Distribution of the sizes of metastases: Mathematical and biomedical considerations

Handbook Of Cancer Models With Applications

Volumn , Issue , 2008, Pages 149-172

  Hanin, Leonid ^a  

^a Nucl Eng Idaho State University   (United States)

Author keywords

Cancer natural history; Metastasis; Model identifiability; Parameter estimation; Poisson process; Primary tumor

Indexed keywords

EID: 74149084913     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1142/9789812779489_0006     Document Type: Chapter

References (59)

1. Barbour A and Gotley DC. Current concepts of tumour metastasis. Ann. Acad. Med. Singapore 2003; 32: 176-184.
2. Bartoczyński R, Edler L, Hanin L, Kopp-Schneider A, Pavlova L, Tsodikov A, Zorin A and Yakovlev A. Modeling cancer detection: tumor size as a source of information on unobservable stages of carcinogenesis. Math. Biosci. 2001; 171: 113-142.
3. Bernhardt P, Forssell-Aronsson E, Jacobsson L and Skarnemark G. Lowenergy electron emitters for targeted radiotherapy of small tumors. Acta Oncol. 2001; 40: 602-608.
4. Chambers AF, Macdonald IF, Schmidt E, Koop S, Morris VL, Khokha R and Groom AC. Steps in tumor metastasis: new concepts from intravital videomicroscopy. Cancer Metastasis Rev. 1995; 14: 279-301.
5. Demicheli R. Tumour dormancy: findings and hypotheses from clinical research on breast cancer. Semin. Cancer Biol. 2001; 11: 297-306.
6. Douglas JRS. Significance of the size distribution of bloodborne metastases. Cancer 1971; 27: 379-390.
7. Evans CW. The Metastatic Cell: Behavior and Biochemistry. Chapman & Hall, London, 1991.
8. Fidler IJ. Critical factors in the biology of human cancer metastasis. 28th G.H.A. Clowes memorial award lecture. Cancer Res. 1990; 50: 6130-6138.
9. Fidler IJ. The biology of human cancer metastasis. 7th Jan Waldenstrom lecture. Acta Oncol. 1991; 30: 668-675.
10. Fidler IJ. Molecular biology of cancer: invasion and metastasis. In: Cancer Principles and Practice of Oncology, 5th ed. DeVita VT, Hellman S and Rosenberg SA (eds.) Lippincott Raven Publishers, Philadelphia, 1997, pp. 135-152.
11. Fidler IJ. The pathogenesis of cancer metastasis: the “seed and soil” hypothesis revisited. Nat. Rev. Cancer 2003; 3: 453-458.
12. Fodstad O, Faye R, Hoifodt HK, Skovlund E and Aamdal S. Immunobeadbased detection and characterization of circulating tumor cells in melanoma patients. Recent Results Cancer Res. 2001; 158: 40-50.
13. Goddu SM, Rao DV and Howell RW. Multicellular dosimetry for micrometastases:dependence of self-dose versus cross-dose to cell nuclei on type and energy of radiation and subcellular distribution of radionuclides. J. Nucl. Med. 1994; 35: 521-530.
14. Hanin LG. Identification problem for stochastic models with application to carcinogenesis, cancer detection and radiation biology. Disc. Dynam. Nat. Soc. 2002; 7: 177-189.
15. Hanin LG, Rose J and Zaider M. A stochastic model for the sizes of detectable metastases. J. Theor. Biol. 2006; 243: 407-417.
16. Hanin LG, Miller AB, Yakovlev AY and Zorin AV. The University of Rochester model of breast cancer detection and survival. In: Journal of the National Cancer Institute, Monograph 36. The Impact of Mammography and Adjuvant Therapy on U.S. Breast Cancer Mortality (1975-2000): Collective Results from the Cancer Intervention and Surveillance Modeling Network, 2006, pp. 86-95.
17. Hanin LG and Yakovlev AY. Anonidentifiability aspect of the two-stage model of carcinogenesis. Risk Anal. 1996; 16: 711-715.
18. Harrison D, Sauthoff H, Heitner S, Jagirdar J, Rom WN and Hay JG. Wild-type adenovirus decreases tumor xenograft growth, but despite viral persistence complete tumor responses are rarely achieved - deletion of the viral E1b-19-kD gene increases the viral oncolytic effect. Hum. Gene Ther. 2001; 12: 1323-1332.
