A graph theory model of the glomerular capillary network and its development

Abstract Graph theory methods were used to analyze the topology of the renal glomerular capillary network using data both from a serial reconstruction of a rat glomerulus and from the literature. The graphs obtained were tested for planarity, and all but one were found to be nonplanar. This result indicated that the development of the glomerular capillary network must include a nonplanar growth process, and new growth models were proposed. In addition, the statistical properties of capillary branching patterns were analyzed, and a node degree distribution function estimate was obtained.