104 IEEE ENGINEERING IN MEDICINE AND BIOLOGY September/October 2000
Real-Time Analysis of the Ventricular Fibrillation WaveformCan Reveal Hidden Structures
Until recently, the surface electrocardio-gram (ECG) recorded during ventricu-
lar fibrillation (VF) was thought torepresent disorganized and unstructuredelectrical activity of the heart. This is instark contrast to the information-richECG in states ofhealth and disease[1, 2]. Recent workhas attempted to uti-lize wavelet tech-niques in theanalysis of biomedi-cal signals includingECGs [3-9]. In thisarticle we present ane n e r g y - b a s e dmethod of interro-gating the ECG inVF using high-reso-lut ion, log-scalecontinuous wavelet plots. With thismethod, underlying structures within theVF waveform are made visible in thewavelet time-scale half space.
VF Waveform AnalysisVentricular tachyarrhythmias, in par-
ticular VF, are the primary arrhythmicevents in the majority of patients whopresent with sudden cardiac death [10,11]. Considerable interest has focusedupon these particular rhythms, as it is rec-ognized that prompt therapy can lead to asuccessful outcome. For these reasons,there has been considerable interest inanalysis of the VF waveform. This workhas centered on attempts to understandthe pathophysiological processes occur-ring in sudden cardiac death, analysis of
the VF waveform to predict the efficacyof therapy, and the use of alternative oradjunct therapies (electrical or pharma-cological) to improve resuscitation suc-cess rates.
With the passage of time, the VF wave-form deteriorates inamplitude—proba-bly reflecting the de-pletion of myocardialhigh-energy phos-phate stores [12, 13].Waveform amplitudeassessment is a crudepredictor of outcomefrom resuscitation[14, 15], but it is not areproducible markerof sensit ivity todefibrillation, and itlacks clinical useful-
ness [16]. Fast Fourier transform analysishas been used to identify characteristics ofthe ECG frequency spectrum in VF. Theseresults are relatively resistant to perturba-tion from external factors, and they showsome correlation with resuscitation out-come [17-21] but lack sufficient sensitivityand specificity for clinical application [22].
Wavelet TransformDecomposition of the ECG
Wavelet transforms allow a signal tobe decomposed such that frequency char-acteristics and the location of particularfeatures in a time series may be high-lighted simultaneously. This procedureovercomes the basic shortcoming of Fou-rier analysis, where the spectrum only
contains globally averaged information,which leads to location-specific featuresin the signal being lost. We used the wave-let transform as an interrogation tool forECG signals of ventricular fibrillation.
The wavelet transform of a continuoustime signal x(t) is defined as:
T a ba
gt b
ax t dt( , ) ( )= −
−∞
∞∫
1
(1)
where g t b a(( ) / )− is the analyzing wave-let function. The transform coefficientsT a b( , ) are found for both specific loca-tions on the signal, t b= , and for specificwavelet periods (which are a function of a).It is usual to plot T a b( , ) against a and b ineither a surface or contour plot, known as ascalogram. This equation is a series of con-volutions in time: the original signal andwavelet function of period a. In the Fourierdomain, these convolutions become a se-ries of simple products, thus reducing thecomputing time and lending itself toreal-time applications. Typically, 2048data points (≈ 6 sec of ECG trace sampledat 300 Hz) can be decomposed into 70 lev-els in under 1 sec using a standard PC.
As the analyzing wavelet, by defini-tion, has zero mean, the wavelet transformintrinsically removes the signal meanfrom the transform space. The very lowfrequency components associated withbaseline drift do not, therefore, occur inthe salient regions of the scalogram; i.e.,they are found at very large values of a. Inaddition, Donoho and Johnstone [23]have shown that wavelet-based noise re-duction can be thought of as a near-opti-mal nonlinear noise-reduction method.
