1.

Introduction

The single cell gel electrophoresis (SCGE) assay has been successfully applied for genotoxic evaluation of many physical and chemical agents, such as ultraviolet-radiation,¹ x rays, H ₂ O ₂, acrilamide,² oxidative stress in bovine embryo,³ spermatic deoxyribonucleic acid (DNA) integrity,^{4 5} and biocompatibility of biomaterials.⁶

The electrophoresis releases the segments of the broken strand of the damaged DNA in the surroundings outside of the cell. So, the appearance of the damaged DNA becomes similar to the tail of a comet, whose head is the nucleus of each single cell. By analyzing the microscope images, quantitative descriptors can be determined, which deal with the measurement of the local concentration of DNA molecules. Such a measurement is useful for clastogenicity diagnostic.

At the beginning, manual estimation of the comet features was attempted.⁷ However, the time dependence of the fluorescence strongly limits the procedures respective to the reproducibility of the measurements and the error estimation. Very fast semiautomatic methods^{8 9} that involve digital image acquisition and storing^{10 11 12} overcome this limitation. Image processing routines for both real time and a posteriori analysis (i.e., image segmentation, determination of Euclidean distances, and centers of mass) has been implemented. Nevertheless, many of them can only provide low-order quantitative descriptors.

Distinguishing between the head and the tail on the image of the comet cell is crucial for an accurate quantitative estimation of their geometrical features.¹³ Although high order moments of the light distribution of the comet image can be used to perform it, they are not effective in all cases, because their interpretation is usually very hard.

In this paper we will show that associated density functions and centered reduced moments provide high-order quantitative descriptors with well-defined geometric interpretations for both the head and the tail of the comet cells. Specifically, null, first and second order associated density functions were used for enhancing specific areas of the considered segment of the cell. Position of the centers of mass of such areas, length, and orientation of their semiaxes and their content of light intensity could be accurately determined from the centered reduced moments up to the sixth order.

So, these descriptors of the image intensity distribution can properly characterize the comet cells, and allow determining the DNA concentration by applying suitable proportionality rules.

2.

Comet Cell Images Preprocessing

The images were obtained in a previous study designed to estimate the clastogenicity in vitro. The alkaline protocol for the SCGE assay, described by Singh etal.,¹⁴ was applied on coatings of hybrid layers obtained by sol-gel containing glass, glass-ceramic, and HA particles on stainless steel AISI 304 in peripherical blood mononuclear cells.¹⁵ Microscope images of comet cell were recorded by a conventional eight-bit charge coupled device (CCD) camera (i.e., 256 gray levels) attached at the epifluorescense optical microscope [Fig. 1(a)]. So, each image will be an array of N× M pixels, which can be represented by an N× M matrix of positive whole numbers, from 0 for black to 255 for white.

Figure 1

(a) Image of a comet cell acquired by a conventional CCD camera. (b) Gray-level histogram of this image. The vertical line points out the threshold value for noise suppression. (c) The same image after background noise suppression. (d) The gray-level histogram of the image after background noise suppression. (e) Head and tail of a comet cell in after the image segmentation. (f), (g) Associated density function (i=0,1,2) for the head and the tail of the comet cell. (h) Morphological descriptors of the head and the tail of the comet cell, the first ellipse inside together with its center is corresponding to V₀(u,v), the second one to V₁(u,v), and the third one to V₂(u,v), with u as the horizontal coordinate and v as the vertical coordinate. (i), (j), (k) Showed cells with different states of cleavage of DNA and their respective morphological descriptors. Normal, softly, and strongly DNA damaged. (k) Image was reduced 1/3 the used scale in images (i) and (j).

This matrix contains the information of the comet cell image superimposed onto a background of fluctuating low intensity values named background noise, which is mainly due to the dark currents in the CCD sensor.¹⁰ This noise must be suppressed for accurately determining the high order moments of the image, because it strongly influences such moments. In fact, the higher the moment order the greater the significance of the noise values.⁸

In most cases, the values of the background noise are uniformly distributed onto the region of gray levels below the gray levels of the comet cell image. This region can be identified on the gray-level histogram as reported previously,^{10 16 17 18} so that its highest gray level can be used as a suitable threshold for background noise suppression [Fig. 1(b)].

