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

Sandip Banerjee

International Journal of Applied Mathematics and Computer Science (2008)

  • Volume: 18, Issue: 3, page 389-398
  • ISSN: 1641-876X

Abstract

top
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.

How to cite

top

Sandip Banerjee. "Immunotherapy with interleukin-2: A study based on mathematical modeling." International Journal of Applied Mathematics and Computer Science 18.3 (2008): 389-398. <http://eudml.org/doc/207894>.

@article{SandipBanerjee2008,
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.},
author = {Sandip Banerjee},
journal = {International Journal of Applied Mathematics and Computer Science},
keywords = {effector cells; tumor cells; interleukin-2; discrete time delay},
language = {eng},
number = {3},
pages = {389-398},
title = {Immunotherapy with interleukin-2: A study based on mathematical modeling},
url = {http://eudml.org/doc/207894},
volume = {18},
year = {2008},
}

TY - JOUR
AU - Sandip Banerjee
TI - Immunotherapy with interleukin-2: A study based on mathematical modeling
JO - International Journal of Applied Mathematics and Computer Science
PY - 2008
VL - 18
IS - 3
SP - 389
EP - 398
AB - 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.
LA - eng
KW - effector cells; tumor cells; interleukin-2; discrete time delay
UR - http://eudml.org/doc/207894
ER -

References

top
  1. Adam J. and N. Bellomo E. (1997). A Survey Models for TumorImmune System Dynamics, Birkhäuser, Boston, MA. 
  2. Banerjee S. and Sarkar R. R. (2008). Delay induced model for tumor-immune interaction and control of malignant tumor growth, Biosciences 91(1): 268-288. 
  3. 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. Zbl0947.92015
  4. 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. Zbl1007.34067
  5. Bodnar M. and Foryś U. (2003a). Time delays in proliferation process for solid avascular tumor, Mathematical and Computer Modeling 37(11): 1201-1209. Zbl1046.92026
  6. Bodnar M. and Foryś U. (2003b). Time delays in regulatory apoptosis for solid avascular tumor, Mathematical and Computer Modeling 37(11): 1211-1220. Zbl1047.92025
  7. Byrne H. M. (1997). The effect of time delays on the dynamics of avascular tumor growth, Mathematical Biosciences 144(2): 83-117. Zbl0904.92023
  8. 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 Immunotherapy 19(4): 296-308. 
  9. Foryś U. (2002). Marchuk's model of immune system dynamics with application to tumor growth, Journal of Theoretical Medicine 4(1): 85-93. Zbl1059.92031
  10. 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. Zbl0592.92024
  11. 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. Zbl0535.92024
  12. 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. Zbl1035.92019
  13. 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. 
  14. Hale J. and Lunel S. (1993). Introduction to Functional Differential Equations, Springer-Verlag, New York, NY. Zbl0787.34002
  15. 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. 
  16. 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. 
  17. 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. 
  18. Kirschner D. and Panetta J. C. (1998). Modeling immunotherapy of the tumor-immune interaction, Journal of Mathematical Biology 37(3): 235-252. Zbl0902.92012
  19. Kolev M. (2003). Mathematical modeling of the competition between acquired immunity and cancer, International Journal of Applied Mathematics and Computer Science 13(3): 289-296. Zbl1035.92021
  20. 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 Biology 56(2): 295-321. Zbl0789.92019
  21. 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. Zbl1061.92038
  22. 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. 
  23. 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. 
  24. 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. 
  25. 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. 
  26. Sarkar R. R. and Banerjee S. (2005). Cancer self remission and tumor stability - A stochastic approach, Mathematical Biosciences 196(1): 65-81. Zbl1071.92017
  27. 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. 
  28. 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. Zbl1035.92023
  29. 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. 
  30. 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. Zbl0873.34061
  31. 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. Zbl1035.92024

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.