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Volumn 64, Issue 3, 2012, Pages 557-577

Optimal response to chemotherapy for a mathematical model of tumor-immune dynamics

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[No Author keywords available]

Indexed keywords

ANTINEOPLASTIC AGENT;

EID: 84855706384     PISSN: 03036812     EISSN: 14321416     Source Type: Journal    
DOI: 10.1007/s00285-011-0424-6     Document Type: Article
Times cited : (80)

References (34)
  • 3
    • 33845488897 scopus 로고    scopus 로고
    • Direct trajectory optimization and costate estimation via an orthogonal collocation method
    • Benson DA, Huntington GT, Thorvaldsen TP, Rao AV (2006) Direct trajectory optimization and costate estimation via an orthogonal collocation method. J Guid Control Dyn 29(6): 1435-1440.
    • (2006) J Guid Control Dyn , vol.29 , Issue.6 , pp. 1435-1440
    • Benson, D.A.1    Huntington, G.T.2    Thorvaldsen, T.P.3    Rao, A.V.4
  • 4
    • 11844254028 scopus 로고    scopus 로고
    • Singular trajectories and their role in control theory
    • Springer, Paris
    • Bonnard B, Chyba M (2003) Singular trajectories and their role in control theory. In: Mathématiques & applications, vol 40. Springer, Paris.
    • (2003) Mathématiques & applications , vol.40
    • Bonnard, B.1    Chyba, M.2
  • 7
    • 33746656314 scopus 로고    scopus 로고
    • Optimal control in a model of dendritic cell transfection cancer immunotherapy
    • Castiglione F, Piccoli B (2006) Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull Math Biol 68: 255-274.
    • (2006) Bull Math Biol , vol.68 , pp. 255-274
    • Castiglione, F.1    Piccoli, B.2
  • 8
    • 0035738977 scopus 로고    scopus 로고
    • A mathematical tumor model with immune resistance and drug therapy: an optimal control approach
    • de Pillis LG, Radunskaya A (2001) A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. J Theor Med 3: 79-100.
    • (2001) J Theor Med , vol.3 , pp. 79-100
    • de Pillis, L.G.1    Radunskaya, A.2
  • 9
    • 1542316360 scopus 로고    scopus 로고
    • Dynamic response of cancer under the influence of immunological activity and therapy
    • de Vladar HP, González JA (2004) Dynamic response of cancer under the influence of immunological activity and therapy. J Theor Biol 227: 335-348.
    • (2004) J Theor Biol , vol.227 , pp. 335-348
    • de Vladar, H.P.1    González, J.A.2
  • 10
    • 23144445934 scopus 로고    scopus 로고
    • A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences
    • d'Onofrio A (2005) A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Phys D 208: 220-235.
    • (2005) Phys D , vol.208 , pp. 220-235
    • D'Onofrio, A.1
  • 11
    • 33747088162 scopus 로고    scopus 로고
    • Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy
    • d'Onofrio A (2006) Tumor-immune system interaction: modeling the tumor-stimulated proliferation of effectors and immunotherapy. Math Models Methods Appl Sci 16: 1375-1401.
    • (2006) Math Models Methods Appl Sci , vol.16 , pp. 1375-1401
    • D'Onofrio, A.1
  • 12
    • 65349170905 scopus 로고    scopus 로고
    • The dynamics of tumour-vasculature interaction suggests low-dose, time-dense antiangiogenic schedulings
    • d'Onofrio A, Gandolfi A, Rocca A (2009) The dynamics of tumour-vasculature interaction suggests low-dose, time-dense antiangiogenic schedulings. Cell Prolif 42: 317-329.
    • (2009) Cell Prolif , vol.42 , pp. 317-329
    • D'Onofrio, A.1    Gandolfi, A.2    Rocca, A.3
  • 13
    • 70350339795 scopus 로고    scopus 로고
    • On optimal delivery of combination therapy for tumors
    • doi:10.1016/j.mbs.2009.08.004
    • d'Onofrio A, Ledzewicz U, Maurer H, Schättler H (2009) On optimal delivery of combination therapy for tumors. Math Biosci 222: 13-26. doi: 10. 1016/j. mbs. 2009. 08. 004.
    • (2009) Math Biosci , vol.222 , pp. 13-26
    • D'Onofrio, A.1    Ledzewicz, U.2    Maurer, H.3    Schättler, H.4
  • 14
    • 0037406640 scopus 로고    scopus 로고
    • Optimal scheduling of radiotherapy and angiogenic inhibitors
    • Ergun A, Camphausen K, Wein LM (2003) Optimal scheduling of radiotherapy and angiogenic inhibitors. Bull Math Biol 65: 407-424.
    • (2003) Bull Math Biol , vol.65 , pp. 407-424
    • Ergun, A.1    Camphausen, K.2    Wein, L.M.3
  • 15
    • 34447571170 scopus 로고    scopus 로고
    • Immunotherapy: an optimal control approach
    • Fister KR, Hughes Donnelly J (2005) Immunotherapy: an optimal control approach. Math Biosci Eng (MBE) 2(3): 499-510.
    • (2005) Math Biosci Eng (MBE) , vol.2 , Issue.3 , pp. 499-510
    • Fister, K.R.1    Hughes, D.J.2
  • 19
    • 0032160863 scopus 로고    scopus 로고
    • Modeling immunotherapy of the tumor-immune interaction
