Impedance Boundary Conditions for the Pulmonary Vasculature Including the Effects of Geometry, Compliance, and Respiration

With few exceptions, previous models of the pulmonary vascular system have neglected the effects of respiration. This practice is acceptable for normal cardiac function; however, for compromised function, respiration may be critical. Therefore, we have initiated the steps to develop boundary conditions that incorporate the effects of respiration through the use of an impedance boundary condition derived from a bifurcating structured tree geometry. The benefit to using the geometry based method lies in that strategic changes can be made to the geometry to mimic physiologic changes in vascular impedance. In this paper, a scaling factor was used to modify the radius of resistance vessels of the structured tree to capture the maximum change in impedance caused by respiration. A large vessel geometry was established from a lung cast, the structured trees were applied at the outlets, and an experimental flow waveform was applied at the inlet. Finite-element analysis was used to compute the resulting inlet pressure waveform. An optimization minimizing the difference between measured and computed pressure waveforms was performed for two respiratory states, maximal expiration and inspiration, to determine best-fit models for the pulmonary vasculature, resulting in pressure waveforms with an rms error of 0.4224 and 0.7270 mmHg, respectively.