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Optics Express

Optics Express

  • Editor: Michael Duncan
  • Vol. 11, Iss. 25 — Dec. 15, 2003
  • pp: 3473–3484
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Determining nuclear morphology using an improved angle-resolved low coherence interferometry system

John W. Pyhtila, Robert N. Graf, and Adam Wax  »View Author Affiliations


Optics Express, Vol. 11, Issue 25, pp. 3473-3484 (2003)
http://dx.doi.org/10.1364/OE.11.003473


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Abstract

We outline the process for determining the morphology of subsurface epithelial cell nuclei using depth-resolved light scattering measurements. The measurements are accomplished using a second generation angle-resolved low coherence interferometry system. The new system greatly improves data acquisition and analysis times compared to the initial prototype system. The calibration of the new system is demonstrated in scattering studies to determine the size distribution of polystyrene microspheres in a turbid sample. The process for determining the size of cell nuclei is discussed by analyzing measurements of basal cells in a sub-surface layer of intact, unstained epithelial tissue.

© 2003 Optical Society of America

1. Introduction

Elastically scattered light has been used previously to study cellular morphology [1

1. V. Backman, V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I. Georgakoudi, M. Mueller, C.W. Boone, R.R. Dasari, and M.S. Feld, “Measuring cellular structure at submicrometer scale with light scattering spectroscopy,” IEEE. J. Sel. Top. Quantum Electron. 7, 887–893 (2001). [CrossRef]

4

4. A. Wax, C. Yang, V. Backman, K. Badizadegan, C.W. Boone, R.R. Dasari, and M.S. Feld, “Cell organization and sub-structure measured using angle-resolved low coherence interferometry,” Biophys. J. 82, 2256–2264 (2002). [CrossRef] [PubMed]

] as well as to diagnose dysplasia, a pre-cancerous tissue state [5

5. V. Backman, M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M. Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and M.S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000). [CrossRef] [PubMed]

8

8. A. Wax, C.H. Yang, M.G. Muller, R. Nines, C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Research 63, 3556–3559 (2003). [PubMed]

]. Variations in scattering distributions with angle or wavelength are used to deduce the size and relative refractive index of scattering objects such as cells, nuclei, and even smaller organelles. The use of elastic light scattering techniques as a diagnostic method for detecting neoplastic change has had significant success. Backman and colleagues have used light scattering spectroscopy to detect dysplasia in the colon, bladder, cervix and esophagus of human patients [5

5. V. Backman, M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M. Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and M.S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000). [CrossRef] [PubMed]

]. Other researchers [6

6. M. B. Wallace, L.T. Perelman, V. Backman, J.M. Crawford, M. Fitzmaurice, M. Seiler, K. Badizadegan, S.J. Shields, I. Itzkan, R.R. Dasari, J. Van Dam, and M.S. Feld, “Endoscopic detection of dysplasia in patients with Barrett’s esophagus using light-scattering spectroscopy,” Gastroenterology 119, 677–682 (2000). [CrossRef] [PubMed]

, 7

7. L. B. Lovat, D. Pickard, M. Novelli, P.M. Ripley, H. Francis, I.J. Bigio, and S.G. Bown, “A novel optical biopsy technique using elastic scattering spectroscopy for dysplasia and cancer in Barrett’s esophagus,” Gastrointest. Endosc. 51, 4919 (2000).

] have used light scattering to detect Barrett’s esophagus, a metaplastic condition which can lead to dysplasia. These techniques have one experimental property in common: the use of intensity based measurements which lack the ability to probe selective depths within tissue.

Angle-resolved Low Coherence Interferometry (a/LCI) has been introduced as a method to obtain depth resolved angular scattering distributions. The technique enables selective detection of the optical field scattered from a small region within probed tissue by exploiting the coherence properties of broadband light. The angular scattering distribution is mapped out by using a novel imaging system which exploits the high directional sensitivity of the interferometer. The a/LCI technique was initially validated in studies of polystyrene microspheres [9

9. A. Wax, C. Yang, V. Backman, M. Kalashnikov, R.R. Dasari, and M.S. Feld, “Determination of particle size using the angular distribution of backscattered light as measured with low-coherence interferometry,” J. Opt. Soc. Am. A 19, 737–744 (2002). [CrossRef]

] which showed that sub-wavelength sensitivity and accuracy are obtained by comparing measured angular scattering distributions to the predictions of Mie theory. The technique was first used to probe nuclear morphometry in a study of monolayers of cultured HT29 epithelial cells, a line of human tumor cells [4