0739-5175/00/$10.00©2000IEEE
Paul S. Addison1, James N. Watson1,Gareth R. Clegg2, Michael Holzer3,
Fritz Sterz3, Colin E. Robertson2
1 Faculty of Engineering and Computing,Napier University, Edinburgh
2 Dept. of Accident and Emergency Medicine,The Royal Infirmary of Edinburgh NHS Trust,
Edinburgh3 Abteilung Fuer Notfallmedizin,
Universitaetskliniken, Allgemeines KrankenhausDes Stadt Wien
These characteristics make the wavelettransform particularly appropriate for an-alyzing transient, nonstationary signalscontaining features that themselves havehigh-frequency components.
The proportional contribution to thesignal energy at a specific scale a and lo-cation b is given by the two-dimensional(2-D) wavelet energy density function:
E a bT a b
C g
( , )( , )
=2
(2)
whereC g is the wavelet-dependent admis-sibility constant that ensures conservationof energy in wavelet space. Dominantstructures in the signal are then character-ized by large local E a b( , ) values [24].
Research in the field of ECG analysisby wavelet techniques has been limitedto characterizing sinus rhythm and heartrates in an attempt to predict the onset ofirregular cardiac events [3-9]. The dis-crete wavelet transform has been appliedin such areas due to its computational ef-ficiency and zero redundancy. Forreal-time applications, however, a win-dowing technique would be required forsuch methods. Also, the dyadic structureof the resultant scalogram leads to lowertemporal resolution for wavelets oflarger dilations (wavelets with lower-fre-quency components). In other cases thecontinuous wavelet transform has beenused, with the resultant wavelet coeffi-cients being presented on a standardscalogram. Here, the inherent redun-dancy in the method increases clarity inthe transform space and allows forgreater temporal resolution at high dila-tions [25].
For these reasons, we have used a con-tinuous wavelet transform process. In thisarticle, however, the wavelet energy coef-ficients are plotted against the bandpasscenter frequency of the wavelets for an in-stant in time. Hence, the data presented iseffectively a smoothed Fourier powerspectrum for each time increment, wherethe smoothing function is described by thescaled wavelet shapes. The Morlet wave-let was used because of its compactness inthe Fourier domain. This wavelet spec-trum is very robust in that it can cope withrepeating features in time that have shift-ing phase, making the method ideal forreal-time applications such as this. The ef-fective window used on the data is alsoscale dependent, such that it is only lim-ited by the temporal support of the dilated
September/October 2000 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 105
250
EC
G R
espo
nse
150
50
−50
−150
QRS
P T
0.08 0.085 0.09 0.095 0.1 0.105 0.11Time (minutes)
(a)
Time (minutes)(b)
Dila
tion−1
102
101
100
P
QRS
T
0.08 0.085 0.09 0.095 0.1 0.105 0.11
0.08 0.085 0.09 0.095 0.1 0.105 0.11
Time (minutes)(c)
Dilation −1
Log
Ene
rgy
3
2
1
100
102
1. (a) Single-channel porcine ECG showing sinus rhythm. (b) The corresponding en-ergy scalogram of temporal location against wavelet scale (frequency of bandpasscenter - fbpc) and (c) in its 3-D energy landscape form.
wavelet, unlike the Fourier case where theclassic time/frequency resolution com-promise holds.
By presenting the log of the waveletenergy coefficients against the log of thebandpass center for each time increment,small changes in amplitude are high-lighted over the lower scales of interest,and a structure for ventricular fibrillationcan be shown.
ResultsSurface ECG traces were taken from
an established porcine experimentalmodel of ventricular fibrillation. Detailsof the experimental procedure have pre-viously been reported [26]. Figure 1(a)and Fig. 1(b) contain three beats of a pigheart sinus rhythm together with its asso-ciated scalogram. The QRS complex ofthe waveform is evident from the conicalstructures in Fig. 1(b), converging to thehigh-frequency components of the RSspike. The P and T waves are also labeledin the plot. The three-dimensional (3-D)landscape plot of Fig. 1(c) shows themorphology of the signal in waveletspace. In Fig. 1(b), the continuous hori-zontal red band is associated with a fre-quency of 1.7 Hz, which is the beatfrequency of the sinus rhythm. The yel-low band occurs at a frequency of ap-proximately 5.1 Hz, which correspondsto the separation of the P-QRS-T compo-nents in time. At higher frequencies, theP, QRS, and T components are individu-ally resolved according to their fre-quency makeup and temporal location.
