| Abstract [eng] |
The thesis is focused on computer modelling of complex chemical and biophysical systems, which are described by partial differential equations with nonlinear boundary conditions and equations in various complex (non-rectangular) domains. The thesis is based on three main studies: 1. modelling of scanning electrochemical microscopy in redox-competition mode, 2. the evaluation of measurement errors in SECM-based experiments using models of electrode geometry, 3. Modelling of fluorescent dyes uptake into the cell spheroid. Mathematical models of those systems are presented. Numerical algorithms, which are used to solve equations of these models, are analyzed. The efficient non-uniform meshing method is proposed for SECM models. Implementations of numerical algorithms are verified by various testing methods. The correctness of each model is confirmed by achieving high correspondence with experimental data. The model of analyzed SECM mode showed, that the oxygen diffusion coefficient is inversely proportional to the concentration of medium components. It was determined by electrode geometry models, that outwarded electrode provides the highest measurement errors, whereas errors of experiments with recessed and cone electrodes are approximately 2 times lower. Using the model of dye uptake, the diffusion coefficient in the cellular matrix has been calculated. |
