Theoretical Analysis of the Vascular System and its Relation to Adrian Bejan's constructal Theory

Abstract

Basically, the main function of the cardiovascular system is to provide oxygen and other nutriments to the tissues, achieved by the pumping action of the heart and the subsequent blood flow through the tree-like vasculature. Classically, in the physical and mathematical analysis of the relationship between form and function of vascular systems, form is given first. The constructal theory, first proposed by Adrian Bejan in 1996, is a thermodynamic principle according to which flow systems, such as watersheds and vascular networks, evolve so that they gain more global performance over time. There are two major points about the constructal theory. The first one is that it provides a unifying concept of form and function, in which the configuration is not postulated, but is to be discovered. The second one is that it is presented as a unifying physical concept of evolution of organic and inorganic flow systems. By comparing non-living (watersheds) and living (vasculature) systems, we show that the processes of morphological "change upon time" in watersheds and those of developmental morphogenesis and evolutionary modifications through generations in a population are not equivalent. Mechanistic explanations in biology include physico-mathematical models but, from the biological point of view, the epistemic value of the constructal law is not its unifying power by subsumption of biological processes under a general nomological principle, but, to the contrary, to provide an idealized physicomathematical model of living systems that is embedded in general mechanistic explanatory frameworks of biological processes such as development and evolution.

Fluid Shear Stress Sensing by the Endothelial Layer

“…In the case of vessel regression and stabilization, an exuberant process of vessel sprouting and random connection, followed by vessel regression below a threshold WSS value, associated with vessel inward or outward remodeling of the remaining vessels until the set point value is obtained, will produce an organized network optimally designed. Uniform shear stress in vascular morphogenesis can hence be viewed as a constructal process that tends to shape vascular networks following thermodynamic constructal principles (Roux and Marhl, 2017). Adult vascular remodeling can also be analyzed in term of uniform shear stress.…”