Wave Propagation in the Pulmonary Circulation
FRED WIENER, EUGENE MORKIN, RICHARD SKALAK, ALFRED P. FISHMAN
A mathematical model of the entire pulmonary circulation of the dog, based on branching elastic tubes, is shown to yield a useful description of the propagation of pulmonary vascular pressure and flow waves. The pressure and flow pulses throughout the model are computed from the pressures measured at the arterial and venous ends of the system. Computed flow pulses at each end of the system agree with experimental findings. Contour changes in the pressure and flow pulses are shown to be
... due to dispersion and amplitude changes associated with reflected waves. Wave reflections are distributed throughout the model, and no specific site can be designated as the major source for reflections. Blood pressure and flow computed from the model remain pulsatile in the microcirculation; pressure pulses are attenuated but flow pulses pass essentially unchanged through the microcirculation. The computed results support the conclusion previously drawn from experimental evidence that pressure and flow pulses in the pulmonary veins originate primarily in the right ventricle and are propagated through the pulmonary capillary bed. A retrograde pulse, resulting from pressure fluctuations in the left atrium, is also present in both arteries and veins, but has only a secondary effect on the contours of pulmonary vascular pressures and flows. ADDITIONAL KEY WORDS pressure and flow pulses mathematical modeling wave reflections input impedance pulmonary venous flow branching elastic tube model pulmonary hemodynamics and mechanics vascular pulse distortion pulsatile blood flow unancstherized dogs uniform tube as the basic element, and using the most reliable data obtainable on the anatomical and physical characteristics of pulmonary blood vessels, we constructed a mathematical model of the entire pulmonary circulation. This approach differs from that of previous workers who have developed models applicable either to single arteries (1, 2) or to an arterial system that terminates in a lumped impedance representing both the capillary and venous systems (3, 4). With blood pressures recorded from the main pulmonary artery and left atrium in intact dogs as boundary conditions, pressures and flows at various locations within the pulmonary vasculature were calculated. In order to verify the model, the contours of the calculated flow pulses were compared with the contours of flow pulses recorded directly from the pulmonary artery and a pulmonary vein.