A Homology-Based Application to Diagnose Colorectal Adenoma and Early-Stage Cancer

Homology is a mathematical concept involving two Betti numbers-b₀, representing the number of independent objects, and b₁, representing the number of holes formed by surrounding objects-which can be used to quantify the contact degree. We previously demonstrated the use of a homology-based method to diagnose advanced colorectal cancer. It is clinically important to discriminate adenoma, especially high-grade adenoma, and early-stage cancer from non-cancerous tissue; thus, it was of interest to evaluate whether our homology-based method could also diagnose adenoma and early-stage cancer. In the present study, we developed a homology-based application to calculate b₁ values for a region of interest, and used it to analyze normal tissue, adenoma, and early-stage cancer from the colorectum. Area correction was required for proper comparison of b₁ values. We found that area-corrected b₁ values were significantly higher in high-grade adenoma and early-stage cancer, compared to normal tissue. Although there remains a need for further development of the algorithm to discriminate low-grade adenoma and inflammatory regions, our present findings indicate that our homology-based method using Betti numbers can be useful for distinguishing high-grade adenoma and early-stage cancer from normal tissue, as well as advanced colorectal cancer.