One-dimensional models of the human biliary system

Analysis and numerical investigation of bile flow dynamics within the strictured biliary duct

The mechanics of bile flow in the biliary system plays an important role in studying bile stasis and gallstone formation. Bile duct stricture is an abnormal phenomenon that refers to the bile duct getting smaller or narrower. The main objective of this study is to study the influence of stricture on bile flow dynamics using numerical methods. We employed a numerical Computational Fluid Dynamics model of the bile flow within a strictured hepatic duct. We studied and compared the influence of stricture severity, stricture length, eccentricity, and bile flow property on the bile flow dynamics. The bile flow velocity, pressure distribution, pressure drop, and wall shear stress are provided in detail. The stricture alters the normal bile flow pattern and increases flow resistance. At the location upstream and downstream of the stricture, bile flow slows down. In the area of the stricture throat, bile flow is accelerated, and recirculation forms behind the stricture. The maximum pressure drop of the biliary system increases with the stricture length. The eccentricity makes the flow deflect away from the duct's centerline. The behavior of the deflected flow is significantly altered downstream of the stricture. Such bile flow behavior as deceleration and recirculation may lead to cholestasis. Stricture alters bile flow in the biliary tract, causing changes in biliary hydrodynamic indexes, which could potentially serve as an omen for gallstone formation and other related diseases. The consideration of the bile duct stricture could lead to better patient stratification.

Review on bile dynamics and microfluidic-based component detection: Advancing the understanding of bilestone pathogenesis in the biliary tract

Bilestones are solid masses found in the gallbladder or biliary tract, which block the normal bile flow and eventually result in severe life-threatening complications. Studies have shown that bilestone formation may be related to bile flow dynamics and the concentration level of bile components. The bile flow dynamics in the biliary tract play a critical role in disclosing the mechanism of bile stasis and transportation. The concentration of bile composition is closely associated with processes such as nucleation and crystallization. Recently, microfluidic-based biosensors have been favored for multiple advantages over traditional benchtop detection assays for their less sample consumption, portability, low cost, and high sensitivity for real-time detection. Here, we reviewed the developments in bile dynamics study and microfluidics-based bile component detection methods. These studies may provide valuable insights into the bilestone formation mechanisms and better treatment, alongside our opinions on the future development of in vitro lithotriptic drug screening of bilestones and bile characterization tests.

Patient-specific fluid-structure interaction model of bile flow: comparison between 1-way and 2-way algorithms

Gallbladder disease is one of the most spread pathologies in the world. Despite the number of operations dealing with biliary surgery increases, the number of postoperative complications is also high. The aim of this study is to show the influence of the biliary system pathology on bile flow character and to numerically assess the effect of surgical operation (cholecystectomy) on the fluid dynamics in the extrahepatic biliary tree, and also to reveal the difference between 1-way and 2-way FSI algorithms on the results. Moreover, the bile viscosity and biliary tree geometry influence on the choledynamics were evaluated. Bile velocity, pressure, wall shear stress (WSS), displacements and von Mises stress distributions in the extrahepatic biliary tree are presented, and comparison is made between a healthy and a lithogenic bile. The patient-specific biliary tree model is created using magnetic resonance imaging (MRI) and imported in a commercial finite element analysis software. It is found that in the case of lithogenic bile, velocities have lower magnitude while pressures are higher. Furthermore, stress analysis of the bile ducts shows that the WSS distribution is found mostly prevailing in the common hepatic duct and common bile duct areas. It is shown that when it is necessary to evaluate the bile flow dynamics in urgent medical situations, 1-way analysis is acceptable. Nevertheless, 2-way FSI provides more accurate data, if necessary to evaluate the stress-strain state of bile ducts. The proposed model can be applied to medical practice to reduce the number of post-operative complications.

Porcine bile viscosity is proportional to density

BACKGROUND

The gallbladder filling and emptying cycle controls bile flow into the duodenum. Disruption of this emptying and refilling cycle leads to bile stasis and subsequent gallstone formation. The bile flow rate is inversely proportional to its viscosity. Moreover, bile is a complex material with varying density in different people because of its diverse components. These density changes alter the viscosity. Prediction of shear viscosity from density measurements may thus contribute to medical assessment and treatment of the patient.

