P1 was fixed at that angle such that it allows maximum transmission of the incident light. Keeping polarizer P1 fixed at the maximum transmission angle, the analyzer polarizer P2 was inserted and rotated from 0◦ to 360◦ , and the intensity variations were observed on the oscilloscope. The orientation angles of polarizer P2 at which the maximum and minimum intensity values were obtained were marked. When both polarizers P1 and P2 are oriented for maximum transmission, they are said to be co-polarized or parallel to each other and when P1 is oriented for maximum transmission and P2 is oriented for minimum transmission, they are said to be cross-polarized or perpendicular to each other. Polarizers P1 and P2 used with the broadband light source were also calibrated similarly except that the 830 nm laser was replaced by the broadband light source with 655 nm filter.

3.3. First set of experiments using an 830 nm laser beam An 830 nm, solid-state laser (Intellite Inc., Minden, NV) was used on the first set of experiments. The experiments were performed at low magnification. The experimental setup is shown in figure 4. The imaging system contained two arms: a polarization generating branch and a polarization analyzing branch. Light from the 830 nm laser source was sent through the polarization generating branch that consists of a neutral density filter (attenuator), a linear polarizer P1, a quarter-wave retarder R1 and a beam expander. The light from the laser was passed through a neutral density filter onto a linear polarizer P1. The linearly polarized light then passed through a quarter-wave retarder R1 which converted it into circularly polarized light. The circularly polarized light was then allowed to illuminate the phantom. The polarization analyzing branch contained a quarter-wave retarder R2 followed by a linear polarizer P2 (parallel to P1) which was placed in front of a CCD camera in backscattering geometry as shown in figure 4. The retarder 4

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Figure 6. The high-magnification experimental setup using the 655 nm filtered broadband light source.

Figure 4. The low-magnification experimental setup using the 830 nm laser beam.

illumination source for the study. An emission filter (Qdot D655/40m, Chroma Technology Corp, San Diego, CA) of central wavelength 655 nm was used with the broadband light source to illuminate the target with visible light. Specifically, the setup included a broadband light source which emits visible light with the help of a filter of wavelength 655 nm and a fiber-optic cable that connects the light source and the light guide and a visible wavelength polarizer P1 on the polarization generating side. There was no need of an optical attenuator since the broadband light source was equipped with an intensity control knob to control the intensity of the light beam. The polarization analyzing branch contained an infinity-corrected objective lens system followed by an analyzing polarizer P2 and a CCD camera to acquire images. A phantom with multiple refractive index variations as shown in figure 6 was used with the setup to which 16.8 ml of water was initially added. The light from the broadband laser source was passed through the 655 nm optical filter to allow light of only that particular wavelength into the fiber-optic cable. A light guide was attached to the other end of the fiber-optic cable from which the light was emitted onto polarizer P1 oriented for maximum transmission of light. The linearly polarized light then illuminated the phantom. The light that was backscattered in the direction of the analyzing branch was then detected with the help of the objective lens system which was made to pass onto the CCD camera through an analyzing linear polarizer P2. The images were then acquired by setting the analyzer polarizer P2 parallel (co-polarized) and perpendicular (cross-polarized) to the generating polarizer P1 [5]. Thus, a pair of images was acquired through this method which was then processed to obtain the corresponding DOLP images, according to Ico-polarized − Icross-polarized . (9) DOLP = Ico-polarized + Icross-polarized A fiber optic light guide (Edmund Optics Inc., Barrington, NJ) of bundle diameter 0.0625 inches (1.6 mm) and length 36 inches (914 mm) was used to illuminate the phantom. The spectrum of the filtered broadband source has been recorded by means of a spectrometer (Ocean Optics OOIBase32 Spectrometer). An infinity-corrected long working distance objective lens system (Mitutoyo 46-144 M-Plan Apo Objective combined

Figure 5. The objective lens system used in both the 830 nm and the 655 nm broadband excitation experiments.

