Novel application of multi dynamic trend analysis as a sensitive tool for detecting theeffects of aging and congestive heart failure on heart rate variabilityYu-Cheng Lin, Yu-Hsuan Lin, Men-Tzung Lo, Chung-Kang Peng, Norden E. Huang, Cheryl C. H. Yang, andTerry B. J. Kuo Citation: Chaos 26, 023109 (2016); doi: 10.1063/1.4941673 View online: http://dx.doi.org/10.1063/1.4941673 View Table of Contents: http://scitation.aip.org/content/aip/journal/chaos/26/2?ver=pdfcov Published by the AIP Publishing Articles you may be interested in Complexity in congestive heart failure: A time-frequency approach Chaos 26, 033105 (2016); 10.1063/1.4941374 Modeling heart rate variability including the effect of sleep stages Chaos 26, 023101 (2016); 10.1063/1.4940762 Symbolic dynamics marker of heart rate variability combined with clinical variables enhance obstructive sleepapnea screening Chaos 24, 024404 (2014); 10.1063/1.4869825 Analysis of heart rate variability signal in meditation using second-order difference plot J. Appl. Phys. 109, 114703 (2011); 10.1063/1.3586270 Interpretation of heart rate variability via detrended fluctuation analysis and αβ filter Chaos 13, 467 (2003); 10.1063/1.1562051

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

Novel application of multi dynamic trend analysis as a sensitive toolfor detecting the effects of aging and congestive heart failureon heart rate variability

Yu-Cheng Lin,1,2 Yu-Hsuan Lin,1,2 Men-Tzung Lo,3,4 Chung-Kang Peng,3,5

Norden E. Huang,4 Cheryl C. H. Yang,1,2,6 and Terry B. J. Kuo1,2,6,7,a)

1Institute of Brain Science, National Yang-Ming University, Taipei, Taiwan2Sleep Research Center, National Yang-Ming University, Taipei, Taiwan3Center for Dynamical Biomarkers and Translational Medicine, National Central University, Jhongli, Taiwan4Research Center for Adaptive Data Analysis, National Central University, Taoyuan, Taiwan5Division of Interdisciplinary Medicine and Biotechnology and Margret and H.A. Rey Institute for NonlinearDynamics in Medicine, Beth Israel Deaconess Medical Center, Harvard Medical School, Boston,Massachusetts 02215, USA6Brain Research Center, National Yang-Ming University, Taipei, Taiwan7Institute of Translational and Interdisciplinary Medicine, National Central University, Taoyuan, Taiwan

(Received 29 June 2015; accepted 28 January 2016; published online 11 February 2016)

The complex fluctuations in heart rate variability (HRV) reflect cardiac autonomic modulation and

are an indicator of congestive heart failure (CHF). This paper proposes a novel nonlinear approach to

HRV investigation, the multi dynamic trend analysis (MDTA) method, based on the empirical mode

decomposition algorithm of the Hilbert–Huang transform combined with a variable-sized sliding-

window method. Electrocardiographic signal data obtained from the PhysioNet database were used.

These data were from subjects with CHF (mean age¼ 59.4 6 8.4), an age-matched elderly healthy

control group (59.3 6 10.6), and a healthy young group (30.3 6 4.8); the HRVs of these subjects

were processed using the MDTA method, time domain analysis, and frequency domain analysis.

Among all HRV parameters, the MDTA absolute value slope (MDTS) and MDTA deviation

(MDTD) exhibited the greatest area under the curve (AUC) of the receiver operating characteristics

in distinguishing between the CHF group and the healthy controls (AUC¼ 1.000) and between the

healthy elderly subject group and the young subject group (AUC¼ 0.834 6 0.067 for MDTS;

0.837 6 0.066 for MDTD). The CHF subjects presented with lower MDTA indices than those of the

healthy elderly subject group. Furthermore, the healthy elderly subjects exhibited lower MDTA indi-

ces than those of the young controls. The MDTA method can adaptively and automatically identify

the intrinsic fluctuation on variable temporal and spatial scales when investigating complex fluctua-

tions in the cardiac autonomic regulation effects of aging and CHF. VC 2016 AIP Publishing LLC.

[http://dx.doi.org/10.1063/1.4941673]

Heart rate variability (HRV) is considered a noninvasive

indicator of the autonomic nervous system and is widely

applied in analyzing several cardiovascular diseases,

including congestive heart failure (CHF). Technically,

three approaches to determining HRV, time domain

analysis, frequency domain analysis, and nonlinear anal-

ysis have been used. However, these approaches have

some limitations and not suitable for analysis complex

fluctuations. Based on the empirical mode decomposition

(EMD) algorithm of the Hilbert–Huang transform

(HHT) combined with a variable-sized sliding-window

method, this article describes a novel nonlinear approach

to HRV investigation, the multi dynamic trend analysis

(MDTA) method, and more proposed two HRV parame-

ters for assessing the effects of aging and CHF on auto-

nomic function: the slope of the absolute value of MDTA

(MDTS) and the deviation in MDTA (MDTD). The

results reveal that the novel MDTA parameters have

higher discriminating power than the parameters for

aging and CHF obtain through time domain analysis and

frequency domain analysis. Further, it has higher acute

sensitivity and specificity when identifying CHF than

time domain analysis and frequency domain analysis.