The image gray levels under this threshold are set to null and those equal or greater than the threshold will remain unchanged. Thereafter, the threshold value will be subtracted from the unchanged image values to perform an offset reset.^{10 17} The result is an image similar to that in Fig. 1(c), whose gray-level histogram is shown in Fig. 1(d).

Then, the comet image can be segmented into head and tail by applying a further threshold. Comet images show that the gray levels of the tail are not higher than the gray levels of the head. This means that the gray level corresponding to the main maximum of the gray-level histogram of the image provides the suitable threshold for segmentation, i.e., gray levels below it will correspond to the tail and those equal or greater than it will conform the head.

Thus, the head can be isolated by setting to null the gray levels greater than or equal to the threshold and applying the corresponding offset reset. The tail is isolated by setting to null the gray levels lower than the threshold and resetting the offset.

3.

Centered Reduced Moments and Associated Density Functions

An image recorded by the CCD camera is numerically represented as a matrix of N× M elements with values 0⩽f(n,m)⩽255. (n,m) are pairs of whole numbers that label the pixel addresses, i.e., 0⩽n⩽N−1 and 0⩽m⩽M−1. Let us introduce the function V₀(u,v)=f(u,v)/‖f‖, with u=n−〈n〉 and v=m−〈m〉 called the centered coordinates, because 〈n〉=(1/‖f‖)∑_n=0 ^N−1∑_m=0 ^M−1nf(n,m) and 〈m〉=(1/‖f‖)∑_n=0 ^N−1∑_m=0 ^M−1mf(n,m) denote the position of the center of mass of the image, and ‖f‖=∑_n=0 ^N−1∑_m=0 ^M−1f(n,m) is the image energy content.

Thus, V₀(u,v) exhibits the properties of the discrete density functions,^{10 17} i.e., V₀(u,v)⩾0, ∑_u=−U ^U∑_v=−V ^VV₀(u,v)=1 and V₀(u,v)→0 for (u,v) far away from the coordinate origin. Then, let us introduce its centered reduced moments ^{10 15} as follows:

Low-order centered reduced moments provide a quantitative estimation of specific geometrical features of the image. Indeed, Eq. (1) yields μ₀₀ ⁽⁰⁾=1 and μ₀₁ ⁽⁰⁾=μ₁₀ ⁽⁰⁾=0 which denote the normalization of V₀(u,v) and the position of its center of mass at the coordinate origin. The centered reduced moments of second order μ₀₂ ⁽⁰⁾, μ₁₁ ⁽⁰⁾, μ₂₀ ⁽⁰⁾ determine an ellipse of area A₀ that encloses the main intensity values of the image (Fig. 2). If μ₁₁ ⁽⁰⁾≠0 the semiaxis of the ellipse will be rotated with respect to the coordinate axis by an angle ${\varphi }_0=\frac{1}{2}\text{arctan}\left[2{\mu }_{11}^{\left(0\right)}/\left({\mu }_{20}^{\left(0\right)}-{\mu }_{02}^{\left(0\right)}\right)\right]$ After the rotation of V₀(u,v) by −ϕ₀, the semiaxis of the ellipse will be parallel to the coordinate axis and the centered reduced moments of second order will have new values [η₀₂ ⁽⁰⁾,0,η₂₀ ⁽⁰⁾].

Figure 2

(a) V₀(u,v) of an isolated cell nucleus in reduced coordinates. (b) Ellipse (shadowed area) determined by μ₀₂ ⁽⁰⁾, μ₁₁ ⁽⁰⁾, μ₂₀ ⁽⁰⁾.

Then, $a_0=\sqrt{{\eta }_{20}^{\left(0\right)}}$ and $b_0=\sqrt{{\eta }_{02}^{\left(0\right)}}$ will denote the lengths of the semiaxes of V₀(u,v). Assuming η₀₂ ⁽⁰⁾⩾η₂₀ ⁽⁰⁾, i.e., b₀⩾a₀, the eccentricity of the ellipse will be given by $E_0=\sqrt{1-{\left(a_0/b_0\right)}^2}=\sqrt{1-{\eta }_{20}^{\left(0\right)}/{\eta }_{02}^{\left(0\right)},}$ so that 0⩽E₀⩽1. The condition η₀₂ ⁽⁰⁾=η₂₀ ⁽⁰⁾ implies a₀=b₀ and E₀=0. Consequently, V₀(u,v) will be circular symmetric, i.e., η₀₂ ⁽⁰⁾=η₂₀ ⁽⁰⁾=μ₀₂ ⁽⁰⁾=μ₂₀ ⁽⁰⁾ and η₁₁ ⁽⁰⁾=μ₁₁ ⁽⁰⁾=0. In practical applications V₀(u,v) can be regarded as circular symmetric if the condition a₀⩾0.9b₀ holds, i.e., E₀⩽0.4359. On the other hand, E₀=1 is obtained if η₂₀ ⁽⁰⁾=0. It means that the rotated V₀(u,v) is concentrated along a straight-line parallel to the v axis, because a₀=0.

