Colon samples with both healthy and cancerous regions have been imaged in diffuse light and backscattering geometry by using a Mueller imaging polarimeter. The tumoral parts at the early stage of cancer are found to be less depolarizing than the healthy ones. This trend clearly shows that polarimetric imaging may provide useful contrasts for optical biopsy. Moreover, both types of tissues are less depolarizing when the incident polarization is linear rather than circular. However, to really optimize an optical biopsy technique based on polarimetric imaging a realistic model is needed for polarized light scattering by tissues. Our approach to this goal is based on numerical Monte-Carlo simulations of polarized light propagation in biological tissues modeled as suspensions of monodisperse spherical scatterers representing the cell nuclei. The numerical simulations were validated by comparison with measurements on aqueous polystyrene sphere suspensions, which are commonly used as tissue phantoms. Such systems exhibit lower depolarization for incident linear polarization in the Rayleigh scattering regime, i.e. when the sphere diameters are smaller than the wavelength, which is obviously not the case for cell nuclei. In contrast, our results show that this behaviour can also be seen for “large” scatterers provided the optical index contrast between the spheres and the surrounding medium is small enough, as it is likely to be the case in biological tissues.
©2010 Optical Society of America
Light propagating through a scattering medium undergoes elastic scattering and absorption. Hence, the measurements of the angular distribution of the light intensity, spectroscopic diffuse reflectance or degree of polarization of the backscattered light can carry important information about the optical properties of the medium. Probing scattering media with either unpolarized or polarized light is common practice in meteorology, oceanography, chemistry and particle sizing, biology, and especially in medicine [1–7]. Usually the cancerous cells show structural abnormalities because of their fast growth and multiple divisions. Differentiation of diseased versus healthy tissues by means of optical measurements is of particular interest, as it could improve early cancer detection rates by innocuous and relatively inexpensive techniques.
Polarimetric imaging can provide useful contrasts, which are quite different from those obtained by usual spectroscopic or angular intensity measurements. Hielscher et al.  demonstrated that diffusely backscattered, linearly polarized light can be used to determine scattering coefficients μ s, anisotropy factors g and average particle sizes of both polystyrene sphere and biological cell suspensions. Yang et al.  showed the sensitivity of the diagonal elements of backscattering Mueller matrix to the particle shape. The possibility to distinguish the cancerous cell suspensions from noncancerous ones was discussed in the paper of Hielscher et al. . Mueller matrix characterization of biological tissue by optical coherence tomography was suggested by Yao and Wang . Orthogonal state contrast imaging  and Mueller matrix imaging [11,12] were explored as potential diagnostic tool for various dermatologic diseases.
Many studies were carried out on the modeling of light propagation in scattering media for an adequate interpretation of experimental results. Statistical Monte Carlo methods have been implemented to solve the vector radiative transfer equation (VRTE) which describes polarized light propagation in scattering media [13–17]. Biological tissues have very complex structures, so the choice of the relevant optical models is crucial. These models have to include the essential features of tissue in order to reproduce the experimental measurements, while remaining simple enough to allow efficient calculations and unambiguous parameter determinations from the experiments. A typical tissue can be modeled as a stack of layers of different thicknesses on semi-infinite substrate. Each layer may contain spherical scatterers of different sizes which represent the main cell components (nuclei, mitochondria, lysosomes). Refractive index of almost all cell components depends mainly on the amount of protein they contain and can be found elsewhere . The presence of organized collagen fibers can be modeled by introducing optical anisotropy.
In this paper we show the experimentally measured backscattering Mueller matrix images of ex-vivo human colon tissue, and discuss the depolarization properties of both healthy and cancerous tissues for linearly and circularly polarized incident light. Then we present the numerical Monte Carlo model for polarized light propagation in a multi-layered scattering medium and validate the model by experiments on tissue phantoms. Finally, we present numerical simulations with realistic values of the optical contrast between the scatterers and the surrounding medium for biological tissues, which may account for the observed Rayleigh-like scattering behavior.
