A polarization-sensitive light field imager for multi-channel angular spectroscopy of light scattering in biological tissues

Introduction

Reliable detection of precancerous cells is an essential step to ensure timely treatments which can reduce the risk of malignant development of tumors. Biological cells undergo morphological changes during cancerous development. Histological biomarkers such as nuclear enlargement (1) and hyperchromasia (darker staining because of denser chromatin) (2,3) provide indicators for early diagnosis of precancerous cells. However, conventional histological examination requires biopsies which involve painful procedure and complicated sample preparation. It is known that light scattering characteristics in cells are sensitive to the size, distribution, and relative refractive index of subcellular scatters such as nuclei (4-6). Light scattering spectroscopy has been explored for vital study of subcellular organelles (7-10), cellular volume (11) and physiological condition of biological tissues (12). It promises a new methodology to complement histological examination for in vivo detection of precancerous and cancerous cells in optically accessible organs (13,14). Morphological and physiological abnormalities of cells or nuclei have been revealed by spectral and angular spectroscopy of scattered light. The spectral spectroscopy is employed to disclose wavelength (color) dependent differences; while the angular spectroscopy is used to detect angle-resolved changes in light scattering (9,15).

Angular distribution of light scattering has been known to be highly dependent on the orientation of tested specimens such as deformed elongated cells and well-packed fibers (16,17). The angular spectroscopy is typically implemented through a single-channel goniometric setup, which suffers from low spatial resolution or requires time-consuming scanning over extended area. Alternatively, angular resolution can be achieved by using a spatial filter at the Fourier plane that only allows scattered light with a specific scattering angle to pass through (18,19). However, this scheme requires physical manipulation of the spatial filter and it only samples one angle at a time which makes it time-consuming again for two-dimensional (2D) recording. Projecting the Fourier plane to the 2D camera could realize 2D recording of the scattering (11). However, this approach lacks the spatial resolution and the whole illuminated area could contribute to the scattering, which might overwhelm the useful signals. To address this issue, we developed a light field imager which employed a microlens array (MLA) at the image plane to realize 2D recording of the angular distribution of the light scattering while maintaining an acceptable spatial resolution. Polarization-sensitive recording capability was integrated to enable quantitative analysis of scattering signals at high sensitivity. Lobster leg nerves were employed to demonstrate polarization-sensitive light field differentiation of normal and unhealthy tissues. Experiments on the lobster leg nerves revealed 2D elliptical scattering patterns which were highly dependent on the orientation of the nerves, while as the nerves deteriorated, the elliptical scattering patterns gradually lost the ellipticity and became rotationally symmetric (i.e., circular). We anticipate that further development of the polarization-sensitive light field imager promises a method for in vivo screening of precancerous cells by rapid multi-channel angular spectroscopy at high resolution.

Materials and methods

Experimental setup

Figure 1A shows the optical diagram of polarization-sensitive light field imager. A near infrared (NIR) superluminescent diode (SLD-351, Superlum) was employed for illumination. The center wavelength was λ=830 nm and the band width was Δλ=60 nm. A 20× objective with 0.5 numerical aperture (NA) was used. The equivalent focal length of the objective was f₀=9 mm in the air. Camera 1 was conjugate to the specimen for the position adjustment of the specimen. The MLA was also conjugate to the specimen. The back focal plane (i.e., Frourier plan) of the MLA was imaged to Camera 2. The lenslet of the MLA was rectangular. The length of each side was d=0.3 mm. The focal length of each lenslet was f_m=3 mm. The red NIR light emission diode (LED) below the sample was used for light illumination to monitor the sample through Camera 1. It was turned off during light field imaging. According to the Rayleigh criteria, the angular resolution of the system was determined by the light wavelength, diameter of the lenslet of the MLA and optical magnification of the optical system:

Figure 1 Polarization-sensitive light field imager. (A) Optical schematic diagram of polarization-sensitive light field imager. L1, L2 and L3, lenses; LP1 and LP2, linear polarizers; OB, objective; SLD, superluminescent diode; CO, collimator; MLA, microlens array; LF, long-pass filter; DM, dichroic mirror; BS1 and BS2, beam splitters. The focal lengths of lenses L1, L2, L3 and L4 were 150, 75, 75 and 200 mm, respectively. The objective was 20× with 0.5 numerical aperture (NA). The MLA had a focal length of 3 mm and a pitch of 0.3 mm. Different color rays represent different scattering angels. The Camera 1 was conjugated to the specimen and was used to monitor the specimen, while Camera 2 was placed on a plane conjugate to the focal plane of the MLA to record angle-resolved scattering signals. The red NIR LED below the sample was used for light illumination to monitor the sample through Camera 1. It was turned off during light field signal recording. (B) Illustration of the orientation of the lobster leg nerves with respect to the polarization direction of the incident light.

where f₁ was the focal length of the lens L1. The transverse resolution of the system was:

If we multiple Eq. [1] with Eq. [2], we obtain:

Eq. [3] indicates a tradeoff between spatial and angular resolutions for light field imaging.

