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Mathematical Modeling of Biological Systems, Volume I pp 226–238Cite as

Morphology of Tumor Vasculature A Theoretical Model

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A theoretical model based on the molecular interactions between a growing tumor and a dynamically evolving blood vessel network describes the transformation of the regular vasculature in normal tissues into a highly inhomogeneous tumor-specific capillary network. The emerging morphology, characterized by the compartmentalization of the tumor into several regions differing in vessel density, diameter and degree of tumor necrosis, is in accordance with experimental data for human melanoma. Vessel collapse, due to a combination of severely reduced blood flow and solid stress exerted by the tumor, leads to a correlated percolation process that is driven towards criticality by the mechanism of hydrodynamic vessel stabilization.

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References

  1. Carmeliet, P., Jain, R.K. : Angiogenesis in cancer and other diseases. Nature, 407, 249–257 (2000).

    Article  Google Scholar 

  2. Acker, T., Plate, K.H. : A role for hypoxia and hypoxia-inducible transcription factors in tumor physiology. J. Mol. Med., 80, 562–575 (2002).

    Article  Google Scholar 

  3. Holash, J. Maisonpierre, P.C., Compton, D., Boland, P., Alexander, C.R., Zagzag, D., Yancopoulos, G.D., Wiegand, S.J. : Vessel cooption, regression, and growth in tumors mediated by angiopoietins and VEGF. Science, 284, 1994–1998 (1999). Holash, J., Wiegand, S.J., Yancopoulos, G.D. : New model of tumor angiogenesis : Dynamic balance between vessel regression and growth mediated by angiopoietins and VEGF. Oncogene, 18, 5356–5362 (1999).

    Article  Google Scholar 

  4. Döme, B., Paku, S., Somlai, B., Tímár, J. : Vascularization of cutaneous melanoma involves vessel co-option and has clinical significance. J. Path., 197, 355–362 (2002).

    Article  Google Scholar 

  5. Gazit, Y., Berk, D.A., Leunig, M., Baxter, L.T., Jain, R.K. : Scale-Invariant Behavior and Vascular Network Formation in Normal and Tumor Tissue. Phys. Rev. Lett., 75, 2428 (1995). Baish, J.W., Jain, R.K. : Cancer, angiogenesis and fractals [4]. Nature Med., 4, 984 (1998).

    Google Scholar 

  6. Hlatky, L., Hahnfeld, P., Folkman, P. : Clinical application of antiangiogenic therapy : Microvessel density, what it does and doen’t tell us. J. Nat. Canc. Inst., 94, 883–893 (2002).

    Google Scholar 

  7. Baish, J.W., Jain, R.K. : Fractals and cancer. Canc. Res., 60, 3683–3683 (2000).

    Google Scholar 

  8. Bartha, K., Rieger, H. : J. Theor. Biol., 241, 903–918 (2006).

    Google Scholar 

  9. Mantzaris, N.V., Webb, S., Othmer, H.G. : Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol., 49, 111–187 (2004).

    Article  MATH  MathSciNet  Google Scholar 

  10. Preziosi, L. (ed.) : Cancer Modelling and Simulation. Chapman & Hall/CRC, Boca Raton, FL, (2003).

    MATH  Google Scholar 

  11. Byrne, H.M., Chaplain, M.A.J. : Mathematical models for tumour angiogenesis : Numerical simulations and nonlinear wave solutions. B. Math. Biol., 57, 461–486 (1995).

    MATH  Google Scholar 

  12. Levine, H.A., Sleeman, B.D., Nilsen-Hamiltion, M. : Mathematical modeling of the onset of capillary formation initiating angiogenesis. J. Math. Biol., 42, 195–238 (2001).

    Article  MATH  MathSciNet  Google Scholar 

  13. Sansone, B.C., Scalerandi, M., Condat, C.A. : Emergence of taxis and synergy in angiogenesis. Phys. Rev. Lett., 87, 128102 (2001).

    Article  Google Scholar 

  14. 14. Anderson, A.R.A., Chaplain, M.A.J. : Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol., 60, 857–899 (1998).

    Article  MATH  Google Scholar 

  15. McDougall, S.R., Anderson, A.R.A, Chaplain, M.A.J., Sherrat, J.A. : Mathematical modelling of flow through vascular networks : Implications for tumour-induced angiogenesis and chemotherapy strategies. B. Math. Biol., 64, 673–702 (2002).

    Article  Google Scholar 

  16. Tong, S., Yuan, F. : Numerical Simulations of Angiogenesis in the Cornea. Microvasc. Res., 61, 14–27 (2002).

    Google Scholar 

  17. Sun, S.Y., Wheeler, M.F., Obeyesekere, M., Patrick, C.W. : A deterministic model of growth factor-induced angiogenesis. B. Math. Biol., 67, 313–337 (2005).

