Advertisement

Bulletin of Mathematical Biology

, Volume 80, Issue 3, pp 519–539 | Cite as

Suppression of Metastasis by Primary Tumor and Acceleration of Metastasis Following Primary Tumor Resection: A Natural Law?

  • Leonid Hanin
  • Jason Rose
Original Article

Abstract

We study metastatic cancer progression through an extremely general individual-patient mathematical model that is rooted in the contemporary understanding of the underlying biomedical processes yet is essentially free of specific biological assumptions of mechanistic nature. The model accounts for primary tumor growth and resection, shedding of metastases off the primary tumor and their selection, dormancy and growth in a given secondary site. However, functional parameters descriptive of these processes are assumed to be essentially arbitrary. In spite of such generality, the model allows for computing the distribution of site-specific sizes of detectable metastases in closed form. Under the assumption of exponential growth of metastases before and after primary tumor resection, we showed that, regardless of other model parameters and for every set of site-specific volumes of detected metastases, the model-based likelihood-maximizing scenario is always the same: complete suppression of metastatic growth before primary tumor resection followed by an abrupt growth acceleration after surgery. This scenario is commonly observed in clinical practice and is supported by a wealth of experimental and clinical studies conducted over the last 110 years. Furthermore, several biological mechanisms have been identified that could bring about suppression of metastasis by the primary tumor and accelerated vascularization and growth of metastases after primary tumor resection. To the best of our knowledge, the methodology for uncovering general biomedical principles developed in this work is new.

Keywords

Angiogenesis Dormancy Metastasis Method of maximum likelihood Poisson process Primary tumor 

Notes

Acknowledgements

Incisive and constructive comments by the two anonymous reviewers have helped the authors to considerably improve the manuscript. The reviewers’ suggestions are greatly appreciated.

