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Modeling Vascular Branching Alterations in Polycystic Kidney Disease

The analysis of biological networks encompasses a wide variety of fields from genomic research of protein-protein interaction networks, to the physiological study of biologically optimized tree-like vascular networks. It is certain that different biological networks have different optimization criteria and we are interested in those networks optimized for fluid transport within the circulatory system. Many theories currently exist. For instance, distributive vascular geometry data is typically consistent with a theoretical model that requires simultaneous minimization of both the power loss of laminar flow and a cost function proportional to the total volume of material needed to maintain the system (Murray's law). However, how this optimized system breaks down (or is altered) due to disease has yet to be characterized in detail in terms of branching geometry and geometric interrelationships. This is important for understanding how vasculature remodels under changes of functional demands. For instance, in polycystic kidney disease (PKD), drastic cyst development may lead to a significant alteration of the vascular geometry (or vascular changes may be a preceding event). Understanding these changes could lead to a better understanding of early disease as well as development and characterization of treatment interventions. We have developed an optimal transport network model which simulates distributive vascular systems in health as well as disease in order to better understand changes that may occur due to PKD. We found that reduced perfusion territories, dilated distributive vasculature, and vessel rarefaction are all consequences of cyst development derived from this theoretical model and are a direct result of the increased heterogeneity of local renal tissue perfusion demands.