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

Abstract

We review our studies on how to identify the most appropriate models of diseases, and how to determine their parameters in a quantitative manner given a short time series of biomarkers, using intermittent androgen deprivation therapy of prostate cancer as an example. Recently, it has become possible to estimate the specific parameters of individual patients within a reasonable time by employing the information concerning other previous patients as a prior. We discuss the importance of using multiple mathematical methods simultaneously to achieve a solid diagnosis and prognosis in the future practice of personalized medicine.

Graphical abstract

Keywords

mathematical medicine / dynamical model / parameter estimation

References

[1] 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

[2] 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

[3] 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

[4] 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. U.S.A., 108, 19701–19706

[5] 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

[6] 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

[7] 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

[8] 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

[9] 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., (2012) Intermittent androgen suppression for rising PSA level after radiotherapy. N. Engl. J. Med., 367, 895–903

[10] 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., (2013) Intermittent versus continuous androgen deprivation in prostate cancer. N. Engl. J. Med., 368, 1314–1325

[11] 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

[12] 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

[13] 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

[14] Hirata, Y., di Bernardo, M., Bruchovsky, N. and Aihara, K. (2010) Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer. Chaos, 20, 045125

[15] Hirata, Y., Azuma, S. and Aihara, K. (2014) Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer. Methods, 67, 278–281

[16] 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

[17] Kuramae, H., Hirata, Y., Bruchovsky, N., Aihara, K. and Suzuki, H. (2011) Nonlinear systems identification by combining regression with bootstrap resampling. Chaos, 21, 043121

[18] 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

[19] 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

[20] Suzuki, T. and Aihara, K. (2013) Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy. Math. Biosci., 245, 40–48

[21] 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

[22] 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 intermittenthormone therapy. J. Math. Biol., 69, 817–838

[23] Cover, T. M. and Thomas, J. A. (1991) Elements of Information Theory. New York: Wiley Interscience Publication

RIGHTS & PERMISSIONS

Higher Education Press and Springer-Verlag Berlin Heidelberg