# Mathematical Modelling of Tumour Dormancy

Mathematical Modelling of Natural Phenomena (2009)

- Volume: 4, Issue: 3, page 68-96
- ISSN: 0973-5348

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topPage, K. M.. "Mathematical Modelling of Tumour Dormancy." Mathematical Modelling of Natural Phenomena 4.3 (2009): 68-96. <http://eudml.org/doc/222282>.

@article{Page2009,

abstract = {
Many tumours undergo periods in which
they apparently do not grow but remain at a roughly constant size
for extended periods. This is termed tumour dormancy. The
mechanisms responsible for dormancy include failure to develop an
internal blood supply, individual tumour cells exiting the cell
cycle and a balance between the tumour and the immune response to
it. Tumour dormancy is of considerable importance in the natural
history of cancer. In many cancers, and in particular in breast
cancer, recurrence can occur many years after surgery to remove
the primary tumour, following a long period of occult disease.
Mathematical modelling suggested that continuous growth of tumours
was incompatible with data of the times of recurrence in breast
cancer, suggesting that tumour dormancy was a common phenomenon.
Modelling has also been applied to understanding the mechanisms
responsible for dormancy, how they can be manipulated and the
implications for cancer therapy. Here, the literature on
mathematical modelling of tumour dormancy is reviewed. In
conclusion, promising future directions for research are
discussed.
},

author = {Page, K. M.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {cancer; dormancy; mathematical models},

language = {eng},

month = {6},

number = {3},

pages = {68-96},

publisher = {EDP Sciences},

title = {Mathematical Modelling of Tumour Dormancy},

url = {http://eudml.org/doc/222282},

volume = {4},

year = {2009},

}

TY - JOUR

AU - Page, K. M.

TI - Mathematical Modelling of Tumour Dormancy

JO - Mathematical Modelling of Natural Phenomena

DA - 2009/6//

PB - EDP Sciences

VL - 4

IS - 3

SP - 68

EP - 96

AB -
Many tumours undergo periods in which
they apparently do not grow but remain at a roughly constant size
for extended periods. This is termed tumour dormancy. The
mechanisms responsible for dormancy include failure to develop an
internal blood supply, individual tumour cells exiting the cell
cycle and a balance between the tumour and the immune response to
it. Tumour dormancy is of considerable importance in the natural
history of cancer. In many cancers, and in particular in breast
cancer, recurrence can occur many years after surgery to remove
the primary tumour, following a long period of occult disease.
Mathematical modelling suggested that continuous growth of tumours
was incompatible with data of the times of recurrence in breast
cancer, suggesting that tumour dormancy was a common phenomenon.
Modelling has also been applied to understanding the mechanisms
responsible for dormancy, how they can be manipulated and the
implications for cancer therapy. Here, the literature on
mathematical modelling of tumour dormancy is reviewed. In
conclusion, promising future directions for research are
discussed.

