Mathematical Biosciences and Engineering, 2015, 12(4): 879-905. doi: 10.3934/mbe.2015.12.879.

Primary: 58F15, 58F17; Secondary: 53C35.

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Mathematically modeling the biological properties of gliomas: A review

1. Division of Neurosurgery, University of Arizona, Tucson, AZ 85724
2. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85281
3. Creighton Medical School, Phoenix Campus, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013
4. School of Mathematical & Statistical Sciences, Arizona State University, Tempe, AZ 85287
5. School of Mathematics and Statistical Sciences, Arizona State University, Tempe, AZ 85281
6. Division of Neurological Surgery, Barrow Neurological Institute, St. Joseph's Hospital and Medical Center, Phoenix, AZ 85013

Although mathematical modeling is a mainstay for industrial and many scientific studies, such approaches have found little application in neurosurgery. However, the fusion of biological studies and applied mathematics is rapidly changing this environment, especially for cancer research. This review focuses on the exciting potential for mathematical models to provide new avenues for studying the growth of gliomas to practical use. In vitro studies are often used to simulate the effects of specific model parameters that would be difficult in a larger-scale model. With regard to glioma invasive properties, metabolic and vascular attributes can be modeled to gain insight into the infiltrative mechanisms that are attributable to the tumor's aggressive behavior. Morphologically, gliomas show different characteristics that may allow their growth stage and invasive properties to be predicted, and models continue to offer insight about how these attributes are manifested visually. Recent studies have attempted to predict the efficacy of certain treatment modalities and exactly how they should be administered relative to each other. Imaging is also a crucial component in simulating clinically relevant tumors and their influence on the surrounding anatomical structures in the brain.
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Keywords tumor growth simulation; proliferation.; glioma; Biomathematical modeling; forecasting; invasion

Citation: Nikolay L. Martirosyan, Erica M. Rutter, Wyatt L. Ramey, Eric J. Kostelich, Yang Kuang, Mark C. Preul. Mathematically modeling the biological properties of gliomas: A review. Mathematical Biosciences and Engineering, 2015, 12(4): 879-905. doi: 10.3934/mbe.2015.12.879

References

  • 1. Multiscale Modeling & Simulation, 3 (2005), 440-475.
  • 2. Journal of Neurosurgery, 75 (1991), 337-338.
  • 3. Physical Biology, 3 (2006), p93.
  • 4. Cancer Research, 69 (2009), 4493-4501.
  • 5. Physics in Medicine and Biology, 53 (2008), p879.
  • 6. Cell Proliferation, 33 (2000), 219-229.
  • 7. Journal of Mathematical Biology, 58 (2009), 723-763.
  • 8. Cell Proliferation, 34 (2001), 115-134.
  • 9. Cell Proliferation, 42 (2009), 511-528.
  • 10. Physical Review E, 65 (2002), 021907, 8pp.
  • 11. The Journal of Experimental Medicine, 138 (1973), 745-753.
  • 12. New Journal of Physics, 15 (2013), 055001, 10pp.
  • 13. Neuroimage, 37 (2007), S59-S70.
  • 14. Cancer Research, 66 (2006), 1597-1604.
  • 15. Applicable Analysis, 92 (2013), 1379-1392.
  • 16. Cancer Research, 63 (2003), 3847-3854.
  • 17. Journal of Theoretical Biology, 243 (2006), 517-531.
  • 18. Molecular Cell, 37 (2010), 620-632.
  • 19. IEEE Transactions on Medical Imaging, 18 (1999), 875-884.
  • 20. Mathematical Medicine and Biology, 29 (2012), 49-65.
  • 21. {Mathematical Models and Methods in Applied Sciences}, 15 (2005), 1779-1794.
  • 22. Physics in Medicine and Biology, 52 (2007), p6893.
  • 23. Journal of Mathematical Biology, 56 (2008), 793-825.
  • 24. Oncogene, 18 (1999), 5356-5362.
  • 25. Science, 284 (1999), 1994-1998.
  • 26. Magnetic Resonance in Medicine, 54 (2005), 616-624.
  • 27. Stereotactic and functional neurosurgery, 92 (2014), 306-314.
  • 28. Journal of Theoretical Biology, 203 (2000), 367-382.
  • 29. Frontiers in Oncology, 3 (2013), p53.
  • 30. Journal of Theoretical Biology, 260 (2009), 359-371.
  • 31. Discrete & Continuous Dynamical Systems-Series B, 18 (2013), 969-1015.
  • 32. PloS {ONE}, 6 (2011), e28293.
  • 33. Journal of Theoretical Biology, 245 (2007), 112-124.
  • 34. in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2007, Springer, 4791 (2007), 549-556.
  • 35. IEEE Transactions on Medical Imaging, 29 (2010), 77-95.
  • 36. Biology Direct, 6 (2011), p64.
  • 37. IEEE Transactions on Medical Imaging, 18 (1999), 580-592.
  • 38. Bulletin of Mathematical Biology, 74 (2012), 2875-2896.
  • 39. in Mathematical Models and Methods in Biomedicine, eds Ledzewicz U., Schattler H., Friedman A., Kashdan E., Springer, Berlin, (2013), 233-262.
  • 40. in Medical Image Computing and Computer-Assisted Intervention-MICCAI 2005, Springer, 3749 (2005), 400-408.
  • 41. Journal of Biological Dynamics, 6 (2012), 118-127.
  • 42. Theoretical Biology and Medical Modelling, 10 (2013), p47.
  • 43. Journal of Theoretical Biology, 213 (2001), 315-331.
  • 44. Physics in Medicine and Biology, 52 (2007), p3291.
  • 45. The Canadian journal of neurological sciences. Le journal canadien des sciences neurologiques, 25 (1998), 13-22.
  • 46. Journal of Mathematical Biology, 58 (2009), 561-578.
  • 47. Physical Review E, 66 (2002), 051901.
  • 48. The Canadian Journal of Neurological Sciences, 36 (2009), 696-706.
  • 49. Journal of neurosurgery, 116 (2012), 1172-1181.
  • 50. 1810-1815.
  • 51. IEEE Transactions on Biomedical Engineering, 53 (2006), 1467-1477.
  • 52. The British Journal of Radiology, 79 (2004), 389-400.
  • 53. Biophysical Journal, 92 (2007), 356-365.
  • 54. Applied Optics, 46 (2007), 5110-5118.
  • 55. New England Journal of Medicine, 352 (2005), 987-996.
  • 56. Cancer and Metastasis Reviews, 26 (2007), 319-331.
  • 57. Cell Proliferation, 33 (2000), 317-330.
  • 58. Clinical Oncology, 20 (2008), 301-308.
  • 59. Cancer Research, 71 (2011), 7366-7375.
  • 60. Cancer Research, 69 (2009), 4502-4509.
  • 61. Journal of Neuro-oncology, 91 (2009), 287-293.
  • 62. Cell Proliferation, 28 (1995), 17-31.
  • 63. Journal of Theoretical Biology, 216 (2002), 85-100.
  • 64. Methods, 37 (2005), 208-215.
  • 65. Cancer Research, 69 (2009), 9133-9140.
  • 66. Journal of Theoretical Biology, 253 (2008), 524-543.
  • 67. Applicable Analysis, 92 (2013), 1541-1558.
  • 68. IEEE Transactions on Biomedical Engineering, 55 (2008), 1233-1236.
  • 69. Bulletin of Mathematical Biology, 67 (2005), 211-259.

 

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Copyright Info: 2015, Nikolay L. Martirosyan, et al., licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution Licese (http://creativecommons.org/licenses/by/4.0)

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