Figure 2 contains an energy scalogramfor a 5 min period of VF followed by a 2.5min period of cardiopulmonary resuscita-tion (CPR) seen as the distinct red featurein the lower right quadrant. Over the first5 min, three bands can be clearly seen inthe scalogram: a high-energy band ataround 10 Hz and two lower-energybands at lower frequencies, labeled A, B,and C. Band A corresponds to the easilyvisible gross morphology of the VF wave-form, whereas bands B and C, we specu-late, correspond to underlying structure
previously unreported in such signals.These lower-frequency bands bear a strik-ing resemblance to those seen in the regu-lar sinus rhythm of Fig. 1(b).
Figure 3 shows a typical segment ofone of the VF traces examined, togetherwith its associated energy scalogram.Low-frequency coherent periodic struc-ture within the 10 Hz bandpass compo-nent is clearly evident in the red band ofFig. 3(b) and the 10 Hz ridge in Fig. 3(c)and Fig. 3(d). These features occur ataround 2 Hz, which is a frequency in theorder of the original sinus rhythm. Thisfeature is not observable using conven-tional Fourier techniques.
Figure 4 contains an interesting seg-ment of signal from one of the experi-ments. It shows that VF can be highlystructured in wavelet space. The featuresseen at the high-frequency end of thescalogram in Fig. 4(b) show a surprisingdegree of regularity, which is not discern-ible looking at the original ECG tracing.This is emphasized by comparing the 3-Dlandscape plot in Fig. 4(c) with the plotgenerated from sinus rhythm in Fig. 1(c).
Concluding RemarksWe have described a novel method for
the decomposition and display of the ECGsignal in VF using wavelet transforms,which enables hidden characteristics to bedisplayed and measured. We suggest thatthis wavelet decomposition can be used inthe following ways:
1. Provision of measurable character-istics of the ECG signal for estimation ofdowntime of the subject. This may be im-portant for the determination of the cor-rect therapy for the patient; for example,measures to improve the myocardial sub-strate prior to defibrillation [27, 28].
2. Disassociation of cardiopulmonaryresuscitation (CPR) artifact from the ECGsignal through temporal filtering per-formed using a modulus maxima tech-nique. This method would allow the stateof the heart to be assessed during resusci-tation without stopping CPR.
3. Detection of new specific featureswithin the VF waveform that may leadto modifications of the defibrillationtechnique.
These applications will require the useof advanced postprocessing techniques,which may include artificial neural net-works (adaptive wavelet networks),intermittency measurements, entropytechniques, and Bayesian statistics. Thispreliminary work shows how a new wave-
106 IEEE ENGINEERING IN MEDICINE AND BIOLOGY September/October 2000
CPR
f(H
z)bp
c
A
B
C
101
100
0 1 2 3 4 5 6 7Time (minutes)
2. The energy scalogram of the first 7 min of porcine ventricular fibrillation. CPR isinitiated at 5 min, as indicated.
Wavelet transforms
allow a signal to be
decomposed such that
frequency
characteristics and the
location of particular
features in a time
series may be
highlighted
simultaneously.
let-based interrogation of the ECG in VFallows rapid real-time analyses to revealhidden structure. We have indicated po-tential applications of this technique thatwe hope will increase success rates for thetreatment of this condition. Further workby the authors will concentrate on the de-velopment of these applications.
AcknowledgmentsWe wish to thank Ken Morallee of
Laerdal Medical Ltd. for his assistance. Theporcine experimental work is supported bygrant No. 6168 of the “Jubilaeumsfond” ofthe Oesterreichische Nationalbank, Vienna,Austria, and was carried out in accordancewith institutional guidelines.