R2 was used to convert the circularly polarized light remitted by the phantom into linearly polarized light and this light was sent to the CCD camera through a linear polarizer P2 which was oriented parallel to polarizer P1. Polarizer P2 was always kept fixed parallel to P1 to account for the polarization sensitivity of the detector. The retarder R2 was rotated from 0◦ to 180◦ in steps of 22.5◦ such that the backscattered light intensity contributions by the phantom in the direction of the analyzing branch were acquired by the CCD camera. Therefore, eight intensity images were obtained. The degree of polarization (DOP) was estimated, using equation (8), by measuring the Stokes parameters of backscattered signals via Fourier analysis, relating the detected backscattered signal intensities to the Stokes parameters, through the Mueller matrices of the analyzer optics, by means of the ‘Fourier analysis using a rotating quarter-wave retarder method’ [5]. An infinity-corrected long working distance objective lens system (Mitutoyo 46-144 M-Plan Apo Objective combined with Edmund Optics 54-774 MT-1 Tube Lens), as shown in figure 5, was used for this set of experiments (830 nm) as well as for the 655 nm broadband imaging experiments described into the following section. 3.4. Second set of experiments (655 nm broadband filtered light source) The second set of experiments was performed at high magnification (×40) using a filtered 655 nm light beam from a broadband source (figure 6). Specifically, a fiber-optic R light illuminator (Fiber-Lite MI-150W Illuminator, DolanJenner, Boxborough, MA) was used as the broadband light 5

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Figure 7. The experimental phantom used in the 655 nm filtered broadband light source.

(a)

(b)

(d )

(e)

(c)

(f )

Figure 8. S0 (total intensity) images of a portion of the phantom obtained for l-phenylalanine concentrations (from (a) to (f )) 0 (only water), 2.22, 4.44, 6.66, 8.88, 11.1 mg mL−1 with 40× magnification using the NIR laser source (830 nm).

S0 (total intensity) and DOP (polarimetric) images obtained at different concentrations of aqueous l-phenylalanine, namely at 0 (only water), 2.22, 4.44, 6.66, 8.88 and 11.1 mg mL−1 , are shown in figures 8 and 9, respectively. By observing figures 8 and 9, the potential of optical polarimetry to detect objects under extremely low-illumination conditions is pronounced; the S0 (total intensity) target images shown in figure 8 are below the detection threshold, and therefore are indistinguishable from the surrounding background. In contrast, the polarimetric target images (DOP) shown in figure 9 exhibit a net contrast over the background, mainly because of the pronounced index of the refraction difference between the target and the surrounding background which is distinguishable upon the application of polarimetric principles. In order to compute the signal-to-background (SBR) values of the DOP images, a 50 × 50 pixel region-of-interest (ROI)

with Edmund Optics 54-774 MT-1 Tube Lens), as shown in figure 5, was used for the second set of experiments (655 nm).

4. Experimental results and discussion 4.1. First set of experiments (830 nm laser beam) Experiments with the enzyme l-phenylalanine involved the use of an infinity-corrected objective lens system on the receiver side of the setup shown in figure 4 and the images were acquired with a magnification of 40×. A twisted plastic wire phantom with a refractive index of 1.46, similar to hydrated collagen (n = 1.47), and diameter 1 mm, attached to a glass test tube was used as the phantom for this set of experiments, as shown in figure 7. A 40× magnification processed image of the portion of the phantom is shown for clarification purposes. The 6

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(a)

(b)

(c)

(d )

(e)

(f )

Figure 9. DOP (polarimetric) images of a portion of the phantom obtained for l-phenylalanine concentrations (from (a) to (f )) 0 (only water), 2.22, 4.44, 6.66, 8.88, 11.1 mg mL−1 , with 40× magnification, using the NIR laser source (830 nm). 1.7 1.69

SBR

1.68 1.67 1.66 1.65 1.64 1.63 0 F=103.15, Pr > F = 0.0005

2.22

4.44

6.66

8.88

11.1

Aqueous concenntrations of L-Phenylalanine (mg/mL)

Figure 10. SBR of DOP images versus concentrations of l-phenylalanine.

