Model predictive control for optimal treatment in a spatial cancer game

Francisco Javier Muros, Jose M. Maestre , Li You, Katerina Stankova

Research output: Chapter in Book/Report/Conference proceedingConference article in proceedingAcademicpeer-review


This work focuses on modeling tumorigenesis as
a spatial evolutionary game and on finding optimal cancer
treatment using a model predictive control approach. Extending
a nonspatial cancer game from the literature into a spatial
setting, we consider a solid tumor composed of cells of two
different types: proliferative and motile. In our agent-based
spatial game, cells represent vertices of an undirected dynamic
graph where a link between any two cells indicates that these
cells can interact with each other. A focal cell can reproduce
only if it interacts with another cell, where the proliferation
probabilities are given by the fitness matrix of the original
nonspatial game. Without treatment, the cancer cells grow
exponentially. Subsequently, we use nonlinear model predictive
control to find an optimal time-varying treatment, with an
objective representing a trade-off between minimization of the
tumor mass and treatment toxicity. As for example androgen-
deprivation treatment in metastatic castrate-resistant prostate
cancer, this treatment is assumed to decrease the chances for
interaction between the cancer cells and hereby decrease cells’
proliferation rate. In case studies, we show that the optimal
treatment often leads to a decrease of the tumor mass. This
suggests that model predictive control has a high potential in
designing cancer treatments.
Original languageEnglish
Title of host publicationProceedings of the 2017 IEEE 56th Annual Conference on Decision and Control (CDC)
Place of PublicationMelbourne, VIC, Australia
Pages5539 - 5544
Number of pages6
ISBN (Electronic)978-1-5090-2873-3
ISBN (Print)978-1-5090-2874-0
Publication statusPublished - 23 Jan 2018


  • cancer modeling and treatment
  • spatial evolutionary game theory
  • nonlinear model predictive control
  • dynamic graphs

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