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2013 | OriginalPaper | Buchkapitel

A Mathematical Model of Gene Therapy for the Treatment of Cancer

verfasst von : Alexei Tsygvintsev, Simeone Marino, Denise E. Kirschner

Erschienen in: Mathematical Methods and Models in Biomedicine

Verlag: Springer New York

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Abstract

Cancer is a major cause of death worldwide, resulting from the uncontrolled growth of abnormal cells in the body. Cells are the body’s building blocks, and cancer starts from normal cells. Normal cells divide to grow in order to maintain cell population equilibrium, balancing cell death. Cancer occurs when unbounded growth of cells in the body happens fast. It can also occur when cells lose their ability to die. There are many different kinds of cancers, which can develop in almost any organ or tissue, such as lung, colon, breast, skin, bones, or nerve tissue. There are many known causes of cancers that have been documented to date including exposure to chemicals, drinking excess alcohol, excessive sunlight exposure, and genetic differences, to name a few [38]. However, the cause of many cancers still remains unknown. The most common cause of cancer-related death is lung cancer. Some cancers are more common in certain parts of the world. For example, in Japan, there are many cases of stomach cancer, but in the USA, this type of cancer is pretty rare [49]. Differences in diet may play a role. Another hypothesis is that these different populations could have different genetic backgrounds predisposing them to cancer. Some cancers also prey on individuals who are either missing or have altered genes as compared to the mainstream population. Unfortunately, treatment of cancer is still in its infancy, although there are some successes when the cancer is detected early enough. To begin to address these important issues, in this work we will focus solely on genetic issues related to cancer so that we can explore a new treatment area known as gene therapy as a viable approach to treatment of cancer.

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Literatur
1.
Zurück zum Zitat Adam, J.A., Bellomo, N.: A Survey of Models for tumor-immune system dynamics, Birkhauser Series on Modeling and Simulation in Science, Engineering and Technology. Birkhauser, Boston (1997) Adam, J.A., Bellomo, N.: A Survey of Models for tumor-immune system dynamics, Birkhauser Series on Modeling and Simulation in Science, Engineering and Technology. Birkhauser, Boston (1997)
2.
Zurück zum Zitat Aguda, B.D., Kim, Y., Piper-Hunter, M.G., Friedman, A., Marsh, C.: MicroRNA regulation of a cancer network: Consequences of the feedback loops involving miR-17-92, E2F and Myc. Proc. Natl. Acad. Sci. USA 105, 19678–19683 (2008)CrossRef Aguda, B.D., Kim, Y., Piper-Hunter, M.G., Friedman, A., Marsh, C.: MicroRNA regulation of a cancer network: Consequences of the feedback loops involving miR-17-92, E2F and Myc. Proc. Natl. Acad. Sci. USA 105, 19678–19683 (2008)CrossRef
3.
Zurück zum Zitat Ambrosi, D., Bellomo, N., Preziosi, L.: Modelling tumor progression, heterogeneity, and immune competition. J. Theor. Med. 4, 51–65 (2002)MATHCrossRef Ambrosi, D., Bellomo, N., Preziosi, L.: Modelling tumor progression, heterogeneity, and immune competition. J. Theor. Med. 4, 51–65 (2002)MATHCrossRef
4.
Zurück zum Zitat Andasari, V., Gerisch, A., Lolas, G., South, A.P., Chaplain, M.A.: Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation. J. Math. Biol. 63(1), 141–71 (2011)MathSciNetMATHCrossRef Andasari, V., Gerisch, A., Lolas, G., South, A.P., Chaplain, M.A.: Mathematical modeling of cancer cell invasion of tissue: Biological insight from mathematical analysis and computational simulation. J. Math. Biol. 63(1), 141–71 (2011)MathSciNetMATHCrossRef
5.