References

  1. Alexander P (1983) Dormant metastases: studies in experimental animals. J Pathol 141:379–383CrossRefGoogle Scholar
  2. Balkwill F, Mantovani A (2001) Inflammation and cancer: back to Virchow? Lancet 357:539–545CrossRefGoogle Scholar
  3. Bashford E, Murray J, Cramer W (1907) The natural and induced resistance of mice to the growth of cancer. Proc R Soc Lond 79:164–187CrossRefGoogle Scholar
  4. Demicheli R, Retsky MW, Swartzendruber DE, Bonadonna G (1997) Proposal for a new model of breast cancer metastatic development. Ann Oncol 8:1075–1080CrossRefGoogle Scholar
  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 19:1821–1828CrossRefGoogle Scholar
  6. DeWys WD (1972) Studies correlating the growth rate of a tumor and its metastases and providing evidence for tumor-related systemic growth-retarding factors. Cancer Res 32:374–379Google Scholar
  7. Ehrlich P (1906) Experimentelle Karzinomstudien an Mäusen. Arch Koiglichen Inst Exp Ther Frankfurt am Main 1:65–103 (in German)Google Scholar
  8. Fakir H, Hlatky L, Li H, Sachs R (2013) Repopulation of interacting tumor cells during fractionated radiotherapy: stochastic modeling of the tumor control probability. Med Phys 40(12):121716CrossRefGoogle Scholar
  9. Fidler IA (1990) Critical factors in the biology of human cancer metastasis: twenty-eighth G. H. A. Clowes memorial award lecture. Cancer Res 50:6130–6138Google Scholar
  10. Fisher B (1999) From Halsted to prevention and beyond: advances in the management of breast cancer during the twentieth century. Eur J Cancer 35:1963–1973CrossRefGoogle Scholar
  11. Folkman J (1974) Tumor angiogenesis factor. Cancer Res 34:2109–2113Google Scholar
  12. Folkman J (2002) Role of angiogenesis in tumor growth and metastasis. Semin Oncol 29(6), Suppl 16:15–18Google Scholar
  13. Forget P, Vandenhende J, Berliere M, Machiels JP, Nussbaum B, Legrand C, DeKock M (2010) Do intraoperative analgesics influence breast cancer recurrence after mastectomy? A retrospective analysis. Anesth Analg 110(6):1630–1635CrossRefGoogle Scholar
  14. Gorelik E (1983) Concomitant tumor immunity and resistance to a second tumor challenge. Adv Cancer Res 39:71–120CrossRefGoogle Scholar
  15. Hadfield G (1954) The dormant cancer cell. Br Med J 2:607–610CrossRefGoogle Scholar
  16. 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
  17. Hanin LG (2013) Seeing the invisible: how mathematical models uncover tumor dormancy, reconstruct the natural history of cancer and assess the effects of treatment. In: Almog N, Enderling H, Hlatky L (eds) Systems biology of tumor dormancy. Advances in experimental medicine and biology, vol 734. Springer, New York, pp 261–282CrossRefGoogle Scholar
  18. Hanin L (2017) Do breast cancer patients benefit from surgery? Hypotheses, mathematical models and false beliefs. In: Retsky M, Demicheli R (eds) Perioperative inflammation as a triggering origin of metastasis development. Springer, New York, pp 161–182CrossRefGoogle Scholar
  19. Hanin LG, Yakovlev AY (1996) A nonidentifiability aspect of the two-stage model of carcinogenesis. Risk Anal 16:711–715CrossRefGoogle Scholar
  20. 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 223:133–141MathSciNetCrossRefMATHGoogle Scholar
  21. 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
  22. Hanin LG, Bunimovich-Mendrazitsky S (2014) Reconstruction of the natural history of metastatic cancer and assessment of the effects of surgery: gompertzian growth of the primary tumor. Math Biosci 247:47–58MathSciNetCrossRefMATHGoogle Scholar
  23. Hanin L, Pavlova L (2016) A quantitative insight into metastatic relapse of breast cancer. J Theor Biol 394:172–181MathSciNetCrossRefMATHGoogle Scholar
  24. Hanin L, Rose J (2016) Uncovering the natural history of cancer from post mortem cross-sectional diameters of hepatic metastases. Math Med Biol 33(4):397–416MathSciNetCrossRefGoogle Scholar
  25. Hanin LG, Rose J, Zaider M (2006) A stochastic model for the sizes of detectable metastases. J Theor Biol 243:407–417MathSciNetCrossRefGoogle Scholar
  26. Hanin L, Seidel K, Stoevesandt D (2016) A “universal” model of metastatic cancer, its parametric forms and their identification: what can be learned from site-specific volumes of metastases. J Math Biol 72(6):1633–1662MathSciNetCrossRefMATHGoogle Scholar
  27. Hiller J, Schier R, Riedel B (2017) Perioperative biologic perturbation and cancer surgery: targeting the adrenergic-inflammatory response and microcirculatory dysregulation. In: Retsky M, Demicheli R (eds) Perioperative inflammation as a triggering origin of metastasis development. Springer, New York, pp 83–107CrossRefGoogle Scholar
  28. Holmgren K, O’Reilly MS, Folkman J (1995) Dormancy of micrometastases: balanced proliferation and apoptosis in the presence of angiogenesis suppression. Nat Med 1:149–153CrossRefGoogle Scholar
  29. Hölzel D, Eckel R, Emeny RT, Engel J (2010) Distant metastases do not metastasize. Cancer Metastasis Rev 29:737–750CrossRefGoogle Scholar
  30. Karr AF (1993) Probability. Springer, New YorkCrossRefMATHGoogle Scholar
  31. Kendal WS (2006) Chance mechanisms affecting the burden of metastases. BMC Cancer 5:138CrossRefGoogle Scholar
  32. Kleffel S, Schatton T (2013) Tumor dormancy and cancer stem cells: two sides of the same coin? In: Almog N, Enderling H, Hlatky L (eds) Systems biology of tumor dormancy. Advances in experimental medicine and biology, vol 734. Springer, New York, pp 145–179CrossRefGoogle Scholar
  33. Maida V, Ennis M, Kuziemsky C, Corban J (2009) Wounds and survival in cancer patients. Eur J Cancer 45:3237–3244CrossRefGoogle Scholar
  34. Marches R, Scheuermann R, Uhr J (2006) Cancer dormancy-from mice to man. Cell Cycle 5(16):1772–1778CrossRefGoogle Scholar
  35. Prehn RT (1993) Two competing influences that may explain concomitant tumor resistance. Cancer Res 53:3266–3269Google Scholar
  36. Retsky M, Demicheli R (2017) Perioperative inflammation as a triggering origin of metastasis development. In: Retsky M, Demicheli R (eds) Perioperative inflammation as a triggering origin of metastasis development. Springer, New York, pp 19–54CrossRefGoogle Scholar
  37. 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
  38. Retsky M, Demicheli R, Hrushesky WJM, Forget P, DeKock M, Gukas I, Rogers RA, Baum M, Sukhatme V, Vaidya JS (2013) Reduction of breast cancer relapses with perioperative non-steroidal anti-inflammatory drugs: new findings and a review. Curr Med Chem 20(33):4163–4176CrossRefGoogle Scholar
  39. Ross SM (1997) Introduction to probability models, 6th edn. Academic Press, San DiegoMATHGoogle Scholar
  40. Spano D, Heck C, De Antonelli P, Christofori G, Zollo M (2012) Molecular networks that regulate cancer metastasis. Semin Cancer Biol 22(3):234–49CrossRefGoogle Scholar
  41. Stigler SM (2007) The epic story of maximum likelihood. Stat Sci 22(4):598–620MathSciNetCrossRefMATHGoogle Scholar
  42. Sugarbaker EV, Ketcham AS, Cohen AM (1971) Studies of dormant tumor cells. Cancer 28:545–552CrossRefGoogle Scholar
  43. Sugarbaker E, Thornswaite J, Ketcham A (1977) Inhibitory effect of a primary tumor on metastasis. In: Day S, Myers W, Stansly P, Garattini S, Lewis M (eds) Progress in cancer research and therapy, vol 5. Raven Press, New York, pp 227–240Google Scholar
  44. Tyzzer EE (1913) Factors in the production and growth of tumor metastases. J Med Res 28:309–332Google Scholar
  45. Vatner RE, Cooper BT, Vanpouille-Box C, Demaria S, Formenti SC (2014) Combinations of immunotherapy and radiation in cancer therapy. Front Oncol 4:325CrossRefGoogle Scholar

Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsIdaho State UniversityPocatelloUSA
  2. 2.Department of Applied Mathematics, Institute of Applied Mathematics and MechanicsSt. Petersburg Polytechnic UniversitySt. PetersburgRussia
  3. 3.Department of MathematicsBrigham Young University - IdahoRexburgUSA

Personalised recommendations