Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-29T01:17:07.994Z Has data issue: false hasContentIssue false
  • English
  • Français

A Review of Optimal Chemotherapy Protocols: From MTD towards Metronomic Therapy

Published online by Cambridge University Press:  20 June 2014

U. Ledzewicz  and
H. Schättler
U. Ledzewicz*
Affiliation:
Dept. of Mathematics and Statistics, Southern Illinois University Edwardsville, Edwardsville, Illinois, 62026-1653, USA
H. Schättler
Affiliation:
Dept. of Electrical and Systems Engr., Washington University, St. Louis, Missouri, 63130-4899, USA
*
⋆Corresponding author. E-mail: [email protected]
Get access

Abstract

We review mathematical results about the qualitative structure of chemotherapy protocols that were obtained with the methods of optimal control. As increasingly more complex features are incorporated into the mathematical model—progressing from models for homogeneous, chemotherapeutically sensitive tumor cell populations to models for heterogeneous agglomerations of subpopulations of various sensitivities to models that include tumor immune-system interactions—the structures of optimal controls change from bang-bang solutions (which correspond to maximum dose rate chemotherapy with restperiods) to solutions that favor singular controls (representing reduced dose rates). Medically, this corresponds to a transition from standard MTD (maximum tolerated dose) type protocols to chemo-switch strategies towards metronomic dosing.

Keywords

optimal controlcancer chemotherapyhomogeneous and heterogeneous tumor populationstumor immune system interactions
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 9 , Issue 4: Optimal control , 2014 , pp. 131 - 152
Copyright
© EDP Sciences, 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

