Glioma is one of the most challenging types of brain tumors to be treated or controlled locally. One
of the main problems is to determine which areas of the apparently normal brain contain glioma
cells, as gliomas are known to infiltrate several centimetres beyond the clinically apparent lesion
that is visualized on standard CT or MRI. To ensure that radiation treatment encompasses the whole
tumor, including the cancerous cells not revealed by MRI, doctors treat the volume of brain that
extends 2cm out from the margin of the visible tumor. This approach does not consider varying
tumor-growth dynamics in different brain tissues, thus it may result in killing some healthy cells
while leaving cancerous cells alive in other areas. These cells may cause recurrence of the tumor
later in time which limits the effectiveness of the therapy.
In this thesis, we propose two models to define the tumor invasion margin based on the fact that
glioma cells preferentially spread along nerve fibers. The first model is an anisotropic reaction-diffusion
type tumor growth model that prioritizes diffusion along nerve fibers, as given by DW-MRI
data. The second proposed approach computes the tumor invasion margin using a geodesic
distance defined on the Riemannian manifold of brain bers. Both mathematical models result
in Partial Differential Equations (PDEs) that have to be numerically solved. Numerical methods
used for solving differential equations should be chosen with great care. A part of this thesis is
dedicated to discuss in detail, the numerical aspects such as stability and consistency of different
finite difference methods used to solve these PDEs. We review the stability issues of several 2D
methods that discretize the anisotropic diffusion equation and we propose an extension of one 2D
stable method to 3D. We also analyze the stability issues of the geodesic model. In comparison, the
geodesic model is numerically more stable than the anisotropic diffusion model since it results in a
rst-order PDE. Finally, we evaluate both models on actual DTI data from patients with glioma by
comparing our predicted growth with follow-up MRI scans. Results show improvement in predicting
the invasion margin when using the geodesic distance model as opposed to the 2cm conventional
Euclidean distance.
| Identifer | oai:union.ndltd.org:LACETR/oai:collectionscanada.gc.ca:AEU.10048/975 |
| Date | 06 1900 |
| Creators | Mosayebi, Parisa |
| Contributors | Martin Jagersand, Computing Science, Dana Cobzas, Computing Science, Thomas Hillen, Mathematical and Statistical Sciences, Russell Greiner, Computing Science |
| Source Sets | Library and Archives Canada ETDs Repository / Centre d'archives des thèses électroniques de Bibliothèque et Archives Canada |
| Language | en_US |
| Detected Language | English |
| Type | Thesis |
| Format | 2524386 bytes, application/pdf |
| Relation | D. Cobzas, P. Mosayebi, A. Murtha, and M. Jagersand. Tumor invasion margin on the riemannian space of brain fibers. In MICCAI, 2009. |
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