A frequency distribution for the number of hematogenous organ metastases

Journal of Theoretical Biology

Volumn 217, Issue 2, 2002, Pages 203-218

  Kendal, Wayne S ^a  

^a OTTAWA REGIONAL CANCER CENTRE   (Canada)

Author keywords

[No Author keywords available]

Indexed keywords

DISEASE;

ARTICLE; BINOMIAL DISTRIBUTION; EXPERIMENTAL MODEL; METASTASIS; MOUSE; NONHUMAN; ORGAN BLOOD FLOW; ORGAN DISTRIBUTION; POISSON DISTRIBUTION; PREDICTION; PRIORITY JOURNAL; PROBABILITY; STOCHASTIC MODEL; THEORETICAL MODEL; VARIANCE;

MURINAE;

EID: 0036384344     PISSN: 00225193     EISSN: None     Source Type: Journal    
DOI: 10.1006/jtbi.2002.3021     Document Type: Article

References (40)

1. BARMAN, S. A., MCCLOUD, L. L., CATRAVASS, J. D. & EHRHART, I. C. (1996). Measurement of pulmonary blood flow by fractal analysis of flow heterogeneity in isolated canine lungs. J. Appl. Physiol. 81, 2039-2045.
2. BASSINGTHWAIGHTE, J. B., KING, R. B. & ROGER, S. A. (1989). Fractal nature of regional myocardial blood flow heterogeneity. Circ. Res. 65, 578-590.
3. BUFFA, F. M., DAVIDSON, S. E., HUNTER, R. D. & WEST, C. M. (2001). Incorporating biologic measurements (SF(2), CFE) into a tumor control probability model increases their prognostic significance: a study in cervical carcinoma treated with radiation therapy. Int. J. Radiat. Oncol. Biol. Phys. 50, 1113-1122.
4. CAMERON, M. D., SCHMIDT, E. E., KERKVLEIT, N., NADKARNI, K. V., MORRIS, V. L., GROOM, A. C., CHAMBERS, A. F. & MACDONALD, I. F. (2000). Temporal progression of metastasis in lung: cell survival, dormancy, and location dependence of metastatic inefficiency. Cancer Res. 60, 2541-2546.
5. CARUTHERS, S. D. & HARRIS, T. R. (1994). Effects of pulmonary blood flow on the fractal nature of flow heterogeneity in sheep lungs. J. Appl. Physiol. 77, 1474-1479.
6. EKBERG, H., TRANBERG, H.-G., ANDERSSON, R., LUNDSTEDt, C., HÄGERSTRAHD, I., RANSTAM, J. & BENGMARK, S. (1986). Determinants of survival in liver resection for colorectal secondaries. Br. J. Surg. 73, 727-731.
7. FIDLER, I. J. (1978). General considerations for studies of experimental cancer metastasis. Methods Cancer Res. 15, 399-439.
8. FIDLER, I. J. & HART, I. J. (1981). The origin of metastatic heterogeneity in tumors. Eur. J. Cancer 17, 487-494.
9. FIDLER, I. J. & KRIPKE, M. L. (1977). Metastasis results form preexisting variant cells within a malignant tumor. Science 197, 893-895.
10. FRIEDEL, G., HÜRTGEN, M., PENZENSTADLER, M., KYRISS, T. & TOOMES, H. (1999). Resection of pulmonary metastases from renal cell carcinoma. Anticancer Res. 19, 1593-1596.
11. GLENNY, R. W., ROBERTSON, H. T., YAMASHIRO, S. & BASSINGTHWAIGHTE, J. B. (1991). Applications of fractal analysis to physiology. J. Appl. Physiol. 70, 2351-2367.
12. HARRIS, J. F., CHAMBERS, A. F., HILL, R. P. & LING, V. (1982). Metastatic variants are generated at a high rate in mouse KHT tumor. Proc. Natl Acad. Sci. U.S.A. 79, 5547-5551.
13. HEYMANN, M. A., PAYNE, B. D., HOFFMAN, J. I. E. & RUDOLF, A. M. (1977). Blood flow measurements with radionuclide-labeled particles. Prog. Cardiovas. Res. 20, 55-79.
14. JØRGENSEN, B. (1997). The Theory of Dispersion Models, pp. 1-7, 71-174, 135-137. London: Chapman & Hall.
15. JØRGENSEN, B., MARTINEZ, J. R. & TSAO, M. (1994). Asymptotic behaviour of the variance function. Scand. J. Statist. 21, 223-243.
16. KENDAL, W. S. (1999). Clustering of murine lung metastases reflects fractal nonuniformity in regional lung blood flow. Invasion Metastasis 18, 285-296.
17. KENDAL, W. S. (2001a). A stochastic model for the self-similar heterogeneity of regional organ blood flow. Proc. Natl Acad. Sci. U.S.A. 98, 837-841.
18. KENDAL, W. S. & FROST, P. (1987). Experimental metastasis: a novel application of the variance-to-mean power function. J. Natl Cancer Inst. 79, 1113-1114.
19. KENDAL, W. S., LAGERWARD, F. J. & AGBOOLA, O. (2000). Characterization of the frequency distribution for human hematogenous metastases: evidence for clustering and a power function. Clin. Exp. Metastasis 18, 219-229.
20. KRIPKE, M. L., GRUYS, E. & FIDLER, I. J. (1978). Metastatic heterogeneity of cells from an ultraviolet light-induced murine fibrosarcoma of recent origin. Cancer Res. 38, 2962-2967.
