Advertisement

Tumour Cords and Their Response to Anticancer Agents

  • Alessandro Bertuzzi
  • Antonio Fasano
  • Alberto Gandolfi
  • Carmela Sinisgalli
Chapter
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)

Keywords

Anticancer Agent Necrotic Core Survival Ratio Cell Velocity Unilateral Constraint 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Anderson, A.R.: A hybrid mathematical model of solid tumour invasion: the importance of cell adhesion. Math. Med. Biol.,22, 163–86 (2005).MATHCrossRefGoogle Scholar
  2. 2.
    Araujo, R.P., McElwain, D.L.S.: New insights into vascular collapse and growth dynamics in solid tumors. J. Theor. Biol.,228, 335–46 (2004).CrossRefMathSciNetGoogle Scholar
  3. 3.
    Araujo, R.P., McElwain, D.L.S.: A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol.,66, 1039–91 (2004).CrossRefMathSciNetGoogle Scholar
  4. 4.
    Berinstein, N.L.: Biological therapy of cancer. In: Tannock, I.F., Hill, R.P. (eds) The Basic Science of Oncology. McGraw-Hill, New York, pp. 420–42 (1998).Google Scholar
  5. 5.
    Bertuzzi, A., Gandolfi, A.: Cell kinetics in a tumour cord. J. Theor. Biol.,204, 587–99 (2000).CrossRefGoogle Scholar
  6. 6.
    Bertuzzi, A., Fasano, A., Gandolfi, A., Marangi, D.: Cell kinetics in tumour cords studied by a model with variable cell cycle length. Math. Biosci.,177/178, 103–25 (2002).CrossRefMathSciNetGoogle Scholar
  7. 7.
    Bertuzzi, A., d’Onofrio, A., Fasano, A., Gandolfi, A.: Regression and regrowth of tumour cords following single-dose anticancer treatment. Bull. Math. Biol.,65, 903–31 (2003).CrossRefGoogle Scholar
  8. 8.
    Bertuzzi, A., Fasano, A., Gandolfi, A.: A free boundary problem with unilateral constraints describing the evolution of a tumour cord under the influence of cell killing agents. SIAM J. Math. Anal.,36, 882–915 (2004).MATHCrossRefMathSciNetGoogle Scholar
  9. 9.
    Bertuzzi, A., Fasano, A., Gandolfi, A.: A mathematical model for tumor cords incorporating the flow of interstitial fluid. Math. Mod. Meth. Appl. Sci.,15, 1735–77 (2005).MATHCrossRefMathSciNetGoogle Scholar
  10. 10.
    Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, S.: Interstitial pressure and extracellular fluid motion in tumor cords. Math. Biosci. Engng.,2, 445–60 (2005).MATHMathSciNetGoogle Scholar
  11. 11.
    Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, C.: Cell resensitization after delivery of a cycle-specific anticancer drug and effect of dose splitting: learning from tumour cords. J. Theor. Biol.,244, 388–99 (2007).CrossRefMathSciNetGoogle Scholar
  12. 12.
    Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, C.: The transport of specific monoclonal antibodies in tumour cords. In: Aletti, G., Burger, M., Micheletti, A., Morale, D. (eds) Math Everywhere: Deterministic and Stochastic Modelling in Biomedicine, Economics and Industry. Springer-Verlag, Berlin and Heidelberg, pp. 151–64 (2007).Google Scholar
  13. 13.
    Bertuzzi, A., Fasano, A., Gandolfi, A., Sinisgalli, C.: Reoxygenation and splitdose response to radiation in tumours with Krogh-like vasculature. Bull. Math. Biol., in press. DOI 10.1007/s11538-007-9287-9 (2008).Google Scholar
  14. 14.
    Brenner, D.J., Hlatky, L.R., Hahnfeldt, P.J., Hall, E.J., Sachs, R.K.: A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int. J. Radiat. Oncol. Biol. Phys.,32, 379–90 (1995).CrossRefGoogle Scholar
  15. 15.
    Breward, C.J.W., Byrne, H.M., Lewis, C.E.: A multiphase model describing vascular tumour growth. Bull. Math. Biol.,65, 609–40 (2003).CrossRefGoogle Scholar
  16. 16.
    Bru, A., Albertos, S., Luis Subiza, J., Garcia-Asenjo, J.L., Bru, I.: The universal dynamics of tumor growth. Biophys. J.,85, 2948–61 (2003).CrossRefGoogle Scholar
  17. 17.
    Byrne, H.M.: Modelling avascular tumour growth. In: Preziosi, L. (ed) Cancer Modelling and Simulation. Chapman – Hall/CRC, Boca Raton, pp. 75–120 (2003).Google Scholar
  18. 18.
    Byrne, H.M., Preziosi, L.: Modelling solid tumour growth using the theory of mixtures. Math. Med. Biol.,20, 341–66 (2003).MATHCrossRefGoogle Scholar
  19. 1.
    Casciari, J.J., Sotirchos, S.V., Sutherland, R.M.: Mathematical modelling of microenvironment and growth in EMT6/Ro multicellular tumour spheroids. Cell. Prolif.,25, 1–22 (1992).CrossRefGoogle Scholar
  20. 20.
    Chaplain, M.A., Graziano, L., Preziosi, L.: Mathematical modelling of the loss of tissue compression responsiveness and its role in solid tumour development. Math. Med. Biol.,23, 197–229 (2006).MATHCrossRefGoogle Scholar
  21. 21.
