Seeing the Invisible: How Mathematical Models Uncover Tumor Dormancy, Reconstruct the Natural History of Cancer, and Assess the Effects of Treatment

  • Leonid HaninEmail author
Part of the Advances in Experimental Medicine and Biology book series (AEMB, volume 734)


The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.

In this primarily methodological work, we discuss critically important, yet largely unobservable, aspects of the natural history of cancer, such as (1) early metastatic dissemination; (2) dormancy of secondary tumors; (3) treatment-related interruption of metastatic dormancy, induction of angiogenesis, and acceleration of the growth of vascular metastases; and (4) the existence of cancer stem cells. The hypothesis of early metastasis was debated for several decades. Dormant cancer cells and surgery-induced acceleration of metastatic growth were first observed in clinical studies and animal experiments conducted more than a century ago; later, these findings were confirmed in numerous modern studies.

We focus on the unique role played by very general mathematical models of the individual natural history of cancer that are entirely mechanistic yet, somewhat paradoxically, essentially free of assumptions about specific nature of the underlying biological processes. These models make it possible to reconstruct in considerable detail the individual natural history of cancer and retrospectively assess the effects of treatment. Thus, the models can be used as a tool for generation and validation of biomedical hypotheses related to carcinogenesis, primary tumor growth, its metastatic dissemination, growth of metastases, and the effects of various treatment modalities. We discuss in detail one such general model and review the conclusions relevant to the aforementioned aspects of cancer progression that were drawn from fitting a parametric version of the model to data on the volumes of bone metastases in one breast cancer patient and 12 prostate cancer patients.


Angiogenic switch Breast cancer Cancer stem cell Chemotherapy Metastatic dormancy Model identifiability Poisson process Primary tumor Prostate cancer Radiotherapy Surgery Treatment-induced acceleration of metastasis 


