ВИКОРИСТАННЯ ФУНКЦІЙ ГАУСА ДЛЯ АПРОКСИМАЦІЇ БІОЛОГІЧНИХ СИГНАЛІВ

Abstract

Purpose. Currently, the method of mathematical analysis of various biological signals is increasingly used in medicine. Most of them are random and quasi-periodic processes, which greatly complicates the possibility of using an automated data processing process. Signals of this type include respiratory noises, phonocardiographic and electrocardiographic signals. The shape of the waves of the ECG signal is quite accurately described by asymmetric Gaussian pulses. It is possible to achieve the required approximation accuracy by introducing additional pulses to describe the diagnostically important inhomogeneities of the signal. In the previous work of the authors the simple algorithm of coefficients selection of asymmetric functions in the form of the Labview virtual device is realized. But for the cases of superposition of waves of different polarity and non-standard pulse shapes, the result of applying this algorithm gives a significant error. Methodology. In the analysis of waves of negative polarity, the presence of a positive burst, even a small value, leads to a complete disregard for the negative wave. To eliminate this shortcoming, it is necessary to determine the maximum and minimum values of the amplitudes of the samples in this area and compare their absolute values. A larger value will determine the polarity of the wave coming to the virtual instrument for analysis. The next complication is the presence of a wide flat wave top with an offset maximum value by extreme samples. This is a significant shift in the symmetry of the wave and, as a consequence, incorrect determination of parameters for a wide part of the pulse. To eliminate this shortcoming, it is proposed to determine all the influential extremes, and shift the center of symmetry to the middle of the flat top of the wave. In the case where the wave has a significant violation of symmetry, it is possible that the virtual device determines the midpoints and amplitudes of the left to right parts with a significant deviation from the actual peak value. To prevent the vertices of the Gaussian functions from shifting relative to the real maximum it was proposed to mirror the data sets corresponding to the left and right parts of the wave. Results. In this article, the algorithm of the virtual device operation for automatic determination of the parameters of the approximate asymmetric Gaussian curves in the Labview software environment is improved. It is planned to use approximation by Gaussian impulses to synthesize standard leads from reduced sets of ECG signal leads. According to preliminary studies, a surface of approximation coefficients has been created, which allows synthesizing a cardiac signal for an arbitrary derivation. Originality. Algorithm for approximating biological signals by asymmetric Gaussian functions is improved. In this case, a more confident approximation of waves was obtained in the presence of: bursts of opposite polarity; wide flat top of the wave when the maximum value is shifted to extreme samples; significant violation of the symmetry of the waves; narrow fragments of waves. Practical value. A virtual device was created to approximate signals (including ECG signal leads, respiratory noises and phonocardiosignals) using asymmetric Gaussian functions. The analysis of certain coefficients will make it possible to use them as average criteria for the diagnosis of the corresponding diseases, which requires further research. References 10, figures 11.