Constructal law of vascular trees for facilitation of flow

• Published in: PloS one Vol. 9; no. 12; p. e116260
• Main Authors: Razavi, Mohammad S, Shirani, Ebrahim, Salimpour, Mohammad Reza, Kassab, Ghassan S
• Format: Journal Article
• Language: English
• Published: United States Public Library of Science 31.12.2014; Public Library of Science (PLoS)
• Subjects: Biological Evolution; Biology and Life Sciences; Biomedical engineering; Blood; Blood Circulation; Blood vessels; Blood Viscosity; Branches; Cats; Conductance; Construction; Design; Energy dissipation; Engineering and Technology; Evolution; Flow (Dynamics); Fluid dynamics; Fluid flow; Heart; Laminar flow; Mathematical analysis; Mechanical engineering; Models, Biological; Models, Cardiovascular; Newtonian fluids; Non Newtonian fluids; Organs; Physiology; Resistance; River basins; Rivers; Trees; Turbulence; Turbulent flow
• ISSN: 1932-6203; 1932-6203
• DOI: 10.1371/journal.pone.0116260

Diverse tree structures such as blood vessels, branches of a tree and river basins exist in nature. The constructal law states that the evolution of flow structures in nature has a tendency to facilitate flow. This study suggests a theoretical basis for evaluation of flow facilitation within vascular structure from the perspective of evolution. A novel evolution parameter (Ev) is proposed to quantify the flow capacity of vascular structures. Ev is defined as the ratio of the flow conductance of an evolving structure (configuration with imperfection) to the flow conductance of structure with least imperfection. Attaining higher Ev enables the structure to expedite flow circulation with less energy dissipation. For both Newtonian and non-Newtonian fluids, the evolution parameter was developed as a function of geometrical shape factors in laminar and turbulent fully developed flows. It was found that the non-Newtonian or Newtonian behavior of fluid as well as flow behavior such as laminar or turbulent behavior affects the evolution parameter. Using measured vascular morphometric data of various organs and species, the evolution parameter was calculated. The evolution parameter of the tree structures in biological systems was found to be in the range of 0.95 to 1. The conclusion is that various organs in various species have high capacity to facilitate flow within their respective vascular structures.