LA - eng

KW - cancer; dormancy; mathematical models

UR - http://eudml.org/doc/222282

ER -

## References

top- C.A. Klein, D. Hoelzel. Systemic cancer progression and tumor dormancy: mathematical models meet single cell genomics. Cell Cycle, 5 (2006), No. 16, 1788–1798.
- R.A. Willis. The Spread of Tumors in the Human Body. Butterworth and Co. Ltd., London, 1952.
- J.A. Aguirre-Ghiso. Models, mechanisms and clinical evidence for cancer dormancy. Nature Rev. Cancer, 7 (2007), No. 11, 834–846.
- T.G. Karrison, D.J. Ferguson, P. Meier. Dormancy of Mammary Carcinoma after Mastectomy. J. Natl. Cancer Inst., 91 (1999), No. 1, 80–85.
- D. Weckermann, P. Mueller, F. Wawroschek, R. Harzmann, G. Riethmueller, G. Schlimok. Disseminated Cytokeratin Positive Tumour Cells in the Bone Marrow of Patients with Prostate Cancer: Detection and Prognostic value. J. Urol., 166 (2001), No. 2, 699–703.
- Early Breast Cancer Trialists' Collaborative Group (EBCTCG). Effects of chemotherapy and hormonal therapy for early breast cancer on recurrence and 15-year survival: an overview of the randomised trials. Lancet, 365 (2005), No. 9472, 1687–1717.
- T. Saphner, D.C. Tormey, R. Gray. Annual hazard rates of recurrence for breast cancer after primary therapy. J. Clin. Oncol., 14 (1996), No. 10, 2738–2746.
- L.E. Rutqvist, A. Wallgren, B. Nilsson. Is breast cancer a curable disease? A study of 14,731 women with breast cancer from the cancer registry of Norway. Cancer, 53 (1984), No. 8, 1793–1800.
- S. Meng, D. Tripathy, E.P. Frenkel, S. Shete, E.Z. Naftalis, J.F. Huth, P.D. Beitsch, M. Leitch, S. Hoover, D. Euhus, B. Haley, L. Morrison, T.P. Fleming, D. Herlyn, L.W.M.M. Terstappen, T. Fehm, T.F. Tucker, N. Lane, J. Wang, J.W. Uhr. Circulating tumour cells in patients with breast cancer dormancy. Clin. Cancer Res., 10, (2004), No. 24, 8152–8162.
- L. Norton, R. Simon, H.D. Brereton, A.E. Bogden. Predicting the course of Gompertzian growth. Nature, 264 (1976), No. 5586, 542–545.
- M.W. Retsky, R. Demicheli, D.E. Swartzendruber, P.D. Bame, R.H. Wardwell, G. Bonadonna, J.F. Speer, P. Valagussa. Computer Simulation of a breast cancer metastasis model. Breast Cancer Res. and Treat., 45 (1997), No. 2, 193–202.
- H.J.G. Bloom, W.W. Richardson and E.J. Harries. Natural history of untreated breast cancer (1805-1933). Br. Med. J., 2 (1962), No. 5299, 213–221.
- S.E. Clare, F. Nakhlis, J.C. Panetta. Molecular biology of breast cancer metastasis: the use of mathematical models to determine relapse and to predict response to chemotherapy in breast cancer. Breast Cancer Res., 2 (2000), No. 6, 430–435.
- R. Demicheli, A. Abbatista, R. Micheli, P. Valagussa, G. Bonadonna. Time distribution of the recurrence risk for breast cancer patients undergoing mastectomy: further support about the concept of tumor dormancy. Breast Cancer Res. Treat., 41 (1996), No. 2, 177–185.
- R. Demicheli, R. Micheli, P. Valagussa, G. Bonadonna. re: Dormancy of mammary carcinoma after mastectomy. J. Natl. Cancer Inst., 92 (1999), No. 4, 347–348.
- R. Demicheli. Tumour dormancy: findings and hypotheses from clinical research on breast cancer. Semin. Cancer Biol., 11 (2001), No. 4, 297–305.
- T.G. Karrison, D.J. Ferguson, P. Meier. RESPONSE: re: Dormancy of mammary carcinoma after mastectomy., J. Natl. Cancer Inst., 92 (1999), No. 4, 348.
