A new application of fractional derivatives for predicting human glioblastoma multiforme tumor growth

Glioblastoma is the most common and deadly primary brain tumor in adults. To optimize the treatment strategies, it is essential to understand the tumor growth dynamics in different periods. In this study, we use image processing techniques to combine the available early-stage imaging data and applied a fractional reaction-diffusion equation to predict the human glioblastoma multiforme tumor growth. We consider the heterogeneity of the brain tissue by assigning different diffusion coefficients for the three regions of the human brain. A meshfree method based on the thin plate spline radial basis function is used for the numerical solution of nonlinear time fractional Proliferation-Invasion equation. The results show that the proposed model has a better fit with the experimental data. The prediction of tumor growth at any desired time with no need to repeated imaging is another advantages of the model which could reduce the side effects and cost of diagnostic and therapeutic methods. The model can also incorporate the effects of various treatment modalities such as hyperthermia, radiation, and surgery on tumor growth. Furthermore, it can enable the use of patient-specific characteristics in diagnosis and treatment and facilitate the development of personalized medicine approaches.