Mathematical modeling of the metastatic process

Experimental Metastasis: Modeling and Analysis

Volumn , Issue , 2013, Pages 189-208

  Scott, Jacob G ^a,b   Gerlee, Philip ^c,d   Basanta, David ^a   Fletcher, Alexander G ^b   Maini, Philip K ^b   Anderson, Alexander R A ^a  

^a H LEE MOFFITT CANCER CENTER AND RESEARCH INSTITUTE   (United States)

^b UNIVERSITY OF OXFORD   (United Kingdom)

^c UNIVERSITY OF GOTHENBURG   (Sweden)

^d CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84907434598     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1007/978-94-007-7835-1_9     Document Type: Chapter

References (52)

1. Britta W, Peterse JL, van’t Veer LJ (2005 Aug) Breast cancer metastasis: markers and models. Nat Rev Cancer 5(8):591-602
2. Bos PD, Zhang XH-F, Nadal C, Shu W, Gomis RR, Nguyen DX, Minn AJ, van de Vijver MJ, Gerald WL, Foekens JA, Massagu J (2009 June) Genes that mediate breast cancer metastasis to the brain. Nature 459(7249):1005-1009
3. Minn AJ, Gupta GP, Siegel PM, Bos PD, Shu W, Giri DD, Viale A, Olshen AB, Gerald WL, Massagu J (2005 July) Genes that mediate breast cancer metastasis to lung. Nature 436(7050):518-524
4. Norton L, Massagu J (2006 August) Is cancer a disease of self-seeding? Nat Med 12(8):875-878
5. Norris J (2008) Markov Chains. Cambridge University Press
6. von Neumann J, Burks AW (1966) Theory of Self-Reproducing Automata. University of Illinois Press
7. Moran PAP (1962) The statistical processes of evolutionary theory. Clarendon, Oxford
8. Saidel GM, Liotta LA, Kleinerman J (1976 February) System dynamics of metastatic process from an implanted tumor. J Theoret Biol 56(2):417-434
9. Liotta LA, Saidel GM, Kleinerman J (1976 September) Stochastic model of metastases formation. Biometrics 32(3):535-550
10. Liotta LA, Delisi C, Saidel G, Kleinerman J (1977 September) Micrometastases formation: a probabilistic model. Cancer letters 3(3-4):203-208
11. Liotta LA, Kleinerman J, Saidel GM (1974 May) Quantitative relationships of intravascular tumor cells, tumor vessels, and pulmonary metastases following tumor implantation. Cancer Res 34(5):997-1004
12. Chaffer CL, Weinberg RA (2011 May) A perspective on cancer cell metastasis. Science 331(6024):1559-1564
13. Thiery JP (2003 Dec) Epithelial-mesenchymal transitions in development and pathologies. Curr Opin Cell Biol 15(6):740-746
14. Michor F, Nowak MA, Iwasa Y (2006 June) Stochastic dynamics of metastasis formation. J Theoret Biol 240(4):521-530
15. Dingli D, Michor F, Antal T, Pacheco JM (2007 March) The emergence of tumor metastases. Cancer Biol Therap 6(3):383-390
16. Greco FA (2012 Aug) Cancer of unknown primary site: evolving understanding and management of patients. Clin Adv Hematol Oncol 10(8):518-24
17. Haeno H, Michor F (2010 March) The evolution of tumor metastases during clonal expansion. J Theor Biol 263(1):30-44
18. Milano MT, Zhang H, Metcalfe SK, Muhs AG, Okunieff P (2009 June) Oligometastatic breast cancer treated with curative-intent stereotactic body radiation therapy. Breast Cancer Res Treat 115(3):601-8
19. Milano MT, Katz AW, Zhang H, Okunieff P (2012 July) Oligometastases treated with stereotactic body radiotherapy: long-term follow-up of prospective study. Int JRadiat Oncol Biol Phys 83(3):878-86
20. Iwata K, Kawasaki K, Shigesada N (2000 March) A dynamical model for the growth and size distribution of multiple metastatic tumors. J Theor Biol 203(2):177-186
21. Gerlee P (2013 Feb) The model muddle: in search of tumour growth laws. Cancer Res 73(8):2407-2411
22. Baish JW, Jain RK (1998 Sep) Cancer, angiogenesis and fractals. Nat Med 4(9):984
23. Baish JW, Jain RK (2000 July) Fractals and cancer. Cancer Res 60(14):3683-8
24. Neal ML, Trister AD, Cloke T, Sodt R, Ahn S, Baldock AL, Bridge CA, Lai A, Cloughesy TF, Mrugala MM, Rockhill JK, Rockne R C, Swanson KR (2013) Discriminating survival outcomes in patients with glioblastoma using a simulation-based, patient-specific response metric. PLoSOne 8(1):e51951
25. Bartoszynski R, Edler L, Hanin L, Kopp-Schneider A, Pavlova L, Tsodikov A, Zorin A, Yakovlev AY (2001 June) Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis. Math Biosci 171(2):113—42
26. Hanin L, Rose J, Zaider M (2006 Dec) A stochastic model for the sizes of detectable metasta-ses. J Theor Biol 243(3):407—417