2.1 The instruments
Two different instruments have been used for this study. The first one was an imaging Mueller polarimeter, operated with diffuse illumination from a halogen lamp source. This instrument is an upgraded version of one described in  which was developed from a first imaging system operating in transmission . Briefly, in these instruments the polarization of the incident beam is modulated by a Polarization State Generator (PSG) comprising a linear polarizer followed by two nematic liquid crystal variable retarders. The sample is viewed through suitable imaging optics including a Polarization State Analyser (PSA) made of the same elements as the PSG, but in reverse order. The field of view can be varied from 2 to 5 cm by using a zoom lens. The wavelength is chosen between 500 and 700 nm by 20 nm wide interference filters.
The second instrument was specifically used to validate the simulations, in an experimental scheme quite similar to that described by Hielscher et al . In this setup, the illumination beam (from a HeNe laser, wavelength 633 nm) was focused at the center of the sample surface, which was in turn imaged on a CCD. The PSG was made of a polarizer and a rotatable Babinet-Soleil compensator, while the PSA comprised a quarter-wave plate and a polarizer. Both the PSG and the PSA were operated manually in a series of measurements similar to those described by Hielscher et al. .
2.2 Typical Mueller images of ex-vivo samples
The photos of two samples of human colon with healthy and tumoral parts (liberkünian carcinomas) are shown in Figs. 1(a) and 1(b). The polarimetric images of studied human colon tissue acquired by the Mueller polarimetric imaging system at the Institut Mutualiste Montsouris hospital in Paris are shown in Fig. 1c, 1d. The measurements were performed at the wavelengths of 600 and 700 nm respectively and at near normal incidence. These Mueller matrices are essentially diagonal, showing that the tissue behaves as a partial depolarizer, without neither significant diattenuation nor retardance. Moreover, the M22, M33 images are identical, meaning that the depolarization of backscattered light for the incident linearly polarized light is independent of the orientation of its polarization plane, as expected for such tissues.
For both cases the tumoral and healthy parts of the sample are easily distinguished on these images: the absolute value of M22 and M33 is larger on the diseased tissue (at the upper right corner) than in healthy regions, indicating a better conservation of the incident polarization, i.e. a lower depolarizing power. The same difference between cancerous and healthy regions is seen in the M44 element. However, for both kinds of tissue, we observe that9], for healthy and cancerous cell suspensions, and by Sankaran et al. , who studied the polarimetric response of a variety of tissues (fat, tendon, arterial wall, myocardium, blood), in transmission. Only whole blood displayed the opposite trend
The images of the same samples taken at 500, 550 and 650 nm (not shown here) exhibit quite similar contrasts, with, however, an overall increase of depolarization with increasing wavelength, a trend which can safely be attributed to a decrease of light absorption due to haemoglobin, and thus an increase of the average number of scattering events a photon suffers before emerging.
3. Numerical algorithm
In order to understand the origin of the contrasts observed in polarimetric images of tissues we developed a Monte-Carlo code for the solution of VRTE for multi-layered scattering media. The stochastic path of polarized photon in a scattering medium was simulated numerically. The changes in photon position, direction of propagation and polarization were calculated using the exact Lorenz-Mie solution for the scattering of plane waves by spherical particles , Fresnel formulae for the optical interface and Lambert-Beer extinction law. We made use of two main physical assumptions:
- • All scattering particles are located in the far-field zones of other particles. The observation point is also located in the far-field zones of all scattering particles.
- • The positions of all particles are independent of each other, particles are randomly and uniformly distributed over the scattering medium volume, and there is no coherent scattering.
The implementation of a flux-at-point estimation technique allowed us to accelerate the convergence of statistical algorithm. The detailed description of this technique can be found elsewhere .
