Fluid-Dynamic Determinants of Drainage Through Idealized Residual Intersphincteric Fistula Tracts: A Numerically Verified CFD and Semi-Analytical Study of Tract Geometry and Outlet Pressure

Adequate drainage is central to the management of cryptoglandular anal abscess and fistula, yet anatomical patency of a residual pathway does not quantify its functional drainage capacity. We investigated how tract length, effective diameter, and outlet pressure govern flow through idealized residual intersphincteric fistula tracts. Steady laminar computational fluid dynamics (CFD) used rigid circular tubes and a standardized Newtonian fluid (=1000 kg/m3, =0.01 Pa·s). The implementation was verified against Hagen–Poiseuille flow and mesh refinement, then used to quantify geometry-dependent hydraulic resistance and outlet-pressure sensitivity. Six pressure-driven development cases informed a viscous-plus-quadratic semi-analytical model, which was evaluated in two prespecified predictive cases and two additional out-of-sample robustness checks without refitting. Fine-to-Very-Fine mesh refinement changed hydraulic resistance by 0.0178%, and resistance reproduced the expected L and D−4 scalings. At =0.75, normalized flow was 0.2659 for D = 3 mm and 0.4135 for D = 10 mm. The semi-analytical model achieved R2 = 0.99933; prediction errors were 2.9536% and 0.1191% in the prespecified tests and 6.8070% and 1.5463% in the additional robustness checks. Across the model-based response surface, identical fractional outlet-pressure loading produced geometry-dependent flow reductions as the balance between viscous and quadratic losses shifted continuously. This numerically verified framework provides a mechanistic rigid-flow reference for residual fistula drainage and a hypothesis-generating baseline for subsequent anatomically realistic and mechanically coupled models.