An anatomically grounded human-scale steady hydraulic model of the lymphatic network

Abstract

The lymphatic system returns 2 to 3 L of interstitial fluid per day to the venous circulation and drains the central nervous system. Most models of lymph transport describe one lymphangion or a short chain, so they cannot show how body-wide topology, calibre hierarchy and the venous outlet set pressure and flow. We build a passive steady hydraulic model on an anatomically derived graph of the human lymphatic system, with 1010 vertices and 1126 edges expanded to 89,060 sub-edges. Radii follow a Murray cube law, derived both from minimum work and from wall-shear-stress homeostasis. Pressure and flow follow from nodal hydraulic balance over Hagen-Poiseuille conductances, with an exponential wall law, hysteretic valves, Starling leak, node retention and a Windkessel outlet. Active contraction is off, and only the inflow scale is calibrated. Two quantities that are not fitted land in clinical range at the same operating point. Radii fall inside the vessel-class range, from 1.50 mm in the thoracic duct to 0.16 mm in the cervical collectors, and pressures stay below the 50 mmHg cuff scale on all sub-edges. About 49% of the gross load is removed before the outlet, nearly independent of the outflow scale and of the outlet parameters. On the route that drains the central nervous system, 30% of the superficial cervical load reaches the vein, at 10 to 18 mmHg along a segment that cervical-scale models replace with a prescribed outlet pressure. The model is a passive whole-body baseline for contraction-driven and clinical extensions.