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Structural morphology of renal vasculature

¹Bioengineering Institute, University of Auckland, Auckland 1001, New Zealand; ²Department of Biological Sciences, Minnesota State University, Mankato, Minnesota; ³Department of Physiology and Biomedical Engineering, Mayo Clinic College of Medicine, Rochester, Minnesota

Submitted 31 July 2005 ; accepted in final form 20 December 2005

An automatic segmentation technique has been developed and applied to two renal micro-computer tomography (CT) images. With the use of a 20-µm voxel resolution image, the arterial and venous trees were segmented for the rat renal vasculature, distinguishing resolving vessels down to 30 µm in radius. A higher resolution 4-µm voxel image of a renal vascular subtree, with vessel radial values down to 10 µm, 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 available¹ for further investigation into renal physiology and modeling studies.

kidney; Strahler ordering; vascular statistics; renal modeling; vascular reconstruction

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