Simulation tumor growth in heterogeneous medium based on diffusion equation

In this paper, the diffusion equation is used to model the spatio-temporal dynamics of a tumor, taking into account the heterogeneity of the medium. This approach allows us to take into account the complex geometric shape of the tumor when modeling. The main purpose of the work is to demonstrate the applicability of this approach by comparing the results obtained with the data from clinical observations. We use an algorithm based on an explicit finite-difference approximation of differential operators to solve the diffusion equation. The ranges of possible values that can take the input parameters of the model to match the results of clinical observations are obtained. On the basis of the data of clinical observations, the relative error of the results of computational experiments was determined, which lies in the range from 1.8% to 14.6%. It is concluded that the heterogeneity of the physical parameters of the model, in particular the diffusion coefficient, has a significant effect on the shape of the tumor.