A preliminary study of endothelial cell migration during angiogenesis using a meshless method approach

Area of Science:

• Biomedical Engineering
• Computational Biology
• Cell Biology

Background:

• Angiogenesis, the formation of new blood capillaries, is vital for wound healing and tissue viability.
• Vascular endothelial growth factor (VEGF) is a primary modulator of angiogenesis.
• Computational modeling offers a faster and more economical alternative to experimental methods for studying complex biological processes like angiogenesis.

Purpose of the Study:

• To present a mathematical model for simulating angiogenesis.
• To analyze the effect of vascular endothelial growth factor (VEGF) diffusion gradients on endothelial cell migration.
• To develop a computational tool for studying capillary formation.

Main Methods:

• A mathematical model was developed to simulate endothelial cell migration.
• The Radial Point Interpolation Method (RPIM) was employed for numerical analysis.
• The model utilizes an unorganized nodal cloud and a background mesh with an influence-domain approach for nodal connectivity.

Main Results:

• Numerical results were obtained for an idealized two-dimensional setting.
• The developed RPIM software demonstrates potential as a numerical tool for biological simulations.
• The model focuses on VEGF diffusion gradients influencing cell migration.

Conclusions:

• The developed mathematical model and RPIM software provide a viable numerical approach for studying angiogenesis.
• This computational tool can complement experimental biological and medical research.
• Further development can incorporate more complex biological factors for enhanced accuracy.