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

by Adam E. Glick 1,† and Antonio Mastroberardino 2,*,†
Department of Nuclear Engineering, University of California, Berkeley, Berkeley, CA 94720, USA
School of Science, Penn State Erie, The Behrend College, Erie, PA 16563, USA
Author to whom correspondence should be addressed.
These authors contributed equally to this work.
Mathematics 2017, 5(4), 49;
Received: 24 June 2017 / Revised: 14 September 2017 / Accepted: 29 September 2017 / Published: 10 October 2017
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. View Full-Text
Keywords: anti-angiogenesis therapy; optimal control theory; optimal dosing scheme anti-angiogenesis therapy; optimal control theory; optimal dosing scheme
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Glick, A.E.; Mastroberardino, A. An Optimal Control Approach for the Treatment of Solid Tumors with Angiogenesis Inhibitors. Mathematics 2017, 5, 49.

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