Zurück zum Zitat Arciero, J., Jackson, T., Kirschner, D.: A mathematical model of tumor- immune evasion and siRNA treatment. Discrete Continuous Dyn. Syst. Ser. B 4, 39–58 (2004)MathSciNetMATH Arciero, J., Jackson, T., Kirschner, D.: A mathematical model of tumor- immune evasion and siRNA treatment. Discrete Continuous Dyn. Syst. Ser. B 4, 39–58 (2004)MathSciNetMATH
6.
Zurück zum Zitat Arlotti, L., Gamba, A., Lachowicz, M.: A kinetic model of tumor/immune system cellular interactions. J. Theor. Med. 4, 39–50 (2002)MATHCrossRef Arlotti, L., Gamba, A., Lachowicz, M.: A kinetic model of tumor/immune system cellular interactions. J. Theor. Med. 4, 39–50 (2002)MATHCrossRef
7.
Zurück zum Zitat Banerjee, S., Immunotherapy with Interleukin–2: A Study Based on Mathematical Modeling, Int. J. Appl. Math. Comput. Sci. 18(3), 389–398 (2008)MATHCrossRef Banerjee, S., Immunotherapy with Interleukin–2: A Study Based on Mathematical Modeling, Int. J. Appl. Math. Comput. Sci. 18(3), 389–398 (2008)MATHCrossRef
8.
Zurück zum Zitat Bellomo, N., Delitala, M.: From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Phys. Life Rev. 5, 183–206 (2008)CrossRef Bellomo, N., Delitala, M.: From the mathematical kinetic, and stochastic game theory to modelling mutations, onset, progression and immune competition of cancer cells. Phys. Life Rev. 5, 183–206 (2008)CrossRef
9.
Zurück zum Zitat Bellomo, N., Preziosi, L.: Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comput. Model. 32, 413–452 (2000)MathSciNetMATHCrossRef Bellomo, N., Preziosi, L.: Modelling and mathematical problems related to tumor evolution and its interaction with the immune system. Math. Comput. Model. 32, 413–452 (2000)MathSciNetMATHCrossRef
10.
Zurück zum Zitat Bellomo, N., Bellouquid, A., Delitala, M.: Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Math. Models Methods Appl. Sci. 14, 1683–1733 (2004)MathSciNetMATHCrossRef Bellomo, N., Bellouquid, A., Delitala, M.: Mathematical topics on the modelling complex multicellular systems and tumor immune cells competition. Math. Models Methods Appl. Sci. 14, 1683–1733 (2004)MathSciNetMATHCrossRef
11.
Zurück zum Zitat Bodnar, M., Forys, U.: Three types of simple DDEs describing tumor growth. J. Biol. Syst. 15, 453–471 (2007)MATHCrossRef Bodnar, M., Forys, U.: Three types of simple DDEs describing tumor growth. J. Biol. Syst. 15, 453–471 (2007)MATHCrossRef
12.
Zurück zum Zitat Burden, T., Ernstberger, J., Fister, K.R.: Optimal control applied to immunotherapy. Discrete Continuous Dyn. syst. 4, 135–146 (2004)MathSciNetMATH Burden, T., Ernstberger, J., Fister, K.R.: Optimal control applied to immunotherapy. Discrete Continuous Dyn. syst. 4, 135–146 (2004)MathSciNetMATH
13.
Zurück zum Zitat Caravagna, G., D’Onofrio, A., Milazzo, P., Barbuti, R.: Tumour suppression by immune system through stochastic oscillations. J. theor. biol. 265(3), 336–345 (2010)CrossRef Caravagna, G., D’Onofrio, A., Milazzo, P., Barbuti, R.: Tumour suppression by immune system through stochastic oscillations. J. theor. biol. 265(3), 336–345 (2010)CrossRef
14.
