Ductal Porosity and Thermal Effects on Bile Transport: A Two-Dimensional Peristaltic Flow Model of the Cystic Duct

Abstract

Gallstone disease and cystic duct obstruction remain major clinical challenges in hepatobiliary medicine, where altered bile rheology, ductal porosity due to microlithiasis, and heat transfer significantly influence bile transport and stone formation. The present model provides theoretical insight into the combined effects of thermal gradients, porous resistance, and non-Newtonian bile rheology on cystic duct flow under simplified physiological conditions. The model is developed under low Reynolds number and long wavelength assumptions and does not incorporate full three-dimensional anatomical complexities. Governing equations are solved numerically using a finite difference method. Parametric analysis reveals that axial velocity decreases with increasing baffle height and duct porosity but rises with higher Grashof number (buoyancy effects) and thermal conductivity. Pressure distribution intensifies with thermal conductivity and buoyancy but diminishes with porosity, while wall shear stress increases with all three factors. Importantly, the model captures reflux conditions and shows that the mean flow rate declines under elevated pressure rise when thermal and porous effects dominate. These findings provide mechanistic insight into how ductal heat transfer and microstructural porosity influence bile hydrodynamics, with potential applications in predicting gallstone growth, optimizing endoscopic interventions, and improving biliary drainage strategies. The framework may also guide patient-specific modeling and design of medical devices to manage obstructive biliary disorders.