    Crokart N., Jordan, B.F., Baudelet, C., Ansiaux, R., Sonveaux, P., Gr’egoire, V., Beghein, N., DeWever, J., Bouzin, C., Feron, O., Gallez, B.: Early reoxygenation in tumors after irradiation: determining factors and consequences for radiotherapy regimens using daily multiple fractions. Int. J. Radiat. Oncol. Biol. Phys.,63, 901–10 (2005).Google Scholar
  22. 22.
    Curtis, S.B.: Lethal and potentially lethal lesions induced by radiation-a unified repair model. Radiat. Res.,106, 252–70 (1986).CrossRefGoogle Scholar
  23. 23.
    Dyson, J., Villella-Bressan, R., Webb, G.F.: The evolution of a tumor cord cell population. Comm. Pure Appl. Anal.,3, 331–52 (2004).MATHCrossRefMathSciNetGoogle Scholar
  24. 24.
    Fasano, A., Bertuzzi, A., Gandolfi, A.: Mathematical modelling of tumour growth and treatment. In: Quarteroni, A., Formaggia, L., Veneziani, A. (eds) Complex Systems in Biomedicine. Springer-Verlag Italia, Milano, pp. 71–108 (2006).CrossRefGoogle Scholar
  25. 25.
    Ferreira Junior, S.C., Matrins, M.L., Vilela, M.J.: The reaction diffusion model for the growth of avascular tumors. Phys. Rev. E,65, 1–8 (2002).Google Scholar
  26. 26.
    Friedman, A., Reitich, F.: Analysis of a mathematical model for the growth of tumors. J. Math. Biol.,38, 262–84 (1999).MATHCrossRefMathSciNetGoogle Scholar
  27. 27.
    Friedman, A., Tao, Y.: Analysis of a model of a virus that replicates selectively in tumor cells. J. Math. Biol.,47, 391–423 (2003).MATHCrossRefMathSciNetGoogle Scholar
  28. 28.
    Fujimori, K., Covell, D.G., Fletcher, J.E., Weinstein, J.N.: Modeling analysis of the global and microscopic distribution of immunoglobulin G, F(ab’)2, and Fab in tumors. Cancer Res.,49, 5656–63 (1989).Google Scholar
  29. 29.
    Hirst, D.G., Denekamp, J.: Tumour cell proliferation in relation to the vasculature. Cell Tissue Kinet.,12, 31–42 (1979).Google Scholar
  30. 30.
    Hlatky, L.R., Hahnfeldt, P., Sachs, R.K.: Influence of time-dependent stochastic heterogeneity on the radiation response of a cell population. Math. Biosci.,122, 201–20 (1994).MATHCrossRefGoogle Scholar
  31. 31.
    Jain, R.K.: Normalization of tumor vasculature: an emerging concept in antiangiogenic therapy. Science,307, 58–62 (2005).CrossRefGoogle Scholar
  32. 32.
    Krogh, A.: The number and distribution of capillaries in muscles with calculations of the oxygen pressure head necessary to supply the tissue. J. Physiol.,52, 409–15 (1919).Google Scholar
  33. 33.
    Moore, J.V., Hasleton, P.S., Buckley, C.H.: Tumour cords in 52 human bronchial and cervical squamous cell carcinomas: inferences for their cellular kinetics and radiobiology. Br. J. Cancer,51, 407–13 (1985).Google Scholar
  34. 34.
    Mueller-Klieser, W.: Multicellular spheroids: A review on cellular aggregates in cancer research. J. Cancer Res. Clin. Oncol.,113, 101–22 (1987).CrossRefGoogle Scholar
  35. 35.
    Smallbone, K., Gavaghan, D.J., Gatenby, R.A., Maini, P.K.: The role of acidity in solid tumour growth and invasion. J. Theor. Biol.,235, 476–84 (2005).CrossRefMathSciNetGoogle Scholar
  36. 36.
    Tannock, I.F.: The relation between cell proliferation and the vascular system in a transplanted mouse mammary tumour. Br. J. Cancer,22, 258–73 (1968).Google Scholar
  37. 37.
    Thames, H.D.: An ‘incomplete-repair’ model for survival after fractionated and continuous irradiations. Int. J. Radiat. Biol.,47, 319–39 (1985).CrossRefGoogle Scholar
  38. 38.
    Venkatasubramanian, R., Henson, M.A., Forbes, N.S.: Incorporating energy metabolism into a growth model of multicellular tumor spheroids. J. Theor. Biol.,242, 440–53 (2006).CrossRefMathSciNetGoogle Scholar
  39. 39.
    Webb, G.F.: The steady state of a tumor cord cell population. J. Evolut. Equat.,2, 425–38 (2002).MATHCrossRefMathSciNetGoogle Scholar
  40. 40.
    Wein, L.M., Wu, J.T., Kirn, D.H.: Validation and analysis of a mathematical model of a replication-competent oncolytic virus for cancer treatment: implications for virus design and delivery. Cancer Res.,63, 1317–24 (2003).Google Scholar
  41. 41.
    Wouters, B.G., Brown, J.M.: Cells at intermediate oxygen levels can be more important than the “hypoxic fraction” in determining tumor response to fractionated radiotherapy. Radiat. Res., 147, 541–50 (1997).Google Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Alessandro Bertuzzi
    • 1
  • Antonio Fasano
    • 2
  • Alberto Gandolfi
    • 1
  • Carmela Sinisgalli
    • 1
  1. 1.Istituto di Analisi dei Sistemi ed Informatica‘‘A. Ruberti’’ - CNRItaly
  2. 2.Dipartimento di Matematica “U. Dini”Università di FirenzeItaly

Personalised recommendations