Zurück zum Zitat Chang, Z., Song, J., Gao, G., Shen, Z.: Adenovirus-mediated p53 gene therapy reverses resistance of breast cancer cells to adriamycin. Anticancer Drugs 22(6), 556–62 (2011)CrossRef Chang, Z., Song, J., Gao, G., Shen, Z.: Adenovirus-mediated p53 gene therapy reverses resistance of breast cancer cells to adriamycin. Anticancer Drugs 22(6), 556–62 (2011)CrossRef
15.
Zurück zum Zitat Chaplain, M., Matzavinos, A.: Mathematical modelling of spatio-temporal phenomena in tumour immunology. In: Friedman, A. (ed.) Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer. Lecture Notes in Mathematics, vol. 1872, pp. 131–183. Springer, Berlin (2006) Chaplain, M., Matzavinos, A.: Mathematical modelling of spatio-temporal phenomena in tumour immunology. In: Friedman, A. (ed.) Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer. Lecture Notes in Mathematics, vol. 1872, pp. 131–183. Springer, Berlin (2006)
16.
Zurück zum Zitat De Angelis, E., Delitala, M., Marasco, A., Romano, A.: Bifurcation analysis for a mean field modelling of tumor and immune system competition. Math. Comput. Model. 37, 1131–1142 (2003)MATHCrossRef De Angelis, E., Delitala, M., Marasco, A., Romano, A.: Bifurcation analysis for a mean field modelling of tumor and immune system competition. Math. Comput. Model. 37, 1131–1142 (2003)MATHCrossRef
17.
Zurück zum Zitat Delitala, M.: Critical analysis and perspectives on kinetic (cellular) theory of immune competition. Math. Comput. Model. 35, 63–75 (2002)MathSciNetMATHCrossRef Delitala, M.: Critical analysis and perspectives on kinetic (cellular) theory of immune competition. Math. Comput. Model. 35, 63–75 (2002)MathSciNetMATHCrossRef
18.
Zurück zum Zitat de Pillis, L., Gu, W., Radunskaya, A.: Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations. J. Theor. Biol. 238, 841–862 (2006)CrossRef de Pillis, L., Gu, W., Radunskaya, A.: Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations. J. Theor. Biol. 238, 841–862 (2006)CrossRef
19.
Zurück zum Zitat D’Onofrio, A.: The role of the proliferation rate of effectors in the tumor-immune system competition. Math. Model. Meth. Appl. Sci. 16(8), 1375–1401 (2006)MathSciNetMATHCrossRef D’Onofrio, A.: The role of the proliferation rate of effectors in the tumor-immune system competition. Math. Model. Meth. Appl. Sci. 16(8), 1375–1401 (2006)MathSciNetMATHCrossRef
20.
Zurück zum Zitat d’Onofrio, A., Gatti, F., Cerrai, P., Freschi, L.: Delay-induced oscillatory dynamics of tumour–immune system interaction. Math. Comput. Model. 51, 572–591 (2010) d’Onofrio, A., Gatti, F., Cerrai, P., Freschi, L.: Delay-induced oscillatory dynamics of tumour–immune system interaction. Math. Comput. Model. 51, 572–591 (2010)
21.
Zurück zum Zitat Forys, U.: Marchuks model of immune system dynamics with application to tumour growth. J. Theor. Med. 4, 85–93 (2002)MATHCrossRef Forys, U.: Marchuks model of immune system dynamics with application to tumour growth. J. Theor. Med. 4, 85–93 (2002)MATHCrossRef
22.
Zurück zum Zitat Friedman, A., Kim, Y.: Tumor cells proliferation and migration under the influence of their microenvironment. Math. Biosci. Eng. 8(2), 371–83 (2011)MathSciNetCrossRef Friedman, A., Kim, Y.: Tumor cells proliferation and migration under the influence of their microenvironment. Math. Biosci. Eng. 8(2), 371–83 (2011)MathSciNetCrossRef
23.
