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2014 | OriginalPaper | Buchkapitel

Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach

verfasst von : Urszula Ledzewicz, Heinz Schättler

Erschienen in: Mathematical Oncology 2013

Verlag: Springer New York

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Abstract

In this paper, results about the structure of cancer treatment protocols that can be inferred from an analysis of mathematical models with the methods and tools of optimal control are reviewed. For homogeneous tumor populations of chemotherapeutically sensitive cells, optimal controls are bang-bang corresponding to the medical paradigm of maximum tolerated doses (MTD). But as more aspects of the tumor microenvironment are taken into account, such as heterogeneity of the tumor cell population, tumor angiogenesis and tumor-immune system interactions, singular controls which administer agents at specific time-varying reduced dose rates become optimal and give an indication of what might be the biologically optimal dose (BOD).

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Vorheriges Kapitel Deterministic Mathematical Modelling for Cancer Chronotherapeutics: Cell Population Dynamics and Treatment Optimization

N. André, L. Padovani, E. Pasquier, Metronomic scheduling of anticancer treatment: the next generation of multitarget therapy?. Fut. Oncol. 7(3), 385–394 (2011)CrossRef

T. Boehm, J. Folkman, T. Browder, M.S. O’Reilly, Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance. Nature 390, 404–407 (1997)CrossRef

B. Bonnard,, M. Chyba, Singular trajectories and their role in control theory. Mathématiques & Applications, vol. 40 (Springer, Paris 2003)

A. Bressan, A. Piccoli, Introduction to the Mathematical Theory of Control, American Institute of Mathematical Sciences (2007)

S. Davis, G.D. Yancopoulos, The angiopoietins: Yin and Yang in angiogenesis. Cur. Top. Microbio. Immun. 237, 173–185 (1999)

M. Eisen, Mathematical Models in Cell Biology and Cancer Chemotherapy, Lecture Notes in Biomathematics, vol. 30 (Springer, NewYork 1979)

A. Ergun, K. Camphausen, L.M. Wein, Optimal scheduling of radiotherapy and angiogenic inhibitors, Bull. Math. Biol. 65, 407–424 (2003)CrossRef

J. Folkman, Tumor angiogenesis: therapeutic implications. New Engl. J. Med. 295, 1182–1196 (1971)

J. Folkman, Antiangiogenesis: new concept for therapy of solid tumors, Ann. Surg. 175, 409–416 (1972)CrossRef

10.

J. Folkman, M. Klagsburn, Angiogenic factors. Science 235, 442–447 (1987)

11.

U. Forys, Y. Keifetz, Y. Kogan, Critical-point analysis for three-variable cancer angiogenesis models. Math. Biosci. Eng. 2, 511–525 (2005)CrossRefMATHMathSciNet

12.

R.A. Gatenby, A.S. Silva, R.J. Gillies, B.R. Frieden, Adaptive therapy. Canc. Res. 69, 4894–4903 (2009)

13.

J.H. Goldie, Drug resistance in cancer: a perspective. Canc. Meta. Rev. 20, 63–68 (2001)CrossRef

14.

J.H. Goldie, A. Coldman, Drug Resistance in Cancer (Cambridge University Press, Cambridge 1998)CrossRef

15.

P. Hahnfeldt, L. Hlatky, Cell resensitization during protracted dosing of heterogeneous cell populations. Radiat. Res. 150, 681–687 (1998)CrossRef

16.

P. Hahnfeldt, D. Panigrahy, J. Folkman, L. Hlatky, Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Can. Res. 59, 4770–4775 (1999)

17.

P. Hahnfeldt, J. Folkman, L. Hlatky, Minimizing long-term burden: the logic for metronomic chemotherapy dosing and its angiogenic basis. J. Theo. Biol. 220, 545–554 (2003)CrossRef

18.

D. Hanahan, G. Bergers, E. Bergsland, Less is more, regularly: metronomic dosing of cytotoxic drugs can target tumor angiogenesis in mice. J. Clin. Invest. 105, 1045–1047 (2000)CrossRef

19.

R.K. Jain, Normalizing tumor vasculature with anti-angiogenic therapy: a new paradigm for combination therapy. Nat. Med., 7, 987–989 (2001)CrossRef

20.

R.K. Jain, L.L. Munn, Vascular normalization as a rationale for combining chemotherapy with antiangiogenic agents, Princ. Pract. Oncol. 21, 1–7 (2007)

21.

B. Kamen, E. Rubin, J. Aisner, E. Glatstein, High-time chemotherapy or high time for low dose? J. Clin. Oncol. 18, Editorial, 2935–2937 (2000)

22.

R.S. Kerbel, Tumor angiogenesis: past, present and near future, Carcinogensis, 21, 505–515 (2000)CrossRef

23.

