Geometry of tumor growth in brain

Miguel Martín-Landrove, Francisco Torres-Hoyos

 

Revista de la Facultad de Ingeniería U.C.V., Vol. 28, N° 4, pp. 79-­88, 2013 [article in spanish]

 

The tumor growth can be characterized by using scaling analysis methods performed on the tumor interface, a procedure results obtained through a scaling analysis are shown for tumor lesions in brain, of primary origin, either malignant or benign and metastases. To evaluate different proposed models for tumor growth in brain, several growth simulations for primary brain tumors or gliomas were performed assuming a simple growth model, described through a reaction-­diffusion differential equation or in this context, a proliferation-­invasion equation. The term associated to the proliferation is from logistic type, to take into account the limitation of nutrients and oxygen resources imposed on tumor cells. In order to consider the differences between grey and white matter in the diffusion parameters, the simulations used the brain tissue’s database provided by BrainWeb. Simulations were performed for different relations between the diffusion parameters (invasion) and the reaction parameters (proliferation) covering growth conditions from low grade gliomas up to high grade gliomas (glioblastoma multiforme). The scaling analysis results show a close correspondence with previously results revealed in tumor magnetic resonance images, which suggest that the simple model used for the computer simulations describes in an appropriate manner tumor growth of glioma in the brain and that its use could be extended for describing the brain metastases.