Mathematical Modelling of Breast Carcinogenesis, Treatment with Surgery and Radiotherapy and Local Recurrence

Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


Breast Cancer Local Recurrence Breast Tissue Early Breast Cancer Breast Carcinogenesis 
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.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [AM06]
    Abbot, L.H., Michor, F.: Mathematical models of targeted cancer therapy. Br. J. Cancer, 95(9), 1136–1141 (2006).CrossRefGoogle Scholar
  2. [AHW03]
    Al-Hajj, M., Wicha, M.S., Benito-Hernandez, A., Morrison, S.J., Clarke, M.F.: Prospective identification of tumorigenic breast cancer cells. PNAS, 100(7), 3983–3988 (2003).CrossRefGoogle Scholar
  3. [AC00]
    Anderson, A.R.A., Chaplain, M.A.J., Newman, E.L., Steele, R.J.C., Thompson, A.M.: Mathematical modelling of tumour invasion and metastasis. J. Theoret. Med, 2, 129–154 (2000).MATHGoogle Scholar
  4. [A05]
    Anderson, A.R.A.: A hybrid mathematical model of solid tumour invasion: The importance of cell adhesion. Math. Med. Biol., 22, 163–186 (2005).MATHCrossRefGoogle Scholar
  5. [AM04]
    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, 1039–1091 (2004).CrossRefMathSciNetGoogle Scholar
  6. [BW02]
    Beil, D.R., Wein, L.M.: Sequencing surgery, radiotherapy and chemotherapy: Insights from a mathematical analysis. Breast Cancer Res. Treat., 74(3), 279–286 (2002).Google Scholar
  7. [BS04]
    Boone, J.M., Shah, N., Nelson, T.R.: A comprehensive analysis of DgNCT coefficients for pendant-geometry cone-beam breast computed tomography. Med. Phys., 31(1), 226–235 (2004).CrossRefGoogle Scholar
  8. [BA98]
    Brenner, D., Armour, E., Corry, P., Hall, E.: Sublethal damage repair times for a late-responding tissue relevant to brachytherapy (and external-beam radiotherapy): Implications for new brachytherapy protocols. Int. J. Radiat. Oncol. Biol. Phys., 41(1), 135–138 (1998).Google Scholar
  9. [B00]
    Brwon, P.: UK death rates from breast cancer fall by a third. BMJ, 321(7265), 849 (2000).CrossRefGoogle Scholar
  10. [CL05]
    Chaplain, M.A.J., Lolas, G.: Mathematical modelling of cancer cell invasion of tissue: The role of the urokinase plasminogen activation system. Math. Modell. Methods Appl. Sci., 15, 1685–1734 (2005).MATHCrossRefMathSciNetGoogle Scholar
  11. [C05]
    Clarke, M., Collins, R., Darby, S., Davies, C., Elphinstone, P., Evans, E., Godwin, J., Gray, R., Hicks, C., James, S., MacKinnon, E., McGale, P., McHugh, T., Peto, R., Taylor, C., Wang, Y.: Effects of radiotherapy, of differences in the extent of surgery for early breast cancer on local recurrence, 15-year survival: An overview of the randomised trials. Lancet, 366(9503), 2087–2106 (2005).Google Scholar
  12. [D98]
    Dairkee, S.H.: Allelic loss in normal lobules adjacent to breast cancer. Cancer Detection and Prevention, 22(1), 135A (1998).Google Scholar
  13. [DH06]
    Dawson, A., Hillen, T.: Derivation of the tumour control probability (TCP) from a cell cycle model. Comput. Math. Meth. in Medicine, 7, 121–142 (2006).MATHCrossRefMathSciNetGoogle Scholar
  14. [DL96]
