Benford's Law in histology

Digital pathology is an emerging field that is gaining popularity due to its numerous advantages over traditional pathology methods. Digital pathology allows for the remote examination of tissue samples, increasing efficiency and reducing costs. The field of digital pathology is experiencing a boom of data, creating space for new tools to be implemented that have not been used in pathology prior. Benford's Law is a statistical tool commonly used to analyze large datasets by other top organizations. Benford's Law is a law of frequency of first and second digits and whether they would appear normally in nature. With research in multiple fields of medicine moving into a digital era, tools that had once been used elsewhere to analyze digital images could translate well into pathology. Quantitative histomorphometry is a tool in digital pathology that analyzes digital images and collects morphological and histological data of whole-slide images, with more techniques being developed in digital pathology, such as deep learning, creating a more accurate 3D analysis of the cell. Easy and quick tools are needed to analyze the large datasets that are being extracted quickly. We believe that Benford's Law is a statistical outlook that can be easily implemented for similar use in whole-slide image analysis. When a system is disrupted by disease, it will distort the normal, natural growth of cells throughout the organ.

Open access tools such as QuPath have created a way to obtain categories of data to analyze, such as the size of a cell or the amount of staining it absorbs. Slides of normal liver cells were collected and compared to slides of a liver with cancer. The liver was selected because of its well-demarcated cytoplastic borders and nucleus. A total of 25 liver tissue slides were collected. The graph of naturalness is compared to analyze ways to detect variability between normal liver cells and cancer liver cells. 206,700 cells from 15 slides of 7 cancer patients' liver tissue samples (15 slides total) and 116,339 cells from 5 slides of normal liver tissue were collected, totaling 323,039 cells from 20 slides. Of the seven cancer patients, five were previously diagnosed with cholangiocarcinoma, and two were diagnosed with adenomas/adenocarcinoma.

The study found that of the 13 data categories provided by QuPath, such as cell size, nucleus size, and color absorbance, two met the Chi-square goodness of fit (χ²) criteria compared to Benford's Law of Naturalness, providing the most significant feedback. Due to QuPath's inability to distinguish all cytoplastic borders accurately, categories that depict size measurements were not used. Of the two categories that did correlate, such as those that used stain absorbance, 62.5% of slides that exceeded the critical value contained cells of someone diagnosed with cancer. In contrast, all normal slides showed a very low variance. All slides from a cancer patient showed a test statistic above 6 points, whereas the normal tissue slides showed a test statistic below 1.5, strongly correlating with Benford's Law.