Biomechanical model of bile flow in the biliary system

The biliary system function is to transport bile into the duodenum for the fat digestion. Metabolic disorders and choledynamics disturbances may cause the cholelithiasis. In Russia, the pathology of the biliary system ranks third in the patients number. The surgical treatment of cholelithiasis is the gallbladder removal (cholecystectomy). However, the percentage of postoperative complications is quite high. One of the reasons is the lack of objective methods: surgeons are not always able to evaluate the surgical intervention consequences. Nevertheless, there are very few works devoted to the numerical simulation of processes associated to a bile flow. There was no complete personalized model that could be used in medical practice to the date. This paper presents a new model of the bile flow in the biliary system. The proposed approach is that the biliary system is considered as a combination of the three parts (the gallbladder, extrahepatic bile ducts, and the major duodenal papilla). The Windkessel model was used to simulate the bile flow in the gallbladder. The bile flow in the extrahepatic bile ducts can be considered as a fluid-structure interaction flow. The bile flow in the major duodenal papilla was considered as a peristaltic transport in a finite-length tapered tube. A complex model of the biliary system allowed us to evaluate choledynamics in the healthy state, pathology, as well as to carry out a numerical assessment of the bile flow after cholecystectomy to predict and prevent complications. The utilization of peristaltic flow modelling in the major duodenal papilla allowed us to determine the quantitative criteria for the occurrence of pathological reflux, which made it possible to ensure its prevention. The model can also be used to analyze surgical interventions in the treatment of cholelithiasis and its complications (stenting, anterior abdominal wall suturing). For example, the mathematical model of the installation of a stent with shape memory reduces the number of complications (soft tissue perforation). The numerical model of the accumulation of particles on the surface of the plastic stent made it possible to predict the replacement period for a particular patient and to improve the quality of his life. The biomechanical analysis of the use of suture materials allowed us to provide a differentiated approach to suture materials and to reduce the number of specific postoperative complications. It is shown that the developed model can be used to create a software to support decision-making when performing cholelithiasis treatment to prevent complications.