T.J. Kindt, B.A. Osborne, R.A. Goldsby, Kuby Immunology (W.H. Freeman, New York 2006)

24.

M. Kimmel, A. Swierniak, Control theory approach to cancer chemotherapy: benefiting from phase dependence and overcoming drug resistance, in Tutorials in Mathematical Biosciences III: Cell Cycle, Proliferation, and Cancer. Lecture Notes in Mathematics, vol. 1872 (Springer, Newyork, 2006), pp. 185–221

25.

M. Klagsburn, S. Soker, VEGF/VPF: the angiogenesis factor found?. Curr. Biol. 3, 699–702, (1993)CrossRef

26.

G. Klement, S. Baruchel,, Rak, J., Man, S., Clark, K., Hicklin, D.J., Bohlen, P., Kerbel, R.S.: Continuous low-dose therapy with vinblastine and VEGF receptor-2 antibody induces sustained tumor regression without overt toxicity, J. Clin. Invest. 105, R15–R24 (2000)

27.

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

28.

U. Ledzewicz, K. Bratton, H. Schättler, A 3-compartment model for chemotherapy of heterogeneous tumor populations. Acta Appl. Matem. (2014) doi: 10.1007/s10440-014-9952-6

29.

U. Ledzewicz, M.S. Faraji Mosalman, H. Schättler, Optimal controls for a mathematical model of tumor-immune interactions under targeted chemotherapy with immune boost, Discr. Cont. Dyn. Syst. Ser. B 18, 1031–1051 (2013)CrossRefMATH

30.

U. Ledzewicz, A. d’Onofrio, H. Schättler, Tumor development under combination treatments with anti-angiogenic therapies. in Mathematical Methods and Models in Biomedicine (Springer, NewYork, 2012), pp. 311–337

31.

U. Ledzewicz, J. Marriott, H. Maurer, H. Schättler, Realizable protocols for optimal administration of drugs in mathematical models for novel cancer treatments, Math. Med. Biol. 27, 157–179, (2010).CrossRefMATHMathSciNet

32.

U. Ledzewicz, M. Naghnaeian, H. Schättler, Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. J. Math. Biol. 64, 557–577 (2012)CrossRefMATHMathSciNet

33.

U. Ledzewicz, H. Schättler, Optimal bang-bang controls for a 2-compartment model in cancer chemotherapy. J. Optim. Th. Appl. 114, 609–637 (2002)CrossRefMATH

34.

U. Ledzewicz, H. Schättler, Analysis of a cell-cycle specific model for cancer chemotherapy. J. Biol. Syst. 10, 183–206 (2002)CrossRefMATH

35.

U. Ledzewicz, H. Schättler, Optimal control for a bilinear model with recruiting agent in cancer chemotherapy, Proc. of the 42nd IEEE Conference on Decision and Control (CDC), Maui, Hawaii, 2762–2767 (2003)

36.

U. Ledzewicz, H. Schättler, The influence of PK/PD on the structure of optimal control in cancer chemotherapy models, Math. Biosci. Engr. 2, 561–578 (2005)CrossRefMATH

37.

U. Ledzewicz, H. Schättler, Drug resistance in cancer chemotherapy as an optimal control problem, Discr. Cont. Dyn. Syst. Ser. B, 6, 129–150 (2006)MATH

38.

U. Ledzewicz, H. Schättler, Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Contr. Optim. 46, 1052–1079 (2007)CrossRefMATH

39.

U. Ledzewicz, H. Schättler, Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. J. of Theo. Biol. 252, 295–312, (2008)CrossRef

40.

U. Ledzewicz, H. Schättler, Multi-input optimal control problems for combined tumor anti-angiogenic and radiotherapy treatments. J. of Optim. Th. Appl. 153, 195–224 (2012)CrossRefMATH

41.

U. Ledzewicz, H. Schättler, M. Reisi Gahrooi, S. Mahmoudian Dehkordi, On the MTD paradigm and optimal control for combination cancer chemotherapy. Math. Biosci. Engr. 10, 803–819 (2013)CrossRefMATH

42.

L.A. Loeb, A mutator phenotype in cancer. Canc. Res. 61, 3230–3239 (2001)

43.

R. Martin, K.L. Teo, Optimal Control of Drug Administration in Cancer Chemotherapy (World Scientific Publishers, Singapore 1994)MATH

44.

L. Norton, R. Simon, The Norton-Simon hypothesis revisited. Canc. Treat. Rep. 70, 163–169 (1986)

45.

A. d’Onofrio, A general framework for modelling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedial inferences. Phys. D 208, 202–235, (2005)

46.

A. d’Onofrio, Rapidly acting antitumoral antiangiogenic therapies. Phys. Rev. E Stat. Nonlin. Soft Matter Phys. 76, 031920 (2007)

47.