- M. Brackstone, J.L. Townson, A.F. Chambers. Tumour dormancy in breast cancer: an update. Breast Cancer Res., 9 (2007), No. 3, 208.
- R.P. Araujo and D.L.S. McElwain. A history of the study of solid tumour growth: the contribution of mathematical modelling. Bull. Math. Biol., 66 (2004), No. 5, 1039–1091.
- N. Bellomo, N.K. Li, P.K. Maini. On the foundations of cancer modelling: selected topics, speculations and perspectives. Math. Models Methods Appl. Sci., 18 (2008), No. 4, 593–646. Zbl1151.92014
- J. Folkman. Tumor angiogenesis: therapeutic implications. N. Eng J. Med., 285 (1971), No. 21, 1182–1186.
- J. Folkman. Angiogenesis in cancer, vascular, rheumatoid and other diseases. Nature Med., 1 (1995), No. 1, 27–31.
- L. Holmgren, M.S. O'Reilly, J. Folkman. Dormancy of micrometastases: Balanced proliferation and apoptosis in the presence of angiogenesis suppression. Nature Med., 1 (1995), No. 2, 149–153.
- M.S. O'Reilly, L. Holmgren, Y. Shing, C. Chen, R.A. Rosenthal, M. Moses, W.S. Lane, Y. Cao, E.H. Sage, J. Folkman. Angiostatin: a novel angiogenesis inhibitor that mediates the suppression of metastases by a Lewis lung carcinoma. Cell 79 (1994), No. 2, 315–328.
- D. Hanahan, J. Folkman. Patterns and emerging mechanisms of the angiogenic switch during tumorigenesis. Cell, 86 (1996), No. 3, 353–364.
- W. Risau, H. Sariola, H.-G. Zerwes, J. Sasse, P. Ekblom, R. Kemler, T. Doetschmann. Vasculogenesis and angiogenesis in embryonic-stem-cell-derived embryoid bodies. Development, 102 (1988), No. 3, 471–478.
- W. Risau. Mechansims of angiogenesis. Nature, 386 (1997), No. 6626, 671–674.
- M.F. Bolontrade, R.R. Zhou, E.S. Kleinerman. Vasculogenesis plays a role in the growth of Ewing's sarcoma in vivo. Clin. Cancer Res., 8 (2002), No. 11, 3622–3627.
- D. Ribatti, A. Vacca, F. Dammacco. New non-angiogenesis dependent pathways of tumour growth. Eur. J. Cancer, 39 (2003), No. 13, 1835–1841.
- N.V. Mantzaris, S. Webb, H.G. Othmer. Mathematical modeling of tumor-induced angiogenesis. J. Math. Biol., 49 (2004), No. 2, 111–187. Zbl1109.92020
- M.A.J. Chaplain, S.R. McDougall, A.R.A. Anderson. Mathematical modeling of tumor-induced angiogenesis. Annu. Rev. Biomed. Eng., 8 (2006), 233–257.
- M. Baum, M.A.J. Chaplain, A.R.A. Anderson, M. Douek, J.S. Vaidya. Does breast cancer exist in a state of chaos?, Europ. J. Cancer, 35 (1999), No. 6, 886–891.
- A.R.A Anderson, M.A.J. Chaplain. Continuous and discrete models mathematical models of tumor-induced angiogenesis. Bull. Math. Biol., 60 (1998), No. 5, 857–899. Zbl0923.92011
- V.R. Muthukkaruppan, L. Kubai, R. Auerbach. Tumor-induced neovascularization in the mouse eye. J. Natl. Cancer Inst., 69 (1982), No. 3, 699–705.
- T. Alarcon, H.M. Byrne, P.K. Maini. A cellular automaton model for tumour growth in inhomogeneous environment. J. Theor. Biol., 225 (2003), No. 2, 257–274.
- M.R. Owen, T. Alarcon, P.K. Maini, H.M. Byrne. Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol., 58 (2009), No.s 4-5, 689–721. Zbl1311.92034
- S.R. McDougall, A.R.A. Anderson, M.A.J. Chaplain, J.A. Sherratt. Mathematical modelling of flow through vascular networks: implications for tumour-induced angiogenesis and chemotherapy strategies. Bull. Math. Biol., 64 (2002), No. 4, 673–702.
