Abstract Frequent ventricular ectopy results a great proble

I Kecskes

I Kovacs

I Simon

K Fugedi

N Balogh

S Khoor

S Rubicsek

T Szuszai

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Recurrence Quantification Analysis based on P-P Intervals Measurement in 
Postinfarction Patients with Frequent Ventricular Ectopy 
 
N Balogh1, S Khoor2, T Szuszai1, I Kecskes1,  
K Fugedi2, I Kovacs2, I Simon1, S Rubicsek1 
 
1Medartintech Ltd, Budapest, Hungary 
2Szent Istvan Hospital, Budapest, Hungary 
Abstract 
 Frequent ventricular ectopy results a great problem 
of any heart rate variability analysis method, because the 
interpolation of the R-R intervals significantly disturbs 
the intrinsic rhythm’s features. Recurrence quantification 
analysis (RQA) is a valuable tool for predicting serious 
cardiovascular events. Our ambulatory ECG (AECG) 
system (RhythmPattern, SzivLeso) processes the 1 kHz 
ECG recordings, calculates various non-linear heart rate 
parameters, and analyses the P- and R-waves  
The study population (age 61.9±8.6) consists of 89 
postinfarction patients, where frequent (> 6000/24 hours) 
ventricular ectopic beats were found. The ambulatory 
ECG monitoring was repeated in every month; the mean 
follow-up was 38.8 months. The patients were divided 
into two groups: 72 pts were alive (Group_A), and 17 pts 
(Group_B) died at the end of the study. The P-P 
tachogram was determined instead of R-R intervals. The 
standard parameters of RQA were calculated.  
Significant (p<0.01) differences were found of the 
majority of RQA parameters, when the P-to-P wave 
tachograms were used instead of R-to-R wave ones. 
 
 
1. Introduction 
The method of recurrence plot was introduced to 
visualize the behavior of trajectories in the m-
dimensional phase space. The recurrence of the phase 
space trajectory to a certain state is visualized by plotting 
black (or by changing the basic parameters: in color) dots 
in an NxN matrix. A recurrence plot is simply a graphical 
depiction of the recurrence matrix. The recurrence plot is 
an autocorrelation plot of x(t) with x(i) along the abscissa 
and x(j) along the ordinate. Only those points that satisfy 
x(i) = x(j), defined as values of i and j that fall within a 
specified radius or distance of one another, are plotted. 
The diagonal lines represent dynamic behavior; the 
horizontal and vertical lines show unchanged state 
(Figure 1).  
 
 
 
Figure 1. Recurrence plot of the heart rate representing 
1000 R-R intervals. 
 
The recurrence quantification analysis (RQA) provides 
measures based on the diagonal, horizontal and vertical 
structures [1-2]. Studies examined the usefulness of RQA 
based on heart rate variability (based on R-R tachograms) 
[3-4]. Frequent ventricular ectopy results a great problem 
of any heart rate variability analysis method, because the 
interpolation of the R-R intervals significantly disturbs 
the intrinsic rhythm’s features. Recurrence quantification 
analysis (RQA) is a valuable tool for predicting serious 
cardiovascular events. Our ambulatory ECG (AECG) 
telemedicine system (RhythmPattern, SzivLeso) 
processes the 1 kHz ECG recordings, calculates various 
non-linear heart rate parameters, and analyses the P- and 
R-waves separately. The commercial ambulatory ECG 
(AECG) equipments (Holter) does not calculate the non-
cinc.org Computing in Cardiology 2012; 39:985-988.985
 
linear heart rate variability (HRV) parameters, cannot 
determine the p-waves. Our self-developed equipment 
(HeartPattern, SzivOrzo) [4] registers and stores the full 
24-hour ECG, the “full-disclosure” means really the 
retrieve of the full ECG with the p-waves. Beside the 
view function, the software calculates the following non-
linear heart rate and arrhythmia parameters:  
1. Instantaneous heart-rate variability: from Poincare plot 
the SD1, SD2 and SD1/SD2, the alpha-1 and alpha-2 
from DFA, approximate entropy (ApEn), the sampling 
entropy/scale factor (from scale=3 to 12) based on 
multiscale entropy analysis, the RQA analysis (with the 
10 parameters discussed later),  
2. Ventricular arrhythmia pattern analysis: the ratio of 
ventricular premature beat (VPB) and the total number of 
QRS; the SD1, SD2, SD1/SD2, alpha-1 and alpha-2 of 
DFA, and ApEn of the separately calculated (independent 
of instantaneous sinus heart rate) VPB rhythm, 
3. The synchronization between the instantaneous heart 
rate and VPB “rhythm”: the number and the duration of 
synchronization. 
 
