Teleonomical Representation of the Pulmonary Arterial Bed of the Dog by a Fractal Tree

Abstract

Students of arterial physiology have long been struck by the high degree to which vascular properties are adapted to blood transport function. Since arterial function can be described in well-known physical terms, arterial trees are good objects of study for unravelling the basis of a mathematical teleonomy (neologism¹ denoting the study of the characteristics of living systems resulting from their optimization by evolution²). Teleonomical study of an organ proceeds in six steps:

• establishment of model’s equations and definition of the parameter vector p

• definition of system function in terms of the model

• hypothesis about the cost-function F(p) optimized by evolution

• assumptions representing the constraints imposed on the system by its inclusion in a complete organism

• selection of the optimal p=p*which minimizes F(p)

• comparison between model and real bed.