Zurück zum Zitat Gabhann, F.M., Annex, B.H., Popel, A.S.: Gene therapy from the perspective of systems biology. Curr. Opin. Mol. Ther. 12(5), 570–577 (2010) Gabhann, F.M., Annex, B.H., Popel, A.S.: Gene therapy from the perspective of systems biology. Curr. Opin. Mol. Ther. 12(5), 570–577 (2010)
24.
Zurück zum Zitat Gatenby, R.A., Maini, P.: Modelling a new angle on understanding cancer. Nature 420(6915), 462 (2002)CrossRef Gatenby, R.A., Maini, P.: Modelling a new angle on understanding cancer. Nature 420(6915), 462 (2002)CrossRef
25.
Zurück zum Zitat Gatenby, R.A., Maini, P.K.: Mathematical oncology: Cancer summed up. Nature 421(6921), 321 (2003)CrossRef Gatenby, R.A., Maini, P.K.: Mathematical oncology: Cancer summed up. Nature 421(6921), 321 (2003)CrossRef
26.
Zurück zum Zitat Joshi, B., Wang, X., Banerjee, S., Tian, H., Matzavinos, A., Chaplain, M.A.: On immunotherapies and cancer vaccination protocols: A mathemati cal modelling approach. J. Theor. Biol. 259(4), 820–827 (2009)CrossRef Joshi, B., Wang, X., Banerjee, S., Tian, H., Matzavinos, A., Chaplain, M.A.: On immunotherapies and cancer vaccination protocols: A mathemati cal modelling approach. J. Theor. Biol. 259(4), 820–827 (2009)CrossRef
27.
Zurück zum Zitat Kelly, C., Leek, R., Byrne, H., Cox, S., Harris, A., Lewis, C.: Modelling macrophage infiltration into avascular tumours. J. Theor. Med. 4, 21–38 (2002)MATHCrossRef Kelly, C., Leek, R., Byrne, H., Cox, S., Harris, A., Lewis, C.: Modelling macrophage infiltration into avascular tumours. J. Theor. Med. 4, 21–38 (2002)MATHCrossRef
28.
Zurück zum Zitat Kirschner, D., Panetta, J.: Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol. 37, 235–252 (1998)MATHCrossRef Kirschner, D., Panetta, J.: Modeling immunotherapy of the tumor-immune interaction, J. Math. Biol. 37, 235–252 (1998)MATHCrossRef
29.
Zurück zum Zitat Kirschner, D., Tsygvintsev, A.: On the global dynamics of a model for tumor immunotherapy. J. Math. Biosci. Eng. Vol. 6(3), 573–583 (2009)MathSciNetMATHCrossRef Kirschner, D., Tsygvintsev, A.: On the global dynamics of a model for tumor immunotherapy. J. Math. Biosci. Eng. Vol. 6(3), 573–583 (2009)MathSciNetMATHCrossRef
30.
Zurück zum Zitat Kronik, N., Kogan, Y., Vainstein, V., Agur, Z.: Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics. Cancer Immunol. Immunother. 57, 425–439 (2008)CrossRef Kronik, N., Kogan, Y., Vainstein, V., Agur, Z.: Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics. Cancer Immunol. Immunother. 57, 425–439 (2008)CrossRef
31.
Zurück zum Zitat Kuznetsov, V., Makalkyn, I., Taylor, M., Perelson, A.: Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull. Math.Biol. 56(2), 295–321 (1994)MATH Kuznetsov, V., Makalkyn, I., Taylor, M., Perelson, A.: Nonlinear dynamics of immunogenic tumors: Parameter estimation and global bifurcation analysis, Bull. Math.Biol. 56(2), 295–321 (1994)MATH
32.
Zurück zum Zitat Macklin, P., McDougall, S., Anderson, A.R., Chaplain, M.A., Cristini, V., Lowengrub, J.: Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol. 58(4–5), 765–98 (2009)MathSciNetCrossRef Macklin, P., McDougall, S., Anderson, A.R., Chaplain, M.A., Cristini, V., Lowengrub, J.: Multiscale modelling and nonlinear simulation of vascular tumour growth. J. Math. Biol. 58(4–5), 765–98 (2009)MathSciNetCrossRef
33.
