title: Constructal law of vascular trees for facilitation of flow.
abstract: 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.
authors.affiliation: Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.
authors.forename: Mohammad S
authors.initials: MS
authors.lastname: Razavi
authors.affiliation: Department of Engineering, Foolad Institute of Technology, Fooladshahr, Isfahan, Iran.
authors.forename: Ebrahim
authors.initials: E
authors.lastname: Shirani
authors.affiliation: Department of Mechanical Engineering, Isfahan University of Technology, Isfahan, Iran.
authors.forename: Mohammad Reza
authors.initials: MR
authors.lastname: Salimpour
authors.affiliation: Department of Biomedical Engineering, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, Indiana, United States of America; Department of Surgery, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, Indiana, United States of America; Department of Cellular and Integrative Physiology, Indiana University-Purdue University Indianapolis (IUPUI), Indianapolis, Indiana, United States of America.
authors.forename: Ghassan S
authors.initials: GS
authors.lastname: Kassab
mesh_terms: D005075:Biological Evolution; D001769:Blood; D001775:Blood Circulation; D001809:Blood Viscosity; D008954:Models, Biological; D008955:Models, Cardiovascular