Optimal Immunotherapy Control of Aggressive Tumors Growth

Elnaz Keikhosoro Kiani, Ali Vahidian Kamyad, Hedayatollah Shirzad

Department of Electrical Engineering, Islamic Azad University, Esfahan, Iran.
Department of Mathematical Sciences, Ferdowsi University, Mashhad, Iran.
Department of Microbiology & Immunology, Shahrekord University of Medical Sciences, Shahrekord, Iran.

DOI: 10.4236/ica.2012.32019                

Abstract

Tumor cells can evade immune surveillance by secreting immuno-suppressive factors such as transforming growth factor-beta (TGF-β) and also, Interlukin-10 (IL-10). In this paper the optimal control of mathematical model for aggressive tumor growth via a new and proper approach known as AVK method has been considered. Moreover, we have implemented a special treatment so-called small interfering RNA (siRNA) to reduce presence and effect of TGF-β in tumor cells and also we have added Interlukin-2 (IL-2) into our treatment model to minimize the population of tumor cells. Further research and experimentation with these combination therapies may provide an effective solution in addressing the immuno-suppressive effects of TGF-β. Finally, we analyze the optimal control and system optimality of these equations using numerical techniques.

Keywords

Aggressive Tumor; Immunotherapy; Optimal Control; AVK Method

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	A. K. Abbas, A. H. Lichtman and J. S. Pober, “Cellular and Molecular Immunology,” Elsevier, Amsterdam, 2007.
[2]	K. E. de Visser and W. M. Kast, “Effects of TGF-β on the Immune System: Implications for Cancer Immunotherapy,” Leukemia, Vol. 13, No. 8, 1999, pp. 1188-1199. doi:10.1038/sj.leu.2401477
[3]	M. A. Nash, G. Ferrandina, M. Gordinier, A. Loercher, and R. S. Freedman, “The Role of Cytokines in both the Normal and Malignant Ovary,” Endocrine-Related Cancer, Vol. 6, No. 1, pp. 93-107.
[4]	D. Kirschner and J. C. Panetta, “Modeling Immunotherapy of the Tumor—Immune Interaction,” Journal of Mathematical Biology, Vol. 37, No. 3, 1998, pp. 235-252. doi:10.1007/s002850050127
[5]	R. R. Sarkar and S. Banerjee, “Cancer self Remission and Tumor Stability: A Stochastic Approach,” Mathematical Biosciences, Vol. 196, No. 1, 2005, pp. 65-81. doi:10.1016/j.mbs.2005.04.001
[6]	B. Joshi, X. Wang, S. Banerjee, H. Tian, A. Matzavinos and M. A. Chaplain, “On Immunotherapies and Cancer Vaccination Protocols: A Mathematical Modelling Approach,” Journal of Theoretical Biology, Vol. 259, No. 4, 2009, pp. 820-827
[7]	S. M. Mousavi1, M. M. Gouya, R. Ramazani, M. Davanlou, N. Hajsadeghi and Z. Seddighi, “Cancer Incidence and Mortality in Iran,” Annals of Oncology, Vol. 20, No. 3, pp. 556-563. doi:10.1093/annonc/mdn642
[8]	J. C. Arciero, T. L. Jackson and D. E. Kirschner, “A Mathematical Model of Tumor-Immune Evasion and siRNA Treatment,” Discrete and Continuous Dynamical Systems, Vol. 4, No. 1, 2004, pp. 39-58. doi:10.3934/dcdsb.2004.4.39
[9]	T. Holen, M. Amarzguioui, M. T. Wiiger, E. Babaie and H. Prydz, “Positional Effects of Short Interfering RNAs Targeting the Human Coagulation Trigger Tissue Factor,” Nucleic Acids Research, Vol. 30, No. 8, 2002, pp. 17571766. doi:10.1093/nar/30.8.1757
[10]	S. M. Elbashir, J. Harborth, W. Lendeckel, A. Yalcin, K. Weber and T. Tuschl, “Duplexes of 21-Nucleotide RNAs Mediate RNA Interference in Cultured Mammalian Cells,” Nature, Vol. 411, No. 6836, 2001, pp. 494-49. doi:10.1038/35078107
[11]	F. Wianny and M. Zernicka-Goetz, “Specific Interference with Gene Function by Doublestranded RNA in Early Mouse Development,” Nature Cell Biology, Vol. 2, No. 2, 2000, pp. 70-75. doi:10.1038/35000016
[12]	K. P. Badakhshan, A. V. Kamyad and A. Azemi, “Using AVK Method to Solve Nonlinear Problems with Uncertain Parameters,” Applied Mathematics and Computation, Vol. 189, No. 1, 2007, pp. 27-34. doi:10.1016/j.amc.2006.11.172