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Mechanism of Angiogenesis01:10

Mechanism of Angiogenesis

Blood vessel formation starts early during embryonic development, around day 7. In the extraembryonic yolk sac, mesodermal precursor cells called hemangioblast proliferate and differentiate into angioblast. Angioblasts express vascular endothelial growth factor receptor 2 or VEGFR2, which binds VEGF-A, a proangiogenic factor, guiding blood vessel formation. VEGF signaling promotes angioblasts to form a blood island in the developing embryo. Angioblasts further differentiate, giving rise to...
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Related Experiment Video

Updated: Jun 14, 2026

Monitoring Functionality and Morphology of Vasculature Recruited by Factors Secreted by Fast-growing Tumor-generating Cells
09:03

Monitoring Functionality and Morphology of Vasculature Recruited by Factors Secreted by Fast-growing Tumor-generating Cells

Published on: November 23, 2014

Critical-point analysis for three-variable cancer angiogenesis models.

Urszula Forys1, Yuri Kheifetz, Yuri Kogan

  • 1Institute of Applied Mathematics, Informatics and Mechanics, Warsaw University, Banacha 2, 02-097 Warsaw, Poland. urszula@mimuw.edu.pl.

Mathematical Biosciences and Engineering : MBE
|April 8, 2010
PubMed
Summary

Tumor growth models reveal that while angiogenesis is crucial, it may not solely stabilize tumor size. Mathematical analysis of tumor growth, vascularization, and angiogenic factors indicates potential for unlimited growth with oscillations.

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The Corneal Micropocket Assay: A Model of Angiogenesis in the Mouse Eye
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Related Experiment Videos

Last Updated: Jun 14, 2026

Monitoring Functionality and Morphology of Vasculature Recruited by Factors Secreted by Fast-growing Tumor-generating Cells
09:03

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Published on: November 23, 2014

The Corneal Micropocket Assay: A Model of Angiogenesis in the Mouse Eye
11:49

The Corneal Micropocket Assay: A Model of Angiogenesis in the Mouse Eye

Published on: August 16, 2014

Evaluating the Angiogenetic Properties of Ovarian Cancer Stem-Like Cells using the Three-Dimensional Co-Culture System, NICO-1
07:59

Evaluating the Angiogenetic Properties of Ovarian Cancer Stem-Like Cells using the Three-Dimensional Co-Culture System, NICO-1

Published on: December 5, 2020

Area of Science:

  • Mathematical biology
  • Tumor microenvironment dynamics
  • Angiogenesis research

Background:

  • Tumor growth is intricately linked to vascularization and angiogenic factors.
  • Understanding the regulatory mechanisms of new vessel formation is critical.

Purpose of the Study:

  • To perform critical-point analysis on mathematical models of angiogenic tumor growth.
  • To investigate tumor growth, vascularization, and angiogenic factor generation.
  • To explore models with and without time delays in regulatory processes.

Main Methods:

  • Formulation of two mathematical models: one using ordinary differential equations (ODEs) and another using delay differential equations (DDEs).
  • Critical-point analysis to determine the stability of system states.
  • Simulation of tumor and vascular mass dynamics under different initial conditions.

Main Results:

  • In both ODE and DDE models, the only nontrivial critical point is consistently unstable.
  • One of the trivial critical points is always stable across both models.
  • Models predict unlimited tumor growth with potential oscillations if initial conditions are near the unstable critical point.

Conclusions:

  • Angiogenesis alone may be insufficient to explain the stabilization of vascular tumor size.
  • The stability of tumor growth is highly dependent on the initial conditions and model parameters.
  • Oscillatory dynamics in tumor and vascular mass are possible outcomes predicted by the models.