Transfer Entropy between RR and QT Intervals in Long QT Syndrome
Jiyeong Kim, Matias Kanniainen, Ilya Potapov, Esa Ra¨sa¨nen
Tampere University, Tampere, Finland
Abstract
Healthy subjects exhibit strong information transfer
from RR to QT intervals. In this study, we assess the dy-
namic coupling between RR and QT intervals for subjects
with long QT syndrome (LQTS) - a potentially fatal ge-
netic cardiac disease characterized by delayed myocardial
repolarization. We use transfer entropy (TE) to quantify
the magnitude and direction of the information exchange
between the RR and QT intervals. Using 24-hour Holter
ECGs, we calculate TE as a function of RR and QT his-
tories up to 50 beats and compare the results between the
healthy controls and the subjects of LQTS type 1 and 2.
Asymmetry between TERR→QT and TEQT→RR was ob-
served for the LQTS subjects. Compared to the healthy,
the LQTS subjects had significantly smaller TERR→QT
at RR history lengths longer than about 18 beats, while
TEQT→RR was significantly larger at all RR and QT his-
tory lengths. The average characteristic RR history length
that maximized TERR→QT was 27 beats for the healthy
subjects, which was significantly longer than 21 and 22
beats for LQT1 and LQT2, respectively. Aging had no sig-
nificant effect on TERR→QT , but reduced TEQT→RR for
the LQTS subjects, whereas the gender and beta blocker
were found to have relatively small effects on the TE. In
conclusion, the dynamic coupling between RR and QT in-
tervals is altered by LQTS.
1. Introduction
In an electrocardiogram (ECG), the RR and QT intervals
have been shown to have a relationship [1, 2]. A useful
measure to describe the relation is transfer entropy (TE),
which quantifies the information transfer from the source
to the destination in a coupled process [3]. TE from RR
to QT is formally defined in Eq. (1) of Ref. [4]. The
study showed that there is a bidirectional information flow
between RR and QT intervals in healthy individuals. The
information flow from RR to QT is more prominent, indi-
cating an asymmetry, which becomes stronger when more
previous values of RR and QT are taken into account. This
effect is related to the QT-RR hysteresis, which has been
studied especially in the context of QT correction [5].
In this study, we investigate the information transfer be-
tween RR and QT intervals in long QT syndrome (LQTS)
subjects. LQTS is a genetic condition, characterized by
prolonged QT intervals, caused by delayed ventricular re-
polarization. LQTS affects approximately 1 in every 5000
people [6], and the symptoms range from seizures to po-
tentially lethal arrhythmias [7]. In this study, we consider
the subjects of LQTS types LQT1 and LQT2, where the
mutation is altering the functionality of the myocardial
potassium channels in genes KCNQ1 and KCNH2, respec-
tively [6].
2. Data and Method
We use the Healthy (E-HOL-03-0202-003) and the
congenital long QT syndrome (E-HOL-03-0480-013)
database from the Telemetric and Holter ECG Warehouse
(THEW), administrated by the University of Rochester
Medical Center [8, 9]. Both databases consist of 24-hour
Holter ECG recordings with 2-3 leads. To extract the RR
and QT intervals from the ECGs, we utilize an in-house al-
gorithm (QRS-detection specificity 99.5% and sensitivity
99.6% with a 30 ms threshold for the MIT-BIH Arrhythmia
Database [10]). In order to remove any non-physiological
changes, the interval data is filtered with a moving aver-
age procedure with a window size of 100 intervals and the
maximum deviation from the mean of 150 ms and 500 ms
for QT and RR, respectively.
Table 1. Statistics of the studied groups. The total number
of subjects (N) and the male-to-female ratio are shown.
The age is shown with the mean ± standard deviation, and
the number of RR-QT interval pairs per dataset is specified
in millions (M).