Theoretically, MDTA can adaptively and automatically

identify the intrinsic fluctuation from nonlinear and non-

stationary signals on variable temporal and spatial scales.

INTRODUCTION

Over the past decades, numerous studies have examined

variations in long-term recording of heartbeat intervals,

namely, HRV. HRV is considered a noninvasive indicator of

the autonomic nervous system and is applied in analyzing

several cardiovascular diseases, including hypertension,1

diabetes mellitus,2 sudden cardiac death,3 coronary artery

disease,4 and heart failure.5 Technically, three approaches to

determining HRV, time domain analysis, frequency domain

analysis, and nonlinear analysis have been established.

Our previous study used frequency domain analysis to

a)Author to whom correspondence should be addressed. Electronic mail:

tbjkuo@ym.edu.tw

1054-1500/2016/26(2)/023109/7/$30.00 VC 2016 AIP Publishing LLC26, 023109-1

CHAOS 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

demonstrate that aging plays a critical role in the decrease of

total power (TP), high frequency power (HF), and the ratio

of low frequency power (LF) to HF (LF/HF).6 Time domain

analysis also revealed that the standard deviation of normal

to normal R–R intervals (SDNN) is associated with aging.6

Among subjects with CHF, SDNN has been widely used to

predict mortality,7 with a decreased HF reflecting the loss of

vagal functioning.8 Compared with nonlinear analysis, time

domain analysis and frequency domain analysis are rela-

tively widely used approaches, and most basic research and

clinical applications are based on these two methods.9,10

However, nonlinear analyses of HRV have generally

demonstrated higher acute sensitivity and specificity when

identifying cardiovascular disease than time domain analysis

and frequency domain analysis have.11,12 Nonlinear analysis

provides an improved decomposition of the intrinsic fluctua-

tions in HRV compared with time domain analysis and fre-

quency domain analysis because of technical limitations

associated with the latter two approaches. The superiority of

nonlinear analysis is based on the fact that time domain anal-

ysis and frequency domain analysis improperly process and

analyze the dynamic variation features in HRV generated

from complex physiological systems.13–15

Two types of HRV analysis, long-term (24 h) and short-

term (5 min),9 have been recommended by the Task Force of

the European Society of Cardiology and the North American

Society of Pacing Electrophysiology. However, there is

demand for a more flexible analysis than the single scale

window 5-min or 24-h methods for investigating rapid fluc-

tuations in HRV.16 Consequently, nonlinear analysis has

recently received more attention, especially for investigating

nonlinear and nonstationary physiological signals.17–19

Studies have shown that the HHT,11 multiscale entropy,20

detrended fluctuation analysis,21 stochastic series expansion

quantum Monte Carlo,22 and compression entropy23 can

identify fluctuations and complexity in complex systems;

however, these approaches have usually been need sufficient

data to analyze24–26 and entropy limited by sensitivity to

both N and r27 in previous studies.

Huang et al. proposed a nonlinear approach based on

EMD that is regarded as a revolution of the digital signal

process.13 This technique was designated as the HHT and

has been applied to geophysical signals,28 atmospheric turbu-

lence,29 structural applications,30 and speech recognition.13

The HHT has also been applied to physiological signals in

biomedical engineering and health monitoring.31–33

However, no previous study has combined the HHT with a

variable-sized sliding-window method to investigate the

variable temporal and spatial scales of HRV.

We hypothesized that the autonomic nervous system pro-

duces intrinsically complex fluctuations in HRV. Moreover,

this complexity, similar to the results obtained using nonlinear

methods, is reduced by aging and by CHF.16,34 This study

proposes a novel nonlinear approach to HRV investigation,

MDTA, which is based on the EMD algorithm of the HHT

combined with a variable-sized sliding-window method. The

specific aims of this study were to examine the correlation

between MDTA, time domain analysis, and frequency domain

analysis of R–R intervals and to test whether MDTA can

effectively distinguish the effects of aging and CHF.

MATERIALS AND METHODOLOGY

Subjects

The present study examined three subject groups: (1) 20

subjects with CHF (mean age¼ 59.40 years, range: 43–79

years), (2) 20 age-matched elderly healthy control subjects

(mean age¼ 59.30 years, range: 40–73 years), and (3) 20

healthy young subjects (mean age¼ 30.25 years, range: 20–35

years). Each group consisted of 10 men and 10 women. The

data for all subjects were collected from 24-h electrocardiogram

recordings obtained from the PhysioNet website (www.physio-

net.org/physiobank/database).35–37 The details of this database

were described previously (www.physionet.org/physiobank).38

We used the continuous 500 beat-to-beat interval time series

(approximately 7 min) of the normal sinus rhythm of the sub-

jects while they were awake in the morning, enabling us to

exclude the effects of the circadian rhythm. All subjects and

continuous R–R intervals (RRs) were randomly selected to

avoid subjective influence. The RRs were verified using com-

puter algorithms that recognized each the combination of three

of the graphical deflections seen on a typical electrocardiogram

(QRS complex) and rejected each ventricular premature com-

plex or noise according to likelihood by using a standard QRS

template. The program for preprocessing the artifacts was

designed according to our previous investigations.6,39 For the

artifacts of the RR rejection procedure, a temporary mean and

standard deviation of all RRs were first calculated for a stand-

ard reference. Each RR was then validated: if the standard

score of an RR value exceeded 3, it was considered erroneous

or nonstationary and was rejected. The average percentile of

RR rejection according to this procedure was 1.2%.