4. A. Wax, C. Yang, V. Backman, K. Badizadegan, C.W. Boone, R.R. Dasari, and M.S. Feld, “Cell organization and sub-structure measured using angle-resolved low coherence interferometry,” Biophys. J. 82, 2256–2264 (2002). [CrossRef] [PubMed]

]. This study outlined an analysis for comparing scattering by non-spherical cell nuclei to the predictions of Mie theory and demonstrated that sub-wavelength precision and accuracy was also obtained. In addition, the residual of the fit was analyzed using a fractal dimension framework, giving it a physical interpretation as the texture of smaller sub-cellular components.

Recently, a/LCI has been used in a quantitative study of the nuclear morphometry of epithelial cells in a rat model of esophageal carcinogenesis [8

8. A. Wax, C.H. Yang, M.G. Muller, R. Nines, C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Research 63, 3556–3559 (2003). [PubMed]

]. Changes in the size and texture of cell nuclei due to neoplastic transformation were observed in situ via quantitative measurements of basal epithelial cell nuclei, approximately 50–100 µm beneath the tissue surface. The a/LCI measurements, made without using exogenous contrast agents or tissue fixation, were compared to traditional histopathological images to establish that the method is capable of diagnosing low-grade and high-grade dysplasia with great accuracy. In addition, the a/LCI measurements enabled detection of vacuolization and apoptosis due to application of chemorpreventive agents. These were important findings which illustrate a potential application of a/LCI for assessing the efficacy of chemopreventive agents or the toxic effects of chemicals on tissue health.

In this paper we present a new a/LCI system with improved data acquisition and speed compared to the original method. The capabilities of the new system are demonstrated by determining the size of scatterers in a suspension of polystyrene microspheres using light scattering measurements. We then present an analysis procedure for processing the depth resolved light scattering data to obtain the morphology of cell nuclei in sub-surface layers. To illustrate the applicability, accuracy and limitations of this approach, scattering data from an ex vivo sample of rat esophagus epithelium are analyzed to determine the size of cell nuclei in the basal layer.

2. Experimental scheme

Fig. 1. (a). Schematic of new a/LCI system. L1-L5 - lenses, BS1,BS2 - beamsplitters, D1,D2 - balanced detectors, RR - retroreflector. Shaded area shows scattered light. (b) Diagram illustrating angle selectivity by scanning lens L2 perpendicular to the beam. Light at the top of the collimated beam entering L3 is directed to the detector in the top figure. Light at the center is directed to the detector in the bottom figure.

The basic approach for using a Mach-Zehnder interferometer for examining the wavefront coherence of scattered light was introduced previously by Wax and Thomas [10

10. A. Wax and J.E. Thomas, “Optical heterodyne imaging and Wigner phase space distributions,” Opt. Lett. 21, 1427–1429 (1996). [CrossRef] [PubMed]

] and applied to study ideal scattering media [11

11. A. Wax, S. Bali, and J.E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000). [CrossRef] [PubMed]

]. The new a/LCI system builds on this approach by implementing a new imaging system which enables the full angular aperture of the lens to be used to collect angular scattering distributions. In addition, the experiments with this system represent the first effort to use this approach to examine biological cells and tissues.

In the new a/LCI system, light from a broadband source (SLD or Ti:sapphire fs laser, λo=830 nm) is split into signal and reference fields by a beamsplitter. By exploiting the short coherence length (10–20 µm) of the source, the detected signal field can be resolved by its optical path length. In order to obtain information about the signal field at various depths within a sample, a retroreflector (RR) has been included in the reference beam path to vary its path length by 2 Δz.

The new system probes the angular distribution of the scattered field by scanning lens L2 (25 mm diameter achromat, Edmund Optics) a distance Δy perpendicular to the beam path. It has been shown using Fourier optics that this translation will permit selective detection of the light which arrives at the plane of L2 traveling at an angle θ=Δy/f2 relative to the optical axis, where f2=10 cm is the focal length of L2 [10

10. A. Wax and J.E. Thomas, “Optical heterodyne imaging and Wigner phase space distributions,” Opt. Lett. 21, 1427–1429 (1996). [CrossRef] [PubMed]

]. Thus, the theoretical maximum detectable range of angles is +/-127 mrad (7.3°). Lens L1 (f1=10 cm) is included to alter the wavefront of the reference field to compensate for the effects of L2. Thus, the system (Fig. 1) maps out the angular distribution of the optical field arriving at the plane of L2, simply by translating L2 perpendicular to the beam path.