A pair of crossed linear polarizers LP1 and LP2 was added to provide polarization-sensitive measurement. As shown in Figure 1B and Figure 2A, the lobster leg nerve bundle was placed at 45° with respect to the polarization direction of the incident light. The incident direction of the illumination light was along the z axis and perpendicular to long axis of the nerve fibers. The polarization plane (the gray plane in Figure 1B) of the incident light was parallel to the y-z plane.

Figure 2 Polarization-sensitive light field imaging of lobster leg nerves. (A) Transmitted image acquired by Camera 1. The lobster leg nerves were placed along the y’ axis. (B) 2D angular scattering distribution map of fresh live lobster leg nerves right after dissection. This image contained in total 64 (8 by 8) scattering subunits. Each subunit was a scattering map of an 18 μm by 18 μm retinal area which was determined by the size of the lenslet and the magnification of the system. (C) 2D angular scattering distribution map of deteriorated lobster leg nerves after a series of electrical stimulations. The intensity of (C) was multiplied by a factor of 5 for a better view. The yellow and green squares in (B) indicated a center area (designated as Area 1) and an area relatively closer to the edge of the nerves (designated as Area 2), respectively, for quantitative comparison in Figures 3 and 4. 2D, two-dimensional.

Calculation of ellipticity

2D angular polarization-sensitive scattering patterns of the fresh nerves were elliptical (Figure 2B), while they became circular as the nerves physiologically deteriorated over time, after repeated electrical stimulations (Figure 2C). At intermediate states (Figure 3A), scattering patterns were less elliptical (Figure 3B-D). The ellipticity of an ellipse is defined as:

Figure 3 Polarization-sensitive scattering adaptation as a function of the viability of the lobster leg nerves. (A) Electrophysiological responses of the lobster leg nerves. Peak-to-peak magnitudes of four plots in (A) were around 10, 4, 1.3 and 0.03 mV, respectively. The peak-to-peak magnitude denoted the viability of the nerves. (B) Scattering distribution maps at a center area as the nerves deteriorated. This area was specified by the yellow square in Figure 2B and designated by Area 1. The four images in (B) were scattering maps corresponding to four viability levels (specified by magnitudes of electrophysiological responses: 10, 4, 1.3 and 0.03 mV, respectively). (C) Scattering profiles along and perpendicular to the orientation of the nerves. The sampled data were from region of interest 1 (ROI 1), a scattering subunit at the top-left corner of Area 1. The y’ axis was parallel to the orientation of the nerves, while the x’ axis was perpendicular to it. Red and blue dots were raw intensity data along the x’ axis and the y’ axis, respectively. Red and blue curves were fitted data using Gaussian functions. (D) Scattering distribution maps at an area relatively closer to the edge of the nerves as the nerves deteriorated. This area was specified by the green square in Figure 2B and designated by Area 2. (E) Scattering profiles along and perpendicular to the orientation of the nerves. The sampled data were from ROI 2, the scattering subunit at the top-left corner of Area 2. The y’ axis was parallel to the orientation of the nerves, while the x’ axis was perpendicular to it. Red and blue dots were raw intensity data along the x’ axis and the y’ axis, respectively. Red and blue curves were fitted data using Gaussian functions. The brightness of the second, third and fourth images in both (B) and (D) was adjusted (multiplied by a factor of 1.5, 3 and 5, respectively) for a better visualization of the angular patterns.

where a and b are major radius and minor radius of an ellipse, respectively. Intensity profiles of the scattering signals along the major axis (the x’ axis in Figure 3C,E) and the minor axis (the y’ axis in Figure 3C,E) were Gaussian distributed. The major radius a and the minor radius b of the ellipse were estimated by the full width at the half maximum of the Gaussian curve in the x’ axis and the y’ axis, respectively. If the ellipticity is 0, the scattering pattern is rotationally symmetric (i.e., circular), while the scattering pattern is a single line if the ellipticity is 1. It is an ellipse if the ellipticity is between 0 and 1.

