System identification and parameter estimation in mathematical medicine: examples demonstrated for prostate cancer

Ideta, A. M., Tanaka, G., Takeuchi, T. and Aihara, K. (2008) A mathematical model of intermittent androgen suppression for prostate cancer. J. Nonlinear Sci., 18, 593–614 Shimada, T. and Aihara, K. (2008) A nonlinear model with competition between prostate tumor cells and its application to intermittent androgen suppression therapy of prostate cancer. Math. Biosci., 214, 134–139 Hirata, Y., Bruchovsky, N. and Aihara, K. (2010) Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer. J. Theor. Biol., 264, 517–527 Jain, H. V., Clinton, S. K., Bhinder, A. and Friedman, A. (2011) Mathematical modeling of prostate cancer progression in response to androgen ablation therapy. Proc. Natl. Acad. Sci. USA, 108, 19701–19706 Portz, T., Kuang, Y. and Nagy, J. D. (2012) A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy. AIP Adv., 2, 011002. Akakura, K., Bruchovsky, N., Goldenberg, S. L., Rennie, P. S., Buckley, A. R. and Sullivan, L. D. (1993) Effects of intermittent androgen suppression on androgen-dependent tumors. Apoptosis and serum prostate-specific antigen. Cancer, 71, 2782–2790 Bruchovsky, N., Klotz, L., Crook, J., Malone, S., Ludgate, C., Morris, W. J., Gleave, M. E. and Goldenberg, S. L. (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: clinical parameters. Cancer, 107, 389–395 Bruchovsky, N., Klotz, L., Crook, J. and Goldenberg, S. L. (2007) 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, 858–867 Crook, J. M., O’Callaghan, C. J., Duncan, G., Dearnaley, D. P., Higano, C. S., Horwitz, E. M., Frymire, E., Malone, S., Chin, J., Nabid, A., et al. (2012) Intermittent androgen suppression for rising PSA level after radiotherapy. N. Engl. J. Med., 367, 895–903 Hussain, M., Tangen, C. M., Berry, D. L., Higano, C. S., Crawford, E. D., Liu, G., Wilding, G., Prescott, S., Kanaga Sundaram, S., Small, E. J., et al. (2013) Intermittent versus continuous androgen deprivation in prostate cancer. N. Engl. J. Med., 368, 1314–1325 Morino, K., Hirata, Y., Tomioka, R., Kashima, H., Yamanishi, K., Hayashi, N., Egawa, S. and Aihara, K. (2015) Predicting disease progression from short biomarker series using expert advice algorithm. Sci. Rep., 5, 8953 Hirata, Y., Morino, K., Akakura, K., Higano, C. S., Bruchovsky, N., Gambol, T., Hall, S., Tanaka, G. and Aihara, K. (2015) Intermittent androgen suppression: Estimating parameters for individual patients based on initial PSA data in response to androgen deprivation therapy. PLoS One, 10, e0130372 Suzuki, T., Bruchovsky, N. and Aihara, K. (2010) Piecewise affine systems modelling for optimizing hormone therapy of prostate cancer. Philos. Trans. A Math. Phys. Eng. Sci., 368, 5045–5059 Hirata, Y., di Bernardo, M., Bruchovsky, N. and Aihara, K. (2010) Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer. Chaos, 20, 045125 Hirata, Y., Azuma, S. and Aihara, K. (2014) Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer. Methods, 67, 278–281 Tanaka, G., Hirata, Y., Goldenberg, S. L., Bruchovsky, N. and Aihara, K. (2010) Mathematical modelling of prostate cancer growth and its application to hormone therapy. Philos. Trans. A Math. Phys. Eng. Sci., 368, 5029–5044 Kuramae, H., Hirata, Y., Bruchovsky, N., Aihara, K. and Suzuki, H. (2011) Nonlinear systems identification by combining regression with bootstrap resampling. Chaos, 21, 043121 Hirata, Y., Akakura, K., Higano, C. S., Bruchovsky, N. and Aihara, K. (2012) Quantitative mathematical modeling of PSA dynamics of prostate cancer patients treated with intermittent androgen suppression. J. Mol. Cell Biol., 4, 127–132 Guo, Q., Lu, Z., Hirata, Y. and Aihara, K. (2013) Parameter estimation and optimal scheduling algorithm for a mathematical model of intermittent androgen suppression therapy for prostate cancer. Chaos, 23, 043125 Suzuki, T. and Aihara, K. (2013) Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy. Math. Biosci., 245, 40–48 Suzuki, Y., Sakai, D., Nomura, T., Hirata, Y. and Aihara, K. (2014) A new protocol for intermittent androgen suppression therapy of prostate cancer with unstable saddle-point dynamics. J. Theor. Biol., 350, 1–16 Tao, Y., Guo, Q. and Aihara, K. (2015) A partial differential equation model and its reduction to an ordinary differential equation model for prostate tumor growth under intermitten thormone therapy. J. Math. Biol., 69, 817–838 Cover, T.M. and Thomas, J. A. (1991) Elements of Information Theory. New York: Wiley Interscience Publication