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

Alacia M. Voth; John G. Alford; Edward W. Swim; Alacia M. Voth; John G. Alford; Edward W. Swim

doi:10.3934/mbe.2017043

Mathematical Biosciences and Engineering

2017, Volume 14, Issue 3: 777-804. doi: 10.3934/mbe.2017043

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

1.
United Services Automobile Association, 9800 Fredericksburg Rd, San Antonio, TX 78288, USA
2.
Sam Houston State University, Department of Mathematics and Statistics, Huntsville, TX 77341, USA

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.
- Prostate cancer,
- androgen suppression,
- differential equations,
- sensitivity functions,
- relapse
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

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Abstract

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.

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