André, N., Padovani, L., Pasquier, E.. Metronomic scheduling of anticancer treatment: the next generation of multitarget therapy? Fut. Oncology, 7(3) (2011), 385–394. CrossRefGoogle ScholarPubMed
Andre, N., Abed, S., Orbach, D., Armari Alla, C., Padovani, L., Pasquier, E., Gentet, J.C., Verschuur, A.. Pilot study of a pediatric metronomic 4-drug regimen. Oncotarget, 2 (2011), 960–965. CrossRefGoogle Scholar
Bocci, G., Nicolaou, K., Kerbel, R.S.. Protracted low-dose effects on human endothelial cell proliferation and survival in vitro reveal a selective antiangiogenic window for various chemotherapeutic drugs. Cancer Res., 62 (2002), 6938–6943. Google ScholarPubMed
B. Bonnard, M. Chyba. Singular Trajectories and their Role in Control Theory. Mathématiques & Applications, Vol. 40. Springer Verlag, Paris, 2003.
Browder, T., Butterfield, C.E., Kräling, B.M., Shi, B., Marshall, B., O’Reilly, M.S., Folkman, J.. Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res., 60 (2000), 1878–1886. Google ScholarPubMed
M. Eisen. Mathematical Models in Cell Biology and Cancer Chemotherapy. Lecture Notes in Biomathematics, Vol. 30. Springer Verlag, 1979.
Friedman, A.. Cancer as Multifaceted Disease. Math. Model. Nat. Phenom., 7 (2012), 1–26. CrossRefGoogle Scholar
Gatenby, R.A., Silva, A.S., Gillies, R.J., Frieden, B.R.. Adaptive therapy. Cancer Research, 69 (2009), 4894–4903. CrossRefGoogle ScholarPubMed
Goldie, J.H.. Drug resistance in cancer: a perspective. Cancer and Metastasis Review, 20 (2001), 63–68. CrossRefGoogle ScholarPubMed
J.H. Goldie, A. Coldman. Drug Resistance in Cancer. Cambridge University Press, 1998.
Greene, J., Lavi, O., Gottesman, M., Levy, D.. The impact of cell density and mutations in a model of multidrug resistance in solid tumors. Bull. Math. Biol., 74 (2014), 627–653. CrossRefGoogle Scholar
J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer Verlag, New York, 1983.
Hahnfeldt, P., Hlatky, L.. Cell resensitization during protracted dosing of heterogeneous cell populations. Rad. Res., 150 (1998), 681–687. CrossRefGoogle ScholarPubMed
Hahnfeldt, P., Folkman, J., Hlatky, L.. Minimizing long-term burden: the logic for metronomic chemotherapy dosing and its angiogenic basis. J. of Theo. Biol., 220 (2003), 545–554. CrossRefGoogle Scholar
Hanahan, D., Bergers, G., Bergsland, E.. Less is more, regularly: metronomic dosing of cytotoxic drugs can target tumor angiogenesis in mice. J. Clin. Invest., 105(8) (2000), 1045–1047. CrossRefGoogle ScholarPubMed
Kamen, B., Rubin, E., Aisner, J., Glatstein, E.. High-time chemotherapy or high time for low dose? J. Clinical Oncology, 18(16) (2000), 2935–2937. CrossRefGoogle Scholar
T.J. Kindt, B.A. Osborne, R.A. Goldsby. Kuby Immunology. W.H. Freeman, 2006.
Kirschner, D., Panetta, J.C.. Modeling immunotherapy of the tumor-immune interaction. J. of Math. Biol., 37 (1998), 235–252. CrossRefGoogle Scholar
Klement, G., Baruchel, S., 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(8) (2000), R15–R24. CrossRefGoogle ScholarPubMed
Kuznetsov, V.A., Makalkin, I.A., Taylor, M.A., Perelson, A.S.. Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull. Math. Biol., 56 (1994), 295–321. CrossRefGoogle Scholar
U. Ledzewicz, K. Bratton, H. Schättler. A 3-compartment model for chemotherapy of heterogeneous tumor populations. Acta Mat. Appl., (2014), to appear.
Ledzewicz, U., Naghnaeian, M., Schättler, H.. Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics. J. of Math. Biol., 64 (2012), 557–577. CrossRefGoogle ScholarPubMed
Ledzewicz, U., Olumoye, O., Schättler, H.. On optimal chemotherapy with a stongly targeted agent for a model of tumor-immune system interactions with generalized logistic growth. Math. Biosci. Engr. (MBE), 10(3) (2012), 787–802. CrossRefGoogle Scholar
Ledzewicz, U., Schättler, H.. Optimal bang-bang controls for a 2-compartment model in cancer chemotherapy. J. of Optim. Th. Appl. (JOTA), 114 (2002), 609–637. CrossRefGoogle Scholar
Ledzewicz, U., Schättler, H.. Analysis of a cell-cycle specific model for cancer chemotherapy. J. of Biol. Syst., 10 (2002), 183–206. CrossRefGoogle Scholar
