Nothing Special   »   [go: up one dir, main page]
Skip to main content

Advertisement

Springer Nature Link
Log in

Optimization of Combined Leukemia Therapy by Finite-Dimensional Optimal Control Modeling

  • Published:
Journal of Optimization Theory and Applications Aims and scope Submit manuscript

Abstract

Imatinib is a highly effective treatment for chronic myeloid leukemia, a common type of leukemia. Treatment efficacy of imatinib has been further improved by combination therapy with exogenic cytokine interferon-\(\alpha \). However, the prolonged administration of drug and immunotherapy exacts a significant cost to the patient’s quality of life, due to the treatments side effects. We present a mathematical model for the scheduling of combined treatment with imatinib and interferon-\(\alpha \) by finite-dimensional optimal control problems. The explicit formulas for the optimal controls minimizing the integral quality criterion are obtained, and the corresponding leukemia treatment process is then described by numerical simulation. The attained optimization of treatment holds clinical potential for improving patient’s quality of life, as well as overall prognosis.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Byrne, H.M.: Dissecting cancer through mathematics: from the cell to the animal model. Nat. Rev. Cancer 10, 221–230 (2010)

    Article  Google Scholar 

  2. Michor, F., Iwasa, Y., Nowak, M.: Dynamics of cancer progression. Nat. Rev. Cancer 4(3), 197–205 (2004)

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  4. Kirschner, D., Panetta, J.: Modelling immunotherapy of the tumor–immune interaction. J. Math. Biol. 37(3), 235–252 (1998)

    Article  MATH  Google Scholar 

  5. d’Onofrio, A.: Tumor–immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy. Math. Models Methods Appl. Sci. 16(8), 1375–1401 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Article  MathSciNet  MATH  Google Scholar 

  8. Owen, M., Byrne, H., Lewis, C.: Mathematical modelling of the use of macrophages as vehicles for drug delivery to hypoxic tumour sites. J. Theor. Biol. 226, 377–391 (2004)

    Article  MathSciNet  Google Scholar 

  9. Bunimovich-Mendrazitsky, S., Pisarev, V., Kashdan, E.: Modeling and simulation of a low-grade urinary bladder carcinoma. Comput. Biol. Med. 58, 118–129 (2015)

    Article  Google Scholar 

  10. Faderl, S., Talpaz, M., Estrov, Z., O’Brien, S., Kurzrock, R., Kantarjian, H.: The biology of chronic myeloid leukemia. N. Engl. J. Med. 341(3), 164–172 (1999)

    Article  Google Scholar 

  11. Guilhot, F., Roy, L., Martineua, G., Guilhot, J., Millot, F.: Immunotherapy in chronic myelogenous leukemia. Clin. Lymph. Myeloma 7(Suppl 2), S64–70 (2007)

    Article  Google Scholar 

  12. Burchert, A., Neubauer, A.: Interferon alpha and T-cell responses in chronic myeloid leukemia. Leuk. Lymph. 46(2), 167–75 (2005)

    Article  Google Scholar 

  13. Montoya, M., Schiavoni, G., Mattei, F., Gresser, I., Belardelli, F., Borrow, P., Tough, D.F.: Type I interferons produced by dendritic cells promote their phenotypic and functional activation. Blood 99, 3263–3271 (2002)

    Article  Google Scholar 

  14. Druker, B.J., Talpaz, M., et al.: Efficacy and safety of a specific inhibitor of the BCR-ABL tyrosine kinase in chronic myeloid leukemia. N. Engl. J. Med. 344, 1031–1037 (2001)

    Article  Google Scholar 

  15. Deininger, M.W.N., Buchdunger, E., Druker, B.J.: The development of imatinib as a therapeutic agent for chronic myeloid leukemia. Blood 105, 2640–2653 (2005)

    Article  Google Scholar 

  16. Burchert, A., Saussele, S., Eigendorff, E., et al.: Interferon alpha 2 maintenance therapy may enable high rates of treatment discontinuation in chronic myeloid leukemia. Leukemia 29(6), 1331–5 (2015)

    Article  Google Scholar 

  17. Hardan, I., Stanevsky, A., Volchek, Y., et al.: Treatment with interferon alpha prior to discontinuation of imatinib in patients with chronic myeloid leukemia. Cytokine 57(2), 290–3 (2012)

    Article  Google Scholar 

  18. Preudhomme, C., Guilhot, J., Nicolini, F.E., et al.: Imatinib plus peginterferon alfa-2a in chronic myeloid leukemia. N. Engl. J. Med. 363(26), 2511–2521 (2010)

    Article  Google Scholar 

  19. Simonsson, B., Gedde-Dahl, T., Markevarn, B., et al.: Combination of pegylated IFN-alpha2b with imatinib increases molecular response rates in patients with low- or intermediate-risk chronic myeloid leukemia. Blood 118(12), 3228–35 (2011)

    Article  Google Scholar 

  20. Cappuccio, A., Elishmereni, M., Agur, Z.: Optimization of interleukin-21 immunotherapeutic strategies. J. Theor. Biol. 248, 259–266 (2007)

    Article  MathSciNet  Google Scholar 

  21. d’Onofrio, A., Gandolfi, A.: Tumor eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. Math. Biosci. 191, 159–184 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  22. d’Onofrio, A.: A general framework for modelling tumour immune system and immunotherapy: mathematical analysis and medical inferences. Physica D 208, 220–235 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  23. d’Onofrio, A., Gandolfi, A., Rocca, A.: The dynamics of tumour vasculature interaction suggests low dose, time-dense antiangiogenic scheduling. Cell Prolif. 42, 317–329 (2009)

