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A mechanochemical model of angiogenesis and vasculogenesis

Published online by Cambridge University Press:  15 November 2003

Daphne Manoussaki
Daphne Manoussaki*
Affiliation:
Department of Applied Mathematics, University of Crete, 71409 Heraklion, Greece. daphne@tem.uoc.gr.
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Abstract

Vasculogenesis and angiogenesis are two different mechanisms for bloodvessel formation. Angiogenesis occurs when new vessels sprout from pre-existing vasculature in response to external chemical stimuli. Vasculogenesis occurs via the reorganization of randomly distributed cells into a blood vessel network. Experimental modelsof vasculogenesis have suggested that the cells exert traction forcesonto the extracellular matrix and that these forces may playan important role in the network forming process.In order to study the role of the mechanical and chemical forcesin both of these stages of blood vessel formation, we present amathematical model which assumes that (i) cells exert traction forcesonto the extracellular matrix, (ii) the matrix behaves as a linearviscoelastic material, (iii) the cells move along gradients ofexogenously supplied chemical stimuli (chemotaxis) and (iv) these stimuli diffuse or are uptaken by the cells.We study the equations numerically, present an appropriate finite difference scheme and simulate the formation of vascular networks in a plane. Our results compare very well with experimental observations and suggest that spontaneous formation of networks can be explained via a purely mechanical interaction betweencells and the extracellular matrix. We find that chemotaxis alone is not a sufficient force to stimulate formation of pattern. Moreover, duringvessel sprouting, we find that mechanical forces can help in the formationof well defined vascular structures.

Keywords

Angiogenesisvasculogenesischemotaxisextracellular matrixtheoretical modelsnumerical solution.
Type
Research Article
Information
ESAIM: Mathematical Modelling and Numerical Analysis , Volume 37 , Issue 4: Special issue on Biological and Biomedical Applications , July 2003 , pp. 581 - 599
Copyright
© EDP Sciences, SMAI, 2003

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References

Advani, S.G. and Tucker, C.L.. The use of tensors to describe and predict fiber orientation in short fiber composites. Journal of Rheology , 31:751-784, 1987. CrossRef
Anderson, A.R. and Chaplain, M.A.. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of Mathematical Biology , 60:857-900, 1998. CrossRef
Ausprunk, D.H. and Folkman, J.. Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumour angiogenesis. Microvascular Research , 14:53-65, 1977. CrossRef
Chaplain, M.A.. Mathematical modelling of angiogenesis. Journal of Neurooncology , 50:37-51, 2000. CrossRef
Chaplain, M.A. and Anderson, A.R.. Mathematical modelling, simulation and prediction of tumour-induced angiogenesis. Invasion Metastasis , 16(4-5):222-234, 1996.
J. Cook. Mathematical Models for Dermal Wound Healing: Wound Contraction and Scar Formation. PhD thesis, University of Washington, 1995.
Drake, C.J. and Jacobson, A.G.. A survey by scanning electron microscopy of the extracellular matrix and endothelial components of the primordial chick heart. Anatomical Record , 222:391-400, 1988. CrossRef
C.J. Drake and C.D. Little. The morphogenesis of primordial vascular networks. In Charles D. Little, Vladimir Mironov, and E. Helene Sage, editors, Vascular Morphogenesis: In Vivo, In Vitro, In Mente, chapter 1.1, pages 3-19. Birkauser, Boston, MA, 1998.
Folkman, J. and Haudenschild, C.. Angiogenesis in vitro. Nature , 288:551-556, 1980. CrossRef
Gaffney, E.A., Pugh, K., Maini, P.K., and Arnold, F.. Investigating a simple model of cutaneous would healing angiogenesis. Journal of Mathematical Biology , 45:337-374, 2002. CrossRef
Hanahan, D.. Signaling vascular morphogenesis and maintenance. Science , 227:48-50, 1997. CrossRef
Holmes, M.J. and Sleeman, B.D.. A mathematical model of tumor angiogenesis incorporating cellular traction and viscoelastic effects. Journal of Theoretical Biology , 202:95-112, 2000. CrossRef
Lanir, Y.. Constitutive equations for fibrous connective tissues. Journal of Biomechanics , 16(1):1-12, 1983. CrossRef
Levine, H.A., Sleeman, B.D., and Nilsen-Hamilton, M.. Mathematical modeling of the onset of capillary formation initiating angiogenesis. Journal of Mathematical Biology , 42:195-238, 2001. CrossRef
D. Manoussaki. Modelling the formation of vascular networks in vitro . PhD thesis, University of Washington, 1996.
Manoussaki, D., Lubkin, S.R., Vernon, R.B., and Murray, J.D.. A mechanical model for the formation of vascular networks in vitro. Acta Biotheoretica , 44(3-4):271-282, 1996. CrossRef
Markwald, R.R., Fitzharris, T.P., Bolender, D.L., and Bernanke, D.H.. Sturctural analysis of cell:matrix association during the morphogenesis of atrioventricular cushion tissue. Developmental Biology , 69(2):634-54, 1979. CrossRef
H. Meinhardt. Models for the formation of netline structures. In Charles D. Little, Vladimir Mironov, and E. Helene Sage, editors, Vascular Morphogenesis: In Vivo, In Vitro, In Mente, chapter 3.1, pages 147-172. Birkauser, Boston, MA, 1998.
J.D. Murray, D. Manoussaki, S.R. Lubkin, and R.B. Vernon. A mechanical theory of in vitro vascular network formation. In Charles D. Little, Vladimir Mironov, and E. Helene Sage, editors, Vascular Morphogenesis: In Vivo, In Vitro, In Mente, chapter 3.2, pages 173-188. Birkauser, Boston, MA, 1998.
Murray, J.D., Oster, G.F., and Harris, A.K.. A mechanical model for mesenchymal morphogenesis. Journal of Mathematical Biology , 17:125-129, 1983.
Oster, G.F., Murray, J.D., and Harris, A.K.. Mechanical aspects of mesenchymal morphogenesis. Journal of embryology and experimental morphology , 78:83-125, 1983.
Pardanaud, L., Yassine, F., and Dieterlen-Lievre, F.. Relationship between vasculogenesis, angiogenesis and haemopoiesis during avian ontogeny. Development , 105:473-485, 1989.
Risau, W., Sariola, H., Zerwes, H.G., Sasse, J., Ekblom, P., Kemler, R., and Doetschmann, T.. Vasculogenesis and angiogenesis in embryonic-system-cell-derived embryoid bodies. Development , 102:471-478, 1988.
Tong, S. and Yuan, F.. Numerical simulations of angiogenesis in the cornea. Microvascular Research , 61:14-27, 2001. CrossRef
Vernon, R.B., Angello, J.C., Iruela-Arispe, M.L., Lane, T.F., and Sage, E.H.. Reorganization of basement membrane matrices by cellular traction promotes the formation of cellular networks in vitro. Laboratory Investigation , 66(5):536-547, 1992.
Vernon, R.B., Lara, S.L., Drake, C.J., Iruela-Arispe, M.L., Angello, J.C., Little, C.D., Wight, T.N., and Sage, E.H.. Organized type I collagen influences endothelial patterns during `spontaneous angiogenesis in vitro': Planar cultures as models of vascular development. In Vitro Cellular and Developmental Biology , 31(2):120-131, 1995. CrossRef
Vernon, R.B. and Sage, E.H.. Between molecules and morphology: extracellular matrix and the creation of vascular form. American Journal of Pathology , 147:873-883, 1995.