A Multiscale Modeling Approach to Glioma Invasion with Therapy


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.

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  1. 1.

    1 In particular, this justifies the omission of the “transport” term w.r.t. y on the left hand side of (2).

  2. 2.

    2 The standard treatment for newly diagnosed glioblastoma consists of maximal surgical resection, radiotherapy, and concomitant and adjuvant chemotherapy with temozolomide, see, e.g., [22, 59].

  3. 3.

    3 Arginylglycylaspartic acid.

  4. 4.

    4 Note that the factor r 2 in this expression is often left out, but [1] argued that it is actually essential when considering normalized solid angles.

  5. 5.

    5 provided by Carsten Wolters, Institute of Biosignal Analysis, WWU Münster, see [68].

  6. 6.

    6 For a discussion about the timing of starting radiotherapy after resection see, e.g., [38] and the references therein.

  7. 7.

    7 CTV=clinical target volume, PTV=planning target volume.


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Correspondence to Alexander Hunt.

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This article is dedicated to Professor Willi Jäger on his 75th birthday.

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Hunt, A., Surulescu, C. A Multiscale Modeling Approach to Glioma Invasion with Therapy. Vietnam J. Math. 45, 221–240 (2017). https://doi.org/10.1007/s10013-016-0223-x

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

Mathematics Subject Classification (2000)

  • 92C50
  • 35Q92
  • 92C17