2020/01/20 by Tobias Köppl, Köppl, Tobias, Ettore Vidotto +3 · 6 citations
Mathematics · Medicine · #Mathematical Biology Tumor Growth #Cardiovascular Health and Disease Prevention #MRI in cancer diagnosis
paper · pdf · doi:10.48550/arxiv.2001.07186
In this work, we introduce an algorithmic approach to generate microvascular\nnetworks starting from larger vessels that can be reconstructed without\nnoticeable segmentation errors. Contrary to larger vessels, the reconstruction\nof fine-scale components of microvascular networks shows significant\nsegmentation errors, and an accurate mapping is time and cost intense. Thus\nthere is a need for fast and reliable reconstruction algorithms yielding\nsurrogate networks having similar stochastic properties as the original ones.\nThe microvascular networks are constructed in a marching way by adding vessels\nto the outlets of the vascular tree from the previous step. To optimise the\nstructure of the vascular trees, we use Murray's law to determine the radii of\nthe vessels and bifurcation angles. In each step, we compute the local gradient\nof the partial pressure of oxygen and adapt the orientation of the new vessels\nto this gradient. At the same time, we use the partial pressure of oxygen to\ncheck whether the considered tissue block is supplied sufficiently with oxygen.\nComputing the partial pressure of oxygen, we use a 3D-1D coupled model for\nblood flow and oxygen transport. To decrease the complexity of a fully coupled\n3D model, we reduce the blood vessel network to a 1D graph structure and use a\nbi-directional coupling with the tissue which is described by a 3D homogeneous\nporous medium. The resulting surrogate networks are analysed with respect to\nmorphological and physiological aspects.\n