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Effect of Vascularization on Glioma Tumor Growth

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Modeling Tumor Vasculature

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Abstract

As a tumor grows beyond a critical size and becomes nutrient-limited, it requires delivery of new resources and removal of waste products. The development of a new vascular network to support tumor growth allows then oxygen and nutrient to reach tumor cells. In this chapter, we study the influence of vascularization on tumor growth with the help of a combination of in vivo data from implanted xenografts of U87 MG in nude mice brain and a mathematical model. We identify three different growth regimes occurring during the tumor development and investigate the interplay among these regimes and the vascularization dynamics. Our results show that the initial (avascular) tumor growth is followed by a transient regime characterized by over-vascularization, before relaxing to a dynamics where the tumor radius increases linearly in time. Our model suggests that this linear regime corresponds to the equilibration of vascularization and metabolic dynamics. We use our findings to discuss the initiation of angiogenic processes and the implications for anti-angiogenic therapy.

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Notes

  1. 1.

    A Gaussian Markov process X(t) is a Markov process whose probability density function is Gaussian.

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Acknowledgements

HH, AC, and VC acknowledge support from The Cullen Trust for Health Care and the National Institute for Health, Integrative Cancer Biology Program: 1U54CA149196, for the Center for Systematic Modeling of Cancer Development. JL and VC acknowledge support from the National Science Foundation, Division of Mathematical Sciences. VC also acknowledges support from the National Cancer Institute. H. Hatzikirou and A. Chauvière contributed equally to this work.

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Authors and Affiliations

  1. Department of Pathology, University of New Mexico, 1 University of New Mexico, Albuquerque, NM, 87131, USA

    Haralambos Hatzikirou & Arnaud Chauvière

  2. Department of Mathematics, The University of California at Irvine, Irvine, CA, USA

    John Lowengrub

  3. Department of Neuro-Oncology, Cancer Medicine, The University of Texas M. D. Anderson Cancer Center, Houston, TX, USA

    J. De Groot

  4. Department of Pathology and Department of Chemical and Biomedical, Engineering University of New Mexico, 1 University of New Mexico, Albuquerque, NM, 87131, USA

    Vittorio Cristini

Authors
  1. Haralambos Hatzikirou
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  2. Arnaud Chauvière
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  3. John Lowengrub
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  4. J. De Groot
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  5. Vittorio Cristini
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Corresponding author

Correspondence to Vittorio Cristini .

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Editors and Affiliations

  1. Dept. Mathematics, University of Michigan, 530 Church Street, Ann Arbor, Michigan, 48109, USA

    Trachette L. L. Jackson

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Hatzikirou, H., Chauvière, A., Lowengrub, J., De Groot, J., Cristini, V. (2012). Effect of Vascularization on Glioma Tumor Growth. In: Jackson, T.L. (eds) Modeling Tumor Vasculature. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-0052-3_10

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