27. Xu JL, Prorok PC (1998 Sept) Estimating a distribution function of the tumor size at metastasis. Biometrics 54(3):859—864
28. Piez D, Labonte MJ, Bohanes P, Zhang W, Benhanim L, Ning Y, Wakatsuki T, Loupakis F, Lenz H-J (2013 Feb) Cancer dormancy: a model of early dissemination and late cancer recurrence. Clin Cancer Res 18(3):645—53
29. Demicheli R, Abbattista A, Miceli R, Valagussa P, G Bonadonna (1996) 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(2):177—85
30. Retsky MW, Demicheli R, Swartzendruber DE, Bame PD, Wardwell RH, Bonadonna G, Speer JF, Valagussa P (1997 Sept) Computer simulation of a breast cancer metastasis model. Breast Cancer Res Treat 45(2):193—202
31. Demicheli R, Retsky MW, Swartzendruber DE, Bonadonna G (1997 Nov) Proposal for a new model of breast cancer metastatic development. Ann Oncol 8(11):1075—80
32. Demicheli R, Retsky MW, Hrushesky WJM, Baum Michael (2007 Dec) Tumor dormancy and surgery-driven interruption of dormancy in breast cancer: learning from failures. Nat Clin Pract Oncol 4(12):699—710
33. Retsky M, Demicheli R, Hrushesky WJm, Forget P, De Kock M, Gukas I, Rogers RA, Baum M, Pachmann K, Vaidya JS (2012) Promising development from translational or perhaps anti-translational research in breast cancer. Clin Transl Med 1(1):17
34. Michor F (2008 June) Mathematical models of cancer stem cells. J Clin Oncol: Offic J Am Soc Clin Oncol 26(17):2854—2861
35. Enderling H, Anderson ARA, Chaplain MAJ, Beheshti A, Hlatky L, Hahnfeldt P (2009 Nov) Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res 69(22):8814—8821
36. Enderling H, Hahnfeldt P, Hlatky L, Almog N (2012 May) Systems biology of tumor dormancy: linking biology and mathematics on multiple scales to improve cancer therapy. Cancer Res 72(9):2172—5
37. Enderling H (2013) Cancer stem cells and tumor dormancy. Adv Exp Med Biol 734:55-71
38. Hillen T, Enderling H, Hahnfeldt P (2013 Jan) The tumor growth paradox and immune systemmediated selection for cancer stem cells. Bull Math Biol 75(1):161—84
39. Gao X, McDonald JT, Hlatky L, Enderling Heiko (2013 Jan) Acute and fractionated irradiation differentially modulate glioma stem cell division kinetics. Cancer Res 73(5):1481—1490
40. Boushaba Khalid, Levine HA, Nilsen-Hamilton M (2006 Oct) A mathematical model for the regulation of tumor dormancy based on enzyme kinetics. Bull Math Biol 68(7):1495—526
41. Kim Y, Boushaba K (2013) Regulation of tumor dormancy and role of microenvironment: a mathematical model. Adv Exp Med Biol 734:237—59
42. Eikenberry S, Thalhauser C, Kuang Y (2009 Apr) Tumor-immune interaction, surgical treatment, and cancer recurrence in a mathematical model of melanoma. PLoS ComputBiol 5(4):e1000362
43. Diego D, Calvo GF, Prez-Garca VM (2012 July) Modeling the connection between primary and metastatic tumors. J Math Biol:1—36
44. Peeters CFJM, de Waal RMW, Wobbes T, Ruers TJM (2008 Nov) Metastatic dormancy imposed by the primary tumor: does it exist in humans? Ann Surg Oncol 15(11):3308—15
45. Chen LL, Blumm N, Christakis NA, Barabsi A-L, Deisboeck TS (2009 Sept) Cancer metastasis networks and the prediction of progression patterns. Br J Cancer 101(5):749—758
46. Newton PK, Mason J, Bethel K, Bazhenova LA, Nieva J, Kuhn P (2012) A stochastic Markov chain model to describe lung cancer growth and metastasis. PloS one 7(4):e34637
47. Newton PK, Mason J, Bethel K, Bazhenova L, Nieva J, Norton L, Kuhn P (2013 Feb) Spreaders and sponges define metastasis in lung cancer: A Markov chain mathematical model. Cancer Res 73(9):2760-2769
48. Diaconis P (2009 April) The markov chain monte carlo revolution. Bullet Am Math Soc 46(2):179-205
49. Disibio Guy, French SW (2008 June) Metastatic patterns of cancers: results from a large autopsy study. Arch Pathol Lab Med 132(6):931-939
50. Scott J, Kuhn P, Anderson ARA (2012 July) Unifying metastasis-integrating intravasation, circulation and end-organ colonization. Nat Rev Cancer 12(7):445-6
51. Scott JG, Basanta D, Anderson ARA, Gerlee P (2013) A mathematical model of tumour self-seeding reveals secondary metastatic deposits as drivers of primary tumour growth. J Royal Soc, Interface/Royal Soc 10(82):20130011
52. Anderson ARA, Quaranta V (2008) Integrative mathematical oncology. Nat Reviewscancer 8(3):227-234