One-Dimensional Models of the Human Biliary System

This paper studies two one-dimensional models to estimate the pressure drop in the normal human biliary system for Reynolds number up to 20. Excessive pressure drop during bile emptying and refilling may result in incomplete bile emptying, leading to stasis and subsequent formation of gallbladder stones. The models were developed following the group’s previous work on the cystic duct using numerical simulations. Using these models, the effects of the biliary system geometry, elastic property of the cystic duct, and bile viscosity on the pressure drop can be studied more efficiently than with full numerical approaches. It was found that the maximum pressure drop occurs during bile emptying immediately after a meal, and is greatly influenced by the viscosity of the bile and the geometric configuration of the cystic duct, i.e., patients with more viscous bile or with a cystic duct containing more baffles or a longer length, have the greatest pressure drop. It is found that the most significant parameter is the diameter of the cystic duct; a 1% decrease in the diameter increases the pressure drop by up to 4.3%. The effects of the baffle height ratio and number of baffles on the pressure drop are reflected in the fact that these effectively change the equivalent diameter and length of the cystic duct. The effect of the Young’s modulus on the pressure drop is important only if it is lower than $400Pa$⁠; above this value, a rigid-walled model gives a good estimate of the pressure drop in the system for the parameters studied.