MATHEMATICAL MODELING OF A RHYTHMIC ELECTRORETINOGRAPHIC SIGNAL FOR STUDYING THE FUNCTIONAL STATE OF THE RETINA IN GLAUCOMA

Abstract

The article develops a structural-parametric mathematical model of a rhythmic electroretinographic signal that accounts for the characteristics of the retinal electrical response to periodic light stimulation and enables investigation of retinal functional state under normal conditions and in glaucoma. The proposed model is based on an additive representation of the electroretinographic signal, in which each cycle is considered as a superposition of the main physiologically justified components: the early negative a-wave, positive b-wave, high-frequency oscillatory potentials (OPs), and slow C-wave. A system of Gaussian and localized sinusoidal functions is used for the mathematical description of these components, allowing their amplitude-temporal characteristics to be independently specified and controlled.

A distinctive feature of the proposed approach is the introduction of a mathematical framework for accounting for inter-cycle functional adaptation (fatigue) of the retina. The use of an exponential attenuation coefficient enables the nonlinear decrease in component amplitudes during repeated stimulation to be reproduced, which corresponds to actual physiological patterns. In addition, the model provides the possibility of simulating pathological changes characteristic of glaucoma by selectively reducing the amplitudes of those components, namely the b-wave and oscillatory potentials, that reflect the activity of the inner retinal layers affected by this disease.

The practical applicability of the model was confirmed through software simulation in the MATLAB environment for a series of 10 light flashes with the addition of a noise component model. The obtained temporal and spectral results, as well as the plots of signal decomposition and adaptation dynamics, demonstrate the physiological adequacy of the generated signals. The developed mathematical model can be used as a reliable source of verified synthetic data for testing digital signal processing methods, improving automated analysis algorithms, and developing software for modern computer-based systems for the early functional diagnosis of glaucoma.