Contents
6
xiii
Compari Comparing ng HRV Variabil Variability ity Across Across Differ Different ent Segmen Segments ts of a Recording . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.1 Episod Episodes es and and Physio Physiolog logica icall Events Events . . . . . . . . . . . . . . . . . . . . . . . . . 6.2 6.2 Usin Using g Epis Episod odes es in RHRV RHRV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.2. 6.2.1 1 Mana Managin ging g Episo Episode dess in a HR Recor Record d. . . . . . . . . . . . . . . . . . 6.3 6.3 Usin Using g Epis Episod odes es in in Plot Plotss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.4 6.4 Maki Making ng Use Use of Episod Episodes es in HRV HRV Analy Analysi siss . . . . . . . . . . . . . . . . . . . 6.5 6.5 An Exam Exampl plee . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6.6 Clinic Clinical al Applic Applicati ations ons of HRV HRV Analysi Analysiss by Episodes Episodes . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
117 117 118 119 123 126 128 130 132
Puttin Putting g It All All Togeth Together, er, a Practic Practical al Examp Example le . . . . . . . . . . . . . . . . . . . 7.1 7.1 Prob Proble lem m Stat Stateme ement nt . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2 7.2 Meth Method odol ology ogy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.1 7.2.1 Databa Database se Descri Descriptio ption n. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7.2.2 7.2.2 Applyi Applying ng HRV Analys Analysis is . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
133 133 134 134 136 143
Appendix A: Installing RHRV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
145
Appendix B: How do I Get a Series of RR Intervals from a Clinical/Biological Experiment? . . . . . . . . . . . . . . . .
147
Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
155
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Constantino Antonio Garc ía Mart ínez Abraham Otero Quintana Xosé A. Vila Mar ía José Lado Touriño Leandro Rodr íguez-Liñares Jesús Mar ía Rodr íguez Presedo Arturo José Méndez Penín •
Heart Rate Variability Analysis with the R package RHRV
1 3
Constantino Antonio García Mart ínez University of Santiago de Compostela Santiago de Compostela Spain
Leandro Leandro Rodr íguez-Liñares University of Vigo Ourense Spain
Abraham Otero Quintana CEU San Pablo University Madrid Spain
Jesús Mar ía Rodr íguez Presedo University of Santiago de Compostela Santiago de Compostela Spain
Xosé A. Vila University of Vigo Ourense Spain
Arturo José Méndez Penín University of Vigo Ourense Spain
Mar ía José Lado Touriño University of Vigo Ourense Spain
ISSN 2197-5736 Use R! ISB ISBN 978978-33-31 3199-65 6535 3544-9 9 DOI 10.1007/978-3-319-65355-6
ISSN 2197-5744
(electronic)
ISBN SBN 978978-33-31 3199-65 6535 3555-6 6
(eB (eBook) ook)
Library of Congress Control Number: 2017948618 © Springer
International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the materi material al is concer concerned ned,, speci speci�cally cally the rights rights of transl translati ation, on, reprint reprinting ing,, reuse reuse of illustr illustrati ations ons,, recitation, recitation, broadcastin broadcasting, g, reproduction reproduction on micro�lms or in any other physic physical al way, way, and transmis transmissio sion n or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use use of gene genera rall desc descri ript ptiv ivee name names, s, regis registe tere red d name names, s, trad tradem emar arks ks,, serv servic icee mark marks, s, etc. etc. in this this publication publication does not imply, even in the absence absence of a speci �c statement, statement, that such names are exempt exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book book are believed believed to be true true and accurate accurate at the date of public publicati ation. on. Neither Neither the publis publishe herr nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional af �liations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland
Foreword
