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Vietnam Journal of Mathematics

, Volume 45, Issue 1–2, pp 221–240 | Cite as

A Multiscale Modeling Approach to Glioma Invasion with Therapy

  • Alexander HuntEmail author
  • Christina Surulescu
Article

Abstract

We consider the multiscale model for glioma growth introduced in (Math. Biosci. Eng. 71: 443–460, 2016) to accommodate tumor heterogeneity by relying on the go-or-grow dichotomy and extend it to account for therapy effects. Thereby, three treatment strategies involving surgical resection, radio-, and chemotherapy are compared for their efficiency. The chemotherapy relies on inhibiting the binding of cell surface receptors to the surrounding tissue, which impairs both migration and proliferation. The multiscale features of our model allow to connect subcellular level information to individual cell dynamics and—upon scaling—carry over such information to the population level on which a tumor is clinically observed. This makes it particularly appropriate for investigating the effects of therapy, as both ionizing radiation and chemotherapeutic agents act on the subcellular level, but their outcome is assessed on the macroscopic scale. The model includes patient-specific brain structure available in the form of DTI data and the numerical simulations are performed relying on these.

Keywords

Multiscale model Glioma invasion Cancer therapy approaches Kinetic transport equations Macroscopic scaling 

Mathematics Subject Classification (2000)

92C50 35Q92 92C17 

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Copyright information

© Vietnam Academy of Science and Technology (VAST) and Springer Science+Business Media Singapore 2016

Authors and Affiliations

  1. 1.Fachbereich MathematikTechnische Universität KaiserslauternKaiserslauternGermany

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