Mathematical Modeling of Deposits Accumulationon 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 consideredsatisfactory due to the high incidence of jaundice recurrence which is caused by the occlusion ofplastic 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 thatstimulates the reduction of the stent lumen. The average lifetime of stents is 3-6 months. Despitenumerous experimental studies of the occlusion process, the optimal timing for the replacementof the biliary plastic stent has not been established. Too frequent replacement of the stent canlead to additional complications, so an individualized forecast of the stent’s lifetime for a particularpatient is needed. In this paper, a model of the ﬂow of lithogenic bile as a non-Newtonian ﬂuidis developed taking into account the transport of particles describing the behavior of cholesterolcrystals that accumulate on the inner surface of the stent, stimulating a decrease in its lumen. Acorrelation was found between cholesterol concentration and occlusion time based on the use ofa specially developed iterative procedure. The results of the numerical computations show thatindividual parameters (age, gender, bile viscosity, cholesterol concentration) have a signiﬁcantimpact on the rate of occlusion of the stent.