An important feature of the system is the arrangement of lenses L3 and L4, which form a 4f system, imaging both the phase and amplitude of the scattered field onto the plane of lens L2. This is an essential feature for interferometric detection of scattered light as improperly accounting for phase delays can affect the detected signals. L3 and L4 have unequal focal lengths (f3=10 cm, f4=3.5 cm), resulting in the field scattered by the sample being magnified in space by a factor of 10/3.5 but scaled down in its angular distribution by 0.35. This scaling enables the range of detected angles to be extended beyond the range cited above which would be the maximum achievable using matched focal lengths for L3 and L4. To ensure that this 4f imaging system is properly aligned, a reflectance standard sample is used. Misalignment is evident by uneven or lack of scattered light detection, similar to the rejection of out of focus light in a confocal arrangement.

Lens L5 (f5=10 cm) is included so that L4 does not focus the input beam on the sample but instead re-collimates it into a pencil beam. The beam incident on L5 is approximately 1 mm in diameter, resulting in a beam reaching the sample with a 0.35 mm diameter and a corresponding diffraction angle of 1.8 mrad. The narrow angular distribution of the input beam is essential since using light traveling at many angles will smear the angular scattering patterns, as discussed below in Section 5.

In addition to this role, the lateral displacement of L5 relative to L4 allows the full angular aperture of the lenses to be used to detect angular scattering distributions. For a beam incident through the center of L4, the scattered light would only be collected from -θ to θ, with θ equal to half the numerical aperture of the lens. Instead, this displacement results in the input beam entering the sample at an angle of 290 mrad (16.6°) and permits the maximum clear aperture of the lens (580 mrad=33.2°) to be used to image the angular distribution. Thus the pencil beam strikes the sample obliquely, avoiding obscuring the scattered light by specular reflection. Note, however, that the exact backscattering direction is anti-parallel to the input beam, regardless of the orientation of the sample surface.

3. Results

3.1 Microsphere experiments

To demonstrate the calibration of the new system, we have measured the light scattered by a turbid sample consisting of polystyrene microspheres (n=1.59) suspended in a mixture (n=1.36) of 80% water and 20% glycerol. The mixture is used to provide neutral buoyancy for the microspheres. The microspheres (Duke Scientific, Palo Alto, CA) are specified as NIST traceable with a mean size of 10.1+/-0.3 µm and a standard deviation of 8.9%. The stock solution (1.1% solids) has been concentrated to provide a scattering length l=100 µm.

Figure 2a shows a contour plot of the angular distribution of light scattered by this sample as a function of depth into the medium. The angle is given in radians relative to the backscattering direction, extending over 420 mrad, 75% of our theoretical maximum. The plot shows four lobes of increased intensity (light areas) with decreasing contrast for increasing angle. The contrast of the lobes is also seen to decrease as the light penetrates deeper into the medium (Fig. 2b), until only the central backscattering lobe is seen at approximately 400 µm.

Fig. 2. (a) Contour plot showing angular scattering by suspension of polystyrene microspheres as a function of depth. Light areas indicate increased intensity on a log scale. (b) Angular distributions vs. depth. Top left 0–100 µm, top right 100–200 µm, bottom left, 200–300 µm, bottom right 300–400 µm.
Fig. 3. Fitted angular distribution from surface layer
Fig. 4. Minimization of chi-squared value to determine best fit.

The measured angular distribution for the surface layer (0–100 µm=1 scattering length) is shown in Fig. 3. The size of the particles is determined by comparison to Mie theory. The data are compared to theoretical Mie distributions for a Gaussian distribution of microsphere sizes characterized by a mean diameter (d) ranging from 7 to 13 µm at intervals of 0.1 µm and a 10% standard deviation in size parameter (x=πd/λ with λ the center wavelength of the source) which accounts for both the broad distribution of sizes in our sample as well as the distribution of wavelengths in our broad bandwidth light source [9

9. A. Wax, C. Yang, V. Backman, M. Kalashnikov, R.R. Dasari, and M.S. Feld, “Determination of particle size using the angular distribution of backscattered light as measured with low-coherence interferometry,” J. Opt. Soc. Am. A 19, 737–744 (2002). [CrossRef]

]. The data are compared to each theoretical distribution by computing the chi-squared value with the best fit obtained through minimization. Figure 4 shows that the chi-squared value is minimized at a value of 10.1 +/- 1.1 µm with the uncertainty given by a doubling of the calculated minimum chisquared value. We see that the mean size, determined to within the accuracy and precision of our analysis, is in excellent agreement with the size specified by the manufacturer. We note that the uncertainty of the measurement is given approximately by the 10% variation in the size parameter.

