Mesoscopic and continuum modelling of angiogenesis

Area of Science:

• Biophysics
• Mathematical Biology
• Cell Biology

Background:

• Angiogenesis, the formation of new blood vessels, is crucial for development and disease, involving complex cell behaviors.
• Existing models often simplify these cellular processes, potentially missing key dynamics.

Purpose of the Study:

• To develop and analyze a mesoscopic lattice-based model for angiogenesis.
• To investigate the influence of stochasticity and discrete cell effects on angiogenesis.
• To compare different stochastic models for endothelial tip cell movement.

Main Methods:

• Developed a mesoscopic lattice-based model incorporating stochastic proliferation and cell movement.
• Analyzed the model's dependence on lattice spacing and cell number.
• Derived the deterministic continuum limit and compared it with existing models.
• Evaluated different stochastic models for endothelial tip cell migration.

Main Results:

• Identified conditions where continuum models are valid and where discrete/stochastic effects dominate angiogenesis.
• Demonstrated that different stochastic models with identical macroscopic behavior yield distinct outcomes in new vessel cell production.
• Highlighted the importance of stochasticity in accurately modeling endothelial tip cell dynamics.

Conclusions:

• The proposed mesoscopic model provides a framework for studying angiogenesis with greater biological realism.
• Understanding the interplay between stochasticity and continuum dynamics is essential for accurate angiogenesis modeling.
• The choice of stochastic model significantly impacts predictions of new vessel formation.