Complexity of the short-term heart-rate variability

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NS Complexity of the Short-Term

Heart-Rate Variability

This work has proposed a methodology based on the con-cept of entropy rates to study the complexity of theshort-term heart-rate variability (HRV) for improvingrisk stratification to predict sudden cardiac death (SCD)

of patients with established ischemic-dilated cardiomyopathy(IDC). The short-term HRV was analyzed during daytime andnighttime by means of RR series. An entropy rate was calcu-lated on the RR series, previously transformed to symbolsequences by means of an alphabet. A statistical analysis per-mitted to stratify high- and low-risk patients of suffering SCD,with a specificity (SP) of 95% and sensitivity (SE) of 83.3%.

SCD is a leading cause of mortality worldwide, especiallyamong patients with heart failure due to IDC. It occurs in about300,000 individuals per year in the United States and representsabout one half of the deaths caused by cardiovascular diseases[1]. Therefore, risk stratification is essential to establish anadequate therapy for those patients [2], although risk stratifica-tion of SCD is not yet completely solved.

Decreased left ventricular ejection fraction (LVEF) has beenreported as significant contributors to the prognosis of patientswith heart failure. However, recent reports indicate that LVEFis preserved in more than one third of patients admitted withheart failure [3]. Furthermore, studies using indexed left atrium(LA) size have demonstrated that an enlargement of this indexpredicts mortality and cardiovascular events in patients withcardiovascular disease [1].

Cardiovascular system is characterized by a high complex-ity, partly because of its continuous interactions with otherphysiological systems [4], [5]. It has also been reported thatits complexity breaks down with aging and cardiac diseases,as in [6]. Since this complexity behavior, it is expected thatHRV has a nonlinear and nonstationary behavior. Traditionaltechniques belonging to time-domain and frequency-domainanalyses describe only the linear structure of the HRV, with-out being able to characterize the nonlinear dynamics hiddenin the generation of the heart beats [7], [8]. Therefore, HRVshould be analyzed and characterized using techniquesobtained from nonlinear dynamical system theory and chaostheory [9], [10]. However, many of these techniques are notyet completely explored.

In this work, we propose a methodology based on the con-cept of entropy rates to study the complexity of the short-termHRV for improving risk stratification to predict cardiacmortality (CM) and SCD of patients with established IDC. Anentropy rate was calculated on the RR series, previouslytransformed to symbol sequences by means of a coarsegraining approach based on uniform and nonuniform quanti-zation procedures. To get a better characterization of short-term HRV, the study has also considered the adjustment ofthe parameters involved in the proposed methodology.Finally, a statistical analysis was applied to recognize validprognostic markers.

Methods

Analyzed Data and PreprocessingPatients from MUSIC2 (muerte subita en insuficiencia car-diaca, which means sudden death in heart failure) study wereanalyzed in the present work. All these patients had sympto-matic chronic heart failure [New York Heart Association(NYHA), Classes II–III] and were treated according to theinstitutional guidelines. The MUSIC2 study included patientswith either depressed (<45%) or preserved (�45%) LVEF.The latter were included if they had heart-failure symptomsand a prior hospitalization for heart failure or some objectivesigns of heart failure confirmed by radiography (findings ofpulmonary congestion) and/or echocardiography (abnormalleft ventricular filling pattern and left ventricular hypertro-phy). Patients were excluded from MUSIC2 study if theyrecently had acute coronary syndrome or severe valvular dis-ease amenable for surgical repair. In addition, those patientswith severe pulmonary, hepatic, or renal disease or otherconcomitant noncardiovascular disease expected to reducelife expectancy to less than three years were excluded. Thestudy was approved by the ethical committee of the institution,and all subjects gave their written informed consent beforeparticipation.

A total of 194 patients with IDC from the MUSIC2 databasewere enrolled in the present work. The inclusion criteria wereas follows: male subjects, sinus rhythm, symptomatic chronicheart failure with NYHA functional Class II or III, and ische-mic etiology of heart failure.

BY JOSE F. VALENCIA,MONTSERRAT VALLVERD�U,RICO SCHROEDER, ANDREAS VOSS,RAFAEL V�AZQUEZ, ANTONIO BAY�ES DE LUNA,AND PERE CAMINAL

© STOCKBYTE, BRAND X PICTURES

Digital Object Identifier 10.1109/MEMB.2009.934621

Using Entropy Rates to Improve Risk Stratificationto Predict Cardiac Mortality

72 IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE 0739-5175/09/$26.00©2009IEEE NOVEMBER/DECEMBER 2009

Authorized licensed use limited to: UNIVERSITAT POLITÈCNICA DE CATALUNYA. Downloaded on February 11, 2010 at 13:21 from IEEE Xplore. Restrictions apply.

