Open Access Research article

Quantification of fractal dimension and Shannon’s entropy in histological diagnosis of prostate cancer

Pedro Francisco Ferraz de Arruda16*, Márcio Gatti16, Fernando Nestor Facio Junior1, José Germano Ferraz de Arruda1, Roberto Douglas Moreira26, Luiz Otávio Murta35, Laísa Ferraz de Arruda4 and Moacir Fernandes de Godoy56

Author Affiliations

1 Faculdade de Medicina de São José do Rio Preto (FAMERP), Av. Brig. Faria Lima 5416, 15090-000, São José do Rio Preto, SP, Brazil

2 Disciplina de Cardiologia da FAMERP, São José do Rio Preto, Brazil

3 Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto da Universidade de São Paulo (FFCLRP-USP), Ribeirão Preto, Brazil

4 União das Faculdades dos Grandes Lagos (Unilago), São José do Rio Preto, Brazil

5 Departamento de Cardiologia e Cirurgia Cardiovascular da FAMERP, São José do Rio Preto, Brazil

6 Núcleo Transdisciplinar para Estudo do Caos e da Complexidade (NUTECC-CNPq), São José do Rio Preto, Brazil

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BMC Clinical Pathology 2013, 13:6  doi:10.1186/1472-6890-13-6

Published: 18 February 2013

Abstract

Background

Prostate cancer is a serious public health problem that affects quality of life and has a significant mortality rate. The aim of the present study was to quantify the fractal dimension and Shannon’s entropy in the histological diagnosis of prostate cancer.

Methods

Thirty-four patients with prostate cancer aged 50 to 75 years having been submitted to radical prostatectomy participated in the study. Histological slides of normal (N), hyperplastic (H) and tumor (T) areas of the prostate were digitally photographed with three different magnifications (40x, 100x and 400x) and analyzed. The fractal dimension (FD), Shannon’s entropy (SE) and number of cell nuclei (NCN) in these areas were compared.

Results

FD analysis demonstrated the following significant differences between groups: T vs. N and H vs. N groups (p < 0.05) at a magnification of 40x; T vs. N (p < 0.01) at 100x and H vs. N (p < 0.01) at 400x. SE analysis revealed the following significant differences groups: T vs. H and T vs. N (p < 0.05) at 100x; and T vs. H and T vs. N (p < 0.001) at 400x. NCN analysis demonstrated the following significant differences between groups: T vs. H and T vs. N (p < 0.05) at 40x; T vs. H and T vs. N (p < 0.0001) at 100x; and T vs. H and T vs. N (p < 0.01) at 400x.

Conclusions

The quantification of the FD and SE, together with the number of cell nuclei, has potential clinical applications in the histological diagnosis of prostate cancer.

Keywords:
Prostate cancer; Diagnosis; Fractal dimension; Shannon’s entropy