Skip to main content

Thank you for visiting You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Computational modelling of perivascular-niche dynamics for the optimization of treatment schedules for glioblastoma


Glioblastoma stem-like cells dynamically transition between a chemoradiation-resistant state and a chemoradiation-sensitive state. However, physical barriers in the tumour microenvironment restrict the delivery of chemotherapy to tumour compartments that are distant from blood vessels. Here, we show that a massively parallel computational model of the spatiotemporal dynamics of the perivascular niche that incorporates glioblastoma stem-like cells and differentiated tumour cells as well as relevant tissue-level phenomena can be used to optimize the administration schedules of concurrent radiation and temozolomide—the standard-of-care treatment for glioblastoma. In mice with platelet-derived growth factor (PDGF)-driven glioblastoma, the model-optimized treatment schedule increased the survival of the animals. For standard radiation fractionation in patients, the model predicts that chemotherapy may be optimally administered about one hour before radiation treatment. Computational models of the spatiotemporal dynamics of the tumour microenvironment could be used to predict tumour responses to a broader range of treatments and to optimize treatment regimens.

Access options

Rent or Buy article

Get time limited or full article access on ReadCube.


All prices are NET prices.

Fig. 1: A computational model of the GBM microenvironment.
Fig. 2: Modelling GBM growth and treatment response.
Fig. 3: Prediction of the responses to different chemoradiation administration schedules.
Fig. 4: Prediction of GBM growth and treatment response.
Fig. 5: Validation of modelling predictions in a mouse model of GBM.
Fig. 6: Identification of a combination schedule in mice by optimizing the offset between chemotherapy and radiotherapy.
Fig. 7: Identification of an optimum schedule for human validation.

Data availability

The main data supporting the results in this study are available within the paper and its Supplementary Information. The raw and analysed datasets generated during the study are too large to be publicly shared, yet they are available for research purposes from the corresponding authors on reasonable request.

Code availability

The custom code used in this study is available at GitHub ( under the BSD-3-Clause open-source license.


  1. 1.

    Weller, M. et al. EANO guidelines on the diagnosis and treatment of diffuse gliomas of adulthood. Nat. Rev. Clin. Oncol. 18, 170–186 (2021).

    Google Scholar 

  2. 2.

    Gramatzki, D. Glioblastoma in the Canton of Zurich, Switzerland revisited: 2005 to 2009. Cancer 122, 3740–3741 (2016).

    Google Scholar 

  3. 3.

    Ostrom, Q. T. et al. CBTRUS Statistical Report: primary brain and other central nervous system tumors diagnosed in the United States in 2013–2017. Neuro Oncol. 22, iv1–iv96 (2020).

  4. 4.

    Khan, L. et al. External beam radiation dose escalation for high grade glioma. Cochrane Database Syst. Rev. CD011475 (2016).

  5. 5.

    Louis, D. N. The 2016 World Health Organization classification of tumors of the central nervous system: a summary. Acta Neuropathol. 131, 803–820 (2016).

    Google Scholar 

  6. 6.

    Calabrese, C. et al. A perivascular niche for brain tumour stem cells. Cancer Cell 11, 69–82 (2007).

    CAS  Google Scholar 

  7. 7.

    Eyler, C. E. et al. Glioma stem cell proliferation and tumour growth are promoted by nitric oxide synthase-2. Cell 146, 53–66 (2011).

    CAS  PubMed  PubMed Central  Google Scholar 

  8. 8.

    Charles, N. et al. Perivascular nitric oxide activates notch signaling and promotes stem-like character in PDGF-induced glioma cells. Cell Stem Cell 6, 141–152 (2010).

    CAS  Google Scholar 

  9. 9.

    Bleau, A.-M. et al. PTEN/PI3K/Akt pathway regulates the side population phenotype and ABCG2 activity in glioma tumour stem-like cells. Cell Stem Cell 4, 226–235 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  10. 10.

    Kozin, S. V., Duda, D. G., Munn, L. L. & Jain, R. K. Neovascularization after irradiation: what is the source of newly formed vessels in recurring tumors? J. Natl Cancer Inst. 104, 899–905 (2012).

    PubMed  PubMed Central  Google Scholar 

  11. 11.

    Garcia-Barros, M. et al. Tumor response to radiotherapy regulated by endothelial cell apoptosis. Science 300, 1155–1159 (2003).

    CAS  Google Scholar 

  12. 12.

    Radbruch, A. et al. Quantification of tumour vessels in glioblastoma patients using time-of-flight angiography at 7 Tesla: a feasibility study. PLoS ONE 9, e110727 (2014).

    PubMed  PubMed Central  Google Scholar 

  13. 13.

