Mathematical modeling of capillary formation and development in tumor angiogenesis: Penetration into the stroma


LEVINE H., Pamuk S. , SLEEMAN B., NILSEN-HAMILTON M.

BULLETIN OF MATHEMATICAL BIOLOGY, cilt.63, ss.801-863, 2001 (SCI İndekslerine Giren Dergi) identifier identifier identifier

  • Cilt numarası: 63 Konu: 5
  • Basım Tarihi: 2001
  • Doi Numarası: 10.1006/bulm.2001.0240
  • Dergi Adı: BULLETIN OF MATHEMATICAL BIOLOGY
  • Sayfa Sayıları: ss.801-863

Özet

The purpose of this paper is to present a mathematical model for the tumor vascularization theory of tumor growth proposed by Judah Folkman in the early 1970s and subsequently established experimentally by him and his coworkers [Ausprunk, D. H. and J. Folkman (1977) Migration and proliferation of endothelial cells in performed and newly formed blood vessels during tumor angiogenesis, Microvasc Res., 14, 53-65; Brem, S., B. A. Preis, ScD. Langer, B. A. Brem. and J. Folkman (1997) Inhibition of neovascularization by an extract derived from vitreous Am. J Opthalmol., 84, 323-328; Folkman, J. (1976) The vascularization of tumors, Sci. Am., 234, 58-64; Gimbrone, M. A. Jr, R. S. Cotran, S. B. Leapman and J. Folkman (1974) Tumor growth and neovascularization: an experimental model using the rabbit cornea, J. Nat. Cancer Inst., 52, 413-419]. In the simplest version of this model, an avascular tumor secretes a tumor growth factor (TGF) which is transported across an extracellular matrix (ECM) to a neighboring vasculature where it stimulates endothelial cells to produce a protease that acts as a catalyst to degrade the fibronectin of the capillary wall and the ECM. The endothelial cells then move up the TGF gradient back to the tumor, proliferating and forming a new capillary network. In the model presented here, we include two mechanisms for the action of angiostatin. In the first mechanism, substantiated experimentally, the angiostatin acts as a protease inhibitor. A second mechanism for the production of protease inhibitor from angiostatin by endothelial cells is proposed to be of Michaelis-Menten type. Mathematically, this mechanism includes the former as a subcase.