3.2 Rat esophagus epithelium experiments

To show the capabilities of the new system for assessing nuclear morphometry in situ, Fig. 5 shows data collected from the basal layer of an ex vivo sample of rat esophagus epithelium. The tissue sample was freshly excised, opened longitudinally and laid flat between two coverslips. The data were taken without applying either exogenous contrast agents or fixatives and without freezing or sectioning the tissue.

In order to determine the size of the cell nuclei by comparison to Mie theory, the data are initially processed by applying a low pass filter. The cutoff frequency is chosen to include the first observed peak in the Fourier transform of the angular data. In this example, the frequency is selected to eliminate oscillations originating from spatial correlations occurring at greater than 10.4 µm length scales (see discussion below in Section 4.2). The smoothed data are shown in Fig. 5. The data are further processed by using a second order polynomial to remove the overall trend of the data (see discussion below in Section 4.2). Figure 6 shows the smoothed data with the polynomial fit. The polynomial fit is then subtracted from the smoothed data, yielding the oscillatory component of the data.

The oscillatory component of the data is compared to the oscillatory components of Mie theory distributions to make a size determination by minimizing the chi-squared value. The calculated theoretical predictions include a Gaussian distribution of sizes characterized by a mean diameter (d) ranging from 5 to 15 µm at intervals of 0.1 µm. and standard deviation (δD) at values of 2.5%, 5% and 10% of the mean diameter as well as a distribution of wavelengths, to accurately model the broad bandwidth source. The index of refraction of the nuclei is also varied over a range of 1.42–1.47, corresponding to relative refractive index changes of 1.037–1.073 when compared to the assumed 1.37 index of the cytoplasm [4

4. A. Wax, C. Yang, V. Backman, K. Badizadegan, C.W. Boone, R.R. Dasari, and M.S. Feld, “Cell organization and sub-structure measured using angle-resolved low coherence interferometry,” Biophys. J. 82, 2256–2264 (2002). [CrossRef] [PubMed]

].

Figure 7 shows the best fit Mie component compared to the oscillatory data component. The best fit was determined using the results of the chi-squared minimization shown in Fig. 8. Fig. 8 compares the oscillatory data component in Fig. 7 to Mie theory component for several refractive index differentials and a fixed size distribution. Similar plots are generated for each size distribution used in the comparison with the one yielding the best fit shown in Fig. 8. This figure projects the two dimensional chi-squared function (mean size, refractive index) onto one dimension (mean size only). Near the minimum, the chi-squared values form a parabolic curve (solid line) with a minimum at 9.1 µm. By finding the point on the parabola where the chi-squared value doubles we estimate the uncertainty to be sub-wavelength (0.3 µm vs. λo=0.83um). The minimization also yields the relative refractive index (1.058) and size distribution (δD=0.45 µm). These results agree with our previously published study on nuclear morphometry of normal tissue in this model [8

8. A. Wax, C.H. Yang, M.G. Muller, R. Nines, C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Research 63, 3556–3559 (2003). [PubMed]

], which showed that the mean size was 9.55 +/- 0.25 µm.

Fig. 5. Raw and filtered scattering data from basal cell nuclei
Fig. 6. Filtered data from Fig.5 with low order fit
Fig. 7. Oscillatory component of data with best fit.
Fig. 8. Chi-squared minimization to find best fit. The values are parabolic (solid line) near the minimum. The uncertainty is given by double the minimum value.

4. Data analysis

4.1 Microsphere scattering

In general, a/LCI signals for light scattered by particles which are large compared to the wavelength of light, consist of an oscillatory component superposed on a slowly varying background. For scattering by homogenous dielectric spheres, these two components can be identified respectively as arising from diffraction and from the combination of reflection and refraction [12

12. H. C. van de Hulst, Light scattering by small particles. 1957, New York: Dover Publications.

]. The diffractive component arises from confining the light transverse to the direction of propagation, resulting in oscillations in the angular scattering with a frequency proportional to the size of the particle. The form of this component as a function of angle does not depend on the index of refraction of the scatterer but rather only on the size of the particle relative to the wavelength of light. However, the relative refractive index between scatterer and surroundings will dictate the magnitude of this component but not its form.