area was selected within the region in which the twisted cable was present and this region was considered as signal S while an area of same size selected from the region outside the cable and within the solution region was considered as background B. The SBR values of the DOLP images for all the concentrations of the l-phenylalanine solution were then computed, after removing the outliers from the selected regions in the images, in order to assess the image contrast, by taking the ratio between the signal (S) to the background (B) difference and the arithmetic mean of the signal and the background given by (S − B) . (10) SBR = 1 (S + B) 2

an increase of the DOP signal-to-background (SBR) ratio with increasing l-phenylalanine concentration is observed, as shown in figure 10. The experiments were repeated three times and hence three sets of measurements were obtained for each molecular contrast agent used. Model-I linear regression analysis was performed on the measurements obtained, given by Yˆ = α + βX.

(11)

The regression analysis was performed using MATLAB on the data obtained by the NIR polarimetric imaging system by considering the SBR value as the dependent variable (Y) and the concentration of the dopant added as the independent variable (X). Table 1 shows the source table obtained when l-phenylalanine was used as an optical contrast agent.

The signal-to-background ratio (SBR) values for the DOP images shown in figure 9 are plotted in figure 10. Specifically, 7

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Figure 11. Original, mean and variance images along with their corresponding histogram distributions for 0% concentration of phenylalanine in an aqueous solution.

of Gaussians is essential under the assumption of Gaussian noise contamination in the original image, which is reasonable as demonstrated by the first column of figure 11. The distance of distribution means reflects the structural differences of the two regions. Thus, we propose to use the difference of model modes (means) as a contrast measure of images at different concentrations. For the variance image, however, the appropriate distributions characterizing the two regions become chi-square (χ 2 ) distributions. From both the form of the image and its histogram shown in figure 11, we can verify that the distribution of water imposes fewer degrees of freedom (with smaller variance) than the distribution of the optical dopant, which is spread over the upper part of the dynamic range at high intensity levels. The two distributions are heavily mixed together, especially at higher levels of intensity characterizing the optical dopant. In this case, we model the water distribution through a χ 2 function estimated by the best fit on the histogram through nonlinear regression and use its mode in the proposed contrast measure. Due to its increased value (and degrees of freedom), the second distribution of the optical dopant can be reasonably approximated by a normal distribution. The mean of this second distribution is obtained from the empirical data distribution after removal of the model that is fitted to water. A detailed theoretical approach on the χ 2 distribution is presented in [25]. The two contrast measures for the different concentrations of phenylalanine are depicted in figure 12, indicating a clear contrast increase with concentration, in agreement with the increase of the SBR as shown in figure 10.

Table 1. Source table for l-phenylalanine experiment using the NIR laser source. Source

DF

Sum of squares

Mean square

Regression Unexplained Total

1 4 5

0.000 44 0.000 017 0.000 46

0.000 44 0.000 0043

F value

Pr > F

103.15

0.0005

Regression coefficient (R2 ): 0.96.

From table 1, it can be seen that there exists a significant difference in the SBR values computed for the DOP images obtained using the NIR laser imaging system with increasing concentrations of the l-phenylalanine aqueous solution. In order to further compare the effects of the optically active molecules at different concentration levels, we model the distributions of the acquired images. Within the area of interest, marked by a circle, we find low-intensity water segments mixed with the optical dopant at higher intensity levels. Due to the high magnification of the electron microscope, however, these regions are heavily contaminated by noise, which masks the intensity distributions of individual materials. In order to partially alleviate this problem, we process the local mean images obtained from 5 × 5 moving average filtering. Furthermore, we also consider the local variance images in an attempt to exploit the texture differences between the (smooth) water and (more active) optical dopant regions. A sample set of these three images is illustrated in figure 11, including the original, mean and variance images (first row), along with their histogram distributions (second row). The local mean image reveals two distinct, rather symmetric distributions that can be efficiently modeled by normal distributions. This modeling scheme using the mixture

4.2. Second set of experiments (655 nm broadband light source) 4.2.1. Description of the multi-index of refraction biological phantom. The geometry of the test phantom is highlighted 8

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Distance between the peaks of the two distributions

Comparison of contrast for different concentrations of Phenylalanine using a 5x5 moving window 120.00 100.00 80.00

