Modeling angiogenesis: A discrete to continuum description

Area of Science:

• Biophysics
• Mathematical Biology
• Cell Biology

Background:

• Angiogenesis involves endothelial tip cell migration, anastomosis, and branching to form vascular networks.
• The

Purpose of the Study:

• To systematically derive a continuum model of angiogenesis from a lattice-based cellular automaton.
• To compare discrete and continuum models to understand macroscale manifestations of cell behavior.
• To refine existing continuum models for accurate representation of vessel formation.

Main Methods:

• Developed a mean-field approximation to derive a continuum model from a 2D lattice-based cellular automaton.
• Derived a 1D model from the 2D continuum model to represent angiogenesis in 2D.
• Compared discrete and 1D continuum models to analyze macroscale behavior.

Main Results:

• Endothelial cell creation via the "snail trail" process manifests as a source term for tip cells at the macroscale.
• Phenomenological continuum models qualitatively capture vessel formation but require modification for accuracy.
• Anastomosis imposes cell density restrictions, and violating them leads to model ill-posedness.

Conclusions:

• The derived continuum model offers a more accurate representation of angiogenesis, particularly vessel formation via the snail trail.
• Modifications to existing phenomenological models are necessary for precise representation of vessel formation.
• Excluding self-loops during tip-to-sprout anastomosis is crucial for maintaining vascular front propagation.