Tumor Microenvironment and Anticancer Therapies: An Optimal Control Approach

  • Urszula LedzewiczEmail author
  • Heinz Schättler
Part of the Modeling and Simulation in Science, Engineering and Technology book series (MSSET)


In this paper, results about the structure of cancer treatment protocols that can be inferred from an analysis of mathematical models with the methods and tools of optimal control are reviewed. For homogeneous tumor populations of chemotherapeutically sensitive cells, optimal controls are bang-bang corresponding to the medical paradigm of maximum tolerated doses (MTD). But as more aspects of the tumor microenvironment are taken into account, such as heterogeneity of the tumor cell population, tumor angiogenesis and tumor-immune system interactions, singular controls which administer agents at specific time-varying reduced dose rates become optimal and give an indication of what might be the biologically optimal dose (BOD).


Optimal control Cancer chemotherapy Tumor microenvironment Antiangiogenic treatments Tumor-immune system interactions 



This material is based upon work supported by the National Science Foundation under collaborative research Grants Nos. DMS 1311729/1311733. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.


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Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsSouthern Illinois UniversityEdwardsvilleUSA
  2. 2.Department of Electrical and Systems EngineeringWashington UniversitySt. LouisUSA

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