Martirosyan Nikolay L, Rutter Erica M, Ramey Wyatt L, Kostelich Eric J, Kuang Yang, Preul Mark C
Division of Neurosurgery, University of Arizona, Tucson, AZ 85724, United States.
Math Biosci Eng. 2015 Aug;12(4):879-905. doi: 10.3934/mbe.2015.12.879.
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.
尽管数学建模是工业和许多科学研究的支柱，但此类方法在神经外科领域的应用却很少。然而，生物学研究与应用数学的融合正在迅速改变这种局面，尤其是在癌症研究方面。本综述重点关注数学模型为研究胶质瘤生长提供新途径并将其应用于实际的巨大潜力。体外研究常用于模拟特定模型参数的影响，而这些参数在大规模模型中很难实现。关于胶质瘤的侵袭特性，可以对代谢和血管属性进行建模，以深入了解肿瘤侵袭行为所导致的浸润机制。从形态学上看，胶质瘤表现出不同的特征，这可能有助于预测其生长阶段和侵袭特性，并且模型不断为这些特征如何在视觉上表现提供见解。最近的研究试图预测某些治疗方式的疗效以及它们相对于彼此应如何精确给药。成像也是模拟临床相关肿瘤及其对大脑周围解剖结构影响的关键组成部分。
