Randall L. Adam

Fractal dimension of chromatin is an independent prognostic factor for survival in melanoma

BackgroundPrognostic factors in malignant melanoma are currently based on clinical data and morphologic examination. Other prognostic features, however, which are not yet used in daily practice, might add important information and thus improve prognosis, treatment, and survival. Therefore a search for new markers is desirable. Previous studies have demonstrated that fractal characteristics of nuclear chromatin are of prognostic importance in neoplasias. We have therefore investigated whether the fractal dimension of nuclear chromatin measured in routine histological preparations of malignant melanomas could be a prognostic factor for survival.MethodsWe examined 71 primary superficial spreading cutaneous melanoma specimens (thickness ≥ 1 mm) from patients with a minimum follow up of 5 years. Nuclear area, form factor and fractal dimension of chromatin texture were obtained from digitalized images of hematoxylin-eosin stained tissue micro array sections. Clarks level, tumor thickness and mitotic rate were also determined.ResultsThe median follow-up was 104 months. Tumor thickness, Clarks level, mitotic rate, nuclear area and fractal dimension were significant risk factors in univariate Cox regressions. In the multivariate Cox regression, stratified for the presence or absence of metastases at diagnosis, only the Clark level and fractal dimension of the nuclear chromatin were included as independent prognostic factors in the final regression model.ConclusionIn general, a more aggressive behaviour is usually found in genetically unstable neoplasias with a higher number of genetic or epigenetic changes, which on the other hand, provoke a more complex chromatin rearrangement. The increased nuclear fractal dimension found in the more aggressive melanomas is the mathematical equivalent of a higher complexity of the chromatin architecture. So, there is strong evidence that the fractal dimension of the nuclear chromatin texture is a new and promising variable in prognostic models of malignant melanomas.

Fractal Characteristics of May-Grünwald-Giemsa Stained Chromatin Are Independent Prognostic Factors for Survival in Multiple Myeloma

Background The use of computerized image analysis for the study of nuclear texture features has provided important prognostic information for several neoplasias. Recently fractal characteristics of the chromatin structure in routinely stained smears have shown to be independent prognostic factors in acute leukemia. In the present study we investigated the influence of the fractal dimension (FD) of chromatin on survival of patients with multiple myeloma. Methodology We analyzed 67 newly diagnosed patients from our Institution treated in the Brazilian Multiple Myeloma Study Group. Diagnostic work-up consisted of peripheral blood counts, bone marrow cytology, bone radiograms, serum biochemistry and cytogenetics. The International Staging System (ISS) was used. In every patient, at least 40 digital nuclear images from diagnostic May-Grünwald-Giemsa stained bone marrow smears were acquired and transformed into pseudo-3D images. FD was determined by the Minkowski-Bouligand method extended to three dimensions. Goodness-of-fit of FD was estimated by the R2 values in the log-log plots. The influence of diagnostic features on overall survival was analyzed in Cox regressions. Patients that underwent autologous bone marrow transplantation were censored at the day of transplantation. Principal Findings Median age was 56 years. According to ISS, 14% of the patients were stage I, 39% were stage II and 47% were stage III. Additional features of a bad prognosis were observed in 46% of the cases. When stratifying for ISS, both FD and its goodness-of-fit were significant prognostic factors in univariate analyses. Patients with higher FD values or lower goodness-of-fit showed a worse outcome. In the multivariate Cox-regression, FD, R2, and ISS stage entered the final model, which showed to be stable in a bootstrap resampling study. Conclusions Fractal characteristics of the chromatin texture in routine cytological preparations revealed relevant prognostic information in patients with multiple myeloma.

The Fractal Dimension of Nuclear Chromatin as a Prognostic Factor in Acute Precursor B Lymphoblastic Leukemia

The fractal nature of the DNA arrangement has been postulated to be a common feature of all cell nuclei. We investigated the prognostic importance of the fractal dimension (FD) of chromatin in blasts of patients with acute precursor B lymphoblastic leukemia (B-ALL). In 28 patients, gray scale transformed pseudo-3D images of 100 nuclei (May–Grünwald–Giemsa stained bone marrow smears) were analyzed. FD was determined by the Minkowski–Bouligand method extended to three dimensions. Goodness-of-fit of FD was estimated by the R2 values in the log-log plots. Whereas FD presented no prognostic relevance, patients with higher R2 values showed a prolonged survival. White blood cell count (WBC), age and mean fluorescence intensity of CD45 (MFICD45) were all unfavorable prognostic factors in univariate analyses. In a multivariate Cox-regression, R2, WBC, and MFICD45, entered the final model, which showed to be stable in a bootstrap resampling study. Blasts with lower R2 values, equivalent to accentuated “coarseness” of the chromatin pattern, which may reflect profound changes of the DNA methylation, indicated a poor prognosis. In conclusion the goodness-of-fit of the Minkowski–Bouligand dimension of chromatin can be regarded as a new and biologically relevant prognostic factor for patients with B-ALL.

