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Decoding Breast Cancer in X-ray Mammograms: A Multi-Parameter Approach Using Fractals, Multifractals, and Structural
Santanu Maity1, Mousa Alrubayan1, Prabhakar Pradhan1
1Department of Physics and Astronomy, Mississippi State University, Mississippi State, MS, USA, 39762.
Arxiv
|June 10, 2025
Summary
Quantitative fractal analysis of breast mammograms reveals novel biomarkers for cancer progression. These methods, including fractal-functional distributions and intensity threshold variations, effectively distinguish benign from cancerous tissues, improving diagnostic accuracy.
Area of Science:
- Biomedical Engineering
- Medical Imaging Analysis
- Quantitative Pathology
Background:
- Breast cancer detection relies on accurate tissue characterization.
- Traditional imaging biomarkers may lack sensitivity for early-stage disease.
- Quantitative analysis of microstructural complexity offers potential for improved diagnostics.
Purpose of the Study:
- To explore fractal and multifractal characteristics of breast mammogram micrographs for breast cancer progression biomarkers.
- To investigate the utility of a novel fractal-functional distribution method for statistical robustness.
- To identify novel indicators of disease progression using intensity threshold variations in fractal dimension calculations.
Main Methods:
- Conventional fractal and multifractal analyses of mammogram micrographs.
- Application of a fractal-functional distribution method for Gaussian transformation of fractal measures.
- Analysis of intensity threshold variations for fractal dimension calculations.
- Quantification of microscopic structural disorder using the Inverse Participation Ratio (IPR) light localization technique.
Main Results:
- Fractal, multifractal, and fractal-functional parameters demonstrated effectiveness in differentiating benign from cancerous breast tissue.
- Intensity-based fractal measures exhibited unique, threshold-dependent patterns in cancer cases, indicating potential as novel biomarkers.
- The Inverse Participation Ratio (IPR) successfully quantified structural disorder at the microscopic level.
Conclusions:
- A multi-parametric approach integrating spatial complexity and structural disorder metrics shows promise for enhancing breast cancer detection.
- Novel quantitative biomarkers derived from fractal analysis and intensity variations can improve diagnostic sensitivity and specificity.
- The fractal-functional distribution method offers a more robust statistical interpretation of fractal measures in mammography.
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