Testing hypotheses of glomerular capillary development with geometric and topological data analysis

CoryBrunson

University of Florida

"Testing hypotheses of glomerular capillary development with geometric and topological data analysis"

Blood filtration occurs in renal capillary tufts called glomeruli, the internal structure of which bears on questions of function, development, evolution, and pathology. Due to the low resolution and labor-intensity of imaging technology, only a handful of studies reaching back decades have examined the spatial structure of glomerular capillaries. Several common features have been described, including lobular topology, plausibly associated with robustness to vascular damage, and circuitous geometry, hypothesized to ensure consistent filtration. However, these properties have been neither mathematically defined nor statistically confirmed. Recent developments in serial scanning electron microscopy and virtual reality enabled us to reconstruct the capillary networks of twelve murine glomeruli and trace spatial graph models. We used circuit analysis to represent these as Reeb graphs, the fundamental theorem of calculus to describe a mean trajectory and its curvature, and principal components analysis to reveal lateral and transverse symmetry. Separately, we built a non-spatial random graph growth model based on two mechanisms, angiogenesis and intussusception, which provided evidence that both contribute to development. We then introduced several topological measures of lobularity and found, surprisingly, that empirical glomeruli tend to be less lobular than those generated by our model. Ongoing work focuses on simulation-based attack tolerance and the development of a spatial growth model.
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