Network Analyses of Murine Glomeruli

Kidneys filter blood through capillary bundles called glomeruli. Improved understanding of glomerular topological and spatial structure may inform our understanding of its development and function.

We devised a new imaging approach to 12 murine glomeruli, using automated microtome tape to collect .5-micron serial sections and scanning electron microscopy to image these at 50 nm/pixel resolution. We used virtual reality to trace capillary networks and undertook several network analyses, starting with statistical summaries.

Direct inspections revealed a no-cross zone between afferent and efferent branches on the vascular pole side, consistent with developmental obstacles to vascular shortcuts. Using circuit analysis, centrality analysis, and the fundamental theorem of calculus, we constructed an “average” arteriolar curve that confirms an avoidance of inter-arteriolar space.

The non-planarity of all observed adult glomeruli precludes angiogenesis by splitting alone. As a basis for more precise estimation, we developed an angiogenic growth model with tunable sprouting and splitting rates. We found our empirical models to be consistent with splitting rates between 0% and 50% but that empirical topologies were underdetermined by the model.