The HRV data were processed using the MDTA method,

time domain analysis, and frequency domain analysis.

Multi dynamic trend analysis method

The MDTA method comprises a variable-sized sliding-

window method and the EMD algorithm of the HHT. EMD is

an adaptive data analysis method developed by Huang et al.13

Briefly, unlike Fourier-based time series analysis, EMD is an

adaptive decomposition method without a priori assumptions

that is applicable to nonlinear and nonstationary signals with

multiple periodic component processes. The decomposition

can automatically extract any signal composed of a finite num-

ber of intrinsic components or oscillations and residual compo-

nent (trend) without assumptions regarding signal stationarity.

Each oscillation component, termed an intrinsic mode func-

tion, is sequentially decomposed from the original time series

through a sifting process.13,40

The variable-sized sliding-window method processes

the HRV raw data by using a continuous variable window

size from a minimal time scale, namely, 30 s, to the complete

time scale (approximately 7 min). In each window, the EMD

of HHT was performed. Thus, MDTA delineates intrinsic

fluctuation trends and complex fluctuation patterns on differ-

ent temporal and spatial scales.

023109-2 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

These indicators were applied to a center position of the

variable-sized sliding-window method to create a three-

dimensional color graph of the time, the sliding window

size, and the slope of the trend. An example of application of

the MDTA approach in analyzing raw HRV data is shown in

Fig. 1. The two-dimensional relationship between the degree

of fluctuation and each analysis window size was used as the

standard deviation to calculate the slope change time series

of each window size from the three-dimensional color graph.

We proposed two HRV parameters for assessing the

effects of aging and CHF on autonomic function: MDTS and

MDTD calculated from two dimensions. These parameters

were obtained using the linear regression and mean absolute

deviation methods, respectively (Fig. 2).

Time domain and frequency domain analysis of HRV

The procedures for time domain analysis and frequency

domain analysis were based on standard methods and were

previously described.9 The two essential parameters of the

time domain analysis are the SDNN RRs over 7 min and the

root mean square successive difference of normal-to-normal

RRs (RMSSD).9,14,41

Power spectral analysis was performed using the fast

Fourier transform (FFT). The baseline shift was deleted, and

a Hamming window was used to attenuate the leakage

effect.42 Our algorithm was then used to estimate the power

density of the spectral components based on the FFT. The

resulting power spectrum was corrected for attenuation

resulting from sampling and the application of the Hamming

window. The power spectrum was subsequently quantified

and separated into standard frequency domain measure-

ments, as previously reported,9,43 namely, the very low fre-

quency power (VLF) (0.003–0.04 Hz), LF (0.04–0.15 Hz),

HF (0.15–0.40 Hz), TP, LF/HF, and normalized LF (LF%).

The LF% was calculated using LF/(total power�VLF)

� 100. VLF, LF, HF, and LF/HF were logarithmically trans-

formed to correct for their skewed distributions.6

We developed the MDTA method and conducted the

time domain analysis and frequency domain analysis of HRV

by using a mathematics software package (MathWorks,

Natick, Massachusetts, U.S.A.).

Statistical analysis

We compared the HRV parameters between the CHF

subjects and the age-matched elderly healthy controls and

between the elderly subjects and the young healthy subjects

by using one-way ANOVA. We further used receiver operat-

ing characteristic (ROC) curve analysis to identify whether

the HRV parameters enable distinguishing between the

CHF group and the age-matched elderly healthy group and

between the healthy elderly group and the young group.

C-statistics were used to obtain the area under the ROC

curve (area under the curve, AUC) with a standard error to

examine the significance, and an AUC higher than 0.5 indi-

cated that the parameter can distinguish between two groups.

The sensitivity and specificity cutoff points were also ana-

lyzed. Next, we examined the correlations among the HRV

parameters obtained using the MDTA method, time domain

analysis, and frequency domain analysis by using Pearson’s

correlation coefficient obtained for the CHF subject group,

healthy elderly subject group, and healthy young subject

group. A p value <.05 was considered significant. Values

were expressed as means 6 standard deviation.

RESULTS

Figure 3 illustrates the results of MDTA of HRV for a

healthy young subject, a healthy elderly subject, and a CHF

subject in a three-dimensional color graph. For the CHF sub-

ject, the color changes were smaller and the graph was more

monotonous than those for the healthy young and healthy el-

derly subjects.

FIG. 1. Example of an HRV raw data pass using the multi dynamic trend

analysis method to create a three-dimensional color graph of the time, win-

dow size, and slope of the trend. The color change mean is the slope value.

FIG. 2. The absolute value of the slope jdy/dxj in the multi dynamic trend

analysis and deviation (grey area) of the multi dynamic trend analysis were

calculated in two dimensions, the degree of fluctuation and the analysis

window size, by using the linear regression and mean absolute deviation

methods.

