Structural morphology of renal vasculature

Abstract

An automatic segmentation technique has been developed and applied to two renal micro-computer tomography (CT) images. With the use of a 20-microm voxel resolution image, the arterial and venous trees were segmented for the rat renal vasculature, distinguishing resolving vessels down to 30 microm in radius. A higher resolution 4-microm voxel image of a renal vascular subtree, with vessel radial values down to 10 microm, was segmented. Strahler ordering was applied to each subtree using an iterative scheme developed to integrate information from the two segmented models to reconstruct the complete topology of the entire vascular tree. An error analysis of the assigned orders quantified the robustness of the ordering process for the full model. Radial, length, and connectivity data of the complete arterial and venous trees are reported by order. Substantial parallelism is observed between individual arteries and veins, and the ratio of parallel vessel radii is quantified via a power law. A strong correlation with Murray's Law was established, providing convincing evidence of the "minimum work" hypothesis. Results were compared with theoretical branch angle formulations, based on the principles of "minimum shear force," were inconclusive. Three-dimensional reconstructions of renal vascular trees collected are made freely available for further investigation into renal physiology and modeling studies.

Vascular coupling induces synchronization, quasiperiodicity, and chaos in a nephron tree

“…We make use of a relatively simple model of nephron dynamics 19,20 and consider a tapering cortical radial artery whose dimensions are based on recent measurements made in rat kidneys. 24 …”

“…We assume, therefore, that the field of interacting nephrons consists of all those with afferent arterioles originating from a single cortical radial artery, which includes superficial ͑cortical͒ as well as deep ͑juxtamedullary͒ nephrons. The number of nephrons originating from a single cortical radial artery varies somewhat; estimates are in the range of 20-40; 23,24 we used 22, of which 14 were defined as cortical and 8 as medullary. Figure 1 shows the anatomic basis for the vascular model.…”

“…The values of R k b are calculated as 8 l k / r k 4 , using a blood viscosity of 4.6 cPoise ͑1 cPoise= 10 −3 kg/ m s͒, a segment length of 0.02 cm, and radius values r k taken from the literature. 24 Values of P g and R g are calculated in the nephron model. This formulation ͑1͒ is based on the assumption that the vascular tree can be described as purely resistive and that short term, local accumulation of blood can be neglected.…”

“…The pressure drop was calculated using vessel length and radius data from Ref. 24. There is a pressure drop of a few percent along the cortical radial artery as it distributes blood to the afferent arterioles, and there are minor oscillations in pressure.…”

Exercise-induced maximum metabolic rate scaled to body mass by the fractal dimension of the vascular distribution network

“…Estimates obtained from the literature by Huo & Kassab (2012) for rats, cats, dogs, pigs and humans for pulmonary and heart networks with predominantly pulsatile flow are included in Table 1. Additional estimates of rat kidney arterial and venous networks (Nordsletten et al, 2006) are provided in Table 1, to obtain a total of 14 specie/organ arterial and venous networks. The two estimates of D > 3 are included in the weighed estimate of Table 1 as they exceed the limit D = 3 probably because of measurement error.…”