  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.