    Article  Google Scholar 

  24. de Pillis, L.G., Gu, W., Fister, K.R., Head, T., Maples, K., Murugan, A., Neal, T., Yoshida, K.: Chemotherapy for tumors: an analysis of the dynamics and a study of quadratic and linear optimal controls. Math. Biosci. 209(1), 292–315 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  25. Smieja, J., Swierniak, A., Duda, Z.: Gradient method for finding optimal scheduling in infinite dimensional models of chemotherapy. J. Theor. Med. 3, 25–36 (2001)

    Article  MATH  Google Scholar 

  26. Stengel, R.F., Ghigliazza, R., Kulkarni, N., Laplace, O.: Optimal control of innate immune response. Optim. Control Appl. Methods 23, 91–104 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  27. Burden, T., Ernstberger, J., Fister, K.R.: Optimal control applied to immunotherapy. Discrete Contin. Dyn. Syst. Ser. B 4, 135–146 (2004)

    MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  29. d’Onofrio, A., Ledzewicz, U., Maurer, H., Schattler, H.: On optimal delivery of combination therapy for tumors. Math. Biosci. 222, 13–26 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  30. Jager, E., van der Velden, V.H.J., te Marvelde, J.G., Walter, R.B., Agur, Z., et al.: Targeted drug delivery by gemtuzumab ozogamicin: mechanism-based mathematical model for treatment strategy improvement and therapy individualization. PLoS ONE 6, E24265 (2011)

    Article  Google Scholar 

  31. Moore, H., Li, N.K.: A mathematical model of chronic myelogenous leukemia (CML) and T cell interaction. J. Theor. Biol. 227, 513 (2004)

    Article  MathSciNet  Google Scholar 

  32. Kim, P., Lee, P., Levy, D.: Dynamics and potential impact of the immune response to chronic myelogenous leukemia. PLoS Comput. Biol. 4, e1000095 (2008)

    Article  MathSciNet  Google Scholar 

  33. Michor, F., Hughes, T., Iwasa, Y., Branford, S., Shah, N., Sawyers, C., Nowak, M.: Dynamics of chronic myeloid leukemia. Nature 435, 1267–1270 (2005)

    Article  Google Scholar 

  34. Michor, F., Iwasa, Y., Nowak, M.: The age incidence of chronic myeloid leukemia can be explained by a one-mutation model. Proc. Natl. Acad. Sci. U. S. A. 103, 14931–14934 (2006)

    Article  Google Scholar 

  35. Nanda, S., Moore, H., Lenhart, S.: Optimal control of treatment in a mathematical model of chronic myelogenous leukemia. Math. Biosci. 210, 143 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  36. Roeder, I., Horn, M., Glauche, I., et al.: Dynamic modeling of imatinib-treated chronic myeloid leukemia: functional insights and clinical implications. Nat. Med. 12, 1181–1184 (2006)

    Article  Google Scholar 

  37. Radulescu, I.R., Candea, D., Halanay, A.: Optimal control analysis of a leukemia model under imatinib treatment. Math. Comput. Simul. 121, 1–11 (2016)

    Article  MathSciNet  Google Scholar 

  38. Swierniak, A.: Optimal treatment protocols in leukemia—modelling the proliferation cycle. In: Proceedings of the 12th IMACS World Congress, Paris, vol. 4, pp. 170–172 (1988)

  39. Wodarz, D., Komarova, N.: Emergence and prevention of resistance against small molecule inhibitors. Semin. Cancer Biol. 15, 506–514 (2005)

    Article  Google Scholar 

  40. Fister, K.R., Panetta, J.C.: Optimal control applied to cell-cycle specific cancer chemotherapy. SIAM J. Appl. Math. 60, 1059–1072 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  41. Berezansky, L., Bunimovich-Mendrazitsky, S., Domoshnitsky, A.: A mathematical model with time-varying delays in the combined treatment of chronic myeloid leukemia. Adv. Differ. Equ. 217, 257–266 (2013)

    MATH  Google Scholar 

  42. Berezansky, L., Bunimovich-Mendrazitsky, S., Shklyar, B.: Stability and controllability issues in mathematical modeling of the intensive treatment of leukemia. J. Optim. Theory Appl. 167(1), 326–341 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  43. Norton, L.: A Gompertzian model of human breast cancer growth. Cancer Res. 48, 7067–7071 (1988)

    Google Scholar 

  44. Laird, A.K.: Dynamics of tumor growth. Br. J. Cancer 18, 490–502 (1964)

    Article  Google Scholar 

  45. Pontryagin, L., Boltyanskii, V., Gamkrelidze, R., Mishchenko, E.: The Mathematical Theory of Optimal Processes. Interscience, New York. ISBN 2-88124-077-1 (1962)

  46. Dunford, N., Schwartz, J.T.: Linear Operators, vol. 1. Wiley-Interscience, New York (1958)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Ariel University, Ariel, Israel

    Svetlana Bunimovich-Mendrazitsky

  2. Holon Institute of Technology, Holon, Israel

    Benzion Shklyar

Authors
  1. Svetlana Bunimovich-Mendrazitsky
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Benzion Shklyar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Svetlana Bunimovich-Mendrazitsky.

Additional information

Communicated by Alberto d’Onofrio.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Bunimovich-Mendrazitsky, S., Shklyar, B. Optimization of Combined Leukemia Therapy by Finite-Dimensional Optimal Control Modeling. J Optim Theory Appl 175, 218–235 (2017). https://doi.org/10.1007/s10957-017-1161-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10957-017-1161-9

Keywords

Mathematics Subject Classification

Search

Navigation