Scaling Laws for Branching Vessels of Human Cerebral Cortex

Abstract

Vascular architecture, particularly of cerebral microvessels, has profound implications for both health and disease in a variety of areas, such as neuroimaging, angiogenesis and development, Alzheimer's disease, and vascular tumors. We analyzed the architecture of tree-like vessels of the human cerebral cortex. Digital three-dimensional images of the microvascular network were obtained from thick sections of India ink-injected human brain by confocal laser microscopy covering a large zone of secondary cortex. A novel segmentation method was used to extract the skeleton and measure the diameter at every vertex. In this paper, we focus on the topology of the cortical tree-like vessels. Using stem-crown decomposition, power-scaling laws were shown to govern the relationships between integrated parameters, such as the distal cumulative length, volume, or normalized flow. This led us toward an experimental confirmation of the allometric equation between mass and metabolic rate. Inversely, the power-law model did not match the relationships between local parameters, such as diameter, and integrated ones. As a consequence, Murray's law did not appropriately model the architecture of cerebrovascular bifurcations. This study provides a unique, large database and mathematical characterization that may prove valuable for modeling the cerebral.