The reflection and refraction component of the scattering is slowly varying and depends on the size of the particle, relative to the wavelength of light, as well as its index of refraction. This component can be visualized as the coherent superposition of light which has been reflected by the surfaces of the particle, either once or multiple times, and refracted upon traversing the index differential between the particle and its surroundings.

Fig 9. Original microsphere data and data adjusted by adding a low order polynomial
Fig. 10. Best fit yields incorrect size when an incorrect slowly varying background is present
Fig. 11. Best fit yields correct size when slowly varying background is removed using a low order polynomial prior to fitting. Readjusted data corrects the slowly varying background.

To illustrate the effects of these two components on making size determinations based on comparison to Mie theory predictions, we now conduct our analysis using the data in Fig. 3 with its slowly varying background component intentionally altered, as shown in Fig. 9. The chi-squared minimization now incorrectly determines the size to be 10.4 +/- 1.3 µm with the best fit shown in Fig. 10. In this figure, it can be seen that the frequency of the oscillatory component is correctly determined, but the magnitudes of the individual oscillations are not correctly matched. The fit can be improved by using a low-order polynomial to remove the slowly varying component and comparing to similarly processed Mie theory predictions. The accuracy improves with this approach yielding a best fit at 10.1 +/- 1.1 µm, even though the adjusted data had an incorrect slowly varying background (Fig. 11). It can be seen that this method allows for correction of an undesired or incorrect slowly varying component.

4.2 Nuclei scattering

To analyze the comparison of cell nuclei light scattering to Mie theory, we must consider that Mie theory predicts scattering by homogeneous dielectric spheres while for most cells, and especially cells in tissue or within a monolayer, the nucleus is not a sphere; but rather it is a prolate spheroid with irregular surfaces. However, these irregularities are not correlated from nucleus to nucleus, but may instead be viewed as perturbations relative to an “average” cell nucleus. This is a relevant picture for a/LCI which averages the scattering of many nuclei in a single measurement. The diameter of the input beam to the sample in the above experiments was 350 µm, compared to approximately 10–15 µm for a cell diameter, resulting in simultaneous illumination of hundreds of cells. The ensemble average acquired by examining several hundred cells at once serves to average out the cell-to-cell variations, yielding a light scattering distribution characteristic of an average prolate spheroid nucleus. This is a desirable and necessary feature of this approach for determining nuclear morphology by comparison to Mie theory.

Direct comparison between the filtered a/LCI data and Mie theory is not possible as the chi-squared fitting algorithm tends to match the background slope rather than the characteristic oscillations. Instead, the smoothed data are fit to a low-order polynomial which is then subtracted from the distribution to remove the background trend. Although the first a/LCI study with in vitro cells used a fourth order polynomial, it was subsequently found that a second order polynomial was sufficient for removing the background trend. Thus, all following applications of the technique, including the present work, use a second order polynomial for this purpose. As discussed above in Section 4.1, this step enables a size determination to be made even if the background distribution has been skewed. In the case of the microspheres, a change in the background distribution was intentionally induced for the purpose of illustrating the utility of the approach. In the case of cell nuclei, scattering by inhomogeneities within the nucleus and smaller organelles within the cell contribute to the change in the background distribution. As these particles are smaller than the nucleus, it is expected that they scatter light with broad angular distributions.

The use of the oscillatory component for fitting also addresses the issue of the prolate spheroid shape of the nucleus within tissues. The oscillatory component is identified above with the diffractive component of scattering, which depends on the dimension of the scatterer transverse to the direction of propagation. For a prolate spheroid, this component will be the same as that expected for a sphere with a diameter equal to the long, transverse axis of the spheroid. In the case of cell nuclei, the oscillatory component can then be identified with the dimension of the nucleus which is aligned parallel to the tissue surface. Thus, by using the oscillatory component of both data and Mie theory distributions, the fitting process is matching the longer, transverse dimension of the prolate nucleus.