    • Kirschner D, Panetta JC (1998) Modeling immunotherapy of the tumor-immune interaction. J. Math Biol 37: 235-252.
    • (1998) J. Math Biol , vol.37 , pp. 235-252
    • Kirschner, D.1    Panetta, J.C.2
  • 20
    • 0028388757 scopus 로고
    • Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis
    • Kuznetsov VA, Makalkin IA, Taylor MA, Perelson AS (1994) Nonlinear dynamics of immunogenic tumors: parameter estimation and global bifurcation analysis. Bull Math Biol 56: 295-321.
    • (1994) Bull Math Biol , vol.56 , pp. 295-321
    • Kuznetsov, V.A.1    Makalkin, I.A.2    Taylor, M.A.3    Perelson, A.S.4
  • 21
    • 77955693734 scopus 로고    scopus 로고
    • Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment
    • Ledzewicz U, Marriott J, Maurer H, Schättler H (2010) Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment. Math Med Biol 27: 157-179.
    • (2010) Math Med Biol , vol.27 , pp. 157-179
    • Ledzewicz, U.1    Marriott, J.2    Maurer, H.3    Schättler, H.4
  • 23
    • 79953147879 scopus 로고    scopus 로고
    • Bifurcation of singular arcs in an optimal control problem for cancer immune system interactions under treatment
    • Atlanta, USA
    • Ledzewicz U, Naghnaeian M, Schättler H (2010) Bifurcation of singular arcs in an optimal control problem for cancer immune system interactions under treatment. In: Proceedings of the 49th IEEE conference on decision and control. Atlanta, USA, pp 7039-7044.
    • (2010) Proceedings of the 49th IEEE conference on decision and control , pp. 7039-7044
    • Ledzewicz, U.1    Naghnaeian, M.2    Schättler, H.3
  • 24
    • 84855689899 scopus 로고    scopus 로고
    • An optimal control approach to cancer treatment under immunological activity
    • Ledzewicz U, Naghnaeian M, Schättler H (2011a) An optimal control approach to cancer treatment under immunological activity. Appl Math 38(1): 17-31.
    • (2011) Appl Math , vol.38 , Issue.1 , pp. 17-31
    • Ledzewicz, U.1    Naghnaeian, M.2    Schättler, H.3
  • 26
    • 0003328875 scopus 로고    scopus 로고
    • Analysis of a cell-cycle specific model for cancer chemotherapy
    • Ledzewicz U, Schättler H (2002) Analysis of a cell-cycle specific model for cancer chemotherapy. J Biol Syst 10: 183-206.
    • (2002) J Biol Syst , vol.10 , pp. 183-206
    • Ledzewicz, U.1    Schättler, H.2
  • 27
    • 42749090784 scopus 로고    scopus 로고
    • Anti-angiogenic therapy in cancer treatment as an optimal control problem
    • Ledzewicz U, Schättler H (2007) Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J Control Optim 46: 1052-1079.
    • (2007) SIAM J Control Optim , vol.46 , pp. 1052-1079
    • Ledzewicz, U.1    Schättler, H.2
  • 28
    • 42749096482 scopus 로고    scopus 로고
    • Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis
    • Ledzewicz U, Schättler H (2008) Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. J Theor Biol 252: 295-312.
    • (2008) J Theor Biol , vol.252 , pp. 295-312
    • Ledzewicz, U.1    Schättler, H.2
  • 29
    • 0017736818 scopus 로고
    • Growth curve of an experimental solid tumor following radiotherapy
    • Norton L, Simon R (1977) Growth curve of an experimental solid tumor following radiotherapy. J Natl Cancer Inst 58: 1735-1741.
    • (1977) J Natl Cancer Inst , vol.58 , pp. 1735-1741
    • Norton, L.1    Simon, R.2
  • 30
    • 0024214663 scopus 로고
    • A Gompertzian model of human breast cancer growth
    • Norton L (1988) A Gompertzian model of human breast cancer growth. Cancer Res 48: 7067-7071.
    • (1988) Cancer Res , vol.48 , pp. 7067-7071
    • Norton, L.1
  • 32
    • 1542264910 scopus 로고
    • Course of the immune reaction during the development of a malignant tumour
    • Stepanova NV (1980) Course of the immune reaction during the development of a malignant tumour. Biophysics 24: 917-923.
    • (1980) Biophysics , vol.24 , pp. 917-923
    • Stepanova, N.V.1
  • 33
    • 57749120581 scopus 로고    scopus 로고
    • Direct and indirect control of cancer populations
    • Swierniak A (2008) Direct and indirect control of cancer populations. Bull Pol Acad Sci Tech Sci 56(4): 367-378.
    • (2008) Bull Pol Acad Sci Tech Sci , vol.56 , Issue.4 , pp. 367-378
    • Swierniak, A.1
  • 34
    • 33644539123 scopus 로고    scopus 로고
    • Optimal control for a class of compartmental models in cancer chemotherapy
    • Swierniak A, Ledzewicz U, Schättler H (2003) Optimal control for a class of compartmental models in cancer chemotherapy. Int J Appl Math Comput Sci 13: 357-368.
    • (2003) Int J Appl Math Comput Sci , vol.13 , pp. 357-368
    • Swierniak, A.1    Ledzewicz, U.2    Schättler, H.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.