Healthy LQT1 LQT2
N (Male/Female) 202 (102/100) 227 (96/131) 127 (57/70)
Age (years) 38 ± 16 28 ± 18 24 ± 17
Interval pairs 20,1M 19,9M 11,3M
The original database contains 202 Holter recordings for
the healthy and 480 recordings for the LQTS, from which
246 are of the subtype LQT1, and 145 of LQT2. We con-
sider only the subjects with a history of using beta blockers
Computing in Cardiology 2022; Vol 49 Page 1 ISSN: 2325-887X DOI: 10.22489/CinC.2022.273
or no medication at all. We also discard a few subjects with
undefined or less than one year of age. Table 1 summarizes
the statistics and the metadata of the studied groups.
To calculate the TE, we use the Java Information Dy-
namics Toolkit (JIDT) [11] with the Kraskov-Sto¨gbauer-
Grassberger (KSG) probability estimation. To balance the
statistical and systematical errors in the KSG, we use 4
nearest neighbors, as suggested in [12]. The other param-
eters are set to the default values. We calculate the TE up
to history lengths of 50 RR and QT intervals. For statisti-
cal analyses, we use Welch’s t-test to compare the averages
between the independent samples.
Healthy LQT1 LQT2
0.0
0.2
0.4
0.6
0.8
Tr
an
sfe
r e
nt
ro
py
 (b
it)
p 0.001 p 0.001
p~0.001
RR QT
QT RR
Figure 1. Distributions of TE in the healthy and LQTS
subjects (over 20 years old). The asymmetry between the
two directions is evident in each group.
3. Results
We first consider the information transfer from a single
preceding RR or QT interval as the source. Distributions
of the TE from RR to QT (TERR→QT) and from QT to RR
(TEQT→RR) for the healthy and LQTS are shown in Fig. 1.
In all three groups, there is a clear asymmetry of the TE,
in which the RR→QT transfer is significantly larger than
the QT→RR (p ≤ 0.001). The average TERR→QT is sig-
nificantly different between the healthy and LQT1 and be-
tween LQT1 and LQT2. The average TEQT→RR differs sig-
nificantly in all the pairs (p ≪ 0.001 between the healthy
and either type of LQTS, p < 0.01 between LQT1 and
LQT2).
When more than one RR and QT history value are taken
into account, the gap between the RR→QT and QT→RR
transfer increases with RR history length, as shown in Fig.
2. On the other hand, TERR→QT declines with increasing
QT history length, regardless of the presence of LQTS,
while TEQT→RR persists, becoming larger than the oppo-
site transfer. The results are well in line with the previous
study with the healthy subjects [4] and further confirm that
the dominance of the RR→QT transfer over the opposite
direction is still prominent in the presence of LQTS.
0 10 20 30 40 50
RR history lengths
0.0
0.1
0.2
Tr
an
sfe
r e
nt
ro
py
 (b
it)
0 10 20 30 40 50
QT history lengths
0.0
0.1
0.2
Tr
an
sfe
r e
nt
ro
py
 (b
it)
RR QT (Healthy, N=180)
QT RR (Healthy)
RR QT (LQT1, N=135)
QT RR (LQT1)
RR QT (LQT2, N=64)
QT RR (LQT2)
Figure 2. Average TE as functions of RR and QT history
lengths for the healthy and LQT1 and LQT2 subjects (over
20 years old). The shaded bands represent the 95% confi-
dence intervals.
Healthy LQT1 LQT2
10
20
30
40
50
Ch
ar
ac
ter
ist
ic 
RR
 h
ist
or
y 
len
gt
hs
Figure 3. Distributions of characteristic RR history
lengths, nchar, which maximize the TE from RR to QT.
The healthy subjects have a significantly longer average
nchar than the LQTS.
The mean TERR→QT of the LQTS subjects diverge sig-
nificantly from that of the healthy for RR history length
longer than 18 beats (p < 0.001). On the other hand,
the mean TEQT→RR of the LQTS are significantly larger
than that of the healthy at all RR and QT history lengths
(p≪ 0.001).
Page 2
0.0
0.1
0.2
LQ
T1
 
 T
ra
ns
fe
r e
nt
ro
py
 (b
it) RR QT (Young)
QT RR (Young)
RR QT 
QT RR 
0 10 20 30 40 50
RR history lengths
0.0
0.1
0.2
LQ
T2
 
 T
ra
ns
fe
r e
nt
ro
py
 (b
it)
0 10 20 30 40 50
QT history lengths
Figure 4. Average TE as functions of RR and QT history lengths for age groups younger and older than 20 years, with
95% confidence intervals as shaded bands.
