Lymph doesn’t flow like blood. It moves through lymphangions — small contractile segments that pump autonomously, driven by calcium ion oscillations and nitric oxide regulation. The valves open and close not by smooth gradients but by sharp thresholds, making the dynamics fundamentally nonsmooth. A unified PDE/ODE model coupling fluid mechanics with these biochemical switches reproduces the pumping rhythm that experiments observe: stable oscillatory behavior emerging from the interplay of calcium spikes, nitric oxide suppression, and valve geometry.

The nonsmooth coupling is the essential feature. Smooth models of lymphatic flow miss the abrupt transitions that define valve function. The calcium-driven contraction cycle creates discontinuities in the forcing term — moments where the system jumps rather than evolves. The simplified two-equation reduction captures this, finding conditions under which oscillation is guaranteed rather than assumed.

Biological transport systems often operate not through continuous regulation but through threshold cascades — a chemical signal crosses a line, a valve fires, flow reverses or surges. The smoothness we associate with fluid dynamics is an approximation that breaks exactly where biology takes control. The lymphatic system reveals a general truth about coupled bio-mechanical systems: the discontinuity is the mechanism, not the failure mode.

(arXiv:2603.00779)