A continuous model of angiogenesis: Initiation, extension, and maturation of new blood vessels  modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes

Xiaoming Zheng; Gou Young Koh; Trachette Jackson

doi:10.3934/dcdsb.2013.18.1109

Article Contents

2013, Volume 18, Issue 4: 1109-1154. Doi: 10.3934/dcdsb.2013.18.1109 open access

This issue Previous Article Using fractal geometry and universal growth curves as diagnostics for comparing tumor vasculature and metabolic rate with healthy tissue and for predicting responses to drug therapies Next Article

A continuous model of angiogenesis: Initiation, extension, and maturation of new blood vessels modulated by vascular endothelial growth factor, angiopoietins, platelet-derived growth factor-B, and pericytes

1.
Department of Mathematics, Central Michigan University, Mount Pleasant, MI 48859
2.
National Research Laboratory for Vascular Biology, Korea Advanced Institute of Science and Technology (KAIST), Daejeon, 305-701
3.
Department of Mathematics, University of Michigan, Ann Arbor, MI 48109

Received: September 30, 2011

Revised: February 29, 2012

Published: May 2013

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Abstract

This work presents a continuous model for three early stage events in angiogenesis: initiation, sprout extension, and vessel maturation. We carefully examine the regulating mechanisms of vascular endothelial growth factor (VEGF) and angiopoietins (Ang1 and Ang2) on the proliferation, migration and maturation of endothelial cells through their endothelium-specific receptor tyrosine kinase VEGFR2 and Tie2, respectively. We also consider the effect of platelet-derived growth factor-B (PDGF-B) on the proliferation and migration of pericytes. For growth factors, we present a mathematical model integrating molecular reactions on blood vessels with tissue-level diffusion. For capillary extension, we develop a visco-elastic model to couple tip cell protrusion, endothelium elasticity, and stalk cell proliferation. Our model reproduces corneal angiogenesis experiments and several anti-angiogenesis therapy results. This model also demonstrates that (1) the competition between Ang1 and Ang2 is the angiogenic switch; (2) the maturation process modulated by pericytes and angiopoietins is crucial to vessel normalization and can explain the resistance to anti-VEGF therapy; (3) combined anti-pericyte and anti-VEGF therapy enhances blood vessel regression over anti-VEGF therapy alone.

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Mathematics Subject Classification: Primary: 92C17, 92C30; Secondary: 92C10, 92C37.

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