IDEAS home Printed from https://ideas.repec.org/a/gam/jmathe/v5y2017i4p49-d114464.html
   My bibliography  Save this article

An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors

Author

Listed:
  • Adam E. Glick

    (Department of Nuclear Engineering, University of California, Berkeley, Berkeley, CA 94720, USA
    These authors contributed equally to this work.)

  • Antonio Mastroberardino

    (School of Science, Penn State Erie, The Behrend College, Erie, PA 16563, USA
    These authors contributed equally to this work.)

Abstract

Cancer is a disease of unregulated cell growth that is estimated to kill over 600,000 people in the United States in 2017 according to the National Institute of Health. While there are several therapies to treat cancer, tumor resistance to these therapies is a concern. Drug therapies have been developed that attack proliferating endothelial cells instead of the tumor in an attempt to create a therapy that is resistant to resistance in contrast to other forms of treatment such as chemotherapy and radiation therapy. In this study, a two-compartment model in terms of differential equations is presented in order to determine the optimal protocol for the delivery of anti-angiogenesis therapy. Optimal control theory is applied to the model with a range of anti-angiogenesis doses to determine optimal doses to minimize tumor volume at the end of a two week treatment and minimize drug toxicity to the patient. Applying a continuous optimal control protocol to our model of angiogenesis and tumor cell growth shows promising results for tumor control while minimizing the toxicity to the patients. By investigating a variety of doses, we determine that the optimal angiogenesis inhibitor dose is in the range of 10–20 mg/kg. In this clinically useful range of doses, good tumor control is achieved for a two week treatment period. This work shows that varying the toxicity of the treatment to the patient will change the optimal dosing scheme but tumor control can still be achieved.

Suggested Citation

  • Adam E. Glick & Antonio Mastroberardino, 2017. "An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors," Mathematics, MDPI, vol. 5(4), pages 1-14, October.
  • Handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:49-:d:114464
    as

    Download full text from publisher

    File URL: https://www.mdpi.com/2227-7390/5/4/49/pdf
    Download Restriction: no

    File URL: https://www.mdpi.com/2227-7390/5/4/49/
    Download Restriction: no
    ---><---

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Sana Abdulkream Alharbi & Azmin Sham Rambely, 2020. "A New ODE-Based Model for Tumor Cells and Immune System Competition," Mathematics, MDPI, vol. 8(8), pages 1-14, August.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:gam:jmathe:v:5:y:2017:i:4:p:49-:d:114464. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: MDPI Indexing Manager (email available below). General contact details of provider: https://www.mdpi.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.