86.63

89.34

60.00 40.00

49.00

56.25

90.48 95.66

58.33 62.50

96.83 100.04 68.75

72.92

Use of mean Use of variance

20.00 0.00 0.00%

2.22%

4.44%

6.66%

8.88% 11.10%

Concentration of Phenylalanine in aqueous solution (mg/ML)

Figure 12. Difference of means (DOM) and variances images versus concentration of aqueous insulin for both means and variance moving window.

polarized and cross-polarized images along with the DOLP images were obtained. Thus a total of seven pairs of copolarized and cross-polarized images were obtained for this experiment. 4.2.2. Experimental results. By referring to the optical phantom shown in figure 13, DOLP images with a 40× magnification factor at different concentrations of glucose are shown in figure 14. Within the circular area of focus, two sectors of index of refraction n = 1.49, separated by a strip of index of refraction = 1.65, are depicted. To quantify the image contrast obtained for DOLP images by means of edge density, the Canny edge-detection technique [29] was applied on the obtained DOLP images after setting a lower threshold of 0.05 and a higher threshold of 0.125. These were the values obtained when the Canny operator was implemented on the DOLP images obtained for 16.8 ml water only. The Canny edge detector involves several steps: first the Canny edge detector smoothes the image to minimize the noise through a Gaussian filter using standard convolution methods. Then, it applies the Sobel operator to highlight regions with high spatial derivatives. The Sobel operator performs a 2D spatial gradient measurement on an image. The algorithm then searches along increased gradient regions and eliminates any pixel that is not a local maximum. The gradient array is further reduced using thresholding by hysteresis. The number of edge pixels for each concentration of aqueous glucose was computed and the plots between the numbers of edge pixels and concentration of aqueous glucose are shown in figure 15; confidence intervals are also included for each measurement. The plot shown in figure 15 indicates an increase in the number of edge pixels with increasing concentration of glucose. Again, the experiments throughout this study were repeated three times and hence three sets of measurements were obtained for each optical molecular contrast agent used. A regression analysis was performed, using equation (11), by considering the number of pixels detected as edges as the

Figure 13. The multi-index of refraction phantom.

in figure 13. The biological phantom consisted of a cluster of polypropylene spheres (refractive index n = 1.49) with a diameter of 2 mm and high-density polyethylene spheres (refractive index n = 1.54) with a diameter of 3.5 mm bonded with epoxy adhesive (refractive index n = 1.65) immersed in the water solution. The above indexes of refraction were chosen so that to emulate biological tissues, namely calcified structures (n = 1.53), hydrated collagen (n = 1.47) and highly calcified mineralized structures (n = 1.65). Typically, micro calcifications, depending upon their shape, geometry and composition, can be classified as precursors of malignancies in breast mammography. Indeed, systematic differences between hydrated collagen in the intensities between the collagen of malignant, benign and normal tissue groups appear to be due to a significantly lower structural order within the malignant tissues [23]. The entire cluster was glued to a polystyrene cylindrical fixture that was fixed to the bottom of the test tube for a rigid support. The distance between the cluster surface and the wall of the test tube was 3 mm ± 0.5 mm. The inner diameter of the test tube was 22 mm and the length of the test tube was 95 mm. To perform the experiment with glucose, an aqueous glucose solution was prepared first by adding 12.5 g of glucose to 100 ml of water. The glucose solution was then added to the phantom that contained 16.8 ml of water in concentration increments of 10.42 mg mL−1 up to 62.50 mg mL−1 . For each concentration increment of the glucose solution, the co9

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(a)

(b)

(c)

(d )

(e)

(f )

(g )

Figure 14. DOLP images with 40× magnification obtained for the aqueous glucose solution using the broadband light source (655 nm). 1050

no. of edge pixels

1000

950

900

850

800 0.00 10.42 20.83 31.25 41.67 52.08 F=88.28, Pr > F = 0.0002 concentration of glucose in aqueous solution [mg/mL]

62.50

Figure 15. Number of edge pixels for various concentrations of the glucose solution (655 nm).