    Article  MathSciNet  Google Scholar 

  18. Welter, M., Bartha, K., Rieger, H. : to be published.

    Google Scholar 

  19. 19. Barab’asi, A.-L., Stanley, H.E. : Fractal Concepts in Surface Growth. Cambridge University Press, London, (1995).

    Google Scholar 

  20. Brú, A., Albertos, S., Subiza, J.L., García-Asenjo, J.L., Brúu, I. : The universal dynamics of tumor growth. Biophys. J., 85, 2948–1961 (2003).

    Article  Google Scholar 

  21. Drasdo, D., H\öme, S. : A single-cell-based model of tumor growth in vitro : Monolayers and spheroids. Phys. Biol., 2, 133–147 (2005).

    Article  Google Scholar 

  22. Patel, A.A., Gawlinsky, E.T., Lemieux, S.K., Gatenby, R.A. : A cellular automaton model of early tumor growth and invasion : The effects of native tissue vascularity and increased anaerobic tumor metabolism. J. Theor. Biol., 213, 315–331 (2001).

    Article  Google Scholar 

  23. Alarcon, T., Byrne, H.M., Maini, P.K. : A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol., 225, 257–274 (2003).

    Article  MathSciNet  Google Scholar 

  24. Popel, A.S. : Theory of oxygen transport to tissue. Crit. Rev. Biomed. Eng., 17, 257–321 (1989).

    Google Scholar 

  25. G\ödde, R., Kurz, H. : Structural and biophysical simulation of angiogenesis and vascular remodeling. Dev. Dyn., 220, 387–401 (2001).

    Article  Google Scholar 

  26. Hsu, R., Secomb, T.W. : A Green’s function method for analysis of oxygen delivery to tissue by microvascular networks. Math. Biosci., 96, 61–78 (1989).

    Article  MATH  Google Scholar 

  27. Secomb, T.W., Hsu, R., Park, E.Y.H., Dewhirst, M.W. : Green’s function methods for analysis of oxygen delivery to tissue by microvascular networks. Ann. Biomed. Eng., 32, 1519– 1529 (2004).

    Article  Google Scholar 

  28. Stauffer, D., Aharony, A. : An Introduction to Percolation Theory, revised 2nd ed. Taylor and Francis, London (1994). Lorenz, C.D., Ziff, R.M. : Precise determination of the bond percolation thresholds and finite-size scaling corrections for the sc, fcc, and bcc lattices. Phys. Rev. E, 57, 230–236 (1998).

    Google Scholar 

  29. Furuberg, L., Feder, J., Aharony, A., Jossang, T. : Dynamics of Invasion Percolation. Phys. Rev. Lett., 61, 2117–2120 (1988). Sheppard, A.P., Knackstedt, M.A., Pinczewski, W.V., Sahimi, M. : Invasion percolation : New algorithms and universality classes. J. Phys. A, 32, L521–L529 (1999).

    Google Scholar 

  30. S Lee, D., Rieger, H., Bartha, K. : Flow correlated percolation during vascular remodeling in growing tumors. Phys. Rev. Lett., 96, 058104 (2006).

    Article  Google Scholar 

  31. Huang, J.Z., Soffer, S.Z., Kim, E.S., McCrudden, K.W., New, T., Manley, C.A., Middlesworth, W., O’Toole, K., Yamashiro, D.J., Kandel, J.J. : Vascular Remodeling Marks Tumors That Recur During Chronic Suppression of Angiogenesis. Mol. Canc. Res., 2, 36–42 (2004).

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Medical Biochemistry, Semmelweis University, Budapest, Hungary

    Katalin Bartha

  2. Theoretische Physik, Universität des Saarlandes, 66041 Saarbrücken, Germany

    Heiko Rieger

Authors
  1. Katalin Bartha
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  2. Heiko Rieger
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Editor information

Editors and Affiliations

  1. Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062 Dresden, Germany

    Andreas Deutsch

  2. Center for Information Services and High Performance Computing, Technische Universität Dresden, 01062 Dresden, Germany

    Lutz Brusch

  3. Centre for Mathematical Medicine School of Mathematical Sciences, University of Nottingham, Nottingham, NG7 2RD, U.K

    Helen Byrne

  4. Department of Mathematical and Statistical Sciences, University of Alberta, Edmonton, AB T6G 2G1, Canada

    Gerda de Vries

  5. Institute of Theoretical Biology, Humboldt-Universität zu Berlin Invalidenstraße 43, 10115 Berlin, Germany

    Hanspeter Herzel

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Bartha, K., Rieger, H. (2007). Morphology of Tumor Vasculature A Theoretical Model. In: Deutsch, A., Brusch, L., Byrne, H., Vries, G.d., Herzel, H. (eds) Mathematical Modeling of Biological Systems, Volume I. Modeling and Simulation in Science, Engineering and Technology. Birkhäuser Boston. https://doi.org/10.1007/978-0-8176-4558-8_20

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