- M. Welter, K. Bartha, H. Rieger. Emergent vascular network inhomogeneities and resulting blood flow patterns in a growing tumor. J. Theor. Biol., 250 (2008), No. 2, 257–280.
- A.R. Pries, T.W. Secomb, P. Gaehtgens. Biophysical aspects of blood flow in the microvasculature. Cardiovsacular Research, 32 (1996), No. 4, 654–667.
- A.R. Pries, T.W. Secomb, P. Gaehtgens. Structural adaptation and stability of microvascular networks: theory and simulations. Am. J. Physiol. Heart Circ. Physiol., 275 (1998), No. 2, H349–H360.
- A.R. Pries, B. Reglin, T.W. Secomb. Structural adaptation of microvascular networks: functional roles of adaptive responses. Am. J. Physiol. Heart Circ. Physiol., 281 (2001), No. 3, H1015–H1025.
- H.V. Jain, J.E. Noer, T.L. Jackson. Modeling the VEGF-Bcl-2-CXCL8 pathway in intratumoral angiogenesis. Bull. Math. Biol., 70 (2008), No. 1, 89–117. Zbl1281.92031
- D. Wodarz, Y. Iwasa, N.L. Komarova. On the emergence of multifocal cancers. J. Carcinogenesis, 3 (2004), 13.
- D. Wodarz, N.L. Komarova. Computational biology of cancer: lecture notes and mathematical modeling. World Scientific Publishing, Singapore, 2005. Zbl1126.92029
- S. Ramanujan, G.C. Koenig, T.P. Padera, B.R. Stoll, R.K. Jain. Local imbalance of proangiogenic and antiangiogenic factors: a potential mechanism of focal necrosis and dormancy in tumors. Cancer Research, 60 (2000), No. 5, 1442–1448.
- D. Wodarz, D.C. Krakauer. Genetic instability and the evolution of angiogenic tumor cell lines. Oncology Reports, 8 (2001), No. 6, 1195–1201.
- M.J. Plank, B.D. Sleeman, P.F. Jones. A Mathematical Model of Tumour Angiogenesis, Regulated by Vascular Endothelial Growth Factor and the Angiopoietins. J. Theor. Biol., 229 (2004), No. 4, 435–454.
- H.G. Othmer, A. Stevens. Aggregation, blowup, and collapse: the ABC's of taxis in reinforced random walks. SIAM J. Appl. Math., 57 (1997), No. 4, 1044–1081. Zbl0990.35128
- G.N. Naumov, E. Bender, D. Zurakowski, S.-Y. Kand, D. Sampson, E. Flynn, R.S. Watnick, O. Straume, L.A. Akslen, J. Folkman, N. Almog. A model of human tumor dormancy: an angiogenic switch from the nonangiogenic phenotype. J. Natl. Cancer Inst., 98 (2006), No. 5, 316–325.
- G. Bergers, L.E. Benjamin. Tumorigenesis and the angiogenic switch. Nature Rev. Cancer, 3 (2002), No. 6, 401–410.
- A. Abdollahi, C. Schwager, J. Kleeff, I. Esposito, S. Domhan, P. Peschke, K. Hauser, P. Hahnfelt, L. Hlatky, J. Debus, J.M. Peters, H. Friess, J. Folkman, P.E. Huber. Transcriptional network governing the angiogenic switch in human pancreatic cancer. PNAS, 104 (2007), No. 21, 12890–12895.
- P.T. Logan, B.F. Fernandes, S. Di Cesare, J.-C.A. Marshall, S.C. Maloney, M.N. Burnier. Single-cell tumor dormancy model of uveal melanoma. Clin. Exp. Metastasis, 25 (2008), No. 5, 509–516.
- J.L. Townson, A.F. Chambers. Dormancy of solitary metastatic cells. Cell Cycle, 5 (2006), No. 16, 1744–1750.
- G.N. Naumov, I.C. MacDonald, P.M. Weinmeister, N. Kerkvliet, K.V. Nadkarni, S.M. Wilson, V.L. Morris, A.C. Groom, A.F. Chambers. Persistence of solitary mammary carcinoma cells in a secondary site: a possible contributor to dormancy. Cancer Res., 62 (2002), No. 7, 2162–2168.
- J.A. Aguirre-Ghiso, D. Liu, A. Mignatti, K. Kovalski, L. Ossowaki. Urokinase receptor and fibronectin regulate the ERK(MAPK) to p38(MAPK) activity ratios that determine carcinoma cell proliferation or dormancy in vivo. Mol. Biol. Cell, 12 (2001), No. 4, 863–879.