Zurück zum Zitat Marino, S., Hogue, I.B., Ray, C.J., Kirschner, D.E.: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254, 178–196 (2008) PMID:18572196CrossRef Marino, S., Hogue, I.B., Ray, C.J., Kirschner, D.E.: A methodology for performing global uncertainty and sensitivity analysis in systems biology. J. Theor. Biol. 254, 178–196 (2008) PMID:18572196CrossRef
34.
Zurück zum Zitat Matzavinos, A., Chaplain, M.: Travelling-wave analysis of a model of the immune response to cancer. C.R. Biol. 327, 995–1008 (2004) Matzavinos, A., Chaplain, M.: Travelling-wave analysis of a model of the immune response to cancer. C.R. Biol. 327, 995–1008 (2004)
35.
Zurück zum Zitat Matzavinos, A., Chaplain, M., Kuznetsov, V.: Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. IMA J. Math. Med. Biol. 21, 1–34 (2004)MATHCrossRef Matzavinos, A., Chaplain, M., Kuznetsov, V.: Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. IMA J. Math. Med. Biol. 21, 1–34 (2004)MATHCrossRef
36.
Zurück zum Zitat McDougall, S.R., Anderson, A.R., Chaplain, M.A.: Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241(3), 564–589 (2006)MathSciNetCrossRef McDougall, S.R., Anderson, A.R., Chaplain, M.A.: Mathematical modelling of dynamic adaptive tumour-induced angiogenesis: Clinical implications and therapeutic targeting strategies. J. Theor. Biol. 241(3), 564–589 (2006)MathSciNetCrossRef
37.
Zurück zum Zitat McKay, M.D., Beckman, R.J., Conover, W.J.: A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)MathSciNetMATH McKay, M.D., Beckman, R.J., Conover, W.J.: A Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)MathSciNetMATH
38.
Zurück zum Zitat Moscow, J.A., Cowan, K.H.: Biology of cancer. In: Goldman, L., Ausiello, D. (eds. Cecil. Med. 23rd edn. Saunders Elsevier, Philadelphia (2007), chap 187 Moscow, J.A., Cowan, K.H.: Biology of cancer. In: Goldman, L., Ausiello, D. (eds. Cecil. Med. 23rd edn. Saunders Elsevier, Philadelphia (2007), chap 187
39.
Zurück zum Zitat Nana-Sinkam, S.P., Croce, C.M.: MicroRNAs as therapeutic targets in cancer. Transl. Res. 157(4), 216–225 (2011)CrossRef Nana-Sinkam, S.P., Croce, C.M.: MicroRNAs as therapeutic targets in cancer. Transl. Res. 157(4), 216–225 (2011)CrossRef
40.
Zurück zum Zitat Owen, M., Sherratt, J.: Mathematical modelling of macrophage dynamics in tumours. Math. Model. Meth. Appl. Sci. 9, 513–539 (1999)MATHCrossRef Owen, M., Sherratt, J.: Mathematical modelling of macrophage dynamics in tumours. Math. Model. Meth. Appl. Sci. 9, 513–539 (1999)MATHCrossRef
41.
Zurück zum Zitat Owen, M.R., Alarcon, T., Maini, P.K., Byrne, H.M.: Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58(4–5), 689–721 (2009)MathSciNetCrossRef Owen, M.R., Alarcon, T., Maini, P.K., Byrne, H.M.: Angiogenesis and vascular remodelling in normal and cancerous tissues. J. Math. Biol. 58(4–5), 689–721 (2009)MathSciNetCrossRef
42.