Paul Addison is both achartered engineer andchartered physicist andcurrently holds the postof senior lecturer influid mechanics and dy-namics in the Faculty ofEngineering and Com-puting at Napier Uni-
versity, Edinburgh. He received hisM.Eng. (civil engineering) and Ph.D.(fluid mechanics) degrees both from theUniversity of Glasgow, Scotland. His re-search interests include the use of fractalstatistics in the simulation of non-Fickiandiffusive phenomena and the use of wave-let transforms in the elucidation of bothengineering and medical signals. He is au-thor of the book Fractals and Chaos: AnIllustrated Course, published by the Insti-tute of Physics.
Jamie Watson is a re-search assistant in theFaculty of Engineeringand Computing atNapier University. He iscurrently working onthe use of wavelet trans-form methods in the elu-cidation of engineering
and medical signals, including: nonde-structive testing signals, fluid signals, andECG signals. Other research interests in-clude neural computing applications insignal evaluation. He is a graduate mem-ber of the Institute of Physics, UK.
Gareth Clegg is a spe-cialist registrar in acci-dent and emergencymedicine and surgery atthe Royal Infirmary ofEdinburgh. Dr. Clegg’sinterest in cardiac arrestand resuscitation relatesprimarily to the applica-
September/October 2000 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 107
Time (s)(a)
EC
G R
espo
nse
Ele
ctro
de II
−200
−250
−300
−350
−400125 125.5 126 126.5 127 127.5 128 128.5 129 129.5
Time (s)(b)
125 125.5 126 126.5 127 127.5 128 128.5 129 129.5
60
30
20
10
5
32
1
f(H
z)bp
c
2.5
2
1.5
1
0.5
2
2
1
1
log(
E)
log(
E)
125126
127128
12960 30
10 52
1
f (Hz)bpc
f(H
z)bpc
Time (s)Time (s)
12510
3060 125 126 127 128 129
(c)
3. Surface ECG showing porcine VF with associated scalogram. Coherent periodicstructure of the order of the original sinus rhythm (2 Hz) is shown in the 10 Hz bandpasscenter. This is visible as the red band in the energy scalogram (b) and the oscillationpeaks in the energy landscape plot shown in two orientations (c) indicated by arrows
tion of novel techniques and artificial neu-ral networks to the analysis and potentialtreatment of arrhythmias.
Michael Holzer holds aDr.med.univ. from theUniversitat Wien Schoolof Medicine, Austria. Heis currently training for aDegree of Specialist ininternal medicine withthe University Hospitalof Vienna (Austria).
Fritz Sterz has been anassociate professor inthe Department ofEmergency Medicine atthe University Hospitalof Vienna (Austria)since 1993. He also hasbeen vice-director ofthe Department of
Emergency there since 1996. He has beena member of the Collaborator ComiteEuropeen de Normalisation (CEN) foremergency medicine since 1991 and adelegate to the management committeeCOST B10 “Brain Damage Repair,” Eu-ropean commision, DG XII, since 1998.
Colin Robertson is aconsultant in accidentand emergency medi-cine and surgery at theRoyal Infirmary of Ed-inburgh and honorarysenior lecturer at theFaculty of Medicine ofthe University of Edin-
burgh. He has had a research interest incardiac arrest for over 20 years and is pastchairman of the Resuscitation Council(UK) and European Resuscitation Coun-cil ACLS Committee.
Address for Correspondence: Dr. PaulS. Addison, Senior Lecturer, Faculty ofEngineering and Computing, Napier Uni-versity, Merchistron Campus, 10 Colin-ton Road, Edinburgh EH10 5DT,Scot land U.K. E-mail : p [emailprotected].
