Hopf point analysis for angiogenesis models

In this paper we present several ODE systems encoding the most essential observations and assumptions about the complex hierarchical inter- active processes of tumor neo-vascularization (angiogenesis). From experi- mental results we infer that a significant marker of tumor aggressiveness is the oscillatory behavior of tumor size, which is driven by its vascularization dynamics. To study the forces underlying these oscillations we perform a Hopf point analysis of the angiogenesis models. In the analyzed models Hopf points appear if and only if a nontrivial set of time-delays is introduced into the tu- mor proliferation or the neo-vascularization process. We suggest to examine in laboratory experiments how to employ these results for containing cancer growth.

[1]  H. Augustin,et al.  Analysis of blood vessel maturation processes during cyclic ovarian angiogenesis. , 1998, Laboratory investigation; a journal of technical methods and pathology.

[2]  M. Neeman,et al.  Dynamic remodeling of the vascular bed precedes tumor growth: MLS ovarian carcinoma spheroids implanted in nude mice. , 1999, Neoplasia.

[3]  Z. Agur,et al.  A computer algorithm describing the process of vessel formation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumor growth , 2004, Angiogenesis.

[4]  R. Kerbel.  Tumor angiogenesis: past, present and the near future. , 2000, Carcinogenesis.

[5]  A. Woolf,et al.  Hypoxia up-regulates angiopoietin-2, a Tie-2 ligand, in mouse mesangial cells. , 2000, Kidney international.

[6]  G. Yancopoulos,et al.  New model of tumor angiogenesis: dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF , 1999, Oncogene.

[7]  Pamela F. Jones,et al.  Requisite Role of Angiopoietin-1, a Ligand for the TIE2 Receptor, during Embryonic Angiogenesis , 1996, Cell.

[8]  Y. Dor,et al.  Vascular endothelial growth factor and vascular adjustments to perturbations in oxygen homeostasis. , 2001, American journal of physiology. Cell physiology.

[9]  L. Ellis,et al.  Differential expression of angiopoietin‐1 and angiopoietin‐2 in colon carcinoma , 2001, Cancer.

[10]  Z. Agur,et al.  Vessel maturation effects on tumour growth: validation of a computer model in implanted human ovarian carcinoma spheroids. , 2005, European journal of cancer.

[11]  J. Folkman.  Angiogenesis in cancer, vascular, rheumatoid and other disease , 1995, Nature Medicine.

[12]  E. Keshet,et al.  A plasticity window for blood vessel remodelling is defined by pericyte coverage of the preformed endothelial network and is regulated by PDGF-B and VEGF. , 1998, Development.

[13]  D. Pode,et al.  Selective ablation of immature blood vessels in established human tumors follows vascular endothelial growth factor withdrawal. , 1999, The Journal of clinical investigation.

[14]  Pamela F. Jones,et al.  Isolation of Angiopoietin-1, a Ligand for the TIE2 Receptor, by Secretion-Trap Expression Cloning , 1996, Cell.

[15]  P. Carmeliet,et al.  Angiogenesis in cancer and other diseases , 2000, Nature.

[16]  S. McLeskey,et al.  Expression and function of angiopoietin-1 in breast cancer , 2000, British Journal of Cancer.

[17]  E. Keshet,et al.  Conditional switching of vascular endothelial growth factor (VEGF) expression in tumors: induction of endothelial cell shedding and regression of hemangioblastoma-like vessels by VEGF withdrawal. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

[18]  Thomas N. Sato,et al.  Angiopoietin-2, a natural antagonist for Tie2 that disrupts in vivo angiogenesis. , 1997, Science.

[19]  Atsushi Namiki,et al.  Hypoxia Induces Vascular Endothelial Growth Factor in Cultured Human Endothelial Cells (*) , 1995, The Journal of Biological Chemistry.

[20]  T. Suda,et al.  Role for Angiogenesis Expression of Angiopoietin-2 in Human Glioma Cells and Its Updated Version , 2001 .

[21]  R K Jain,et al.  Endothelial cell death, angiogenesis, and microvascular function after castration in an androgen-dependent tumor: role of vascular endothelial growth factor. , 1998, Proceedings of the National Academy of Sciences of the United States of America.

[22]  K. Suzuma,et al.  Hypoxia and Vascular Endothelial Growth Factor Selectively Up-regulate Angiopoietin-2 in Bovine Microvascular Endothelial Cells* , 1999, The Journal of Biological Chemistry.