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Part of the book series: Series in BioEngineering ((SERBIOENG))

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Abstract

Immunotherapy is a treatment strategy that uses external adjuvants to boost our immune system and thus make use of our body’s inherent mechanisms to fight cancer [1]. In this chapter, first some of the components and mechanisms pertaining to tumor dynamics are provided which are significant in facilitating immunotherapy in particular, then five mathematical models are discussed that depict different aspects of cancer dynamics under immunotherapy.

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References

  1. F.D. Barber, Recent developments in oncology immunotherapy, adverse effects Part 2. J. Nurse Pract. 14(4), 259–266 (2018)

    Article  Google Scholar 

  2. M. Robertson Tessi, A. El Kareh, A. Goriely, A mathematical model of tumor-immune interactions. J. Theor. Biol. 294, 56–73 (2012)

    Google Scholar 

  3. K.E. Hellström, I. Hellström, Lymphocyte-mediated cytotoxicity and blocking serum activity to tumor antigens, in Advances in Immunology, vol. 18 (Elsevier, Amsterdam, 1974), pp. 209–277

    Google Scholar 

  4. C.D. Wimmer, M. Rentsch, A. Crispin, W.D. Illner, H. Arbogast, C. Graeb, K.W. Jauch, M. Guba, The janus face of immunosuppression-de novo malignancy after renal transplantation: the experience of the transplantation center Munich. Kidney Int. 71(12), 1271–1278 (2007)

    Article  Google Scholar 

  5. T. Boon, J.C. Cerottini, B. Van den Eynde, P. Van der Bruggen, A. Van Pel, Tumor antigens recognized by T lymphocytes. Annu. Rev. Immunol. 12(1), 337–365 (1994)

    Article  Google Scholar 

  6. G.P. Dunn, C.M. Koebel, R.D. Schreiber, Interferons, immunity and cancer immunoediting. Nat. Rev. Immunol. 6(11), 836–848 (2006)

    Article  Google Scholar 

  7. S.A. Rosenberg, Decade in review-cancer immunotherapy: entering the mainstream of cancer treatment. Nat. Rev. Clin. Oncol. 11(11), 630 (2014)

    Google Scholar 

  8. C.A. Pennell, K. Ellis, Demystifying cancer immunotherapy for lay audiences. Front. Immunol. 10, 2488 (2019)

    Google Scholar 

  9. A. Cappuccio, M. Elishmereni, Z. Agur, Cancer immunotherapy by interleukin-21: potential treatment strategies evaluated in a mathematical model. Cancer Res. 66(14), 7293–7300 (2006)

    Article  Google Scholar 

  10. A. Ghaffari, N. Naserifar, Optimal therapeutic protocols in cancer immunotherapy. Comput. Biol. Med. 40(3), 261–270 (2010)

    Article  Google Scholar 

  11. B. Piccoli, F. Castiglione, Optimal vaccine scheduling in cancer immunotherapy. Phys. A 370(2), 672–680 (2006)

    Article  MATH  Google Scholar 

  12. B. Alberts, A. Johnson, J. Lewis, M. Raff, K. Roberts, P. Walter, Helper T cells and lymphocyte activation, in Molecular Biology of the Cell, 4th edn. (Garland Science, 2002)

    Google Scholar 

  13. A.M. Brandsma, S. Bondza, M. Evers, R. Koutstaal, M. Nederend, J. Jansen, T. Rösner, T. Valerius, J.H. Leusen, T. Ten Broeke, Potent Fc receptor signaling by Iga leads to superior killing of cancer cells by neutrophils compared to IgG. Front. Immunol. 10, 704 (2019)

    Google Scholar 

  14. K.R. Chaudhari, M. Ukawala, A.S. Manjappa, A. Kumar, P.K. Mundada, A.K. Mishra, R. Mathur, J. Mönkkönen, R.S.R. Murthy, Opsonization, biodistribution, cellular uptake and apoptosis study of PEGylated PBCA nanoparticle as potential drug delivery carrier. Pharm. Res. 29(1), 53–68 (2012)

    Article  Google Scholar 

  15. P.G. Sasikumar, M. Ramachandra, Small-molecule immune checkpoint inhibitors targeting PD-1/PD-L1 and other emerging checkpoint pathways. BioDrugs 32(5), 481–497 (2018)

    Article  Google Scholar 

  16. E.P. Juliá, A. Amante, M.B. Pampena, J. Mordoh, E.M. Levy, Avelumab, an IgG1 anti-PD-L1 immune checkpoint inhibitor, triggers NK cell-mediated cytotoxicity and cytokine production against triple negative breast cancer cells. Front. Immunol. 9, 2140 (2018)

