A mechanochemical model of angiogenesis and vasculogenesis

Daphne Manoussaki

ESAIM: Mathematical Modelling and Numerical Analysis (2010)

  • Volume: 37, Issue: 4, page 581-599
  • ISSN: 0764-583X

Abstract

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Vasculogenesis and angiogenesis are two different mechanisms for blood vessel 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 models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming process. In order to study the role of the mechanical and chemical forces in both of these stages of blood vessel formation, we present a mathematical model which assumes that (i) cells exert traction forces onto the extracellular matrix, (ii) the matrix behaves as a linear viscoelastic material, (iii) the cells move along gradients of exogenously 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 between cells and the extracellular matrix. We find that chemotaxis alone is not a sufficient force to stimulate formation of pattern. Moreover, during vessel sprouting, we find that mechanical forces can help in the formation of well defined vascular structures.

How to cite

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Manoussaki, Daphne. "A mechanochemical model of angiogenesis and vasculogenesis." ESAIM: Mathematical Modelling and Numerical Analysis 37.4 (2010): 581-599. <http://eudml.org/doc/194179>.

@article{Manoussaki2010,
abstract = { Vasculogenesis and angiogenesis are two different mechanisms for blood vessel 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 models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming process. In order to study the role of the mechanical and chemical forces in both of these stages of blood vessel formation, we present a mathematical model which assumes that (i) cells exert traction forces onto the extracellular matrix, (ii) the matrix behaves as a linear viscoelastic material, (iii) the cells move along gradients of exogenously 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 between cells and the extracellular matrix. We find that chemotaxis alone is not a sufficient force to stimulate formation of pattern. Moreover, during vessel sprouting, we find that mechanical forces can help in the formation of well defined vascular structures. },
author = {Manoussaki, Daphne},
journal = {ESAIM: Mathematical Modelling and Numerical Analysis},
keywords = {Angiogenesis; vasculogenesis; chemotaxis; extracellular matrix; theoretical models; numerical solution.; angiogenesis; theoretical models; numerical solutions},
language = {eng},
month = {3},
number = {4},
pages = {581-599},
publisher = {EDP Sciences},
title = {A mechanochemical model of angiogenesis and vasculogenesis},
url = {http://eudml.org/doc/194179},
volume = {37},
year = {2010},
}

TY - JOUR
AU - Manoussaki, Daphne
TI - A mechanochemical model of angiogenesis and vasculogenesis
JO - ESAIM: Mathematical Modelling and Numerical Analysis
DA - 2010/3//
PB - EDP Sciences
VL - 37
IS - 4
SP - 581
EP - 599
AB - Vasculogenesis and angiogenesis are two different mechanisms for blood vessel 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 models of vasculogenesis have suggested that the cells exert traction forces onto the extracellular matrix and that these forces may play an important role in the network forming process. In order to study the role of the mechanical and chemical forces in both of these stages of blood vessel formation, we present a mathematical model which assumes that (i) cells exert traction forces onto the extracellular matrix, (ii) the matrix behaves as a linear viscoelastic material, (iii) the cells move along gradients of exogenously 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 between cells and the extracellular matrix. We find that chemotaxis alone is not a sufficient force to stimulate formation of pattern. Moreover, during vessel sprouting, we find that mechanical forces can help in the formation of well defined vascular structures.
LA - eng
KW - Angiogenesis; vasculogenesis; chemotaxis; extracellular matrix; theoretical models; numerical solution.; angiogenesis; theoretical models; numerical solutions
UR - http://eudml.org/doc/194179
ER -

