An optimal control approach for the treatment of solid tumors with angiogenesis inhibitors
type: Item
instance of: scholarly article
title: An optimal control approach for the treatment of solid tumors with angiogenesis inhibitors
zbMATH Open document ID: 1394.92057
author: Adam E. Glick
author: Antonio Mastroberardino
published in: Mathematics
publication date: 2018-07-05T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 92C50
Mathematics Subject Classification ID: 49K15
Mathematics Subject Classification ID: 49N90
zbMATH DE Number: 6898678
zbMATH Keywords: anti-angiogenesis therapy
zbMATH Keywords: optimal control theory
zbMATH Keywords: optimal dosing scheme
MaRDI profile type: Publication
full work available at URL: math5040049
OpenAlex ID: W2761054131
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DOI: 10.3390/MATH5040049
description: scientific article; zbMATH DE number 6898678