Furthermore, the fraction of the image energy enclosed by the ellipse is given by E ₀=∑_(u,v)∈A0 V₀(u,v). It is customary to perform further analysis based on higher order moments if E ₀⩽0.8. ^{10 17 18} However, geometric descriptors based on higher order moments are not straightforwardly defined at all.

To overcome this limitation, we define the associated density functions ^{10 15} as

Figure 3

(a) Profiles of (u/U)²+(v/V)² and [(u/U)²+(v/V)²]² for v=0. (b) V₁(u,v) and (c) V₂(u,v) associated to the isolated cell nucleus in Fig. 2.

Table 1

It is well known that all the odd order moments of V₀(u,v) are equal to null if the image is symmetric with respect to the coordinates origin.^{17 18} Therefore, the centers of mass of V₀(u,v), V₁(u,v), and V₂(u,v) will coincide in this case, i.e., μ₀₁ ⁽¹⁾=μ₁₀ ⁽¹⁾=μ₀₁ ⁽²⁾=μ₁₀ ⁽²⁾=0. Otherwise, the image asymmetries with respect to the coordinate origin can be estimated by the vectors

The length and orientation of the semiaxes and the eccentricities of the associated density functions are determined from their second order centered reduced moments. For V₁(u,v) these moments are given by

They can also take the values null and one. By example, for μ₀₂ ⁽¹⁾ we obtain A₀₂=1 and all the reminded A_nm are equal to null, whereas A₂₀=1 and all the reminded A_nm are equal to null for μ₂₀ ⁽¹⁾. But for μ₁₁ ⁽¹⁾, the coefficients A_0,m>0, A_n>0,0, and A₁₁ will be different from both null and one. All the reminded ones will be equal to null. A similar analysis can be performed in Eq. (4b). On the other hand, note that the second terms on the right side of Eqs. (4a) and (4b) depend on powers of the centered reduced moments of first order of V₁(u,v) and V₂(u,v), respectively, i.e., the coordinates of the corresponding centers of mass. Thus, these terms do not appear if the associated density functions are symmetric with respect to the origin of coordinates because μ₀₁ ⁽ⁱ⁾=μ₁₀ ⁽ⁱ⁾=0 in these cases. Consequently, Eqs. (4a) and (4b) yield the expressions in Table 1 for the second order centered reduced moments of symmetric associated density functions.

The centered reduced moments μ₀₂ ⁽ⁱ⁾, μ₁₁ ⁽ⁱ⁾, and μ₂₀ ⁽ⁱ⁾ ( i=0,1,2) determine an ellipse of area A_i, centered at the center of mass of V_i(u,v), that encloses the main values of the corresponding associated density function. The semiaxes of such ellipses will be rotated respective to the coordinate axes by angles ${\varphi }_i=\frac{1}{2}\text{arctan}\left\{2{\mu }_{11}^{\left(i\right)}/\left[{\mu }_{20}^{\left(i\right)}-{\mu }_{02}^{\left(i\right)}\right]\right\}.$ Then, a rotation of the corresponding associated density function by −ϕ_i will set their semiaxes parallel to the coordinate axes, allowing an accurate determination of their lengths and the eccentricity of the associated density function. After such rotations, the second order centered reduced moments of the associated density functions will take new values [η₀₂ ⁽ⁱ⁾,0,η₂₀ ⁽ⁱ⁾]. Thus, the lengths of the semiaxes and the eccentricities of the ellipses will be given by

Now, the fraction of the energy content of the image enclosed by each ellipse is given by

In summary, associated density functions allow an accurate geometrical characterization of images based on centered reduced moments of high orders and on the few descriptors they determine (i.e., position of their centers of mass, lengths, and orientations of their semiaxis and their eccentricity).

Centered reduced moments of a specific order are related to a specific associated density function, so that the segments of the image they determine will be separately characterized. The enclosed energy fraction provides a criterion to establish the highest order required to perform an effective analysis.