Ledzewicz, U., Schättler, H.. Drug resistance in cancer chemotherapy as an optimal control problem. Discr. Cont. Dyn. Syst., Ser. B, 6 (2006), 129–150. Google Scholar
Ledzewicz, U., Schättler, H., Reisi Gahrooi, M., Dehkordi, S. Mahmoudian. On the MTD paradigm and optimal control for combination cancer chemotherapy. Math. Biosci. Engr. (MBE), 10 (2013), 803–819. CrossRefGoogle Scholar
R. Martin, K.L. Teo. Optimal Control of Drug Administration in Cancer Chemotherapy. World Scientific Publishers, 1994.
Matzavinos, A., Chaplain, M., Kuznetsov, V.A.. Mathematical modelling of the spatio-temporal response of cytotoxic T-lymphocytes to a solid tumour. Math. Med. Biol., 21 (2004), 1–34. CrossRefGoogle Scholar
d’Onofrio, A.. A general framework for modelling tumor-immune system competition and immunotherapy: Mathematical analysis and biomedial inferences. Physica D, 208 (2005), 202–235. CrossRefGoogle Scholar
d’Onofrio, A.. Tumor evasion from immune control: strategies of a MISS to become a MASS. Chaos, Solitons and Fractals, 31 (2007), 261–268. CrossRefGoogle Scholar
d’Onofrio, A.. Metamodeling tumor-immune system interaction, tumor evasion and immunotherapy. Math. Comp. Modelling, 47 (2008), 614–637. CrossRefGoogle Scholar
Pardoll, D.. Does the immune system see tumors as foreign or self? Ann. Rev. of Immun., 21 (2003), 807–839. CrossRefGoogle ScholarPubMed
Pasquier, E., Ledzewicz, U.. Perspective on “More Is Not Necessarily Better”: Metronomic Chemotherapy. SMB Newsletter, 26(3) 2013, 9–10. Google Scholar
Pasquier, E., Kavallaris, M., André, N.. Metronomic chemotherapy: new rationale for new directions. Nat. Rev.| Clin. Onc., 7 (2010), 455–465. CrossRefGoogle ScholarPubMed
Pietras, K., Hanahan, D.. 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(5) (2005), 939–952. CrossRefGoogle Scholar
de Pillis, L.G., Radunskaya, A.. A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. J. Theo. Med., 3 (2001), 79–100. CrossRefGoogle Scholar
de Pillis, L.G., Radunskaya, A., Wiseman, C.L.. A validated mathematical model of cell-mediated immune response to tumor growth. Cancer Res., 65 (2005), 7950–7958. CrossRefGoogle ScholarPubMed
L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko. The Mathematical Theory of Optimal Processes, MacMillan, New York, 1964.
A.V. Rao, D.A. Benson, G.T. Huntington, C. Francolin, C.L. Darby, M.A. Patterson. User’s Manual for GPOPS: A MATLAB Package for Dynamic Optimization Using the Gauss Pseudospectral Method. University of Florida Report, 2008.
H. Schättler, U. Ledzewicz. Geometric Optimal Control. Springer, New York, 2012.
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 Conference on Decision and Control, Maui, Hawaii, December 2012, 7691–7696.
Stepanova, N.V.. Course of the immune reaction during the development of a malignant tumour. Biophys., 24 (1980), 917–923. Google Scholar
Swan, G.W.. Role of optimal control in cancer chemotherapy. Math. Biosci., 101 (1990), 237–284. CrossRefGoogle ScholarPubMed
Swann, J.B., Smyth, M.J.. Immune surveillance of tumors. J. Clin. Invest., 117 (2007), 1137–1146. CrossRefGoogle ScholarPubMed
Swierniak, A.. Optimal treatment protocols in leukemia - modelling the proliferation cycle. Proc. 12th IMACS World Congress, Paris, 4 (1988), 170–172. Google Scholar
Swierniak, A.. Cell cycle as an object of control. J. of Biol. Syst., 3 (1995), 41–54. CrossRefGoogle Scholar
Swierniak, A., Ledzewicz, U., Schättler, H.. Optimal control for a class of compartmental models in cancer chemotherapy. Int. J. Appl. Math. Comp. Sci., 13 (2003), 357–368. Google Scholar
Swierniak, A., Polanski, A., Kimmel, M.. Optimal control problems arising in cell-cycle-specific cancer chemotherapy. Cell Prolif., 29 (1996), 117–139. CrossRefGoogle ScholarPubMed
Swierniak, A., Smieja, J.. Cancer chemotherapy optimization under evolving drug resistance. Nonlin. Anal., 47 (2000), 375–386. CrossRefGoogle Scholar
de Vladar, H.P., González, J.A.. Dynamic response of cancer under the influence of immunological activity and therapy. J. of Theo. Biol., 227 (2004), 335–348. CrossRefGoogle ScholarPubMed
Weitman, S.D., Glatstein, E., Kamen, B.A.. Back to the basics: the importance of concentration * time in oncology. J. of Clin. Onc., 11 (1993), 820–821.CrossRefGoogle Scholar