023109-3 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

Table I shows the parameters of the MDTA method, the

time domain analysis, and the frequency domain analysis of

HRV for the three subject groups. The CHF subjects had a

lower MDTD and MDTS than those of the two control sub-

ject groups. In addition, the MDTS and MDTD were lower

among the healthy elderly subjects than among the healthy

young subjects. Similarly, the SDNN and TP were signifi-

cantly lower among the CHF subjects than among the

healthy elderly subjects. This was also true for the healthy el-

derly subjects compared with the healthy young subjects.

The LF% and LF/HF were lower for the CHF subjects than

for the healthy elderly subjects but were not significantly

different between the healthy elderly and the healthy young

subjects. The healthy elderly subjects’ RMSSD and HF were

both lower than those of the healthy young subjects, but

there was no significant difference in the RMSSD and HF

between the CHF and the healthy elderly subject groups.

Figure 4 shows the relationship between each degree of

fluctuation and variations in the window size for the CHF,

healthy elderly, and healthy young subject groups. The CHF

subjects showed a lower degree of fluctuation and a smaller

standard deviation range than those of the healthy elderly and

healthy young subject groups when they were determined

FIG. 3. Original beat-to-beat interval time series of continuous 500 beat numbers (7 min) (R–R interval; top); three-dimensional color variation graph plotted

using the multi dynamic trend analysis method by variance of slope (MDTS, bottom); and three-dimensional color variation graph plotted using the multi

dynamic trend-derived quantitative indices (MDTD, bottom) for a 30-year-old man of the young healthy subject group (a), for a 67-year-old man of the elderly

healthy subject group (b), and for a 62-year-old man of the congestive heart failure subject group (c). All data were obtained while the subjects were awake in

the morning.

TABLE I. Multi dynamic trend analysis parameters, time domain analysis

parameters, and frequency domain analysis parameters of heart rate variabil-

ity for young healthy subjects, elderly healthy subjects, and congestive heart

failure subjects. SDNN, standard deviation of normal to normal; RMSSD,

root mean square successive difference; HF, high frequency power; LF%,

normalized low frequency power; LF/HF, LF to HF ratio; ln, natural loga-

rithm; MDTS, multi dynamic trend slope (absolute value); and MDTD,

multi dynamic trend deviation.

Young healthy

(n¼ 20)

Elderly healthy

(n¼ 20)

CHF

(n¼ 20)

Age 30.25 6 4.81 59.30 6 10.56a 59.40 6 8.42

MDTA method

MDTS (absolute slope) 0.60 6 0.19 0.38 6 0.17a 0.06 6 0.02b

MDTD (deviation) 1.00 6 0.33 0.62 6 0.29a 0.09 6 0.04b

Time domain

SDNN, ms 55.29 6 18.51 35.85 6 18.10a 13.66 6 7.57b

RMSSD, ms 30.67 6 11.60 20.88 6 12.32a 16.75 6 12.56

Frequency domain

TP, ln(ms2) 7.87 6 0.63 6.84 6 0.89a 5.41 6 1.50b

HF, ln(ms2) 5.52 6 0.88 4.31 6 1.04a 3.96 6 1.55

LF%, nu 80.31 6 9.24 80.59 6 11.27 44.23 6 20.92b

LF/HF, ln(ratio) 6.11 6 0.62 6.13 6 0.65 4.33 6 0.97b

ap< 0.05 vs. young healthy control group.bp< 0.05 vs. elderly healthy control group.

FIG. 4. Relationship between the degree of fluctuation and each analysis win-

dow size for the young healthy subject group, for the elderly healthy subject

group, and for the congestive heart failure subject group. The dotted blue

line represents the healthy young subject group (multi dynamic trend

slope¼ 0.60 6 0.19; multi dynamic trend deviation¼ 1.00 6 0.33), the

square-shaped red line represents the elderly healthy subject group (multi

dynamic trend slope¼ 0.38 6 0.17; multi dynamic trend deviation¼ 0.62

6 0.29), and the diamond-shaped green line represents the congestive heart

failure subject group (multi dynamic trend slope¼ 0.06 6 0.02; multi dynamic

trend deviation¼ 0.09 6 0.04). Symbols represent the mean values for each

group, and the bars represent the standard deviation.

023109-4 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

using a small analysis window size. In addition, the degree of

fluctuation was lower and the standard deviation range was

smaller in the healthy elderly subject group than in the healthy

young group when they were determined using a small analy-

sis window size.

Among the healthy elderly and healthy young subject

groups, all HRV parameters, except LF% and LF/HF, were

significantly correlated with the MDTS and MDTD (Tables II

and III). The SDNN and TP showed the highest correlation

coefficients. However, among the CHF subjects, only LF%

and LF/HF were moderately correlated with the MDTD.

Among all HRV parameters (Tables IV and V), the

MDTS and MDTD showed the greatest AUC in distinguish-

ing the CHF subjects from the healthy elderly subjects

(AUC¼ 1.000) and in distinguishing the healthy elderly sub-

jects from the healthy young subjects (AUC of MDTS:

0.834 6 0.067; MDTD: 0.837 6 0.066). When the CHF

subjects and age-matched controls were compared, all the

HRV parameters in time domain analysis and frequency do-

main analysis, except the HF, showed a significant AUC.

Furthermore, the lowest AUC was that for TP, 0.792. The

exception, the HF, did not show a significant AUC (0.570).

When the healthy elderly subjects and healthy young sub-

jects were compared, all the HRV parameters showed a sig-

nificant AUC, except for LF% and LF/HF.

DISCUSSION

Consistent with previous studies using nonlinear analy-

sis of HRV, the novel MDTA parameters had higher discrim-

inating power than the parameters obtained through time

domain analysis and frequency domain analysis did when

TABLE II. Correlation coefficients between multi dynamic trend slope

(absolute values) and parameters of time domain analysis and frequency do-

main analysis obtained for young healthy subjects, elderly healthy subjects,

and congestive heart failure subjects. SDNN, standard deviation of normal

to normal; RMSSD, root mean square successive difference; TP, total

power; HF, high frequency power; LF%, normalized low frequency power;

LF/HF, LF to HF ratio; and ln, natural logarithm.

Young healthy Elderly healthy CHF

Time domain

SDNN, ms 0.940a 0.987a 0.199

RMSSD, ms 0.760a 0.648a 0.040

Frequency domain

TP, ln(ms2) 0.934a 0.947a 0.171

HF, ln(ms2) 0.728a 0.832a �0.022

LF%, nu �0.078 0.058 �0.432

LF/HF, ln(ratio) 0.143 0.015 0.442

ap< 0.05; the indices of time domain analysis and frequency domain analy-

sis were significantly correlated with the MDTS (p< 0.05), except for the

LF% and LF/HF (p> 0.05) among the young healthy and the elderly healthy

subjects.

TABLE III. Correlation coefficients between multi dynamic trend deviation

and time domain indices and frequency domain indices for young healthy

subjects, elderly healthy subjects, and congestive heart failure subjects.

SDNN, standard deviation of normal to normal; RMSSD, root mean square

successive difference; TP, total power; HF, high frequency power; LF%,

normalized low frequency power; LF/HF, LF to HF ratio; and ln, natural

logarithm.

Young healthy Elderly healthy CHF

Time domain

SDNN, ms 0.882a 0.970a 0.195

RMSSD, ms 0.743a 0.665a 0.067

Frequency domain

TP, ln(ms2) 0.877a 0.934a 0.205

HF, ln(ms2) 0.714a 0.847a �0.005

LF%, nu �0.083 �0.086 0.470a

LF/HF, ln(ratio) �0.143 �0.015 0.477a

ap< 0.05; the quantitative indices of the time domain analysis and frequency

domain analysis were significantly correlated with the MDTS (p< 0.05),

except for the LF% and LF/HF (p> 0.05) for the young healthy subjects and

the elderly healthy subjects. p< 0.05; the LF% and LF/HF were significantly

correlated with the MDTD (p< 0.05) in the CHF subjects.

TABLE IV. Area under the curve analyses of multi dynamic trend analysis,

time domain analysis, and frequency domain analysis between the young

healthy subject group and the elderly healthy subject group. AUC, area

under the curve; SDNN, standard deviation of normal to normal; RMSSD,

root mean square successive difference; TP, total power; HF, high frequency

power; LF%, normalized low frequency power; LF/HF, LF to HF ratio; ln,

natural logarithm; MDTS, multi dynamic trend slope (absolute value); and

MDTD, multi dynamic trend deviation.

AUC Standard error p value

MDTA method

MDTS (absolute slope) 0.834a 0.067 p< 0.001

MDTD (deviation) 0.837a 0.066 p< 0.001

Time domain

SDNN, ms 0.821a 0.071 p¼ 0.001

RMSSD, ms 0.808a 0.076 p¼ 0.001

Frequency domain

TP, ln(ms2) 0.829a 0.070 p< 0.001

HF, ln(ms2) 0.800a 0.074 p¼ 0.001

LF%, nu 0.484 0.095 p¼ 0.866

LF/HF, ln(ratio) 0.484 0.095 p¼ 0.866

ap< 0.05.

TABLE V. Area under curve analyses for multi dynamic trend analysis,

time domain analysis, and frequency domain analysis between the healthy

control group and the congestive heart failure group. AUC, area under the

curve; SDNN, standard deviation of normal to normal; RMSSD, root mean

square successive difference; TP, total power; HF, high frequency power;

LF%, normalized low frequency power; LF/HF, LF to HF ratio; ln, natural

logarithm; MDTS, multi dynamic trend slope (absolute value); and MDTD,

multi dynamic trend deviation.

AUC Standard error p value

MDTA method

MDTS (absolute slope) 1.000a 0.000 p< 0.001

MDTD (deviation) 1.000a 0.000 p< 0.001

Time domain

SDNN, ms 0.925a 0.043 p< 0.001

RMSSD, ms 0.687a 0.087 p¼ 0.042

Frequency domain

TP, ln(ms2) 0.792a 0.081 p¼ 0.005

HF, ln(ms2) 0.570 0.093 p¼ 0.449

LF%, nu 0.935a 0.041 p< 0.001

LF/HF, ln(ratio) 0.935a 0.041 p< 0.001

ap< 0.05.

