Image-driven simulation of brain tumors using a reaction-diffusion mathematical model

Abstract: Brain tumors pose a big challenge in the field of neuro-oncology. Gliomas are the largest subgroup. Magnetic resonance imaging is a non-invasive tool for detecting and characterizing these tumors. Mathematical models, such as the reaction-diffusion equation, can be used for understanding the intricate behavior of gliomas. This thesis aims to improve the understanding and prediction of tumor growth by modifying and evaluating a reaction-diffusion mathematical model and incorporating magnetic resonance (MR) images, namely intensity from T1-weighted and T2-weighted images, and apparent diffusion coefficient values. Image data from five patients was used. The finite difference method was used to approximate the solution, and brain segmentation is performed using the software package FSL. The Jaccard index is used to compare the simulation results with the ground truth, being the segmented tumor area. A spatially varying proliferation rate is introduced and histology images are used to construct an initial condition for the reaction-diffusion mathematical model. The results show improvement in performance based on the Jaccard index, with the highest values achieved when using a diffusion matrix given as an affine function of intensity in T1-weighted images. Incorporating a spatially varying proliferation rate reduces the number of iterations required to reach the maximum Jaccard index compared to a constant proliferation rate, but this does not influence the simulation time. The introduction of the p-Laplace operator, particularly with a value of p = 1.8 instead of the usual Laplace operator (where p = 2), leads to a higher Jaccard index, indicating an improvement in the model’s performance. The best Jaccard index achieved was 0.4909 with p = 1.8 compared to the basic model (JI = 0.4382 with p = 2). An initial tumor cell density is constructed using histology images. In conclusion, insights are provided into improving tumor growth modeling by incorporating MR images, the p-Laplace operator, a spatially varying proliferation rate and possibility of constructing the initial conditions for tumor cell density based on histology images.