1887
banner image
No data available.
Please log in to see this content.
You have no subscription access to this content.
No metrics data to plot.
The attempt to load metrics for this article has failed.
The attempt to plot a graph for these metrics has failed.
The full text of this article is not currently available.
oa
Parameter estimation and optimal scheduling algorithm for a mathematical model of intermittent androgen suppression therapy for prostate cancer
Rent:
Rent this article for
Access full text Article
/content/aip/journal/chaos/23/4/10.1063/1.4833455
1.
1. R. Siegel, E. Ward, O. Brawley, and A. Jemal, “ Cancer statistics, 2011: The impact of eliminating socioeconomic and racial disparities on premature cancer deaths,” Ca-Cancer J. Clin. 61, 212236 (2011).
http://dx.doi.org/10.3322/caac.20121
2.
2. Y. Hirata, N. Bruchovsky, and K. Aihara, “ Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer,” J. Theor. Biol. 264, 517527 (2010).
http://dx.doi.org/10.1016/j.jtbi.2010.02.027
3.
3. F. Bladou, R. Vessella, K. Buhler, W. Ells, L. True, and P. Lange, “ Cell proliferation and apoptosis during prostatic tumor xenograft involution and regrowth after castration,” Int. J. Cancer 67, 785790 (1996).
http://dx.doi.org/10.1002/(SICI)1097-0215(19960917)67:6<785::AID-IJC6>3.0.CO;2-N
4.
4. P. Rennie, N. Bruchovsky, and A. Coldman, “ Loss of androgen dependence is associated with an increase in tumorigenic stem cells and resistance to cell-death genes,” J. Steroid Biochem. Mol. Biol. 37, 843847 (1990).
http://dx.doi.org/10.1016/0960-0760(90)90430-S
5.
5. M. Kollmeier and M. Zelefsky, “ What is the role of androgen deprivation therapy in the treatment of locally advanced prostate cancer?,” Nat. Clin. Pract. Urol. 5, 584585 (2008).
http://dx.doi.org/10.1038/ncpuro1217
6.
6. K. Akakura, N. Bruchovsky, S. Goldenbeg, P. Rennie, A. Buckley, and L. Sullivan, “ Effects of intermittent androgen suppression on androgen-dependent tumors: Apoptosis and serum prostate-specific antigen,” Cancer 71, 27822790 (1993).
http://dx.doi.org/10.1002/1097-0142(19930501)71:9<2782::AID-CNCR2820710916>3.0.CO;2-Z
7.
7. N. Bruchovsky, P. Rennie, A. Coldman, S. Goldenberg, M. To, and D. Lawson, “ Effects of androgen withdrawal on the stem cell composition of the Shionogi carcinoma,” Cancer Res. 50, 22752282 (1990).
8.
8. P. Abrahamsson, “ Potential benefits of intermittent androgen suppression therapy in the treatment of prostate cancer: A systematic review of the literature,” Eur. Urol. 57, 4959 (2010).
http://dx.doi.org/10.1016/j.eururo.2009.07.049
9.
9. N. Bruchovsky, L. Klotz, M. Sadar, J. Crook, D. Hoffart, L. Godwin, M. Warkentin, M. Gleave, and S. Goldenberg, “ Intermittent androgen suppression for prostate cancer: Canadian prospective trial and related observations,” Mol. Urol. 4, 191199 (2000).
10.
10. N. Bruchovsky, L. Klotz, J. Crook, S. Malone, C. Ludgte, W. Morris, M. Gleave, and S. Goldenberg, “ Final results of the Canadian prospective phase II trial of intermittent androgen suppression for men in biochemical recurrence after radiotherapy for locally advanced prostate cancer: Clinical parameters,” Cancer 107, 389395 (2006).
http://dx.doi.org/10.1002/cncr.21989
11.
11. N. Bruchovsky, L. Klotz, J. Crook, S. Larry, and S. Goldenberg, “ Locally advanced prostate cancer—biochemical results from a prospective phase II study of intermittent androgen suppression for men with evidence of prostate-specific antigen recurrence after radiotherapy,” Cancer 109, 858867 (2007).
http://dx.doi.org/10.1002/cncr.22464
12.
12. T. Jackson, “ A mathematical model of prostate tumor growth and androgen-independent relapse,” Discrete Contin. Dyn. Syst., Ser. B 4, 187201 (2004).
http://dx.doi.org/10.3934/dcdsb.2004.4.187
13.
13. T. Jackson, “ A mathematical investigation of multiple pathways to recurrent prostate cancer: Comparison with experiment data,” Neoplasia 6, 697704 (2004).
http://dx.doi.org/10.1593/neo.04259
14.
14. Y. Tao, Q. Guo, and K. Aihara, “ A mathematical model of prostate tumor growth under hormone therapy with mutation inhibitor,” J. Nonlinear Sci. 20, 219240 (2010).
http://dx.doi.org/10.1007/s00332-009-9056-z
15.
15. A. Ideta, G. Tanaka, T. Takeuchi, and K. Aihara, “ A mathematical model of intermittent androgen suppression for prostate cancer,” J. Nonlinear Sci. 18, 593614 (2008).
http://dx.doi.org/10.1007/s00332-008-9031-0
16.
16. T. Shimada and K. Aihara, “ A nonlinear model with competition between prostate tumor cells and its application to intermittent androgen suppression therapy of prostate cancer,” Math. Biosci. 214, 134139 (2008).
http://dx.doi.org/10.1016/j.mbs.2008.03.001
17.
17. Q. Guo, Y. Tao, and K. Aihara, “ Mathematical modeling of prostate tumor growth under intermittent androgen suppression with partial differential equations,” Int. J. Bifurcation Chaos 18, 37893797 (2008).
http://dx.doi.org/10.1142/S0218127408022743
18.
18. Y. Tao, Q. Guo, and K. Aihara, “ A model at the macroscopic scale of prostate tumor growth under intermittent androgen suppression,” Math. Models Meth. Appl. Sci. 19, 21772201 (2009).
http://dx.doi.org/10.1142/S021820250900408X
19.
19. B. Feldman and D. Feldman, “ The development of androgen-independent prostate cancer,” Nat. Rev. Cancer 1, 3445 (2001).
http://dx.doi.org/10.1038/35094009
20.
20. P. Rennie, J. Read, and L. Murphy, “ Hormones and cancer,” The Basic Science of Oncology (McGraw–Hill, 2005).
21.
21. T. Suzuki, N. Bruchovsky, and K. Aihara, “ Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer,” Philos. Trans. R. Soc. London, Ser. A 368, 50455059 (2010).
http://dx.doi.org/10.1098/rsta.2010.0220
22.
22. T. Suzuki and K. Aihara, “ Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy,” Math. Biosci. 245, 4048 (2013).
http://dx.doi.org/10.1016/j.mbs.2013.04.007
23.
23. Y. Hirata, M. di Bernardo, N. Bruchovsky, and K. Aihara, “ Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer,” Chaos 20, 045125 (2010).
http://dx.doi.org/10.1063/1.3526968
24.
24. G. Tanaka, Y. Hirata, S. Goldenberg, N. Bruchovsky, and K. Aihara, “ Mathematical modelling of prostate cancer growth and its application to hormone therapy,” Philos. Trans. R. Soc. London, Ser. A 368, 50295044 (2010).
http://dx.doi.org/10.1098/rsta.2010.0221
25.
25. Y. Tao, Q. Guo, and K. Aihara, “ A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermittent hormone therapy,” J. Math. Biol. (published online).
http://dx.doi.org/10.1007/s00285-013-0718-y
26.
26. R. Rubinstein, “ Optimization of computer simulation models with rare events,” Eur. J. Oper. Res. 99, 89112 (1997).
http://dx.doi.org/10.1016/S0377-2217(96)00385-2
27.
27. R. Rubinstein, “ The cross-entropy method for combinatorial and continuous optimization,” Methodol. Comput. Appl. Probab. 1, 127190 (1999).
http://dx.doi.org/10.1023/A:1010091220143
28.
28. R. Rubinstein and D. Kroese, The Cross-Entropy Method: A Unified Approach to Combinatorial Optimization, Monte-Carlo Simulation, and Machine Learning (Springer, New York, 2004).
29.
29. P. D. Boer, D. Kroese, S. Mannor, and R. Rubinstein, “ A tutorial on the cross-entropy method,” Ann. Operat. Res. 134, 1967 (2005).
http://dx.doi.org/10.1007/s10479-005-5724-z
30.
30. D. Kroese, S. Porotsky, and R. Rubinstein, “ The cross-entropy method for continuous multi-extremal optimization,” Methodol. Comput. Appl. Probab. 8, 383407 (2006).
http://dx.doi.org/10.1007/s11009-006-9753-0
31.
31. B. Wang, “ Parameter estimation for ODEs using a cross-entropy approach,” MS thesis (University of Toronto, 2012).
32.
32. X. Xu and P. Antsaklis, “ Optimal control of switched autonomous systems,” in Proceedings of the 41st IEEE Conference on Decision and Control (Las Vegas, 2002), pp. 44014406.
33.
33. X. Xu and P. Antsaklis, “ Optimal control of switched systems via nonlinear optimization based on direct differentiations of value functions,” Int. J. Contr. 75, 14061426 (2002).
http://dx.doi.org/10.1080/0020717021000023825
34.
34. X. Xu and P. Antsaklis, “ Optimal control of switched systems based on parametrization of the switching instants,” IEEE Trans. Autom. Control 49, 216 (2004).
http://dx.doi.org/10.1109/TAC.2003.821417
35.
35. M. Kamgarpour and C. Tomlin, “ On optimal control of non-autonomous switched systems with a fixed mode sequence,” Automatica 48, 11771181 (2012).
http://dx.doi.org/10.1016/j.automatica.2012.03.019
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4833455
Loading
/content/aip/journal/chaos/23/4/10.1063/1.4833455
Loading

Data & Media loading...

Loading

Article metrics loading...

/content/aip/journal/chaos/23/4/10.1063/1.4833455
2013-11-22
2014-10-20

Abstract

We propose an algorithm based on cross-entropy to determine parameters of a piecewise linear model, which describes intermittent androgen suppression therapy for prostate cancer. By comparing with clinical data, the parameter estimation for the switched system shows good fitting accuracy and efficiency. We further optimize switching time points for the piecewise linear model to obtain a feasible therapeutic schedule. The simulation results of therapeutic effect are superior to those of previous strategy.

Loading

Full text loading...

/deliver/fulltext/aip/journal/chaos/23/4/1.4833455.html;jsessionid=286xpb087u2m1.x-aip-live-06?itemId=/content/aip/journal/chaos/23/4/10.1063/1.4833455&mimeType=html&fmt=ahah&containerItemId=content/aip/journal/chaos
true
true
This is a required field
Please enter a valid email address
752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: Parameter estimation and optimal scheduling algorithm for a mathematical model of intermittent androgen suppression therapy for prostate cancer
http://aip.metastore.ingenta.com/content/aip/journal/chaos/23/4/10.1063/1.4833455
10.1063/1.4833455
SEARCH_EXPAND_ITEM