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Benford's Law in histology.

Jasmine Caballero1, Daniel Gonzalez2, Dustin La Fleur3

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|July 24, 2025
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Summary

Benford's Law can detect cancer in digital pathology slides by analyzing cell staining patterns. This statistical tool shows significant differences between normal and cancerous liver cells, aiding in disease detection.

Keywords:
Benford's LawCancerCell analysisChi-square goodness of fitDeep learningHealthy individualsHematoxylin OD maxImage varianceMachine learningNaturalnessPathological assesQuantitative histomorphometryTissue analysisWhole-slide imaging

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Area of Science:

  • Digital pathology
  • Computational pathology
  • Statistical analysis in medicine

Background:

  • Digital pathology offers advantages over traditional methods, enabling remote analysis and cost reduction.
  • The increasing volume of data in digital pathology necessitates novel analytical tools.
  • Benford's Law, a statistical tool for analyzing first and second digit frequencies, has potential applications in digital pathology.

Purpose of the Study:

  • To investigate the applicability of Benford's Law for analyzing whole-slide images in digital pathology.
  • To determine if Benford's Law can differentiate between normal and cancerous liver tissue based on quantitative histomorphometry data.
  • To assess the utility of Benford's Law in identifying disruptions in cellular growth patterns caused by disease.

Main Methods:

  • Quantitative histomorphometry was performed on whole-slide images of liver tissue using QuPath software.
  • Data from 323,039 cells (20 slides: 15 cancer, 5 normal) were analyzed.
  • Benford's Law of Naturalness was applied to 13 data categories, with a focus on stain absorbance and size measurements, comparing results against a Chi-square goodness of fit test.

Main Results:

  • Two data categories, specifically those related to stain absorbance, met the Chi-square goodness of fit criteria for Benford's Law.
  • Slides with stain absorbance data exceeding the critical value were associated with cancer in 62.5% of cases.
  • Cancerous liver tissue showed a test statistic above 6, while normal tissue exhibited a statistic below 1.5, indicating strong correlation with Benford's Law.

Conclusions:

  • Benford's Law can serve as an effective statistical tool for analyzing digital pathology data, particularly for detecting anomalies in cellular characteristics like stain absorbance.
  • The distinct statistical signatures observed between normal and cancerous liver tissues when analyzed with Benford's Law suggest its potential for automated cancer detection in digital pathology.
  • Further research into Benford's Law applications can enhance the efficiency and accuracy of disease detection in the rapidly growing field of digital pathology.