Four-dimensional modeling of GBM brain tumor growth using cellular automata

A great number of people are diagnosed with a brain tumor, annually. Glioblastoma multiform (GBM) is the most common and deadliest malignant primary brain tumor. Therefore, the study of the growth of GBM is one of the issues considered by researchers. Many mathematical models to simulate the growth of GBM brain tumor have been proposed. These models help scientists to understand the process of tumor growth in order to achieve effective treatment. To simulate the tumor growth, a four dimensional (4D) model using cellular automata (CA) method is presented in this paper. A three dimensional (3D) lattice constituted by Voronoi tessellation is used. Spatial distribution of grid points in 3D has been generated by using Random Sequential Addition (RSA). In the utilized lattice, each cell is a polyhedron with various number of edges and neighboring. Delaunay triangulation is applied to find neighboring cells. Each cell in this lattice can be necrotic, non-proliferative, proliferative, non-tumorous or normal. The simulation is capable to exhibit a tumor growth of 0.1 mm to 25 mm in radius. The proposed model has been compared with experimental data in four temporal stages: spheroid, detectable lesion, diagnosis and death. Studies show that the accuracy of the presented model is generally about 85%.