Solving the Inverse Problem of Relationship Between Action Potentials and Field Potentials in Cardiac Cells

Multiple electrode array (MEA) systems are the instrument platforms being used for cardiac extracellular electrophysiology investigation. Key applications of MEA technology are disease modeling and screening of drug effects. To solve these problems the efforts of many scientists are directed to signal processing and analysis of field potentials (FP) measured with MEA systems. However, it should be noted the complexity of interpretation of MEA information in non-invasive field potentials measurements of cardiac cells compared to invasive action potential (AP) recordings obtained using patch clamp technology. This study is devoted to the mathematical determination of the relationship between the signals of the electrical activity of cardiomyocytes: internal AP and external FP. Derivation of equations for transfer functions between AP and FP is based on field theory. This article provides a solution to the inverse problems of the relationship between AP and FP. Numerical experiments demonstrate the results of the inverse transformation of simulated field potentials signals. To denoise the potentials of the extracellular field of cardiomyocytes, the method combining wavelet transform and processing in eigensubspaces of cardiac cycles is used. The proposed method, based on transfer functions, can be used to determine AP parameters and expand the capabilities of data analysis in MEA systems for diagnosing heart disease and assessing cardiac toxicity during drug development.