After a follow up of three years, age-matched patients withIDC were studied considering two different endpoints:1) analysis A: 12 patients who suffered SCD as a high-risk

group versus 139 survivor patients (SV) as a low-risk group2) analysis B: 26 patients who suffered CM due to SCD,

progressive heart failure or myocardial infarction, as ahigh-risk group versus 168 SV as a low-risk group.Table 1 presents the clinical factors of these patients: age;

indexed LA size, ratio between LA size and body-surface area;NYHA; LVEF; and indexed left ventricular end-diastolic diam-eter (LVEDD), ratio between LVEDD and body-surface area.

The RR series, intervals between consecutive beats, wereobtained from 24-h ECG-Holter recordings with a samplingfrequency of 200 Hz (Spiderview recorders). An adaptive fil-ter [11] was applied to the RR series to replace ectopic beatsand artifacts by interpolated RR intervals. In this way, thelevel of interpolated beats related to the total number of RRintervals was less than 1.5%. Therefore, a possible alterationof the results due to the filter procedure can be discarded, andthese filtered series were interpolated by cubic splines andresampled at 5 Hz. Then, the RR time series were divided intowindows of N ¼ 1,000 samples without overlapping, corre-sponding to approximately 5 min [7]. Since ECGs wererecorded at different start time, the RR time series werealigned in function of a common start time. In this way, for allthe analyzed subjects, the first window started approximatelyat 16:10 h, and the last window ended at 3:36 h. In total, 206windows were taken into account (11:26 h) from each series.

Entropy Rate MethodologyAn entropy rate, as the conditional entropy (HC) [12], has beenused to calculate the rate of information generation of anonlinear series of length N. Given the series y( j), with1 � j � N, a phase space is constructed using delay coordi-nates [13]. Each point in this phase space is represented by thevector uL(i) ¼ yi, . . . , yiþL�1f g with 1 � i � N � (L� 1)s,where L is the phase-space dimension and s is a fixed delay.Any approximation of the entropy rate is based on a procedurefor estimating the probability that two patterns of lengthL� 1, uL(i) ¼ yi, . . . , yiþL�1f g and uL( j) ¼ yj, . . . , yjþL�1

� �that are similar in the (L� 1) dimensional phase space remainsimilar after adding a new sample y(iþ 1) and y( jþ 1),respectively [i.e., uL(iþ 1) and uL( j þ 1) are still similar]. Inthis sense, HC quantifies the variation of the information nec-essary to specify a new pattern of dimension L, given a patternof dimension L� 1. The definition of the similarity betweenpatterns depends on the coarse graining procedure used forpartitioning the multidimensional phase space [14]. In HC, thedynamical range of the series y( j) is quantized in different dis-joint levels or regions, partitioning the phase space in hyper-cubes. The vectors inside the same hypercube are considered

similar or indistinguishable. In this sense, the entropy HC canbe obtained as [10]:

HC(uL=uL�1) ¼ HS(L)� HS(L� 1), (1)

where HS(L) is the Shannon entropy of uL(i) given by:

HS(L) ¼ �XNi

i¼1

p(uL(i)) � log p(uL(i)), if p(uL(i)) > 0, (2)

where Ni ¼ N � (L� 1)s. The entropy HS(L) can be obtainedby approximating the probabilities p(uL(i)) calculated as therelative frequency of the number of vectors uL(i) inside thesame hypercube. Low values of HC are obtained when a pat-tern of length L can be predicted by a pattern of length L� 1,indicating a higher regularity in the series.

In the present work, an approximation based on (1) was proposed:

DE(L) ¼ H(L)� H(L� 1), (3)

where H(L) was an entropy calculated by Shannon entropy (2)or Renyi entropy:

Hq(L)¼ 1

1� qlog

XNi

i¼1

(p(uL(i)))q

!, if p(uL(i))> 0, (4)

where q is a real number, q > 0 and q 6¼ 1, that determines themanner in which the probabilities are weighted. Whenq! 1, Hq(L) converges to HS(L).

The uniform and nonuniform partitioning of the phasespace were considered in this work. In both cases, the seriesy( j) were quantized by Q ¼ 4 regions using two differentalgorithms. The uniform quantization [14] uses levels of equalamplitude (e) given by:

e ¼ ymax � ymin

Q, (5)

Table 1. Clinical factors of patients with IDC.

