چكيده به لاتين
Cardiac cell electrical behaviour modelling allows the study of the functional mechanisms of heart muscle. Mathematical models makes it possible to simulate and compare healthy and diseased hearts in order to study cardiac arrhythmias. Electrophysiological, simplified, minimal and behavioural models constitute a variety of cellular models. In electrophysiology, Minimal models are models which can simulate specific behviours of cells with minimum numbers of state variables, i.e. differential equations. Electrophysiological models that are based on experimental measurements, have detailed ionic descriptions as well as high computational costs. This type of models is often presented by physiologists, while other threes are developed by biomedical engineers and mathematicians. Accordingly, as biomedical engineers, we follow two approaches; simplifications of electrophysiological model and developing minimal model. In the first approach, we have proposed a mathematical theory to simplify complex electrophysiological models, based on sloppiness theory of biological systems, by using nonlinear functions instead of differential equations, as well as removing ineffective parameters on the behavior of electrophysiologcal model. This method was validated by applying it to a complex ventricular model and reducing it to a simplified model with two state variables. Simplicity of model analysis is a requirement for researches using ventricular cell models. This simplicity leads to easily interpretable in silico experiment results and define role of each parameters on model behavior. Therefore, with aim of simplicity in model analysis, we have proposed a graphical algorithm based on mathematical argumentation and compatible with ventricular cell electrophysiology. Using this algorithm, we have presented and validated a minimal model for ventricular cell. Cell models, except electrophysiological models, can not simulate all behaviors of ventricular cell. So, researchers use the models which have the ability of simulating desire behaviors, depending on the subject matter. Studying cell behaviors, especially various arrhythmias, needs models that can properly simulate plateau phase of ventricular cell action potential. Therefore, in this research, we proposed a nonlinear model for time constants of ionic gates by proof of a mathematical theorem. This model can reproduce different morphologies of plateau phases of cardiac cell action potential. Results of above models indicate that although each of them can simulate behaviors of ventricular cell, third state variable should be added to the models in order to better simulation of pleateau phase and some of abnormal behaviors. Accordingly, we have presented a model with three state variables by mathematical reasoning and using a new parameter, ratio of resonating to inhibition speed. The new parameter defines as ratio of activation to inactivation speed which can be assumed as a pathological control parameter. The final model can reproduce normal behaviors of ventricular cell such as morphology, diffusion and restitution, as well as, abnormal behavior of alternans and reentry.
