3D quantitative brain tumor growth model based on cell proliferation and diffusion

The focus of this work was to develop a 3D mapping of brain tumor (glioma) growth based on cell proliferation and diffusion. In this mathematical model, we incorporated high resolution brain tissue maps (white and gray matter) from an anonymized pediatric patient and initialized the model with a single voxel seed point of tumor with a Gaussian distribution. We used this model to investigate the ratio of growth rate to the diffusion coefficient (ρ/D) which determines the proportion of tumor that is detectable. After expansion of the tumor growth model to three dimensions and solving the differential equations for our specific starting conditions, we performed several simulations to assess tumor growth patterns. After observing the performance of the model at varying time points across a one year time frame with different values for ρ/D, we ascertained that the tumor diffused more rapidly than the cell proliferated for a short period of time followed by an exponential growth in detectable tumor size.