Evaluating Gaussian and Rayleigh-Based Mathematical Models for T and P-waves in ECG

Abstract

This paper presents a comparative study of modelling and segmentation of P and T waves in electrocardiograms, using three different mathematical models: Gaussian function, a composition of two Gaussian functions and Rayleigh probability density function (Rayleigh pdf). In order to evaluate the adaptability and the matching degree between each model and each characteristic wave, we compute the normalized root mean square (RMS) error, as well as the evolution of the fitting parameters related to each kernel throughout ECG records from the well-known QT database. Concerning the delineation of P and T-waves, we apply Wavelet Transform for estimating T-wave and P-wave peak locations and combine each developed model with an approach based on the computation of Trapezium's area to locate the end point of each T-wave and the beginning and end point of each P-wave. The composition of two Gaussian functions has produced the most accurate results concerning wave modelling, providing average values of normalized RMS errors equal to 9,15% and 18,70%, respectively for T-wave and P-wave. Rayleigh pdf provided the most stable fitting parameters. For T-wave end location, the most accurate results were computed when using the kernel composition of two Gaussian functions, for which the average time error was 4,49 ± 14,32 ms. For P-wave begin and P-wave end locations, the most accurate results were computed when using kernel Rayleigh pdf, for which the average time errors were, respectively, -4,23 ± 14,84 ms and 2,26 ± 13,14 ms.