Application of the Minkowski–Bouligand fractal dimension for the differential diagnosis of thyroid follicular neoplasias

Nuclear characteristics are important for the differential diagnosis between benign or malignant neoplasias. 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 basic morphometry [8,10,14, 16,17,21–24,28], or by sophisticated texture analysis based on digitalized images [2–7,11–13,20,25–27,29– 31]. Due to the fractal nature of chromatin organization in interphase nuclei [15], the scale-invariant self similiarity 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-offit (GOF) of the regression line in the loglog 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 adenomas 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 R2 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 Kolmogorov–Smirnov test. Then for each patient the percentage (P ) of cells with normally distributed residuals was calculated [3]. Group comparison was done by the Mann–Whitney test (WinStat software). Patients of both groups were of similar age with a mean for adenomas of 40.3 years (range 17–72 years) and a mean for minimally invasive carcinomas of 49.5 years (range 19 to 88 years; p > 0.05). The same was true for the tumor size (mean for adenomas: 3.6 cm, range 1.0–7.0 cm; mean for minimally invasive carcinomas: 3.4 cm, range 1.3 to 8.5 cm; p > 0.05). There was no statistically significant difference (p > 0.05) of the FD values between both groups: adenoma mean value 2.424 (range 2.347 to 2.505); minimally invasive carcinomas: 2.432 (range 2.339 to 2.499). The R2 values, however, were significantly different (p < 0.05), ranging between 0.922 and 0.953 (mean 0.939) in adenomas and between 0.929 and 0.952 (mean 0.943) in minimally invasive carcinomas. The percentage of cells with a Gaussian distribution of the residuals ranged from 58 to 97% (mean 79%) for adenomas and between 48 and 94% (mean 75%) for minimally invasive carcinomas. The fractal dimension is derived from the slope of the curve in a log–log-diagram, assuming that this

Remodeling of the human dermis after application of salicylate silanol

Recently, a controlled double-blind study in patients with photo-aged facial skin demonstrated the beneficial role of oral intake of silanol for skin, hair and nails. The aim of our pilot study was to investigate histologic alterations in human skin after injection of silanol. Seven healthy female caucasian volunteers with a moderate degree of photoaged skin received ten sessions of weekly injections of 0.1% salicylate silanol in the left ventral lateral forearm. The histologic features of punch biopsies of the treated area and the nontreated contralateral arm were compared and the collagen and elastic fibers quantified. Texture analysis was performed on digitalized microscopic images by analyzing the Sarkar fractal dimension or amplitudes (inertia values) after Fast Fourier transformation. The treated area revealed a statistically significant increase of the density of both collagen and elastic fibers. Texture analysis showed more compact and homogenously distributed collagen fibers after silicon injection. Our results suggest that the application of silicon may stimulate the production of collagen and elastic fibers leading to remodeling of the dermal fiber architecture, which may explain the improvement of the skin surface observed in clinical studies.

Chromatin Texture is Size Dependent in Follicular Adenomas But Not in Hyperplastic Nodules of the Thyroid

To the Editor In their interesting publication Arora et al. [1] postulate that benign thyroid nodules, such as follicular adenomas, particularly the Hurthle cell variant, but not hyperplastic nodules, might have malignant potential. Thus in the thyroid an adenoma–carcinoma sequence was postulated not only for Hurthle cell tumors [2] but also for follicular adenomas, much like that described in colon or salivary glands[3–5]. If this were the case, we would expect, in analogy to colon tumors [3], that (pre)-malignant transformations of nuclei would be more common and accentuated in larger follicular adenomas. Because epigenetic and genetic alterations related to patient prognosis may modify the chromatin texture in routine slides [3, 6–9], we tried to find out whether nuclear texture features would change with increasing size of follicular adenomas. For this purpose, we routinely reanalyzed hematoxylin & eosin-stained paraffin sections from a previous study based on the WHO Histological Classification of Tumors [10, 11]: 11 hyperplastic nodules, 18 follicular adenomas, and 24 microinvasive follicular carcinomas. Analyses were based on digitalized images of 100 randomly captured nuclei [6, 7, 9, 11–13]. We compared texture features derived from the gray value co-occurrence matrix [11–14] and the Minkowski fractal dimension [6, 11] between the three groups and then looked for correlations between texture features and the size of the nodules. Patients of all groups were of similar age with a mean of 46 years (range: 17–88 years; analysis of variance [ANOVA] p [ .0.10). The results are summarized in Table 1. Whereas the chromatin of the hyperplastic nodules is relatively homogeneous (local homogeneity) and ‘‘smooth’’ (angular second moment), its architecture in minimally invasive carcinomas is more complex (fractal dimension), with a more irregular (diagonal moment) and contrasted (entropy) chromatin arrangement. Nuclei of follicular adenomas showed intermediate texture features that were significantly correlated with the size of the nodules. In larger adenomas the entropy values (r = 0.626; p = 0.0054; Fig. 1), the fractal dimension (r = 0.482; p = 0.042; Fig. 2), and the diagonal moment (r = 0.59; p = 0.01) were increased, whereas the second angular moment (r = -0.603; p = 0.008), and local homogeneity (r = -0.627; p = 0.0053; Fig. 3) decreased. Thus the nuclear texture of smaller adenomas was more like that of hyperplastic nodules, and the chromatin of larger adenomas resembled more closely that of minimally invasive carcinomas. Nevertheless there were no significant correlations between texture and the size of hyperplastic nodules. Our results are comparable with the findings in colon tumors [3], where an increasing irregularity and loss of nuclear texture homogeneity during the adenoma–carcinoma progression was described and was supposed to be influenced by accumulated alterations in cancer-associated genes. By analogy, we believe that larger follicular adenomas might have suffered more genetic alterations than smaller ones, thus supporting the hypothesis of Arora et al. [1] positing an adenoma–carcinoma sequence for follicular K. Metze (&) R. C. Ferreira P. S. de Matos Department of Pathology, Faculty of Medicine, University of Campinas, P.O. Box 6111, 13083-887 Campinas, SP, Brazil e-mail: kmetze@fcm.unicamp.br

Shannon's entropy and fractal dimension provide an objective account of bone tissue organization during calvarial bone regeneration

The regeneration of compact bone involves the deposition of a poorly organized connective tissue template that remodels into compact lamellar bone. An objective description of this process is difficult because classical histomorphometry is unable to correctly characterize qualitative changes in tissue complexity. In this study, we demonstrated the use of two distinct methods of image texture analysis, the Shannons entropy [standard error (SE)], and the fractal dimension (FD) to characterize the formation and remodeling of newly formed compact bone within two different polyanionic collagen‐elastin matrices. The matrices were implanted in defects created into parietal bones of rats. The SE and FD were calculated for histological images of the experimental groups collected 3, 7, 15, 30, 60, and 365 days postsurgery and for the original bone only at day 365. Results showed that the SE and the FD initially increased and then diminished for all groups from day 3 to day 365 approaching the values of the original bone. These results are consistent with poor tissue organization during early osteogenesis that remodels into an organized lamellar structure, showing that these methods can be valuable tools to describe bone tissue remodeling during the regeneration process of compact bones. Microsc. Res. Tech., 2008.

Goodness-of-fit of the fractal dimension as a prognostic factor

One of the most important tasks in quantitative pathology is to elaborate methods which help to improve diagnosis [2,3,6,7,9,12,16,20] or prognosis [1,3–5,8–11,14,15,17,19,21]. In a previous investigation we found that the fractal dimension (based on the Minkowski–Bouligand method extended to three dimensions) of nuclear chromatin was not a prognostic factor in patients with acute precursor B lymphoblastic leukemia [1]. When looking at the log–log plots (area versus ε) containing 30 points used to calculate the regression line, we noticed that in most of the cases the real values were not located very closely to the calculated linear regression. This prompted us to investigate, whether the goodness-offit of the regression line could be of prognostic value. Therefore we calculated the coefficient of determination, i.e., the R2 value of the regression between the real and the estimated values on the y-axis. R2 characterizes the goodness-of-fit of the regression line and is therefore an estimate of the “quality of fractality”. It could be demonstrated that this goodness-of-fit is an independent prognostic factor for overall survival when applied to the chromatin texture of MGG-stained routine bone marrow smears of patients with acute precursor B lymphoblastic leukemia [1]. Furthermore, it could be shown that this variable is relatively robust against variations of the staining process [13]. We agree with the arguments of Prof. Albregtsen. Therefore we reanalyzed the data [1] in the following way: The fractal dimension (FD) was determined as described earlier: FD was estimated by the volume/2ε (being ε the radius, varying between 1 and 30 pixels) of the non-planar structuring element in form of a ball. The linear regression was calculated in a log–log plot (area versus ε) containing 30 points. The difference between the “real” y value and its corresponding “Ŷ ” on the regression line was called “res”. The square value of the correlation coefficient between “y” and “Ŷ ” was called R2 (the coefficient of determination). Now we calculated the sum of the square values of the 30 residuals per case “Sum res2”. In a second step we determined the perpendicular residuals “res p”, calculating in analogy the variable “Sum res p2”. In a third step the above mentioned point distribution was rotated so that the slope was at 45 degrees and then we calculated the coefficient of determination between “y” and “Ŷ ”, now called “R2 45”. Finally the prognostic relevance of all these parameters was analyzed in univariate and multivariate Cox regressions (p = 0.05 for input and p = 0.1 for output, backward conditional step-wise selection), comparing them with established prognostic factors such as age, white blood cell count and MFI of CD45 (MFICD45). Each of the new values entered as the mean value of 100 nuclei per case. “Sum res2” was highly correlated with R2 (r = 0.99; p < 0.0001), and also “Sum res p2” with “R2 45” (r = 0.99; p < 0.0001). In a linear multivariate regression R2 could be calculated from the sum of the square values of perpendicular residuals, “Sum res2” and the slope of the fractal dimension. The coefficient of determination between R2 and the slope was 0.337, and between R2 and “Sum res p2” it was 0.974. In a multivariate linear regression both slope and “Sum res p2” entered the regression as independent significant variables the regression and together explained 99.1% of the variance of R2. When combining slope and “R2 45” in a multivariate linear regression, its coefficient of determination reached 0.9996. Thus in our data set the influence of the slope (fractal dimension) on R2 is very small. When recalculating the prognostic relevance regarding survival, in the univariate Cox-regressions, R2 (p = 0.049), “R2 45” (p = 0.05), “Sum res2” (p = 0.047) and “Sum res p2” (p = 0.048) were all significant prognostic factors. In the multivariate Cox regression, when tested together with well known prognostic factors, the final model was composed of “R2 45”, white blood cell count and MFICD45, whereas “Sum res p2” and age had been eliminated. These results, obtained with an improved methodology, indicate that the “goodness-of-fit” of the regression line may be an interesting new variable for

Robust variables in texture analysis

Sir,In his interesting review article in Pathology, Tadrous1 comments on the use of the term ‘objective’ and addresses several technical and conceptual problems in image analysis. We totally agree ...

Pathophysiology of Cancer and the Entropy Concept

Entropy may be seen both from the point of view of thermodynamics and from the information theory, as an expression of system heterogeneity. Entropy, a system-specific entity, measures the distance between the present and the predictable end-stage of a biological system. It is based upon statistics of internal characteristics of the system. A living organism maintains its low entropy and reduces the entropy level of its environment due to communication between the system and its environment. Carcinogenesis is characterized by accumulating genomic mutations and is related to a loss of internal cellular information. The dynamics of this process can be investigated with the help of information theory. It has been suggested that tumor cells might regress to a state of minimum information during carcinogenesis and that information dynamics are integrally related to tumor development and growth. The great variety of chromosomal aberrations in solid tumors has limited its use as a variable to measure tumor aggressiveness or to predict prognosis. The introduction of Shannon’s entropy to express karyotypic diversity and uncertainty associated to sample distribution has overcome this problem. During carcinogenesis, mutations of the genome and epigenetic alterations (e.g. changes in methylation or protein composition) occur, which reduce the information content by increasing the randomness and raising the spatial entropy inside the nucleus. Therefore, we would expect a raise of entropy of nuclear chromatin in cytological or histological preparations with increasing malignancy of a tumor. In this case, entropy is calculated based on the co-occurrence matrix or the histogram of gray values of digitalized images. Studies from different laboratories based on various types of tumors demonstrated that entropy derived variables describing chromatin texture are independent prognostic features. Increasing entropy values are associated with a shorter survival. In summary, the entropy concept helped us to create in a parsimonious way a theoretical model of carcinogenesis, as well as prognostic models regarding survival.