0 25 50 75
Age
0.0
0.1
0.2
0.3
TE
RR
Q
T (
n=
1)
0 25 50 75
Age
TE
RR
Q
T (
n=
n c
ha
r)
0 25 50 75
Age
TE
Q
T
RR
 (n
=
1)
Healthy
LQT1
LQT2
Figure 5. TE from preceding RR to QT (left) and at characteristic RR history lengths (center) and TE from preceding QT
to RR (right) as functions of age. Only the ages < 60 years are used for computing the LOWESS.
The declining trends in TERR→QT as a function of RR
history length that clearly deviate from that of the healthy,
which has a flat profile, may be a unique feature of LQTS.
In particular, the critical history length ncrit, after which
TE remains constant [4], is absent in LQT1 and LQT2. A
further calculation of TE for RR history length up to 100
beats shows that TEQT→RR does not reach a plateau for
LQT1 or LQT2. Therefore, we define a different charac-
teristic RR history length, nchar, as the RR history length
at which TERR→QT is maximized. Distributions of nchar
for the healthy and LQTS individuals are shown in Fig. 3.
The average nchar is 27±14 beats for the healthy subjects,
which is significantly larger than 21±14, 22±16 for LQT1
(p≪ 0.001) and LQT2 (p < 0.01), respectively.
Next we investigate the age effect on TE. We first divide
the subjects into two age groups, younger and older than
20 years. For the healthy, age has little effect on the TE at
any given RR or QT history length (p > 0.001). However,
as shown in Fig. 4, for the LQTS subjects, TEQT→RR is re-
duced significantly, especially as a function of QT history
length (p < 0.001 for QT history> 5 beats). TERR→QT has
a crossover at QT history of about 10 beats, after which the
TERR→QT of the younger group dominates over that of the
older.
Figure 5 shows the TE values at a few chosen RR and
QT history lengths (n = 1, nchar) as a function of age.
Page 3
Due to large variation among the individuals, the locally
weighted scatter plot smoothing (LOWESS) curves are
used to depict the age dependency. The healthy group
exhibits a flat trend in TERR→QT at n = 1, nchar. For
the LQT1 and LQT2, very different trends are suggested.
In particular, LQT2 subjects exhibit a prominent positive
slope as a function of the age > 20 years, diverging from
the negative slope of the LQT1. All three groups share a
similar age dependency of TEQT→RR at n = 1, in which
the TE declines in those younger than about 20 years.
Females who are healthy or have LQTS exhibit longer
QT intervals (see e.g., [13]), compared to males. However,
we do not find any significant differences in the average
TE between the male and female subjects. We also studied
the effect of beta blockers, which are the most commonly
used medication for LQTS, as it increases the QT intervals
at a resting heart rate (e.g., [14]). For the analysis, 40 sub-
jects with LQT1 (N = 28) and LQT2 (N = 12) with a
pair of recordings, before and after the use of beta block-
ers were analyzed. However, we do not find any significant
differences in the average TE.
4. Conclusion
We have used transfer entropy (TE) to show that the
dynamic coupling between RR and QT is altered by the
LQTS. In particular, on average, TE from RR to QT is
reduced, while TE to the opposite direction is enhanced
compared to the TE of the healthy. However, the asymme-
try of the information flow previously observed in healthy
subjects is preserved. Due to the large variation among
the individuals, further systematic studies are necessary to
make the implications clear. However, the altered dynam-
ics between RR and QT in LQTS provides insights, which
may influence the current models and methods in QT cor-
rection and in the detection of LQTS.
Acknowledgments
The study is funded by Novo Nordisk Fonden Pioneer
Innovator Grant (2021-2022).
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Address for correspondence:
Jiyeong Kim
Computational Physics Laboratory
Faculty of Engineering and Natural Sciences
P.O. Box 692, FI-33014 Tampere, Finland
jiyeong.kim@tuni.fi
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