Background

Pancreatitis is an inflammatory disease of the pancreas with worldwide incidence of acute pancreatitis and chronic pancreatitis is 34 cases and 10 casess per 100,000 population (Petrov and Yadav, 2019). Though healthy pancreas is almost sterile, greater amount of bacteria are found in the pancreas with pancreatitis (Maekawa et al., 2018), intrapapillary mucinous neoplasms (IPMNs) (Gaiser et al., 2019), and pancreatic cancer (Geller et al., 2017). Bacteria in the pancreas can be a trigger for pancreatitis (Vaccaro et al., 2000; Vonlaufen et al., 2007), damage healthy cells (Halimi et al., 2021), and influence suppressive tumor immune-environment (Pushalkar et al., 2018). Bacterial infiltration from the duodenum (Del Castillo et al., 2019) is an initial factor for inflammation (Vonlaufen et al., 2007); however, the mechanisms are poorly understood.

Bile flow from the liver inhibits infiltration (Sung et al., 1982). In addition, the sphincter of Oddi a muscle around the duct near the duodenum, is periodically contracted so that the duct’s pressure is higher than the duodenum to prevent duodenal reflux (Geenen et al., 1980). This sphincter serves a boundary for bacterial colonization (Sung et al., 1980). Since the sphincter of Oddi motility is affected by alcoholic drinking (Guelrud et al., 1991, Goff, 1993), it may possibly contribute to pancreatitis by influencing bacterial infiltration (Fig. 1) (Bateman et al., 2002, Criddle et al., 2004, Sah and Saluja, 2011, Vonlaufen, 2007a).

Some studies have reviewed biliary transport (Vartak et al., 2021), the biomechanics of the gastrointestinal tract (Gregersen and Kassab, 1996), and the human biliary system (Luo et al., 2007). In addition, a gut-on-a-chip that modeled intestinal peristalsis demonstrated acceleration of bacterial invasion and thus destruction of tissue (Boquet-Pujadas et al., 2022). Furthermore, bacterial migration into the duct due to random motility and pH-taxis and aerotaxis in a homogeneous fluid flow condition has also been mathematically modeled (Shirai et al., 2022).

In spite of aforementioned advances, mechanisms of bacterial infiltration of the pancreas were poorly understood. In particular, it remains missing how bacterial infiltration is affected by the sphincter of Oddi motility. The sphincter’s periodic contraction influences the internal fluid flow by changing the surrounded deformable duct structure (Duch et al., 2002, Duch et al., 2004). Deformation changes the fluid flow velocity, which in turn influences bacterial infiltration. Therefore, this study presents a mathematical model of bacterial infiltration of a deformable pancreatic duct, partly surrounded by the sphincter of Oddi. The goal of this study is to understand how each factor of the ducts, bile and pancreatic juice flow, and the contraction of the sphincter of Oddi, in combination with others, contribute to the bacterial infiltration to the pancreas.