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

48.

A. d’Onofrio, A. Gandolfi, The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation. Appl. Math. and Comp. 181, 1155–1162 (2006)

49.

A. d’Onofrio, A. Gandolfi, A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy. Math. Med. Biol., 26, 63–95 (2009)

50.

A. d’Onofrio, A. Gandolfi, Chemotherapy of vascularised tumours: role of vessel density and the effect of vascular “pruning”. J. Theo. Biol. 264, 253–265, (2010)

51.

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

52.

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

53.

A. d’Onofrio, U. Ledzewicz, H. Schättler, On the dynamics of tumor immune system interactions and combined chemo- and immunotherapy, in: New Challenges for Cancer Systems Biomedicine eds. by A. d’Onofrio, P. Cerrai, A Gandolfi, vol. 1 (SIMAI Springer series, 2012). pp. 249–266

54.

D. Pardoll, Does the immune system see tumors as foreign or self? Ann. Rev. Immun. 21, 807–839 (2003)CrossRef

55.

E. Pasquier, U. Ledzewicz, Perspective on “More is not necessarily better”: Metronomic Chemotherapy. Newslet. Soc. Math. Biol. 26(2), 9–10, (2013)

56.

E. Pasquier, M. Kavallaris, N. André, Metronomic chemotherapy: new rationale for new directions. Nat. Rev. | Clin. Onc. 7, 455–465 (2010)

57.

K. Pietras, D. Hanahan, A multi-targeted, metronomic and maximum tolerated dose “chemo-switch” regimen is antiangiogenic, producing objective responses and survival benefit in a mouse model of cancer. J. Clin. Onc. 23, 939–952 (2005)CrossRef

58.

J. Poleszczuk, U. Forys, Derivation of the Hahnfeldt et al. model (1999) revisited, Proceedings of the 16th Nat. Conf. on Applications of Mathematics in Biology and Medicine, Krynica, Poland 87–92 (2010)

59.

L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes (MacMillan, New York 1964)MATH

60.

H. Schättler, U. Ledzewicz, B. Cardwell, Robustness of optimal controls for a class of mathematical models for tumor anti-angiogenesis. Math. Biosci. Engr. 8, 355–369 (2011)CrossRefMATH

61.

H. Schättler, U. Ledzewicz: Geometric Optimal Control (Springer, NewYork 2012)CrossRefMATH

62.

H. Schättler, U. Ledzewicz, S. Mahmoudian Dehkordi, M. Reisi Gahrooi, A geometric analysis of bang-bang extremals in optimal control problems for combination cancer chemotherapy, Proc. of the 51st IEEE Conf. on Decision and Control, Maui, Hawaii, 7691–7696, (2012)

63.

N.V. Stepanova, Course of the immune reaction during the development of a malignant tumour. Biophys. 24, 917–923 (1980)

64.

G.W. Swan, Role of optimal control in cancer chemotherapy. Math. Biosci., 101, 237–284 (1990)CrossRefMATH

65.

J.B. Swann, M.J. Smyth, Immune surveillance of tumors. J. Clin. Invest. 117 1137–1146, (2007)CrossRef

66.

A. Swierniak, Optimal treatment protocols in leukemia-modelling the proliferation cycle, Proc. of the 12th IMACS World Congress, Paris, vol. 4, 170–172 (1988)

67.

A. Swierniak, Cell cycle as an object of control, J. Biol. Syst. 3, 41–54 (1995)CrossRef

68.

A. Swierniak, Direct and indirect control of cancer populations. Bul. Pol. Acad. Sci. Techn. Sci. 56, 367–378 (2008)

69.

A. Swierniak, U. Ledzewicz, H. Schättler, Optimal control for a class of compartmental models in cancer chemotherapy. Int. J. Appl. Math. Comp. Sci. 13, 357–368 (2003)MATH

70.

A. Swierniak, A. d’Onofrio, A. Gandolfi, Optimal control problems related to tumor angiogenesis. Proc. IEEE-IECON’2006, 667–681 (2006)

71.

A. Swierniak, J. Smieja, Cancer chemotherapy optimization under evolving drug resistance. Nonlin. Ana. 47, 375–386 (2000)CrossRefMathSciNet

72.

H.P. de Vladar, J.A. González, Dynamic response of cancer under the influence of immunological activity and therapy. J. Theo. Biol. 227, 335–348 (2004)CrossRef

Titel: Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach
verfasst von: Urszula Ledzewicz
Heinz Schättler
Verlag: Springer New York
Buch: Mathematical Oncology 2013
Print ISBN: 978-1-4939-0457-0

Electronic ISBN: 978-1-4939-0458-7

Copyright-Jahr: 2014
DOI: https://doi.org/10.1007/978-1-4939-0458-7_10

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