Micro-polarimetry for Pre-Clinical Diagnostics of Pathological Changes in Human Tissues

Andrzej Golnik*a, Natalia Golnikb, Tadeusz Pałkob, Tomasz Sołtysińskib a Institute of Experimental Physics, Warsaw University, Hoza 69, PL-00-681 Warsaw, Poland

b Institute of Precision and Biomedical Engineering, Warsaw University of Technology, Sw. A. Boboli 8, PL-02-525 Warsaw, Poland

ABSTRACT

The paper presents a practical study of several methods of image analysis applied to polarimetric images of regular and malignant human tissues. The images of physiological and pathologically changed tissues from body and cervix of uterus, intestine, kidneys and breast were recorded in transmitted light of different polarization state. The set up of the conventional optical microscope with CCD camera and rotating polarizer's were used for analysis of the polarization state of the light transmitted through the tissue slice for each pixel of the camera image. The set of images corresponding to the different coefficients of the Stockes vectors, a 3x3 subset of the Mueller matrix as well as the maps of the magnitude and in-plane direction of the birefringent components in the sample were calculated. Then, the statistical analysis and the Fourier transform as well as the autocorrelation methods were used to analyze spatial distribution of birefringent elements in the tissue samples. For better recognition of tissue state we proposed a novel method that takes advantage of multiscale image data decomposition The results were used for selection of the optical characteristics with significantly different values for regular and malignant tissues

Keywords: collagen fibers, birefringent properties, polarimetry

1. INTRODUCTION Biological tissue exhibits natural birefringent behavior mainly due to the orientation of collagen fibers1,2. The pathological changes in the tissue change also the collagen structure and thus the images observed in polarization microscopy 3. Especially, the cancer affected malignant tissue changes its birefringent properties4,5. This fact makes possible the construction of the diagnostic method based on light propagation through the tissue6. Such methodology allows, in principle, for fast, cheap and efficient way of tissue diagnostics suitable for common use with widely available equipment. However, the precise quantification of tissue damage due to the cancer is still hard to perform7. This is caused by the little difference between physiological and cancer tissue that also changes between tissue types. This difference is observed in a number of observables derived from the collected data.

This work was aimed at tests of numerical methods for detection of neoplastic transformation in different human tissues. Besides standard observables like visual pattern of pixel intensities coming from polarized light passing through the tissue, its Fourier transform, the autocorrelation function together with statistical analysis of obtained image data, we tested also a novel method that takes advantage of multiscale image data decomposition. The image data is decomposed by means of a trous algorithm8. After multiscale image components are found they serve independently for the derivation of previously used observables as well as the construction of a new one, the multiscale entropy9. The latter is calculated independently on each scale as well as for all scales. Comparing the new observable for physiological and cancer affected tissue we are able to support the tissue diagnostics. The preliminary data obtained by this method has been already published in Ref. 10.

2. METHODOLOGY The samples of physiological and pathologically changed tissues from body and cervix of uterus, intestine, kidneys and breast were studied. Specially prepared, non-stained tissue sections were used for this work. The sections were of

* *Andrzej.Golnik@fuw.edu.pl; fax +48 22 621 97 12

Invited Paper

Eighth International Conference on Correlation Optics, edited by Malgorzata Kujawinska, Oleg V. Angelsky,Proc. of SPIE Vol. 7008, 70081X, (2008) 0277-786X/08/$18 doi: 10.1117/12.797125

Proc. of SPIE Vol. 7008 70081X-12008 SPIE Digital Library -- Subscriber Archive Copy

standard thickness of 5-9 µm. The images of physiological and pathologically changed tissues from body and cervix of uterus, intestine, kidneys and breast were recorded in transmitted light of different polarization state

2.1 Experimental setup

The set up containing the conventional optical microscope with CCD camera and rotating linear polarizer's was used to analyze the polarization state of the light transmitted through the tissue slice for each pixel of the camera image. The setup was similar to those used by the group of from the University in Chernivtsi1,4,5,7,11. The set of additional polarizer and quarter wave plate was initially placed before the rotating polarizer in order to ensure circular polarization of the light before polarizer. It has been found however that the light from the red LED used as a light source was unpolarized and finally, this element was not used.

Since the images from the CCD camera are directly transferred to the Matlab environment, it was fast and straightforward to calculate from the initial pictures the set of images corresponding to the coefficients of the Stockes vectors, a 3x3 subset of the Mueller matrix as well as the maps of the magnitude and in-plane direction of the birefringent components in the sample. The selflimitation to the first 3 components of the Stockes vector and 3x3 subset of Mueller matrix allowed simplification of the polarization setup. We were able to omit the quarter wave plates between polarizer and object and between object and analyzer.

The initial setup contained a simple Watec LCL-903k CCD camera connected to AVERMedia® AVer EZCapture Card. This ensured full 8 bit resolution for each pixel, however, for the tissues with low birefringence the dynamics of the setup (signal of 30 for darkness and 255 for saturation) was not sufficient. The problem was partially solved by taking additional pictures with neutral density filter when pictures showed saturation. Finally the CCD camera was replaced by the Hamamatsu C8484-05G digital camera ensuring the 12 bit dynamics (390 by darkness and 4095 by saturation) and collecting 1024 by 1344 pictures. The signal is transferred directly by IEEE1394 cable.

2.2 Statistical analysis

Similarly like in Ref. 11 the histograms of images collected for crossed polarizer and analyzer, of images of Stockes vector and Mueller matrix components were analyzed by computing four first moments.

2.3 Autocorrelation

In order to calculate the 2D autocorrelation function of the images we first subtracted the mean value of the pixel value of the whole image, thus reducing the numerical artifacts caused by the finite image size. The vertical and horizontal cross-sections of the 2D autocorrelation function were also analyzed.

2.4 Fourier transform

The 2D Fourier transform of the images was calculated also after mean-value subtraction thus reducing the artifact of the strong peak at zero spatial frequency. Instead of vertical or horizontal cross-sections we analyzed the radial distribution of spatial frequencies, i.e. after integration over angles.

2.5 A trous decomposition and multiscale entropy

We have adapted 2D version of the algorithm that works on morphological structures. The basis is constrained by cubic B3 splines and serves as a kernel for convolution with the noisy image. The image convolved with the kernel on particular scale is subtracted from its original predestor. The remaining data corresponds to decomposition on this particular scale representing the details that are within this scale. In other words we do some filtering or smoothing by the kernel on each scale. The size of the kernel changes from scale to scale what results in decomposed images representing different details on subsequent scales. The a trous algorithm [8,9] may be summarized as follows:

1. Initialize j, the scale index, to 0, starting with an image cj,k where k ranges over all pixels.

2. Carry out a discrete convolution of the data cj,k using a wavelet filter, yielding cj+1,k. The convolution is an interlaced one, where the filter's pixel values have a gap (growing with level j) between them of 2j pixels, giving rise to the name a trous – with holes.

3. From this smoothing it is obtained the discrete wavelet transform, wj+1,k=cj,k-cj+1,k.

4. If j is less than the number J of resolution levels wanted, then increment j and return to step 2.

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The original image is reconstructed by the summation of all wj,k and the smoothed array cJ,k, where J is the maximum that j may reach.

For the purpose of this study, further in the paper, the reversed notation is used that, as it is believed, makes the analysis more intuitive and convenient. The smoothed component (originally cJ,k) has index 0 and all subsequent components, with increasing level of details have growing indexes. Hence, level w1,k with index 1 has low details but of higher resolution than the base level with index 0, level w2,k contains details with higher resolution than level 2 but lower than these ones at level 3, etc.

Multiscale entropy concept is coming directly from Shannon’s information theory extended by the state-of-the-art ways of image decomposition [9]. It has been defined by:

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with h(wj,k) = -ln p(wj,k) where p is the probability of coefficient w existence, at the place of pixel k at scale j. Equation 1 defines the entropy summed over all scales of decomposed image data and is directly related to information content of the image.

After the multiscale representation of an image is prepared the mean entropy vector E(j) is calculated for each scale:

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This quantity allows for study the behavior of the information at a given scale, taking into account the image content.

3. RESULTS An example of the images obtained for two pairs of samples of breast tissue is shown on Figures 1 and 2.

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Fig. 1. The images for parallel (left) and crossed (right) polarizer and analyzer for the pair of physiological (up) and

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Fig. 2. The images for parallel (left) and crossed (right) polarizer and analyzer for the pair of physiological (up) and

malignant (down) breast tissue samples No 15038 .

Except of the physiological sample No 14856 with very strong birefringence, the both samples of 15038 pair and malignant from 14856 pair show rather weak birefringence.

3.1 Mueller Matrix

An example of the images corresponding to the Mueller matrix coefficients for the pair of breast sample tissue14856 are presented on Fig 3.

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Fig. 3. The examples of 3 by 3 subset of Mueller matrices for the pair of physiological (left) and malignant (right) breast

tissue samples No 14856 .

The significant difference on the images of M22 element is confirmed by the difference in higher order moments.

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The mean value of M22 image histogram is equal -0.029 and 0.243 for physiological and malignant tissue respectively and the kurtosis 1.484 and 0.422. For the 15038 pair of samples the values of mean value were 0.235 and 0.312 and of kurtosis 1.077 and 1.197 respectively, thus were not significantly different.

3.2 Autocorrelation

The example of autocorrelation function images for the pictures obtained for the 14856 pair of samples and crossed polarizers (left pair of Fig.1) is presented in Fig.. 4, and their horizontal and vertical cross-sections in Fig. 5.

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Fig. 1) for the pair of physiological (left) and malignant (right) breast tissue samples No 14856.

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obtained for the pair of physiological (solid) and malignant (dashed) breast tissue samples No 14856.

The Figure 5 suggest that the central peak of the autocorrelation function is much higher for physiological tissue. This can be expected from the fact that the health tissue from 14856 pair has much higher birefringence. For the 15038 pair of tissue samples the patterns on images of the polarization function differ slightly, but the cross-section for physiological and malignant tissues are undistinguishable.

3.3 Fourier transform

The example of the pair of the 2D Fourier transform maps is displayed on Fig. 6

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The corresponding radial power dependences are presented on Fig. 7.

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of physiological (solid) and malignant (broken) breast tissue samples No 14856 .

As before the only difference between the tissue images is the amplitude of the Fourier power at all frequencies what corresponds to the difference in amplitude of birefringent elements.

3.4 A trous decomposition and multiscale entropy

This data for the pair of samples of the breast tissue was decomposed by a trous algorithm, as shown on Fig. 8. The decomposed components were rescaled for publication, and their intensities differ from the real ones in magnitudes. They also resembles the collagen tissue orientation and density seen on particular scales. The rough qualitative estimation suggests the visible difference between tissues on almost all scales.

The third and fourth column of figures 5 and 6 shows the autocorrelation functions of the tissues shown in the two previous columns, the third for physiological case and the fourth for cancer case. Each row corresponds to particular scale, as explained in the figure caption.

Figure 9 presents the comparison of autocorrelation functions for scale j=3. 2D version of these functions is also shown in figure 8, the third row from the bottom. The shape of autocorrelation function remains similar for both, malignant and physiological samples. The most dominant effect is a significantly lower amplitude of the autocorrelation function in both, horizontal and vertical directions for malignant tissue.

It is seen, that the tissue has the tendency to gather into fibers directed along a particular lines in the case of malignancy while the tissue remains randomly oriented when it is physiological. The malignancy leads to large fields of low intensity pixels and groups of high intensity islands of pixels while in the physiological case the image pixels distribution remains more or less equally split between low and high intensity fields. These facts influence significantly the entropy or multiscale entropy of the image, what is further confirmed by analysis shown on Fig. 10 and is observed for the original images as well as their particular components.

The method applied does not distinguish any particular direction in the planes of the images. It seems that the malignancy in this case orients the tissue into the structure of fibers situated in a particular direction. This information may be extracted and included into an analysis. At the present study it is lost due to application of symmetric kernel based on B3-spline wavelet. This directional information may be recovered by different strategy based on application of asymmetric, orthogonal wavelets of any kind. This issue is under investigation and should significantly improve the construction of new observables for polarimetric analysis of physiological and malignant tissue.

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Fig. 8. The a trous decomposed images of the breast tissue samples. The left two columns is the physiological and cancer

tissue represented by its particular scale components, from j=0, lower scale, at the bottom, to j=6 the highest scale, at the top. The right two columns are corresponding autocorrelation functions for each scale, the third column is the physiological case and the fourth column is the cancer one..

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above plots illustrate the case for scale j=3. Horizontal slice across the centre of autocorrelation function is shown on top, and the vertical one at the bottom. Solid line is the physiological tissue and the dashed line represents the cancer case

Fig. 10 Comparison of mean entropy vectors of physiological (solid line) and cancer tissue (dashed line). The

entropy is calculated for each scale independently

4. CONCLUSIONS Taking into account the studies made for samples of different physiological and pathologically changed tissues from body and cervix of uterus, intestine, kidneys and breast, the conclusion can be made that the polarimetric method enables recognition of the malignant state of tissues. Quantification of the image parameters offers a potential for automatic fast evaluation of non-stained tissue section. However, it is hard to select a specific image analysis method working satisfactory for all tissues and cancers.

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Multiscale entropy analysis seems to be complementary method for comparison of autocorrelation functions. The multiscale decomposition facilitates the latter. Analysis of entropy may be a valuable direction in search for proper quantification method of observed collagen tissue changes due to a cancer.

5. ACKNOWLEDGMENTS The authors are indebted to A.G. Ushenko, O.V. Angelsky for fruitful discussions. This work was partially supported by the Polish Ministry of Science and Higher Education as research grant 3T11B 020 28

REFERENCES

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