21. LIOTTA, L. A., SAIDEL, G. M. & KLEINERMAN, J. (1976). Stochastic model of metastasis formation. Biometrics 32, 535-550.
22. LUZZI, K. J., MACDONALD, I. C., SCHMIDT, E. E., KERKVLIET, N., MORRIS, V. L., CHAMBERS, A. F. & GROOM A. C. (1998). Multistep nature of metastatic inefficiency: dormancy of solitary cells after successful extravasation and limited survival of early micrometas-tases. Am. J. Pathol. 153, 865-873
23. NAGLICH, J. C., JURE-KUNKEL, M., GUPTA, E., FARGNOLI, J., HENDERSON, A. J., LEWIN, A. C., TALBOT, R., BAXTER, A., BIRD, J., HENDERSON, A. J., WILLS, R., KRAMER, R. A. & TRAIL, P. A. (2001). Inhibition of angiogenesis and metastasis in two murine models by the matrix metalloproteinase inhibitor, BMS-275291. Cancer Res. 23, 8480-8485.
24. NAUMOV, G. N., WILSON, S. M., MACDONALD, I. C., SCHMIDT, E. E., MORRIS, V. L., GROOM, A. C., HOFFMAN, R. M. & CHAMBERS, A. F. (1999). Cellular expression of green fluorescent protein, coupled with high-resolution in vivo videomicroscopy, to monitor steps in tumor metastasis. J. Cell Sci. 112, 1835-1842.
25. NEAVE, H. R. & WORTHINGTON, P. L. (1988). Distribution Free Tests, pp. 98-99, London: Unwin Hyman Ltd.
26. NICOLSON, G. L. & DULSKI, K. M. (1986). Organ specificity of metastatic tumor colonization is related to organ-selective growth properties of malignant cells. Int. J. Cancer 38, 289-294.
27. NICOLSON, G. L., DULSKI, K. M., BASSON, C. & WELCH, D. R. (1985). Preferential organ attachment and invasion in vitro by B16 melanoma cells selected for differing metastatic colonization and invasive properties. Invasion Metastasis 5, 144-158.
28. POPPER, K. (1965). The Logic of Scientific Discovery. New York: Harper & Collins.
29. RAZ, A. (1982). Regional emergence of metastatic heterogeneity in a growing tumor. Cancer Lett. 17, 153-160.
30. STETLER-STEVENSON, W. G. & KLEINER, D. E. JR (2001). Molecular biology of cancer: invasion and metastasis. In: Cancer Principles & Practice of Oncology, (Devita, V. T., Hellman, S. & Rosenberg, S. A., eds), 6th Edn., pp. 123-136, Philadelphia: Lippincott-Raven Publishers.
31. SURBONE, A., GILEWSKI, T. A. & NORTON, L. (1997). Cytokinetics. In: Cancer Medicine, (Holland, J. F., Blast, R. C., Jr., Morton, D. L., Frei, E. III, Kufe, D. W. & Weichselbaum, R. R. eds), 4th Edn., Vol. 1, pp. 769-798, Baltimore, MD: Williams & Wilkins.
32. THOMAS, G. M. & WILLIAMS S. D. (1997). Testis. In: Principles and Practice of Radiation Oncology, (Perez, C. A. & Brady, L. W. eds), 3rd Edn., pp. 1695-1715, Philadelphia: Lippincott-Raven Publishers.
33. TOKUYAMA, S., MORIYA, S., TANIGUCHI, S., YASUI, A. & MIYAZAKI, J. (1997). Suppression of pulmonary metastasis in murine B16 melanoma cells by transfection of a sialidase cDNA. Int. J. Cancer 73, 410-415.
34. TWEEDIE, M. C. K. (1981). An index which distinguishes between some important exponential families. In: Statistics: Applications and New Directions. Proceedings of the Indian Statistical Institute Golden Jubilee International Conference, (Ghosh, J. K. & Roy, J. eds), pp. 579-604, Calcutta: Indian Statistical Institute.
35. VAN BEEK, J. H. G. M., ROGER, S. A. & BAS-SINGTHWAIGHTE, J. B. (1989). Regional myocardial flow heterogeneity explained with fractal networks. Am J. Physiol. 257, H1670-H1680.
36. WEISS, L., HAYDOCK, B. A., PICKREN, J. W. & LANE, W. W. (1980). Organ vascularity and metastatic frequency. Am. J Pathol. 101, 101-113.
37. WEISS, L., MAYHEW, E., RAPP, D. G. & HOLMES, J. C. (1982). Metastatic inefficiency in mice bearing B16 melanomas. Br. J. Cancer 45, 44-53.
38. WITHERS, H. R. & MCBRIDE, W. H. (1997). Biologic basis of radiation therapy. In: Principles and Practice of Radiation Oncology, (Perez, C. A. & Brady, L. W. eds), 3rd Edn., pp. 97-99, Philadelphia: Lippincott-Raven Publishers.
39. WITHERS, H. R., PETERS, L. J. & TAYLOR, J. M. G. (1995). Dose-response relationship for radiation therapy of subclinical disease. Int. J. Radiat. Oncol. Biol. Phys. 31, 353-359.
40. YU, H. & SCHULTZ, R. M. (1990). Relationship between secreted urokinase plasminogen activator activity and metastatic potential in murine B16 cells transfected with human urokinase sense and antisense genes. Cancer Res. 50, 7623-7633.