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Shahin Heydari - NSFD and FEM Methods for Mathematical Models of Cancer Invasion

Date: 15/05/2019 12:20 - 15/05/2019 13:50
Place: Seminární místnost MÚUK
Using mathematical model to simulate dynamic biological processes has a long story. Over the past decades or so, quantitative approaches have also made their way into Cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspect of tumor growth. Herein we describe fundamentals of some mathematical modeling of biological system, in particular, of Cancer growth. Then we design some nonstandard finite difference (NSFD) schemes to solve the models, which are dynamically consistent with respect to the positivity property of the solution. Finally, a finite element method (FEM) for the solution of Cancer invasion models will be introduced. The main question is how generating a finite element mesh of the patient specific biological domain, using MRI (Magnetic Resonance Imaging) data, can provide useful information to the surgeons in laser treatment process.

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