Mechanistic model: Analysis of diffusion dynamics of Lugol’s chromoendoscopy in Basal layer-type squamous cell carcinoma in situ via Euler’s method and Law of mass action

Basal layer-type squamous cell carcinoma in situ(BLSCC) is an aggressive malignancy tumor. In the past, it usually went ignored because its aggressive biological behavior is different from typical esophageal squamous cancer(SCC). For our mechanistic model, we analyzed diffusion dynamics of iodine stain in BLSCC with the help of Euler’s method. We used the law of mass action description of the forming process of the iodine-glycogen Complex. Based on the above analysis, our mechanistic model reveals that the efficacy of Lugol’s chromoendoscopy is determined by the thickness of the squamous epithelial cell layer, which contains glycogen granules, and the convection of the interpupillary capillary loop(IPCL). A further inference can be made: the unique histological structure of BLSCC suggests Lugol’s chromoendoscopy does not detect some components of it because these components neither break enough squamous epithelial cells which contain glycogen granules nor contain enough number of IPCL in a specific time frame. Besides, if our mechanistic model starting point is BLSCC and typical SCC share the same evolution path, we found both their cytoplasm tends to solid phase from the iodine diffusion dynamics analysis in “pink color sign.”