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Control and the Analysis of Cancer Growth Models

  • Allen TannenbaumEmail author
  • Tryphon T. Georgiou
  • Joseph O. Deasy
  • Larry Norton
Chapter
Part of the Operator Theory: Advances and Applications book series (OT, volume 272)

Abstract

We analyze two dynamical models of cancer growth from a systemtheoretic point of view. The first model is based upon stochastic controlled versions of the classical Lotka–Volterra equations. Here we investigate from a controls point of view the utility of employing ultrahigh dose flashes in radiotherapy. The second is based on the Norton–Simon–Massagué growth model that takes into account the heterogeneity of a tumor cell population. We indicate an optimal strategy based on linear quadratic control applied to a linear transformed model. The models and analysis are very preliminary and only give an indication of possible therapies in the treatment of cancer.

Keywords

Cancer growth models Lotka–Voltera equations linear-quadratic control 

Mathematics Subject Classification (2010)

Primary 37N25 Secondary 37N25 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Allen Tannenbaum
    • 1
    Email author
  • Tryphon T. Georgiou
    • 2
  • Joseph O. Deasy
    • 3
  • Larry Norton
    • 4
  1. 1.Departments of Computer Science and Applied Mathematics & StatisticsStony Brook UniversityStony BrookUSA
  2. 2.Department of Mechanical & Aerospace EngineeringUniversity of CalforniaIrvineUSA
  3. 3.Department of Medical PhysicsMemorial Sloan Kettering Cancer CenterNew York CityUSA
  4. 4.Department of MedicineMemorial Sloan Kettering Cancer CenterNew York CityUSA

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