FactorsAnalysis A(n ¼ 151)

Analysis B(n ¼ 194)

Age (year) 64.0 � 7.11 62.8 � 8.21Indexed LA size [mm/m2] 22.8 � 3.10 23.1 � 3.30NYHA III (%) 15.2% 17%LVEF (%) 34.7 � 10.3 34.9 � 10.7Indexed LVEDD [mm/m2] 32.5 � 4.62 32.4 � 4.79

Analysis A: SCD versus SV; Analysis B: CM versus SV.Mean � SD is provided for continuous variables andpercentage for categorical variables.

The clinical factor NYHA was useful in

identifying individuals at high risk of cardiac

death, but with a low sensitivity.

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE NOVEMBER/DECEMBER 2009 73


where ymax and ymin represent the maximum and the minimumvalue of y( j), respectively. On the other hand, the followingcriteria, used in symbolic dynamics to transform RR series tosymbols (Sj) [11], were used as a nonuniform quantization:

Sj ¼

1 if ( 1þ a) 3l < y(j) <10 if l < y(j) � (1þ a) 3l

2 if (1� a) 3 l < y(j) � l

3 if 0 < y(j) � (1� a) 3l

8>>><>>>:

j ¼ 1, . . . , N,

(6)

where N and l are the length and the mean value of the seriesy( j), respectively, and a is a constant that quantifies thestandard deviations of the series.

The proposed methodology has been applied to everywindow in the RR time series. The different values of phase-space dimension L ¼ f2, 3, 4, 5, 6g, different values of param-eter q ¼ f0:1, 0:15, 0:25, 1, 2, 4g, where q ¼ 1 denotes HS(L),and a constant value of a ¼ 0:07 [15] were taken into account.Finally, DE(L) measure was calculated on each window.

As example, Figure 1 showsthe evolution of the averagedDE(L) measure for all patientswith SV and SCD, respectively.This measure was computedusing R�enyi entropy with q ¼0:15, for each one of the 206windows. Uniform quantization[Figure 1(a)] and nonuniformquantization [Figure 1(b)] of thephase space with L ¼ 2 wasconsidered. In Figure 1(b), twowell-differentiated regions canbe observed, regions 1 and 2.Region 1 goes from window 40to 110 (18:23–22:15 h), andregion 2 goes from window 176to 206 (1:56–3:36 h). In thiscase, region 1 fits to daytimeand region 2 to the nighttime.Consequently, the measure

DE(L) was studied during daytime and nighttime for each oneof the proposed values of L and q in both analyses A and B.

Traditional HRV MeasuresAs time domain measures of the RR time series, the mean[MRR(ms)] and the standard deviation [SRR(ms)] were calculatedfor each window. In addition, the following frequency domainmeasures were computed for each window by means of an autor-egressive model (Burg algorithm) of order 12: total power½Ptot(ms2)�; power in the high-frequency (HF) band [(ms2),0.15–0.4 Hz]; power in the low-frequency (LF) band [(ms2),0.04–0.15 Hz]; power in the very low-frequency (VLF) band[(ms2), below 0.04 Hz]; LF and HF in normalized units (LFn andHFn); and the LF/HF ratio.

Statistical AnalysisThe Fisher’s exact test was used to classify patients by theclinical factor NYHA, and the Mann–Whitney U test was usedfor the remainder clinical factors considered in this work. Oth-erwise, a statistical analysis based on repeated measure analy-

sis of variance was appliedto the linear and nonlinearmeasures calculated on eachwindow. Discriminant linearfunctions were constructed onindividual and combined mea-sures, and diagnostic test in-dexes were calculated: SP, SE,positive predictive value (PPV),and negative predictive value(NPV). A statistical significantlevel P < 0:05 was consideredfor comparing statistically therisk groups.

Results

Clinical FactorsTable 2 shows that indexedLA size was significantly moreenlarged in high-risk-group

0.8

0.75

0.7

0.65

18:23 h 20:36 h 22:50 h 1:03 h 3:16 hTime

Windows

Region 2:NighttimeRegion 1: Daytime

DE

(L)

0.60 20 40 60 80 100 120 140 160 180 200

(a)

(b)

16:10 h

Fig. 1. Evolution of the averaged DE (L) measure for all patients with SV (blue line) and SCD(black line), respectively, along 206 windows of length N ¼ 1,000 samples. Measure com-puted using R�enyi entropy with q ¼ 0:15 and L ¼ 2. Phase space was quantized (a) uniformlyand (b) nonuniformly.

Table 2. Statistical analysis of clinical factors.

