The results of the fractal dimension, entropy and number of cell nuclei demonstrate that such analyses can contribute toward the diagnosis of prostate cancer. The fractal dimension analysis of the histological slides revealed that the highest median values at magnifications of 40x and 400x were obtained in the prostate tissue with benign hyperplasia, whereas the lowest values were obtained in normal tissue. Significant differences were found between the T and N groups at 40x and 100x as well as between the H and N groups at 40x at 400x. After utilizing the Bonferroni correction, the differences were significant at magnifications of 100x and 400x. Among the three magnifications studied, 100x differed in the T group, suggesting that this degree of magnification may be used in clinical practice. However, this magnification did not constitute satisfactory parameter for differentiating hyperplastic tumors.
These findings are in agreement with data described by Tambasco et al.,  who investigated the architectonic complexity of fragments from 63 patients with benign prostate tissue and 19 patients with high-grade carcinoma based on histological slides and found that the mean of the fractal dimension was higher in the group with high-grade carcinoma. In the present study, the three types of tissue analyzed (normal, benign hyperplastic and tumor) were from the same patient and same gland. Moreover, the tumors studied herein were selected randomly, with no knowledge on the histological grade.
Tambasco et al.  report 84.2 and 89.5% sensitivity and 82.5% and 90.5% specificity using hematoxylin-eosin (HE) and pan-keratin, respectively, in the comparison of benign prostate tissue and high-grade carcinoma. These differences may be due to the fact that pan-keratin is more specific for glandular tissue than HE, which was the technique used in the present study. Moreover, the authors cited only used high-grade carcinoma (Gleason 8 to 10). Investigating the detection of prostate cancer using ultrasound on seven patients, Moradi et al.  found a low degree of specificity (61.9%), suggesting that this diagnostic imaging method is not as specific as the results obtained with the processing of images of histological slides.
The present results suggest the possibility of using fractal dimension analysis in the diagnosis of prostate cancer, as exams such as the determination of PSA exhibit a low degree of specificity (25 and 33%), [10, 11] generating doubts regarding the actual need for a biopsy. According to Arruda & Arruda,  there are divergent opinions regarding the importance of the PSA exam in the diagnosis of prostate cancer, as this antigen does not offer all the characteristics of an ideal tumor marker.
Investigating the computerized detection of prostate cancer on T2-weighted magnetic resonance images with a combination between fractal and multifractal features to perform textural analysis of the image, Lopes et al.  found that method was more accurate than the classical texture based method.
Quantifying the complexity of the epithelial-conjunctive tissue interface of 377 normal, dysplastic and neoplastic human oral mucosae using digital images and applying the box-counting method to estimate the fractal dimension, Abu Eid & Landini  found significant differences been normal, pre-malignant and malignant tissues. The authors concluded that fractal geometry is useful in the evaluation alterations of the tissue complexity that occur due to malignant transformations and can be used as a quantitative marker of epithelial complexity.
Fractal geometry can also provide data to forge a consensus among pathologists on a relatively large amount of cases of diagnostic doubt, thereby minimizing variability regarding medical opinion. Moreover, this method can serve as a screening tool, identifying low-grade tumors and reducing the time pathologists spend on the study of areas of compromised tissue .
The results of the entropy analysis revealed the highest median value was obtained in the hyperplastic tissue at a magnification of 40x and in the tumor tissue at 100x and 400x. In the comparison between groups, significant differences were found between the T x N groups at 100x and 400x as well as between the T and H groups at 100x and 400x. However, after utilizing the Bonferroni correction the difference was only significant at 400x Thus, magnification at 400x differentiated tumor tissue from both normal tissue and hyperplastic tissue, indicating the possibility of using these degrees of magnification in the identification of prostate cancer.
As Shannon’s entropy quantifies the degree of complexity in information (as that contained in histological slides), there is a high probability of differentiating tumor tissue from normal tissue, indicating that this method could be useful in the diagnosis of prostate cancer. Yogesan et al.  carried out the only study in the literature on the diagnostic contribution of the calculation of entropy in nuclear images of cases of prostate cancer, demonstrating the possibility of using entropy analysis for differentiating cases of a good prognosis from those with a poor prognosis. Investigating the applicability of the calculation of Shannon’s entropy in the evaluation of the texture of images in normal and abnormal regions of digital mammograms, Pharwaha & Singh  concluded that this method is useful in the diagnosis of breast cancer.
The results of the analysis of cell nuclei revealed that the highest median values at all three magnifications occurred in tumor tissue. The paired comparison revealed significant differences between the T and N groups as well as between the T and H groups at all three magnifications. Thus, the three degrees of magnification differentiated tumor tissue from both normal and hyperplastic tissue, achieving a better performance than the fractal dimension and entropy analyses. The findings support the use of the analysis of cell nuclei at these different degrees of magnification in the diagnosis of prostate cancer. As the number of cell nuclei is higher with a greater degree of differentiation due to the physiopathologic mechanisms of tumor growth and tissue infiltration, this method can be used in the histological diagnosis and decisions regarding the best form of treatment.
No studies were found in the literature on the use of Shannon’s entropy and the analysis of cell nuclei in the diagnosis of prostate cancer. Considering the fact that this form of cancer has the second highest incidence among men,  fractal dimension analysis can contribute toward clarifying the histological diagnosis of prostate cancer based on biopsies used in the detection of this disease and the determination of the Gleason classification, as such information is often dubious and depends on the subjective opinion of the pathologist.