Esophageal epithelium modeling based on globally coupled map: an approach toward precancerous lesion diagnosis

Esophageal squamous cell carcinoma is the most predominant malignancy of the esophagus. Its histological precursors (dysplasia) emerge in the esophageal epithelium that their progression into the underlying layers leads to cancer. The epithelium is the origin of many solid cancers and, accordingly, the focus of numerous computational models. In this work, we proposed a framework to establish a two-dimensional, globally coupled map to model the epithelium dynamics. The model aims at diagnosing the early stage of dysplasia based on microscopic images of endoscopic biopsies. We used the logistic map as a black-box model for the epithelial cells. By relating between the structure and dynamic of the epithelium, we defined the coupling function and proposed a case-dependent model in which the parameters were adjusted based on fractal geometry of each pathological image. Thus, by assigning different attractors to the cells' behavior, the lattice dynamic was investigated by the Lyapunov exponent. The decreasing pattern of Lyapunov exponent variations across the epithelium thickness had reasonable performance in diagnosing the normal specimens from the low-grade dysplasia ones. The results showed that there could be a direct relationship between the structural complexity of this system and its uncertainty of dynamics. Graphical abstract The modeling process of the esophageal epithelium to classify the experimental data at normal and LGD stages.