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.

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The field modelling language FieldML is being developed as a standard for modelling and interchanging field descriptions in software, suitable for a wide range of computation techniques. It comprises a rich set of operators for defining generalized fields as functions of other fields, starting with basic domain fields including sets of discrete objects and coordinate systems. It is extensible by adding new operators and by their arbitrary combination in expressions, making it well suited for describing the inherent complexity of biological materials and organ systems. This paper describes the concepts behind FieldML, including a simple example of a spatially varying finite-element field. It outlines current implementations in established, open source computation and visualization software, both drawing on decades of bioengineering modelling software development experience.

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