Ureteral Peristalsis — Lubrication-Theory Flow Network (2D)

This 2D companion to the 3D ureteral-peristalsis simulator replaces scripted wave kinematics with a real hydraulic-network solve. The ureter is discretized into fifty compliant segments; a traveling contraction still prescribes each segment's local lumen radius, but the resulting inlet flow, the full pressure profile along the tube, and the delivered urine transport are all computed every frame from continuity (mass conservation) combined with Hagen–Poiseuille viscous resistance — the same lubrication-theory approach classical peristaltic-pumping analyses use. Because the wave's own volume displacement (not a pressure gradient) is what drives net flow, the model reproduces peristalsis's defining property: it can pump forward even against a zero or adverse pressure difference. The ureterovesical junction is modeled as a real check valve whose resistance jumps roughly sixty-fold to block backflow, failing only once bladder pressure exceeds its closing pressure — so vesicoureteral reflux appears here as a genuine sign-reversal of the solved flow rather than a scripted event. Tune contraction frequency, amplitude, propagation speed and bladder back-pressure to see how each reshapes the pressure network and the resulting transport.