2020 **Abstract:** 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 origin…

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“…In Fig 8(c), we show the iteration numbers required to make the relative difference smaller than 1 × 10 −3 . We can see that the iteration numbers are comparable for the simple and refined vessel network structures, while both of them increase slightly with the mesh size N. The increase in iteration numbers is mainly due to the choice of the temporal step size Δt in Eq (14). As we have discussed above, a large Δt is helpful for convergence while a too large Δt can induce instability in the iteration.…”

confidence: 79%

“…In Fig 8(c), we show the iteration numbers required to make the relative difference smaller than 1 × 10 −3 . We can see that the iteration numbers are comparable for the simple and refined vessel network structures, while both of them increase slightly with the mesh size N. The increase in iteration numbers is mainly due to the choice of the temporal step size Δt in Eq (14). As we have discussed above, a large Δt is helpful for convergence while a too large Δt can induce instability in the iteration.…”

confidence: 79%

“…., i d ) is the index of the mesh point. Due to the nonlinearity in the consumption function M(�), we use the standard multigrid algorithm combined with the Newton's method to solve Eq (14). According to our numerical tests, only a few steps of Newton-iteration are sufficient to make the numerical error small enough.…”

confidence: 99%

“…The first area Figure 4 of focus (panel a in Figure 4 ) bridges the cell to tissue scale by modeling the formation and evolution of tumor-induced angiogenic networks which are predominately modeled using a discrete (lattice-based and lattice-free), continuous, or hybrid strategy similar to those discussed in Section 3 [ 87 , 88 , 123 , 130 , 131 , 132 ]. Discrete approaches typically model individual TEC movement, while continuous approaches model the change in a spatially averaged, continuous variable (e.g., vasculature density or vascular volume fraction).…”

confidence: 99%

“…However, attempts to compare transport properties of vascular networks with different morphological features are still quite limited. This could be achieved by artificially removing/adding vessels from a reference structure based on statistical or empirical rules [14,15]. However, the resultant structures are no longer real, and experimental validation is prohibitive.…”

confidence: 99%