title: Do Vascular Networks Branch Optimally or Randomly across Spatial Scales?
abstract: Modern models that derive allometric relationships between metabolic rate and body mass are based on the architectural design of the cardiovascular system and presume sibling vessels are symmetric in terms of radius, length, flow rate, and pressure. Here, we study the cardiovascular structure of the human head and torso and of a mouse lung based on three-dimensional images processed via our software Angicart. In contrast to modern allometric theories, we find systematic patterns of asymmetry in vascular branching, potentially explaining previously documented mismatches between predictions (power-law or concave curvature) and observed empirical data (convex curvature) for the allometric scaling of metabolic rate. To examine why these systematic asymmetries in vascular branching might arise, we construct a mathematical framework to derive predictions based on local, junction-level optimality principles that have been proposed to be favored in the course of natural selection and development. The two most commonly used principles are material-cost optimizations (construction materials or blood volume) and optimization of efficient flow via minimization of power loss. We show that material-cost optimization solutions match with distributions for asymmetric branching across the whole network but do not match well for individual junctions. Consequently, we also explore random branching that is constrained at scales that range from local (junction-level) to global (whole network). We find that material-cost optimizations are the strongest predictor of vascular branching in the human head and torso, whereas locally or intermediately constrained random branching is comparable to material-cost optimizations for the mouse lung. These differences could be attributable to developmentally-programmed local branching for larger vessels and constrained random branching for smaller vessels.
authors.affiliation: Department of Biomathematics, University of California, Los Angeles, David Geffen School of Medicine, Los Angeles, California, United States of America.
authors.forename: Elif
authors.identifier: http://orcid.org/0000-0001-5432-5511
authors.initials: E
authors.lastname: Tekin
authors.affiliation: Department of Biomathematics, University of California, Los Angeles, David Geffen School of Medicine, Los Angeles, California, United States of America.
authors.forename: David
authors.identifier: http://orcid.org/0000-0003-0590-874X
authors.initials: D
authors.lastname: Hunt
authors.affiliation: Department of Biology, University of Pennsylvania, Philadelphia, Pennsylvania, United States of America.
authors.forename: Mitchell G
authors.initials: MG
authors.lastname: Newberry
authors.affiliation: Department of Biomathematics, University of California, Los Angeles, David Geffen School of Medicine, Los Angeles, California, United States of America.|Department of Ecology and Evolutionary Biology, University of California, Los Angeles, Los Angeles, California, United States of America.|Santa Fe Institute, Santa Fe, New Mexico, United States of America.
authors.forename: Van M
authors.initials: VM
authors.lastname: Savage
mesh_terms: D000818:Animals; D001808:Blood Vessels / Q000033:anatomy & histology* / Q000254:growth & development*; D019521:Body Patterning / Q000502:physiology*; D006801:Humans; D051379:Mice; D008953:Models, Anatomic; D008955:Models, Cardiovascular; D015233:Models, Statistical