The transverse dimension can be difficult to measure using photomicrographs of fixed and stained tissue sections. As tissue sections are thin slices of tissue, many of the nuclei in a given field are sectioned away from the maximum nuclear diameter. The issue of statistically measuring the average nucleus size is further complicated when attempting to use automated image analysis programs which determine cell nuclei size by calculating nuclear area and then backing out an average radius. As a/LCI probes the transverse nucleus dimension, it is reasonable to expect that a/LCI size determinations will be larger than average cell nuclei measurements made by image analysis of photomicrographs. We further note that wavelength-based light scattering techniques [1

1. V. Backman, V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I. Georgakoudi, M. Mueller, C.W. Boone, R.R. Dasari, and M.S. Feld, “Measuring cellular structure at submicrometer scale with light scattering spectroscopy,” IEEE. J. Sel. Top. Quantum Electron. 7, 887–893 (2001). [CrossRef]

, 5

5. V. Backman, M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M. Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and M.S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000). [CrossRef] [PubMed]

] may be more sensitive to the longitudinal axis of the nucleus suggesting that a combination of angular and spectral measurements will obtain the maximal information of cell nucleus structure.

5. Discussion

5.1 Comparison of a/LCI with image analysis

Traditionally, nuclear morphometry has been determined by examining fixed and stained tissue sections under the light microscope. Today, advanced microscopy techniques hold the promise of providing in situ images with sufficient resolution to assess morphological change. The a/LCI technique offers an important advantage over other approaches. By using coherence gating, a/LCI can assess nuclear morphology from sub-surface tissue layers, which can be difficult with other approaches due to tissue turbidity. However, an additional strength of a/LCI, as an alternative method for probing nuclear morphology, can be illustrated by comparing its resolution to that obtained with image analysis.

Figure 12 shows a photomicrograph of the polystyrene microspheres used for the above experiments. By analyzing the image, we can determine the size of an individual microsphere to within the resolution afforded by the 40× (0.75 NA) objective which is 0.45 µm, assuming a center wavelength of 550 nm. To determine the average size of the microspheres in this image, each microsphere must be individually measured and then the results analyzed statistically. As an alternative to this laborious process, we can instead examine a Fourier transform of this image (Fig. 13).

The pattern in Fig. 13 resembles the diffraction pattern by a circular aperture, which is appropriate for the image which shows two-dimensional circular slices of the microspheres. As the microspheres are randomly placed in the image field, the correlation between their positions is averaged out, resulting in a pattern that appears as if coming from a single circular aperture, albeit with some residual random noise.

Analysis of the pattern in Fig. 13 shows that there are roughly 5 “diffraction” rings over the range of spatial frequencies from 0 to 0.5 µm-1. Thus, the periodicity is 0.1 µm-1, corresponding to a size of 10 µm, in good agreement with the size determined above and that stated by the manufacturer. A more rigorous analysis shows that the periodicity is 11 to 12 pixels with each pixel corresponding to 1/119 µm=0.0084 µm-1, yielding a size of 10.8 to 9.9 µm, an uncertainty that corresponds to the optical resolution. The pixel size for the spatial frequency is determined by the overall range of the real space image. For the Fourier transform in Fig. 13, a 512×512 section of the image in Fig. 12 is used, with each pixel having a 0.233 µm dimension.

Fig. 12. Micrograph of microspheres (bars=10, 50 µm)
Fig. 13. Fourier transform of a portion of image in Fig. 12

In a/LCI the spatial frequencies are measured directly via the angular distribution. We sample the angular distribution with 12 mrad spacing, corresponding to a spatial frequency (k sin θ/2π) of 0.014 µm-1. Thus, using the above analysis, it would appear that a/LCI is limited to knowledge of the particle size to between 10.2 and 8.9 µm (7 or 8 pixels). However, a/LCI benefits by comparing the measured data to the predictions of Mie theory which specifies not only the frequency of the angular oscillations but also their magnitude, permitting the method to circumvent but not break the diffraction limit. It is worth noting that if a good model was determined for the Fourier transform in Fig. 13, it should in theory be possible to determine the size of the microspheres more precisely. However, as Fig. 13 only resembles the diffraction by a spherical aperture but does not accurately reproduce it, we cannot use a diffraction model and are instead limited to analyzing the periodicity of the rings.

5.2 Comparison of a/LCI with Optical Coherence Tomography

The a/LCI technique makes use of coherence gating to obtain depth resolution, similar to the method used in Optical Coherence Tomography (OCT). OCT is a LCI-based technique for biomedical imaging which enables non-invasive cross-sectional imaging with high spatial resolution, typically about 10 microns in the axial direction and a few microns in the lateral direction with depth penetration typically in the millimeter range. While cellular resolution has been achieved with laboratory OCT systems, technical hurdles may prevent clinical OCT systems from achieving the cellular resolution needed to assess morphological changes [13

13. A. F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Reports on Progress in Physics 66, 239–303 (2003). [CrossRef]

]. In contrast, a/LCI, as a combination of light scattering and LCI techniques, can provide a viable means for detecting nuclear morphology in situ. Such measurements can serve as biomarkers of disease progression, particularly as indicators of dysplasia, a pre-cancerous tissue state.

