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Optimal controls for a mathematical model of tumorimmune interactions under targeted chemotherapy with immune boost
A mathematical model for the immunotherapeutic control of the Th1/Th2 imbalance in melanoma
1.  10 Hate'ena St., P.O.B. 282, Bene Ataroth 60991, Israel, Israel, Israel 
References:
[1] 
J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma,, J. Clin. Oncol., 26 (2008), 3445. 
[2] 
G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape,, Nat. Immunol., 3 (2002), 991. 
[3] 
W. H. Fridman, F. Pages, C. SautesFridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome,, Nat. Rev. Cancer, 12 (2012), 298. 
[4] 
A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumourinduced immune modulation of sentinel lymph nodes,, Nat. Rev. Immunol., 6(9) (2006), 659. 
[5] 
L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response,, Neoplasma, 49 (2002), 159. 
[6] 
R. BotellaEstrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma,, Eur. Cytokine Netw., 16 (2005), 47. 
[7] 
W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2driven chronic inflammation in patients with metastatic melanoma,, Clin. Cancer Res., 15 (2009), 1931. 
[8] 
W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin10 in patients with metastatic malignant melanoma,, Melanoma Res., 5 (1995), 67. 
[9] 
A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma,, Melanoma Res., 11 (2001), 401. 
[10] 
R. BotellaEstrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes,, Melanoma Res., 15 (2005), 99. 
[11] 
J. H. Lee, H. TorisuItakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanomainduced cytokinemediated immunosuppression in melanoma sentinel nodes,, Clin. Cancer Res., 11 (2005), 107. 
[12] 
T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. MuellerBerghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Diseaseassociated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE6 in HLADRB10401+ patients with renal cell carcinoma or melanoma,, J. Experimental Medicine, 196 (2002), 619. 
[13] 
D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumorspecific Thelper 2 cells in tumorinfiltrating lymphocytes from a patient with metastatic melanoma,, Int. J. Cancer, 58 (1994), 317. 
[14] 
G. Trinchieri, Interleukin12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigenspecific adaptive immunity,, Annu. Rev. Immunol., 13 (1995), 251. 
[15] 
M. P. Colombo and G. Trinchieri, Interleukin12 in antitumor immunity and immunotherapy,, Cytokine Growth Factor Rev., 13 (2002), 155. 
[16] 
G. Trinchieri, Interleukin12 and the regulation of innate resistance and adaptive immunity,, Nat. Rev. Immunol., 3 (2003), 133. 
[17] 
M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin12: biological properties and clinical application,, Clin. Cancer Res., 13 (2007), 4677. 
[18] 
M. A. Cheever, Twelve immunotherapy drugs that could cure cancers,, Immunol. Rev., 222 (2008), 357. 
[19] 
Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology,, Future Oncol., 6 (2010), 917. 
[20] 
R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of nonspatial mathematical models,, Bull. Math. Biol., 73 (2011), 2. doi: 10.1007/s1153801095263. 
[21] 
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumorimmune interaction,, J. Math. Biol., 37 (1998), 235. 
[22] 
F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy,, Math. Biosci., 163 (2000), 159. doi: 10.1016/S00255564(99)000589. 
[23] 
L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations,, J. Theor. Biol., 238 (2006), 841. doi: 10.1016/j.jtbi.2005.06.037. 
[24] 
A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin21: Potential treatment strategies evaluated in a mathematical model,, Cancer Res, 66 (2006), 7293. 
[25] 
A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin21 immunotherapeutic strategies,, J. Theor. Biol., 248 (2007), 259. doi: 10.1016/j.jtbi.2007.05.015. 
[26] 
M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin21 regimens validated prospectively for mouse solid cancers,, PLoS Comput. Biol., 7 (2011). 
[27] 
N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics,, Cancer Immunol. Immunother., 57 (2008), 425. 
[28] 
N. Kronik, Y. Kogan, M. Elishmereni, K. HaleviTobias, S. VukPavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models,, PLoS One, 5 (2010). 
[29] 
Y. Kogan, K. HaleviTobias, M. Elishmereni, S. VukPavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided realtime personalization,, Cancer Res., 72 (2012), 2218. 
