A quantitative evaluation method utilizing the homology concept to assess the state of chromatin within the nucleus of lung cancer

Homology is a mathematical tool to quantify "the contact degree", which can be expressed in terms of Betti numbers. The Betti numbers used in this study consisted of two numbers, b0 (a zero-dimensional Betti number) and b1 (a one-dimensional Betti number). We developed a chromatin homology profile (CHP) method to quantify the chromatin contact degree based on this mathematical tool. Using the CHP method we analyzed the number of holes (surrounded areas = b1 value) formed by the chromatin contact and calculated the maximum value of b1 (b1MAX), the value of b1 exceeding 5 for the first time or Homology Value (HV), and the chromatin density (b1MAX/ns(2)). We attempted to detect differences in chromatin patterns and differentiate histological types of lung cancer from respiratory cytology using these three features. The HV of cancer cells was significantly lower than that of non-cancerous cells. Furthermore, b1MAX and b1MAX/ns(2) showed significant differences between small cell and non-small cell carcinomas and between adenocarcinomas and squamous cell carcinomas, respectively. We quantitatively analyzed the chromatin patterns using homology and showed that the CHP method may be a useful tool for differentiating histological types of lung cancer in respiratory cytology.