Abstract
Introduction. The method of electrical analogies for the analysis of bioelectric dynamic processes in cardiomyocytes is used in the study. This method allows for replacing investigation of phenomena in non-electrical systems by research of analogous phenomena in electrical circuits. The investigation of time processes in cardiac cells is based on the solution of the system of ordinary differential equations for an electrical circuit. Electrophysiological properties of cardiomyocytes such as refractory period, maximum capture rate and electrical restitution are studied. Mathematical modeling. Computational simulation of the action potential and currents for $K^+$, $Na^+$, $Ca^{2+}$ ions in cardiomyocytes is performed by using the parallel conductance model. This model is based on the assumption of the presence of independent ion channels for $K^+$, $Na^+$, $Ca^{2+}$ ions, as well as leakage through the membrane of cardiac cell. Each branch of the electrical circuit reflects the contribution of one type of ions to total membrane current. Results. The obtained electrical restitution curves for ventricular and atrial cardiomyocytes are presented in the paper. The proposed model makes it possible to identify the areas with the maximum slope on the restitution curves, which are crucial in the development of cardiac arrhythmias. Dependences of calcium current on stimulation frequency for atrial and ventricular cardiomyocytes are obtained. Analysis of the kinetics of calcium ions under various protocols of external influences can be useful for predicting the contractile force of cardiomyocytes. Conclusion. The results of calculations can be used to interpret the experimental results obtained in investigations of cardiomyocytes using the laboratory on a chip technology, as well as in the design of new experiments with cardiomyocytes for drug screening, cell therapy and personalized studies of heart diseases.
Highlights
The method of electrical analogies for the analysis of bioelectric dynamic processes in cardiomyocytes is used in the study
The aim of the paper is to focus on the cardiomyocyte electrophysiological properties at the functional level, including the generation of action potentials, activativation/inactivativation processes in calcium ions channels, the frequency-dependent changes in action potential duration and the intracellular calcium release or uptake, that enables to explain the changes in excitation-contraction coupling of cardiomyocytes
Membrane conductances for K+, N a+, Ca2+ channels are described by the following equations: gK = gK maxn4(vm, t), gNa(vm, t) = gNamaxm3(vm, t)h(vm, t), gCa(vm, t) = gCamaxd(vm, t)f, where gK max, gNamax and gCamax are conductances for potassium, sodium and calcium ions, respectively, in the case that all the channels for this type of ions are in the open state; n is activation function of K+ channels; m is activation function and h is inactivation function for N a+ channels; d is activation function and f is inactivation function for Ca2+ channels
Summary
The method of dynamic analogies is widely used for a long time as a basis for interdisciplinary research of technical systems and physical models in medicine, biology, ecology [1,2,3,4]. Analyzing the components and topological equations of various types of systems, we can detect their dynamic analogies This makes it possible to use Kirchhoff’s laws of electrical engineering and component equations, in particular, for analyzing bioelectric processes in living tissues and cells. In this case, the cell membrane is represented by a circuit model that includes a capacitive element, and in which the ion channel conductivities are represented in the form of resistive linear and nonlinear components, but nonequilibrium electrochemical processes are described by voltage sources. Al equations for a nonlinear model of an electrical circuit that describes the dynamics of cardiac cells functioning
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