Journal Article A Mathematical Model of the Pathophysiology of Reflux Esophagitis

Hideki, Tanaka  ,  Yoshihisa, Urita  ,  Naoyuki, Kawagoe  ,  Yosuke, Sasaki  ,  Toshiyasu, Watanabe  ,  Takaaki, Kawaguchi

2 ( 1 )  , pp.8 - 15 , 2016-03 , The Medical Society of Toho University
Background: We used a 1-dimensional cellular automaton (CA) model to investigate reflux esophagitis (RE), which is caused by increased gastroesophageal reflux. The reflux route is usually 1-way, from the stomach to the esophagus, and reflux content advances upward over time, which suggests that the next state is decided by the prior state of interaction between gastric acid and the esophageal epithelium. The present study evaluated whether a 1-dimensional CA model accurately simulated endoscopic findings from RE. Methods: Using Microsoft Excel 2013, we programmed a 1-dimensional CA with 3 neighbors and 2 states: 0 or 1. The initial state was defined as the gastroesophageal junction, and reflux of gastric acid moved in accordance with CA calculations. Because the CA rules determined how the states of given cells changed, the rules yielded other cell states. We attempted to identify CA rules that, after repeated calculations, yielded shapes consistent with endoscopic findings of RE. Results: Images from 1-dimensional CA resembled endoscopic findings of RE. Overall, 23 (9.0%) of 256 CA rules generated progressive growth patterns. This frequency approximates the reported prevalence of RE. Rule 232 was most likely to simulate the various patterns of mucosal breaks identified by endoscopy. Conclusions: Endoscopic findings were readily simulated by a simple mathematical method, a 1-dimensional CA. A simple local rule between adjacent cells might predict endoscopic findings of RE.

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