  In this work, we introduce an algorithmic approach to generate microvascular
networks starting from larger vessels that can be reconstructed without
noticeable segmentation errors. Contrary to larger vessels, the reconstruction
of fine-scale components of microvascular networks shows significant
segmentation errors, and an accurate mapping is time and cost intense. Thus
there is a need for fast and reliable reconstruction algorithms yielding
surrogate networks having similar stochastic properties as the original ones.
The microvascular networks are constructed in a marching way by adding vessels
to the outlets of the vascular tree from the previous step. To optimise the
structure of the vascular trees, we use Murray's law to determine the radii of
the vessels and bifurcation angles. In each step, we compute the local gradient
of the partial pressure of oxygen and adapt the orientation of the new vessels
to this gradient. At the same time, we use the partial pressure of oxygen to
check whether the considered tissue block is supplied sufficiently with oxygen.
Computing the partial pressure of oxygen, we use a 3D-1D coupled model for
blood flow and oxygen transport. To decrease the complexity of a fully coupled
3D model, we reduce the blood vessel network to a 1D graph structure and use a
bi-directional coupling with the tissue which is described by a 3D homogeneous
porous medium. The resulting surrogate networks are analysed with respect to
morphological and physiological aspects.
