Simulating glioblastoma growth consisting both visible and invisible parts of the tumor using a diffusion–reaction model followed by resection and radiotherapy

Glioblastoma is known to be among one of the deadliest brain tumors in the world today. There have been major improvements in the detection of cancerous cells in the twenty-first century. However, the threshold of detection of these cancerous cells varies in different scanning techniques such as magnetic resonance imaging (MRI) and computed tomography (CT). The growth of these tumors and different treatments have been modeled to assist medical experts in better predictions of the related tumor growth and in the selection of more accurate treatments. In clinical terms the tumor consisted of two parts known as the visible part, which is the part of the tumor that is above the threshold of the detecting device and the invisible part, which is below the detecting threshold. In this study, the common reaction–diffusion model of tumor growth is used to simulate the growth of the glioblastoma tumor. Also resection and radiotherapy have been modeled as methods to prevent the growth of the tumor. The results demonstrate that although the selected treatments were effective in reducing the number of cancerous cells to under the threshold of detection, they did not eliminate all cancerous cells and if no further treatments were applied, the cancerous cells would spread and become malignant again. Although previous studies have suggested that the ratio of proliferation to diffusion could describe the malignancy of the tumor, this study in addition shows the importance of each of the coefficients regarding the malignancy of the tumor.