Histopathology is a well-established standard diagnosis employed for the majority of malignancies, including breast cancer. Nevertheless, despite training and standardization, it is considered operator-dependent and errors are still a concern. Fractal dimension analysis is a computational image processing technique that allows assessing the degree of complexity in patterns. We aimed here at providing a robust and easily attainable method for introducing computer-assisted techniques to histopathology laboratories. Slides from two databases were used: A) Breast Cancer Histopathological; and B) Grand Challenge on Breast Cancer Histology. Set A contained 2480 images from 24 patients with benign alterations, and 5429 images from 58 patients with breast cancer. Set B comprised 100 images of each type: normal tissue, benign alterations, in situ carcinoma, and invasive carcinoma. All images were analyzed with the FracLac algorithm in the ImageJ computational environment to yield the box count fractal dimension (Db) results. Images on set A on 40x magnification were statistically different (p = 0.0003), whereas images on 400x did not present differences in their means. On set B, the mean Db values presented promissing statistical differences when comparing. Normal and/or benign images to in situ and/or invasive carcinoma (all p < 0.0001). Interestingly, there was no difference when comparing normal tissue to benign alterations. These data corroborate with previous work in which fractal analysis allowed differentiating malignancies. Computer-aided diagnosis algorithms may beneficiate from using Db data; specific Db cut-off values may yield ~ 99% specificity in diagnosing breast cancer. Furthermore, the fact that it allows assessing tissue complexity, this tool may be used to understand the progression of the histological alterations in cancer.

中文翻译：

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分形维数分析作为一种简单的计算方法来改善乳腺癌组织病理学诊断


组织病理学是一种成熟的标准诊断，适用于包括乳腺癌在内的大多数恶性肿瘤。然而，尽管进行了培训和标准化，但它被认为依赖于操作员，并且错误仍然是一个问题。分形维数分析是一种计算图像处理技术，可以评估模式的复杂程度。我们的目标是提供一种稳健且易于实现的方法，将计算机辅助技术引入组织病理学实验室。使用来自两个数据库的载玻片：A)乳腺癌组织病理学； B) 乳腺癌组织学的重大挑战。 A 组包含来自 24 名良性病变患者的 2480 张图像，以及来自 58 名乳腺癌患者的 5429 张图像。 B 组包含每种类型 100 张图像：正常组织、良性改变、原位癌和浸润性癌。所有图像均在 ImageJ 计算环境中使用 FracLac 算法进行分析，以获得框计数分形维数 (Db) 结果。 A 组在 40 倍放大倍率下的图像存在统计差异 (p = 0.0003)，而在 400 倍放大倍率下的图像在平均值上没有差异。在 B 组上，比较时平均 Db 值呈现出令人鼓舞的统计差异。原位癌和/或浸润性癌的正常和/或良性图像（所有 p < 0.0001）。有趣的是，将正常组织与良性改变进行比较时没有差异。这些数据证实了之前的工作，其中分形分析可以区分恶性肿瘤。计算机辅助诊断算法可以受益于使用 Db 数据；特定的 Db 截止值可在诊断乳腺癌时产生约 99% 的特异性。 此外，由于它可以评估组织的复杂性，因此该工具可用于了解癌症组织学改变的进展。