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. 2007 May 1;92(9):3105-21.
doi: 10.1529/biophysj.106.101501. Epub 2007 Feb 2.

A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis

Amy L Bauer  1 , Trachette L Jackson, Yi Jiang
Affiliations

A cell-based model exhibiting branching and anastomosis during tumor-induced angiogenesis

Amy L Bauer et al. Biophys J. .

Abstract

This work describes the first cell-based model of tumor-induced angiogenesis. At the extracellular level, the model describes diffusion, uptake, and decay of tumor-secreted pro-angiogenic factor. At the cellular level, the model uses the cellular Potts model based on system-energy reduction to describe endothelial cell migration, growth, division, cellular adhesion, and the evolving structure of the stroma. Numerical simulations show: 1), different tumor-secreted pro-angiogenic factor gradient profiles dramatically affect capillary sprout morphology; 2), average sprout extension speeds depend on the proximity of the proliferating region to the sprout tip, and the coordination of cellular functions; and 3), inhomogeneities in the extravascular tissue lead to sprout branching and anastomosis, phenomena that emerge without any prescribed rules. This model provides a quantitative framework to test hypotheses on the biochemical and biomechanical mechanisms that control tumor-induced angiogenesis.

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Figures

FIGURE 1
FIGURE 1
An illustration of early events in sprouting angiogenesis: VEGF-mediated endothelial cell activation and degradation of the basement membrane, subsequent migration and invasion into the stroma led by tip cells extending filopodia, cell division, and endothelial cell interaction with extracellular matrix fibers. This illustration emphasizes that the processes involved in angiogenesis are controlled at the level of individual cells. In this context, cellular dynamics are a discrete process and a cell-based model is a better description over continuous models, which deal with cell densities.
FIGURE 2
FIGURE 2
The geometry of the initial domain. An EC bud (dark gray) protrudes into the domain from the parent blood vessel on the left; an avascular tumor resides outside the domain on the right-hand side and supplies VEGF to the stroma. The space between represents the stroma and is composed of extracellular matrix fibers (light gray), tissue-specific cells (black), and interstitial fluid (gray).
FIGURE 3
FIGURE 3
Representative simulation showing the model's ability to reproduce realistic capillary sprout morphologies. Sprouts migrate along matrix fibers up chemical gradients of VEGF. The structure of the matrix guides sprout migration and affects cell shape and orientation. The arrow identifies a cell that has elongated due to chemotactic forces and adhesion to the matrix. Parameters used are given in the parameter table except γe = 0.7 and γt = 0.8. Snapshot at 16.6 days.
FIGURE 4
FIGURE 4
The markedly different capillary sprout morphologies that result from shallow (a) versus steep (c) VEGF gradients. Swollen, invasive sprouts result from shallow VEGF gradients that develop when freely soluble VEGF is expressed (b), whereas when matrix-bound VEGF isoforms are assumed, steep gradients develop and result in narrower capillary sprouts (d). Both results concur with the experimental observations of Lee et al. (32). Parameters are given in the parameter table. Snapshots at (b) 9.4 and (d) 16.6 days.
FIGURE 5
FIGURE 5
The relationship between the average rate of sprout extension and the location of the proliferating region. The further the proliferating region from the migrating tip, the faster the average rate of sprout extension due to the interplay between the chemotactic forces exerted by the migrating tip and competition for space by the proliferating cells. Error bars represent standard deviations from the mean using a sample of 12 simulations. Parameters used are as given in the parameter table except γe = 0.7 and γt = 0.8.
FIGURE 6
FIGURE 6
Numerical simulations ruling out the possibility that branching is induced solely by the tessellated structure of the stroma. For an identical parameter set, (a) depicts a branch emerging from the main capillary as a result of anisotropies in the stroma, (b) demonstrates that the structure of the matrix fibers alone can induce branching, and (c) shows branch formation induced by resident tissue cells. No branching occurs in a homogeneous extracellular environment due to a loss of adhesive guidance cues (d). Parameters are given in Table 1. Results suggest two plausible mechanisms for sprout branching: the resistance created by other cells in the tissue and the structure of matrix fibers. Snapshot at 16.6 days.
FIGURE 7
FIGURE 7
The development of capillary sprouts from five endothelial cell buds. Two neighboring sprouts have fused together forming a loop, a process known as anastomosis. In this simulation, anastomosis was a preferred lower energy state structure given the known physical dynamics at the cellular level (Supplementary Material, Movie S4). Parameters are given in the parameter table. Snapshot at 16.6 days.
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