Shpotak M. Modelling and analysis of extracellular potentials of cardiac cells

The dissertation is devoted to the development and research of methods for modelling and processing of signals of heart cells' electrical activity and aimed at improvement of methodical and algorithmic support of microelectrode systems. In the first chapter, a review of scientific sources was conducted regarding the study of electrophysiology of cardiomyocytes and assessment of cardiotoxicity using modern technologies. It has been established that the patch-clamp method is the gold standard for studying the effects of drugs on cells. However, its use may not be optimal for long experiments or when high throughput is required. Although systems with microelectrode arrays are easier to use and have high throughput, they also have critical limitations. First, the recordings of extracellular potentials in microelectrode array systems have low amplitude and are often mixed with noise from various sources. Second, the inability of microelectrode array systems to record cell action potentials without significant device modifications limits the possibilities for cardiac cell research. Mathematical reconstruction of action potentials from field potentials can be used as a safe alternative that allows obtaining information about action potentials without physically interfering with the cellular structure, which can contribute to a more accurate assessment of the risk of drug cardiotoxicity. Thus, the main directions of the development of methodical and algorithmic support of microelectrode systems for evaluating the cardiotoxicity of drugs are the improvement and development of methods for processing and modelling of signals of heart cells' electrical activity. The second chapter reviews the mathematical models of action potentials and approaches to obtaining extracellular potentials. Modern cardiac cell models are highly detailed and try to incorporate all discovered ion channels, transporters and dynamics of ion concentrations. This approach allows to obtain realistic simulations of action potentials and bioelectrical processes. To streamline the process of model parameter identification and minimize the computational load of simulating the electrical activity of a large population of cells, a modified model of parallel conductances with K, Na, and Ca currents has been proposed. The currents of the highly detailed model of the electrical activity of the human sinoatrial node cell were integrated into groups of three general currents. The parameters of the modified model were finetuned in such a way that the waveforms of its currents corresponded to the generalized currents of the highly detailed model. As a result, the obtained model has significantly fewer differential equations and parameters, but is able to simulate action potentials with a morphology similar to that of a highly detailed model. Supplementing the model of parallel conductions with the equations of extracellular potentials based on the field theory made it possible to obtain a two-domain model. The use of a bidomain approach allowed to model the extracellular potentials of human sinoatrial heart cells for further study and analysis. In the third chapter, a technique for reconstructing the action potentials of multiple cardiac cells from their extracellular potentials for multielectrode systems was developed. This technique has been adapted for different cases, including synchronous and asynchronous action potentials, identical and different action potentials, and groups of cells with synchronous and identical action potentials. To solve the problem when the number of cells exceeds the number of electrodes, an approach was developed to divide the cells into groups in which the action potentials are assumed to be synchronous and identical. The method of determining the synchronicity of action potentials based on the proposed reconstruction approach is described. An analytical solution was derived to calculate the distances from the electrodes to the cell in 1-dimensional and 2-dimensional cases based on the proposed bidomain approach and the geometry of the microelectrode array. In the fourth chapter, a comparative analysis of field potential denoising methods was carried out, including wavelet transform, the method of eigen subspaces and the complex denoising method. The study found that the complex method showed the best results. The cardiotoxicity risk of drugs was analysed using reconstructed action potentials. An approach to expanding the data set for machine learning was proposed and the classification of extracellular potentials by cardiotoxicity risk groups and drug concentrations using the k-nearest neighbours method was performed. An evaluation of the parameters used for classification revealed that incorporating additional parameters, derived from reconstructed action potentials, could enhance the accuracy of classification.