Glioblastoma multiforme growth prediction using a Proliferation-Invasion model based on nonlinear time-fractional 2D diffusion equation

The glioblastoma multiforme (GBM) is the fast-growing and aggressive type of tumor of the brain or spinal cord that is associated with high morbidity and mortality. Therefore, accurate knowledge of the tumor growth process in different time intervals seems necessary to adopt optimal treatment methods. In this study, with a combination of available early stages imaging data and using image processing methods, a time fractional reaction-diffusion equation based on the moving least squares method was implemented for predicting the growth of the GBM tumor model implemented in the mouse brain. The obtained results demonstrate that the Proliferation-Invasion model implemented by a time fractional form shows more agreement with the experimental results. As a result, using a fractional derivative of order ������ = 0.9 results in the lowest prediction error of the tumor surface (less than 1%). In addition, to reducing the cost and side effects of theranostic methods, the presented model will have the possibility to consider the effects of therapeutic factors, such as hyperthermia, radiography, and surgery, on tumor growth. The ability to use the patient's characteristics in diagnostic and treatment considerations and the development of personalized medicine can also be considered one of the capabilities of the presented model.

Automated summary

In this study, a time fractional reaction-diffusion equation based on the moving least squares method was used to predict the growth of the GBM tumor model in the mouse brain. The results showed that the Proliferation-Invasion model implemented in a time fractional form had a better agreement with experimental results, with a prediction error of less than 1%. The presented model also has the potential to consider the effects of therapeutic factors on tumor growth and can be applied in personalized medicine.