References

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  1. S.G. Advani and C.L. Tucker. The use of tensors to describe and predict fiber orientation in short fiber composites. Journal of Rheology, 31:751-784, 1987.  
  2. A.R. Anderson and M.A. Chaplain. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bulletin of Mathematical Biology, 60:857-900, 1998.  
  3. D.H. Ausprunk and J. Folkman. Migration and proliferation of endothelial cells in preformed and newly formed blood vessels during tumour angiogenesis. Microvascular Research, 14:53-65, 1977.  
  4. M.A. Chaplain. Mathematical modelling of angiogenesis. Journal of Neurooncology, 50:37-51, 2000.  
  5. M.A. Chaplain and A.R. Anderson. Mathematical modelling, simulation and prediction of tumour-induced angiogenesis. Invasion Metastasis, 16(4-5):222-234, 1996.  
  6. J. Cook. Mathematical Models for Dermal Wound Healing: Wound Contraction and Scar Formation. PhD thesis, University of Washington, 1995.  
  7. C.J. Drake and A.G. Jacobson. A survey by scanning electron microscopy of the extracellular matrix and endothelial components of the primordial chick heart. Anatomical Record, 222:391-400, 1988.  
  8. 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.  
  9. J. Folkman and C. Haudenschild. Angiogenesis in vitro. Nature, 288:551-556, 1980.  
  10. E.A. Gaffney, K. Pugh, P.K. Maini, and F. Arnold. Investigating a simple model of cutaneous would healing angiogenesis. Journal of Mathematical Biology, 45:337-374, 2002.  
  11. D. Hanahan. Signaling vascular morphogenesis and maintenance. Science, 227:48-50, 1997.  
  12. M.J. Holmes and B.D. Sleeman. A mathematical model of tumor angiogenesis incorporating cellular traction and viscoelastic effects. Journal of Theoretical Biology, 202:95-112, 2000.  
  13. Y. Lanir. Constitutive equations for fibrous connective tissues. Journal of Biomechanics, 16(1):1-12, 1983.  
  14. H.A. Levine, B.D. Sleeman, and M. Nilsen-Hamilton. Mathematical modeling of the onset of capillary formation initiating angiogenesis. Journal of Mathematical Biology, 42:195-238, 2001.  
  15. D. Manoussaki. Modelling the formation of vascular networks in vitro. PhD thesis, University of Washington, 1996.  
  16. D. Manoussaki, S.R. Lubkin, R.B. Vernon, and J.D. Murray. A mechanical model for the formation of vascular networks in vitro. Acta Biotheoretica, 44(3-4):271-282, 1996.  
  17. R.R. Markwald, T.P. Fitzharris, D.L. Bolender, and D.H. Bernanke. Sturctural analysis of cell:matrix association during the morphogenesis of atrioventricular cushion tissue. Developmental Biology, 69(2):634-54, 1979.  
  18. 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.  
  19. 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.  
  20. J.D. Murray, G.F. Oster, and A.K. Harris. A mechanical model for mesenchymal morphogenesis. Journal of Mathematical Biology, 17:125-129, 1983.  
  21. G.F. Oster, J.D. Murray, and A.K. Harris. Mechanical aspects of mesenchymal morphogenesis. Journal of embryology and experimental morphology, 78:83-125, 1983.  
  22. L. Pardanaud, F. Yassine, and F. Dieterlen-Lievre. Relationship between vasculogenesis, angiogenesis and haemopoiesis during avian ontogeny. Development, 105:473-485, 1989.  
  23. W. Risau, H. Sariola, H.G. Zerwes, J. Sasse, P. Ekblom, R. Kemler, and T. Doetschmann. Vasculogenesis and angiogenesis in embryonic-system-cell-derived embryoid bodies. Development, 102:471-478, 1988.  
  24. S. Tong and F. Yuan. Numerical simulations of angiogenesis in the cornea. Microvascular Research, 61:14-27, 2001.  
  25. R.B. Vernon, J.C. Angello, M.L. Iruela-Arispe, T.F. Lane, and E.H. Sage. Reorganization of basement membrane matrices by cellular traction promotes the formation of cellular networks in vitro. Laboratory Investigation, 66(5):536-547, 1992.  
  26. R.B. Vernon, S.L. Lara, C.J. Drake, M.L. Iruela-Arispe, J.C. Angello, C.D. Little, T.N. Wight, and E.H. Sage. 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.  
  27. R.B. Vernon and E.H. Sage. Between molecules and morphology: extracellular matrix and the creation of vascular form. American Journal of Pathology, 147:873-883, 1995.  

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