-
1
-
-
0015311426
-
Antiangiogenesis: new concept for therapy of solid tumors
-
Folkman J. Antiangiogenesis: new concept for therapy of solid tumors. Ann. Surg. 175 (1972) 409
-
(1972)
Ann. Surg.
, vol.175
, pp. 409
-
-
Folkman, J.1
-
2
-
-
0000004505
-
VEGF/VPF: the angiogenesis factor found?
-
Klagsburn M., and Soker S. VEGF/VPF: the angiogenesis factor found?. Curr. Biol. 3 (1993) 699
-
(1993)
Curr. Biol.
, vol.3
, pp. 699
-
-
Klagsburn, M.1
Soker, S.2
-
3
-
-
0031469819
-
Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance
-
Boehm T., Folkman J., Browder T., and O'Reilly M.S. Antiangiogenic therapy of experimental cancer does not induce acquired drug resistance. Nature 390 (1997) 404
-
(1997)
Nature
, vol.390
, pp. 404
-
-
Boehm, T.1
Folkman, J.2
Browder, T.3
O'Reilly, M.S.4
-
4
-
-
0031443206
-
A cancer therapy resistant to resistance
-
Kerbel R.S. A cancer therapy resistant to resistance. Nature 390 (1997) 335
-
(1997)
Nature
, vol.390
, pp. 335
-
-
Kerbel, R.S.1
-
5
-
-
0030404170
-
The mathematical modelling, simulation and prediction of tumour-induced angiogenesis
-
Chaplain M., and Anderson A. The mathematical modelling, simulation and prediction of tumour-induced angiogenesis. Invas. Metast. 16 (1997) 222
-
(1997)
Invas. Metast.
, vol.16
, pp. 222
-
-
Chaplain, M.1
Anderson, A.2
-
6
-
-
0032170064
-
Continuous and discrete mathematical models of tumor-induced angiogenesis
-
Anderson A., and Chaplain M. Continuous and discrete mathematical models of tumor-induced angiogenesis. Bull. Math. Biol. 60 (1998) 857
-
(1998)
Bull. Math. Biol.
, vol.60
, pp. 857
-
-
Anderson, A.1
Chaplain, M.2
-
7
-
-
0037840352
-
A computer algorithm describing the process of vessel, rmation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumour growth
-
Arakelyan L., Vainstain V., and Agur Z. A computer algorithm describing the process of vessel, rmation and maturation, and its use for predicting the effects of anti-angiogenic and anti-maturation therapy on vascular tumour growth. Angiogenesis 5 (2002) 203
-
(2002)
Angiogenesis
, vol.5
, pp. 203
-
-
Arakelyan, L.1
Vainstain, V.2
Agur, Z.3
-
8
-
-
33750093051
-
Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy
-
Alarcon T., Owen M.R., Byrne H.M., and Maini P.K. Multiscale modelling of tumour growth and therapy: the influence of vessel normalisation on chemotherapy. Comput. Math. Meth. Med. 7 (2006) 85
-
(2006)
Comput. Math. Meth. Med.
, vol.7
, pp. 85
-
-
Alarcon, T.1
Owen, M.R.2
Byrne, H.M.3
Maini, P.K.4
-
9
-
-
33746260079
-
Vascular network remodelling via vessel cooption, regression and growth in tumours
-
Bartha K., and Rieger H. Vascular network remodelling via vessel cooption, regression and growth in tumours. J. Theor. Biol. 241 (2006) 903
-
(2006)
J. Theor. Biol.
, vol.241
, pp. 903
-
-
Bartha, K.1
Rieger, H.2
-
10
-
-
63249119539
-
Stochastic modelling of tumour induced angiogenesis
-
Capasso V., and Morale D. Stochastic modelling of tumour induced angiogenesis. J. Math. Biol. 58 (2009) 219
-
(2009)
J. Math. Biol.
, vol.58
, pp. 219
-
-
Capasso, V.1
Morale, D.2
-
11
-
-
0033213978
-
Tumor development under angiogenic signaling: a dynamical theory of tumor growth treatment, response, and postvascular dormancy
-
Hahnfeldt P., Panigrahy D., Folkman J., and Hlatky L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth treatment, response, and postvascular dormancy. Cancer Res. 59 (1999) 4770
-
(1999)
Cancer Res.
