АНАЛІЗ МАТЕМАТИЧНИХ МОДЕЛЕЙ РИТМІЧНОГО ЕРГ-СИГНАЛУ ТА РОЗРОБЛЕННЯ ЙОГО СТРУКТУРНО-ПАРАМЕТРИЧНОГО ПРЕДСТАВЛЕННЯ ДЛЯ ЗАДАЧ ДІАГНОСТИКИ ГЛАУКОМИ

The paper considers the problem of mathematical representation of the rhythmic ERG signal generated in response to periodic light stimulation for the study of retinal functional state in glaucoma. An analysis of established approaches to the mathematical description of rhythmic ERG is presented, including frequency-domain, spectral, amplitude-phase, nonlinear, component-based, resonance, and statistical models. It has been established that the considered approaches make it possible to characterize individual properties of the rhythmic ERG signal, including its frequency and spectral characteristics, nonlinear effects, component composition, phase relationships, and resonance dynamics; however, they do not provide a unified structural-parametric description of changes in successive ERG responses within a continuous signal realization. A structural-parametric representation of the rhythmic ERG signal is proposed, in which each i-th ERG response is described by a set of structural components, while their relative contributions are determined by cycle-dependent coefficients kA,i, kB,i, kO,i, and kC,i. Based on these coefficients, a structural vector ki is formed, whose sequence characterizes changes in the relative contributions of the structural components of ERG responses from cycle to cycle. This approach makes it possible to distinguish between an overall change in response scale and a change in its internal structure resulting from changes in the relative contributions of individual structural components. An important feature of the proposed model is the preservation of the continuous nature of the recorded rhythmic ERG signal x(t). The structural components are used as a mathematical level of its parametric representation rather than as physically separated signals. The direct object of recording and subsequent digital processing remains a single time-domain realization of the rhythmic ERG signal. The scientific novelty lies in combining structural and cycle-dependent parametric descriptions of the continuous rhythmic ERG for quantitative assessment of inter-cycle changes in its structural properties. The proposed representation can serve as a basis for further digital processing of the rhythmic ERG signal in the time, spectral, correlation, and time-frequency domains, including the use of wavelet transform. The obtained structural-parametric characteristics can be used to form informative (diagnostic) features and subsequently applied in machine learning and artificial intelligence algorithms for automated assessment of the functional state of the retina and support of glaucoma diagnosis