  1. 1.
    Retsky M, Demicheli R, Hrushesky W (2003) Breast cancer screening: controversies and future directions. Curr Opin Obstet Gynecol 15:1–8PubMedCrossRefGoogle Scholar
  2. 2.
    Retsky M, Demicheli R, Hrushesky W (2001) Premenopausal status accelerates relapse in node positive breast cancer: hypothesis links angiogenesis, screening controversy. Breast Cancer Res Treat 65:217–224PubMedCrossRefGoogle Scholar
  3. 3.
    Retsky M, Demicheli R, Hrushesky W, Baum M, Gukas I (2010) Surgery triggers outgrowth of latent distant disease in breast cancer: an inconvenient truth? Cancers 2:305–337CrossRefGoogle Scholar
  4. 4.
    Baum M, Chaplain M, Anderson A, Douek M, Vaidya JS (1999) Does breast cancer exist in a state of chaos? Eur J Cancer 35:886–891PubMedCrossRefGoogle Scholar
  5. 5.
    Demicheli R, Retsky M, Hrushesky WJM, Baum M, Gukas ID (2008) The effects of surgery on tumor growth: a century of investigations. Ann Oncol 19:1821–1828PubMedCrossRefGoogle Scholar
  6. 6.
    Hanin L (2010) Why victory in the war on cancer remains elusive: biomedical hypotheses and mathematical models. Cancers 3:340–367CrossRefGoogle Scholar
  7. 7.
    Hanin L, Zaider M (2011) Effects of surgery and chemotherapy on metastatic progression of prostate cancer: evidence from the natural history of the disease reconstructed through mathematical modeling. Cancers 3:3632–3660CrossRefGoogle Scholar
  8. 8.
    Folkman J, Watson K, Ingber D, Hanahan D (1989) Induction of angiogenesis during the transition from hyperplasia to neoplasia. Nature 339:58–61PubMedCrossRefGoogle Scholar
  9. 9.
    Douglas JRS (1971) Significance of the size distribution of bloodborne metastases. Cancer 27:379–390PubMedCrossRefGoogle Scholar
  10. 10.
    Barbour A, Gotley DC (2003) Current concepts of tumour metastasis. Ann Acad Med Singapore 32:176–184PubMedGoogle Scholar
  11. 11.
    Fisher B (1980) Laboratory and clinical research in breast cancer: a personal adventure. The David A. Karnofsky memorial lecture. Cancer Res 40:3863–3874PubMedGoogle Scholar
  12. 12.
    Hadfield G (1954) The dormant cancer cell. Br Med J 2:607–610PubMedCrossRefGoogle Scholar
  13. 13.
    Ashworth TR (1869) A case of cancer in which cells similar to those in the tumour were seen in the blood after death. Aust Med J 14:146–147Google Scholar
  14. 14.
    Goldmann EE (1897) Anatomische Untersuchungen über die Verbreitungswege bösartiger Geschwülstle. Beitr Z Klin Chir 18:595Google Scholar
  15. 15.
    Fodstad O, Faye R, Hoifodt HK, Skovlund E, Aamdal S (2001) Immunobead-based detection and characterization of circulating tumor cells in melanoma patients. Recent Results Cancer Res 158:40–50PubMedCrossRefGoogle Scholar
  16. 16.
    Pantel K, Otte M (2001) Occult micrometastases: enrichment, identification and characterization of single disseminated tumour cells. Semin Cancer Biol 11:327–337PubMedCrossRefGoogle Scholar
  17. 17.
    Jiao X, Krasna MJ (2002) Clinical significance of micrometastasis in lung and esophageal cancer: a new paradigm in thoracic oncology. Ann Thorac Surg 74:278–284PubMedCrossRefGoogle Scholar
  18. 18.
    Sugio K, Kase S, Sakada T, Yamazaki K, Yamaguchi M, Ondo K, Yano T (2002) Micrometastasis in the bone marrow of patients with lung cancer associated with a reduced expression of E-cadherin and beta-catenin: risk assessment by immunohistochemistry. Surgery 131:S226–S231PubMedCrossRefGoogle Scholar
  19. 19.
    Ellis WJ, Pfitzenmaier J, Colli J, Arfman E, Lange PH, Vessella RL (2003) Detection and isolation of prostate cancer cells from peripheral blood and bone marrow. Urology 61:277–281PubMedCrossRefGoogle Scholar
  20. 20.