    Deng, G., Lu, Y., Zlotnikov, G., Thor, A.D., Smith, H.S.: Loss of heterozygosity in normal tissue adjacent to breast carcinomas. Science, 274, 2057–2059 (1996).CrossRefGoogle Scholar
  15. [DS04]
    Dionysiou, D.D., Stamatakos, G.S., Uzunogly, N.K., Nikita, K.S., Marioli, A.: A four-dimensional simulation model of tumour response to radiotherapy in vivo: Parametric validation considering radiosensitivity, genetic profile, fractionation. J. Theor. Biol., 230, 1–20 (2004).CrossRefGoogle Scholar
  16. [E06]
    Enderling, H.: Mathematical modelling of breast cancer development, local treatment, recurrence. PhD Thesis, Dundee University, Dundee (2006).Google Scholar
  17. [EA06]
    Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Munro, A.J., Vaidya, J.S.: Mathematical modelling of radiotherapy strategies for early breast cancer. J. Theor. Biol., 241(1), 158–171 (2006).CrossRefMathSciNetGoogle Scholar
  18. [EA06b]
    Enderling, H., Anderson, A.R.A., Chaplain, M.A.J., Rowe, G.W.: Visualisation of the numerical solution of partial differential equation systems in three space dimensions and its importance for mathematical models in biology. Math. Biosci. Eng., 3(4), 571–582 (2006).MATHMathSciNetGoogle Scholar
  19. [EC07]
    Enderling, H., Chaplain, M.A.J., Anderson, A.R.A., Vaidya, J.S.: A mathematical model of breast cancer development, local treatment, recurrence. J. Theor. Biol., 264(2), 245–259 (2007).CrossRefMathSciNetGoogle Scholar
  20. [FL01]
    Försti, A., Louhelainen, J., Söderberg, M., Wijkström, H., Hemminki, K.: Loss of heterozygosity in tumour-adjacent normal tissue of breast and bladder cancer. Eur. J. Cancer, 37, 1372–1380 (2001).CrossRefGoogle Scholar
  21. [GAL03]
    Guerrero, M., Allen Li, X.: Analysis of a large number of clinical studies for breast cancer radiotherapy: Estimation of radiobiological parameters for treatment planning. Phys. Med. Biol., 48(20), 3307–3326 (2003).CrossRefGoogle Scholar
  22. [HW00]
    Hanahan, D., Weinberg, R.A: The hallmarks of cancer. Cell, 100, 57–70 (2000).CrossRefGoogle Scholar
  23. [K06]
    Komarova, N.: Stochastic modeling of drug resistance in cancer. J Theor. Biol., 239(3), 351–366 (2006).CrossRefMathSciNetGoogle Scholar
  24. [KJ04]
    Krag, D.N., Julian, T.B., Harlow, S.P., Weaver, D.L., Ashikaga, T., Bryant, J., Single, R.M., Wolmark, N.: NSABP-32: Phase III, randomized trial comparing axillary resection with sentinal lymph node dissection: A description of the trial. Ann. Surg. Oncol., 11(3 Suppl), 208S– 210S (2004).Google Scholar
  25. [MB06]
    Massarut, S., Baldassare, G., Belleti, B., Reccanello, S., D’Andrea, S., Ezio, C., Perin, T., Reccanello, S., Roncadin, M., Vaidya, J.S.: Intraoperative radiotherapy impairs breast cancer cell motility induced by surgical wound fluid. J. Clin. Oncol., 24(18S), 10611 (2006).Google Scholar
  26. [M92]
    Matrisian, L.N.: The matrix-degrading metalloproteinases. Bioessays, 14, 455–463 (1992).CrossRefGoogle Scholar
  27. [MO06]
    McAneney, H., O’Rourke, SFC.: Investigation of various growth mechanisms within the linear-quadratic model for radiotherapy. Phys. Med. Biol., 52, 1039–1054.Google Scholar
  28. [MIN04]
    Michor, F., Iwasa, Y., Nowak, M.A.: Dynamics of cancer progression. Nat. Rev. Can., 4, 197–205 (2004).CrossRefGoogle Scholar