It would be very dif �cult if not impossible to �nd a signal processing technique applie applied d to cardia cardiacc electr electroph ophysi ysiolo ology gy data data that that gained gained more more popular popularity ity than than the methods of heart rate variability. The two decades old HRV standardisation document belongs to the most cited publications in cardiovascular literature and the stream of new technical approaches to HRV analyses and of new clinical HRV studies is not showing any sign of decline. Whil Whilee this this is of cour course se most most plea pleasi sing ng to spec specia iali list stss in the the HRV HRV �eld, eld, the the widespread popularity also brings problems and challenges. Among others, technical agreement on the details of signal processing and HRV measurement exists practically only with the most simple statistical methods. Only a small number of more advanced techniques are suf �ciently standardized. With all others, different nuances in data acquisition, artifact removal, and settings used to implement signal processing methods may influence the numerical values of HRV measurements to that extent that comparisons of results obtained by different research groups are at best best prob proble lema matic tic and and at wors worstt misl mislea eadin ding. g. The The more more elab elabora orate te math mathem emati atica call apparatus beyond a signal processing method, the more implementation variants exist, hampering both the physiological understanding of the measurements and conseq consequent uently ly their their clinic clinical al and/or and/or epidem epidemiolo iologic gic potent potential ial.. Indeed Indeed,, the recent recent extension of the HRV standard that aimed at reviewing and organizing the novel nonlinear HRV methods observed growing divergence between technological HRV advances and their clinical utilization. This divergence exists mainly because the clinical researchers �nd it dif �cult to be guided by scienti �c reports from different centers that might agree in principal observations but not in numerical details. Soluti Solution on of these these proble problems ms clearl clearly y lies lies in furthe furtherr standa standardi rdizat zation ion.. The more more research and clinical groups would use the very same technical setting of HRV processing packages, the more mutually comparable measurements would become available for critical scienti �c review, and consequently the more chances would exist to agree on the correct physiologic and clinical interpretation of the advanced signal processing processing technologies. technologies. Of course, course, without without providing providing the necessary necessary devices to everybody, this all is easier to declare than to achieve. Obviously, widespread tool toolss are are need needed ed.. Havi Having ng this this in mind mind,, the the auth author orss of this this book book need need to be v
vi
Foreword
commended for their contribution to the attempts of standardizing, under a common umbrella, all the different facets of HRV analyses ranging from data preparation and signal inputs to the more mathematically intricate processing tools. Offering the RHRV RHRV pack packag agee for for free free and and unre unrest stri rict cted ed use use by all all is an exam example ple of welc welcome ome assistance to the research community. For this unsel �sh approach, the developers of the package and the authors of this book deserve our thanks. February 2016
Marek Malik Imperial Imperial College College London, UK
Preface
The rhythm of the heart is in fluenced by both the sympathetic and parasympathetic branches of the autonomic nervous system. There are also some feedback mechanisms modulating the heart rate that try to maintain cardiovascular homeostasis by respond responding ing to the pertur perturbat bations ions sensed sensed by barorec barorecept eptors ors and chemore chemorecep ceptor tors. s. Another major influence of the heart rate is the respiratory sinus arrhythmia: the heartbeat synchronization with the respiratory rhythm. All these mechanisms are responsible for continuous variations in the heart rate of a healthy individual, even at rest rest.. Thes Thesee vari variat atio ions ns are are refe referr rred ed to as heart heart rate rate vari variabi abili lity ty (HRV (HRV). ). Subt Subtle le characteristics of these small variations conceal information about all the mechanism nismss unde underl rlyi ying ng hear heartt rate rate cont contro rol, l, and and henc hencee abou aboutt the the heal health th stat status us of the the individual. Sinc Sincee the the 1960s 1960s,, rese researc arche hers rs have have deve develo loped ped a wide wide rang rangee of algo algorit rithm hmss to extr extrac actt the the info inform rmat atio ion n hidd hidden en in thes thesee vari variat atio ions ns.. Usin Using g thes thesee algo algori rith thms ms,, researchers have found markers for many pathologies such as myocardial infarction, diabetic neuropathy, sudden cardiac death, and ischemia. The starting point for all these algorithms is a simple recording of the instantaneous heart