References1. Rude RE, Poole KW, Muler JE, Turi Z,Rutherford J, Pet al.: Electrocardiographic andclinial criteria for recognition of acute myocardialinfarction based on analysis of 3,697 patients. AmJ Cardiol 52: 936-41, 1983.2. Brush JE, Brand DA, Acampora D, ChalmerB, and Wackers FJ: Use of the initial electrocar-diogram to predict in-hospital complications ofacute myocardial infarction. N Engl J Med 312:1137-41, 1985.
108 IEEE ENGINEERING IN MEDICINE AND BIOLOGY September/October 2000
EC
G R
espo
nse
Ele
ctro
de II
100
50
−50
−100
−150
−200
−250250 250.5 251 251.5 252 252.5 253 253.5 254 254.5
Time (s)(a)
250 250.5 251 251.5 252 252.5 253 253.5 254 254.5Time (s)
(b)
3.5
3
2.5
2
1.5
1
0.5
60
30
20
10
5
3
2
1
f(H
z)bp
c
Time (s)(c)
f(H
z)
bpc
3
2
1
12
510
30
60250
250.5251
251.5252
log(
E)
4. Here the energy scalogram (b) shows a surprisingly structured form when com-pared with the corresponding surface ECG (a). There is a marked similarity be-tween this scalogram (b) and the energy landscape plot (c) and those shown for sinusrhythm in Fig. 1.
3. Tutuer FB: Wavelet transforms in signal de-tection. In: Combes et al. (Eds.), Wavelets: TimeFrequency Methods and Phase Space. Ne York:Springer-Verlag, 132-138, 1989.4. Sahambi JS, Tandon SN, and Bhatt RKP:Using wavelet transforms for ECG characteriza-tion, IEEE EMB Mag 16(1): 77-83, Jan./Feb.1997.5. Li C, Zheng C, and Tai C: Detection of ECGcharacteristic points using wavelet transforms.IEEE Trans Biomed Eng 42(1): 21-28, 1995.6. Ivanov PC, Rosenblum MG, Peng et C-K,Mietus J, Havlin S, et al.: Scaling behaviour ofheartbeat intervals obtained by wavelet-basedtime-series analysis Nature, 383: 323-327, 1996.7. Wiklund U, Akay M, and Niklasson U: Anal-ysis of heart-rate variability by adapted wavelettransforms, IEEE EMB Mag 16(5): 113-118,Sept./Oct. 1997.8. Thurner S, Feurstein MC, and Teich MC:Multiresolution wavelet analysis of heartbeat in-tervals discriminates healthy patients from thosewith cardiac pathology. Physical Rev Lett 80(7):1544-1547, 1998.9. Figliola A and Serrano E: Analysis of physio-logical time series using wavelet transforms.IEEE EMB Mag 16(3): 74-79, May/June 1997.10. Goldstein S, Landis JR, Leighton R, RitterG, Vasu CM: Characteristics of the resuscitatedout-of-hospital cardiac arrest victim with coro-nary disease. Circulation 64 (5): 977-986, 1981.11. Jacobs IG and Oxer HF: A review ofprehospital defibrillation by ambulance officersin Perth, Western Australia. Med J Aust 153,(11-12): 662-664, 1990.12. Neumar RW, Brown CG, Robitaille PM,and Altschuld RA: Myocardial high energy
phosphate metabolism during ventricular fibrilla-tion with total circulatory arrest. Resuscitation 19:199-226, 1990.13. Mapin DR, Brown CG, and Dzuonczyk R:Frequency analysis of the human and swine elec-trocardiogram during ventricular fibrillation. Re-suscitation 22: 85-91, 1991.14. Weaver WD, Cobb LA, Dennis D, Ray R,and Hallstrom AP: Amplitude of ventricular fi-brillation waveform and outcome after cardiac ar-rest. Ann Intern Med 102: 53-55, 1985.15. Stutts KR, Brown DD, Kerber RE: Ventric-ular fibrillation amplitude predicts ability todefibrillate. Am J Emerg Med 4: 423, 1986.16. Jones DL and Klein GJ: Ventricular fibrilla-tion: The importance of being coarse. JElectrocardiol 17: 393-400,1984.17. Stewart AJ, Allen JD, and Adgey AAJ: Fre-quency analysis of ventricular fibrillation and re-suscitation success. Quarterly J Med 85(306):761-769, 1992.18. Brown CG, Dzwonczyk R, Werman HA,and Hamlin RL: Estimating the duration of ven-tricular fibrillation. Ann Emerg Med 18: 1181-85,1989.19. Brown CG, Griffith RF, Van Lighten P,Hoekstra J, Nejman G, Mitchell L: Median fre-quency - A new parameter for predictingdefibrillation success rate. Ann Emerg Med 10:787-89, 1991.20. Strohmenger HU, Lindner KH, Keller A,Lindner IM, Pfenninger E, Bothner U: Effectsof graded doses of vasopressin on median fibrilla-t ion frequency in a porcine model ofcardiopulmonary resuscitation: Results of a pro-spective, randomized, controlled trial. Crit CareMed 24:1360-65, 1996.