, vol.59
, pp. 4770
-
-
Hahnfeldt, P.1
Panigrahy, D.2
Folkman, J.3
Hlatky, L.4
-
12
-
-
0037406640
-
Optimal scheduling of radiotherapy and angiogenic inhibitors
-
Ergun A., Camphausen K., and Wein L.M. Optimal scheduling of radiotherapy and angiogenic inhibitors. Bull. Math. Biol. 65 (2003) 407
-
(2003)
Bull. Math. Biol.
, vol.65
, pp. 407
-
-
Ergun, A.1
Camphausen, K.2
Wein, L.M.3
-
13
-
-
4444221249
-
Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al.
-
d'Onofrio A., and Gandolfi A. Tumour eradication by antiangiogenic therapy: analysis and extensions of the model by Hahnfeldt et al. Math. Biosci. 191 (2004) 159
-
(2004)
Math. Biosci.
, vol.191
, pp. 159
-
-
d'Onofrio, A.1
Gandolfi, A.2
-
14
-
-
34247401423
-
Critical-point analysis for three-variable cancer angiogenesis models
-
Forys U., Keifetz Y., and Kogan Y. Critical-point analysis for three-variable cancer angiogenesis models. Math. Biosci. Eng. 2 (2005) 511
-
(2005)
Math. Biosci. Eng.
, vol.2
, pp. 511
-
-
Forys, U.1
Keifetz, Y.2
Kogan, Y.3
-
15
-
-
35649006861
-
Modelling the role of angiogenesis vasculogenesis in solid tumour growth
-
Stamper I.J., Byrne H.M., Owen M.R., and Maini P.K. Modelling the role of angiogenesis vasculogenesis in solid tumour growth. Bull. Math. Biol. 69 (2007) 2737
-
(2007)
Bull. Math. Biol.
, vol.69
, pp. 2737
-
-
Stamper, I.J.1
Byrne, H.M.2
Owen, M.R.3
Maini, P.K.4
-
16
-
-
33750446670
-
The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation
-
d'Onofrio A., and Gandolfi A. The response to antiangiogenic anticancer drugs that inhibit endothelial cell proliferation. Appl. Math. Comput. 181 (2006) 1155
-
(2006)
Appl. Math. Comput.
, vol.181
, pp. 1155
-
-
d'Onofrio, A.1
Gandolfi, A.2
-
17
-
-
33847219672
-
A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors
-
Sevilla, Spain
-
U. Ledzewicz, H. Schättler, A synthesis of optimal controls for a model of tumor growth under angiogenic inhibitors, in: Proceedings of the 44th IEEE Conference on Dec. and Control, Sevilla, Spain, 2005, pp. 945-950.
-
(2005)
Proceedings of the 44th IEEE Conference on Dec. and Control
, pp. 945-950
-
-
Ledzewicz, U.1
Schättler, H.2
-
18
-
-
42749096736
-
Application of optimal control to a system describing tumor anti-angiogenesis
-
Kyoto, Japan, July
-
U. Ledzewicz, H. Schättler, Application of optimal control to a system describing tumor anti-angiogenesis, in: Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS), Kyoto, Japan, July 2006, pp. 478-484.
-
(2006)
Proceedings of the 17th International Symposium on Mathematical Theory of Networks and Systems (MTNS)
, pp. 478-484
-
-
Ledzewicz, U.1
Schättler, H.2
-
19
-
-
42749090784
-
Anti-angiogenic therapy in cancer treatment as an optimal control problem
-
Ledzewicz U., and Schättler H. Anti-angiogenic therapy in cancer treatment as an optimal control problem. SIAM J. Control Optim. 46 (2007) 1052
-
(2007)
SIAM J. Control Optim.
, vol.46
, pp. 1052
-
-
Ledzewicz, U.1
Schättler, H.2
-
20
-
-
40449120191
-
Analysis of a mathematical model for tumor anti-angiogenesis
-
Ledzewicz U., and Schättler H. Analysis of a mathematical model for tumor anti-angiogenesis. Opt. Control Appl. Meth. 29 1 (2008) 41
-
(2008)
Opt. Control Appl. Meth.
, vol.29
, Issue.1
, pp. 41
-
-
Ledzewicz, U.1
Schättler, H.2
-
21
-
-
42749096482
-
Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis
-
Ledzewicz U., and Schättler H. Optimal and suboptimal protocols for a class of mathematical models of tumor anti-angiogenesis. J. Theor. Biol. 252 (2008) 295
-
(2008)
J. Theor. Biol.
, vol.252
, pp. 295
-
-
Ledzewicz, U.1
Schättler, H.2
-
22
-
-
67650860391
-
On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis
-
Ledzewicz U., and Schättler H. On the optimality of singular controls for a class of mathematical models for tumor anti-angiogenesis. Disc. Cont. Dyn. Syst. Ser. B 11 (2009) 691
-
(2009)
Disc. Cont. Dyn. Syst. Ser. B
, vol.11
, pp. 691
-
-
Ledzewicz, U.1
Schättler, H.2
-
23
-
-
70349932156
-
Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models
-
Ledzewicz U., Munden J., and Schättler H. Scheduling of angiogenic inhibitors for Gompertzian and logistic tumor growth models. Disc. Cont. Dyn. Syst. Ser. B 12 (2009) 415
-
(2009)
Disc. Cont. Dyn. Syst. Ser. B
, vol.12
, pp. 415
-
-
Ledzewicz, U.1
Munden, J.2
Schättler, H.3
-
24
-
-
50249189054
-
Control problems related to tumor angiogenesis
-
IEEE Press, New York
-
A. Swierniak, A. d'Onofrio, A. Gandolfi, Control problems related to tumor angiogenesis, in: Proceedings of the IECON 2006, IEEE Press, New York, 2006, pp. 677-681.
-
(2006)
Proceedings of the IECON
, pp. 677-681
-
-
Swierniak, A.1
d'Onofrio, A.2
Gandolfi, A.3
-
25
-
-
57749120581
-
Direct and indirect control of cancer populations
-
Swierniak A. Direct and indirect control of cancer populations. Bull. Pol. Acad. Sci. Technol. Sci. 56 (2008) 367
-
(2008)
Bull. Pol. Acad. Sci. Technol. Sci.
, vol.56
, pp. 367
-
-
Swierniak, A.1
-
26
-
-
0003297714
-
Mathematical models in cell biology and cancer chemotherapy
-
Springer, Berlin
-
Eisen M. Mathematical models in cell biology and cancer chemotherapy. Lecture Notes in Biomathematics vol. 30 (1979), Springer, Berlin
-
(1979)
Lecture Notes in Biomathematics
, vol.30
-
-
Eisen, M.1
-
27
-
-
67650875107
-
Optimal treatment protocols in leukemia - modelling the proliferation cycle
-
Paris
-
A. Swierniak, Optimal treatment protocols in leukemia - modelling the proliferation cycle, in: Proceedings of the 12th IMACS World Congress, Paris, vol. 4, 1988, pp. 170-172.
-
(1988)
Proceedings of the 12th IMACS World Congress
, vol.4
, pp. 170-172
-
-
Swierniak, A.1
-
28
-
-
0025049681
-
Role of optimal control in cancer chemotherapy
-
Swan G.W. Role of optimal control in cancer chemotherapy. Math. Biosci. 101 (1990) 237
-
(1990)
Math. Biosci.
, vol.101
, pp. 237
-
-
Swan, G.W.1
-
29
-
-
0002747592
-
Cell cycle as an object of control
-
Swierniak A. Cell cycle as an object of control. J. Biol. Syst. 3 (1995) 41
-
(1995)
J. Biol. Syst.
, vol.3
, pp. 41
-
-
Swierniak, A.1
-
30
-
-
0029938149
-
Optimal control problems arising in cell-cycle-specific cancer chemotherapy
-
Swierniak A., Polanski A., and Kimmel M. Optimal control problems arising in cell-cycle-specific cancer chemotherapy. Cell Prolif. 29 (1996) 17
-
(1996)
Cell Prolif.
, vol.29
, pp. 17
-
-
Swierniak, A.1
Polanski, A.2
Kimmel, M.3
-
31
-
-
0033687699
-
Optimal control applied to cell-cycle-specific cancer chemotherapy
-
Fister K.R., and Panetta J.C. Optimal control applied to cell-cycle-specific cancer chemotherapy. SIAM J. Appl. Math. 60 (2000) 1059
-
(2000)
SIAM J. Appl. Math.
, vol.60
, pp. 1059
-
-
Fister, K.R.1
Panetta, J.C.2
-
32
-
-
1542517195
-
Optimal bang-bang controls for a two-compartment model in cancer chemotherapy
-
Ledzewicz U., and Schättler H. Optimal bang-bang controls for a two-compartment model in cancer chemotherapy. J. Optim. Theor. Appl. - JOTA 114 (2002) 609
-
(2002)
J. Optim. Theor. Appl. - JOTA
, vol.114
, pp. 609
-
-
Ledzewicz, U.1
Schättler, H.2
-
33
-
-
0003328875
-
Analysis of a cell-cycle-specific model for cancer chemotherapy
-
Ledzewicz U., and Schättler H. Analysis of a cell-cycle-specific model for cancer chemotherapy. J. Biol. Syst. 10 (2002) 183
-
(2002)
J. Biol. Syst.
, vol.10
, pp. 183
-
-
Ledzewicz, U.1
Schättler, H.2
-
36
-
-
33947585997
-
Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy
-
Ledzewicz U., and Schättler H. Optimal controls for a model with pharmacokinetics maximizing bone marrow in cancer chemotherapy. Math. Biosci. 206 (2007) 320
-
(2007)
Math. Biosci.
, vol.206
, pp. 320
-
-
Ledzewicz, U.1
Schättler, H.2
-
38
-
-
33746656314
-
Optimal control in a model of dendritic cell transfection cancer immunotherapy
-
Castiglione F., and Piccoli B. Optimal control in a model of dendritic cell transfection cancer immunotherapy. Bull. Math. Biol. 68 (2006) 255
-
(2006)
Bull. Math. Biol.
, vol.68
, pp. 255
-
-
Castiglione, F.1
Piccoli, B.2
-
39
-
-
0035738977
-
A mathematical tumor model with immune resistance and drug therapy: an optimal control approach
-
de Pillis L.G., and Radunskaya A. A mathematical tumor model with immune resistance and drug therapy: an optimal control approach. J. Theor. Med. 3 (2001) 79
-
(2001)
J. Theor. Med.
, vol.3
, pp. 79
-
-
de Pillis, L.G.1
Radunskaya, A.2
-
40
-
-
34748922274
-
Rapidly acting antitumoral anti-angiogenic therapies
-
d'Onofrio A. Rapidly acting antitumoral anti-angiogenic therapies. Phys. Rev. E 76 3 (2007) 031920
-
(2007)
Phys. Rev. E
, vol.76
, Issue.3
, pp. 031920
-
-
d'Onofrio, A.1
-
43
-
-
0035953488
-
Simple ODE models of tumor growth and anti-angiogenic or radiation treatment
-
Sachs R.K., Hlatky L.R., and Hahnfeldt P. Simple ODE models of tumor growth and anti-angiogenic or radiation treatment. Math. Comput. Mod. 33 (2001) 1297
-
(2001)
Math. Comput. Mod.
, vol.33
, pp. 1297
-
-
Sachs, R.K.1
Hlatky, L.R.2
Hahnfeldt, P.3
-
44
-
-
65349170905
-
The dynamics of tumour-vasculature interaction suggests low-dose, time-dense antiangiogenic schedulings
-
d'Onofrio A., Gandolfi A., and Rocca A. The dynamics of tumour-vasculature interaction suggests low-dose, time-dense antiangiogenic schedulings. Cell Prolif. 42 (2009) 317
-
(2009)
Cell Prolif.
, vol.42
, pp. 317
-
-
d'Onofrio, A.1
Gandolfi, A.2
Rocca, A.3
-
45
-
-
67349108817
-
Fractal growth of tumors and other cellular populations: linking the mechanistic to the phenomenological modeling and vice versa
-
d'Onofrio A. Fractal growth of tumors and other cellular populations: linking the mechanistic to the phenomenological modeling and vice versa. Chaos, Sol. Frac. 41 (2009) 875
-
(2009)
Chaos, Sol. Frac.
, vol.41
, pp. 875
-
-
d'Onofrio, A.1
-
46
-
-
23144445934
-
A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences
-
d'Onofrio A. A general framework for modeling tumor-immune system competition and immunotherapy: mathematical analysis and biomedical inferences. Physica D 208 (2005) 220
-
(2005)
Physica D
, vol.208
, pp. 220
-
-
d'Onofrio, A.1
-
48
-
-
59149085863
-
A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy
-
d'Onofrio A., and Cerrai A. A bi-parametric model for the tumour angiogenesis and antiangiogenesis therapy. Math. Comput. Model. 49 (2009) 1156
-
(2009)
Math. Comput. Model.
, vol.49
, pp. 1156
-
-
d'Onofrio, A.1
Cerrai, A.2
-
49
-
-
62249148684
-
A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy
-
d'Onofrio A., and Gandolfi A. A family of models of angiogenesis and anti-angiogenesis anti-cancer therapy. Math. Med. Biol. 26 (2009) 63
-
(2009)
Math. Med. Biol.
, vol.26
, pp. 63
-
-
d'Onofrio, A.1
Gandolfi, A.2
-
50
-
-
0742304073
-
Simulation of tumour-induced angiogenesis and its response to anti-angiogenic drug treatment: mode of drug delivery and clearance rate dependencies
-
Tee D., and Di Stefano III J. Simulation of tumour-induced angiogenesis and its response to anti-angiogenic drug treatment: mode of drug delivery and clearance rate dependencies. J. Cancer Res. Clin. Oncol. 130 (2004) 15
-
(2004)
J. Cancer Res. Clin. Oncol.
, vol.130
, pp. 15
-
-
Tee, D.1
Di Stefano III, J.2
-
51
-
-
34250345272
-
Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies
-
Kohandel M., Kardar M., Sivaloganathan S., and Milosevic M. Dynamics of tumor growth and combination of anti-angiogenic and cytotoxic therapies. Phys. Med. Biol. 52 (2007) 3665
-
(2007)
Phys. Med. Biol.
, vol.52
, pp. 3665
-
-
Kohandel, M.1
Kardar, M.2
Sivaloganathan, S.3
Milosevic, M.4
-
52
-
-
0034032882
-
Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer
-
Browder T., Butterfield C.E., Kraling B.M., Shi B., Marshall B., O'Reilly M.S., and Folkman J. Antiangiogenic scheduling of chemotherapy improves efficacy against experimental drug-resistant cancer. Cancer Res. 60 (2000) 1878
-
(2000)
Cancer Res.
, vol.60
, pp. 1878
-
-
Browder, T.1
Butterfield, C.E.2
Kraling, B.M.3
Shi, B.4
Marshall, B.5
O'Reilly, M.S.6
Folkman, J.7
-
53
-
-
0036225350
-
Low-dose oral methotrexate and cyclophosphamide in metastatic breast cancer: antitumour activity and correlation with vascular endothelial growth factor levels
-
Colleoni M., Rocca A., Sandri M.T., Zorzino L., Masci G., Nole F., Peruzzotti G., Robertson C., Orlando L., Cinieri S., de Braud F., Viale G., and Goldhirsch A. Low-dose oral methotrexate and cyclophosphamide in metastatic breast cancer: antitumour activity and correlation with vascular endothelial growth factor levels. Ann. Oncol. 13 (2002) 73
-
(2002)
Ann. Oncol.
, vol.13
, pp. 73
-
-
Colleoni, M.1
Rocca, A.2
Sandri, M.T.3
Zorzino, L.4
Masci, G.5
Nole, F.6
Peruzzotti, G.7
Robertson, C.8
Orlando, L.9
Cinieri, S.10
de Braud, F.11
Viale, G.12
Goldhirsch, A.13
-
54
-
-
34248997771
-
Understanding the role of the tumour vasculature in the transport of drugs to solid cancer tumors
-
Wijeratne N.S., and Hoo K.A. Understanding the role of the tumour vasculature in the transport of drugs to solid cancer tumors. Cell Prolif. 40 (2007) 283
-
(2007)
Cell Prolif.
, vol.40
, pp. 283
-
-
Wijeratne, N.S.1
Hoo, K.A.2
-
55
-
-
85128563124
-
-
U. Ledzewicz, H. Schättler, A. d'Onofrio, Optimal control for combination therapy in cancer, in: Proceedings of the 47th IEEE Conference on Dec. and Control, Cancun, Mexico, 2008, pp. 1537-1542.
-
U. Ledzewicz, H. Schättler, A. d'Onofrio, Optimal control for combination therapy in cancer, in: Proceedings of the 47th IEEE Conference on Dec. and Control, Cancun, Mexico, 2008, pp. 1537-1542.
-
-
-
-
57
-
-
11844254028
-
Singular trajectories and their role in control theory
-
Springer, Paris
-
Bonnard B., and Chyba M. Singular trajectories and their role in control theory. Mathématiques & Applications vol. 40 (2003), Springer, Paris
-
(2003)
Mathématiques & Applications
, vol.40
-
-
Bonnard, B.1
Chyba, M.2
-
59
-
-
1542373172
-
Sensitivity analysis and real-time optimization of parametric nonlinear programming problems
-
Grötschel M., et al. (Ed), Springer, Berlin
-
Büskens C., and Maurer H. Sensitivity analysis and real-time optimization of parametric nonlinear programming problems. In: Grötschel M., et al. (Ed). Online Optimization of Large Scale Systems (2001), Springer, Berlin 3
-
(2001)
Online Optimization of Large Scale Systems
, pp. 3
-
-
Büskens, C.1
Maurer, H.2
-
60
-
-
0034255101
-
SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control
-
Büskens C., and Maurer H. SQP-methods for solving optimal control problems with control and state constraints: adjoint variables, sensitivity analysis and real-time control. J. Comput. Appl. Math. 120 (2000) 85
-
(2000)
J. Comput. Appl. Math.
, vol.120
, pp. 85
-
-
Büskens, C.1
Maurer, H.2
-
61
-
-
21244449627
-
Optimization methods for the verification of second order sufficient conditions for bang-bang controls
-
Maurer H., Büskens C., Kim J.-H.R., and Kaya C.Y. Optimization methods for the verification of second order sufficient conditions for bang-bang controls. Opt. Control Appl. Meth. 26 (2005) 129
-
(2005)
Opt. Control Appl. Meth.
, vol.26
, pp. 129
-
-
Maurer, H.1
Büskens, C.2
Kim, J.-H.R.3
Kaya, C.Y.4
-
62
-
-
72149107680
-
Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment, Math
-
in press
-
U. Ledzewicz, J. Marriott, H. Maurer, H. Schättler, Realizable protocols for optimal administration of drugs in mathematical models for anti-angiogenic treatment, Math. Med. Biol., in press.
-
Med. Biol
-
-
Ledzewicz, U.1
Marriott, J.2
Maurer, H.3
Schättler, H.4
|