Seeing the Invisible: How Mathematical Models Uncover Tumor Dormancy, Reconstruct the Natural History of Cancer, and Assess the Effects of Treatment
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.
KeywordsAngiogenic switch Breast cancer Cancer stem cell Chemotherapy Metastatic dormancy Model identifiability Poisson process Primary tumor Prostate cancer Radiotherapy Surgery Treatment-induced acceleration of metastasis
- 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.Goldmann EE (1897) Anatomische Untersuchungen über die Verbreitungswege bösartiger Geschwülstle. Beitr Z Klin Chir 18:595Google Scholar
- 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.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
- 29.Ehrlich P, Apolant H (1905) Beobachtungen über maligne Mäusetumoren. Berl Klin Wochenschr 42:871–874Google Scholar
- 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.Tyzzer EE (1913) Factors in the production and growth of tumor metastases. J Med Res 23:309–332Google Scholar
- 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
- 46.Boyd W (1966) The spontaneous regression of cancer. Thomas, Springfield, ILGoogle Scholar
- 47.Everson TC, Cole WH (2006) Spontaneous regression of cancer. Saunders, PhiladelphiaGoogle Scholar
- 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