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.

Rediscovering and Reviving Old Observations and Explanations of Metabolic Scaling in Living Systems

“…New RTN-based models (e.g., [84,[173][174][175][176]) or applications (e.g., [22,172,177]) continue to appear that have not sufficiently heeded the history of accumulating negative evidence against the assumptions, logic and predictions of previous RTN models.…”

A general model for metabolic scaling in self-similar asymmetric networks

“…This suggests that 3/4 metabolic scaling is robust to maximal variation in the physical length scale factors ( γ μ or γ ν within [0, 1]), as long as the variations in physical diameter scale factors ( β μ or β ν ) are restricted to the range of approximately [0.47, 0.89]. While asymmetry in scale factors has not been directly measured, these qualitative differences in variation in the scale factors have been observed in cardiovascular data both for the human head and torso as well as for mouse lungs [30, 31]. …”

“…A fundamental assumption of the theory is that vascular networks exhibit symmetric branching, where every branch in a given generation has identical geometric properties (namely radius and length). Branching symmetry is rarely, if ever, the case within biology where vascular networks are observed to branch asymmetrically [25–31]. …”

Ecology of ontogenetic body-mass scaling of gill surface area in a freshwater crustacean

“…Fourth, no direct (e.g. experimental) evidence supporting predicted effects of RTNs on metabolic scaling yet exists (Glazier, 2014b), though future research may address this deficiency (see Tekin et al, 2016). Fifth, multiple lines of evidence contradict the predictions of RTN models.…”