Avaliação de Modelos Matemáticos baseados nas Funções Gaussiana e Rayleigh para as ondas P e T em ECG (Evaluating Gaussian and Rayleigh-Based Mathematical Models for T and P-waves in ECG)

João Paulo do Vale Madeiro (jpaulo.vale@unilab.edu.br)1, Elves Mauro Boa Esperança dos Santos (elvesfixe14@gmail.com)1, Paulo César Cortez (cortez@lesc.ufc.br)2, John Hebert da Silva Felix (johnfelix@unilab.edu.br)1, Fernando Soares Schlindwein (fss1@le.ac.uk)3


1Universidade da Integração Internacional da Lusofonia Afro-Brasileira
2Universidade Federal do Ceará
3University of Leicester

This paper appears in: Revista IEEE América Latina

Publication Date: May 2017
Volume: 15,   Issue: 5 
ISSN: 1548-0992


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.

Index Terms:
electrocardiogram (ECG), P and T waves, mathematical models, normalized RMS error, Gaussian function, Rayleigh pdf   


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