Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert

Detalhes bibliográficos
Ano de defesa: 2013
Autor(a) principal: Madeiro, João Paulo do Vale
Orientador(a): Cortez, Paulo César
Banca de defesa: Não Informado pela instituição
Tipo de documento: Tese
Tipo de acesso: Acesso aberto
Idioma: por
Instituição de defesa: Não Informado pela instituição
Programa de Pós-Graduação: Não Informado pela instituição
Departamento: Não Informado pela instituição
País: Não Informado pela instituição
Palavras-chave em Português:
Link de acesso: http://www.repositorio.ufc.br/handle/riufc/5655
Resumo: A utomatic diagnostic aid systems aim the extraction of speci c parameters in order to support the analysis of a patient's physiological conditions possibly using computing algorithms. In the context of cardiology, such systems are particularly important when applied over long-term ECG signals, for example the 24-h holter examinations. The digital signal processing techniques for ECG waves segmentation and automatic feature extraction, which are proposed in this thesis, cover various research elds. Firstly, the proposed system performs QRS complex detection and segmentation, which is related to ventricular depolarization. The used methodology combines the adaptive threshold technique, Hilbert and Wavelet transforms and the rst-derivative lter with a new approach of preprocessing suppression over the whole ECG signal and selection of Wavelet scale factor for a given predominant QRS morphology. As output information we obtain the RR time-series (tachogram), the time-series of QRS complex durations and amplitudes. In the second stage, the developed system performs T-wave detection and segmentation, whose waveform is related to ventricular repolarization activity. It is proposed a new mathematical model concerning the possible T-wave morphologies based on a Gaussian function, modi ed by a mathematical procedure to insert asymmetry. Once the template is computed, cross-correlation and an approach based on the computation of Trapezium's area are used to locate, respectively, the peak, or the peaks for biphasic waves, and end point of each T-wave throughout the whole raw ECG signal. Among the metrics derived from the detected ducial points, we emphasize the QT intervals, which are the time intervals between the QRS onset and the T-wave end. After the segmentation of the ECG waves, we perform two important case studies using the ducial points and segments detected in the previous stages: ventricular activity subtraction in intracardiac atrial brillation electrogram and heart hate variability (HRV) analysis for a set of elderly patients which were selected in the Geriatric Outpatient Clinic of the Walter Cantidio University Hospital. After evaluating the overall methodology of QRS detection and segmentation over various manually annotated databases, inclusive the public MIT-BIH Arrhythmia database and QT database, we have obtained the following detection rates and delineation time errors: sensitivity of 99.51%, positive predictivity of 99.44%, QRS onset time error of 2.85 9.90 ms and QRS o set time error of 2.83 12.26 ms. Regarding T-wave detection and delineation, the proposed method has attained sensitivity of 99.48%, positive predictivity of 99.53%, and average time errors of 0.51 8.06 ms, for T-wave peak location, and 0.11 11.73 ms, for T-wave end location. Regarding the rst case study concerning the use of the ducial points detected from the segmented QRS complexes and T-waves over intracardiac atrial brillation electrogram, the method of ventricular activity subtraction has attained a signi cant attenuation for frequencies above 10 Hz, and also for components of frequency range around 3 Hz to 6 Hz, respectively due to ventricular depolarization and repolarization subtraction. For the second application, the analysis of the evolution of heart rate variability metrics in frequency domain associated to sympathetic branch activity allows recognizing speci c tendencies regarding aspects of proper functioning/dysautonomia of the autonomic nervous system for each predetermined elderly class according to the concepts of frailty phenotype: frail, pre-frail and robust ones. The overall results suggest that the set of methodologies developed for ECG waves segmentation provides high rates of accurate and robust detections for a wide variety of morphologies, such that they can be applied in various situations for aid to diagnosis. Given the set of possible metrics and time-series which can be extracted from the ECG signals, after their segmentation, the referred methods can support projects of clinical research and development of markers/indicators of adverse cardiovascular events.
