Assessment of cancer immunotherapy outcome in terms of the immune response time features

Mathematical Medicine and Biology

Volumn 25, Issue 1, 2008, Pages 287-300

  Rodriguez Perez D ^a   Sotolongo Grau, Oscar ^a   Riquelme, Ramón Espinosa ^a   Sotolongo Costa, Oscar ^b   Antonio Santos Miranda, J ^c   Antoranz, J C ^a,b  

^a UNIVERSIDAD NACIONAL DE EDUCACIÓN A DISTANCIA   (Spain)

^b UNIVERSITY OF HAVANA   (Cuba)

^c HOSPITAL GENERAL UNIVERSITARIO GREGORIO MARAÑÓN   (Spain)

Author keywords

Delay differential equations; Immunodepression; Immunotherapy; Tumour growth

Indexed keywords

DIFFERENTIAL EQUATIONS; TUMORS;

ADVERSE EFFECT; CANCER IMMUNOTHERAPY; CYTOKINES; DELAY DIFFERENTIAL EQUATIONS; IMMUNE RESPONSE; IMMUNODEPRESSION; IMMUNOTHERAPY; META-STABLE STATE; TIME FEATURES; TUMOR GROWTH;

IMMUNE SYSTEM;

EID: 77950363817     PISSN: 14778599     EISSN: 14778602     Source Type: Journal    
DOI: None     Document Type: Article

References (32)

1. ASACHENKOV, A. L., MARCHUK, G. I., MOHLER, R. R. & ZUEV, S. M. (1994) Immunology and disease control: a systems approach. IEEE Trans. Biomed. Eng., 41, 943-953.
2. BEGG, A. & STEEL, G. G. (1977) Cell Proliferation and Growth Rate. Oxford.
3. BERETTA, E. & KUANG, Y. (2002) Geometric stability switch criteria in delay differential systems with delay dependent parameters. SIAM J. Math. Anal., 33, 1144-1165.
4. BERMAN, B., PEREZ, O. A. & ZELL, D. (2006) Immunological strategies to fight skin cancer. Skin Therapy Lett., 11.
5. BRASSARD, D. L., GRACE, M. J. & BORDENS, R. W. (2002) Interferon-alpha as an immunotherapeutic protein. J. Leukoc. Biol., 71, 565-581.
6. BYRNE, H. M. (1997) The effect of time delays on the dynamics of avascular tumor growth. Math. Biosci., 144, 83-117.
7. CROSS, D. & BURMESTER, J. K. (2006) Gene therapy for cancer treatment: past, present and future. Clin. Med. Res., 4, 218-227.
8. DE BOER, R., HOGEWEG, P. & DULLENS, H. (1985) Macrophage T lymphocyte interactions in the anti-tumor immune response: a mathematical model. J. Immunol., 134, 2748-2758.
9. DE PILLIS, L., RADUNSKAYA, A. E. & WISEMAN, C. L. (2005) A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res., 65, 7950-7958.
10. DEZFOULI, S., HATZINISIRIOU, I. & RALPH, S. (2005) Use of cytokines in cancer vaccines/immunotherapy: recent developments improve survival rates for patients with metastatic malignancy. Curr. Pharm. Des., 11, 3511-3530.
11. D'ONOFRIO, A. (2005) A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D, 208, 220-235.
12. DRIVER, R. D. (1977) Ordinary and Delay Differential Equations. New York: Springer.
13. FORYS, U. (2002) Marchuk's model of immune system dynamics with application to tumor growth. J. Theor. Med., 4, 85-93.
14. FORYS, U. & BODNAR, M. (2003) Time delays in proliferation process for solid avascular tumor. Math. Comput. Model., 37, 1201-1209.
15. GALACH, M. (2003) Dynamics of the tumor-immune system competition: the effect of time delay. Int. J. Appl. Math. Comput. Sci., 13, 395-406.
16. GOPALSAMY, K. (1992) Stability and Oscillations in Delay Differential Equations of Populations Dynamics. Dordrecht, The Nederlands: Kluwer Academic Publishers.
17. GREENSPAN, H. P. (1972) Models for the growth of a solid tumour by diffusion. Stud. Appl. Math., 52, 317-340.
18. HALE, J. (1977) Introduction to Functional Differential Equations, vol. 99. New York: Springer.
19. HORTON, H. M., ANDERSON, D., HERNANDEZ, P., BARNHART, K. M., NORMAN, J. A. & PARKER, S. E. (1999) A gene therapy for cancer using intramuscular injection of plasmid DNA encoding interferon alpha. Proc. Natl. Acad. Sci. USA, 96, 1553-1558.
20. KIRSCHNER, D. & PANETTA, J. (1998) Modelling immunotherapy of the tumor-immune system interaction. J. Math. Biol., 38, 235-252.
21. KUZNETSOV, V. A., MAKALKIN, I., TAYLOR, M. A. & PERELSON, A. S. (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56, 295-321.
22. LIU, Y., HUANG, H., SAXENA, A. & XIANG, J. (2002) Intratumoral coinjection of two adenoviral vectors expressing functional interleukin-18 and inducible protein-10, respectively, synergizes to facilitate regression of established tumors. Cancer Gene Therapy, 9, 533-542.
23. MARCHUK, G. (1997) Mathematical Modelling of Immune Response in Infectious Diseases. Dordrecht, The Nederlands: Kluwer Academic Publishers.
24. NANI, F. & FREEDMAN, H. I. (2000) A mathematical model of cancer treatment by inmunotherapy. Math. Biosci., 163, 159-199.
25. SALEH, F., RENNO, W., KLEPACEK, I., IBRAHIM, G., ASFAR, S., DASHTI, H., ROMERO, P., DASHTI, A. & BEHBEHANI, A. (2005) Melanoma immunotherapy: past, present and future. Curr. Pharm. Des., 11, 3459-3460.
26. SCHUSTER, M., NECHANSKY, A., LOIBNER, H. & KIRCHEIS, R. (2006) Cancer immunotherapy. Biotechnol. J., 1, 138-147.
27. SOTOLONGO-COSTA, O., MORALES MOLINA, L., RODRÍGUEZ-PÉREZ, D., ANTORANZ, J. & CHACÓN REYES, M. (2003) Behavior of tumors under nonstationary therapy. Physica D, 178, 242-253.
28. STEEL, G. G. (ed.) (1993) Basic Clinical Radiobiology for Radiation Oncologists. London: Edward Arnold Publishers.
29. SZYMANSKA, Z. (2003) Analysis of immunotherapy models in the context of cancer dynamics. Int. J. Appl. Math. Comput. Sci., 13, 407-418.
30. TORTORA, G. & GRABOWSKI, S. (1999) Principles of Anatomy and Physiology. New York: John Wiley.
31. VILLASANA, M. & RADUNSKAYA, A. (2003) A delay differential equation model for tumor growth. J. Math. Biol., 47, 270-294.
32. WHITESIDE, T. L. (2002) Apoptosis of immune cells in the tumor microenvironment and peripheral circulation of patients with cancer: implications for immunotherapy. Vaccine, 20, A46-A51