Three types of vascular architecture: (a) point-like vessels, (b) parallel linear vessels (in a 3D view and a 2D-projection), and (c) linear vessels in 3D.
Distributions of parallel linear vessels: completely randomly distributed pattern (a) and partially randomly distributed pattern with σ = 0 (b), σ = IVD0/10 (c) and σ = IVD0 (d).
Simulated oxygen distributions and histograms for different vascular architectures (top: point-like vessels; middle: parallel linear vessels; bottom: linear vessels in 3D) and vascular fractions (1%, 4%, and 7%, from left to right). The 2D oxygenation maps have an area of 1 × 1 mm2 and the colored scale goes from 0 to 40 mmHg, as indicated in the upper left figure. The grey bins in the histograms mark the HF. Note: For visualization, representative images of the oxygen distribution were selected. Error bars of the bins of the histograms indicate the standard deviation of repeated simulations (n = 20).
Simulated oxygenation histograms for the parallel line architectures of different heterogeneity (top: completely random; middle: partially random with σ = IVD0; bottom: partially random with σ = IVD0/4) and different vascular fractions (1%, 4%, and 7% from left to right). The grey bins in the histograms mark the HF. Error bars indicate the standard deviation of repeated simulations (n = 20).
Intervessel distance distributions for the parallel line architecture assuming different heterogeneities (completely random and partially random distributed with σ = IVD0 and IVD0/4, respectively) and vascular fractions (1%, 4%, and 7% from left to right) for the vessels distribution. To increase statistics, a larger reference volume of 12 × 12 mm2 instead of 1 × 1 mm2 was used for the simulation.
Simulated oxygenation maps and histograms for different types of hypoxia: (a) chronic hypoxia alone, and additional impact of (b) ischemic hypoxia and (c) hypoxemic hypoxia. The grey bins in the histograms mark the HF. Note: For all three cases the same vessel distribution was assumed.
The continuous line shows the measured IVD distribution of a murine carcinoma [data points taken from Konerding et al. (Ref. 40 )] while the dotted line represents the IVD distribution generated by our model for the same mean IVD (corresponding to a vascular fraction of 0.2%) and using the completely random approach to define the heterogeneity.
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