Electronic supplementary material for:

Markus R. Owen, Tomás Alarcón, Philip K. Maini and Helen M. Byrne
Angiogenesis and vascular remodelling in normal and cancerous tissues

Journal of Mathematical Biology, doi: 10.1007/s00285-008-0213-z

The following provides links to animations that correspond to simulations illustrated in the manuscript:

  • Fig. 3 in manuscript: Evolution, from an initial pair of straight vessels (both with inflow at the left and outflow at the right), of an irregular vascular network via angiogenesis. Note that the normal cells most distant from the original two parent vessels initially die, until angiogenesis provides sufficient oxygen to sustain them. Parameter values are as in Tables 1-4 in the manuscript.
    Click for movie: jmb_normal11dup3_vt5rs2low.mov

  • Fig. 5 in manuscript: Pruning followed by angiogenesis.
    (A) The chemotactic sensitivity γ=8 x 104, and the new vessels are poorly directed and hence lead to poorer vascularisation.
    Click for movie: jmb_prune21dup3_vt5rs2low.mov
    (B) Increasing the chemotaxis coefficient to γ=8 x 105 gives more rapid and better directed sprout growth, hence effectively remodelling the vasculature and oxygenating the whole tissue region.
    Click for movie: jmb_prune19dup3_vt5rs11low.mov

  • Fig. 5 in manuscript: Angiogenesis from a single initial vessel.
    (B) Parameters as for Figure 5B, including an inflow pressure Pin=22 mmHg. From a single initial vessel the whole tissue region is fully oxygenated after 800 time units. At first, normal cells far from the parent vessel die, and then the whole region is repopulated in a wave-like manner as new vessels and normal cells grow together.
    Click for movie: jmb_prune22dup3_vt4rs5low.mov
    (C) For a lower inflow pressure, Pin=19 mmHg, the balance between angiogenesis and vessel regression is altered, so that the vessel network cannot extend across the whole region, and hypoxia induced VEGF production is not eliminated.
    Click for movie: jmb_prune25dup3_vt4low.mov

  • A simulation with tumour cells implanted in a tissue with normal cells and two linear initial vessels (as in Figure 3). Notice how the tumour remains confined close to the upper vessel until connections are made that allow it to spread fully into the lower half of the domain. Also worth noting is that tumour cells' increased oxygen consumption triggers VEGF expression by more normal cells as well, since they also experience resultant low oxygen levels. The final vascular density is significantly higher than with normal cells only (see Figure 12). Parameter values are as in Tables 1-4.
    Click for movie: jmb_tumour14dup3_vt4low.mov