rate of the patient, usually extracted from an electrocardiogram. Therefore, a diagnostic based on a HRV HRV mark marker er is inex inexpe pens nsiv ive, e, simp simple le to perf perform orm,, and and requ requir ires es no inva invasi sive ve procedure, making it a very attractive test. This is probably the reason behind the increasing amount of research related to HRV (see Fig. 1). From the point of view of the authors, the main hindrance in the HRV research �eld is the dif �culty in reproducing results from other researchers. When a new analysis technique or a new �nding is published in the HRV literature, thinking it will be easy to reproduce the same result on your own data often is a mistake. We have tried it on several occasions. But the exact reproduction of the results was not possible, although we obtained results that qualitatively were similar to the originals. This is due to the lack of standardization in the values of many parameters and othe otherr impl implem emen enta tatio tion n detai details ls in the the HRV HRV algor algorit ithm hms. s. Some Some exam exampl ples es are are how exactly ectopic beats are �ltered, the algorithm used to interpolate the RR intervals to obtain a time series of constant sampling frequency, how to remove the DC component (from all the RR series, from each window, etc.), the window type vii
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Fig. 1 Papers Papers on HRV published published per year according according to Google Scholar
(Hamming, Welch, etc.), window size, and window overlap used in the Fast fourier transform, or the mother wavelet used. Explic Explicitl itly y or implic implicitl itly, y, in any HRV analys analysis is dozens dozens of decisi decisions ons on either either parameters or implementation details are made. Some of these decisions are dif �cult to document in a scienti �c paper. But they are essential for the faithful and accurate reproduction of the results. Furthermore, the analyses are often performed with a third party tool, whose source code is probably not available. In this case, many of these decisions have been made by the tool developers, and researchers may be unaware of some (even most) of them. Another hindrance in the �eld is that researchers often use analytical techniques that are not the current state of the art, simply because their tool of choice does not support them, and they do not have the time and/or the necessary expertise to implem implement ent the technique techniquess themse themselve lves. s. There There is often often a disconn disconnect ect in the HRV lite litera ratur turee betw betwee een n rese resear arch cher erss who who deve develo lop p new new and and more more powe powerf rful ul anal analys ysis is techniques (often engineers), and those performing applied research in humans or animals animals (often physicians). physicians). The latter latter still still often uses older less powerful techniques techniques and does not bene�t from the progress made by the former. For example, in the lite litera ratur turee ther theree are are many many more more HRV HRV studi studies es usin using g the the Four Fourie ierr tran transf sfor orm m than than the wavelet transform, despite the theoretically superior properties of the latter for the analysis of nonstationary signals. We believe that the main reason for this is the
Preface
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9 1 1 0 1 0 3 0 5 0 7 0 9 1 1 0 1 0 3 0 5 0 7 0 9 1 1 0 1 0 3 0 5 0 7 0 9 1 1 0 1 0 − − − − − − − − − − − − − − − − − − − 2 1 2 1 3 1 3 1 3 1 3 1 3 1 3 1 4 1 4 1 4 1 4 1 4 1 4 1 5 1 5 1 5 1 5 1 5 1 5 − 1 6 − 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 2 Date
Fig. 2 Monthly Monthly RHRV downloads downloads in the RStudio RStudio s CRAN mirror ’
historical lack of HRV analysis tools with support for spectral analysis based on wavelets. RHRV is our attempt to address these problems. RHRV is a free of charge and open-source package for the R environment that comprises a complete set of tools for heart rate variability analysis. RHRV can import data �les containing heartbeat positions in the most broadly used formats and supports time domain, frequency domain, and nonlinear (fractal and chaotic) HRV analysis. The vast majority of the commonly used HRV analysis algorithms used in the literature have already been implemented in the tool. For example, the tool supports frequency analysis using the Fourie Fourierr transf transform orm (with (with and without without Daniel Danielll smoothe smoothers) rs),, shortshort-tim timee Fourie Fourier