Computational protocol: Fractal analysis of the structural complexity of the connective tissue in human carotid bodies

Similar protocols

Protocol publication

[…] All the image analysis procedures were performed by using the ImageJ software (Schneider et al., ), freely available at http://rsb.info.nih.gov/ij/. They can be summarized as follows. [...] The obtained gray-level and binary images illustrated in Figure , however, can also represent the input data for procedures aimed at estimating indices able to capture more detailed morphological features, such as a characterization of the overall shape of the patterns generated by connective tissue, and of the way it arranges itself in the tissue. In these respect, three methods were considered in the present study. They are briefly detailed in the sections that follow.Analysis of dispersion. To provide a quantitative evaluation of the dispersion in the tissue space of the binary pattern corresponding to connective tissue, Morisita's index (Morisita, ), one of the most robust distribution measures (Myers, ), was estimated. For this purpose, the binary image was divided into 12 sub-images and the number of pattern pixels in each sub-picture was evaluated. The index of dispersal (Id) was then calculated using Id=n(∑i=1nXi2−NN(N−1)) where n is the number of sub-images, whereas N and Xi represent the number of pattern pixels in the image, and in each sub-image, respectively. The index value increases with increasing spatial dispersion of the pattern.Gray level co-occurrence matrix analysis. Gray level co-occurrence matrix (GLCM) is a fast mathematical method for assessing image structural properties such as homogeneity, complexity, and level of disorder (see Pantic et al., ). It was first introduced by Haralick et al. () and is based on a quantitation of the relationship between pixel brightness values in an image. This information can be extracted from a matrix Pθ d(i,j) (GLCM) describing how frequently two pixels with gray level i and j appear in the image separated by a distance d in the direction θ (Aggarwal and Agrawal, ). Haralick et al. () described 14 parameters that can be calculated from the GLCM with the intent of describing the texture of an image. Today, however, those proven as the most useful in experimental and clinical medicine applications (see Losa and Castelli, ; Alvarenga et al., ; Pantic et al., ) are the following ones:            Entropy=−∑i∑jP(i,j)log(P(i,j))Angular second moment=∑i∑j[P(i,j)]2                     Variance=∑i∑j(1−μ)2P(i,j)              Correlation=∑i∑jijP(i,j)−μxμyσxσy where i and j are coordinates of the co-occurrence matrix, σ′s and μ′s represent means and standard deviations along rows and columns of the matrix. They were computed with ImageJ by using the “texture analysis” plugin, developed by Julio E. Cabrera and Toby C. Cornish, and freely available at http://rsbweb.nih.gov/ij/plugins/texture.html.Fractal analysis. To globally describe the complexity of form in quantitative terms the “Fractal dimension” (D) can be a valuable parameter (Guidolin et al., ). It measures the rate of addition of structural detail with increasing magnification, scale, or resolution (Cutting and Garvin, ). D of the binary skeleton (Figure ) was estimated using the “box counting” method at multiple origins as indicated by Smith et al. (). Briefly, from grids of increasing size overlying the image, the number of boxes containing any pixel was counted. This number was recorded as a function of grid size and D was calculated, as −1 times the slope of the regression line, from a plot of the log of size on the x-axis and the log of box count on the y-axis. To minimize grid location effects, the algorithm started from a number (10 in our case) of locations, generating a set of values for D. The average value over all locations was considered as the final estimate of D. During the same analytical process “Lacunarity” was also calculated. This parameter is a measure of the nonuniformity (heterogeneity) of structure or the degree of structural variance within an object (Smith et al., ). It was estimated as the average of the coefficient of variation for pixel density over all grid sizes and locations (Bassinghtwaighte et al., ).To perform the abovementioned analysis, the “FracLac for ImageJ” plugin by Audrey Karperien was used (freely available at http://rsb.info.nih.gov/ij/plugins/fraclac/fraclac.html). […]

Pipeline specifications

Software tools ImageJ, FracLac
Application Microscopic phenotype analysis
Organisms Homo sapiens