Application of the Minkowski–Bouligand Fractal Dimension for the Differential Diagnosis of Thyroid Follicular Neoplasias

Application of the Minkowski–Bouligand fractal dimension for the differential diagnosis of thyroid follicular neoplasias To the Editor, Nuclear characteristics are important for the differential diagnosis between benign or malignant neo-plasias. Subjective interpretation by an observer, however , may cause diagnostic insecurity [5]. Quantitative morphologic analyses can be helpful in this situation [19]. There are several ways to perform karyometry, which may be done by Due to the fractal nature of chromatin organization in interphase nuclei [15], the scale-invariant self simil-iarity is an important texture feature, which can be estimated by the fractal dimension (FD) [1,3,9,13,31]. For the analysis of nuclear chromatin in routinely stained slides it has been suggested that besides the FD, the goodness-of-fit (GOF) of the regression line in the log-log plots, which are essential for the FD estimation, could be important [3]. In this investigation we tried to find out whether this new parameter GOF could also be useful for differential diagnosis in surgical pathology. We compared the FD and GOF of nuclear chromatin in routinely HE stained paraffin sections of follicular ade-nomas and minimally invasive follicular carcinomas of the thyroid. Our study consisted of 18 follicular adenomas and 24 microinvasive follicular carcinomas from our files. Tumors with a diameter up to 6 cm had been completely embedded in paraffin. For larger tumors the number of paraffin blocks taken had been d + 4 (d representing the largest diameter in cm). Diagnosis was based on criteria of the World Health Organization Histological Classification [18]. From each tumor 100 nuclei were randomly taken from routinely stained 5 µm HE stained paraffin sections using the Kontron Zeiss KS300 system (0.1 µm/pixel spatial resolution; 1.25 numerical aperture; 100× oil immersion objective) by one examiner blinded to the diagnosis. The images were converted to grayscale format with levels of luminance ranging between 0 (absence of light) and 255 (very bright). Then a pseudo-three-dimensional " landscape-like " representation was created using the gray level (luminance) of each pixel (picture element) as the height of a z-axis. The fractal dimension (FD) was determined according to Minkowski–Bouligand extended to three dimensions, as described earlier [3]. The linear regression was estimated in a log-log plot composed of 30 points. The goodness-of-fit (GOF) was determined by the R 2 value of the regression between the real and the estimated values. For each nucleus the distribution of the residuals was compared with the normal distribution by the …