Immunotherapy with Interleukin-2: A Study Based on Mathematical Modeling

Sandip Banerjee

doi:10.2478/v10006-008-0035-6

.blurhash-client-img { display: none !important; }

Immunotherapy with Interleukin-2: A Study Based on Mathematical Modeling

International Journal of Applied Mathematics and Computer Science

Volume 18 (2008): Issue 3 (September 2008)

By: Sandip Banerjee

Open Access

|Oct 2008

Abstract

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.

References

Adam J. and N. Bellomo E. (1997). A Survey Models for Tumor-Immune System Dynamics, Birkhäuser, Boston, MA.10.1007/978-0-8176-8119-7
Search in Google Scholar
Banerjee S. and Sarkar R. R. (2008). Delay induced model for tumor-immune interaction and control of malignant tumor growth, Biosciences91(1): 268-288.10.1016/j.biosystems.2007.10.002
Search in Google Scholar
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 Science10(1): 97-112.
Search in Google Scholar
Bodnar M. and Foryś U. (2000b). Periodic dynamics in the model of immune system, International Journal of Applied Mathematics and Computer Science10(1): 113-126.10.4064/am-27-1-113-126
Search in Google Scholar
Bodnar M. and Foryś U. (2003a). Time delays in proliferation process for solid avascular tumor, Mathematical and Computer Modeling37(11): 1201-1209.10.1016/S0895-7177(03)80019-5
Search in Google Scholar
Bodnar M. and Foryś U. (2003b). Time delays in regulatory apoptosis for solid avascular tumor, Mathematical and Computer Modeling37(11): 1211-1220.10.1016/S0895-7177(03)00131-6
Search in Google Scholar
Byrne H. M. (1997). The effect of time delays on the dynamics of avascular tumor growth, Mathematical Biosciences144(2): 83-117.10.1016/S0025-5564(97)00023-0
Search in Google Scholar
Curti B. D., Ochoa A. C., Urba W. J., Alvord W. G., Kopp W. C., Powers G., Hawk C., Creekmore S. P., Gause B. L., Janik J. E., Holmlund J. T., Kremers P., Fenton R. G., Miller L., Sznol M., II J. W. S., Sharfman W. H. and Longo D. L. (1996). Influence of interleukin-2 regimens on circulating populations of lymphocytes after adoptive transfer of anticd3-stimulated t cells: Results from a phase i trial in cancer patients, Journal of Immunotherapy19(4): 296-308.10.1097/00002371-199607000-00005
Search in Google Scholar
Foryś U. (2002). Marchuk's model of immune system dynamics with application to tumor growth, Journal of Theoretical Medicine4(1): 85-93.10.1080/10273660290052151
Search in Google Scholar
Freedman H. I., Erbe L. and Rao V. S. H. (1986). Three species food chain models with mutual interference and time delays, Mathematical Biosciences80(1): 57-80.10.1016/0025-5564(86)90067-2
Search in Google Scholar
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 Biology45(6): 991-1004.10.1016/S0092-8240(83)80073-1
Search in Google Scholar
Galach M. (2003). Dynamics of the tumor-immune system competition-the effect of time delay, International Journal of Applied Mathematics and Computer Science13(3): 395-406.
Search in Google Scholar
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 Oncology14(8): 2234-2241.10.1200/JCO.1996.14.8.2234
Search in Google Scholar
Hale J. and Lunel S. (1993). Introduction to Functional Differential Equations, Springer-Verlag, New York, NY.10.1007/978-1-4612-4342-7
Search in Google Scholar
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 Research87(7): 724-729.10.1111/j.1349-7006.1996.tb00284.x
Search in Google Scholar
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 Oncology14(6): 1778-1786.10.1200/JCO.1996.14.6.1778
Search in Google Scholar
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 Cancer30A(7): 955-958.10.1016/0959-8049(94)90122-8
Search in Google Scholar
Kirschner D. and Panetta J. C. (1998). Modeling immunotherapy of the tumor — immune interaction, Journal of Mathematical Biology37(3): 235-252.10.1007/s002850050127
Search in Google Scholar
Kolev M. (2003). Mathematical modeling of the competition between acquired immunity and cancer, International Journal of Applied Mathematics and Computer Science13(3): 289-296.
Search in Google Scholar
Kuznetsov V. A., Makalkin I. A., Taylor M. A. and Perelson A. S. (1994). Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis, Bulletin of Mathematical Biology56(2): 295-321.10.1016/S0092-8240(05)80260-5
Search in Google Scholar
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 Biology21(1): 1-34.10.1093/imammb/21.1.115065736
Search in Google Scholar
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 Research2(8): 1263-1274.
Search in Google Scholar
Rosenberg S. A. and Lotze M. T. (1986). Cancer immunotherapy using interleukin-2 and interleukin-2-activated lymphocytes, Annual Review of Immunology4(1): 681-709.10.1146/annurev.iy.04.040186.0033413518753
Search in Google Scholar
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 Association271(12): 907-913.10.1001/jama.271.12.907
Search in Google Scholar
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 Immunology137(5): 1735-1742.10.4049/jimmunol.137.5.1735
Search in Google Scholar
Sarkar R. R. and Banerjee S. (2005). Cancer self remission and tumor stability — A stochastic approach, Mathematical Biosciences196(1): 65-81.10.1016/j.mbs.2005.04.001
Search in Google Scholar
Schwartzentruber D. J. (1993). In vitro predictors of clinical response in patients receiving interleukin-2-based immunotherapy, Current Opinion in Oncology5(6): 1055-1058.10.1097/00001622-199311000-00018
Search in Google Scholar
Szymańska Z. (2003). Analysis of immunotherapy models in the context of cancer dynamics, International Journal of Applied Mathematics and Computer Science13(3): 407-418.
Search in Google Scholar
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 Oncology14(5): 1697-1703.10.1200/JCO.1996.14.5.1697
Search in Google Scholar
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 Applications32(4): 109-116.10.1016/0898-1221(96)00129-0
Search in Google Scholar
Zhivkovc P. and Waniewski J. (2003). Modeling tumor-immunity interactions with different stimulation functions, International Journal of Applied Mathematics and Computer Science13(3): 307-315.
Search in Google Scholar