On a kinetic (cellular) theory for competition between tumors and the host immune system

Journal of Biological Systems

Volumn 4, Issue 4, 1996, Pages 479-502

  Bellomo, N ^a   Preziosi, L ^a   Forni, G ^b  

^a POLITECNICO DI TORINO   (Italy)

^b UNIVERSITY OF TURIN   (Italy)

Author keywords

Cellular theory; Immune system; Kinetic models; Tumor growth modelling

Indexed keywords

EID: 0001692786     PISSN: 02183390     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218339096000326     Document Type: Article

References (42)

1. Abundo M. and Rossi C., Numerical simulation of a stochastic model for cancerous cells submitted to chemiotherapy, J. Math. Biol. 27 (1989) pp. 81-90.
2. Adam J., Diffusion models of prevascular and vascular tumor growth -A review, in Mathematical Population Dynamics, ed. by Arino O. et al (Dekker, 1991).
3. Adam J. and Noren R., Equilibrium model of a vascularized spherical carcinoma with central necrosis - Some properties of the solution, Math. Biosci. 33 (1993) pp. 735-745.
4. Albert A., Freedman M. and Perelson A. S., Tumors and the immune system: The effects of a tumor growth modulator, Math. Biosci. 50 (1980) pp. 25-58.
5. Arlotti L. and Bellomo N., On a new model of population dynamics with stochastic interaction, Transp. Theory Statist. Phys. 24 (1995) pp. 431-443.
6. Arlotti L. and Lachowicz M., Qualitative analysis of a nonlinear integro-differential equation modelling tumor-host dynamics, Math. Comp. Modelling -Special Issue on Modelling Tumor Immune System Dynamics, ed. by Bellomo N., 23 (1996) pp. 11-30.
7. Bellomo N. ed., Lectures Notes on the Mathematical Theory of the Boltzmann Equation (World Scientific, Singapore, 1995).
8. Bellomo N. and Forni G., Dynamics of tumor interaction with the host immune system, Math. Comp. Modelling 20 (1994) pp. 107-122.
9. Bellomo N. and Preziosi L., Modelling, Mathematical Methods and Scientific Computation (CRC Press, Florida, 1995).
10. Bosco M., Giovarelli M., Forni M., Scarpa S., Masuelli L. and Forni G., Low doses of 11-4 injected perilymphatically in tumor-bearing mice inhibit the growth of poorly and apparently nonimmunogenic tumors and induce a tumor specific immune memory, J. Immunol. 145 (1990) pp. 3136-3143.
11. Cavallo F., Di Pierro F., Giovarelli M., Gulino A., Vacca A., Stoppacciaro A., Forni M., Modesti A. and Forni G., Protective and curative potential of vaccination with Interleukin-2 gene-transfected cells from a spontaneous mouse mammary adenocarcinoma, Cancer Res. 53 (1993) pp. 5067-5070.
12. Chaplain M., Benson D. and Maini P. K., Nonlinear diffusion and growth inhibitory factor in multicell spheroids, Math. Biosci. 121 (1994) pp. 1-13.
13. Chaplain M., A vascular growth, angiogenesis and vascular growth in solid tumors: The mathematical modelling of stages of tumor developments, Math. Comp. Modelling - Special Issue on Modelling Tumor Immune System Dynamics, ed. by Bellomo N., 23 (1996) pp. 47-88.
14. De Boer R. J. and Hogeweg P., Tumor escape from immune elimination: Simplified precursor bound cytotoxicity models, J. Theor. Biol. 113 (1985) pp. 719-736.
15. De Boer R. J. and Hogeweg P., Interactions between macrophages and T-lymphocytes: Tumor sneaking through intrinsic to helper T cell dynamics, J. Theor. Biol. 120 (1986) pp. 331-354.
16. Den Otter W. and Ruitenberg E. J., eds., Tumor Immunology. Mechanisms, Diagnosis, Therapy (Elsevier, Amsterdam, 1987).
17. Forni G. and Comoglio P. M., Growth of syngenetic tumors in unimmunized newborn and adult hosts, Brit. J. Cancer 27 (1973) pp. 120-127.