We performed the measurements and simulations of polarimetric images of two different suspensions of polystyrene spheres in water (radii R1 = 50 nm, R2 = 1500 nm, optical index contrast m = 1.59/1.33 for both). The suspensions filling cylindrical container with circular metallic sidewall and glass top and bottom (diameter - 2 cm, depth - 1 cm) were studied with the second setup described above, with its focused illumination beam (λ = 633 nm) propagating along the cylindrical cell axis.
From ballistic photon intensity measurements and calculated value of anisotropy parameter g we found that the photon mean free path (mfp) was equal to 1 mm for the small particle suspension (corresponding particle concentration was 1.8·1013 cm−3), and 0.5 mm for the large particle suspension. (corresponding particle concentration was 1.7·108 cm−3) The simulated normalized (Mij = Mij/M11, i·j ≠ 1) Mueller matrix images (see Fig. 2c , 2d) show good agreement with the experimental data (see Fig. 2a, 2b).
In particular, they reproduce the butterfly-like patterns observed for some Mueller matrix coefficients. The azimuthal cross-sections of measured and simulated images for two suspensions at radius equal to 0.46 cm are shown in Fig. 3 . There is good quantitative agreement between experiments and simulations for both particle suspensions. The polarimetric measurements were performed at near normal incidence. This experimental configuration had slightly perturbed the azimuthal periodicity of the measured Mueller matrix coefficients at chosen radius (Fig. 3a,3b open symbols).
In all simulations the polarized light was normally incident to the surface of the sample. Consequently, the simulated coefficients of Mueller matrix were periodic functions of azimuthal angle at at chosen radius (Fig. 3a, 3b solid lines). The small amplitude discrepancy between the simulated and measured data can be attributed to the accuracy of the ballistic photon intensity measurements used for the photon mean free path calculation.
The simulated backscattering Mueller matrix images of the same tissue phantoms but with diffuse light illumination are presented in Fig. 4 ) is actually very similar to that of the suspension of small polystyrene particles (R = 50 nm, λ = 633 nm) in water and the relation (1) also holds for diagonal coefficients of the backscattering matrix coefficients averaged over the entrance point. This behavior is reminiscent of the Rayleigh-Gans scattering regime , where “large” scatterers behave as if they were “small”, due to a sufficiently small optical index contrast between the spheres and the surrounding medium.
The relation (1) holds for diagonal coefficients of the backscattering matrix of the suspension of small (R = 50 nm) polystyrene particles (Fig. 4a). In backscattered light this tissue phantom preserves more the linear polarization of incident light compared to the circular one and is considered to be in Rayleigh scattering regime. The reverse relation (2) holds for diagonal coefficients of the backscattering matrix of the suspension of large (R = 1500 nm) polystyrene particles (Fig. 4b) and it is referred as Mie scattering regime. In backscattered light this tissue phantom preserves more the circular polarization of incident light compared to the linear one. This effect was previously reported and suggested for particle sizing .
4. Results and discussion
Normal colon tissue has a multi-layered structure. Each layer has specific components and different optical properties. The most superficial epithelial layer is a one-cell layer of epithelial cells, whose nuclei are 4 – 7 μm in diameter and have higher refractive index than the cytoplasm. Measurements on isolated organelles of mammalian cell suspensions show that small size cell components (mitochondria, lysosomes) contribute to the large-angle scattering, whereas nuclei are responsible for the small-angle scattering .
If we link cancer proliferation to the increase in number of abnormal large size nuclei within the cells of epithelium layer, we would expect the transition from Rayleigh scattering regime to Mie scattering regime and consequently the inversion of the relation between diagonal elements of backscattering Mueller matrix of the tissue. Nevertheless in our experiments we have never observed Mie scattering regime for both healthy and cancerous colon tissue. To understand this phenomenon we simulated the backscattering Mueller matrix images of the suspension of large soft spherical particles (R = 3000 nm, ns = 1.4) in liquid with nm = 1.36 representing the cell nuclei in cytoplasm.
