A subway train races through a tunnel, yet passengers in the last car barely sway. Blood flow in the lungs works much the same way: the heart pumps blood in powerful spurts, but by the time it reaches the veins, the pulsation has almost vanished. For a long time, no one could build a complete mathematical picture of this transformation — the most crucial piece, the capillary network, was missing.

In the new study, researchers assembled a unified model for the first time, where large arteries and veins connect through a realistic capillary network. They used a "structured tree" approach — arteries branch into ever smaller vessels like a tree canopy, and veins similarly merge back. Between them sits a "capillary sheet," an elastic mesh of microscopic tubes that acts as a shock absorber.

They compared two cases: a healthy person and a patient with pulmonary hypertension (elevated pressure in the lung vessels). Without capillaries in the model, the venous flow remained unnaturally pulsatile, like a train arriving at the terminal station without slowing down. When capillaries were added, the pulsations were damped, and the waveform became smooth, as it should be in reality. In the hypertensive patient, the capillary network was altered and could no longer fully shield the veins from the impulses — part of the pulse energy broke through.

The result can be finely tuned: by changing the stiffness of vessel walls in the model, one can track how the disease progresses. Such a tool will help clinicians assess how much the pulmonary circulation has changed and choose therapy without unnecessary invasive procedures.