  29. [MN06]
    Michor, F., Nowak, M.A., Iwasa, Y.: Evolution of resistance to cancer therapy. Curr. Pharm. Des., 12(3), 161–271 (2006).CrossRefGoogle Scholar
  30. [N05]
    Norton, L.: Conceptual, practical implications of breast tissue geometry: Toward a more effective, less toxic therapy. Oncologist, 10(6), 370–381 (2005).CrossRefMathSciNetGoogle Scholar
  31. [NMK04]
    Nowak, M.A., Michor, F., Komarova, N.L., Iwasa, Y.: Evolutionary dynamics of tumor suppressor gene inactivation. PNAS, 101(29), 10635– 10638 (2004).CrossRefGoogle Scholar
  32. [O01]
    Oldham, M.: Radiation physics, applications in therapeutic medicine. Phys. Educ., 36, 460–467 (2001).CrossRefGoogle Scholar
  33. [PA95]
    Panetta, J.C., Adam, J.: A mathematical model of cycle-specific chemotherapy. Math. Comp. Modell., 22(2), 67–82 (1995).MATHCrossRefMathSciNetGoogle Scholar
  34. [PG05]
    Piccart-Gebhart, M.J., Procter, M., Leyland-Jones, B., Goldhirsch, A., Untch, M., Smith, I., Gianni, L., Baselga, J., Bell, R., Jackisch, C., Cameron, D., Dowsett, M., Barrios, C.H., Steger, G., Huang, C.S., Andersson, M., Inbar, M., Lichinitser, M., Lang, I., Nitz, U., Iwata, H., Thomssen, C., Lohrisch, C., Suter, T.M., Ruschoff, J., Suto, T., Greatorex, V., Ward, C., Straehle, C., McFadden, E., Dolci, M.S., Gelber, R.D.: Herceptin adjuvant (HERA) trial study team. Trastuzumab after adjuvant chemotherapy in HER2-positive breast cancer. N. Engl. J. Med., 353(16), 1659–1672 (2005).CrossRefGoogle Scholar
  35. [PK07]
    Powathil, G., Kohandel, M., Sivaloganathan, S., Oza, A., Milosevic, M.: Mathematical modeling of brain tumors: Effects of radiotherapy, chemotherapy. Phys. Med. Biol., 52, 3291–3306 (2007).CrossRefGoogle Scholar
  36. [RC06]
    Ribba, B., Colin, T., Schnell, S.: A multiscale mathematical model of cancer, its use in analyzing irradiation therapies. Theor. Biol. Med. Model, 3(7), (2006).Google Scholar
  37. [RP05]
    Romond, E.H., Perez, E.A., Bryant, J., Suman, V.J., Geyer, C.E. Jr, Davidson, N.E., Tan-Chiu, E., Martino, S., Paik, S., Kaufman, P.A., Swain, S.M., Pisansky, T.M., Fehrenbacher, L., Kutteh, L.A., Vogel, V.G., Visscher, D.W., Yothers, G., Jenkins, R.B., Brown, A.M., Dakhil, S.R., Mamounas, E.P., Lingle, W.L., Klein, P.M., Ingle, J.N., Wolmark, N.: Trastuzumab plus adjuvant chemotherapy for operable HER2- positive breast cancer. N. Engl. J. Med., 353(16), 1673–1684 (2005).CrossRefGoogle Scholar
  38. [SH97]
    Sachs, R.K., Hahnfeld, P., Brenner, D.J.: The link between low-LET dose-response relations, the underlying kinetics of damage production/repair/misrepair. Int. J. Biol., 72(4), 351–374 (1997).Google Scholar
  39. [SH01]
    Sachs, R.K., Hlatky, L.R., Hahnfeldt, P.: Simple ODE models of tumour growth, anti-angiogenic or radiation treatment. Math. Comput. Modelling, 33, 1297–1305 (2001).MATHCrossRefMathSciNetGoogle Scholar
  40. [SLB04]
    Sancar, A., Lindsey-Boltz, L.A., Ünsal-Kaçcmaz, K., Linn, S.: Molecular mechanisms of mammalian DNA repair, the DNA damage checkpoints. Annu. Rev. Biochem., 73, 39–85 (2004).CrossRefGoogle Scholar
  41. [SG05]