19. Iwata K, Kawasaki K and Shigesada N. A dynamical model for the growth and size distribution of multiple metastatic tumors. J. Theor. Biol. 2000; 203: 177-186.
20. Jiao X and Krasna MJ. Clinical significance of micrometastasis in lung and esophageal cancer: a new paradigm in thoracic oncology. Ann. Thorac. Surg. 2002; 74: 278-284.
21. Kaplan JM. Adenovirus-based cancer gene therapy. Curr. Gene Ther. 2005; 5: 595-605.
22. Karrison TG, Ferguson DJ and Meier P. Dormancy of mammary carcinoma after mastectomy. J. Natl Cancer Inst. 1999: 19: 80-85.
23. Kasuya H, Takeda S, Nomoto S and Nakao A. The potential of oncolytic virus therapy for pancreatic cancer. Cancer Gene Ther. 2005; 12: 725-736.
24. Kaufman HL, Deraffele G, Mitcham J, Moroziewicz D, Cohen SM, Hurst-Wicker KS, Cheung K, Lee DS, Divito J, Voulo M, Donovan J, Dolan K, Manson K, Panicali D, Wang E, Horig H and Marincola FM. Targeting the local tumor microenvironment with vaccinia virus expressing B7.1 for the treatment of melanoma. J. Clin. Invest. 2005; 115: 1903-1912.
25. Kendal WS. The size distribution of human hematogenous metastases. J. Theor. Biol. 2001; 211: 29-38.
26. Kendal WS. Chance mechanisms affecting the burden of metastases. BMC Cancer 2005; 5: 138-146.
27. Khuri FR, Nemunaitis J, Ganly I, Arseneau J, Tannock IF, Romel L, Gore M, Ironside J, MacDougall RH, Heise C, Randlev B, Gillenwater AM, Bruso P, Kaye SB, Hong WK and Kirn DH. A controlled trial of intratumoral ONYX-015, a selectively-replicating adenovirus, in combination with cisplatin and 5-fluorouracil in patients with recurrent head and neck cancer. Nat. Med. 2000; 6: 879-885.
28. Kirn D, Hermiston T and McCormick F. ONYX-015: clinical data are encouraging. Nat. Med. 1998; 4: 1341-1342.
29. Kirn DH and McCormick F. Replicating viruses as selective cancer therapeutics. Mol. Med. Today 1996; 2: 519-527.
30. Luebeck EG and Moolgavkar SH. Multistage carcinogenesis and the incidence of colorectal cancer. Proc. Natl. Acad. Sci. USA 2002; 99: 15095-15100.
31. McCormick F. Cancer-specific viruses and the development of ONYX-015. Cancer Biol. Ther. 2003; 2: S157-160.
32. Moolgavkar SH, Dewanji A and Venzon DJ. A stochastic two stage model for cancer risk assessment. I. The hazard function and the probability of tumor. Risk Anal. 1988; 8: 383-392.
33. Moolgavkar SH and Knudson AG. Mutation and cancer: a model for human carcinogenesis. J. Natl. Cancer Inst. 1981; 66: 1037-1052.
34. Moolgavkar SH and Luebeck EG. Two-event model for carcinogenesis:biological, mathematical and statistical considerations. Risk Anal. 1990; 10: 323-341.
35. Moolgavkar SH and Venzon DJ. Two event model for carcinogenesis: incidence curves for childhood and adult tumors. Math. Biosci. 1979; 47: 55-77.
36. Nemunaitis J, Khuri F, Ganly I, Arseneau J, Posner M, Vokes E, Kuhn J, McCarty T, Landers S, Blackburn A, Romel L, Randlev B, Kaye S and Kirn D. Phase II trial of intratumoral administration of ONYX-015, a replicationselective adenovirus, in patients with refractory head and neck cancer. J. Clin. Oncol. 2001; 19: 289-298.
37. O’Donoghue JA. Dosimetric principles of targeted radiotherapy. In: Radioimmunotherapy of Cancer. Abrams PG and Fritzberg A (eds.) Marcel Dekker, New York, 2000, pp. 1-20.
38. Paget S. The distribution of secondary growths in cancer of the breast. Lancet 1889; 1: 571-573.
39. Pantel K and Otte M. Occult micrometastases: enrichment, identification and characterization of single disseminated tumour cells. Semin. Cancer Biol. 2001; 11: 327-337.
40. Parato KA, Senger D, Forsyth PA and Bell JC. Recent progress in the battle between oncolytic viruses and tumours. Nat. Rev. Cancer 2005; 5: 965-976.
