Computational and mathematical modeling of angiogenesis

Area of Science:

• * Mathematical and computational modeling
• * Biomedical engineering
• * Cell biology

Background:

• * Angiogenesis, the formation of new blood vessels, is crucial in physiological and pathological processes.
• * Diverse mathematical and computational models have been developed over the last 20 years to study angiogenesis.
• * These models address various scales, from molecular signaling to whole-tissue vascular networks.

Purpose of the Study:

• * To review and synthesize knowledge gained from mathematical and computational models of angiogenesis.
• * To explore the application of these models in normal physiological growth, tumorigenesis, wound healing, and tissue engineering.
• * To guide the design of therapeutic strategies by understanding model-based insights.

Main Methods:

• * Categorization of angiogenesis models based on modeling approach, spatial-temporal scales, and research questions.
• * Review of simplification strategies and assumptions employed in model development.
• * Discussion of model validation techniques and their importance.

Main Results:

• * Models have elucidated mechanisms of endothelial cell proliferation, vessel assembly, and tumor-induced angiogenesis.
• * Insights from modeling inform understanding of angiogenesis in diverse contexts including cancer and tissue repair.
• * A framework is provided for classifying and understanding different types of angiogenesis models.

Conclusions:

• * Mathematical and computational modeling has significantly advanced the understanding of angiogenesis.
• * Continued development and application of validated models are essential for addressing unresolved questions in angiogenesis research.
• * Modeling provides a powerful tool for therapeutic strategy design in angiogenesis-related diseases.