4.

Results

To illustrate the earlier procedure, let us consider the comet cell image in Fig. 1, which was split into head and tail. The electrophoresis device was prepared in such a way that the uniform electrical field was applied parallel to the coordinate axis u (horizontal axis in the images), and therefore orthogonal to the v axis (vertical axis in the images).

Table 2 shows the centered reduced moments μ_pq ⁽⁰⁾ up to the fourth order for the head and the tail, respectively. The convergence of the moments is apparent in both cases, i.e., their values significantly decrease when the order increases. It means that the information we are looking for can be exhaustively provided by a finite and small number of centered reduced moments. Fourth order moments of the head are essentially equal to null because the corresponding coefficients (u/U)^p(v/V)^q, for p+ q=4, screen the relevant information of the head.

Table 2

Table 3 shows the morphological descriptors of such comet cell, which are represented by the central points and the ellipses in Figs. 1(i), 1(j), and 1(k). As expected, the displacement of the centers of mass along the direction of the applied electrical field in the strongly affected cell is more significantly than along the v axis (vertical axis). However, these displacements are shorter in the cell head as in the cell tail. It means that DNA molecules remain concentrated around the nucleus in head, but they are nonsymmetrically distributed onto an extended region in the tail. In addition, the eccentricity is smaller than 0.24 for the head and greater than that for the tail. Therefore, the head essentially exhibits circular symmetry, but the tail distributes onto an elliptical region as confirmed by the lengths of the semiaxes. Indeed, the horizontal semiaxis of the tail is bigger than the vertical one because of the orientation of the electrical field. Furthermore, the percent of the energy content corresponding to the above descriptors were greater than 81.27% of the total energy of the respective images. It allows us to state that such descriptors accurately characterize the cell features of interest.

Table 3

Cells with nondamaged DNA [Fig. 1(i)] are circular symmetric at all, so that the associated density functions of the cell nucleus yield concentric circles. As the analysis for the tail is performed, a small ellipse is generated. However, its center of mass is practically located at the nucleus membrane, its minor semiaxis is parallel to the electrical field direction, its length will be significantly smaller than the nucleus radius, and its major semiaxis will be also smaller than the nucleus radius but orthogonal to the electrical field direction. Therefore the structure identified by the tail analysis will be in fact a halo around the cell but not a comet tail. This analysis is confirmed by the corresponding numerical results in Table 3.

Cells with softly affected DNA [Fig. 1(j)] remains circular symmetric, but the centers of mass of its associated density functions will be displaced to each other. The major semiaxis of the tail ellipse remains orthogonal to the electric field direction but its length is now comparable to the nucleus diameter. Furthermore, the center of mass of this ellipse lies at a certain distance of the nucleus membrane. That means that DNA molecules migrate outside the cell through the membrane, although a significant concentration of DNA even remains inside the cell. Thus, the cell exhibits a relative small comet tail.

To compare the performance of the proposed method [centered reduced moments and associated density functions (CRM&ADF)] with a conventional procedure, we have applied the “comet score” free software (CSS) to the same comet cells in Figs. 1(i), 1(j), and 1(k). The noise threshold was fixed at 0.94 and the magnification was calibrated by means of the micrometric grid of a hemocytometer.

Table 4 shows the percent differences between the results given by two methods (CSS and CRM&ADF). The values of the comet heights are close similar. Probably, the small absolutes differences (<8.7%) are related to the threshold value chosen by the user of the CSS.

Table 4

Bigger differences were obtained in the estimation of the head area in Figs. 1(i) and 1(j). They can be attributed to the better processing of diffuse borders of CRM&ADF method. Indeed, other methods usually consider the concept of “extent head” in the analysis of the cell head, which neglect the values close to the diffuse borders. A similar reason explains the differences in the estimation of the tail length. However, the tail areas estimated by CRM&ADF method are not determined by the pixels of the tails in the images, but by mathematical ellipses determined by the tail descriptors. Therefore their values are greater than the size of the regions occupied by the pixels.

5.

Conclusion

Image processing based on centered reduced moments and associated density functions constitutes an effective tool for quantitative characterization of comet cells from SCGE assay. It could be separately applied to the nucleus and the tail of the comet and also perform a global evaluation of the cell. By using relative simple software, exhaustive evaluation is performed by calculating high order moments.