- C.M. Shachaf, A.M. Kopelman, C. Arvanitis, Å. Karlsson, S. Beer, S. Mandl, M.H. Bachmann, A.D. Borowsky, B. Ruebner, R.D. Cardiff, Q. Yang, J.M. Bishop, C.H. Contag, D.W. Felsher. MYC inactivation uncovers pluripotent differentiation and tumour dormancy in hepatocellular carcinoma. Nature, 431 (2004), No. 7012, 1112–1117.
- M. Guba, G. Cernaianu, G. Koehl, E.K. Geissler, K.-W. Jauch, M. Anthuber, W. Falk, M. Steinbauer. A primary tumor promotes dormancy of solitary tumor cells before inhibiting angiogenesis. Cancer Res., 61 (2001), No. 14, 5575–5579.
- A.L. Allan, S.A. Vantyghem, A.B. Tuck, A.F. Chambers. Tumor dormancy and cancer stem cells: implications for the biology and treatment of breast cancer metastasis. Breast Disease, 26 (2006, 2007), No. 1, 87–98.
- M. Balic, H. Lin, L. Young, D. Hawes, A. Giuliano, G. McNamara, R.H. Datar, R.J. Cote. Most early disseminated cancer cells detected in bone marrow of breast cancer patients have a putative stem cell phenotype. Clin. Cancer Res., 12 (2006), No. 19, 5615–5621.
- T. Alarcon, R. Marches, K.M. Page. Mathematical models of the fate of lymphoma B cells after antigen receptor ligation with specific antibodies. J. Theor. Biol., 240 (2006), No. 1, 54–71.
- T. Alarcon, H.M. Byrne, P.K. Maini. Towards whole organ modelling of tumour growth. Prog. Biophys. Mol. Biol. 85 (2004), No.s 2–3, 451–472.
- T. Alarcon, H.M. Byrne, P.K. Maini. A multiple scale model for tumor growth. Multiscale Model. Simul., 3 (2005), No. 2, 440–475. Zbl1107.92019
- H.M. Byrne, M.R. Owen, T. Alarcon, J. Murphy, P.K. Maini. Modelling the response of vascular tumours to chemotherapy. Math. Mod. Meth. Appl. Sci., 16 (2006), No. 7S, 1219–1241. Zbl1094.92038
- B. Ribba, T. Colin, S. Schnell. A mathematical model of cancer and its use in analyzing irradiation therapies. Theor. Biol. Med. Model., 3 (2006), 7.
- V. Hatzimanikatis, K.H. Lee, J.E. Bailey. A mathematical description of refulation of the G1-S transition of the mammalian cell cycle. Biotechnol. bioeng., 65 (1999), No. 6, 631–637.
- M. Gyllenberg. G.F. Webb. Quiescence as an explanation of Gompertzian tumor growth. Growth, dev. aging, 86 (1987), No.s 1-2, 67–95. Zbl0632.92014
- N.L. Komarova, D. Wodarz. Effect of cellular quiescence on the success of targeted CML therapy. PLoS ONE, 2 (2007), No. 10, e990.
- J.W. Uhr, R.H. Scheuermann, N.E. Street, E.S. Vitetta. Cancer dormancy: opportunities for new therapeutic approaches. Nature Med., 3 (1997), No. 5, 505–509.
- B. Quesnel. Dormant tumor cells as a therapeutic target? Cancer Lett., 267 (2008), No. 1, 10–17.
- G.P. Dunn, A.T. Bruce, H. Ikeda, L.J. Old, R.D. Schreiber. Cancer immunoediting: from immunosurveillance to tumor escape. Nature Immunology, 3 (2002), No. 11, 991–999.
- K.J. Weinhold, L.T. Goldstein, E.F. Wheelock. Tumour-dormant states established with L5178Y lymphoma cells in immunised syngeneic murine hosts. Nature, 270 (1977), No. 5632, 59–61.
- H. Siu, E.S. Vitetta, R.D. May, J.W. Uhr. Tumor dormancy. I. Regression of BCL1 tumor and induction of a dormant tumor state in mice chimeric at the major histocompatibility complex. J. Immunol., 137 (1986), No. 4, 1376–1382.