Zurück zum Zitat Rabinowich, H., Banks, M., Reichert, T.E., Logan, T.F., Kirkwood, J.M., Whiteside, T.L.: Expression and activity of signaling molecules n T lymphocytes obtained from patients with metastatic melanoma before and after interleukin 2 therapy. Clin. Canc. Res. 2, 1263–1274 (1996) Rabinowich, H., Banks, M., Reichert, T.E., Logan, T.F., Kirkwood, J.M., Whiteside, T.L.: Expression and activity of signaling molecules n T lymphocytes obtained from patients with metastatic melanoma before and after interleukin 2 therapy. Clin. Canc. Res. 2, 1263–1274 (1996)
43.
Zurück zum Zitat Robbins, P.F., Morgan, R.A., Feldman, S.A., Yang, J.C., Sherry, R.M., Dudley, M.E., Wunderlich, J.R., Nahvi, A.V., Helman, L.J., Mackall, C.L., Kammula, U.S., Hughes, M.S., Restifo, N.P., Raffeld, M., Lee, C.-C.R., Levy, C.L., Li, Y.F., El-Gamil, M., Schwarz, S.L., Laurencot, C., Rosenberg, S.A.: Tumor regression in patients with metastatic synovial cell sarcoma and melanoma using genetically engineered lymphocytes reactive with NY-ESO-1. J. Clin. Oncol. 29, 917–924 (2011)CrossRef Robbins, P.F., Morgan, R.A., Feldman, S.A., Yang, J.C., Sherry, R.M., Dudley, M.E., Wunderlich, J.R., Nahvi, A.V., Helman, L.J., Mackall, C.L., Kammula, U.S., Hughes, M.S., Restifo, N.P., Raffeld, M., Lee, C.-C.R., Levy, C.L., Li, Y.F., El-Gamil, M., Schwarz, S.L., Laurencot, C., Rosenberg, S.A.: Tumor regression in patients with metastatic synovial cell sarcoma and melanoma using genetically engineered lymphocytes reactive with NY-ESO-1. J. Clin. Oncol. 29, 917–924 (2011)CrossRef
44.
Zurück zum Zitat Rosenberg, S.A., Lotze, M.T.: Cancer immunotherapy using interleukin-2 and interleukin- 2-activated lymphocytes. Ann. Rev. Immunol. 4, 681–709 (1986)CrossRef Rosenberg, S.A., Lotze, M.T.: Cancer immunotherapy using interleukin-2 and interleukin- 2-activated lymphocytes. Ann. Rev. Immunol. 4, 681–709 (1986)CrossRef
45.
Zurück zum Zitat Rosenberg, S.A., Yang, J.C., Topalian, S.L., Schwartzentruber, D.J., Weber, J.S., Parkinson, D.R., Seipp, C.A., Einhorn, J.H., White, D.E.: Treatment of 283 consecutive patients with metastatic melanoma or renal cell cancer using high-dose bolus interleukin 2. JAMA 271, 907–913 (1994)CrossRef Rosenberg, S.A., Yang, J.C., Topalian, S.L., Schwartzentruber, D.J., Weber, J.S., Parkinson, D.R., Seipp, C.A., Einhorn, J.H., White, D.E.: Treatment of 283 consecutive patients with metastatic melanoma or renal cell cancer using high-dose bolus interleukin 2. JAMA 271, 907–913 (1994)CrossRef
46.
Zurück zum Zitat Rosenstein, M., Ettinghousen, S.E., Rosenberg, S.A.: Extravasion of intravascular uid mediated by the systemic administration of recombinant interleukin 2. J. Immunol. 137, 1735–1742 (1986) Rosenstein, M., Ettinghousen, S.E., Rosenberg, S.A.: Extravasion of intravascular uid mediated by the systemic administration of recombinant interleukin 2. J. Immunol. 137, 1735–1742 (1986)
47.
Zurück zum Zitat Sherratt, J., Perumpanani, A., Owen, M.: Pattern formation in cancer. In: Chaplain, M., Singh, G., McLachlan, J. (eds.) On Growth and Form: Spatio- temporal Pattern Formation in Biology. Wiley, New York (1999) Sherratt, J., Perumpanani, A., Owen, M.: Pattern formation in cancer. In: Chaplain, M., Singh, G., McLachlan, J. (eds.) On Growth and Form: Spatio- temporal Pattern Formation in Biology. Wiley, New York (1999)
48.
Zurück zum Zitat Szymanska, Z. (2003). Analysis of immunotherapy models in the context of cancer dynamics. Appl. Math. Comput. Sci. 13, 407–418.MathSciNetMATH Szymanska, Z. (2003). Analysis of immunotherapy models in the context of cancer dynamics. Appl. Math. Comput. Sci. 13, 407–418.MathSciNetMATH
49.
Zurück zum Zitat Thun, M.J.: Biology of cancer. In: Goldman L, Ausiello D (eds.) Cecil. Med. 23rd edn. Saunders Elsevier, Philadelphia, Pa (2007), chap 185 Thun, M.J.: Biology of cancer. In: Goldman L, Ausiello D (eds.) Cecil. Med. 23rd edn. Saunders Elsevier, Philadelphia, Pa (2007), chap 185
50.
Zurück zum Zitat Tran, K.Q., Zhou, J., Durflinger, K.H., et al.: Mini- mally cultured tumor-infiltrating lymphocytes display optimal characteristics for adoptive cell therapy. J. Immunother. 31, 742–751 (2008)CrossRef Tran, K.Q., Zhou, J., Durflinger, K.H., et al.: Mini- mally cultured tumor-infiltrating lymphocytes display optimal characteristics for adoptive cell therapy. J. Immunother. 31, 742–751 (2008)CrossRef
51.
Zurück zum Zitat Webb, S., Sherratt, J., Fish, R.: Cells behaving badly: A theoretical model for the Fas/FasL system in tumour immunology. Math. Biosci. 179, 113–129 (2002)MathSciNetMATHCrossRef Webb, S., Sherratt, J., Fish, R.: Cells behaving badly: A theoretical model for the Fas/FasL system in tumour immunology. Math. Biosci. 179, 113–129 (2002)MathSciNetMATHCrossRef
52.
Zurück zum Zitat Wu, F.T., Stefanini, M.O., Mac Gabhann, F., Kontos, C.D., Annex, B.H., Popel, A.S.: A systems biology perspective on sVEGFR1: Its biological function, pathogenic role and therapeutic use. J. Cell Mol. Med. 14(3), 528–52 (2010) Wu, F.T., Stefanini, M.O., Mac Gabhann, F., Kontos, C.D., Annex, B.H., Popel, A.S.: A systems biology perspective on sVEGFR1: Its biological function, pathogenic role and therapeutic use. J. Cell Mol. Med. 14(3), 528–52 (2010)
53.
Zurück zum Zitat Zhao, Y., Lam, D.H., Yang, J., Lin, J., Tham, C.K., Ng, W.H., Wang, S.: Targeted suicide gene therapy for glioma using human embryonic stem cell-derived neural stem cells genetically modified by baculoviral vectors. Gene Therapy 19, 189–200 (2012)CrossRef Zhao, Y., Lam, D.H., Yang, J., Lin, J., Tham, C.K., Ng, W.H., Wang, S.: Targeted suicide gene therapy for glioma using human embryonic stem cell-derived neural stem cells genetically modified by baculoviral vectors. Gene Therapy 19, 189–200 (2012)CrossRef
Metadaten
Titel
A Mathematical Model of Gene Therapy for the Treatment of Cancer
verfasst von
Alexei Tsygvintsev
Simeone Marino
Denise E. Kirschner
Copyright-Jahr
2013
Verlag
Springer New York
DOI
https://doi.org/10.1007/978-1-4614-4178-6_13