    Mustafa, D. et al. Expression sites of colligin 2 in glioma blood vessels. Brain Pathol. 20, 50–65 (2010).

    PubMed  PubMed Central  Google Scholar 

  14. 14.

    Houghton, P. J. et al. Antitumor activity of temozolomide combined with irinotecan is partly independent of O6-methylguanine-DNA methyltransferase and mismatch repair phenotypes in xenograft models. Clin. Cancer Res. 6, 4110–4118 (2000).

    CAS  Google Scholar 

  15. 15.

    Gilbert, M. R. et al. Dose-dense temozolomide for newly diagnosed glioblastoma: a randomized phase III clinical trial. J. Clin. Oncol. 31, 4085–4091 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  16. 16.

    Brada, M. et al. Temozolomide versus procarbazine, lomustine, and vincristine in recurrent high-grade glioma. J. Clin. Oncol. 28, 4601–4608 (2010).

    CAS  Google Scholar 

  17. 17.

    Minchinton, A. I. & Tannock, I. F. Drug penetration in solid tumours. Nat. Rev. Cancer 6, 583–592 (2006).

    CAS  Google Scholar 

  18. 18.

    Leder, K. Mathematical modelling of PDGF-driven glioblastoma reveals optimized radiation dosing schedules. Cell 7, 603–616 (2014).

    Google Scholar 

  19. 19.

    Stevens, M. F. et al. Antitumor activity and pharmacokinetics in mice of 8-carbamoyl-3-methyl-imidazo[5,1-d]−1,2,3,5-tetrazin-4(3H)-one (CCRG 81045; M & B 39831), a novel drug with potential as an alternative to dacarbazine. Cancer Res. 47, 5846–5852 (1987).

    CAS  Google Scholar 

  20. 20.

    Newlands, E. S. et al. Phase I trial of temozolomide (CCRG 81045: M&B 39831: NSC 362856). Br. J. Cancer 65, 287–291 (1992).

    CAS  PubMed  PubMed Central  Google Scholar 

  21. 21.

    Ostermann, S. et al. Plasma and cerebrospinal fluid population pharmacokinetics of temozolomide in malignant glioma patients. Clin. Cancer Res. 10, 3728–3736 (2004).

    CAS  Google Scholar 

  22. 22.

    Charles, N. A. & Holland, E. C. TRRAP and the maintenance of stemness in gliomas. Cell Stem Cell 6, 6–7 (2010).

    CAS  Google Scholar 

  23. 23.

    Stupp, R. et al. Radiotherapy plus concomitant and adjuvant temozolomide for glioblastoma. N. Engl. J. Med. 352, 987–996 (2005).

    CAS  PubMed  Google Scholar 

  24. 24.

    Perry, J. R. et al. Short-course radiation plus temozolomide in elderly patients with glioblastoma. N. Engl. J. Med. 376, 1027–1037 (2017).

    CAS  Google Scholar 

  25. 25.

    Agarwala, S. S. & Kirkwood, J. M. Temozolomide, a novel alkylating agent with activity in the central nervous system, may improve the treatment of advanced metastatic melanoma. Oncologist 5, 144–151 (2000).

    CAS  Google Scholar 

  26. 26.

    Carlson, B. L. et al. Radiosensitizing effects of temozolomide observed in vivo only in a subset of O6-methylguanine-DNA methyltransferase methylated glioblastoma multiforme xenografts. Int. J. Radiat. Oncol. Biol. Phys. 75, 212–219 (2009).

    CAS  PubMed  PubMed Central  Google Scholar 

  27. 27.

    Banissi, C., Ghiringhelli, F., Chen, L. & Carpentier, A. F. Treg depletion with a low-dose metronomic temozolomide regimen in a rat glioma model. Cancer Immunol. Immunother. 58, 1627–1634 (2009).

    CAS  Google Scholar 

  28. 28.

    Weller, M. et al. MGMT promoter methylation is a strong prognostic biomarker for benefit from dose-intensified temozolomide rechallenge in progressive glioblastoma: the DIRECTOR trial. Clin. Cancer Res. 21, 2057–2064 (2015).

    CAS  Google Scholar 

  29. 29.

    Thorsson, V. et al. The immune landscape of cancer. Immunity 48, 812–830 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  30. 30.

    Wang, J. et al. Clonal evolution of glioblastoma under therapy. Nat. Genet. 48, 768–776 (2016).

    CAS  PubMed  PubMed Central  Google Scholar 

  31. 31.

    Snuderl, M. et al. Mosaic amplification of multiple receptor tyrosine kinase genes in glioblastoma. Cancer Cell 20, 810–817 (2011).

    CAS  PubMed  Google Scholar 

  32. 32.

