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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