023109-5 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

investigating the effects of aging and CHF.16,34,44 More spe-

cifically, the intrinsic trend fluctuations of the complex HRV

analyzed using MDTA were found to be decreased in healthy

elderly subjects and CHF subjects. Because the MDTA

method is a nonlinear approach to HRV analysis comprising

EMD and a variable-sized sliding-window method, our find-

ings indirectly support the hypothesis that HRV is a nonlin-

ear and nonstationary biosignal, and consequently, that a

nonlinear approach is more appropriate for analyzing it.

Technically, time domain analysis is unable to include

dynamic structural information from heart rate time series

and may not fully delineate these time–space varying proper-

ties because it improperly analyzes dynamic variation fea-

tures and the intrinsic fluctuation in HRV. Furthermore, the

most commonly used types of frequency domain analysis,

either the nonparametrically windowed FFT or parametri-

cally autoregressive modeling, are limited by the implicit

assumption of a linear and stationary signal, a characteristic

that biological oscillations rarely exhibit.13,16,45 In addition

to executing EMD, MDTA involves applying a variable-

sized sliding-window method that simultaneously enhances

the time resolution (by using a different window size on dif-

ferent time frames) and the spatial resolution (by using a

flexible analysis window size). Almost all HRV studies41,46

have applied an approach that uses a fixed window with a

minimum window size of 5 min.9 However, the transient na-

ture of rapidly changing physiological effects makes them

difficult to detect with the limitations imposed by such a

fixed window.

The physiological interpretation of MDTA can be based

on the association between parameters in both time domain

analysis and frequency domain analysis; this has been estab-

lished in previous studies and is widely accepted. In brief,

the SDNN and TP reflect both sympathetic and parasympa-

thetic activities and serve as predictors that can be used to

obtain a prognosis for cardiovascular disease, especially

CHF.7,47 The RMSSD and HF represent parasympathetic

activity and act as predictors of aging and cardiovascular dis-

ease. Conversely, the LF/HF and LF% represent sympathetic

activity.9 In this study, the MDTA parameters of healthy

subjects were found to be highly correlated with all predic-

tors of aging and disease, and with various parasympathetic

activities.

HF obtained through spectral analysis has also been

found to correlate with MDTA among healthy subjects; it

has been commonly used in previous studies as a measure of

parasympathetic function when predicting disease and the

effects of aging.6,48 However, some pilot studies that exam-

ined EMD of HRV eliminated the fundamental limitations of

the FFT and avoided the spurious harmonics generated under

the conditions used.11,12,44 Furthermore, the variable-sized

sliding-window method can be used to assess the temporal

and spatial variations in HF and LF discrimination without

resorting to fixed high-pass and low-pass filtering. The com-

bination of the HHT and variable-sized sliding-window

method seems to enhance both the temporal and spatial reso-

lution simultaneously and therefore can isolate the main fre-

quency components more adaptively. Thus, MDTA showed

a higher capacity to differentiate the CHF subjects from the

healthy elderly subjects, and the healthy elderly control sub-

jects from the healthy young control subjects, than HF did in

the present study.

It is consequential that MDTA was correlated only with

the LF/HF and LF% among the CHF subjects. Heart failure

is characterized by decreased HRV, with sympathetic domi-nance and loss of parasympathetic activity.7,49,50 Therefore,

the decrease in parasympathetic activity, that is, vagal func-

tion,8 provided evidence of a poor correlation between

MDTA and HF among the CHF subjects. In this situation,

the characteristics of MDTA were amplified and the EMD

served as a powerful adaptive filter with the variable-sized

sliding-window method contributing toward identifying the

intrinsic trend fluctuation. The MDTA indices were found to

be correlated with the low-frequency sympathetic parameters

of HRV. Theoretically, MDTA more accurately represents

the intrinsic trend fluctuations at low frequencies than does

the LF determined by the FFT by using a fixed 5-min win-

dow. Although the LF% and LF/HF are considered by some

investigators to mirror sympathetic modulation, it is note-

worthy that the LF/HF might be inappropriate for examining

CHF subjects.51 This is because subjects with a marked

reduction in ventricular functioning commonly present with

a paradoxical reduction rather than an increase in LF despite

clinical signs of sympathetic activation.52

The cross-sectional design of this study involved using a

convenience sample from the PhsyioNet database. This lim-

ited our ability to make causal inferences on the relationship

between HRV and the effects of aging and CHF.

CONCLUSION

Theoretically, MDTA can adaptively and automatically

identify the intrinsic fluctuation from nonlinear and nonsta-

tionary signals on variable temporal and spatial scales. In an

experiment using HRV data, it proved to be a powerful

approach to obtaining a prognosis of cardiovascular disease

and the effects of aging as well as a potential indicator of

cardiac autonomic sympathetic and parasympathetic modula-

tion. This pilot study developed a novel technique that pro-

vides new insights into the complex fluctuations in cardiac

autonomic regulation.

