Bulletin of Mathematical Biology

, Volume 80, Issue 5, pp 1292–1309 | Cite as

Simulating PDGF-Driven Glioma Growth and Invasion in an Anatomically Accurate Brain Domain

  • Susan Christine Massey
  • Russell C. Rockne
  • Andrea Hawkins-Daarud
  • Jill Gallaher
  • Alexander R. A. Anderson
  • Peter Canoll
  • Kristin R. Swanson
Special Issue : Mathematical Oncology


Gliomas are the most common of all primary brain tumors. They are characterized by their diffuse infiltration of the brain tissue and are uniformly fatal, with glioblastoma being the most aggressive form of the disease. In recent years, the over-expression of platelet-derived growth factor (PDGF) has been shown to produce tumors in experimental rodent models that closely resemble this human disease, specifically the proneural subtype of glioblastoma. We have previously modeled this system, focusing on the key attribute of these experimental tumors—the “recruitment” of oligodendroglial progenitor cells (OPCs) to participate in tumor formation by PDGF-expressing retrovirally transduced cells—in one dimension, with spherical symmetry. However, it has been observed that these recruitable progenitor cells are not uniformly distributed throughout the brain and that tumor cells migrate at different rates depending on the material properties in different regions of the brain. Here we model the differential diffusion of PDGF-expressing and recruited cell populations via a system of partial differential equations with spatially variable diffusion coefficients and solve the equations in two spatial dimensions on a mouse brain atlas using a flux-differencing numerical approach. Simulations of our in silico model demonstrate qualitative agreement with the observed tumor distribution in the experimental animal system. Additionally, we show that while there are higher concentrations of OPCs in white matter, the level of recruitment of these plays little role in the appearance of “white matter disease,” where the tumor shows a preponderance for white matter. Instead, simulations show that this is largely driven by the ratio of the diffusion rate in white matter as compared to gray. However, this ratio has less effect on the speed of tumor growth than does the degree of OPC recruitment in the tumor. It was observed that tumor simulations with greater degrees of recruitment grow faster and develop more nodular tumors than if there is no recruitment at all, similar to our prior results from implementing our model in one dimension. Combined, these results show that recruitment remains an important consideration in understanding and slowing glioma growth.


Reaction–diffusion Brain tumor Glioma Cancer Platelet-derived growth factor (PDGF) 



This material is based upon work supported by the National Science Foundation Graduate Research Fellowship Program under Grant No. DGE-0781824, by the National Institutes of Health under awards R01NS060752, U54CA143970, and R01CA164371, and by the James S. McDonnell Foundation Collaborative Activity Award #220020264. The content is solely the responsibility of the authors. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation, the National Institutes of Health, or the James S. McDonnell Foundation.


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Copyright information

© Society for Mathematical Biology 2017

Authors and Affiliations

  1. 1.Precision Neurotherapeutics Innovation ProgramMayo ClinicPhoenixUSA
  2. 2.Division of Mathematical Oncology, Department of Information SciencesCity of HopeDuarteUSA
  3. 3.Integrative Mathematical OncologyMoffitt Cancer Research CenterTampaUSA
  4. 4.Division of Neuropathology, Department of Pathology and Cell BiologyColumbia University School of MedicineNew YorkUSA

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