OBJECTIVE

To investigate the relationship between the shear viscosity and density of bile.

METHODS

Natural and filtered bile samples were prepared for density, viscosity and pressure drop measurements. The density and shear viscosity were measured by a density meter and viscometer, respectively, and a relationship was established between them. Measurements of the pressure drop in a glass tube were used to estimate the apparent viscosity and compared with shear viscosity obtained with the viscometer.

RESULTS

The natural bile with higher density showed a greater shear viscosity than the filtered bile, especially at low shear rates. Bile viscosity was proportional to density. In addition, the pressure drop of the natural samples was greater than that of the filtered sample. The viscosity measured by the viscometer deviated from the results obtained using Poiseuille's law and the tube pressure drop measurements. The density difference between the natural and filtered bile samples was smaller than 1%. However, the viscosities of the natural and filtered bile samples varied by up to >30%.

CONCLUSIONS

Porcine bile viscosity is proportional to density. Based on the bile density, one can easily evaluate the shear viscosity using a linear relationship. The density considerably influences the bile viscosity, with small density increases greatly increasing the shear viscosity.

Biomechanical behaviour of human bile duct wall and impact of cadaveric preservation processes

Biliary diseases are the third most common cause of surgical digestive disease. There is a close relationship between the mechanical performance of the bile duct and its physiological function. Data of biomechanical properties of human main bile duct are scarce in literature. Furthermore, mechanical properties of soft tissues are affected by these preservation procedures. The aim of the present work was, on the one hand, to observe the microstructure of the human bile duct by means of histological analysis, on the other hand, to characterize the mechanical behavior and describe the impact of different preservation processes. A mechanical study in a controlled environment consisting of cyclic tests was made. The results of the mechanical tests are discussed and explained using the micro-structural observations. The results show an influence of the loading direction, which is representative of an anisotropic behavior. A strong hysteresis due to the viscoelastic properties of soft tissues was also observed. Embalming and freezing preservation methods had an impact on the biomechanical properties of human main bile duct, with fiber network deterioration. That may further provide a useful quantitative baseline for anatomical and surgical training using embalming and freezing.

Patient-Specific Bile Flow Simulation to Evaluate Cholecystectomy Outcome

Gallbladder disease has one of the leading positions by patients’ number in the World. About 16% of the adult population is suffering now from this disease. Cholecystectomy is believed to be a general surgical method of the gallbladder disease treatment, but the success rate is quite low because the surgeons do not take into account the patient-specific features during the treatment and cannot predict operation results.The main purpose of the paper is to create a computational tool for numerical evaluation of cholecystectomy outcome compared with healthy state and current pathological state based on the patient-specific patients’ data. The patient-specific features of the biliary tree were studied by 1-way FSI bile flow simulation. The extra-hepatic biliary tree geometries were extracted from MRI and after that imported to ANSYS CFX for the subsequent fluid dynamics analysis.It was revealed that in the pathology state, velocities were found to have lower magnitude while the pressures were higher. The patient-specific features have a dramatic influence on the bile flow patterns. Cholecystectomy leads to the decrease of bile flow rate in the extra-hepatic biliary tree. The proposed computational approach can be applied to medical practice to evaluate the circumstances of surgical interventions.

Volume Preserved Mass-Spring Model with Novel Constraints for Soft Tissue Deformation

An interactive surgical simulation system needs to meet three main requirements, speed, accuracy, and stability. In this paper, we present a stable and accurate method for animating mass-spring systems in real time. An integration scheme derived from explicit integration is used to obtain interactive realistic animation for a multiobject environment. We explore a predictor-corrector approach by correcting the estimation of the explicit integration in a poststep process. We introduce novel constraints on positions into the mass-spring model (MSM) to model the nonlinearity and preserve volume for the realistic simulation of the incompressibility. We verify the proposed MSM by comparing its deformations with the reference deformations of the nonlinear finite-element method. Moreover, experiments on porcine organs are designed for the evaluation of the multiobject deformation. Using a pair of freshly harvested porcine liver and gallbladder, the real organ deformations are acquired by computed tomography and used as the reference ground truth. Compared to the porcine model, our model achieves a 1.502 mm mean absolute error measured at landmark locations for cases with small deformation (the largest deformation is 49.109 mm) and a 3.639 mm mean absolute error for cases with large deformation (the largest deformation is 83.137 mm). The changes of volume for the two deformations are limited to 0.030% and 0.057%, respectively. Finally, an implementation in a virtual reality environment for laparoscopic cholecystectomy demonstrates that our model is capable to simulate large deformation and preserve volume in real-time calculations.