    Pfitzenmaier J, Vessella RL, Ellis WJ, Lange PH (2003) Detection, isolation and study of disseminated prostate cancer cells in the peripheral blood and bone marrow. In: Pantel K (ed) Micrometastasis. Kluwer Academic Publishers, Norwell, MA, pp 87–116, Chapter 5Google Scholar
  21. 21.
    Meng S, Tripathy D, Frenkel EP, Shete S, Naftalis EZ, Huth JF, Beitsch PD, Leitch M, Hoover S, Euhus D, Haley B, Morrison L, Fleming TP, Herlyn D, Terstappen LWMM, Fehm T, Tucker TF, Lane N, Wang J, Uhr JW (2004) Circulating tumour cells in patients with breast cancer dormancy. Clin Cancer Res 10:8152–8162PubMedCrossRefGoogle Scholar
  22. 22.
    Marches R, Scheuermann R, Uhr J (2006) Cancer dormancy: from mice to man. Cell Cycle 5:1772–1778PubMedCrossRefGoogle Scholar
  23. 23.
    Chambers AF, Macdonald IF, Schmidt E, Koop S, Morris VL, Khokha R, Groom AC (1995) Steps in tumor metastasis: new concepts from intravital videomicroscopy. Cancer Metastasis Rev 14:279–301PubMedCrossRefGoogle Scholar
  24. 24.
    Luzzi KJ, MacDonald IC, Schmidt EE, Kerkvliet N, Morris VL, Chambers AF, Groom AC (1998) Multistep nature of metastatic inefficiency. Dormancy of solitary cells after successful extravasation and limited survival of early micrometastases. Am J Pathol 153:865–873PubMedCrossRefGoogle Scholar
  25. 25.
    Naumov GN, MacDonald IC, Weinmeister PM, Kerkvliet N, Nadkarni KV, Wilson SM, Morris VL, Groom AC, Chambers AF (2002) Persistence of solitary mammary carcinoma cells in a secondary site: a possible contributor to dormancy. Cancer Res 62:2162–2168PubMedGoogle Scholar
  26. 26.
    Jonas S, Bechstein WO, Lemmens H-P, Neuhaus R, Thalmann U, Neuhaus P (1996) Liver graft-transmitted glioblastoma multiforme. A case report and experience with 13 multiorgan donors suffering from primary cerebral neoplasia. Transpl Int 9:426–429PubMedCrossRefGoogle Scholar
  27. 27.
    Loh E, Couch FG, Hendricksen C, Farid L, Kelly PF, Acker MA, Tomaszewski JE, Malkowicz SB, Weber BL (1997) Development of donor-derived prostate cancer in a recipient following orthotopic heart transplantation. JAMA 277:133–137PubMedCrossRefGoogle Scholar
  28. 28.
    Karrison TG, Ferguson DJ, Meier P (1999) Dormancy of mammary carcinoma after mastectomy. Natl Cancer Inst 19:80–85CrossRefGoogle Scholar
  29. 29.
    Ehrlich P, Apolant H (1905) Beobachtungen über maligne Mäusetumoren. Berl Klin Wochenschr 42:871–874Google Scholar
  30. 30.
    Bashford E, Murray JA, Cramer W (1907) The natural and induced resistance of mice to the growth of cancer. Proc R Soc Lond 79:164–187CrossRefGoogle Scholar
  31. 31.
    Marie P, Clunet J (1910) Fréquences des métastases viscérales chez les souris cancéreuses après ablation chirurgicale de leur tumeur. Bull Assoc Franç L’Étude Cancér 3:19–23Google Scholar
  32. 32.
    Tyzzer EE (1913) Factors in the production and growth of tumor metastases. J Med Res 23:309–332Google Scholar
  33. 33.
    Prehn RT (1993) Two competing influences that may explain concomitant tumor resistance. Cancer Res 53:3266–3269PubMedGoogle Scholar
  34. 34.
    Lange PH, Hekmat K, Bosl G, Kennedy BJ, Fraley EE (1980) Accelerated growth of testicular cancer after cytoreductive surgery. Cancer 45:1498–1506PubMedCrossRefGoogle Scholar
  35. 35.
    De Giorgi V, Massi D, Gerlini G, Mannone F, Quercioli E, Carli P (2003) Immediate local and regional recurrence after the excision of a polypoid melanoma: tumor dormancy or tumor activation? Dermatol Surg 29:664–667PubMedCrossRefGoogle Scholar
  36. 36.
    Tseng WW, Doyle JA, Maguiness S, Horvai AE, Kashani-Sabet M, Leong SPL (2009) Giant cutaneous melanomas: evidence for primary tumour induced dormancy in metastatic sites? BMJ Case Rep. doi: 10.1136/bcr.07.2009.2073
  37. 37.