41. Puri PS. A class of stochastic models of response after infection in the absence of defense mechanism. In: Proceedings of the Fifth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4. University of California Press, Berkeley and Los Angeles, 1967, pp. 511-535.
42. Puri PS. Aquantal response process associated with integrals of certain growth processes. In: Mathematical Aspects of Life Sciences, Queen’s Papers in Pure and Applied Mathematics, No. 26, Wasan MT (ed.) Queen’s University, Kingston, Ontario, Canada, 1971.
43. Puri PS and Senturia J. On a mathematical theory of quantal response assays. In: Proceedings of the Sixth Berkeley Symposium on Mathematical Statistics and Probability, Vol. 4. University of California Press, Berkeley and Los Angeles, 1972, pp. 231-247.
44. Reid T, Warren R and Kirn D. Intravascular adenoviral agents in cancer patients: lessons from clinical trials. Cancer Gene Ther. 2002; 9: 979-986.
45. Retsky M, Bonadonna G, Demicheli R, Folkman J, Hrushesky W and Valagussa P. Hypothesis: induced angiogenesis after surgery in premenopausal node-positive breast cancer patients is a major underlying reason why adjuvant chemotherapy works particularly well for those patients. Breast Cancer Res. 2004; 6: R372-374.
46. Retsky M, Demicheli R and Hrushesky W. Breast cancer screening: controversies and future directions. Curr. Opin. Obstet. Gynecol. 2003; 15: 1-8.
47. Ross SM. Introduction to Probability Models, 6th ed. Academic Press, San Diego, 1997.
48. Schell MC, Bova FJ, Larson DA, Leavitt DD, Lutz WR, Podgorsak EB and Wu A. TG-42 Report on stereotactic external beam irradiation. AAPM Report No. 54, Stereotactic Radiosurgery, 1995.
49. Schulz W and Borchard F. Größe der Lebermetastasen bei geringer Metastasenzahl. Eine quantitative Studie an postmortalen Lebern. Fortschr. Röntgenstr. 1992; 156: 320-324.
50. Schulz W and Hort W. The distribution of metastases in the liver. Virchows Arch. Pathol. Anat. 1981; 394: 89-96.
51. Shah AC, Benos D, Gillespie GY and Markert JM. Oncolytic viruses: clinical applications as vectors for the treatment of malignant gliomas. J. Neurooncol. 2003; 65: 203-226.
52. Shen Y and Nemunaitis J. Herpes simplex virus 1 (HSV-1) for cancer treatment. Cancer Gene Ther. 2006; 13: 975-992.
53. Smolle J, Soyer HP, Smolle-Juttner FM, Rieger E and Kerl H. Does surgical removal of primary melanoma trigger growth of occult metastases? An analytical epidemiological approach. Dermatol. Surg. 1997; 23: 1043-1046.
54. Sugio K, Kase S, Sakada T, Yamazaki K, Yamaguchi M, Ondo K, et al. Micrometastasis in the bone marrow of patients with lung cancer associated with reduced expression of E-cadherin and beta-catenin: risk assessment by immunohistochemistry. Surgery 2002; 131: S226-231.
55. Thorne SH, Negrin RS and Contag CH. Synergistic antitumor effects of immune cell-viral biotherapy. Science 2006; 311: 1780-1784.
56. Yakovlev AY and Polig E. A diversity of responses displayed by a stochastic model of radiation carcinogenesis allowing for cell death. Math. Biosci. 1996; 132: 1-33.
57. Yamanati H, Chiba R, Kobari M, Matsuno S and Takahashi T. Total number and size distribution of hepatic metastases of carcinoma. Anal. Quant. Cytol. Histol. 1999; 21: 216-226.
58. Yorke ED, Fuks Z, Norton L, Whitmore W and Ling CC. Modeling the development of metastases from primary and locally recurrent tumors: comparison with a clinical data base for prostatic cancer. Cancer Res. 1993; 53: 2987-2993.
59. Zorin AV, Hanin LG, Edler L and Yakovlev AY. Estimating the natural history of breast cancer from bivariate data on age and tumor size at diagnosis. In:Quantitative Methods for Cancer and Human Health Risk Assessment. Edler L and Kitsos CP (eds.) John Wiley & Sons, Chichester, 2005, pp. 317-327.