The pattern of calculated Mueller matrix (see Fig. 5 is actually very similar to that of the suspension of small polystyrene particles (R = 50 nm, λ = 633 nm) in water and the relation (1) also holds for diagonal coefficients of the backscattering matrix coefficients averaged over the entrance point. This behavior is reminiscent of the Rayleigh-Gans scattering regime , where “large” scatterers behave as if they were “small”, due to a sufficiently small optical index contrast between the spheres and the surrounding medium.
The important parameters for a more quantitative analysis of scattering medium properties are particle size parameter x, optical index contrast m, phase shift ρ acquired by a light ray directed along a sphere diameter with respect to a parallel ray passing outside the sphere, and the efficiency factor Q which is the ratio of extinction cross-section (equal to scattering cross-section in our case since we deal with dielectric spheres) to geometrical cross-section of the particle. For three simulated tissue phantoms the corresponding values are presented in Table 1 (λ = 633 nm, k = 2π/ λ).
Suspension I is characterized by the small values of x, ρ and Q, which is typical for “true” Rayleigh scattering regime. The values of x, ρ and Q are much larger for suspension II compared to suspension I. Consequently, the Mie scattering determines the polarized optical response of the suspension II. The largest particles form suspension III, their efficiency factor does not change too much compared to suspension II, but the optical index contrast and phase shift are smaller than corresponding values for suspension II. According to ref . the suspension III (|m-1| << 1) can be described as intermediate case between Rayleigh-Gans scattering (large x, ρ << 1, Q→0) and anomalous diffraction regime (large x, ρ >> 1, Q→2). There is no valid general analytical approximation for this transitional regime and only the numerical simulations can provide the valuable information. In case of Rayleigh-Gans scattering the intensity of light scattered by spherical particles can be found by multiplying the intensity for Rayleigh scattering by the factor, depending on scattering angle only. Polarization of the scattered light is exactly the same as for Rayleigh scattering.
As a result, the basic reason why almost all tissues exhibit polarimetric contrasts typical of the Rayleigh regime is probably the low index contrast between nuclei and cytoplasm. The simple hypothesis of a gradual shift from the Rayleigh to the Mie regime with cancer proliferation must be considerably refined, with numerical exploration of the effects of all the relevant parameters, such as layer thicknesses, scatterer densities in all layers, absorption by haemoglobin, etc.
Ex-vivo measurements of both healthy and cancerous colon tissues were performed with a Mueller polarimetric imaging system at near-normal incidence and five different wavelengths: 500 nm, 550 nm, 600 nm, 650 nm and 700 nm. The experimental data showed that:
- • tumoral tissues at the early stage of cancer are less depolarizing than healthy ones;
- • depolarization is always higher for circular than for linear incident polarization, both for healthy and cancerous tissues.
Experimentally observed relation |M22| = |M33| > |M44| between the spatially averaged diagonal elements of Mueller matrix images is believed to be the signature of the light scattering by small particles. The Monte Carlo simulations of the backscattering Mueller matrix images of three different tissue phantoms showed that not only the size of scatterers but the optical index contrast also affects the ratio of linear to circular polarization of the backscattered light and, consequently, the contrasts of polarimetric images. The presence of “soft” large compared to the wavelength particles in the model does not reverse the relation |M22| = |M33| > |M44|. The Rayleigh-like optical response of cancerous tissues can be attributed to the light scattering on both small and large scatterers as optical index contrast in biological tissues is quite small.
Thus, care should be taken when evaluating the properties of real biological tissues (e. g. sizes of scatterers) based on the predictions of the phantom tissues optical measurements and modeling. The work is ongoing towards creating realistic models of healthy and cancerous colon tissue for adequate analysis of the results of polarimetric imaging measurements of real ex-vivo samples. The experimentally confirmed relation between diagonal Mueller matrix elements |M22| = |M33| > |M44| will help us to discard wrong optical models of human colon tissue.
This research was supported by the Agence Nationale de la Recherche (ANR) under contract RNTS-Polarimétrie.
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