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2008 | 18 | 3 | 389-398
Tytuł artykułu

Immunotherapy with interleukin-2: A study based on mathematical modeling

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The role of interleukin-2 (IL-2) in tumor dynamics is illustrated through mathematical modeling, using delay differential equations with a discrete time delay (a modified version of the Kirshner-Panetta model). Theoretical analysis gives an expression for the discrete time delay and the length of the time delay to preserve stability. Numerical analysis shows that interleukin-2 alone can cause the tumor cell population to regress.
Rocznik
Tom
18
Numer
3
Strony
389-398
Opis fizyczny
Daty
wydano
2008
otrzymano
2007-08-03
poprawiono
2008-02-22
Twórcy
  • Indian Institute of Technology and Science Rooorkee (IITR), Roorkee 247667, Uttarakhand, India
Bibliografia
  • Adam J. and N. Bellomo E. (1997). A Survey Models for TumorImmune System Dynamics, Birkhäuser, Boston, MA.
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  • Bodnar M. and Foryś U. (2000a). Behaviour of solutions to Marchuk's model depending on a time delay, International Journal of Applied Mathematics and Computer Science 10(1): 97-112.
  • Bodnar M. and Foryś U. (2000b). Periodic dynamics in the model of immune system, International Journal of Applied Mathematics and Computer Science 10(1): 113-126.
  • Bodnar M. and Foryś U. (2003a). Time delays in proliferation process for solid avascular tumor, Mathematical and Computer Modeling 37(11): 1201-1209.
  • Bodnar M. and Foryś U. (2003b). Time delays in regulatory apoptosis for solid avascular tumor, Mathematical and Computer Modeling 37(11): 1211-1220.
  • Byrne H. M. (1997). The effect of time delays on the dynamics of avascular tumor growth, Mathematical Biosciences 144(2): 83-117.
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  • Foryś U. (2002). Marchuk's model of immune system dynamics with application to tumor growth, Journal of Theoretical Medicine 4(1): 85-93.
  • Freedman H. I., Erbe L. and Rao V. S. H. (1986). Three species food chain models with mutual interference and time delays, Mathematical Biosciences 80(1): 57-80.
  • Freedman H. I. and Rao V. S. H. (1983). The trade-off between mutual interference and time lags in predator-prey systems, Bulletin of Mathematical Biology 45(6): 991-1004.
  • Galach M. (2003). Dynamics of the tumor-immune system competition-the effect of time delay, International Journal of Applied Mathematics and Computer Science 13(3): 395-406.
  • Gause B. L., Sznol M., Kopp W. C., Janik J. E., II J. W. S., Steis R. G., Urba W. J., Sharfman W., Fenton R. G., Creekmore S. P., Holmlund J., Conlon K. C., VanderMolen L. A. and Longo, D. L. (1996). Phase i study of subcutaneously administered interleuking-2 in combination with interferon alfa-2a in patients with advanced cancer, Journal of Clinical Oncology 14(8): 2234-2241.
  • Hale J. and Lunel S. (1993). Introduction to Functional Differential Equations, Springer-Verlag, New York, NY.
  • Hara I., Hotta H., Sato N., Eto H., Arakawa S. and Kamidono S. (1996). Rejection of mouse renal cell carcinoma elicited by local secretion of interleukin-2, Japanese Journal of Cancer Research 87(7): 724-729.
  • Kaempfer R., Gerez L., Farbstein H., Madar L., Hirschman O., Nussinovich R. and Shapiro A. (1996). Prediction of response to treatment in superficial bladder carcinoma through pattern of interleukin-2 gene expression, Journal of Clinical Oncology 14(6): 1778-1786.
  • Keilholz U., Scheibenbogen C., Stoelben E., Saeger H. D. and Hunstein W. (1994). Immunotherapy of metastatic melanoma with interferon-alpha and interleukin-2: Pattern of progression in responders and patients with stable disease with or without resection of residual lesions, European Journal of Cancer 30A(7): 955-958.
  • Kirschner D. and Panetta J. C. (1998). Modeling immunotherapy of the tumor-immune interaction, Journal of Mathematical Biology 37(3): 235-252.
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  • Matzavinos A., A.J.Chaplain M. and Kuznetsov V. A. (2004). Mathematical modelling of the spatio-temporal response of cytotoxic t-lymphocytes to a solid tumor, Mathematical Medicine and Biology 21(1): 1-34.
  • Rabinowich H., Banks M., Reichert T. E., Logan T. F., Kirkwood J. M. and Whiteside T. L. (1996). Expression and activity of signaling molecules in t-lymphocytes obtained from patients with metastatic melanoma before and after interleukin-2 therapy, Clinical Cancer Research 2(8): 1263-1274.
  • Rosenberg S. A. and Lotze M. T. (1986). Cancer immunotherapy using interleukin-2 and interleukin-2-activated lymphocytes, Annual Review of Immunology 4(1): 681-709.
  • Rosenberg S. A., Yang J. C., Topalian S. L., Schwartzentruber D. J., Weber J. S., Parkinson D. R., Seipp C. A., Einhorn J. H. and White D. E. (1994). Treatment of 283 consecutive patients with metastatic melanoma or renal cell cancer using high-dose bolus interleukin 2, Journal of the American Medical Association 271(12): 907-913.
  • Rosenstein M., Ettinghousen S. E. and Rosenberg S. A. (1986). Extravasion of intravascular fluid mediated by the systemic administration of recombinant interleukin-2, Journal of Immunology 137(5): 1735-1742.
  • Sarkar R. R. and Banerjee S. (2005). Cancer self remission and tumor stability - A stochastic approach, Mathematical Biosciences 196(1): 65-81.
  • Schwartzentruber D. J. (1993). In vitro predictors of clinical response in patients receiving interleukin-2-based immunotherapy, Current Opinion in Oncology 5(6): 1055-1058.
  • Szymańska Z. (2003). Analysis of immunotherapy models in the context of cancer dynamics, International Journal of Applied Mathematics and Computer Science 13(3): 407-418.
  • Tartour E., Blay J. Y., Dorval T., Escudier B., Mosseri V., Douillard J. Y., Deneux L., Gorin I., Negrier S., Mathio C., Pouillart P. and Fridman W. H. (1996). Predictors of clinical response to interleukin-2-based immunotherapy in melanoma patients: A French multi-institutional study, Journal of Clinical Oncology 14(5): 1697-1703.
  • Yang X., Chen L. and Chen J. (1996). Permanence and positive periodic solution for the single-species nonautonomous delay diffusive model, Computers and Mathematics with Applications 32(4): 109-116.
  • Zhivkovc P. and Waniewski J. (2003). Modeling tumorimmunity interactions with different stimulation functions, International Journal of Applied Mathematics and Computer Science 13(3): 307-315.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-amcv18i3p389bwm
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