The a/LCI technique is based on measuring the angular distribution of scattered light to probe the elastic scattering properties of the sample of interest. By comparison to theory, changes in structure are detected which cannot be seen with conventional OCT imaging. The key difference between the two techniques is that in a/LCI, the beam input to the sample is collimated rather than focused. In OCT, a focused beam, typically a few microns across, is used to obtain lateral resolution. However, a focused beam necessarily contains a broad angular distribution. When this broad angular distribution is incident on a scattering object, the angular scattering pattern of the object is convoluted with the angular distribution of the incident light. The convolution process serves to smooth out the features in the measured angular distribution. In a/LCI, the incident light is a pencil beam (0.35 mm-diameter), with a very narrow angular distribution determined by the diffraction angle of the collimated beam, (angular resolution=1.8 mrad). This narrow angular resolution permits accurate measurement of the scattered angular distribution.

6. Conclusion

Acknowledgments

We gratefully acknowledge experimental help from Derrick Chou and Neil Terry. This research was supported in part by a grant by the National Cancer Institute. JWP is supported by a training grant from the National Institutes of Health.

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K. Sokolov, J. Galvan, A. Myakov, A. Lacy, R. Lotan, and R. Richards-Kortum, “Realistic threedimensional epithelial tissue phantoms for biomedical optics,” J. Biomed. Opt. 7, 148–156 (2002). [CrossRef] [PubMed]

3.

J. R. Mourant, T.M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J.P. Freyer, “Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures,” J. Biomed. Opt. 7, 378–387 (2002). [CrossRef] [PubMed]

4.

A. Wax, C. Yang, V. Backman, K. Badizadegan, C.W. Boone, R.R. Dasari, and M.S. Feld, “Cell organization and sub-structure measured using angle-resolved low coherence interferometry,” Biophys. J. 82, 2256–2264 (2002). [CrossRef] [PubMed]

5.

V. Backman, M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M. Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and M.S. Feld, “Detection of preinvasive cancer cells,” Nature 406, 35–36 (2000). [CrossRef] [PubMed]

6.

M. B. Wallace, L.T. Perelman, V. Backman, J.M. Crawford, M. Fitzmaurice, M. Seiler, K. Badizadegan, S.J. Shields, I. Itzkan, R.R. Dasari, J. Van Dam, and M.S. Feld, “Endoscopic detection of dysplasia in patients with Barrett’s esophagus using light-scattering spectroscopy,” Gastroenterology 119, 677–682 (2000). [CrossRef] [PubMed]

7.

L. B. Lovat, D. Pickard, M. Novelli, P.M. Ripley, H. Francis, I.J. Bigio, and S.G. Bown, “A novel optical biopsy technique using elastic scattering spectroscopy for dysplasia and cancer in Barrett’s esophagus,” Gastrointest. Endosc. 51, 4919 (2000).

8.

A. Wax, C.H. Yang, M.G. Muller, R. Nines, C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, “In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry,” Cancer Research 63, 3556–3559 (2003). [PubMed]

9.

A. Wax, C. Yang, V. Backman, M. Kalashnikov, R.R. Dasari, and M.S. Feld, “Determination of particle size using the angular distribution of backscattered light as measured with low-coherence interferometry,” J. Opt. Soc. Am. A 19, 737–744 (2002). [CrossRef]

10.

A. Wax and J.E. Thomas, “Optical heterodyne imaging and Wigner phase space distributions,” Opt. Lett. 21, 1427–1429 (1996). [CrossRef] [PubMed]

11.

A. Wax, S. Bali, and J.E. Thomas, “Time-resolved phase-space distributions for light backscattered from a disordered medium,” Phys. Rev. Lett. 85, 66–69 (2000). [CrossRef] [PubMed]

12.

H. C. van de Hulst, Light scattering by small particles. 1957, New York: Dover Publications.

13.

