CARD Subgroup Contributed Talks

Jared Barber

IU Indianapolis

"Mathematical model of blood flow in the brain after a major arterial occlusion."

Blood vessel adaptation plays an important role in maintaining healthy and well-oxygenated tissue throughout the body. This is especially true for the brain. To better characterize how blood flow changes when the brain suffers a major arterial occlusion (e.g. during a stroke) and to identify major factors that may affect flow restoration to downstream regions, we created a mathematical model of blood flow in the brain. The network is modeled as multiple larger vessels interconnected with multiple compartments of smaller vessels with each compartment consisting of identical vessels situated in parallel. The model further includes vessel adaptation in response to changes in pressure (myogenic response), wall shear stress (shear response), and oxygen saturation (metabolic response). By varying tissue oxygen demand and incoming pressure, we are able to identify that the number of collateral vessels moving flow from unobstructed to obstructed regions is a major factor. We also predicted a loss of normal function particularly reflected by a shift in the “autoregulation curve”, a curve that reflects the ability of vessels to reasonably respond to increases in pressure. Such results were consistent with experiment and reinforce the appropriateness of treatments that raise flow and oxygenation by minimizing tissue oxygen demand and raising vascular pressure.

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Cory Brunson

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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