[30] 
E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanismbased mathematical model for treatment strategy improvement and therapy individualization,, PLoS One, 6 (2011). 
[31] 
Z. Agur and S. VukPavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials,, Mol. Ther., 20 (2012), 1. 
[32] 
F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control,, J. Theor. Biol., 247 (2007), 723. doi: 10.1016/j.jtbi.2007.04.003. 
[33] 
L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cellmediated immune response to tumor growth,, Cancer Res., 65 (2005), 7950. 
[34] 
M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation,, J. Theor. Biol., 170 (1994), 25. 
[35] 
M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy,, Bull. Math. Biol., 58 (1996), 1099. 
[36] 
M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and crossregulation,, Bull. Math. Biol., 61 (1999), 403. 
[37] 
A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokinemodulated regulation of helper T cell populations,, J. Theor. Biol., 206 (2000), 539. 
[38] 
C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made,, Bull. Math. Biol., 63 (2001), 405. 
[39] 
A. Yates, R. Callard and J. Stark, Combining cytokine signalling with Tbet and GATA3 regulation in Th1 and Th2 differentiation: a model for cellular decisionmaking,, J. Theor. Biol., 231 (2004), 181. doi: 10.1016/j.jtbi.2004.06.013. 
[40] 
R. E. Callard, Decisionmaking by the immune response,, Immunol. Cell Biol., 85 (2007), 300. 
[41] 
F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1Th2Treg interactions,, J. Theor. Biol., 269 (2011), 70. 
[42] 
M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy,, Cancer Immunol. Immunother., 60 (2011), 433. 
[43] 
J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of singledose interleukin12 exposure on interleukin12associated toxicity and interferongamma production,, Blood, 90 (1997), 2541. 
[44] 
J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL12based cytokine combinations,, Expert Opin. Biol. Ther., 7 (2007), 1705. 
show all references
References:
[1] 
J. M. Kirkwood, A. A. Tarhini, M. C. Panelli, S. J. Moschos, H. M. Zarour, L. H. Butterfield and H. J. Gogas, Next generation of immunotherapy for melanoma,, J. Clin. Oncol., 26 (2008), 3445. 
[2] 
G. P. Dunn, A. T. Bruce, H. Ikeda, L. J. Old and R. D. Schreiber, Cancer immunoediting: From immunosurveillance to tumor escape,, Nat. Immunol., 3 (2002), 991. 
[3] 
W. H. Fridman, F. Pages, C. SautesFridman and J. Galon, The immune contexture in human tumours: impact on clinical outcome,, Nat. Rev. Cancer, 12 (2012), 298. 
[4] 
A. J. Cochran, R. R. Huang, J. Lee, E. Itakura, S. P. L. Leong and R. Essner, Tumourinduced immune modulation of sentinel lymph nodes,, Nat. Rev. Immunol., 6(9) (2006), 659. 
[5] 
L. Lauerova, L. Dusek, M. Simickova, I. Kocak, M. Vagundova, J. Zaloudik and J. Kovarik, Malignant melanoma associates with Th1/Th2 imbalance that coincides with disease progression and immunotherapy response,, Neoplasma, 49 (2002), 159. 
[6] 
R. BotellaEstrada, M. Escudero, J. E. O'Connor, E. Nagore, B. Fenollosa, O. Sanmartin, C. Requena and C. Guillen, Cytokine production by peripheral lymphocytes in melanoma,, Eur. Cytokine Netw., 16 (2005), 47. 
[7] 
W. K. Nevala, C. M. Vachon, A. A. Leontovich, C. G. Scott, M. A. Thompson and S. N. Markovic, Evidence of systemic Th2driven chronic inflammation in patients with metastatic melanoma,, Clin. Cancer Res., 15 (2009), 1931. 
[8] 
W. Dummer, J. C. Becker, A. Schwaaf, M. Leverkus, T. Moll and E. B. Brocker, Elevated serum levels of interleukin10 in patients with metastatic malignant melanoma,, Melanoma Res., 5 (1995), 67. 
[9] 
A. M. Lana, D. R. Wen and A. J.Cochran, The morphology, immunophenotype and distribution of paracortical dendritic leucocytes in lymph nodes regional to cutaneous melanoma,, Melanoma Res., 11 (2001), 401. 
[10] 
R. BotellaEstrada, F. Dasi, D. Ramos, E. Nagore, M. J. Herrero, J. Gimenez, C. Fuster, O. Sanmartin, C. Guillen and S. Alino, Cytokine expression and dendritic cell density in melanoma sentinel nodes,, Melanoma Res., 15 (2005), 99. 
[11] 
J. H. Lee, H. TorisuItakara, A. J. Cochran, A. Kadison, Y. Huynh, D. L. Morton and R. Essner, Quantitative analysis of melanomainduced cytokinemediated immunosuppression in melanoma sentinel nodes,, Clin. Cancer Res., 11 (2005), 107. 
[12] 
T. Tatsumi, L. S. Kierstead, E. Ranieri, L. Gesualdo, F. P. Schena, J. H. Finke, R. M. Bukowski, J. MuellerBerghaus, J. M. Kirkwood, W. W. Kwok and W. J. Storkus, Diseaseassociated bias in T helper type 1 (Th1)/Th2 CD4+ T cell responses against MAGE6 in HLADRB10401+ patients with renal cell carcinoma or melanoma,, J. Experimental Medicine, 196 (2002), 619. 
[13] 
D. D. Kharkevitch, D. Seito, G. C. Balch, T. Maeda, C. M. Balch and K. Itoh, Characterization of autologous tumorspecific Thelper 2 cells in tumorinfiltrating lymphocytes from a patient with metastatic melanoma,, Int. J. Cancer, 58 (1994), 317. 
[14] 
G. Trinchieri, Interleukin12: A proinflammatory cytokine with immunoregulatory functions that bridge innate resistance and antigenspecific adaptive immunity,, Annu. Rev. Immunol., 13 (1995), 251. 
[15] 
M. P. Colombo and G. Trinchieri, Interleukin12 in antitumor immunity and immunotherapy,, Cytokine Growth Factor Rev., 13 (2002), 155. 
[16] 
G. Trinchieri, Interleukin12 and the regulation of innate resistance and adaptive immunity,, Nat. Rev. Immunol., 3 (2003), 133. 
[17] 
M. Del Vecchio, E. Bajetta, S. Canova, M. T. Lotze, A. Wesa, G. Parmiani and A. Anichini, Interleukin12: biological properties and clinical application,, Clin. Cancer Res., 13 (2007), 4677. 
[18] 
M. A. Cheever, Twelve immunotherapy drugs that could cure cancers,, Immunol. Rev., 222 (2008), 357. 
[19] 
Z. Agur, From the evolution of toxin resistance to virtual clinical trials: The role of mathematical models in oncology,, Future Oncol., 6 (2010), 917. 
[20] 
R. Eftimie, J. L. Bramson and D. J. Earn, Interactions between the immune system and cancer: A brief review of nonspatial mathematical models,, Bull. Math. Biol., 73 (2011), 2. doi: 10.1007/s1153801095263. 
[21] 
D. Kirschner and J. C. Panetta, Modeling immunotherapy of the tumorimmune interaction,, J. Math. Biol., 37 (1998), 235. 
[22] 
F. Nani and H. I. Freedman, A mathematical model of cancer treatment by immunotherapy,, Math. Biosci., 163 (2000), 159. doi: 10.1016/S00255564(99)000589. 
[23] 
L. G. de Pillis, W. Gu and A. E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: Modeling, applications and biological interpretations,, J. Theor. Biol., 238 (2006), 841. doi: 10.1016/j.jtbi.2005.06.037. 
[24] 
A. Cappuccio, M. Elishmereni and Z. Agur, Cancer immunotherapy by interleukin21: Potential treatment strategies evaluated in a mathematical model,, Cancer Res, 66 (2006), 7293. 
[25] 
A. Cappuccio, M. Elishmereni and Z. Agur, Optimization of interleukin21 immunotherapeutic strategies,, J. Theor. Biol., 248 (2007), 259. doi: 10.1016/j.jtbi.2007.05.015. 
[26] 
M. Elishmereni, Y. Kheifetz, H. Sondergaard, R. V. Overgaard and Z. Agur, An integrated disease/pharmacokinetic/pharmacodynamic model suggests improved interleukin21 regimens validated prospectively for mouse solid cancers,, PLoS Comput. Biol., 7 (2011). 