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spelling Madeiro, João Paulo do ValeCortez, Paulo César2013-08-20T14:50:06Z2013-08-20T14:50:06Z2013MADEIRO, J. P. V. Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert. 2013. 130 f. Tese (Doutorado em Engenharia de Teleinformática)-Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2013.http://www.repositorio.ufc.br/handle/riufc/5655A utomatic diagnostic aid systems aim the extraction of speci c parameters in order to support the analysis of a patient's physiological conditions possibly using computing algorithms. In the context of cardiology, such systems are particularly important when applied over long-term ECG signals, for example the 24-h holter examinations. The digital signal processing techniques for ECG waves segmentation and automatic feature extraction, which are proposed in this thesis, cover various research elds. Firstly, the proposed system performs QRS complex detection and segmentation, which is related to ventricular depolarization. The used methodology combines the adaptive threshold technique, Hilbert and Wavelet transforms and the rst-derivative lter with a new approach of preprocessing suppression over the whole ECG signal and selection of Wavelet scale factor for a given predominant QRS morphology. As output information we obtain the RR time-series (tachogram), the time-series of QRS complex durations and amplitudes. In the second stage, the developed system performs T-wave detection and segmentation, whose waveform is related to ventricular repolarization activity. It is proposed a new mathematical model concerning the possible T-wave morphologies based on a Gaussian function, modi ed by a mathematical procedure to insert asymmetry. Once the template is computed, cross-correlation and an approach based on the computation of Trapezium's area are used to locate, respectively, the peak, or the peaks for biphasic waves, and end point of each T-wave throughout the whole raw ECG signal. Among the metrics derived from the detected ducial points, we emphasize the QT intervals, which are the time intervals between the QRS onset and the T-wave end. After the segmentation of the ECG waves, we perform two important case studies using the ducial points and segments detected in the previous stages: ventricular activity subtraction in intracardiac atrial brillation electrogram and heart hate variability (HRV) analysis for a set of elderly patients which were selected in the Geriatric Outpatient Clinic of the Walter Cantidio University Hospital. After evaluating the overall methodology of QRS detection and segmentation over various manually annotated databases, inclusive the public MIT-BIH Arrhythmia database and QT database, we have obtained the following detection rates and delineation time errors: sensitivity of 99.51%, positive predictivity of 99.44%, QRS onset time error of 2.85 9.90 ms and QRS o set time error of 2.83 12.26 ms. Regarding T-wave detection and delineation, the proposed method has attained sensitivity of 99.48%, positive predictivity of 99.53%, and average time errors of 0.51 8.06 ms, for T-wave peak location, and 0.11 11.73 ms, for T-wave end location. Regarding the rst case study concerning the use of the ducial points detected from the segmented QRS complexes and T-waves over intracardiac atrial brillation electrogram, the method of ventricular activity subtraction has attained a signi cant attenuation for frequencies above 10 Hz, and also for components of frequency range around 3 Hz to 6 Hz, respectively due to ventricular depolarization and repolarization subtraction. For the second application, the analysis of the evolution of heart rate variability metrics in frequency domain associated to sympathetic branch activity allows recognizing speci c tendencies regarding aspects of proper functioning/dysautonomia of the autonomic nervous system for each predetermined elderly class according to the concepts of frailty phenotype: frail, pre-frail and robust ones. The overall results suggest that the set of methodologies developed for ECG waves segmentation provides high rates of accurate and robust detections for a wide variety of morphologies, such that they can be applied in various situations for aid to diagnosis. Given the set of possible metrics and time-series which can be extracted from the ECG signals, after their segmentation, the referred methods can support projects of clinical research and development of markers/indicators of adverse cardiovascular events.Sistemas automáticos de auxílio ao diagnóstico visam à extração de métricas específicas, podendo ser por algoritmos computacionais, de forma a subsidiar a análise por parte do especialista de condições orgânicas e fisiológicas do paciente. No contexto da cardiologia, referidos sistemas são particularmente importantes quando aplicados no processamento de sinais de longa duração, como o eletrocardiograma (ECG) de 24 horas. As técnicas para segmentação e extração automática de parâmetros do sinal ECG propostas nesta tese abrangem diversos campos de pesquisa. Inicialmente, o sistema realiza a detecção e a segmentação do complexo QRS, relacionado à despolarização ventricular. Como metodologia, utiliza-se a combinação das técnicas do limiar adaptativo, das transformadas de Hilbert e Wavelet e do filtro derivativo com