    Smallbone, K., Gavaghan, D.J., Gatenby, R.A., Maini, P.K.: The role of acidity in solid tumour growth, invasion. J. Theor. Biol., 235, 476–484 (2005).CrossRefMathSciNetGoogle Scholar
  42. [SA03]
    Smalley, M. and Ashworth, A.: Stem cells and breast cancer: A field in transit. Nat. Rev. Can., 3, 832–844 (2003).CrossRefGoogle Scholar
  43. [SB04]
    Spencer, S.L., Berryman, M.J., Garcia, J.A. , Abbott, D.: An ordinary differential equation model for the multistep transformation to cancer. J. Theor. Biol, 231, 515–524 (2004).CrossRefMathSciNetGoogle Scholar
  44. [SA02]
    Swanson, K.R., Alvord, E.C. Jr, Murray, J.D.: Quantifying efficacy of chemotherapy of brain tumors with homogeneous, heterogeneous drug delivery. Acta Biotheor., 50(4), 223–237 (2002).CrossRefGoogle Scholar
  45. [TNB96]
    Tomlinson, I.P.M., Novelli, M.R., Bodmer, W.F.: The mutation rate, cancer. PNAS, 93(25), 14800–14803 (1996).CrossRefGoogle Scholar
  46. [T01]
    Tomlinson, I.P.M.: Mutations in normal breast tissue, breast tumours. Breast Cancer Res., 3(5), 299–303 (2001).CrossRefGoogle Scholar
  47. [TC03]
    Turesson, I., Carlsson, J., Brahme, A., Glimelius, B., Zackrisson, B., Stenerlöw, B.: Biological response to radiation therapy. Acta Oncologica, 42(2), 92–106 (2003).CrossRefGoogle Scholar
  48. [TS02]
    Turner S., Sherrat, J.A.: Intercellular adhesion and cancer invasion: A discrete simulation using the extended Potts model. J. Theor. Biol., 216, 85–100 (2002).CrossRefGoogle Scholar
  49. [VB01]
    Vaidya, J.S., Baum, M., Tobias, J.S., D’Souza, D.P., Naidy, S.V., Morgan, S., Metaxas, M., Harte, K.J., Sliski, A.P., Thomson, E.: Targeted intra-operative radiotherapy (Targit): An innnovative method of treatment for early breast cancer. Annals of Oncology, 12, 1075–1080 (2001).CrossRefGoogle Scholar
  50. [VD05]
    Vaidya, J.S., Dewar, J.A., Brown, D.C., Thompson, A.M.: A mathematical model for the effect of a false-negative sentinel node biopsy on breast cancer mortality: A tool for everyday use. Breast Cancer Res., 7(5), 225–227 (2005).CrossRefGoogle Scholar
  51. [VT04]
    Vaidya, J.S., Tobias, J.S., Baum, M., Keshtgar, M., Joseph, D., Wenz, F. et al.: Intraoperative radiotherapy for breast cancer. Lancet Oncol., 5(3), 165–173 (2004).CrossRefGoogle Scholar
  52. [V07]
    Vaidya, J.S.: Breast cancer: An artistic view. Lancet Oncol., 8(7), 583– 558 (2007).CrossRefGoogle Scholar
  53. [V07b]
    Vaidya, J.S.: Partial breast irradiation using targeted intraoperative radiotherapy (Targit). Nat. Clin. Pract. Oncol., 4(7), 384–385 (2007).CrossRefGoogle Scholar
  54. [VVH05]
    Verschraegen, C., Vinh-Hung, V., Cserni, G., Gordon, R., Royce, M.E., Vlastos, G., Tai, P., Storme, G.: Modeling the effect of tumor size in early breast cancer. Annals of Surgery, 241, 309–318 (2005).CrossRefGoogle Scholar
  55. [WC05]
    Woodward, W.A., Chen, M.S., Behbod, F., Rosen, J.M: On mammary stem cells. J. Cell Science, 118, 3585–3594 (2005).CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  1. 1.Center of Cancer Systems Biology, Caritas St. Elizabeth’s Medical CenterTufts University School of MedicineBostonUSA
  2. 2.Division of Surgery and Molecular Oncology, Ninewells Hospital and Medical SchoolUniversity of DundeeDundeeUK

Personalised recommendations