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Related Experiment Video

Updated: Mar 23, 2026

In Vitro Three-Dimensional Sprouting Assay of Angiogenesis Using Mouse Embryonic Stem Cells for Vascular Disease Modeling and Drug Testing
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Mathematical modelling of angiogenesis using continuous cell-based models.

F D Bookholt1, H N Monsuur2, S Gibbs2,3

  • 1Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands.

Biomechanics and Modeling in Mechanobiology
|April 3, 2016
PubMed
Summary
This summary is machine-generated.

This study introduces a 3D mathematical model simulating early angiogenesis, incorporating cell migration and protein dynamics. The model successfully replicates endothelial cell behavior and interactions, validated by experimental data.

Keywords:
AngiogenesisCell-based modelEndothelial cellsFinite-element methodIn vitro experimentsStalk cellsTip cells

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Area of Science:

  • Biophysics
  • Computational Biology
  • Cell Biology

Background:

  • Angiogenesis, the formation of new blood vessels, is crucial for development and disease.
  • Simulating early-stage angiogenesis requires models that capture cell migration and molecular signaling.
  • Endothelial cells differentiate into tip and stalk phenotypes during angiogenesis.

Purpose of the Study:

  • To develop a 3D mathematical formalism for simulating early angiogenesis.
  • To model endothelial cell migration driven by chemotaxis and durotaxis.
  • To investigate the dynamic interactions between stalk and tip cells and key signaling proteins.

Main Methods:

  • A 3D in vitro model treating cells as individual migrating entities.
  • Incorporation of chemotaxis and durotaxis for cell movement.
  • Modeling of vascular endothelial growth factor, delta-like ligand 4, and other proteins via reaction-diffusion equations.
  • Hybrid approach combining individual cell-based and continuum methods.

Main Results:

  • The 3D model successfully simulates early angiogenesis.
  • The model captures dynamic interactions and phenotype switching between endothelial cell types.
  • Qualitative confirmation of the model's feasibility through experimental results.

Conclusions:

  • The developed mathematical formalism provides a feasible approach for simulating early angiogenesis.
  • The model's ability to integrate cell behavior and molecular signaling offers insights into blood vessel formation.
  • This computational framework can be extended for further studies in vascular biology.