uma nova abordagem de redução de pré-processamento e de seleção do fator de escala da Wavelet. Ao final desta etapa, obtêm-se a série de intervalos RR, a série de durações de cada complexo QRS e de suas amplitudes. No segundo momento, tem-se a detecção e a segmentação da onda T, relacionada à repolarização ventricular. Propõe-se um novo modelo matemático do comportamento morfológico da onda T baseado na função Gaussiana, modificada por um procedimento matemático de inserção de assimetria. Uma vez obtidos os parâmetros de modelagem para uma dada morfologia predominante de onda T, a função de correlação cruzada é utilizada para a detecção do pico e uma técnica baseada no cálculo da área de trapézios é utilizada para a localização do final da forma de onda. Dentre as métricas derivadas das informações extraídas, destaca-se a série de intervalos QT, segmento que vai do início de cada complexo QRS ao final de cada onda T. Finalizado o processo de segmentação, dois estudos de caso são realizados: subtração da atividade ventricular em sinais eletrogramas atriais de pacientes com fibrilação atrial (FA) e análise de séries de variabilidade da frequência cardíaca (VFC) de um conjunto de pacientes idosos selecionados pelo Ambulatório de Geriatria do Hospital Universitário Wálter Cantídio. A partir de experimentos de validação em bases de dados diversas com anotações manuais dos batimentos, obtêm-se as seguintes taxas de detecção e erros de delineamento para o complexo QRS: sensibilidade de 99,51%, preditividade positiva de 99,44%, erro médio de início (QRS onset) de 2,85 ± 9,90 ms e erro médio de final (QRS offset) de 2,83 ± 12,26 ms. Com relação à detecção e segmentação da onda T, obtêm-se os seguintes resultados: sensibilidade de 99,48%, preditividade positiva de 99,53%, erro médio de localização de pico de 0,51 ± 8,06 ms e erro médio de localização de final da forma de onda de 0,11 ± 11,73 ms. Quanto ao primeiro estudo de caso de uso dos pontos fiduciais detectados, a potência média dos sinais eletrogramas atriais, após a subtração da atividade ventricular, é significativamente reduzida para frequências acima de 10 Hz, predominantemente associadas ao complexo QRS, bem como para frequências na faixa de 3 a 5 Hz, relacionadas à atividade elétrica de repolarização ventricular. Para o segundo estudo, a análise do comportamento de métricas no domínio da frequência associadas à atividade do sistema nervoso simpático permite o reconhecimento de tendências próprias e características, no que tange a aspectos de funcionamento/disautonomia do sistema nervoso autonômico, de cada classe pré-determinada de idosos segundo os conceitos de fenótipo de fragilidade: idosos frágeis, pré-frágeis e robustos. Os resultados obtidos sugerem que o conjunto de metodologias desenvolvidas para a segmentação do sinal ECG apresenta altas taxas de precisão, repetibilidade e robustez a uma ampla gama de morfologias, podendo ser aplicado em diversos contextos de auxílio ao diagnóstico. Dadas as métricas e séries temporais que podem ser extraídas, os referidos métodos também podem dar suporte a processos de investigação clínica e desenvolvimento de marcadores/indicadores de eventos cardiovasculares adversos.TeleinformáticaEletrocardiografiaWavelet, transformadaDetecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de HilbertAutomatic detection and segmentation of heartbeats in ECG signals based on a mathematical model and the combination of wavelet and Hilbert transformsinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/doctoralThesisporreponame:Repositório Institucional da Universidade Federal do Ceará (UFC)instname:Universidade Federal do Ceará (UFC)instacron:UFCinfo:eu-repo/semantics/openAccessORIGINAL2013_tese_jpvmadeiro.pdf2013_tese_jpvmadeiro.pdfapplication/pdf13133519http://repositorio.ufc.br/bitstream/riufc/5655/1/2013_tese_jpvmadeiro.pdfc99737b92e3dcc3bab14e2da30c002dfMD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81786http://repositorio.ufc.br/bitstream/riufc/5655/2/license.txt8c4401d3d14722a7ca2d07c782a1aab3MD52riufc/56552021-08-13 13:18:42.571oai:repositorio.ufc.br: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Repositório InstitucionalPUBhttp://www.repositorio.ufc.br/ri-oai/requestbu@ufc.br || repositorio@ufc.bropendoar:2021-08-13T16:18:42Repositório Institucional da Universidade Federal do Ceará (UFC) - Universidade Federal do Ceará (UFC)false
dc.title.pt_BR.fl_str_mv Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
dc.title.en.pt_BR.fl_str_mv Automatic detection and segmentation of heartbeats in ECG signals based on a mathematical model and the combination of wavelet and Hilbert transforms
title Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
spellingShingle Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
Madeiro, João Paulo do Vale
Teleinformática
Eletrocardiografia
Wavelet, transformada
title_short Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
title_full Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
title_fullStr Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
title_full_unstemmed Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
title_sort Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert
author Madeiro, João Paulo do Vale
author_facet Madeiro, João Paulo do Vale
author_role author
dc.contributor.author.fl_str_mv Madeiro, João Paulo do Vale