r transf transform, orm, autoreg autoregres ressiv sivee models models,, Lomb-Sc Lomb-Scarg argle le period periodogr ogram, am, and the wavele wavelet t transform. And we will continue adding new functionality to RHRV. Furthermore, as any good open-source project, contributions are welcome. Beyond Beyond being being an invalu invaluabl ablee help help when when perform performing ing HRV analys analysis is (a typica typicall HRV analysis with RHRV usually has just 10 –15 lines of R code), we believe that RHRV can help the whole HRV �eld. Simply by posting the RHRV analysis script as supplementary material of a paper, the reproduction of the results over the same, or over new data, will be trivial: just run the script. Being RHRV an open and free package, no one should have any impediment to reproduce the results. And given that the state-of-the-art analysis techniques are implemented in RHRV, there is no
x
Pr ef a c e
reason not to use them. For example, in RHRV the difference between carrying out a spectral analysis based on Fourier or wavelets is simply changing a parameter in a function call. Many researchers have already noticed the advantages of RHRV, and a strong community community has already already formed around it. During 2015 on average, the package was downloaded 450 times a month just from the RStudio CRAN mirror (see Fig. 2). We hope that the trend shown in Fig. 2 continues, and that RHRV will become the de facto tool for performing HRV analysis. And this book, as the best documentation written so far about RHRV, will contribute to this end. Santia ntiag go de Compostela, Spain Madrid, Spain Ourense, Spain Ourense, Spain Ourense, Spain Santiago de Compostela, Spain Ourense, Spain December 2015
Const nstantino Antonio nio García Mart ínez Abraham Otero Quintana Xosé A. Vila María José Lado Touriño Leandro Rodríguez-Li ñares Jesús Mar ía Rodr íguez Presedo Arturo José Méndez Penín
Contents
1
Introdu Introducti ction on to Heart Heart Rate Rate Varia Variabil bility ity . . . . . . . . . . . . . . . . . . . . . . . . 1.1 Histori Historical cal Perspe Perspecti ctive ve . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2 Physio Physiolog logica icall Basis Basis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.1 1.2.1 Cardia Cardiacc Outpu Outputt and and Heart Heart Rate Rate . . . . . . . . . . . . . . . . . . . . . . 1.2.2 1.2.2 Autono Autonomous mous Nervous Nervous System System . . . . . . . . . . . . . . . . . . . . . . . 1.2.3 1.2.3 Autono Autonomous mous Nerv Nervous ous Syste System m and Heart Heart Rate Rate Regulation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.2.4 1.2.4 Nonlin Nonlinear ear Dyna Dynamic micss of the Heart Heart . . . . . . . . . . . . . . . . . . . . . 1.3 Clinic Clinical al Applic Applicati ations ons . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3. 1.3.1 1 Monit Monitor orin ing g ..................................... 1.3. 1.3.2 2 Acut Acutee Care Care . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1.3.3 1.3.3 Chroni Chronicc Disord Disorders ers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6 7 8 9 10 11 12
2
Loading Loading,, Plotti Plotting, ng, and and Filter Filtering ing RR Inter Intervals vals. . . . . . . . . . . . . . . . . . . 2.1 2.1 Gett Gettin ing g Star Started ted . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.2 2.2 Data Data File File Form Format at . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.3 2.3 Load Loadin ing g Beat Beat Seri Series es int into o RHRV RHRV . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4 2.4 Prep Prepro roce cess ssin ing g . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.1 2.4.1 Instant Instantane aneous ous Heart Heart Rate Rate Signal Signal Extract Extraction ion . . . . . . . . . . . . . 2.4.2 2.4.2 Removin Removing g Artifa Artifacts cts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2.4.3 2.4.3 Interp Interpolat olation ion of the the Heart Heart Rate Rate Signa Signall . . . . . . . . . . . . . . . . . 2.5 Preproc Preprocess essing ing Beat Data Data with with RHRV RHRV . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
15 15 16 17 20 21 21 23 23 27
3
