BIOMECHANICAL MODELING OF CHOLEDOCH BILE FLOW IN CHOLEDOCHOLITHIASIS IN THE PROJECT “VIRTUAL PHYSIOLOGICAL HUMAN”

Aim. To ground the role of biomechanics in development of the model of biliary system within the norm and pathology in the frame of the project “Virtual Physiological Human”. The model will be based on the methods of computational biomechanics using anatomical, experimental, physiological data of hepatopancreatoduodenal (HPD) organs obtained by means of radial diagnostic methods determining the unique anatomy of a patient. Mathematical solution of the task of bile flow in the common bile duct in case of chloledocholithiasis is presented as an initial stage in realization of dynamic modeling of bile flow in the anhepatic bile-excreting tracts. Materials and methods. The problem was posed and the mathematical model of bile flow in the choledoch with concretion in its acute blockade was developed. The model is based on solution of the Navier-Stokes equation recorded for non-newton fluid (Casson fluid) in special conditions. Results. Flow rate profiles, dependence of duct lumen bile flow on time and concretion size as well as dependence of biliary pressure on choledoch and concretion diameter are presented in the paper. Conclusions. The worked out mathematical model permits to estimate dynamics of the postoperative period and to predict the development of specific complications based on changes in the values of choledoch biliary pressure from the side of HPD organs. Moreover, estimation of biliary pressure in the duct is objective for determination of biliary decompression efficiency during endoscopic transpapillary interventions on the large duodenal papilla when the pressure is high and the bile excretion volume is less than 35 % of the proposed standard.

Biliary system, bile, concretion, non-newton fluid