A Recommendation to Oncologists for Cancer Treatment by Immunotherapy: Quantitative and Qualitative Analysis

Authors: Mandana Kariminejad, Ali Ghaffari

Abstract:

Today, the treatment of cancer, in a relatively short period, with minimum adverse effects is a great concern for oncologists. In this paper, based on a recently used mathematical model for cancer, a guideline has been proposed for the amount and duration of drug doses for cancer treatment by immunotherapy. Dynamically speaking, the mathematical ordinary differential equation (ODE) model of cancer has different equilibrium points; one of them is unstable, which is called the no tumor equilibrium point. In this paper, based on the number of tumor cells an intelligent soft computing controller (a combination of fuzzy logic controller and genetic algorithm), decides regarding the amount and duration of drug doses, to eliminate the tumor cells and stabilize the unstable point in a relatively short time. Two different immunotherapy approaches; active and adoptive, have been studied and presented. It is shown that the rate of decay of tumor cells is faster and the doses of drug are lower in comparison with the result of some other literatures. It is also shown that the period of treatment and the doses of drug in adoptive immunotherapy are significantly less than the active method. A recommendation to oncologists has also been presented.

Keywords: Tumor, immunotherapy, fuzzy controller, Genetic algorithm, mathematical model.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.3607743

References:

[1] Araujo, R.P. and McElwain, D.S., 2004. A history of the study of solid tumour growth: the contribution of mathematical modelling. Bulletin of mathematical biology, 66(5), pp.1039-1091.
[2] Enderling, H., Chaplain, M.A., Anderson, A.R. and Vaidya, J.S., 2007. A mathematical model of breast cancer development, local treatment and recurrence. Journal of theoretical biology, 246(2), pp.245- 259.
[3] Sachs, R.K., Hlatky, L.R. and Hahnfeldt, P., 2001. Simple ODE models of tumor growth and anti- angiogenic or radiation treatment. Mathematical and Computer Modelling, 33(12-13), pp.1297-1305.
[4] Anderson, A.R., Chaplain, M.A., Newman, E.L., Steele, R.J. and Thompson, A.M., 2000. Mathematical modelling of tumour invasion and metastasis. Computational and Mathematical Methods in Medicine, 2(2), pp.129-154.
[5] Swanson, K.R., Bridge, C., Murray, J.D. and Alvord, E.C., 2003. Virtual and real brain tumors: using mathematical modeling to quantify glioma growth and invasion. Journal of the neurological sciences, 216(1), pp.1-10.
[6] Szymańska, Z., 2003. Analysis of immunotherapy models in the context of cancer dynamics. International Journal of Applied Mathematics and Computer Science, 13(3), pp.407-418.
[7] O'Byrne, K.J., Dalgleish, A.G., Browning, M.J., Steward, W.P. and Harris, A.L., 2000. The relationship between angiogenesis and the immune response in carcinogenesis and the progression of malignant disease. European journal of cancer, 36(2), pp.151-169.
[8] Stewart, T.H., 1996. Immune Mechanisms and Tumor Dormancy. Revista Medicina, 56(1), p.
[9] Restifo, N.P., Dudley, M.E. and Rosenberg, S.A., 2012. Adoptive immunotherapy for cancer: harnessing the T cell response. Nature Reviews Immunology, 12(4), p.269.
[10] de Pillis, L.G., Gu, W. and Radunskaya, A.E., 2006. Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. Journal of theoretical biology, 238(4), pp.841-862.
[11] Pena-Reyes, C.A. and Sipper, M., 1999. A fuzzy-genetic approach to breast cancer diagnosis. Artificial intelligence in medicine, 17(2), pp.131-155.
[12] Swierniak, A., Kimmel, M. and Smieja, J., 2009. Mathematical modeling as a tool for planning anticancer therapy. European journal of pharmacology, 625(1-3), pp.108-121.
[13] Itik, M., Salamci, M.U. and Banks, S.P., 2010. SDRE optimal control of drug administration in cancer treatment. Turkish Journal of Electrical Engineering & Computer Sciences, 18(5), pp.715- 730.
[14] Burden, T.N., Ernstberger, J. and Fister, K.R., 2004. Optimal control applied to immunotherapy. Discrete and Continuous Dynamical Systems Series B, 4(1), pp.135-146.
[15] Ghaffari, A. and Naserifar, N., 2010. Optimal therapeutic protocols in cancer immunotherapy. Computers in biology and medicine, 40(3), pp.261-270.
[16] Vignard, V., Lemercier, B., Lim, A., Pandolfino, M.C., Guilloux, Y., Khammari, A., Rabu, C., Echasserieau, K., Lang, F., Gougeon, M.L. and Dreno, B., 2005. Adoptive transfer of tumor- reactive Melan-Aspecific CTL clones in melanoma patients is followed by increased frequencies of additional Melan-A-specific T cells. The Journal of Immunology, 175(7), pp.4797-4805.