Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy

Mathematical Biosciences - Tập 245 - Trang 40-48 - 2013
Taiji Suzuki1, Kazuyuki Aihara1,2
1Department of Mathematical Informatics, Graduate School of Information Science and Technology, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-8656, Japan
2Institute of Industrial Science, The University of Tokyo, 4-6-1, Komaba, Meguro-ku, Tokyo 153-8505, Japan

Tài liệu tham khảo

K. Aihara (Ed.), Theme Issue, Theory of hybrid dynamical systems and its applications to biological and medical systems, Philosophical Transactions of The Royal Society A 368 (1930) (2010). Akakura, 1993, Effects of intermittent androgen suppression on androgen-dependent tumors-apoptosis and serum prostate-specific antigen, Cancer, 71, 2782, 10.1002/1097-0142(19930501)71:9<2782::AID-CNCR2820710916>3.0.CO;2-Z H. Attias, Inferring parameters and structure of latent variable models by variational Bayes, in: Proceedings of the Conference on Uncertainty in Artificial Intelligence (UAI), Stockholm, Sweden, 1999, pp. 21–30. A. Bemporad, F. Borrelli, M. Morari, Optimal controllers for hybrid systems: stability and piecewise linear explicit form, in: Proceedings of the 39th IEEE Conference on Decision and Control, Sydney, Australia, 2001, pp. 1810–1815. Bemporad, 2002, On the optimal control law of linear discrete time hybrid systems, Lecture Notes in Computer Science, 2289, 105, 10.1007/3-540-45873-5_11 Bennett, 1994, Multicategory discrimination via linear programming, Optim. Methods Softw., 3, 27, 10.1080/10556789408805554 Berges, 1993, Cell proliferation, DNA repair, and p53 function are not required for programmed death of prostatic glandular cells induced by androgen ablation, Proc. Natl. Acad. Sci. USA, 90, 8910, 10.1073/pnas.90.19.8910 Bredensteiner, 1999, Multicategory classification by support vector machines, Comput. Optim. Appl., 12, 53, 10.1023/A:1008663629662 Bruchovsky, 2006, 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, Cancer, 107, 385, 10.1002/cncr.21989 Bruchovsky, 1975, Hormonal effects on cell proliferation in rat prostate, Vitam. Horm., 33, 61, 10.1016/S0083-6729(08)60951-6 Bruchovsky, 1990, Effects of androgen withdrawal on the stem cell composition of the Shionogi carcinoma, Cancer Res., 50, 2275 Crook, 1999, Intermittent androgen suppression in the management of prostate cancer, Urology, 53, 530, 10.1016/S0090-4295(98)00547-0 Dempster, 1977, Maximum likelihood from incomplete data via the EM algorithm, J. R. Stat. Soc. Ser. B (Methodological), 39, 1 Evens, 1998, Intermittent androgen suppression as a treatment for prostate cancer: a review, The Oncologist, 3, 419, 10.1634/theoncologist.3-6-419 Goldenberg, 1995, Intermittent androgen suppression in the treatment of prostate cancer: a preliminary report, Urology, 45, 839, 10.1016/S0090-4295(99)80092-2 Heemels, 2001, Equivalence of hybrid dynamical models, Automatica, 37, 1085, 10.1016/S0005-1098(01)00059-0 Higano, 1997, Intermittent androgen suppression with leuprolide and flutamide for prostate cancer: a pilot study, Urology, 49, 79 Hirata, 2010, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer, J. Theor. Biol., 264, 517, 10.1016/j.jtbi.2010.02.027 Huggins, 1941, Studies on prostatic cancer. I. The effect of castration, estrogen and of androgen injection on serum phosphatases in metastatic carcinoma of the prostate, Cancer Res., 1, 293 Huggins, 1941, Studies on prostatic cancer. II. The effect of castration on advanced carcinoma of the prostate gland, Arch. Surg., 43, 209, 10.1001/archsurg.1941.01210140043004 Klotz, 1986, Intermittent endocrine therapy for advanced prostate-cancer, Cancer, 58, 2546, 10.1002/1097-0142(19861201)58:11<2546::AID-CNCR2820581131>3.0.CO;2-N Kuramae, 2011, Nonlinear systems identification by combining regression with bootstrap resampling, Chaos, 21, 043121, 10.1063/1.3657919 Kyprianou, 1987, Quantal relationship between prostatic dihydrotestosterone and prostatic cell content: critical threshold concept, Prostate, 11, 41, 10.1002/pros.2990110106 Noakes, 1991, The Takens embedding theorem, Int. J. Bifur. Chaos, 1, 867, 10.1142/S0218127491000634 Noble, 1977, Hormonal control of growth and progression tumors of NB rats and a theory of action, Cancer Res., 37, 82 Rashid, 2004, Intermittent androgen deprivation therapy for prostate cancer, The Oncologist, 9, 295, 10.1634/theoncologist.9-3-295 Rasmussen, 2006 Sauer, 1991, Embedology, J. Stat. Phys., 65, 579, 10.1007/BF01053745 Siegel, 2012, Cancer statistics, A Cancer J. Clin., 62, 10, 10.3322/caac.20138 Sontag, 1981, Non-linear regulation: the piecewise linear approach, IEEE Trans. Autom. Control, 26, 346, 10.1109/TAC.1981.1102596 Suzuki, 2010, Piecewise affine systems modelling for optimizing hormonal therapy of prostate cancer, Philos. Trans. A R. Soc., 368, 5045, 10.1098/rsta.2010.0220 Takens, 1981, Detecting strange attractors in turbulence, Lecture Notes Math., 898, 366, 10.1007/BFb0091924 Ueda, 2002, Bayesian model search for mixture models based on optimizing variational bounds, Neural Netw., 15, 1223, 10.1016/S0893-6080(02)00040-0 Van Der Schaft, 1998, Complementarity modelling of hybrid systems, IEEE Trans. Autom. Control, 43, 483, 10.1109/9.664151 Waterhouse, 1995, Bayesian methods for mixture of experts, Adv. Neural Inf. Proces. Syst. NIPS8, 351