Swanson Kristin R, Bridge Carly, Murray J D, Alvord Ellsworth C
Department of Pathology, University of Washington and Laboratory of Neuropathology, Harborview Medical Center, 325 9th Avenue, Box 359791, Seattle, WA 98104-2499, USA.
J Neurol Sci. 2003 Dec 15;216(1):1-10. doi: 10.1016/j.jns.2003.06.001.
Over the last 10 years increasingly complex mathematical models of cancerous growths have been developed, especially on solid tumors, in which growth primarily comes from cellular proliferation. The invasiveness of gliomas, however, requires a change in the concept to include cellular motility in addition to proliferative growth. In this article we review some of the recent developments in mathematical modeling of gliomas. We begin with a model of untreated gliomas and continue with models of polyclonal gliomas following chemotherapy or surgical resection. From relatively simple assumptions involving homogeneous brain tissue bounded by a few gross anatomical landmarks (ventricles and skull) the models have recently been expanded to include heterogeneous brain tissue with different motilities of glioma cells in grey and white matter on a geometrically complex brain domain, including sulcal boundaries, with a resolution of 1 mm(3) voxels. We conclude that the velocity of expansion is linear with time and varies about 10-fold, from about 4 mm/year for low-grade gliomas to about 3 mm/month for high-grade ones.
在过去十年中，人们已经开发出越来越复杂的癌症生长数学模型，尤其是针对实体瘤，其生长主要源于细胞增殖。然而，神经胶质瘤的侵袭性需要改变概念，除了增殖性生长外，还需纳入细胞运动。在本文中，我们回顾了神经胶质瘤数学建模的一些最新进展。我们首先介绍未经治疗的神经胶质瘤模型，接着介绍化疗或手术切除后的多克隆神经胶质瘤模型。这些模型最初基于相对简单的假设，即由一些大体解剖标志（脑室和颅骨）界定的均匀脑组织，最近已扩展到包括几何结构复杂的脑域中具有不同运动能力的神经胶质瘤细胞的异质脑组织，该脑域包括脑沟边界，体素分辨率为1立方毫米。我们得出结论，扩张速度与时间呈线性关系，变化幅度约为10倍，从低级别神经胶质瘤的约4毫米/年到高级别神经胶质瘤的约3毫米/月。
