Mathematical modeling of deposits accumulation on the plastic biliary stent surface for predicting its occlusion

Endoprosthetics with plastic stents has been used to restore bile drainage through the percutaneous or endoscopic method since the late 1970s. The long-term results cannot be considered satisfactory due to the high incidence of jaundice recurrence which is caused by the occlusion of plastic stents with a biliary sludge (accumulation of cholesterol crystals, pigment crystals, bacteria and calcium salts). Cholesterol is considered to be the main component of biliary sludge that stimulates the reduction of the stent lumen. The average lifetime of stents is 3–6 months. Despite numerous experimental studies of the occlusion process, the optimal timing for the replacement of the biliary plastic stent has not been established. Too frequent replacement of the stent can lead to additional complications, so an individualized forecast of the stent's lifetime for a particular patient is needed. In this paper, a model of the flow of lithogenic bile as a non-Newtonian fluid is developed taking into account the transport of particles describing the behavior of cholesterol crystals that accumulate on the inner surface of the stent, stimulating a decrease in its lumen. A correlation was found between cholesterol concentration and occlusion time based on the use of a specially developed iterative procedure. The results of the numerical computations show that individual parameters (age, gender, bile viscosity, cholesterol concentration) have a significant impact on the rate of occlusion of the stent.