    Google Scholar 

  17. T.F. Chen, K.K. Li, E.F. Zhu, C.F. Opel, M.J. Kauke, H. Kim, E. Atolia, K.D. Wittrup, Artificial anti-tumor opsonizing proteins with fibronectin scaffolds engineered for specificity to each of the murine Fc\(\gamma \)R types. J. Mol. Biol. 430(12), 1786–1798 (2018)

    Article  Google Scholar 

  18. I. Faiena, A.L. Cummings, A.M. Crosetti, A.J. Pantuck, K. Chamie, A. Drakaki, Durvalumab: an investigational anti-PD-L1 monoclonal antibody for the treatment of urothelial carcinoma. Drug Des., Dev. Ther. 12, 209 (2018)

    Google Scholar 

  19. L. Chen, Co-inhibitory molecules of the B7-CD28 family in the control of T-cell immunity. Nat. Rev. Immunol. 4(5), 336–347 (2004)

    Article  Google Scholar 

  20. K. Peggs, S. Quezada, J.P. Allison, Cancer immunotherapy: co-stimulatory agonists and co-inhibitory antagonists. Clin. Exp. Immunol. 157(1), 9–19 (2009)

    Article  Google Scholar 

  21. E. Contardi, G.L. Palmisano, P.L. Tazzari, A.M. Martelli, F. Fala, M. Fabbi, T. Kato, E. Lucarelli, D. Donati, L. Polito et al., CTLA-4 is constitutively expressed on tumor cells and can trigger apoptosis upon ligand interaction. Int. J. Cancer 117(4), 538–550 (2005)

    Article  Google Scholar 

  22. R. Padmanabhan, H.S. Kheraldine, N. Meskin, S. Vranic, A.E. Al Moustafa, Crosstalk between HER2 and PD-1/PD-L1 in breast cancer: from clinical applications to mathematical models. Cancers 12, no. 3, 636 (2020)

    Google Scholar 

  23. Y. Wang, H. Wang, H. Yao, C. Li, J.Y. Fang, J. Xu, Regulation of PD-L1: emerging routes for targeting tumor immune evasion. Front. Pharmacol. 9, 536 (2018)

    Google Scholar 

  24. V. Velcheti, K. Schalper, Basic overview of current immunotherapy approaches in cancer. Am. Soc. Clin. Oncol. Educ. Book 36, 298–308 (2016)

    Article  Google Scholar 

  25. N. Jorgensen, G. Persson, T.V.F. Hviid, The tolerogenic function of regulatory T cells in pregnancy and cancer. Front. Immunol. 10, 911 (2019)

    Google Scholar 

  26. F. Salamanna, V. Borsari, D. Contartese, V. Costa, G. Giavaresi, M. Fini, What is the role of interleukins in breast cancer bone metastases? A systematic review of preclinical and clinical evidence. Cancers 11(12), 2018 (2019)

    Google Scholar 

  27. B.E. Lippitz, R.A. Harris, Cytokine patterns in cancer patients: a review of the correlation between interleukin 6 and prognosis. OncoImmunology 5, no. 5 (2016)

    Google Scholar 

  28. J.A. Bridge, J.C. Lee, A. Daud, J.W. Wells, J.A. Bluestone, Cytokines, chemokines, and other biomarkers of response for checkpoint inhibitor therapy in skin cancer. Front. Med. 5, 351 (2018)

    Google Scholar 

  29. N. Nagarsheth, M. Wicha, W. Zou, Chemokines in the cancer microenvironment and their relevance in cancer immunotherapy. Nat. Rev. Immunol. 17, 05 (2017)

    Google Scholar 

  30. A.E. Vilgelm, A. Richmond, Chemokines modulate immune surveillance in tumorigenesis, metastasis and response to immunotherapy. Front. Immunol. 10, 333 (2019)

    Google Scholar 

  31. A. Zlotnik, Chemokines and cancer. Int. J. Cancer 119(9), 2026–2029 (2006)

    Article  Google Scholar 

  32. H. Zhao, N. Dong, T. Liu, P. Zhang, Y. Zheng, L. Yang, X. Ren, Clinical significance of serum Type III interferons in patients with gastric cancer. J. Interf. Cytokine Res. 39(3), 155–163 (2019)

    Article  Google Scholar 

  33. A.K. Knuth, S. Rösler, B. Schenk, L. Kowald, S.J. van Wijk, S. Fulda, Interferons transcriptionally up-regulate MLKL expression in cancer cells. Neoplasia 21(1), 74–81 (2019)

    Article  Google Scholar 

  34. J.J. Huang, G.C. Blobe, Dichotomous roles of TGF-\(\beta \) in human cancer. Biochem. Soc. Trans. 44(5), 1441–1454 (2016)

