zbMATH — the first resource for mathematics

A gradient-driven mathematical model of antiangiogenesis. (English) Zbl 0962.92018
Summary: We present a mathematical model describing the angiogenic response of endothelial cells to a secondary tumour. It has been observed experimentally that while the primary tumour remains in situ, any secondary tumours that may be present elsewhere in the host can go undetected, whereas removal of the primary tumour often leads to the sudden appearance of these hitherto undetected metastases – called occult metastases.
In this paper, a possible explanation for this suppression of secondary tumours by the primary tumour is given in terms of the presumed migratory response of endothelial cells in the neighbourbood of the secondary tumour. Our model assumes that the endothelial cells respond chemotactically to two opposing chemical gradients: a gradient of tumour angiogenic factor, set up by the secretion of angiogenic cytokines from the secondary tumour; and a gradient of angiostatin, set up in the tissue surrounding any nearby vessels. The angiostatin arrives there through the blood system (circulation), having been originally secreted by the primary tumour. This gradient-driven endothelial cell migration therefore provides a possible explanation of how secondary tumours (occult metastases) can remain undetected in the presence of the primary tumour yet suddenly appear upon surgical removal of the primary tumour.

92C50 Medical applications (general)
92C37 Cell biology
35Q92 PDEs in connection with biology, chemistry and other natural sciences
Full Text: DOI
[1] Folkman, J., Angiogenesis in cancer, vascular, rheumatoid and other disease, Nature med., 1, 27-31, (1995)
[2] Folkman, J.; Klagsburn, M., Angiogenic factors, Science, 235, 442-447, (1987)
[3] Muthukkaruppan, V.R.; Kubai, L.; Auerbach, R., Tumour-induced neovascularization in the mouse eye, J. natl. cancer inst., 69, 699-705, (1982)
[4] Chambers, A.F.; Matrisian, L.M., Changing views of the role of matrix metalloproteinases in metastasis, J. natl. cancer inst., 89, 1260-1270, (1997)
[5] Lawrence, J.A.; Steeg, P.S., Mechanisms of tumour invasion and metastasis, World J. urol., 14, 124-130, (1996)
[6] Stetler-Stevenson, W.G.; Aznavoorian, S.; Liotta, L.A., Tumor cell interactions with the extracellular matrix during invasion and metastasis, Ann. rev. cell biol., 9, 541-573, (1993)
[7] Folkman, J., Angiogenesis in cancer, vascular, rheumatoid and other disease, Nature med., 1, 27-31, (1995)
[8] O’Reilly, M.S.; Holmgren, L.; Shing, Y.; Chen, C.; Rosenthal, R.A.; Moses, M.; Lane, W.S.; Cao, Y.; Sage, E.H.; Folkman, J., Angiostatin: A novel angiogenesis inhibitor that mediates the suppression of metastases by Lewis lung carcinoma, Cell, 79, 315-328, (1994)
[9] O’Reilly, M.S.; Boehm, T.; Shing, Y.; Fukami, N.; Vasios, G.; Lane, W.S.; Flynn, E.; Birkhead, J.R.; Olsen, B.R.; Folkman, J., Endostatin: an endogenous inhibitor of angiogenesis and tumour growth, Cell, 88, 277-285, (1997)
[10] Ji, W.-R.; Castellino, F.J.; Chang, Y.; Deford, M.E.; Gray, H.; Villarreal, X.; Kondri, M.E.; Marti, D.N.; Llinas, M.; Schaller, J.; Kramer, R.A.; Trail, P.A., Characterization of kringle domains of angiostatin as antagonists of endothelial cell migration, an important process in angiogenesis, Faseb, 12, 1731-1738, (1998)
[11] Himmele, J.C.; Rabenhorst, B.; Werner, D., Inhibition of Lewis lung tumor growth and metastasis by ehrlich ascites tumor growing in the same host, J. cancer res. clin. oncol., 111, 160-165, (1986)
[12] Anderson, A.R.A.; Chaplain, M.A.J., A mathematical model for capillary network formation in the absence of endothelial cell proliferation, Appl. math. lett., 11, 3, 109-114, (1998) · Zbl 0935.92024
[13] Chaplain, M.A.J., Avascular growth, angiogenesis and vascular growth in solid tumours: the mathematical modelling of the stages of tumour development, Mathl. comput. modelling, 23, 6, 47-88, (1996) · Zbl 0859.92012
[14] Balding, D.; McElwain, D.L.S., A mathematical model of tumour-induced capillary growth, J. theor. biol., 114, 53-73, (1985)
[15] Anderson, A.R.A.; Chaplain, M.A.J., Continuous and discrete mathematical models of tumour-induced angiogenesis, Bull. math. biol., 60, 857-899, (1998) · Zbl 0923.92011
[16] Stokes, C.L.; Lauffenburger, D.A., Analysis of the roles of microvessel endothelial cell random motility and chemotaxis in angiogenesis, J. theor. biol., 152, 377-403, (1991)
[17] Orme, M.E.; Chaplain, M.A.J., Two-dimensional models of tumour angiogenesis and anti-angiogenesis strategies, IMA J. math. appl. med. biol., 14, 189-205, (1997) · Zbl 0894.92022
[18] Chaplain, M.A.J.; Orme, M.E., Mathematical modeling of tumor-induced angiogenesis, (), 205-240, Chapter 3.4 · Zbl 0894.92022
[19] Paweletz, N.; Knierim, M., Tumour-related angiogenesis, Crit. rev. oncol. hematol., 9, 197-242, (1989)
[20] Chaplain, M.A.J.; Stuart, A.M., A model mechanism for the chemotactic response of tumour cells to tumour angiogenesis factor, IMA J. math. appl. med. biol., 10, 149-168, (1993) · Zbl 0783.92019
[21] Bray, D., Cell movements, (1992), Garland Publishing New York
[22] Sherratt, J.A.; Murray, J.D., Models of epidermal wound healing, Proc. R. soc. lond., B241, 29-36, (1990)
[23] Chen, C.; Parangi, S.; Tolentino, M.J.; Folkman, J., A strategy to discover circulating angiogenesis inhibitors generated by human tumours, Cancer res., 55, 4230-4233, (1995)
[24] Restky, M.W.; Demicheli, R.; Swartzendruber, D.E.; Bame, P.D.; Wardwell, R.H.; Bonadonna, G.; Speer, J.F.; Valagussa, P., Computer simulation of a breast cancer metastasis model, Breast cancer res. treat., 45, 193-202, (1997)
[25] Holmberg, L.; Baum, M., Work on your theories!, Nat. med., 2, 844-846, (1996)
[26] Paku, S.; Paweletz, N., First steps of tumor-related angiogenesis, Lab. invest., 65, 334-346, (1991)
[27] Sholley, M.M.; Ferguson, G.P.; Seibel, H.R.; Montour, J.L.; Wilson, J.D., Mechanisms of neovascularization. vascular sprouting can occur without proliferation of endothelial cells, Lab. invest., 51, 624-634, (1984)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.