2. Methods 
The study population (age 61.9±8.6 years) consists of 
89 postinfarction patients with normal ejection fraction, 
where frequent (> 6000/24 hours) ventricular ectopic 
beats were found.  
The ambulatory ECG monitoring was repeated in 
every month; the mean follow-up was 38.8 months. The 
patients were divided into two groups: Group_A (72 pts) 
alive, and 17 pts (Group_B) died at the end of the study. 
The RQA was performed on the 4 hours daily registration 
of AECG in all patients; in Group_B before at least 4 
weeks of death. 
The signal analysis of the P-waves of the 24-hour 
AECGs was much more similar to the signal averaged 
ECG: p-wave detection in the ectopic QRS based on the 
matching of the ectopy-QRS waves, and the signal-
averaging enhances the hidden P-waves. 
The signal analysis program consists of the following 
parts: 
1. Filtering, 
2. R-wave detection, 
3. Clusterization the QRS complexes into three 
categories:  narrow (N), where QRS duration is less than 
120 ms, wide (W): longer, than 120 ms, and undefined 
(X),  
4. Searching for N-W-N’ template (pattern), where N-W 
< 0.2*mean R-R AND W-N’ > 0.2*mean R-R 
5. Finding the p-waves before N and N’, 
6. Determining the region of interest (ROI) at the middle 
between P-wave (N) and P-wave (N’) ±10%, 
7. Signal averaging of premature ventricular complex 
with the use of N-W-N’ template, 
8. Searching for the local minima of the smoothed first 
derivative of ECG in the ROI segment (virtual P-wave), 
9. Extracting the actual (virtual) P-wave max from the 
signal averaged ROI segment. 
10. Determining the P-P heart rate tachogram for RQA. 
The critical steps are illustrated in the next two figures 
(Figure 2. and 3.) 
 
 
 
 
Figure 2. Signal processing:  Step 5-6. 
 
 
 
 
Figure 3. Signal processing:  Step 7-9. 
 
 
986
 
The standard parameters of RQA were calculated: 
recurrence rate (%RR), determinism (%DET), laminarity 
(LAM), the ratio between DET and RR (RATIO), 
averaged diagonal line length (L), trapping time (TT), the 
longest diagonal (Lmax) and vertical (Vmax), divergence 
(DIV), the entropy (ENTR), and the trend (TREND).  
1. Recurrence Rate (RR), which is the density of 
recurrence points in a recurrence plot. 
2. Determinism (DET), which is the fraction of 
recurrence points forming diagonal lines. Diagonal lines 
represent epochs of similar time evolution of states of the 
system. 
3. Mean diagonal line length, corresponding to a mean 
prediction time or to the inverse of the divergence of the 
system ( K 2 entropy). 
4. Entropy of the line distribution, measures the 
complexity of the recurrence structure. 
5. Laminarity (LAM), which is the fraction of recurrence 
points forming vertical lines. Vertical lines are typical for 
intermittency. 
6. Trapping time (TT), which is the mean length of 
vertical lines. TT measures the mean time that the system 
is trapped in one state or change only very slowly. 
Embedding dimension = 10, radius of 15%, time delay=4, 
window size=1024 were used. 
The statistical calculation (Mann-Whitney (M-W) U test, 
multivariate discriminant analysis) was performed with 
SPSS V 15.0. 
3. Results 
At the first step, the above-mentioned standard RQA 
was performed in the two scenarios: “P-P” means that the 
heart rate tachogram was calculated by the P-wave-to-P-
wave intervals, “R-R” means the R-wave-to-R-wave 
intervals. Table 1. and 2. show the statistics of Group_A 
and Group_B. 
 
 Table 1. Descriptive statistics of the two groups’ RQA 
values, when “P-P” heart rate tachogram was calculated. 
 
“P-P” Group_A N=72 Group_B N=17 
 Mean Std. 
Dev. 
Mean Std. 
Dev. 
%REC 2.25 1.31 4.29 1.85 
%DET 0.338 0.132 0.647 0.224 
L 19.1 8.8 31.4 11.5 
Lmax 299.4 117.2 425.5 84.9 
Vmax 365.6 99.7 173.1 71.6 
ENT 1.114 0.423 2.334 0.643 
TT 29.99 7.42 20.37 6.19 
RATIO 0.177 0.084 0.160 0.041 
DIV 0.004 0.002 0.002 0.001 
%LAM 0.087 0.021 0.060 0.018 
Table 2. Descriptive statistics of the two groups’ RQA 
values, when “R-R” heart rate tachogram was calculated. 
 
“R-R”   Group_A:  N=72 Group_B:  N=17 
Parameter Mean Std. 
Dev. 
Mean Std. 
Dev. 
%REC 3.292 1.329 3.595 1.965 
%DET 0.884 0.348 1.071 0.406 
L 23.77 8.69 26.57 11.88 
Lmax 326.9 119.5 316.9 95.91 
Vmax 429.8 96.79 389.2 91.2 
ENT 1.392 0.505 1.770 0.776 
TT 33.52 7.52 27.54 8.21 
RATIO 0.289 0.123 0.347 0.184 
DIV 0.004 0.002 0.004 0.001 
%LAM 0.148 0.037 0.112 0.044 
 
 
The two groups were compared with the M-W U test; 
Table 3. shows the  results based on “P-to-P” wave 
tachogram, Table 4. based on “R-to-R” ones.  
 
