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In this work, we introduce an algorithmic approach to generate microvascularnetworks starting from larger vessels that can be reconstructed withoutnoticeable segmentation errors. Contrary to larger vessels, the reconstructionof fine-scale components of microvascular networks shows significantsegmentation errors, and an accurate mapping is time and cost intense. Thusthere is a need for fast and reliable reconstruction algorithms yieldingsurrogate networks having similar stochastic properties as the original ones.The microvascular networks are constructed in a marching way by adding vesselsto the outlets of the vascular tree from the previous step. To optimise thestructure of the vascular trees, we use Murray's law to determine the radii ofthe vessels and bifurcation angles. In each step, we compute the local gradientof the partial pressure of oxygen and adapt the orientation of the new vesselsto this gradient. At the same time, we use the partial pressure of oxygen tocheck whether the considered tissue block is supplied sufficiently with oxygen.Computing the partial pressure of oxygen, we use a 3D-1D coupled model forblood flow and oxygen transport. To decrease the complexity of a fully coupled3D model, we reduce the blood vessel network to a 1D graph structure and use abi-directional coupling with the tissue which is described by a 3D homogeneousporous medium. The resulting surrogate networks are analysed with respect tomorphological and physiological aspects.

A 3D-1D coupled blood flow and oxygen transport model to generate microvascular networks