Analysis A

Factors SV (n = 139) SCD (n = 12) P

Indexed LA size [mm/m2] 22.7 � 3.05 24.7 � 3.12 0.048NYHA III (%) 12.9% 41.7% 0.020LVEF (%) 35.0 � 10.5 31.1 � 7.86 0.212Indexed LVEDD [mm/m2] 32.5 � 4.70 32.6 � 3.80 0.799

Analysis B

SV (n = 168) CM (n = 26) P

Indexed LA size [mm/m2] 22.7 � 3.21 25.4 � 2.97 <0.0005NYHA III (%) 11.3% 53.8% <0.0005LVEF (%) 35.5 � 10.9 30.7 � 7.83 0.047Indexed LVEDD [mm/m2] 32.1 � 4.70 34.2 � 5.03 0.068

SV: survivor; SCD: sudden cardiac death; and CM: cardiac mortality.Mean � SD is provided for continuous variables and percentage for categorical variables.

IEEE ENGINEERING IN MEDICINE AND BIOLOGY MAGAZINE NOVEMBER/DECEMBER 200974


patients, SCD (P ¼ 0:048),and CM (P < 0:0005), than inpatients with SV. In addition,the clinical measure NYHAwas significantly higher inSCD (P ¼ 0:020) and in CM(P < 0:0005), than in patientswith SV. LVEF was also ableto statistically differentiate(P ¼ 0:047) between SV andCM. However, indexed LVEDDwas not significantly differentin analyses A and B. Identify-ing individuals by indexed LAsize presented a 64% SP and58% SE in analysis A and 69%SP and 65% SE in analysis B.The functional class NYHA had87.1% SP and 41.7% SE inanalysis A and 88.6% SP and53.8% SE in analysis B. A 60%SP and 53.8% SE were obtainedby LVEF in analysis B.

Linear and Nonlinear HRV MeasuresThe linear measures of HRV in time domain and frequencydomain contribute to risk stratification only during daytimebut not during nighttime, for both analyses A and B. In partic-ular (see Table 3), only SRR and LFn have statistically differ-entiated groups during daytime in analysis A (SRR: P ¼0:0361, LFn: P ¼ 0:0259) and in analysis B (SRR: P ¼0:0048, LFn: P ¼ 0:0011).

The nonlinear measure DE(L) calculated using uniformquantization of the phase space was not able to statisticallydifferentiate the risk groups for both analysis during daytimeand nighttime for all values of L and q. Using nonuniformquantization, DE(L) presented statistical significance forL ¼ 2 and q ¼ f0:1, 0:15, 0:25g in analysis A and L ¼ 2 andq ¼ f0:1, 0:15g in analysis B during daytime and nighttime.Figure 2 shows the statistical significant level concerning toanalysis A during nighttime for DE(L), calculated using uni-form quantization [Figure 2(a)] and nonuniform quantization[Figure 2(b)].

Figure 3 graphically presents the mean and 95% confidenceinterval values of DE(2) for q ¼ f0:1, 0:15, 0:25g and the statis-tical differences between the risk groups in analyses A and B.This figure evidences that the higher statistical differences wereobtained with q ¼ 0:1, decreasing these differences when thevalue of q was increased. In both analyses, the mean value ofDE(2)q¼0:1 was significantly lower in high-risk groups than inlow-risk groups, denoting an increase of regularity of the short-term HRV in high-risk groups compared with that in low-riskgroups. Nonsignificant differences were found comparing day-time and nighttime in any of the analysis. However, mean valuesof DE(2)q¼0:1 during daytime have tended to be higher than dur-ing nighttime, denoting a lower regularity of the short-term HRVduring daytime.

Tables 4 and 5 show those measures that presented aP < 0:05 and diagnostic test indexes SP > 55% and SE >55% obtained by a discriminant linear function. Thesemeasures are indexed LA size, SRR, LFn, and DE(2)q¼0:1. It isevidenced that DE(2)q¼0:1 is a higher risk marker than the

clinical measure indexed LA size and the linear measures LFnand SRR; even this last one is slightly higher than DE(2)q¼0:1

during daytime in analysis A. The linear combination of thesemeasures with the best diagnostic test values is also shown:combination of DE(2)q¼0:1 and SRR for daytime and DE(2)q¼0:1

and indexed LA size for nighttime. Combining DE(2)q¼0:1 and

Table 3. Statistical analysis of linear measures: daytime.

