Modelling Glioblastoma Growth in Anisotropic Tissue

Examensarbete för masterexamen
Engineering mathematics and computational science (MPENM), MSc
Berggren, Henrik
Glioblastoma, or glioma grade IV is one of the most common types of brain cancer, unfortunately, the cancer is highly aggressive with short survival times related to the diffuse and invasive behaviour of the disease. In many cases, the cancer cells spread to large areas of the brain resulting in difficulties for therapeutic methods used to treat the disease. The mechanisms of glioblastoma spread and growth are still poorly understood, hence this study aims to contribute to the subject by an attempt to characterize tumour growth patterns observed in experimental studies. With support in previous studies, we propose a novel modelling approach consisting of a stochastic, agent-based mathematical model for simulations of glioblastoma development. Anisotropic tissue properties of the brain, in terms of white matter tracts and the brain vasculature, are taken into consideration and influence the proliferation and migration of individual cells. The model is included in a framework for parameter inference, Approximate Bayesian Computation, to identify tumour characteristics from experimental data, originating from cell line-derived xenograft mouse models. By studying parameters of synthetic data, tumours generated by the model itself, we show that model parameters are identifiable to a large extent. Specifically, the method is successful in the task of estimating known tumour properties such as the rate of migration and proliferation as well as the preference of migration in relation to the brain tissue. Furthermore, we investigate three experimental data sets in terms of coronal brain slices with respect to rates governing growth and spread as well as a quantification of the influence from the microenvironment. We present results showing a partial ability of the model to estimate parameters from the experimental data. To improve the estimation of parameters there is a need for an increased number of simulations to enhance the sampling density. Moreover, the growth patterns possible to simulate are affected by the available medical data which originates from different individuals compared to the experimental results. This introduces sources of error in the task to characterize observed tumour development.
Glioblastoma, Glioma grade IV, Agent-based mathematical modelling, Approximate Bayesian Computation (ABC).
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