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

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• 作者：Yoshito Hirata ; Kai Morino ; Taiji Suzuki ; Qian Guo…
• 关键词：mathematical medicine ; dynamical model ; parameter estimation
• 刊名：Quantitative Biology
• 出版年：2016
• 出版时间：March 2016
• 年：2016
• 卷：4
• 期：1
• 页码：13-19
• 全文大小：161 KB
• 参考文献：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, 593–614CrossRef
  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, 134–139CrossRef PubMed
  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, 517–527CrossRef PubMed
  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. USA, 108, 19701–19706CrossRef PubMed PubMedCentral
  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.CrossRef
  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, 2782–2790PubMed
  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, 389–395CrossRef PubMed
  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, 858–867CrossRef PubMed
  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., et al. (2012) Intermittent androgen suppression for rising PSA level after radiotherapy. N. Engl. J. Med., 367, 895–903CrossRef PubMed PubMedCentral
  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., et al. (2013) Intermittent versus continuous androgen deprivation in prostate cancer. N. Engl. J. Med., 368, 1314–1325CrossRef PubMed PubMedCentral
  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, 8953CrossRef PubMed
  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, e0130372CrossRef PubMed PubMedCentral
  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, 5045–5059CrossRef PubMed
  14.Hirata, Y., di Bernardo, M., Bruchovsky, N. and Aihara, K. (2010) Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer. Chaos, 20, 045125CrossRef PubMed
  15.Hirata, Y., Azuma, S. and Aihara, K. (2014) Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer. Methods, 67, 278–281CrossRef PubMed
  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, 5029–5044CrossRef PubMed
  17.Kuramae, H., Hirata, Y., Bruchovsky, N., Aihara, K. and Suzuki, H. (2011) Nonlinear systems identification by combining regression with bootstrap resampling. Chaos, 21, 043121CrossRef PubMed
  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, 127–132CrossRef PubMed PubMedCentral
  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, 043125CrossRef PubMed
  20.Suzuki, T. and Aihara, K. (2013) Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy. Math. Biosci., 245, 40–48CrossRef PubMed
  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, 1–16CrossRef PubMed
  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 intermitten thormone therapy. J. Math. Biol., 69, 817–838CrossRef
  23.Cover, T.M. and Thomas, J. A. (1991) Elements of Information Theory. New York: Wiley Interscience PublicationCrossRef
  
• 作者单位：Yoshito Hirata (1) (2)
  Kai Morino (2)
  Taiji Suzuki (3)
  Qian Guo (4)
  Hiroshi Fukuhara (5)
  Kazuyuki Aihara (1) (2)
  
  1. Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan
  2. Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan
  3. Department of Mathematical and Computing Sciences, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan
  4. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China
  5. Department of Urology, Graduate School of Medicine, The University of Tokyo, Tokyo, 113-8655, Japan
  
• 刊物主题：Bioinformatics; Computational Biology/Bioinformatics; Computer Appl. in Life Sciences; Mathematical and Computational Biology;
• 出版者：Springer Berlin Heidelberg
• ISSN：2095-4697

文摘

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. Keywords mathematical medicine dynamical model parameter estimation Page %P Close Plain text Look Inside Reference tools Export citation EndNote (.ENW) JabRef (.BIB) Mendeley (.BIB) Papers (.RIS) Zotero (.RIS) BibTeX (.BIB) Add to Papers Other actions Register for Journal Updates About This Journal Reprints and Permissions Share Share this content on Facebook Share this content on Twitter Share this content on LinkedIn Related Content Supplementary Material (0) References (23) References1.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, 593–614CrossRef2.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, 134–139CrossRefPubMed3.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, 517–527CrossRefPubMed4.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, 19701–19706CrossRefPubMedPubMedCentral5.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.CrossRef6.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, 2782–2790PubMed7.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, 389–395CrossRefPubMed8.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, 858–867CrossRefPubMed9.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, 895–903CrossRefPubMedPubMedCentral10.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, 1314–1325CrossRefPubMedPubMedCentral11.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, 8953CrossRefPubMed12.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, e0130372CrossRefPubMedPubMedCentral13.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, 5045–5059CrossRefPubMed14.Hirata, Y., di Bernardo, M., Bruchovsky, N. and Aihara, K. (2010) Hybrid optimal scheduling for intermittent androgen suppression of prostate cancer. Chaos, 20, 045125CrossRefPubMed15.Hirata, Y., Azuma, S. and Aihara, K. (2014) Model predictive control for optimally scheduling intermittent androgen suppression of prostate cancer. Methods, 67, 278–281CrossRefPubMed16.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, 5029–5044CrossRefPubMed17.Kuramae, H., Hirata, Y., Bruchovsky, N., Aihara, K. and Suzuki, H. (2011) Nonlinear systems identification by combining regression with bootstrap resampling. Chaos, 21, 043121CrossRefPubMed18.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, 127–132CrossRefPubMedPubMedCentral19.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, 043125CrossRefPubMed20.Suzuki, T. and Aihara, K. (2013) Nonlinear system identification for prostate cancer and optimality of intermittent androgen suppression therapy. Math. Biosci., 245, 40–48CrossRefPubMed21.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, 1–16CrossRefPubMed22.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, 817–838CrossRef23.Cover, T.M. and Thomas, J. A. (1991) Elements of Information Theory. New York: Wiley Interscience PublicationCrossRef About this Article Title System identification and parameter estimation in mathematical medicine: examples demonstrated for prostate cancer Journal Quantitative Biology Volume 4, Issue 1 , pp 13-19 Cover Date2016-03 DOI 10.1007/s40484-016-0059-0 Print ISSN 2095-4689 Online ISSN 2095-4697 Publisher Higher Education Press Additional Links Register for Journal Updates Editorial Board About This Journal Manuscript Submission Topics Bioinformatics Computational Biology/Bioinformatics Computer Appl. in Life Sciences Mathematical and Computational Biology Keywords mathematical medicine dynamical model parameter estimation Authors Yoshito Hirata (1) (2) Kai Morino (2) Taiji Suzuki (3) Qian Guo (4) Hiroshi Fukuhara (5) Kazuyuki Aihara (1) (2) Author Affiliations 1. Institute of Industrial Science, The University of Tokyo, Tokyo, 153-8505, Japan 2. Graduate School of Information Science and Technology, The University of Tokyo, Tokyo, 113-8656, Japan 3. Department of Mathematical and Computing Sciences, Graduate School of Information Science and Engineering, Tokyo Institute of Technology, Tokyo, 152-8552, Japan 4. Department of Mathematics, Shanghai Normal University, Shanghai, 200234, China 5. Department of Urology, Graduate School of Medicine, The University of Tokyo, Tokyo, 113-8655, Japan Continue reading... To view the rest of this content please follow the download PDF link above.