Data fitting

To better understand the relationship between quantitative parameters (e.g., ellipticity and mean scattering intensity) and the peak-to-peak magnitude of the electrophysiological responses of the nerves M, curve fitting with least squares was applied. The fitting function employed in Figure 4A was:

Figure 4 Quantitative comparison of scattering adaptations between two areas. (A) Ellipticities of ROI 1 and ROI 2 as a function of the peak-to-peak magnitude of the electrophysiological responses of the nerves. The curve fitting function was defined in Eq. [5]. (B) Mean scattering intensity of ROI 1 and ROI 2 as a function of the peak-to-peak magnitude of the electrophysiological responses of the nerves. The curve fitting function was defined in Eq. [6]. (C) Ellipticities of Area 1 and Area 2 as a function of the peak-to-peak magnitude of the electrophysiological responses of the nerves. (D) Mean scattering intensities of Area 1 and Area 2 as a function of the peak-to-peak magnitude of the electrophysiological responses of the nerves. Shadows in (C) and (D) indicate the standard deviations. ROI, region of interest

where c₁, c₂ and c₃ were coefficients estimated by data fitting. In contrast, the fitting function used in Figure 4B was a logistic function:

where a₁, a₂ and a₃ were coefficients estimated by data fitting, and was the mean scattering intensity.

Specimen preparation

We used lobster leg nerves for experimental validation of the polarization-sensitive light field imaging system. The lobster leg nerves provide a simple anisotropic specimen for technical validation of 2D recording of the angular distribution. The 2D distribution profile underwent changes as the nerves deteriorated. We used the electrophysiological response of the nerves as the physiological biomarker of functional integrity of the nerves. All animal handling procedures were approved by the Institutional Animal Care and Use Committee of the University of Alabama at Birmingham. Details of the sample preparation have been reported in our previous publications (20). Briefly, the Furusawa pulling out method was applied to extract the nerves (21). The recording chamber was filled with the Ringer solution of lobster leg nerves. At the center of the chamber, a square cover glass was placed on the top of the recording chamber to reduce the effect of water fluctuation on the optical recording. A pair of silver electrodes was used to stimulate the nerves. Another pair of silver electrodes was used to record stimulus-evoked electrophysiological response of the nerves. Each stimulus pulse lasted for 0.1 ms. The current of the stimulus was 10 mA. Repeated stimulations were applied to accelerate physiological degeneration of the nerves. Scattering patterns of the nerves were recorded after every 20 stimulations.

Results

Figure 2 shows comparison of 2D angular polarization-sensitive scattering distribution between fresh and unhealthy lobster leg nerves. Figure 2A shows an image acquired by Camera 1 using the NIR LED illumination below the specimen. Figure 2A illustrates the orientation of the nerves. As shown in Figure 1B, the long axis of the nerves was parallel to the x-y plane and 45° with respect to the x axis (i.e., along the y’ axis in Figure 2A). Figure 2B shows elliptical scattering distribution patterns of the fresh nerves. The long axis of the ellipse was perpendicular to the orientation of the nerves. In contrast, as shown in Figure 2C, the deteriorated nerves showed more rotationally symmetric scattering patterns which were independent from the orientation of the nerves. Moreover, the scattering intensity of the deteriorated nerves was much weaker than that of the fresh nerves (intensity of the image Figure 2C was multiplied by a factor of 5 for a better view). We selected two areas, Area 1 (specified by yellow) and Area 2 (specified by green squares in Figure 2B) to better illustrate how the scattering distribution patterns were altered by the deterioration of the nerves.