    Article  Google Scholar 

  35. C.M. Filippi, A.E. Juedes, J.E. Oldham, E. Ling, L. Togher, Y. Peng, R.A. Flavell, M.G. von Herrath, Transforming growth factor-\(\beta \) suppresses the activation of CD8+ T-cells when naive but promotes their survival and function once antigen experienced: A two-faced impact on autoimmunity. Diabetes 57(10), 2684–2692 (2008)

    Article  Google Scholar 

  36. A. Dahmani, J.S. Delisle, TGF-\(\beta \) in T cell biology: implications for cancer immunotherapy. Cancers 10(6), 194 (2018)

    Google Scholar 

  37. M.J. Gorbet, A. Ranjan, Cancer immunotherapy with immunoadjuvants, nanoparticles, and checkpoint inhibitors: recent progress and challenges in treatment and tracking response to immunotherapy. Pharmacol. Ther. 207, 107456 (2020)

    Google Scholar 

  38. D. Sansom, CD28, CTLA-4 and their ligands: who does what and to whom? Immunology 101(2), 169 (2000)

    Google Scholar 

  39. P.T. Sage, A.M. Paterson, S.B. Lovitch, A.H. Sharpe, The coinhibitory receptor CTLA-4 controls B cell responses by modulating T follicular helper, T follicular regulatory, and T regulatory cells. Immunity 41(6), 1026–1039 (2014)

    Article  Google Scholar 

  40. R.K. Vaddepally, P. Kharel, R. Pandey, R. Garje, A.B. Chandra, Review of indications of FDA-approved immune checkpoint inhibitors per NCCN guidelines with the level of evidence. Cancers 12(3), 738 (2020)

    Google Scholar 

  41. M.W. Rohaan, S. Wilgenhof, J.B. Haanen, Adoptive cellular therapies: the current landscape. Virchows Arch. 474(4), 449–461 (2019)

    Article  Google Scholar 

  42. D.A. Lee, Cellular therapy: adoptive immunotherapy with expanded natural killer cells. Immunol. Rev. 290(1), 85–99 (2019)

    Article  Google Scholar 

  43. L.G. de Pillis, W. Gu, A.E. Radunskaya, Mixed immunotherapy and chemotherapy of tumors: modeling, applications and biological interpretations. J. Theor. Biol. 238(4), 841–862 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  44. C.J. Wheeler, A. Das, G. Liu, J.S. Yu, K.L. Black, Clinical responsiveness of glioblastoma multiforme to chemotherapy after vaccination. Clin. Cancer Res. 10(16), 5316–5326 (2004)

    Article  Google Scholar 

  45. A.G. Dalgleish, Vaccines versus immunotherapy: overview of approaches in deciding between options. Hum. Vaccines Immunother. 10(11), 3369–3374 (2014)

    Article  Google Scholar 

  46. A. Diefenbach, E.R. Jensen, A. Jamieson, D.H. Raulet, Rae1 and H60 ligands of the NKG2D receptor stimulate tumor immunity. Nature 413, 165–71 (2001)

    Article  Google Scholar 

  47. A.S. Novozhilov, F.S. Berezovskaya, E.V. Koonin, G.P. Karev, Mathematical modeling of tumor therapy with oncolytic viruses: regimes with complete tumor elimination within the framework of deterministic models. Biol. Direct 1, 6 (2006)

    Google Scholar 

  48. A.L. Jenner, A.C.F. Coster, P.S. Kim, F. Frascoli, Treating cancerous cells with viruses: insights from a minimal model for oncolytic virotherapy. Lett. Biomath. 5(sup1), S117–S136 (2018)

    Article  MathSciNet  Google Scholar 

  49. R. Eftimie, J.L. Bramson, D.J.D. Earn, Interactions between the immune system and cancer: a brief review of non-spatial mathematical models. Bull. Math. Biol. 73(1), 2–32 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  50. D. Kirschner, J.C. Panetta, Modeling immunotherapy of the tumor-immune interaction. J. Math. Biol. 37(3), 235–252 (1998)

    Article  MATH  Google Scholar 

  51. A. Rivaz, M. Azizian, M. Soltani, Various mathematical models of tumor growth with reference to cancer stem cells: a review. Iran. J. Sci. Technol., Trans. A: Sci. 43(2), 687–700 (2019)

    Article  MathSciNet  Google Scholar 

  52. F. Castiglione, B. Piccoli, Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull. Math. Biol. 68(2), 255–274 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  53. A. Tsygvintsev, S. Marino, D.E Kirschner, A mathematical model of gene therapy for the treatment of cancer. Math. Methods Model. Biomed., 01 (2013)

    Google Scholar 

  54. J. Arciero, T. Jackson, D. Kirschner, A mathematical model of tumor-immune evasion and siRNA treatment. Discret. Contin. Dyn. Syst.-B 4, 39 (2004)