ACKNOWLEDGMENTS

We thank the Research Center for Adaptive Data

Analysis of National Central University of Taiwan for support

with numerous techniques. Professor Terry B. J. Kuo was

supported by a Grant (No. YM-104AC-B3) from the Ministry

of Education, Aim for the Top University Plan and a Grant

(No. NSC 102-2314-B-010-033) from the National Science

Council, Taiwan. We also thank the Ministry of Science and

Technology for their support for the Center for Dynamical

Biomarkers and Translational Medicine, National Central

University, Taiwan (MOST 103-2911-I-008-001).

1R. Virtanen, A. Jula, T. Kuusela, H. Helenius, and L. M. Voipio-Pulkki,

J. Hum. Hypertens. 17(3), 171–179 (2003).2H. H. Osterhues, G. Grossmann, M. Kochs, and V. Hombach,

J. Endocrinol. Invest. 21(1), 24–30 (1998).3H. L. Kennedy, Am. J. Cardiol. 80(9B), 29J–34J (1997).

023109-6 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28

4M. Kupari, J. Virolainen, P. Koskinen, and M. J. Tikkanen, Am. J.

Cardiol. 72(12), 897–903 (1993).5M. G. Kienzle, D. W. Ferguson, C. L. Birkett, G. A. Myers, W. J. Berg,

and D. J. Mariano, Am. J. Cardiol. 69(8), 761–767 (1992).6T. B. Kuo, T. Lin, C. C. Yang, C. L. Li, C. F. Chen, and P. Chou,

Am. J. Physiol. 277(6 Pt 2), H2233–2239 (1999); available at http://

ajpheart.physiology.org/content/277/6/H2233.7J. Nolan, P. D. Batin, R. Andrews, S. J. Lindsay, P. Brooksby, M. Mullen,

W. Baig, A. D. Flapan, A. Cowley, R. J. Prescott, J. M. Neilson, and K. A.

Fox, Circulation 98(15), 1510–1516 (1998).8L. J. Badra, W. H. Cooke, J. B. Hoag, A. A. Crossman, T. A. Kuusela, K.

U. Tahvanainen, and D. L. Eckberg, Am. J. Physiol. Heart Circ. Physiol.

280(6), H2674–2688 (2001); available at http://ajpheart.physiology.org/

content/280/6/H2674.full.pdf+html?.9Task Force of the European Society of Cardiology and the North

American Society of Pacing and Electrophysiology, Circulation 93(5),

1043–1065 (1996).10P. Siegel, J. Sperber, W. Kindermann, and A. Urhausen, Los Alamos

Preprint Archive: Quantitative Biology arXiv:q-bio/0410010 (2004).11Souza E. P. Neto, M. A. Custaud, J. C. Cejka, P. Abry, J. Frutoso, C.

Gharib, and P. Flandrin, Methods Inf. Med. 43(1), 60–65 (2004).12J. C. Echeverria, J. A. Crowe, M. S. Woolfson, and B. R. Hayes-Gill, Med.

Biol. Eng. Comput. 39(4), 471–479 (2001).13N. E. Huang, Z. Shen, S. R. Long, M. C. Wu, H. H. Shih, Q. Zheng, N.-C.

Yen, C. C. Tung, and H. H. Liu, Proc. R. Soc. London. Ser. A 454(1971),

903–995 (1998).14A. Bravi, A. Longtin, and A. J. Seely, Biomed. Eng. 10, 90 (2011).15S. Aronson, M. Stafford-Smith, B. Phillips-Bute, A. Shaw, J. Gaca, and M.

Newman, Cardiothorac. Anesthesiol. Res., E. Anesthesiology 113(2),

305–312 (2010).16C. K. Peng, M. Costa, and A. L. Goldberger, Adv. Adapt. Data Anal. 1(1),

61–70 (2009).17P. C. Ivanov, L. A. Amaral, A. L. Goldberger, S. Havlin, M. G.

Rosenblum, Z. R. Struzik, and H. E. Stanley, Nature 399(6735), 461–465

(1999).18A. J. Seely and P. T. Macklem, Crit. Care 8(6), R367–384 (2004).19B. Francesco, B. Maria Grazia, G. Emanuele, F. Valentina, C. Sara, F.

Chiara, M. Riccardo, and F. Francesco, Comput. Math. Methods Med.

2012, 219080.20M. Costa, A. L. Goldberger, and C. K. Peng, Phys. Rev. Lett. 89(6),

068102 (2002).21C. K. Peng, S. Havlin, H. E. Stanley, and A. L. Goldberger, Chaos 5(1),

82–87 (1995).22S. Wessel, A. Jagannathan, and S. Haas, Phys. Rev. Lett. 90(17), 177205

(2003).23M. Baumert, V. Baier, J. Haueisen, N. Wessel, U. Meyerfeldt, A.

Schirdewan, and A. Voss, Methods Inf. Med. 43(2), 202–206 (2004).24J. S. Richman and J. R. Moorman, Am. J. Physiol.: Heart Circ. Physiol.

278(6), H2039–H2049 (2000); available at http://ajpheart.physiology.org/

content/278/6/H2039.long.25R.-G. Yeh, G.-Y. Chen, J.-S. Shieh, and C.-D. Kuo, J. Med. Biol. Eng.