Figure 3 shows that the ellipticity of the polarization-sensitive scattering patterns degraded when the nerves were physiologically deteriorated due to repeated electrical stimulations. Scattering patterns of two representative areas, Area 1 (Figure 3B) and Area 2 (Figure 3D), were illustrated. Figure 3A shows electrophysiological responses of the nerves with various magnitudes sequentially recorded at 20^th, 160^th, 220^th and 480^th stimulation, respectively. We used peak-to-peak magnitude of electrophysiological responses as a biomarker to represent the viability level of the nerves. Peak-to-peak magnitudes of four curves in Figure 3A were around 10, 4, 1.3 and 0.03 mV, respectively. Figure 3B,D shares a similar trend overall. First, the elliptical scattering patterns gradually became rotationally symmetric as the nerves got more degenerated. Second, the polarization-sensitive scattering intensity was decreased as the nerves lost the viability. The brightness of the second, third and fourth images in both Figure 3B,D was adjusted (multiplied by a factor of 1.5, 3 and 5, respectively) for a better view. Therefore, the intensity of images in both Figure 3B,D was decreased in sequence, although the presented images render similar brightness. As shown in Figure 3C,E, scattering intensity profiles along the x’ axis and the y’ axis at the region of interest 1 (ROI 1) and ROI 2 confirmed these two observations: the loss of the ellipticity and the decrease of scattering intensity due to the deterioration of the nerves.

Two quantitative parameters, the ellipticity as defined in Eq. [4] and the scattering intensity, were plotted as a function of the peak-to-peak magnitude of electrophysiological responses of the nerves. Figure 4A shows the values of the ellipticity of ROI 1 (specified by the white arrow in Figure 3B) and ROI 2 (specified by the white arrow in Figure 3D) as the nerves got deteriorated, while Figure 4B shows the mean of the scattering intensity of ROI 1 and ROI 2. To reliably compare the ellipticity and the mean of the scattering intensity between Area 1 and Area 2, we investigated all scattering subunits of Area 1 and Area 2 and plotted the data in Figure 4C,D. Shadow in Figure 4C,D indicates the standard deviation. In Figure 4C, the overall trend of the ellipticity at Area 1 and Area 2 was in common: the value of the ellipticity was high when the nerves were fresh and was decreased due to physiological deterioration of the nerves. However, distinct spatial variations existed. First, at any given point of the electrophysiological magnitude, Area 1 always had a smaller ellipticity value than Area 2. Second, the changing rate of Area 1 was bigger than that of Area 2, since the length of the green bar was longer than that of the black bar in Figure 4C. Figure 4D shows that both Area 1 and Area 2 had a decreased scattering intensity when the magnitudes of the electrophysiological responses were small because of the degeneration of the nerves. The length of the green bar was shorter than that of the black bar in Figure 4D, which implied that the scattering intensity of Area 1 decreased faster than that of Area 2 as the electrophysiological magnitude got smaller.

Discussion and conclusions

In summary, we developed a polarization-sensitive light field imager to conduct multi-channel [64] angular spectroscopy of light scattering with both spatial and angular resolutions. Light filed imaging of freshly isolated lobster leg nerves revealed elliptical scattering patterns (Figure 2B), which reflects highly orientation dependent light distributions. Values of the ellipticity and the scattering intensity were also location dependent. Area 1 always had a smaller ellipticity (Figure 4C) and a bigger scattering intensity (Figure 4D) comparing to Area 2. The spatial variations might attribute to localized difference of nerve fiber sizes and numbers (22). Comparative light field imaging and electrophysiological examination of freshly isolated and physiologically deteriorated lobster nerves was conducted to demonstrate the potential of light field identification of tissue dysfunctions. First, as the nerves got deteriorated, the elliptical scattering patterns became more and more rotationally symmetric (Figures 3,4A and C). Second, the mean scattering intensity was attenuated as the deterioration of the nerves got advanced. Moreover, this relationship was spatially various (Figure 4C,D), which demonstrated the advantage of the multi-channel imaging for reliable longitudinal (i.e., chronological) studies. Reflected polarization light signals might be produced by scattering (23) and birefringence (24). The disease or deterioration of the nerves might cause structural and morphological changes, e.g., disruption of well-organized cell membranes, alternation of refractive index, and cell swelling or shrinking, which could in turn lead to the change of optical properties of the nerves. The axial resolution of our current light field system is limited by the NA of the objective. To enhance the axial resolution, the optical coherence tomography technique can be integrated in future systems to gate the signal from individual depths (25,26). We anticipate that further development of polarization-sensitive light field imager promises a reliable strategy to screen precancerous cells in vivo at optically accessible organs to complement in vitro histological examination. The multi-channel angular spectroscopy is also providing an important tool to investigate biophysical mechanisms of transient polarization light changes in excitable nerve tissues (20,22).

Acknowledgements

This research is supported in part by NIH R21 EB012264, NIH R01 EY023522, NIH R01 EY024628, and NSF CBET-1055889.

Disclosure: The authors declare no conflict of interest.

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