Analysis A

Measures SV (n = 139) SCD (n = 12) P

MRR [ms] 853.2[826.3–880.0] 807.2[715.8–898.6] 0.3420SRR [ms] 37.2[34.09–40.33] 25.4[14.76–35.99] 0.0361LFn 54.56[52.03–57.08] 44.36[35.78–52.95] 0.0259HFn 29.11[27.27–30.96] 32.32[26.04–38.61] 0.3347LF/HF 2.81[2.49–3.13] 2.04[0.94–3.13] 0.1820

Analysis B

SV (n = 168) CM (n = 26) P

MRR [ms] 853.2[830.1–876.3] 806.1[747.3–864.8] 0.1425SRR [ms] 36.7[34.06–39.33] 26.28[19.58–32.98] 0.0048LFn 55.05[52.68–57.43] 44.13[38.10–50.16] 0.0011HFn 28.62[26.90–30.34] 31.50[27.14–35.86] 0.2275LF/HF 2.95[2.64–3.25] 2.12[1.33–2.9] 0.0521

SV: survivor; SCD: sudden cardiac death; and CM: cardiac mortality. Data are expressedas mean (95% of confidence interval).

100

10–1

10–2

Sta

tistic

al S

igni

fican

t Lev

el

100

10–1

10–2Sta

tistic

al S

igni

fican

t Lev

el

2 3 4 5 6L

2 3 4

(a)

(b)

5 6L

P = 0.05q = 0.10q = 0.15q = 0.25

q = 2q = 4

SH

P = 0.05q = 0.10q = 0.15q = 0.25

q = 2q = 4

SH

Fig. 2. Statistically significant level (P) of DE (L) during nighttime,comparing low-risk (SV) and high-risk (SCD) groups. Phasespace was quantized (a) uniformly and (b) nonuniformly.



SRR, a 58.8% PPV was obtained for the analysis A (Table 4)and 45.7% PPV for the analysis B (Table 5) during daytime.On the other hand, combining DE(2)q¼0:1 and indexed LA size,a 50% PPV was obtained for the analysis A (Table 4) and42.9% PPV for the analysis B (Table 5) during nighttime.

Discussion and ConclusionIn the present study, the clinical factor NYHA was useful inidentifying individuals at high risk of cardiac death, but with

a low SE, as it is also reported in [1]. Furthermore, accordingto Guzzetti et al. [16], we incurred that the LVEF factor wasnot related to the risk of SCD, as it was observed in Table 2.Finally, indexed LA size emerged as the best clinical factorto classify patients at high-risk groups in both analyses A andB. These results confirmed the association between indexedLA size enlargement and increased risk of death [1].

From the applied linear methods, the measures SRR and LFnseem to be suitable for an enhanced risk classification during

1

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0.6

0.4

0.2

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(L)

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0.4

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DE

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0.4

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DE

(L)

0SV SV CMSCDAnalysis A Analysis B

(a)

SV SV CMSCDAnalysis A Analysis B

(b)

SV SV CMSCDAnalysis A Analysis B

(c)

DaytimeNighttime

DaytimeNighttime

DaytimeNighttime

Fig. 3. Mean and 95% confidence interval values of DE (L) index with L ¼ 2: (a) q ¼ 0:1; (b) q ¼ 0:15; (c) q ¼ 0:25.�P < 0:05: ��P < 0:01.

Table 4. Diagnostic test indexes: Analysis A(SV versus SCD).

MeasuresSP(%)

SE(%)

PPV(%)

NPV(%)

Indexed LA size 64.0 58.3 12.3 94.7Daytime

SRR 88.5 75.0 36.0 97.6LFn 80.6 58.3 20.6 95.7DE (2)q¼0:1 81.3 75.0 25.7 97.4

DE (2)q¼0:1, SRR� �

95.0 83.3 58.8 98.5Nighttime

DE (2)q¼0:1 87.1 83.3 35.7 98.4{DE (2)q¼0:1, Indexed LA Size} 92.8 83.3 50.0 98.5

The best diagnostic test values are indicated in bold.SP: specificity; SE: sensitivity; PPV: positive predictive value;and NPV: negative predictive value.

Table 5. Diagnostic test indexes: Analysis B(SV versus CM).

MeasuresSP(%)

SE(%)

PPV(%)

NPV(%)

Indexed LA size 69.0 65.4 24.6 92.8Daytime

SRR 67.9 88.5 29.2 97.4LFn 70.2 50.0 20.6 90.1DE (2)q¼0:1 79.2 69.2 34.0 94.3

DE (2)q¼0:1, SRR� �

85.1 80.8 45.7 96.6Nighttime

DE (2)q¼0:1 76.2 73.1 32.2 94.8{DE (2)q¼0:1, Indexed LA Size} 83.3 80.8 42.9 96.6

The best diagnostic test values are indicated in bold.SP: specificity; SE: sensitivity; PPV: positive predictive value;and NPV: negative predictive value.

