Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer

  • Received: 04 August 2016 Published: 01 June 2017
  • MSC : Primary: 92C50, 93A30; Secondary: 34C60

  • Prostate cancer is one of the most prevalent types of cancer among men. It is stimulated by the androgens, or male sexual hormones, which circulate in the blood and diffuse into the tissue where they stimulate the prostate tumor to grow. One of the most important treatments for advanced prostate cancer has become androgen deprivation therapy (ADT). In this paper we present three different models of ADT for prostate cancer: continuous androgen suppression (CAS), intermittent androgen suppression (IAS), and periodic androgen suppression. Currently, many patients in the U.S. receive CAS therapy of ADT, but many undergo a relapse after several years and experience adverse side effects while receiving treatment. Some clinical studies have introduced various IAS regimens in order to delay the time to relapse, and/or to reduce the economic costs and adverse side effects. We will compute and analyze parameter sensitivity analysis for CAS and IAS which may give insight to plan effective data collection in a future clinical trial. Moreover, a periodic model for IAS is used to develop an analytical formulation for relapse times which then provides information about the sensitivity of relapse to the parameters in our models.

    Citation: Alacia M. Voth, John G. Alford, Edward W. Swim. Mathematical modeling of continuous and intermittent androgen suppression for the treatment of advanced prostate cancer[J]. Mathematical Biosciences and Engineering, 2017, 14(3): 777-804. doi: 10.3934/mbe.2017043

    Related Papers:

    [1] Ewa Majchrzak, Mikołaj Stryczyński . Dual-phase lag model of heat transfer between blood vessel and biological tissue. Mathematical Biosciences and Engineering, 2021, 18(2): 1573-1589. doi: 10.3934/mbe.2021081
    [2] Salman Lari, Hossein Rajabzadeh, Mohammad Kohandel, Hyock Ju Kwon . A holistic physics-informed neural network solution for precise destruction of breast tumors using focused ultrasound on a realistic breast model. Mathematical Biosciences and Engineering, 2024, 21(10): 7337-7372. doi: 10.3934/mbe.2024323
    [3] Dora Luz Castro-López, Macarena Trujillo, Enrique Berjano, Ricardo Romero-Mendez . Two-compartment mathematical modeling in RF tumor ablation: New insight when irreversible changes in electrical conductivity are considered. Mathematical Biosciences and Engineering, 2020, 17(6): 7980-7993. doi: 10.3934/mbe.2020405
    [4] Thaweesak Trongtirakul, Sos Agaian, Adel Oulefki . Automated tumor segmentation in thermographic breast images. Mathematical Biosciences and Engineering, 2023, 20(9): 16786-16806. doi: 10.3934/mbe.2023748
    [5] EYK Ng, Leonard Jun Cong Looi . Numerical analysis of biothermal-fluids and cardiac thermal pulse of abdominal aortic aneurysm. Mathematical Biosciences and Engineering, 2022, 19(10): 10213-10251. doi: 10.3934/mbe.2022479
    [6] Hu Dong, Gang Liu, Xin Tong . Influence of temperature-dependent acoustic and thermal parameters and nonlinear harmonics on the prediction of thermal lesion under HIFU ablation. Mathematical Biosciences and Engineering, 2021, 18(2): 1340-1351. doi: 10.3934/mbe.2021070
    [7] Chii-Dong Ho, Jr-Wei Tu, Hsuan Chang, Li-Pang Lin, Thiam Leng Chew . Optimizing thermal efficiencies of power-law fluids in double-pass concentric circular heat exchangers with sinusoidal wall fluxes. Mathematical Biosciences and Engineering, 2022, 19(9): 8648-8670. doi: 10.3934/mbe.2022401
    [8] Haiyan Song, Cuihong Liu, Shengnan Li, Peixiao Zhang . TS-GCN: A novel tumor segmentation method integrating transformer and GCN. Mathematical Biosciences and Engineering, 2023, 20(10): 18173-18190. doi: 10.3934/mbe.2023807
    [9] Hsiu-Chuan Wei . Mathematical modeling of tumor growth: the MCF-7 breast cancer cell line. Mathematical Biosciences and Engineering, 2019, 16(6): 6512-6535. doi: 10.3934/mbe.2019325
    [10] Xiao Zou, Jintao Zhai, Shengyou Qian, Ang Li, Feng Tian, Xiaofei Cao, Runmin Wang . Improved breast ultrasound tumor classification using dual-input CNN with GAP-guided attention loss. Mathematical Biosciences and Engineering, 2023, 20(8): 15244-15264. doi: 10.3934/mbe.2023682
  • Prostate cancer is one of the most prevalent types of cancer among men. It is stimulated by the androgens, or male sexual hormones, which circulate in the blood and diffuse into the tissue where they stimulate the prostate tumor to grow. One of the most important treatments for advanced prostate cancer has become androgen deprivation therapy (ADT). In this paper we present three different models of ADT for prostate cancer: continuous androgen suppression (CAS), intermittent androgen suppression (IAS), and periodic androgen suppression. Currently, many patients in the U.S. receive CAS therapy of ADT, but many undergo a relapse after several years and experience adverse side effects while receiving treatment. Some clinical studies have introduced various IAS regimens in order to delay the time to relapse, and/or to reduce the economic costs and adverse side effects. We will compute and analyze parameter sensitivity analysis for CAS and IAS which may give insight to plan effective data collection in a future clinical trial. Moreover, a periodic model for IAS is used to develop an analytical formulation for relapse times which then provides information about the sensitivity of relapse to the parameters in our models.


    [1] [ P.-A. Abrahamsson, Potential benefits of intermittent androgen suppression therapy in the treatment of prostate cancer: A systematic review of the literature, European Urology, 57 (2010): 49-59.
    [2] [ H. T. Banks,S. Dediu,S. L. Ernstberger, Sensitivity functions and their uses in inverse problems, J. Inverse Ill-Posed Probl., 15 (2007): 683-708.
    [3] [ H.T. Banks,D.M. Bortz, A parameter sensitivity methodology in the context of HIV delay equation models, J. Math. Biol., 50 (2005): 607-625.
    [4] [ N. C. Buchan,S. L. Goldenberg, Intermittent androgen suppression for prostate cancer, Nature Reviews Urology, 7 (2010): 552-560.
    [5] [ N. Chitnis,J.M. Hyman,J.M. Chushing, Determining important parameters in the spread of malaria through the sensitivity analysis of a mathematical model, Bull. Math. Biol., 70 (2008): 1272-1296.
    [6] [ R.A. Everett,A.M. Packer,Y. Kuang, Can mathematical models predict the outcomes of prostate cancer patients undergoing intermittent androgen deprivation therapy?, Biophys. Rev. Lett., 9 (2014): 139-157.
    [7] [ J. K. Hale, Ordinary Differential Equations, 2nd edition, Krieger Publishing, Malabar FL, 1980.
    [8] [ Y. Hirata,N. Bruchovsky,K. Aihara, Development of a mathematical model that predicts the outcome of hormone therapy for prostate cancer, J. Theor. Biol., 264 (2010): 517-527.
    [9] [ A.M. Ideta,G. Tanaka,T. Takeuchi,K. Aihara, A mathematical model of intermittent androgen suppression for prostate cancer, J. Nonlinear Sci., 18 (2008): 593-614.
    [10] [ H. Lepor,N.D. Shore, LHRH agonists for the treatment of prostate cancer: 2012, Reviews in Urology, 14 (2012): 1-12.
    [11] [ Prostate cancer treatment (PDQ) -Patient Version National Cancer Institute, 2016. Available from: https://www.cancer.gov/types/prostate/patient/prostate-treatment-pdq.
    [12] [ T. Portz,Y. Kuang,J.D. Nagy, A clinical data validated mathematical model of prostate cancer growth under intermittent androgen suppression therapy, AIP Advances, 2 (2012): 1-14.
    [13] [ M.H. Rashid,U.B. Chaudhary, Intermittent androgen deprivation therapy for prostate cancer, The Oncologist, 9 (2004): 295-301.
    [14] [ F.G. Rick,A.V. Schally, Bench-to-bedside development of agonists and antagonists of luteinizing hormone-releasing hormone for treatment of advanced prostate cancer, Urologic Oncology: Seminars and Original Investigations, 33 (2015): 270-274.
    [15] [ A. Sciarra,P.A. Abrahamsson,M. Brausi,M. Galsky,N. Mottet,O. Sartor,T.L.J. Tammela,F.C. da Silva, Intermittent androgen-depravation therapy in prostate cancer: a critical review focused on phase 3 trials, European Urology, 64 (2013): 722-730.
    [16] [ L.G. Stanley, Sensitivity equation methods for parameter dependent elliptic equations, Numer. Funct. Anal. Optim., 22 (2001): 721-748.
    [17] [ Y. Suzuki,D. Sakai,T. Nomura,Y. Hirata,K. Aihara, A new protocol for intermittent androgen suppresion therapy of prostate cancer with unstable saddle-point dynamics, J. Theor. Biol., 350 (2014): 1-16.
    [18] [ G. Tanaka,K. Tsumoto,S. Tsuji,K. Aihara, Analysis on a hybrid systems model of intermittent hormonal therapy for prostate cancer, Physica D, 237 (2008): 2616-2627.
    [19] [ F. Verhulst, Nonlinear Differential Equations and Dynamical Systems, 2nd edition, Springer-Verlag, Berlin, 1996.
    [20] [ L. Voth, The Exploration and Computations of Mathematical Models of Intermittent Treatment for Prostate Cancer, M. S. thesis, Sam Houston University, 2012.
  • This article has been cited by:

    1. Ephraim Agyingi, Tamas Wiandt, Sophia Maggelakis, 2016, Chapter 16, 978-3-319-30377-2, 167, 10.1007/978-3-319-30379-6_16
    2. Itzel A. Avila-Castro, Angel Ramon Hernández-Martínez, Miriam Estevez, Martha Cruz, Rodrigo Esparza, Ramiro Pérez, Angel Luis Rodríguez, Thorax thermographic simulator for breast pathologies, 2017, 15, 16656423, 143, 10.1016/j.jart.2017.01.008
    3. Mamta Agrawal, K. R. Pardasani, 2019, Chapter 28, 978-981-13-1902-0, 241, 10.1007/978-981-13-1903-7_28
    4. Ephraim Agyingi, Tamas Wiandt, Sophia Maggelakis, 2021, Chapter 2, 978-3-030-84595-7, 5, 10.1007/978-3-030-84596-4_2
  • Reader Comments
  • © 2017 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(4116) PDF downloads(686) Cited by(3)

Article outline

Figures and Tables

Figures(18)  /  Tables(3)

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog