Evaluating the Effect of Tissue Anisotropy on Brain Tumor Growth Using a Mechanically Coupled Reaction–Diffusion Model

  • Daniel AblerEmail author
  • Russell C. Rockne
  • Philippe Büchler
Part of the Lecture Notes in Computational Vision and Biomechanics book series (LNCVB, volume 33)


Glioblastoma (GBM) is the most frequent malignant brain tumor in adults and presents with different growth phenotypes. We use a mechanically coupled reaction–diffusion model to study the influence of structural brain tissue anisotropy on tumor growth. Tumors were seeded at multiple locations in a human MR-DTI brain atlas and their spatiotemporal evolution was simulated using the Finite Element Method. We evaluated the impact of tissue anisotropy on the model’s ability to reproduce the aspherical shapes of real pathologies by comparing predicted lesions to publicly available GBM imaging data. The impact of tissue anisotropy on tumor shape was strongly location dependent and highest for tumors in brain regions with a single dominating white matter fiber direction, such as the corpus callosum. Despite strongly anisotropic growth assumptions, all simulated tumors remained more spherical than real lesions at the corresponding anatomic location and similar volume. These findings confirm previous simulation studies, suggesting that cell migration along WM fiber tracks is not a major determinant of tumor shape in the setting of reaction–diffusion-based tumor growth models and for most locations across the brain.


Glioma Anisotropy DTI Mass effect Reaction–diffusion model Biomechanics 



The research leading to these results has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skodowska-Curie grant agreement No 753878. Calculations were performed on UBELIX (, the HPC cluster at the University of Bern.


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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Daniel Abler
    • 1
    • 2
    Email author
  • Russell C. Rockne
    • 2
  • Philippe Büchler
    • 1
  1. 1.ARTORG Center for Biomedical Engineering Research, University of BernBernSwitzerland
  2. 2.Beckman Research Institute, City of HopeDuarteUSA

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