[27] 
N. Kronik, Y. Kogan, V. Vainstein and Z. Agur, Improving alloreactive CTL immunotherapy for malignant gliomas using a simulation model of their interactive dynamics,, Cancer Immunol. Immunother., 57 (2008), 425. 
[28] 
N. Kronik, Y. Kogan, M. Elishmereni, K. HaleviTobias, S. VukPavlovic and Z. Agur, Predicting outcomes of prostate cancer immunotherapy by personalized mathematical models,, PLoS One, 5 (2010). 
[29] 
Y. Kogan, K. HaleviTobias, M. Elishmereni, S. VukPavlovic and Z. Agur, Reconsidering the paradigm of cancer immunotherapy by computationally aided realtime personalization,, Cancer Res., 72 (2012), 2218. 
[30] 
E. Jager, V. H. van der Velden, J. G. te Marvelde, R. B. Walter, Z. Agur and V. Vainstein, Targeted drug delivery by gemtuzumab ozogamicin: mechanismbased mathematical model for treatment strategy improvement and therapy individualization,, PLoS One, 6 (2011). 
[31] 
Z. Agur and S. VukPavlovic, Mathematical modeling in immunotherapy of cancer: Personalizing clinical trials,, Mol. Ther., 20 (2012), 1. 
[32] 
F. Castiglione and B. Piccoli, Cancer immunotherapy, mathematical modeling and optimal control,, J. Theor. Biol., 247 (2007), 723. doi: 10.1016/j.jtbi.2007.04.003. 
[33] 
L. G. de Pillis, A. E. Radunskaya and C. L. Wiseman, A validated mathematical model of cellmediated immune response to tumor growth,, Cancer Res., 65 (2005), 7950. 
[34] 
M. A. Fishman and A. S. Perelson, Th1/Th2 cross regulation,, J. Theor. Biol., 170 (1994), 25. 
[35] 
M. A. Fishman and L. A. Segel, Modeling immunotherapy for allergy,, Bull. Math. Biol., 58 (1996), 1099. 
[36] 
M. A. Fishman and A. S. Perelson, Th1/Th2 differentiation and crossregulation,, Bull. Math. Biol., 61 (1999), 403. 
[37] 
A. Yates, C. Bergmann, J. L. Van Hemmen, J. Stark and R. Callard, Cytokinemodulated regulation of helper T cell populations,, J. Theor. Biol., 206 (2000), 539. 
[38] 
C. Bergmann, J. L. Van Hemmen and L. A.Segel, Th1 or Th2: How an appropriate T helper response can be made,, Bull. Math. Biol., 63 (2001), 405. 
[39] 
A. Yates, R. Callard and J. Stark, Combining cytokine signalling with Tbet and GATA3 regulation in Th1 and Th2 differentiation: a model for cellular decisionmaking,, J. Theor. Biol., 231 (2004), 181. doi: 10.1016/j.jtbi.2004.06.013. 
[40] 
R. E. Callard, Decisionmaking by the immune response,, Immunol. Cell Biol., 85 (2007), 300. 
[41] 
F. Gross, G. Metzner and U. Behn, Mathematical modeling of allergy and specific immunotherapy: Th1Th2Treg interactions,, J. Theor. Biol., 269 (2011), 70. 
[42] 
M. L. Disis, Immunologic biomarkers as correlates of clinical response to cancer immunotherapy,, Cancer Immunol. Immunother., 60 (2011), 433. 
[43] 
J. P. Leonard, M. L. Sherman, G. L. Fisher, L. J. Buchanan, G. Larsen, M. B. Atkins, J. A. Sosman, J. P. Dutcher, N. J. Vogelzang and J. L. Ryan, Effects of singledose interleukin12 exposure on interleukin12associated toxicity and interferongamma production,, Blood, 90 (1997), 2541. 
[44] 
J. M. Weiss, J. J. Subleski, J. M. Wigginton, R. H. Wiltrout, Immunotherapy of cancer by IL12based cytokine combinations,, Expert Opin. Biol. Ther., 7 (2007), 1705. 
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