Bulletin of Mathematical Biology

, Volume 80, Issue 8, pp 2026–2048 | Cite as

Predictive Modeling of Neuroblastoma Growth Dynamics in Xenograft Model After Bevacizumab Anti-VEGF Therapy

  • Yixuan He
  • Anita Kodali
  • Dorothy I. Wallace
Original Article


Neuroblastoma is the leading cause of cancer death in young children. Although treatment for neuroblastoma has improved, the 5-year survival rate of patients still remains less than half. Recent studies have indicated that bevacizumab, an anti-VEGF drug used in treatment of several other cancer types, may be effective for treating neuroblastoma as well. However, its effect on neuroblastoma has not been well characterized. While traditional experiments are costly and time-consuming, mathematical models are capable of simulating complex systems quickly and inexpensively. In this study, we present a model of vascular tumor growth of neuroblastoma IMR-32 that is complex enough to replicate experimental data across a range of tumor cell properties measured in a suite of in vitro and in vivo experiments. The model provides quantitative insight into tumor vasculature, predicting a linear relationship between vasculature and tumor volume. The tumor growth model was coupled with known pharmacokinetics and pharmacodynamics of the VEGF blocker bevacizumab to study its effect on neuroblastoma growth dynamics. The results of our model suggest that total administered bevacizumab concentration per week, as opposed to dosage regimen, is the major determining factor in tumor suppression. Our model also establishes an exponentially decreasing relationship between administered bevacizumab concentration and tumor growth rate.


Cancer modeling Neuroblastoma Mathematical model VEGF Tumor growth 



This work was supported by the Women in Science Program, Sophomore Science Scholars Program, James O. Freedman Presidential Scholar, and Undergraduate Leave Term Research Grant to Yixuan He from the Office of Undergraduate Research at Dartmouth College.

Supplementary material

11538_2018_441_MOESM1_ESM.pdf (284 kb)
Supplementary material 1 (PDF 284 kb)


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Copyright information

© Society for Mathematical Biology 2018

Authors and Affiliations

  1. 1.Department of MathematicsDartmouth CollegeHanoverUSA
  2. 2.Department of Biological SciencesDartmouth CollegeHanoverUSA

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