skip to main content
DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach

Abstract

We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations.

Authors:
 [1];  [2]
  1. Harvey Mudd College, Claremont, CA 91711, USA, Argonne National Laboratory, Argonne, IL 60439, USA
  2. Pomona College, Claremont, CA 91711, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1198190
Grant/Contract Number:  
W-3 1-109-ENG-38
Resource Type:
Published Article
Journal Name:
Journal of Theoretical Medicine
Additional Journal Information:
Journal Name: Journal of Theoretical Medicine Journal Volume: 3 Journal Issue: 2; Journal ID: ISSN 1027-3662
Publisher:
Hindawi Publishing Corporation
Country of Publication:
Country unknown/Code not available
Language:
English

Citation Formats

De Pillis, L. G., and Radunskaya, A. A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach. Country unknown/Code not available: N. p., 2001. Web. doi:10.1080/10273660108833067.
De Pillis, L. G., & Radunskaya, A. A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach. Country unknown/Code not available. doi:10.1080/10273660108833067.
De Pillis, L. G., and Radunskaya, A. Mon . "A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach". Country unknown/Code not available. doi:10.1080/10273660108833067.
@article{osti_1198190,
title = {A Mathematical Tumor Model with Immune Resistance and Drug Therapy: An Optimal Control Approach},
author = {De Pillis, L. G. and Radunskaya, A.},
abstractNote = {We present a competition model of cancer tumor growth that includes both the immune system response and drug therapy. This is a four-population model that includes tumor cells, host cells, immune cells, and drug interaction. We analyze the stability of the drug-free equilibria with respect to the immune response in order to look for target basins of attraction. One of our goals was to simulate qualitatively the asynchronous tumor-drug interaction known as “Jeffs phenomenon.” The model we develop is successful in generating this asynchronous response behavior. Our other goal was to identify treatment protocols that could improve standard pulsed chemotherapy regimens. Using optimal control theory with constraints and numerical simulations, we obtain new therapy protocols that we then compare with traditional pulsed periodic treatment. The optimal control generated therapies produce larger oscillations in the tumor population over time. However, by the end of the treatment period, total tumor size is smaller than that achieved through traditional pulsed therapy, and the normal cell population suffers nearly no oscillations.},
doi = {10.1080/10273660108833067},
journal = {Journal of Theoretical Medicine},
number = 2,
volume = 3,
place = {Country unknown/Code not available},
year = {2001},
month = {1}
}

Journal Article:
Free Publicly Available Full Text
Publisher's Version of Record
DOI: 10.1080/10273660108833067

Save / Share: