Tumor growth can be characterized by using scaling analysis methods performed upon the tumor interface; the procedure yields key parameters that define growth geometry according different universality classes. In the present work, results obtained by 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 by a reaction-diffusion differential equation or in this context, a proliferation-invasion equation. The proliferation term was of the logistic type to take into account the limitation of nutrients and oxygen resources on tumor cells. To take into account the differences between grey and white matter for the diffusion parameter, the simulations used the brain tissue 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). Scaling analysis results reveal a close correspondence to results previously obtained on tumor magnetic resonance images, which suggests that the simple model used for the computer simulations describes in an appropriate manner tumor growth of gliomas in brain and potentially its use can be extended to describe brain metastases.
Tópico:
Mathematical Biology Tumor Growth
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4
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FuenteRevista de la Facultad de Ingeniería Universidad Central de Venezuela