A. F. Fercher, W. Drexler, C.K. Hitzenberger, and T. Lasser, “Optical coherence tomography - principles and applications,” Reports on Progress in Physics 66, 239–303 (2003). [CrossRef]

OCIS Codes
(170.1530) Medical optics and biotechnology : Cell analysis
(290.0290) Scattering : Scattering

ToC Category:
Research Papers

History
Original Manuscript: November 12, 2003
Revised Manuscript: December 5, 2003
Published: December 15, 2003

Citation
John Pyhtila, Robert Graf, and Adam Wax, "Determining nuclear morphology using an improved angle-resolved low coherence interferometry system," Opt. Express 11, 3473-3484 (2003)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-11-25-3473


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References

  1. Backman, V., V. Gopal, M. Kalashnikov, K. Badizadegan, R. Gurjar, A. Wax, I. Georgakoudi, M. Mueller, C.W. Boone, R.R. Dasari, and M.S. Feld, "Measuring cellular structure at submicrometer scale with light scattering spectroscopy," IEEE. J. Sel. Top. Quantum Electron. 7, 887-893 (2001). [CrossRef]
  2. Sokolov, K., J. Galvan, A. Myakov, A. Lacy, R. Lotan, and R. Richards-Kortum, "Realistic three-dimensional epithelial tissue phantoms for biomedical optics," J. Biomed. Opt. 7, 148-156 (2002). [CrossRef] [PubMed]
  3. Mourant, J.R., T.M. Johnson, S. Carpenter, A. Guerra, T. Aida, and J.P. Freyer, "Polarized angular dependent spectroscopy of epithelial cells and epithelial cell nuclei to determine the size scale of scattering structures," J. Biomed. Opt. 7, 378-387 (2002). [CrossRef] [PubMed]
  4. Wax, A., C. Yang, V. Backman, K. Badizadegan, C.W. Boone, R.R. Dasari, and M.S. Feld, "Cell organization and sub-structure measured using angle-resolved low coherence interferometry," Biophys. J. 82, 2256-2264 (2002). [CrossRef] [PubMed]
  5. Backman, V., M.B. Wallace, L.T. Perelman, J.T. Arendt, R. Gurjar, M.G. Muller, Q. Zhang, G. Zonios, E. Kline, T. McGillican, S. Shapshay, T. Valdez, K. Badizadegan, J.M. Crawford, M. Fitzmaurice, S. Kabani, H.S. Levin, M. Seiler, R.R. Dasari, I. Itzkan, J. Van Dam, and M.S. Feld, "Detection of preinvasive cancer cells," Nature 406, 35-36 (2000). [CrossRef] [PubMed]
  6. Wallace, M.B., L.T. Perelman, V. Backman, J.M. Crawford, M. Fitzmaurice, M. Seiler, K. Badizadegan, S.J. Shields, I. Itzkan, R.R. Dasari, J. Van Dam, and M.S. Feld, "Endoscopic detection of dysplasia in patients with Barrett's esophagus using light-scattering spectroscopy," Gastroenterology 119, 677-682 (2000). [CrossRef] [PubMed]
  7. Lovat, L.B., D. Pickard, M. Novelli, P.M. Ripley, H. Francis, I.J. Bigio, and S.G. Bown, "A novel optical biopsy technique using elastic scattering spectroscopy for dysplasia and cancer in Barrett's esophagus," Gastrointest. Endosc. 51, 4919 (2000).
  8. Wax, A., C.H. Yang, M.G. Muller, R. Nines, C.W. Boone, V.E. Steele, G.D. Stoner, R.R. Dasari, and M.S. Feld, "In situ detection of neoplastic transformation and chemopreventive effects in rat esophagus epithelium using angle-resolved low-coherence interferometry," Cancer Research 63, 3556-3559 (2003). [PubMed]
  9. Wax, A., C. Yang, V. Backman, M. Kalashnikov, R.R. Dasari, and M.S. Feld, "Determination of particle size using the angular distribution of backscattered light as measured with low-coherence interferometry," J. Opt. Soc. Am. A 19, 737-744 (2002). [CrossRef]
  10. Wax, A. and J.E. Thomas, "Optical heterodyne imaging and Wigner phase space distributions," Opt. Lett. 21, 1427-1429 (1996). [CrossRef] [PubMed]
  11. Wax, A., S. Bali, and J.E. Thomas, "Time-resolved phase-space distributions for light backscattered from a disordered medium," Phys. Rev. Lett. 85, 66-69 (2000). [CrossRef] [PubMed]
  12. van de Hulst, H.C., Light scattering by small particles. 1957, New York: Dover Publications.
  13. Fercher, A.F., W. Drexler, C.K. Hitzenberger, and T. Lasser, "Optical coherence tomography �?? principles and applications," Reports on Progress in Physics 66, 239-303 (2003). [CrossRef]

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