21. Strohmenger HU, Lindner KH, PrengelAW, Pfenninger EG, Bothner U, and LurieKG: Effects of epinephrine and vasopressin onmedian fibrillation frequency and defibrillationsuccess in a porcine model of cardiopulmonaryresuscitation. Resuscitation 31:65-73, 1996.
22. Brown CG, Dzwonczyk R: Signal analysis ofthe human electrocardiogram during ventricularfibrillation: Frequency and amplitude parametersas predictors of successful countershock - a pre-liminary report. presented at Eighth Purdue Con-ference on Cardiac Defibrillation, 1994.
23. Donoho D and Johnstone I: Ideal spatial ad-aptation via wavelet shrinkage. Biometrika 81:425-455, 1995.
24. Addison PS: Wavelet: Analysis of the break-down of a pulsed vortex flow. In: Proc. I.Mech.E.,Part C, J Mechan Eng Sci 213: 217-229, 1999.
25. Farge M: Wavelet Transforms and Their Ap-plications to Turbulence, Ann. Rev. Fluid Mech.,24: 395-456, 1992.
26. Behringer W, Sterz F, Domanovits H,Hohenberger B, and Schorkuber W: Effects ofmanual high-impulse CPR on myocardial perfu-sion during cardiac arrest in pigs. Resuscitation34: 271-279, 1997.
27. Cobb LA, Fahrenbruch CE, Walsh TR,Copass MK, Olsufka M, et al.: Influence ofcardiopulmonary resusci ta t ion prior todefibrillation in patients with out-of-hospital ven-tricular fibrillation. JAMA 281: 1182-1188, 1999.
28. Niemann JT, Cairns CB, Sharma J, andLewis Roger J: Treatment of prolonged ventricu-lar fibrillation: immediate countershock versushigh-dose epinephrine and CPR precedingcountershock. Circulation 85: 281-287, 1992.
September/October 2000 IEEE ENGINEERING IN MEDICINE AND BIOLOGY 109
Moratorium
The purpose of IEEE Engineering in Medicine and BiologyMagazine is to promote and display all aspects of biomedicalengineering. We do this by publishing both theme issues, whichare devoted to particular topics, and individual feature articles.
Wavelet transformation is a relatively new method of sig-nal analysis. As such, many biomedical engineers find thistechnique useful in studying different physiological signals. Inconsequence, we have recently received a large number of pa-pers using wavelet analysis. We would like to publish themall, but that would delay the publication of all articles, and es-pecially those articles on other equally interesting topics.
Therefore, for at least a while, we must regrettably ask allof our readers not to submit articles based on wavelet meth-ods to us. Instead, please submit your work to some of theother excellent IEEE publications that can deal with thistopic; e.g., the IEEE Transactions on Biomedical Engi-neering, the IEEE Transactions on Information Technologyin Biomedicine, the IEEE Transactions on Signal Pro-cessing, or IEEE Signal Processing Magazine.
Thank you for understanding that the purpose of this an-nouncement is to benefit all of our readers.
