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A patient-specific anisotropic diffusion model for brain tumour spread. (English) Zbl 1394.92064

Summary: Gliomas are primary brain tumours arising from the glial cells of the nervous system. The diffuse nature of spread, coupled with proximity to critical brain structures, makes treatment a challenge. Pathological analysis confirms that the extent of glioma spread exceeds the extent of the grossly visible mass, seen on conventional magnetic resonance imaging (MRI) scans. Gliomas show faster spread along white matter tracts than in grey matter, leading to irregular patterns of spread. We propose a mathematical model based on Diffusion Tensor Imaging, a new MRI imaging technique that offers a methodology to delineate the major white matter tracts in the brain. We apply the anisotropic diffusion model of K. J. Painter and T. Hillen [J. Theor. Biol. 323, 25–39 (2013; Zbl 1314.92083)] to data from 10 patients with gliomas. Moreover, we compare the anisotropic model to the state-of-the-art Proliferation-Infiltration (PI) model of K. R. Swanson et al. [“A quantitative model for differential motility of gliomas in grey and white matter”, Cell. Prolif. 33, 317–329 (2000)]. We find that the anisotropic model offers a slight improvement over the standard PI model. For tumours with low anisotropy, the predictions of the two models are virtually identical, but for patients whose tumours show higher anisotropy, the results differ. We also suggest using the data from the contralateral hemisphere to further improve the model fit. Finally, we discuss the potential use of this model in clinical treatment planning.

MSC:

92C50 Medical applications (general)
92C17 Cell movement (chemotaxis, etc.)
35K57 Reaction-diffusion equations

Citations:

Zbl 1314.92083
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References:

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