Using nonuniform quantization regions

can also improve the performance

of the conditional entropy.



daytime but not during nighttime. The independent prognosticvalue of SRR has indicated a lower variability in high-riskgroups than in low-risk groups in both analyses A and B. More-over, considering that chronic heart failure is characterized by ahigh-sympathetic drive, spectral analysis of the RR series wouldbe reasonably expected to manifest predominantly LF component.However, our results have revealed a decreased LFn componentin high-risk groups in comparison with low-risk groups. The inter-pretation of a reduced LFn in patients with chronic heart failure isstill an open question, including a depressed sinus node respon-siveness, central abnormality in autonomic modulation, limitationin responsiveness to high levels of cardiac sympathetic activation,depressed baroreflex, and increased chemoreceptor SE [16].

Measures based on symbolic dynamics with uniform quantiza-tion regions of the RR series as in Maestri et al. [17] or with non-uniform quantization regions as in Wessel et al. [11] have beensuccessful to detect pathological conditions characterized by aconcomitant increased risk for cardiac events. Porta et al. [18]applied corrected conditional entropy using a uniform quantiza-tion with different number of regions and concluded that enlarg-ing the number of uniform quantization regions improves theperformance of the conditional entropy. Our work has revealedthat a nonuniform quantization, based on symbolic dynamics[11], can also improve the performance of the conditional entropyeven with a few number of quantization regions. Four regionswere adjusted as function of the mean value of the RR series in asliding window, allowing the algorithm to be adapted along thetime series to retain the dynamical information of the signal.

The adjustment of the involved parameters in the calculus ofDE(L) has allowed L ¼ 2 and q ¼ 0:1 to provide the best results.The low value of the dimensional phase space is according toPorta et al. [14]. They reported that the spreading of the points ofthe reconstructed phase space while increasing the dimension Lguarantees that the prediction becomes worse and worse.DE(2)q¼0:1 has been able to significantly differentiate betweenthe risk groups during daytime and nighttime. The lower valuesof DE(2)q¼0:1 obtained in high-risk groups have indicated anincrease in regularity of the short-term HRV in patients withSCD and CM in comparison with patients with SV. Since regu-larity is under sympathetic control [18], the increased regularitymight suggest that the high-risk patients have higher levels ofsympathetic tone, thus prompting for a more aggressive therapyto reduce sympathetic overactivity in subjects at risk.

After the discriminant analysis for clinical, linear, and nonlin-ear measures of the HRV, DE(2)q¼0:1 seems to emerge as a goodrisk marker of SCD in patients with IDC. Indeed, the linear com-bination of DE(2)q¼0:1 and SRR (during daytime) or DE(2)q¼0:1

and indexed LA size (during nighttime) were longer predictivewhen comparing survivors with SCD and survivors with CM.

The results seem to indicate that DE(L) can provide aquantitative estimation of the regularity of short-term heart-

rate dynamics involved in the IDC. However, the clinicalutility of this nonlinear measure with SRR and indexed LA sizeshould be studied in a larger number of patients.

AcknowledgmentsThis work was supported within the framework of the CICYTgrant TEC2004-02274, the research fellowship grant FPIBES-2005-9852 from the Spanish Government, and CIBERof Bioengineering, Biomaterials and Nanomedicine (CIBER-BBN), which is an initiative of ISCIII. The MUSIC trial wascoordinated by University Hospital St. Pau, Barcelona, Spain(I. Carlos III—Spain network group).

Jose F. Valencia received the electricalengineering degree and the communica-tion network specialist degree from theUniversidad del Valle, Cali, Colombia,in 1995 and 2003, respectively. He is cur-rently pursuing his Ph.D. degree in bio-medical engineering at Technical Universityof Catalonia (UPC), Barcelona, Spain. He

obtained a research fellowship from the Spanish Govern-ment to work on a project for the analysis of biomedical sig-nals to clinical evaluation and rehabilitation. His researchinterests include time series analysis and complexity analy-sis of HRV.

Montserrat Vallverd�u received her M.S.and Ph.D. degrees in industrial engineeringin the program of biomedical engineering atUPC, Barcelona, Spain. She is an assistantprofessor in the Department of AutomaticControl at the Biomedical Engineering Re-search Center, UPC. Her research interestsinclude complexity analysis of the hidden

information in cardiac and respiratory signals.

Rico Schroeder was graduated as an engi-neer of biomedical engineering from theUniversity of Applied Sciences, Jena, Ger-many, in 2001. He is currently a scientificcoworker of a biomedical research group atthe same university and is supported bygrant from the German Federation of Indus-trial Research Associations (AiF/PRO INNO

II No. KF0104503WM7). His research interests include signalprocessing, particularly with regard to linear and nonlinearinteractions of the cardiorespiratory and cardiovascular systemin patients with different heart diseases (heart failure, dilatedcardiomyopathy, and myocardial infarction), as well as heartsound analyses in patients with congestive heart failure.

DE(L) seems to emerge as a good risk marker

of SCD in patients with IDC.



Andreas Voss received his diploma in con-trol engineering from the Technical Univer-sity Dresden, Germany, in 1972. In 1990,he obtained his Ph.D. degree in biomedicalengineering from the German Academy ofSciences. In 1997, he was appointed as aprofessor and chair of biosignal analysisand medical informatics at the University

of Applied Sciences, Jena. From 1999 to 2001 and 2005 to2008, he was dean of the Department of Medical Engineeringand Biotechnology, and from 2001 to 2003, he was a vice pres-ident of the University. His research interests include linearand nonlinear analyses of multivariate data to investigate com-plex cardiovascular variability for diagnosing and risk stratifi-cation in cardiology, neurology, and pregnancy. He is alsodeveloping and applying new methods of electronic senses fordiagnosing different internal diseases.

Rafael V�azquez was graduated from theMedical School of the Valencia Univer-sity, Spain, in 1978. His postdoctoral train-ing was carried out in a full-residencyprogram in the Cardiology Service of the‘‘V. Rocio’’ University Hospital, Seville,Spain, from 1979 to 1982. He was licensedas a ‘‘Specialist in Cardiology’’ in Madrid,

Spain, on 30 June 1981. The theme of his doctoral thesis wasretrograde ventriculoatrial conduction, which was presentedat the University of Seville on 10 July 1989, with the maxi-mum score. From 1984 until April 2008, he worked as a cardi-ologist in the Valme University Hospital, Seville, Spain, andfrom 1999 until April 2008, he was the chief of the ResearchUnit in the same hospital. Currently, he is the chief of theCardiology Service of Puerta del Mar University Hospital,Cadiz, Spain.

Antonio Bay�es de Luna was trained as acardiologist in the School of Cardiologyof the University of Barcelona, and theInstitute of Cardiology and HammersmithHospital in London. In 1971, he became anassociate professor at the UniversidadAutonoma de Barcelona and chief ofElectrocardiography and Arrhythmic Unit

in Hospital de Sant Pau. He was chair of the Cardiology andCardiac Surgery Department in Hospital de Sant Pau. He isnow Emeritus Professor of the Universidad Autonoma de Bar-celona. His scientific production specially devoted to ECG,arrhythmias, sudden death, Holter technology, risk stratifica-tion, and silent ischemia is very extensive. He is the authorof more than 180 papers in scientific journals.

Pere Caminal received his M.S. and Ph.D.degrees in industrial engineering at UPC, Bar-celona, Spain. He is a professor in the Depart-ment of Automatic Control, at the BiomedicalEngineering Research Center, UPC. His re-search interests include modeling biologicalsystems and biomedical signal processing.

Address for Correspondence: Jose F. Valencia, DepartmentESAII, Universitat Politecnica de Catalunya, C/Pau Gargallo 5,08028 Barcelona, Spain. E-mail: [email protected].

