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Mathematical Modelling of Glioma Stem Cell Fractions After Irradiation Treatments Open Access


Other title
ordinary differential equations
glioblastoma multiforme
glioma stem cell
Type of item
Degree grantor
University of Alberta
Author or creator
Veljee, Wafa S
Supervisor and department
Hillen, Thomas (Mathematics and Statistical Sciences)
Examining committee member and department
Wang, Hao (Mathematics and Statistical Sciences)
Safouhi, Hassan (Mathematics and Statistical Sciences)
Hillen, Thomas (Mathematics and Statistical Sciences)
De Vries, Gerda (Mathematics and Statistical Sciences)
Department of Mathematical and Statistical Sciences
Applied Mathematics
Date accepted
Graduation date
Master of Science
Degree level
Glioblastoma Multiforme (GBM) is a grade IV brain tumour. It is the most common brain malignancy and is extremely aggressive. Ionizing radiation plays a vital role in the treatment of this tumour. Growth of the GBM is sustained by a subpopulation of the tumour cells often called the glioma stem cells (GSC). Kim et al. and Gao et al. presented in vitro and in silico data respectively where GSC population seemed unnaturally increased. We created four nested ODE models for GBM growth. Parameters were estimated from the available data using the least squares error method and the Akaike Information Criterion was used to choose a suitable model for tumour growth. The aspect of irradiation treatment was incorporated into the glioma growth model using the linear-quadratic model. My analysis on the treatment ODE model supports the findings of Gao et al. that the increased stem cell ratios can only be explained if the stem cell population divides more aggressively after radiotherapy.
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