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Mathematical Biosciences and Engineering

2013, Volume 10, Issue 3: 591-608. doi: 10.3934/mbe.2013.10.591
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A partial differential equation model of metastasized prostatic cancer

  • 1.
    Department of Mathematics, Ohio State University, Columbus, OH 43210
  • 2.
    Department of Mathematics, Florida State University, Tallahassee, FL 32308
  • Received: 01 October 2012 Accepted: 29 June 2018 Published: 01 April 2013

  • MSC : Primary: 92C40, 92C50; Secondary: 37N25.

  • Biochemically failing metastatic prostate cancer is typically treated with androgen ablation. However, due to the emergence of castration-resistant cells that can survive in low androgen concentrations, such therapy eventually fails. Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. Existence and uniqueness results are derived for the resulting free boundary problem. In particular, existence and uniqueness of solutions for all time are proven for the radially symmetric case. Finally, numerical simulations of a tumor growing in 2-dimensions with radial symmetry are carried in order to evaluate the therapeutic potential of different treatment strategies. These simulations are able to reproduce a variety of clinically observed responses to treatment, and suggest treatment strategies that may result in tumor remission, underscoring our model's potential to make a significant contribution in the field of prostate cancer therapeutics.

    Citation: Avner Friedman, Harsh Vardhan Jain. A partial differential equation model of metastasized prostatic cancer[J]. Mathematical Biosciences and Engineering, 2013, 10(3): 591-608. doi: 10.3934/mbe.2013.10.591

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  • Biochemically failing metastatic prostate cancer is typically treated with androgen ablation. However, due to the emergence of castration-resistant cells that can survive in low androgen concentrations, such therapy eventually fails. Here, we develop a partial differential equation model of the growth and response to treatment of prostate cancer that has metastasized to the bone. Existence and uniqueness results are derived for the resulting free boundary problem. In particular, existence and uniqueness of solutions for all time are proven for the radially symmetric case. Finally, numerical simulations of a tumor growing in 2-dimensions with radial symmetry are carried in order to evaluate the therapeutic potential of different treatment strategies. These simulations are able to reproduce a variety of clinically observed responses to treatment, and suggest treatment strategies that may result in tumor remission, underscoring our model's potential to make a significant contribution in the field of prostate cancer therapeutics.


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  • © 2013 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)
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