dc.contributor.advisor1.fl_str_mv Cortez, Paulo César
contributor_str_mv Cortez, Paulo César
dc.subject.por.fl_str_mv Teleinformática
Eletrocardiografia
Wavelet, transformada
topic Teleinformática
Eletrocardiografia
Wavelet, transformada
description A utomatic diagnostic aid systems aim the extraction of speci c parameters in order to support the analysis of a patient's physiological conditions possibly using computing algorithms. In the context of cardiology, such systems are particularly important when applied over long-term ECG signals, for example the 24-h holter examinations. The digital signal processing techniques for ECG waves segmentation and automatic feature extraction, which are proposed in this thesis, cover various research elds. Firstly, the proposed system performs QRS complex detection and segmentation, which is related to ventricular depolarization. The used methodology combines the adaptive threshold technique, Hilbert and Wavelet transforms and the rst-derivative lter with a new approach of preprocessing suppression over the whole ECG signal and selection of Wavelet scale factor for a given predominant QRS morphology. As output information we obtain the RR time-series (tachogram), the time-series of QRS complex durations and amplitudes. In the second stage, the developed system performs T-wave detection and segmentation, whose waveform is related to ventricular repolarization activity. It is proposed a new mathematical model concerning the possible T-wave morphologies based on a Gaussian function, modi ed by a mathematical procedure to insert asymmetry. Once the template is computed, cross-correlation and an approach based on the computation of Trapezium's area are used to locate, respectively, the peak, or the peaks for biphasic waves, and end point of each T-wave throughout the whole raw ECG signal. Among the metrics derived from the detected ducial points, we emphasize the QT intervals, which are the time intervals between the QRS onset and the T-wave end. After the segmentation of the ECG waves, we perform two important case studies using the ducial points and segments detected in the previous stages: ventricular activity subtraction in intracardiac atrial brillation electrogram and heart hate variability (HRV) analysis for a set of elderly patients which were selected in the Geriatric Outpatient Clinic of the Walter Cantidio University Hospital. After evaluating the overall methodology of QRS detection and segmentation over various manually annotated databases, inclusive the public MIT-BIH Arrhythmia database and QT database, we have obtained the following detection rates and delineation time errors: sensitivity of 99.51%, positive predictivity of 99.44%, QRS onset time error of 2.85 9.90 ms and QRS o set time error of 2.83 12.26 ms. Regarding T-wave detection and delineation, the proposed method has attained sensitivity of 99.48%, positive predictivity of 99.53%, and average time errors of 0.51 8.06 ms, for T-wave peak location, and 0.11 11.73 ms, for T-wave end location. Regarding the rst case study concerning the use of the ducial points detected from the segmented QRS complexes and T-waves over intracardiac atrial brillation electrogram, the method of ventricular activity subtraction has attained a signi cant attenuation for frequencies above 10 Hz, and also for components of frequency range around 3 Hz to 6 Hz, respectively due to ventricular depolarization and repolarization subtraction. For the second application, the analysis of the evolution of heart rate variability metrics in frequency domain associated to sympathetic branch activity allows recognizing speci c tendencies regarding aspects of proper functioning/dysautonomia of the autonomic nervous system for each predetermined elderly class according to the concepts of frailty phenotype: frail, pre-frail and robust ones. The overall results suggest that the set of methodologies developed for ECG waves segmentation provides high rates of accurate and robust detections for a wide variety of morphologies, such that they can be applied in various situations for aid to diagnosis. Given the set of possible metrics and time-series which can be extracted from the ECG signals, after their segmentation, the referred methods can support projects of clinical research and development of markers/indicators of adverse cardiovascular events.
publishDate 2013
dc.date.accessioned.fl_str_mv 2013-08-20T14:50:06Z
dc.date.available.fl_str_mv 2013-08-20T14:50:06Z
dc.date.issued.fl_str_mv 2013
dc.type.status.fl_str_mv info:eu-repo/semantics/publishedVersion
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dc.identifier.citation.fl_str_mv MADEIRO, J. P. V. Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert. 2013. 130 f. Tese (Doutorado em Engenharia de Teleinformática)-Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2013.
dc.identifier.uri.fl_str_mv http://www.repositorio.ufc.br/handle/riufc/5655
identifier_str_mv MADEIRO, J. P. V. Detecção e segmentação automática de batimentos cardíacos do eletrocardiograma por modelagem matemática e combinação das transformadas Wavelet e de Hilbert. 2013. 130 f. Tese (Doutorado em Engenharia de Teleinformática)-Centro de Tecnologia, Universidade Federal do Ceará, Fortaleza, 2013.
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