A Patient-Specific Anisotropic Diffusion Model for Brain Tumour Spread

• Published in: Bulletin of mathematical biology Vol. 80; no. 5; pp. 1259 - 1291
• Main Authors: Swan, Amanda, Hillen, Thomas, Bowman, John C., Murtha, Albert D.
• Format: Journal Article
• Language: English
• Published: New York Springer US 01.05.2018; Springer Nature B.V
• Subjects: Anisotropy; Brain; Brain cancer; Brain Neoplasms - diagnostic imaging; Brain tumors; Cell Biology; Computer Simulation; Diffusion; Diffusion Tensor Imaging - methods; Diffusion Tensor Imaging - statistics & numerical data; Glial cells; Glioma; Glioma - diagnostic imaging; Humans; Image Interpretation, Computer-Assisted; Imaging, Three-Dimensional; Infiltration; Life Sciences; Magnetic resonance imaging; Mathematical and Computational Biology; Mathematical Concepts; Mathematical models; Mathematics; Mathematics and Statistics; Metastases; Neoplasm Invasiveness - diagnostic imaging; Nervous system; Neuroimaging; NMR; Nuclear magnetic resonance; Patient-Specific Modeling; Patients; Special Issue : Mathematical Oncology; Substantia alba; Substantia grisea; Tumors; Mathematical modelling; Mathematical medicine; Partial differential equations; Gliomas; Anisotropic diffusion
• ISSN: 0092-8240; 1522-9602
• DOI: 10.1007/s11538-017-0271-8

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 Painter and Hillen (J Thoer Biol 323:25–39, 2013 ) to data from 10 patients with gliomas. Moreover, we compare the anisotropic model to the state-of-the-art Proliferation–Infiltration (PI) model of Swanson et al. (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.