 
 
Table 3. Comparing the “P-P” RQA measurements, 1= 
Group_A, 2= Group_B (1 vs. 2). 
 
1 vs. 2 M-W U Sign. 
%REC 178.5 6E-06 
%DET 95 6.8E-08 
L 237 9.1E-05 
Lmax 233.5 7.8E-05 
Vmax 72 1.7E-08 
ENT 42 2.7E-09 
TT 198 1.6E-05 
RATIO 612 1 
DIV 233.5 7.8E-05 
%LAM 201 1.8E-05 
  
Abbreviations: 1 vs. 2  means to compare the “P-P” RQA 
measurements;    1= Group_A,      2= Group_B. 
 
 
Using the “P-to-P” analysis, only one parameter (RATIO) 
showed non-significant relation. Table 4. shows the high 
percentage of non significant changes of RQA 
parameters, when the R-to-R” wave solution was 
performed (exceptions were ENT, TT and %LAM 
parameters). 
 
 
 
 
 
987
 
Table 4. Comparing the “R-R” RQA measurements; 
3= Group_A,      4= Group_B (3 vs. 4). 
 
3 vs. 4 M-W U Sign. 
%REC 606 0.9501 
%DET 446 0.0832 
L 553 0.5380 
Lmax 605 0.9418 
Vmax 470 0.1383 
ENT 422 0.0474 
TT 340 0.0045 
RATIO 513 0.3015 
DIV 608 0.9667 
%LAM 335 0.0038 
   
Figure 4 shows the statistical results of the combined 
analysis, where both methods (“P-P” and “R-R”) in the 
two groups (alive and died) were used. 
 
 
 
Figure 4. The combined MW U-test result of the 
various group: 1= Group_A (alive), 2= Group_B (died) 
based on “P-to-P-wave” RQA, 3= Group_A (alive),  
4= Group_B (died) based on “R-to-R-wave” RQA.  
The x-axis represents the statistical significance in 
logarithmic scale. 
 
4. Discussion and conclusions 
The most important features in RQA is to select the 
Main. Firstly, we have to discuss the automatic 
measurement of our system (included the P-wave 
detection), and the traditional AE (without it). Figure 3. 
shows a patient recording, where the wide QRS does not 
represent ventricular ectopy: it is sinus rhythm with 
aberrant conduction (Figure 5.)  
 Secondly, the problem of measurement HRV in the 
case of frequent ectopy. The interpolated R-R interval 
does not represent the real R-R interval. The non-linear 
method just remembers one arbitrary value to the other. 
The third important question is how to select the 
following nonlinear parameters: a.) the embedding 
dimension (suggested 8-10), b.) the radius (the three 
guidelines for selecting the proper radius: 1.) it must fall 
with the linear scaling region of the double logarithmic 
plot 2.) %REC must be kept low (e.g., 0.1 to 2.0%) and 
3.) it may or may not coincide with the first minimum 
hitch in %DET. So the radius of 15% was selected), c.) 
the time delay, and d.) the window size. 
 
 
 
Figure 5. Misinterpretation of commercial AECG 
systems: the wide QRS is not a PVB, detection of p-wave 
(middle) shows the conduction aberrancy. 
 
References 
[1] Marwan N, Wessel N, Meyerfeldt U, et al. Recurrence-plot 
based measures of complexity and their application to 
heart rate variability data. Physical Review E 2002;66:1-8. 
[2] Kurths J, Voss A, Witt A, et al. Quantitative analysis of 
heart rate variability. Chaos 1995;5:88–94. 
[3] Wessel N, Marwan N, Schirdewan A, Kurths J. Beat-to-beat 
complexity analysis before the onset of ventricular 
tachycardia. Computers in Cardiology 2003;30:477−480. 
[4] Balogh N, Khoor S, Fugedi K, et al. Telemedicine assisted                    
secondary prevention with individual forecasting based on  
ECG monitoring. Computing in Cardiology 
2011;38:685−688 
  
Address for correspondence 
 
Nandor Balogh PhD 
Medartintech Ltd 
Attila u 30 IV.15. 
Budapest. Hungary. H-1201 
email: balnan2@gmail.com 
 
 
988


Recurrence Quantification Analysis based on P-P Intervals Measurement in Postinfarction Patients with Frequent Ventricular Ectopy

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Recurrence Quantification Analysis based on P-P Intervals Measurement in Postinfarction Patients with Frequent Ventricular Ectopy

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