30(5), 277–282 (2010).26S.-D. Wu, C.-W. Wu, S.-G. Lin, K.-Y. Lee, and C.-K. Peng, Phys. Lett. A

378(20), 1369–1374 (2014).

27J. M. Yentes, N. Hunt, K. K. Schmid, J. P. Kaipust, D. McGrath, and N.

Stergiou, Ann. Biomed. Eng. 41(2), 349–365 (2013).28P. Gloersen and N. Huang, IEEE Trans. Geosci. Remote Sens. 41(5),

1062–1074 (2003).29N. E. Huang and N. O. Attoh-Okine, The Hilbert-Huang Transform in

Engineering (CRC Press, 2010).30J. N. Yang, Y. Lei, S. Lin, and N. Huang, J. Eng. Mech. 130(1), 85–95

(2004).31W. Huang, Z. Shen, N. E. Huang, and Y. C. Fung, Proc. Natl. Acad. Sci.

U. S. A. 95(9), 4816–4821 (1998).32T. B. Kuo, C. C. Yang, and N. E. Huang, Adv. Adapt. Data Anal. 1(2),

295–307 (2009).33M. T. Lo, K. Hu, Y. Liu, C. K. Peng, and V. Novak, EURASIP J. Adv.

Signal Process. 2008, 785243.34M. Costa, A. L. Goldberger, and C. K. Peng, Phys. Rev. E: Stat. Nonlinear

Soft Matter Phys. 71(2 Pt 1), 021906 (2005).35R. L. Goldsmith, J. T. Bigger, Jr., R. C. Steinman, and J. L. Fleiss, J. Am.

Coll. Cardiol. 20(3), 552–558 (1992).36P. K. Stein, A. A. Ehsani, P. P. Domitrovich, R. E. Kleiger, and J. N.

Rottman, Am. Heart J. 138(3 Pt 1), 567–576 (1999).37J. T. Bigger, Jr., J. L. Fleiss, R. C. Steinman, L. M. Rolnitzky, W. J.

Schneider, and P. K. Stein, Circulation 91(7), 1936–1943 (1995).38A. L. Goldberger, L. A. Amaral, L. Glass, J. M. Hausdorff, P. C. Ivanov,

R. G. Mark, J. E. Mietus, G. B. Moody, C.-K. Peng, and H. E. Stanley,

Circulation 101(23), e215–e220 (2000).39C. C. Yang, C.-W. Lai, H. Y. Lai, and T. B. Kuo, Neurosci. Lett. 329(2),

213–216 (2002).40Z. Wu, N. E. Huang, S. R. Long, and C. K. Peng, Proc. Natl. Acad. Sci. U.

S. A. 104(38), 14889–14894 (2007).41M. V. Kamath, M. Watanabe, and A. Upton, Heart Rate Variability (HRV)

Signal Analysis: Clinical Applications (CRC Press, 2012).42T. B. Kuo and S. H. Chan, American J. Physiol. 264(6 Pt 2), H2208–2213

(1993); available at http://ajpheart.physiology.org/content/264/6/

H2208.long.43G. Ernst, Heart Rate Variability (Springer, 2014).44H. Li, S. Kwong, L. Yang, D. Huang, and D. Xiao, IEEE/ACM Trans.

Comput. Biol. Bioinf. 8(6), 1557–1567 (2011).45A. L. Goldberger, L. A. Amaral, J. M. Hausdorff, P. C. Ivanov, C.-K.

Peng, and H. E. Stanley, Proc. Natl. Acad. Sci. 99(suppl 1), 2466–2472

(2002).46U. R. Acharya, K. P. Joseph, N. Kannathal, C. M. Lim, and J. S. Suri,

Med. Biol. Eng. Comput. 44(12), 1031–1051 (2006).47L. Fauchier, D. Babuty, P. Cosnay, and J. P. Fauchier, J. Am. Coll.

Cardiol. 33(5), 1203–1207 (1999).48H. K. Yuan, C. Lin, P. H. Tsai, F. C. Chang, K. P. Lin, H. H. Hu, M. C.

Su, and M. T. Lo, Acta Neurol. Scand. 123(3), 187–192 (2011).49B. M. Szabo, D. J. van Veldhuisen, N. van der Veer, J. Brouwer, P. A. De

Graeff, and H. J. Crijns, Am. J. Cardiol. 79(7), 978–980 (1997).50P. Ponikowski, S. D. Anker, T. P. Chua, R. Szelemej, M. Piepoli, S.

Adamopoulos, K. Webb-Peploe, D. Harrington, W. Banasiak, and K.

Wrabec, Am. J. Cardiol. 79(12), 1645–1650 (1997).51F. Lombardi and P. K. Stein, Front. Physiol. 2, 95 (2011).52P. van de Borne, N. Montano, M. Pagani, R. Oren, and V. K. Somers,

Circulation 95(6), 1449–1454 (1997).

023109-7 Lin et al. Chaos 26, 023109 (2016)

Reuse of AIP Publishing content is subject to the terms at: https://publishing.aip.org/authors/rights-and-permissions. Downloaded to IP: 128.103.149.52 On: Tue, 26 Jul

2016 20:44:28