References[1] A. Bay�es-Genis, R. Vazquez, T. Puig, C. Fernandez-Palomeque, J. Fabregat,A. Bardaji, D. Pascual-Figal, J. Ordonez-Llanos, M. Valdes, A. Gabarr�us,R. Pavon, L. Pastor, J. R. G. Juanatey, J. Almendral, M. Fiol, V. Nieto,C. Macaya, J. Cinca, and A. B. d. Luna, ‘‘Left atrial enlargement and NT-proBNPas predictors of sudden cardiac death in patients with heart failure,’’ Eur. J. HeartFail., vol. 9, no. 8, pp. 802–807, 2007.[2] M. Baumert, N. Wessel, A. Schirdewan, A. Voss, and D. Abbott, ‘‘Scalingcharacteristics of heart rate time series before the onset of ventricular tachycar-dia,’’ Ann. Biomed. Eng., vol. 35, no. 2, pp. 201–207, 2007.[3] A. Varela-Roman, J. R. Gonzalez-Juanatey, P. Basante, R. Trillo,J. Garcia-Seara, J. L. Martinez-Sande, and F. Gude, ‘‘Clinical characteristicsand prognosis of hospitalised inpatients with heart failure and preserved orreduced left ventricular ejection fraction,’’ Heart, vol. 88, no. 3, pp. 249–254, 2002.[4] S. Truebner, I. Cygankiewicz, R. Schroeder, M. Baumert, M. Vallverd�u,P. Caminal, A. B. d. Luna, and A. Voss, ‘‘Compression entropy contributes to riskstratification in patients with cardiomyopathy,’’ Biomed. Tech., vol. 51, no. 2,pp. 77–82, 2006.[5] M. Ferrario, M. G. Signorini, and G. Magenes, ‘‘Estimation of long-term cor-relations from fetal heart rate variability signal for the identification of pathologi-cal fetuses,’’ in Proc. 29th Ann. Int. Conf. IEEE Engineering in Medicine andBiology Society (EMBS’07), 2007, pp. 295–298.[6] M. Costa, A. L. Goldberger, and C.-K. Peng, ‘‘Multiscale entropy analysis ofbiological signals,’’ Phys. Rev. E, vol. 71, no. 2, p. 021906, 2005.[7] Task Force of the Europe Society of Cardiology and the North AmericanSociety of Pacing and Electrophysiology, ‘‘Heart rate variability-standards ofmeasurement, physiological interpretation and clinical use,’’ Circulation, vol. 93,no. 5, pp. 1043–1065, 1996.[8] P. K. Stein, P. P. Domitrovich, H. V. Huikuri, and R. E. Kleiger, ‘‘Traditionaland nonlinear heart rate variability are each independently associated with mortal-ity after myocardial infarction,’’ J. Cardiovasc. Electrophysiol., vol. 16, no. 1,pp. 13–20, 2005.[9] A. Voss, R. Schroeder, and S. Truebner, ‘‘Comparison of nonlinear methodssymbolic dynamics, detrended fluctuation, and Poincar�e plot analysis in riskstratification in patients with dilated cardiomyopathy,’’ Chaos, vol. 17, no. 1,p. 015120, 2007.[10] A. Porta, L. Faes, M. Mas�e, G. D’Addio, G. D. Pinna, R. Maestri,N. Montano, R. Furlan, R. Furlan, G. Nollo, and A. Malliani, ‘‘An inte-grated approach based on uniform quantization for the evaluation of com-plexity of short-term heart period variability: Application to 24 h Holterrecordings in healthy and heart failure humans,’’ Chaos, vol. 17, no. 1,p. 015117, 2007.[11] N. Wessel, C. Ziehmann, J. Kurths, U. Meyerfeldt, A. Schirdewan, andA. Voss, ‘‘Short-term forecasting of life-threatening cardiac arrythmias based onsymbolic dynamics and finite time growth rates,’’ Phys. Rev. E, vol. 61, no. 1,pp. 733–739, 2000.[12] A. Papaulis, Probability, Random Variables and Stochastic Processes. NewYork: McGraw-Hill, 1984, pp. 515–533.[13] F. Takens, ‘‘Detecting strange attractors in turbulence,’’ in DynamicalSystems and Turbulence (Lecture Notes in Mathematics, vol. 898), D.A. Rand and L. S. Young, Eds. Berlin, Germany: Springer-Verlag, 1981,pp. 366–381.[14] A. Porta, S. Guzzetti, R. Furlan, T. Gnecchi-Ruscone, N. Montano, andA. Malliani, ‘‘Complexity and nonlinearity in short-term heart period variability:Comparison of methods based on local nonlinear prediction,’’ IEEE Trans.Biomed. Eng., vol. 54, no. 1, pp. 94–106, 2007.[15] J. F. Valencia, M. Vallverd�u, I. Cygankiewicz, A. Voss, R. Vazquez, A. B.d. Luna, and P. Caminal, ‘‘Multiscale regularity analysis of the heart rate variabil-ity: Stratification of cardiac death risk,’’ in Proc. 29th Annu. Int. IEEE-EMBSConf., 2007, pp. 5946–5949.[16] S. Guzzetti, M. T. L. Rovere, G. D. Pinna, R. Maestri, E. Borroni, A. Porta,A. Mortara, and A. Malliani, ‘‘Different spectral components of 24 h heart ratevariability are related to different modes of death in chronic heart failure,’’ Eur.Heart J., vol. 26, no. 4, pp. 357–362, 2005.[17] R. Maestri, G. D. Pinna, A. Accardo, P. Allegrini, R. Balocchi, G. D’Addio,M. Ferrario, D. Menicucci, A. Porta, R. Sassi, M. G. Signorini, M. T. L. Rovere,and S. Cerutti, ‘‘Nonlinear indices of heart rate variability in chronic heart failurepatients: Redundancy and comparative clinical value,’’ J. Cardiovasc. Electrophy-siol., vol. 18, no. 4, pp. 425–433, 2007.[18] A. Porta, T. Gnecchi-Ruscone, E. Tobaldini, S. Guzzetti, R. Furlan, andN. Montano, ‘‘Progressive decrease of heart rate period variability entropy-basedcomplexity during graded head-up tilt,’’ J. Appl. Physiol., vol. 103, no. 4,pp. 1143–1149, 2007.



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Complexity of the short-term heart-rate variability