18. Forni G., Giovarelli M., Santoni A., Modesti A. and Forni M., Interleukin-2 activated tumor inhibition in vivo depends on the systemic involvement of host immunoreactivity, J. Immunol. 138 (1987) pp. 4031-4033.
19. Forni G., Varesio L., Giovarelli M. and Cavallo G., Dynamic state of a spontaneous immune reactivity towards a mammary adenocarcinoma, in Tumor Associate Antigens and Their Specific Immune Response, ed. by Spreafico F. and Arnon R. (Academic Press, California, 1979) pp. 167-192.
20. Giovarelli M., Comoglio P. and Forni G., Induction of resistance or enhancement to a transplantable murine plasmacytoma by transfer of non-immune leukocytes, Brit. J. Cancer 34 (1976) pp. 233-238.
21. Grossman Z. and Berke G., Tumor escape from immune elimination, J. Theor. Biol. 83 (1980) pp. 276-296.
22. Green I., Cohen S. and McCluskey R., eds., Mechanisms of Tumor Immunity (John Wiley & Sons, New York, 1977).
23. Greenspan H., On the growth and stability of cell cultures and solid tumors, J. Theor. Biol. 56 (1976) pp. 229-242.
24. Herberman R. B., NK Cells and Other Natural Effector Cells (Academic Press, California, 1982).
25. Kustnetsov V. A., Dynamics of Immune Processes During Tumor Growth (Nauka, 1992), in Russian.
26. Kustnetsov V. A., Malakin A. M., Taylor M. A. and Perelson A. S., Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull. Math. Biol. 56 (1994) pp. 295-321.
27. Jager E. and Segel L., On the distribution of dominance in a population of interacting anonymous organisms, SIAM J. Appl. Math. 52 (1992) pp. 1442-1468.
28. Lefever R. J., Hiernaux J., Urbain J. and Meyers P., On the kinetics and optimal specificity of cytotoxic reactions mediated by T-lymphocytes clones, Bull. Math. Biol. 54 (1992) pp. 839-873.
29. Maggelakis S. and Adam J., Mathematical model for prevascular growth of a spherical carcinoma, Comp. Math. Modelling 13 (1990) pp. 23-38.
30. Maggelakis S., Type α and type β transforming growth factors as regulators of cancer cellular growth: A mathematical model, Comp. Math. Modelling 18 (1993) pp. 9-16.
31. Markovitch S., The particular role of cell loss in tumor growth, Comp. Math. Modelling 18 (1993) pp. 83-89.
32. Marusic M., Bajzer Z., Freyer J. P. and Vuk-Pavlovic S., Modelling autostimulation of growth in multicellular tumor spheroids, Int. J. Biomed. Comp. 149 (1991) pp. 149-158.
33. Marusic M. and Vuk-Pavlovic S., Prediction power of mathematical models for tumor growth, J. Biol Syst. 1 (1993) pp. 69-78.
34. Perelson A. S. and Bell G. I., Delivery of lethal hits by cytotoxic T lymphocytes in multicellular conjugates occurs sequentially but randomly, J. Immunol. 129 (1982) pp. 2796-2801.
35. Perelson A. S. and MacKean C. A., Kinetics of cell-mediated cytotoxicity: Stochastic and deterministic multistage models, J. Math. Biol. 170 (1984) pp. 161-194.
36. Prehn R. T., Stimulatory effects of immune reactions upon the growth of transplanted tumors, Cancer Res. 55 (1994) pp. 908-914.
37. Nossal G. J. V., Life, death and the immune system, Sci. Amer. 269 (1993) pp. 53-72.
38. Segel L., Modelling Dynamic Phenomena in Molecular and Cellular Biology (Cambridge Univ. Press, 1984).
39. Steel G. G., Growth Kinetics of Tumors (Clarendon, 1977).
40. Stenger F., Numerical Methods Based on Sinc and Analytic Functions (Springer-Verlag, Heidelberg, 1993).
41. Truesdell C. and Muncaster R. G., Fundamentals of Maxwell Kinetic Theory of a Simple Monoatomic Gas (Academic Press, California, 1980).
42. Van der Bruggen P., Traversari C., Chomez P., Lurquin C., De Plaen E.. Van den Eynde B., Knuth A. and Boon T., A gene encoding an antigen recognized by cytolytic T lymphocytes on a human melanoma, Science 254 (1991) pp. 1643-1647.