Simulation of anisotropic growth of low‐grade gliomas using diffusion tensor imaging

Abstract

A recent computational model of brain tumor growth, developed to better describe how gliomas invade through the adjacent brain parenchyma, is based on two major elements: cell proliferation and isotropic cell diffusion. On the basis of this model, glioma growth has been simulated in a virtual brain, provided by a 3D segmented MRI atlas. However, it is commonly accepted that glial cells preferentially migrate along the direction of fiber tracts. Therefore, in this paper, the model has been improved by including anisotropic extension of gliomas. The method is based on a cell diffusion tensor derived from water diffusion tensor (as given by MRI diffusion tensor imaging). Results of simulations have been compared with two clinical examples demonstrating typical growth patterns of lowgrade gliomas centered around the insula. The shape and the kinetic evolution are better simulated with anisotropic rather than isotropic diffusion. The best fit is obtained when the anisotropy of the cell diffusion tensor is increased to greater anisotropy than the observed water diffusion tensor. The shape of the tumor is also influenced by the initial location of the tumor. Anisotropic brain tumor growth simulations provide a means to determine the initial location of a low-grade glioma as well as its cell diffusion tensor, both of which might reflect the biological characteristics of invasion. Key words: computational modeling; glioma; anisotropic growth; diffusion tensor; cell migration Low-grade (WHO grade II) gliomas are initially slowly evolving tumors, but can become rapidly fatal after anaplastic transformation. Because of their infiltrative characteristics, surgery alone fails to cure these tumors, even in their premalignant stage. Indeed, these tumors may not form a solid mass but may invade diffusely throughout the brain parenchyma as "gliomatosis cerebri."Recently, a biomathematical model (1) has been proposed to quantitatively describe the growth rates of gliomas visualized radiologically. This model takes into account the two major biological phenomena underlying the growth of gliomas at the cellular scale: proliferation and diffusion. The simplest choice for the proliferation term is a constant growth rate , leading to an exponentially growing total number of glioma cells. For the invasive properties of gliomas, cell migration is assumed to be a random walk, corresponding to a passive (Fickian) diffusion characterized by a single coefficient D. Simulations of this proliferation-diffusion equation are performed on a 3D T 1 MR structural image of the brain, with segmentation of CSF (which corresponds to the boundaries of the parenchyma), white matter, and gray matter images.In previous publications (2), the diffusion of cells in white matter is assumed to be 5 (to 100) times higher than in gray matter, consistent with observations that glioma cells migrate more quickly in white matter than in gray. Within white (or gray) matter, cell diffusion was considered an isotropic phenomenon. However, it is commonly accepted that gl...

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