Глушен С.В. Белорусский государственный университет кафедра генетики. Цитометрия опухолей. Significance of cytometry for the investigation of tumors.
Белорусский государственный университет
Significance of cytometry for the investigation of tumors
At high power of microscope it is seen that the adenoma possess small heterogeneity caused by proliferation. Being limited in number of cell divisions adenomas of the thyroid have not a great potency to permanent growth and acquisition of malignancy.
There are the number of differences between cells of adenoma and carcinoma of the thyroid. Apart from enlarged size and irregular shape of some nuclei it is clear seen that the adenoma has got abnormality of chromatin. Light zones - “watch-glasses” appeared in separate cells.
Representation of digital image of cell nucleus as a three dimentional surface
A digital image of cell nucleus may be considered the surface with coordinates X, Y and Brightness instead of Z. In this case the problem to create invariant in some sense “numerical portrait” of a nucleus brings about quantitative evaluations of the pseudosurface.
Quantification of 3d-surface by isophotes dimentional surface
One of possible ways to estimate
roughness of 3d-surface of cell
nucleus image (A) is to draw on it
lines with equal brightness -
isophotes (B). The following
calculation of total length of
isophotes on preset level of
brightness will be a quantitative
descriptor of chromatin structure detected at this level of brightness. Changing level of brightness from zero to maximum we shall get the nonlinear curve that describes a distribution of chromatin in cell nucleus (C).
Fractal area profile of cell nucleus dimentional surface
If isophotes are drawn at every level of brightness they correspond to sums of perimeters of intranuclear structures.
The dependence between total length of perimeters and image brightness named by us as "Fractal Area Profile" (FAP). FAP has the maximum (B) that divides it into two parts. The left part (A - B) reflects distribution of heterochromatin and the right one (B - C) describes distribution of euchromatin. Shapes of FAPs may differ amongst cells of thyroid tumors and correlate with morphological alterations of cell nuclei.
Relative fractal areas of cell nuclei dimentional surface of thyroid tumors
To statistical analysis of thyroid tumors a FAP was fragmented using its derivatives into separate squares - fractal areas of heterochromatin grains (1) and ties (2), euchromatin transitions (3) and spots (4) , diffuse component (5), total heterochromatin (6), and total euchromatin (7). Dividing these parameters by total fractal area of nucleus we shall get the set of relative fractal areas (RFA). Statistical
estimation of 20 FNAB’s specimens by RFA revealed significant differences of almost all of the parameters between follicular adenoma and papillary carcinoma of the thyroid.
Relative fractal dimentional surface areas of nucleiin thyroid tumor cell lines
We invesigated also RFAs of nuclei in three cell cultures of thyroid tumors: HDC - high differentiated cancer, LDC - low differentiated cancer and AnaC - anaplastic cancer. It is clear some changes of chromatin structures in cell lines with different levels of malignity.
Segmentation of image of cell nucleus dimentional surface on the basis of its fractal area profile
Besides the application of FAP for evaluation of morphology of cancer cells this curve may be used for segmentation of its images into components. This method is based on ability of FAP to display transitions of brightness in chromatin pattern. Using this method images of adenoma and cancer cell nuclei (Ad and Cr) may be segmented into 3 parts: full nucleus (blue), intermediate heterochromatin (green), dark heterochromatin (yellow).
Influence of optical resolution dimentional surface on fractal area profile
Optical resolution is the main characteristics of any image analysis system. It may be measured after Fast Fourie Transform of digital images to frequency domain. Optical distortions may be corrected by deconvolution of images with point spread function of microscope. It is clear that high optical resolution increases fractal area of cell nucleus and height of its FAP. In such the manner fractal nature of FAP is manifested.
Similarity of fractal area profile dimentional surface and histogram of brightness
There is the obvious similarity of fractal area profile of cell nucleus and its histogram of brightness (blue). This similarity is displayed in shape of these curves but their absolute values are still quite different. For images of cell nuclei absolute values of fractal area profiles are significantly higher in comparison with the histograms of brightness. It may be shown yet there are some transformations of images that it is not true for.
Randomized images of cell nuclei dimentional surface
One of these transformations is the randomization of pixels within an area occupated by picture of cell nucleus. The algorithm of randomization applied here accomplishes twin permutations of pixels all over that area. As a result the image preserves information only about size, shape and optical density of nucleus. It is important to point out that the histogram of brightness does not changed. However these randomized images have not any information about inner structure of cell nucleus.
Difference between fractal area profile dimentional surface and histogram of brightness
In spite of the invariability of histogram of brightness fractal area profile of randomized images alters drastically. This takes place due to principal differencies between histogram of brightness and fractal area profile. Randomly distributed permutations of pixels do not affect the first oder statistics of image but disturb some other properties. Among them there is a connectivity of chromatin structures that may be determined through the notion of “frontier”. Since FAP counts just pixels of frontiers it must contain topological information.
Conclusions dimentional surface