- C.G. Clemente, M.C. Mihm Jr., R. Bufalino, S. Zurrida, P. Collini, N. Cascinelli. Prognostic value of tumor infiltrating lymphocytes in the vertical growth phase of primary cutaneous melanoma. Cancer, 77 (1996), No. 7, 1303–1310.
- J. Galon, A. Costes, F. Sanchez-Cabo, A. Kirilovsky, B. Mlecnik, C. Lagorce-Pagès, M. Tosolini, M. Camus, A. Berger, P. Wind, F. Zinzindohoué, P. Bruneval, P.-H. Cugnenc, Z. Trajanoski, W.-H. Fridman, F. Pagès. Type, density and location of immune cells within human colorectal tumors predict clinical outcome. Science, 313 (2006), No. 5795, 1960–1964.
- E. Sato, S. H. Olson, J. Ahn, B. Bundy, H. Nishikawa, F. Qian, A.A. Jungbluth, D. Frosina, S. Gnjatic, C. Ambrosone, J. Kepner, T. Odunsi, G. Ritter, S. Lele, Y.-T. Chen, H. Ohtani, L.J. Old, K. Odunsi. Intraepithelial CD8+ tumor-infiltrating lymphocytes and a high CD8+/regulatory T cell ratio are associated with favorable prognosis in ovarian cancer. Proc. Natl. Acad. Sci., 102 (2005), No. 51, 18538–18543.
- C.M. Koebel, W. Vermi, J.B. Swann, N. Zerafa, S.J. Rodig, L.J. Old, M.J. Smyth, R.D. Schreiber. Adaptive immunity maintains occult cancer in an equilibrium state. Nature, 450 (2007), No. 7171, 903–907.
- K.M. Page, J.W. Uhr. Mathematical models of cancer dormancy. Leukemia and Lymphoma, 46 (2005), No. 3, 313–327.
- V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, S. Perelson. Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56 (1994), No. 2, 295–321. Zbl0789.92019
- V.A. Kuznetsov, G.D. Knott. Modeling tumor regrowth and immunotherapy. Math. Comp. Modelling, 33 (2001), No.s 12–13, 1275–1287. Zbl1004.92021
- J.A. Adam, N. Bellomo. A survey of tumor-immune system dynamics (modeling and simulation in science, engineering and technology). Birkhaeuser, Boston, 1996.
- N. Bellomo, L. Preziosi. Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comp. Model., 32 (2000), No.s 3–4, 413–452. Zbl0997.92020
- D. Kirschner, J.C. Panetta. Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol., 37 (1998), No. 3, 235–252. Zbl0902.92012
- L.G. De Pillis, W. Gu, A.E. Radunskaya. Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol., 238 (2006), No. 4, 841–862.
- A. Diefenbach, E.R. Jensen, A.M. Jamison, D. Raulet. Rae1 and H60 ligands of the NKG2D receptor stimulate tumor immunity. Nature, 413 (2001), No. 6852, 165–171.
- D. Wodarz. Use of oncolytic viruses for the eradication of drug-resistant cancer cells. J. R. Soc. Interface, 6 (2009), No. 31, 179–186.
- D. Wodarz, N. Komarova. Towards predictive computational models of oncolytic virus therapy: basis for experimental validation and model selection. PLoS One, 4 (2009) , No. 1, e4271.
- A. Matzavinos, M.A.J. Chaplain, V.A. Kuznetsov. Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. Math. Medicine and Biology: A Journal of the IMA, 21 (2004), No. 1, 1–34. Zbl1061.92038
- A. Matzavinos. Dynamic irregular patterns and invasive wavefronts: the control of tumour growth by cytotoxic T-lymphcytes. In: Selected topics in cancer modeling (modeling and simulation in science engineering and technology), Birkhauser, Boston, 2008.
- A.W. Le Serve, K. Hellman. Metastases and the normalization of tumour blood vessels by ICRF 159: a new type of drug action. Br. Med. J., 1 (1972), No. 5800, 597–601.

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