Time Time-Do -Domai main n Analy Analysi siss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.1 Time-D Time-Doma omain in Measure Measuress . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3.2 Time-D Time-Doma omain in Anal Analysi ysiss with with RHRV RHRV . . . . . . . . . . . . . . . . . . . . . . . . 3.3 Changes Changes in HRV Time-Ba Time-Based sed Statis Statistic ticss Under Pathol Pathologi ogical cal Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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Frequ Frequen ency cy Doma Domain in Anal Analysi ysiss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.1 Freque Frequency ncy Comp Componen onents ts of the the HRV HRV . . . . . . . . . . . . . . . . . . . . . . . . 4.2 Freque Frequency ncy Analys Analysis is Techni Technique quess . . . . . . . . . . . . . . . . . . . . . . . . . . . 4.2.1 4.2.1 Freque Frequency ncy Analys Analysis is of Statio Stationar nary y Signals Signals . . . . . . . . . . . . . . 4.2.2 4.2.2 Freque Frequency ncy Analys Analysis is of Nonstat Nonstation ionary ary Signa Signals ls . . . . . . . . . . . 4.3 Freque Frequency ncy Doma Domain in Analy Analysis sis with with RHRV RHRV . . . . . . . . . . . . . . . . . . . . 4.3.1 4.3.1 Freque Frequency ncy Analys Analysis is of Statio Stationar nary y Signals Signals . . . . . . . . . . . . . . 4.3.2 4.3.2 Freque Frequency ncy Analys Analysis is of Nonstat Nonstation ionary ary Signa Signals ls . . . . . . . . . . . 4.4 Changes in HRV Frequency-Ba Frequency-Based sed Statis Statistics tics Under Under Patholo Pathological gical Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
37 37 39 39 41 43 43 54
Nonline Nonlinear ar and Fractal Fractal Analysis Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.1 An Over Overvie view w of Nonlin Nonlinear ear Dynami Dynamics cs. . . . . . . . . . . . . . . . . . . . . . . 5.2 Chaotic Chaotic Nonlin Nonlinear ear Statis Statistics tics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.1 5.2.1 Nonlin Nonlinear earity ity Tests Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.2 5.2.2 Phase Phase Space Space Recons Reconstru tructi ction on . . . . . . . . . . . . . . . . . . . . . . . . 5.2.3 5.2.3 Correl Correlati ation on Dimens Dimension ion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.4 Generalized Generalized Correlation Correlation Dimension Dimension and Information Information Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.5 5.2.5 Kolmogo Kolmogorov rov-Si -Sinai nai Entropy Entropy . . . . . . . . . . . . . . . . . . . . . . . . . 5.2.6 5.2.6 Maxima Maximall Lyapun Lyapunov ov Expone Exponent nt . . . . . . . . . . . . . . . . . . . . . . . . 5.2.7 5.2.7 Recurr Recurrence ence Quanti Quanti�cation Analysis (RQA) . . . . . . . . . . . . . 5.2. 5.2.8 8 Poin Poinca car r é Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.3 An Over Overvie view w of Fracta Fractall Dynami Dynamics cs . . . . . . . . . . . . . . . . . . . . . . . . . 5.3.1 5.3.1 Detren Detrended ded Fluc Fluctua tuatio tion n Analys Analysis is. . . . . . . . . . . . . . . . . . . . . . 5.3.2 5.3.2 Power Power Spect Spectral ral Dens Density ity Anal Analysi ysiss . . . . . . . . . . . . . . . . . . . . . 5.4 Chaotic Chaotic Nonlin Nonlinear ear Anal Analysi ysiss with with RHRV RHRV . . . . . . . . . . . . . . . . . . . . 5.4.1 5.4.1 Nonlin Nonlinear earity ity Tests Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.2 5.4.2 Phase Phase Space Space Recons Reconstru tructi ction on . . . . . . . . . . . . . . . . . . . . . . . . 5.4.3 5.4.3 Nonlin Nonlinear ear Stat Statist istics ics Compu Computat tation ion . . . . . . . . . . . . . . . . . . . . 5.4.4 Generalized Generalized Correlation Correlation Dimension Dimension and Information Information Dimension . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. 5.4.5 5 Samp Sample le Entr Entropy opy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4.6 5.4.6 Maxima Maximall Lyapun Lyapunov ov Expone Exponent nt . . . . . . . . . . . . . . . . . . . . . . . . 5.4.7 RQA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.4. 5.4.8 8 Poin Poinca car r é Plot . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5 Fracta Fractall Anal Analysi ysiss with with RHRV RHRV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.5.1 5.5.1 Detren Detrended ded Fluc Fluctua tuatio tion n Analys Analysis is. . . . . . . . . . . . . . . . . . . . . . 5.5.2 5.5.2 Power Power Spectr Spectral al Analys Analysis is . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.6 Nonlin Nonlinear ear and Fracta Fractall Analysis Analysis of HRV Under Under Patholo Pathologic gical al Conditions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5.7 Some Some Final Final Remarks Remarks Regardi Regarding ng HRV Analys Analysis is with with Chaotic Chaotic and Fractal Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
69 69 70 70 71 72
65 66
73 74 75 76 79 80 81 82 83 85 87 94 94 100 101 104 106 108 109 111 112 113 114