    Google Scholar 

  55. K.R. Fister, J.H. Donnelly, Immunotherapy: an optimal control theory approach. Math. Biosci. Eng. 2(3), 499–510 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  56. A. Konstorum, A.T. Vella, A.J. Adler, R.C. Laubenbacher, Addressing current challenges in cancer immunotherapy with mathematical and computational modelling. J. R. Soc. Interface 14(131), 20170150 (2017)

    Google Scholar 

  57. V.A. Kuznetsov, I.A. Makalkin, M.A. Taylor, A.S. Perelson, Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol. 56(2), 295–321 (1994)

    Article  MATH  Google Scholar 

  58. R. De Boer, P. Hogeweg, H. Dullens, R.A. De Weger, W. Den Otter, Macrophage T lymphocyte interactions in the anti-tumor immune response: a mathematical model. J. Immunol. 134(4), 2748–2758 (1985)

    Article  Google Scholar 

  59. S. Banerjee, Immunotherapy with interleukin-2: a study based on mathematical modeling. Int. J. Appl. Math. Comput. Sci. 18(3), 389–398 (2008)

    Article  MATH  Google Scholar 

  60. F.S. Cyprian, H.F. Al Farsi, S. Vranic, S. Akhtar, A.E. Al Moustafa, Epstein–Barr virus and human papillomaviruses interactions and their roles in the initiation of epithelial-mesenchymal transition and cancer progression. Front. Oncol. 8, 111 (2018)

    Google Scholar 

  61. H. Al Thawadi, L. Ghabreau, T. Aboulkassim, A. Yasmeen, S. Vranic, G. Batist, A.E. Al Moustafa, Co-incidence of epstein–Barr virus and high-risk human papillomaviruses in cervical cancer of Syrian women. Front. Oncol. 8, 250 (2018)

    Google Scholar 

  62. A. Radunskaya, L. de Pillis, A. Gallegos, A model of dendritic cell therapy for melanoma. Front. Oncol. 3, 56 (2013)

    Google Scholar 

  63. A. Minelli, F. Topputo, F. Bernelli Zazzera, Controlled drug delivery in cancer immunotherapy: stability, optimization, and Monte Carlo analysis. SIAM J. Appl. Math. 71, no. 6, 2229–2245 (2011)

    Google Scholar 

  64. X. Lai, A. Friedman, Combination therapy of cancer with cancer vaccine and immune checkpoint inhibitors: a mathematical model. PloS One 12, no. 5 (2017)

    Google Scholar 

  65. E. Nikolopoulou, L.R. Johnson, D. Harris, J.D. Nagy, E.C. Stites, Y. Kuang, Tumour-immune dynamics with an immune checkpoint inhibitor. Lett. Biomath. 5(sup1), S137–S159 (2018)

    Article  MathSciNet  Google Scholar 

  66. M. Qomlaqi, F. Bahrami, M. Ajami, J. Hajati, An extended mathematical model of tumor growth and its interaction with the immune system, to be used for developing an optimized immunotherapy treatment protocol. Math. Biosci. 292, 1–9 (2017)

    Article  MathSciNet  MATH  Google Scholar 

  67. S. Banerjee, R.R. Sarkar, Delay-induced model for tumor-immune interaction and control of malignant tumor growth. Biosystems 91(1), 268–288 (2008)

    Article  Google Scholar 

  68. M. Mackey, Unified hypothesis for the origin of aplastic anemia and periodic hematopoiesis. Blood 51(5), 941–956 (1978)

    Article  Google Scholar 

  69. Y. Dong, G. Huang, R. Miyazaki, Y. Takeuchi, Dynamics in a tumor immune system with time delays. Appl. Math. Comput. 252, 99–113 (2015)

    MathSciNet  MATH  Google Scholar 

  70. C.K. Osborne, D.H. Boldt, G.M. Clark, J.M. Trent, Effects of tamoxifen on human breast cancer cell cycle kinetics: accumulation of cells in early G1 Phase. Cancer Res. 43(8), 3583–3585 (1983)

    Google Scholar 

  71. H.E. Skipper, Kinetics of mammary tumor cell growth and implications for therapy. Cancer 28(6), 1479–1499 (1971)

    Article  Google Scholar 

  72. B. Joshi, X. Wang, S. Banerjee, H. Tian, A. Matzavinos, M.A. Chaplain, On immunotherapies and cancer vaccination protocols: a mathematical modelling approach. J. Theor. Biol. 259(4), 820–827 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  73. M.A. Postow, R. Sidlow, M.D. Hellmann, Immune-related adverse events associated with immune checkpoint blockade. N. Engl. J. Med. 378(2), 158–168 (2018)

    Article  Google Scholar 

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Padmanabhan, R., Meskin, N., Moustafa, AE.A. (2021). Immunotherapy Models. In: Mathematical Models of Cancer and Different Therapies. Series in BioEngineering. Springer, Singapore. https://doi.org/10.1007/978-981-15-8640-8_4

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