    Deylgat B, Van Rooy F, Vansteenkiste F, Devriendt D, George C (2011) Postsurgery activation of dormant liver micrometastasis: a case report and review of literature. J Gastrointest Cancer 42:1–4PubMedCrossRefGoogle Scholar
  38. 38.
    Hoover HC, Ketcham AS (1975) Techniques for inhibiting tumor metastases. Cancer 35:5–14PubMedCrossRefGoogle Scholar
  39. 39.
    Isern AE, Manjer J, Malina J, Loman N, Mårtensson T, Bofin A, Hagen AI, Tengrup I, Landberg G, Ringberg A (2011) Risk of recurrence following delayed large flap reconstruction after mastectomy for breast cancer. Br J Surg 98:659–666PubMedCrossRefGoogle Scholar
  40. 40.
    Maida V, Ennis M, Kuziemsky C, Corban J (2009) Wounds and survival in cancer patients. Eur J Cancer 45:3237–3244PubMedCrossRefGoogle Scholar
  41. 41.
    Bonnet D, Dick JE (1997) Human acute myeloid leukemia is organized as a hierarchy that originates from a primitive hematopoietic cell. Nat Med 3:730–737PubMedCrossRefGoogle Scholar
  42. 42.
    Al-Hajj M, Wicha MS, Benito-Hernandez A, Morrison SJ, Clarke MF (2003) Prospective identification of tumorigenic breast cancer cells. Proc Natl Acad Sci USA 100(7):3983–3988PubMedCrossRefGoogle Scholar
  43. 43.
    Dick JE (2003) Breast cancer stem cells revealed. Proc Natl Acad Sci USA 100(7): 3547–3549PubMedCrossRefGoogle Scholar
  44. 44.
    Kai K, Arima Y, Kamiya T, Saya H (2010) Breast cancer stem cells. Breast Cancer 17:80–85PubMedCrossRefGoogle Scholar
  45. 45.
    Collins AT, Berry PA, Hyde C, Stower MJ, Maitland NJ (2005) Prospective identification of tumorigenic prostate cancer stem cells. Cancer Res 65:10946–10951PubMedCrossRefGoogle Scholar
  46. 46.
    Boyd W (1966) The spontaneous regression of cancer. Thomas, Springfield, ILGoogle Scholar
  47. 47.
    Everson TC, Cole WH (2006) Spontaneous regression of cancer. Saunders, PhiladelphiaGoogle Scholar
  48. 48.
    Cole WH (1976) Spontaneous regression of cancer and the importance of finding its cause. Natl Cancer Inst Monogr 44:5–9PubMedGoogle Scholar
  49. 49.
    Zahl P-H, Mæhlen J, Welch HG (2008) The natural history of invasive breast cancer detected by screening mammography. Arch Intern Med 168:2311–2316PubMedCrossRefGoogle Scholar
  50. 50.
    Kendal WS (2005) Chance mechanisms affecting the burden of metastases. BMC Cancer 5:138–146PubMedCrossRefGoogle Scholar
  51. 51.
    Hanin LG, Yakovlev AY (1996) A nonidentifiability aspect of the two-stage model of carcinogenesis. Risk Anal 16:711–715PubMedCrossRefGoogle Scholar
  52. 52.
    Hanin LG, Rose J, Zaider M (2006) A stochastic model for the sizes of detectable metastases. J Theor Biol 243:407–417PubMedCrossRefGoogle Scholar
  53. 53.
    Bartoszyński R, Edler L, Hanin L, Kopp-Schneider A, Pavlova L, Tsodikov A, Zorin A, Yakovlev A (2001) Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis. Math Biosci 171:113–142PubMedCrossRefGoogle Scholar
  54. 54.
    Hanin LG (2008) Distribution of the sizes of metastases: mathematical and biomedical considerations. In: Tan WY, Hanin LG (eds) Handbook of cancer models with applications. World Scientific, Singapore, pp 141–169Google Scholar
  55. 55.
    Hanin LG, Korosteleva O (2010) Does extirpation of the primary breast tumor give boost to growth of metastases? Evidence revealed by mathematical modeling. Math Biosci 223:133–141PubMedCrossRefGoogle Scholar
  56. 56.
    Hanin LG (2002) Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology. Disc Dyn Nat Soc 7:177–189CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.Department of MathematicsIdaho State UniversityPocatelloUSA
  2. 2.Biomedical Engineering, Center for Bioinformatics and Computational GenomicsGeorgia Institute of TechnologyDuluthUSA

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