  Microvessels -blood vessels with diameter less than 200 microns- form large,
intricate networks organized into arterioles, capillaries and venules. In these
networks, the distribution of flow and pressure drop is a highly interlaced
function of single vessel resistances and mutual vessel interactions. In this
paper we propose a mathematical and computational model to study the behavior
of microcirculatory networks subjected to different conditions. The network
geometry is composed of a graph of connected straight cylinders, each one
representing a vessel. The blood flow and pressure drop across the single
vessel, further split into smaller elements, are related through a generalized
Ohm's law featuring a conductivity parameter, function of the vessel cross
section area and geometry, which undergo deformations under pressure loads. The
membrane theory is used to describe the deformation of vessel lumina, tailored
to the structure of thick-walled arterioles and thin-walled venules. In
addition, since venules can possibly experience negative transmural pressures,
a buckling model is also included to represent vessel collapse. The complete
model including arterioles, capillaries and venules represents a nonlinear
system of PDEs, which is approached numerically by finite element
discretization and linearization techniques. We use the model to simulate flow
in the microcirculation of the human eye retina, a terminal system with a
single inlet and outlet. After a phase of validation against experimental
measurements, we simulate the network response to different interstitial
pressure values. Such a study is carried out both for global and localized
variations of the interstitial pressure. In both cases, significant
redistributions of the blood flow in the network arise, highlighting the
importance of considering the single vessel behavior along with its position
and connectivity in the network.