dependent variable (Y) and the concentration of the optically active molecule as the independent variable (X). The source tables obtained when the glucose solution was obtained as an optically active medium is shown in table 2. By examining the results shown in table 2, it can be observed that there exists a significant difference in the number of pixels detected as edges computed for the DOLP images obtained using the broadband light imaging system with increasing concentrations of the glucose solution. The number of edge pixels as a measure of contrast may be affected by noise contamination, altering the contrastspecific effects. Aiming at a more concrete way of quantifying

Table 2. Glucose solution experiment using the broadband light source. Source

DF

Sum of squares

Mean square

Regression Unexplained Total

1 5 6

13 245.35 750.17 13 995.52

13 245.35 150.034

F value

Pr > F

88.28

0.0002

Regression coefficient (R2 ): 0.94.

the contrast effects with increased concentration, we further consider a statistical modeling scheme of the DOLP images. 10

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Input image

Input image after using a mean window 5x5

GLUCOSE 0% concentration

GLUCOSE 0 % concentration

Histogram of the input image(GLUCOSE 0 %) Histogram of input image after using a mean window 5x5

700

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600 500 Num ber of pix els

N um ber of pix els

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Figure 16. Original and mean processed DOLP images along with their corresponding histogram distributions. Comparison of contrast for different concentrations of glucose using a moving 5x5 window

Distance between the peaks of the two distributions

0.16

0.14

0.14 0.12

0.12

0.10

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Use of mean

0.08

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10.42

20.83

31.25

41.67

52.08

62.5

Concentration of glucose in aqueous solution[mg/ml]

Figure 17. Comparison of contrast with increasing concentrations of aqueous glucose.

From the appearance of the images at this wavelength and magnification level, it becomes obvious that the information at various segments can be differentiated in terms of intensity levels. Within the circular area of focus, the texture of the various sub-regions is smooth and similar everywhere, thus rendering the local variance quite inefficient for region differentiation. Instead, the illumination levels of the regions of interest are different due to the different absorption characteristics, appropriating the use of mean intensity as an efficient metric for discrimination. Toward this direction, we processed the local mean images obtained from 5 × 5 moving average filtering. A sample set of these images is illustrated in figure 16, including the original

and mean images (first row), along with their histogram distributions (second row). The averaging operator smoothens out the intensities of regions, making their histograms more compact and appropriate for modeling. The local mean image reveals two distinct, rather symmetric distributions that can be efficiently modeled by normal distributions. The distance of distribution means reflects the structural differences of the two regions. Thus, we propose to use the difference of model modes (means) as a contrast measure of images at different concentrations. The results extracted for the experiment glucose aqueous solution in different concentrations are illustrated in figure 17, clearly revealing a contrast improvement over increased concentration levels. 11

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5. Conclusion A novel imaging technique aimed at providing both improved penetration depth and imaging contrast has been presented. By combining fluid solutions doped with optically active molecules in conjunction to Stokes parameter imaging, this imaging technique provides both optical clearing and enhanced contrast capabilities. The acquired images were further analyzed statistically and processed using different contrast measures and analysis techniques, such as model-I linear regression analysis, edge detector analysis and modeling of the distributions of the acquired images, for the different concentrations of optically active molecules and enzymes. The outcome of this analysis indicates that enhanced DOP and DOLP result with increasing concentration of the high index of refraction/optically active molecules which in turn introduce an analogous increase of the image contrast. A study is in process aimed at identifying suitable, biocompatible, optically active contrast agents and effective polarimetric methodologies for an array of clinical applications. However, the difficulty of the applicability of the above methodology into the clinical applications should not be underestimated; in a typical in vivo environment, tissue linear birefringence and inhomogeneity of tissue are some of the factors that could impact the in vitro observation of the DOP/DOLP SBR enhancement. One clinical application could be medical endoscopy where application of Stokes parameter principles with concominant administration of fluids containing optical active dopants could enhance the detection process of internal structures, by providing enhanced penetration depth, high contrast and high scatter rejection.

Acknowledgments Figures 6, 13–15 have been presented at the 2008 IEEE Workshop on Imaging Systems and Techniques and published in its proceedings.

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