    Körber, V. et al. Evolutionary trajectories of IDHWT glioblastomas reveal a common path of early tumorigenesis instigated years ahead of initial diagnosis. Cancer Cell 35, 692–704 (2019).

    Google Scholar 

  33. 33.

    Wang, Q. et al. Tumor evolution of glioma-intrinsic gene expression subtypes associates with immunological changes in the microenvironment. Cancer Cell 32, 42–56 (2017).

    PubMed  PubMed Central  Google Scholar 

  34. 34.

    Patel, A. P. et al. Single-cell RNA-seq highlights intratumoral heterogeneity in primary glioblastoma. Science 344, 1396–1401 (2014).

    CAS  PubMed  PubMed Central  Google Scholar 

  35. 35.

    Capper, D. et al. DNA methylation-based classification of central nervous system tumours. Nature 555, 469–474 (2018).

    CAS  PubMed  PubMed Central  Google Scholar 

  36. 36.

    Hu, X. et al. mTOR promotes survival and astrocytic characteristics induced by Pten/AKT signaling in glioblastoma. Neoplasia 7, 356–368 (2005).

    CAS  PubMed  PubMed Central  Google Scholar 

  37. 37.

    Mirams, G. R. et al. Chaste: an open source C++ library for computational physiology and biology. PLoS Comput. Biol. 9, e1002970 (2013).

    CAS  PubMed  PubMed Central  Google Scholar 

  38. 38.

    Charles, N. & Holland, E. C. The perivascular niche microenvironment in brain tumour progression. Cell Cycle 9, 3012–3021 (2010).

    CAS  PubMed  PubMed Central  Google Scholar 

  39. 39.

    Verlet, L. Computer ‘experiments’ on classical fluids. I. Thermodynamical properties of Lennard-Jones molecules. Phys. Rev. 159, 98–103 (1967).

    CAS  Google Scholar 

  40. 40.

    Fuchs, E., Tumbar, T. & Guasch, G. Socializing with the neighbors: stem cells and their niche. Cell 116, 769–778 (2004).

    CAS  Google Scholar 

  41. 41.

    Wedge, S. R., Porteous, J. K., Glaser, M. G., Marcus, K. & Newlands, E. S. In vitro evaluation of temozolomide combined with X-irradiation. Anticancer Drugs 8, 92–97 (1997).

    CAS  Google Scholar 

  42. 42.

    Brock, C. S. et al. Phase I trial of temozolomide using an extended continuous oral schedule. Cancer Res. 58, 4363–4367 (1998).

    CAS  Google Scholar 

  43. 43.

    Thomas, V., Kumari, T. V. & Jayabalan, M. In vitro studies on the effect of physical cross-linking on the biological performance of aliphatic poly(urethane urea) for blood contact applications. Biomacromolecules 2, 588–596 (2001).

    CAS  Google Scholar 

  44. 44.

    Kirkpatrick, S., Gelatt, C. D. & Vecchi, M. P. Optimization by simulated annealing. Science 220, 671–680 (1983).

    CAS  Google Scholar 

  45. 45.

    Aarts, E. & Korst, J. Simulated Annealing and Boltzmann Machines: A Stochastic Approach to Combinatorial Optimization and Neural Computing. (John Wiley & Sons, 1989).

Download references


We acknowledge feedback and advice from members of the Michor laboratory, and D. Puleri for figure editing. We also acknowledge support from the Dana-Farber Physical Sciences Oncology Center (NIH U54CA193461, to F.M. and E.C.H.), the NIH Office of the Director (NIH, DP5OD019876, to A.R.), and the Lawrence Livermore National Laboratory Lawrence Fellowship (to A.R.). The mouse work was supported by P30 CA015704 at the Fred Hutchinson Cancer Research Center. This work was performed under the auspices of the US Department of Energy by Lawrence Livermore National Laboratory under Contract DE-AC52-07NA27344. Computing support for this work was provided by the Lawrence Livermore National Laboratory Institutional Computing Grand Challenges. F.M. acknowledges support from the Ludwig Center at Harvard.

Author information




A.R., H.-G.W., E.C.H. and F.M. contributed to the design of the study. A.R., J.A.D. and Y.-K.C. performed the computational modelling. H.-G.W., S.E. and S.S.P. performed the mouse experiments. E.C.H. and F.M. supervised the study. All of the authors contributed to the writing of the paper.

Corresponding authors

Correspondence to Eric C. Holland or Franziska Michor.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Supplementary information

Supplementary Information

Supplementary figures and tables.

Reporting Summary

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Randles, A., Wirsching, HG., Dean, J.A. et al. Computational modelling of perivascular-niche dynamics for the optimization of treatment schedules for glioblastoma. Nat Biomed Eng 5, 346–359 (2021).

Download citation


Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing