Teleonomical optimization of a fractal model of the pulmonary arterial bed

Modeling the pulmonary arterial tree (PAT) is considered here as an optimal synthesis problem. Firstly, a class of candidate models is specified: the three-dimensional symmetric dichotomous fractal trees of elastic tubes described by Womersley's equations. Secondly, the parameters are shown to be constrained by interactions of PAT with the rest of the body; these constraints are used to limit the volume of the parametric space to which attention will be directed in the synthesis step. Thirdly, a teleonomical hypothesis is proposed: a naturally selected PAT must have a minimal input impedance under conditions keeping total arterial volume and distensibility as small as possible. This hypothesis is translated in mathematical terms and the resulting cost-function minimized in the limited parametric volume. The optimal model has parameter values and an impedance spectrum corresponding satisfactorily with real data. Moreover this model gives a clear picture of the internal hemodynamic behavior of PAT as an impedance matching device.