The heart is one the most important organs in the human body and many other live creatures. The electrical activity in the heart controls the heart function, and many heart diseases are linked to the abnormalities in the electrical activity in the heart. Mathematical equations and computer simulation can be used to model the electrical activity in the heart. The heart models are challenging to solve because of the complexity of the models and the huge size of the problems. Several cell models have been proposed to model the electrical activity in a single heart cell. These models must be coupled with a heart model to model the electrical activity in the entire heart. The bidomain model is a popular model to simulate the propagation of electricity in myocardial tissue. It is a continuum-based model consisting of non-linear ordinary differential equations (ODEs) describing the electrical activity at the cellular scale and a system of partial differential equations (PDEs) describing propagation of electricity at the tissue scale. Because of this multi-scale, ODE/PDE structure of the model, splitting methods that treat the ODEs and PDEs in separate steps are natural candidates as numerical methods. First, we need to solve the problem at the cellular scale using ODE solvers. One of the most popular methods to solve the ODEs is known as the Rush-Larsen (RL) method. Its popularity stems from its improved stability over integrators such as the forward Euler (FE) method along with its easy implementation. The RL method partitions the ODEs into two sets: one for the gating variables, which are treated by an exponential integrator, and another for the remaining equations, which are treated by the FE method. The success of the RL method can be understood in terms of its relatively good stability when treating the gating variables. However, this feature would not be expected to be of benefit on cell models for which the stiffness is not captured by the gating equations. We demonstrate that this is indeed the case on a number of stiff cell models. We further propose a new partitioned method based on the combination of a first-order generalization of the RL method with the FE method. This new method leads to simulations of stiff cell models that are often one or two orders of magnitude faster than the original RL method. After solving the ODEs, we need to use bidomain solvers to solve the bidomain model. Two well-known, first-order time-integration methods for solving the bidomain model are the semi-implicit method and the Godunov operator-splitting method. Both methods decouple the numerical procedure at the cellular scale from that at the tissue scale but in slightly different ways. The methods are analyzed in terms of their accuracy, and their relative performance is compared on one-, two-, and three-dimensional test cases. As suggested by the analysis, the test cases show that the Godunov method is significantly faster than the semi-implicit method for the same level of accuracy, specifically, between 5 and 15 times in the cases presented. Second-order bidomain solvers can generally be expected to be more effective than first-order bidomain solvers under normal accuracy requirements. However, the simplest and the most commonly applied second-order method for the PDE step, the Crank-Nicolson (CN) method, may generate unphysical oscillations. We investigate the performance of a two-stage, L-stable singly diagonally implicit Runge-Kutta method for solving the PDEs of the bidomain model and present a stability analysis. Numerical experiments show that the enhanced stability property of this method leads to more physically realistic numerical simulations compared to both the CN and Backward Euler (BE) methods.

Title: The effect of sensomotoric stimulation on flat foot of children Introduction: Flat foot is a common health problem in childhood. Its development is related to congenital or acquired dysfunction of the plantar vault. There is no single opinion on the criteria for diagnosis and therapy forms. The aftereffects and health risks of flat foot are often neglected. The therapy form of sensomotoric stimulation, including balance exercises and walking barefoot over different surfaces, could be an appropriate part of the physical activities and games for children in kindergarten. Objectives: The main objective of this thesis was to compare foot prints of a group of children from one kindergarten class before and after six months of sensomotoric stimulation by three different methods (the Chippaux-Šmiřák method, the Godunov-Sztriter method and the Mayer method.). The second objective was to determine at what age category will be the highest prevalence of flat feet and also at what age group is the biggest improvement of the foot arch. The third objective was to compare each other method and determine whether the results will match. Hypothesis 1: After six months of sensomotoric stimulation of the feet of children occurs in the majority of feet of probands the improvement of the longitudinal foot arch...

Title: The effect of sensomotoric stimulation on flat foot of children Introduction: Flat foot is a common health problem in childhood. Its development is related to congenital or acquired dysfunction of the plantar vault. There is no single opinion on the criteria for diagnosis and therapy forms. The aftereffects and health risks of flat foot are often neglected. The therapy form of sensomotoric stimulation, including balance exercises and walking barefoot over different surfaces, could be an appropriate part of the physical activities and games for children in kindergarten. Objectives: The main objective of this work is to evaluate the effect of sensomotoric stimulation of flat foot at preschool age. Methods: The research contains 21 children. Forty-two foot prints were taken at the beginning of the therapy. Three methods were used to evaluate the foot prints: the Chippaux-Šmiřák method, the Godunov-Sztriter method and the Mayer method. The therapy form of sensomotoric stimulation included balance exercises and walking barefoot over different surfaces. The duration of therapy was 15 minutes each school day for six months. The control foot prints of 15 children were taken after the therapy and the results were compared with the foot prints before therapy. Results: The research contains twenty-one...