Experimental Investigation of the Flow of Bile in Patient Specific Cystic Duct Models

Three-dimensional scaled-up transparent models of three human cystic ducts were prepared on the basis of anatomical specimens. The measurement of pressure drop across the cystic duct models and visualization of the flow structures within these ducts were performed at conditions replicating the physiological state. The flow visualization study confirmed the laminar nature of the flow of bile inside the cystic duct and values of pressure drop coefficient (Cp) decreased as the Reynolds number (Re) increased. The three tested models showed comparable behavior for the curve of Reynolds number versus the pressure drop coefficient. The results show that the tested cystic ducts have both increased pressure drop and complicated flow structures when compared with straight conduits. High resistance in a cystic duct may indicate that the gallbladder has to exert large force in expelling bile to the cystic duct. For patients with diseased gallbladder, and even in healthy persons, gallbladder is known to stiffen with age and it may lose its compliance or flexibility. A high resistance cystic duct coupled with a stiffened gallbladder may result in prolonged stasis of bile in the gallbladder, which is assumed to encourage the formation of gallstones.

Decreased postprandial gallbladder emptying in patients with black pigment stones

AIM: To analyze gallbladder contractility in patients with black pigment stones (BPSs) and to compare this with patients with cholesterol stones (CSs) and healthy volunteers.

METHODS: The pattern of bile evacuation from the gallbladder was quantified by computer cholescintigraphy in 28 normal subjects, 22 patients with CSs and 14 with BPSs. The parameters of gallbladder contractility included ejection period (EP), ejection fraction (EF) and ejection rate (ER).

RESULTS: A significantly shorter EP was observed in patients with BPSs in comparison to those with CSs (t = 2.4, P < 0.05). EF in BPS patients significantly decreased in comparison to that in CS and normal subjects (t = 6.4, P < 0.0001; t = 2.1, P < 0.05). EF in CS patients also significantly decreased in comparison to that in normal subjects (t = -3.0, P < 0.005). Consequently, ER in patients with BPSs and CSs was significantly smaller than that in normal subjects (t = 3.1, P < 0.005; t = -3.5, P < 0.001). Moreover, in cases where postprandial reflux of a radioisotope into the common hepatic duct from the gallbladder was observed, EF and ER of either CS or BPS patients showed a significant reduction.

CONCLUSION: Bile evacuation from the gallbladder is reduced in patients with BPSs, in comparison to those with CSs and to healthy volunteers. Bile stagnation due to impaired gallbladder kinetics seems to be one of the predisposing factors for the development of BPSs.

On the mechanical behavior of the human biliary system

This paper reviews the progress made in understanding the mechanical behaviour of the biliary system. Gallstones and diseases of the biliary tract affect more than 10% of the adult population. The complications of gallstones, i.e. acute pancreatitis and obstructive jandice, can be lethal, and patients with acalculous gallbladder pain often pose diagnostic difficulties and undergo repeated ultrasound scans and oral cholecystograms. Moreover, surgery to remove the gallbladder in these patients, in an attempt to relieve the symptoms, gives variable results. Extensive research has been carried out to understand the physiological and pathological functions of the biliary system, but the mechanism of the pathogenesis of gallstones and pain production still remain poorly understood. It is believed that the mechanical factors play an essential role in the mechanisms of the gallstone formation and biliary diseases. However, despite the extensive literature in clinical studies, only limited work has been carried out to study the biliary system from the mechanical point of view. In this paper, we discuss the state of art knowledge of the fluid dynamics of bile flow in the biliary tract, the solid mechanics of the gallbladder and bile ducts, recent mathematical and numerical modelling of the system, and finally the future challenges in the area.