Single-Fea u e Me hod o Fas A ial Fib illa ion De ec ion in ECG Signals
Lucie Ma sano a1, And ea Nemco a1, Rado an Smisek1,2, Ma in Vi ek1, Lukas Smi al1
1 Depa men o Biomedical Enginee ing, B no Uni e si y o Technology, B no, Czech Republic
2 Academy o Sciences, B no, Czech Republic
Abs ac
A ial ib illa ion (AF) is he mos common a hy hmia
in adul s and is associa ed wi h a highe isk o hea
ailu e o dea h. He e, we in oduce simple and e icien
me hod o au oma ic AF de ec ion based on symbolic
dynamics and Shannon en opy. This me hod comp ises o
h ee pa s. Fi s ly, QRS complex de ec ion is p o ided,
han he aw RR sequence is ans o med in o a sequence
o speci ic symbols and subsequen ly in o a wo d sequence
and inally, Shannon en opy o he wo d sequence is
calcula ed. Acco ding o he alue o Shannon en opy, i
is decided, whe he AF is p esen in he cu en ca diac
bea . We achie ed sensi i i y Se=96.32% and speci ici y
Sp=98.61% on MIT-BIH A ial Fib illa ion da abase,
Se=91.30% and Sp=90.8% on MIT-BIH A hy hmia
da abase, Se=95.6% and Sp=80.27% o Long Te m A ial
Fib illa ion da abase and Se=93.04% and Sp=87.30% o
CinC Challenge da abase 2020. The achie ed esul s o
ou one- ea u e me hod a e compa able wi h o he au ho s
o mo e complica ed and compu a ionally expensi e
me hods. Ou ECG expe s ound ha public da abases
con ain e o s in anno a ions (in sense o AF). I means
ha esul s a e a ec ed by e o s in anno a ions. Many
e o s we e ound in Long-Te m AF da abase, se e al also
in MIT-BIH AF da abase and MIT-BIH A hy hmia
da abase. Tes ing algo i hms on poo ly anno a ed
da abases canno b ing eliable esul s and algo i hms
use ul in eal medical p ac ice. The examples o such
anno a ions a e epo ed in his s udy.
1. In oduc ion
Ca dio ascula diso de s a e s ill he mos common
cause o dea h wo ldwide. Due o he ease o use, non-
in asi eness and cheapness, elec oca diog am (ECG) is
nowadays s ill he mos a ailable and widely used me hod
o he ca dio ascula sys em examina ion [1]. A ial
ib illa ion (AF) is he mos common a hy hmia in adul s
and is associa ed wi h a highe isk o hea ailu e o dea h.
AF is a sup a en icula achya hy hmia which is
ep esen ed by incons an a ial ac i a ion and, he e o e,
dys egula ion o a ial con ac ions. This cause
uncomple ed blood ans e om a ia o en icles and
dec ease he e iciency o hea unc ioning. This can esul
in se ious complica ions such as ischemia, s oke, o ea ly
mo ali y [1]. The e o e, ea ly de ec ion o AF is c ucial
o e ec i e ea men . Au oma ic de ec ion o AF in ECG
is s ill p oblema ic, as was shown by he esul s o p e ious
s udies. He e, we in oduce simple and e icien me hod o
au oma ic AF de ec ion based on symbolic dynamics and
Shannon en opy.
2. Me hod
This me hod comp ises o h ee pa s. Fi s ly, QRS
complex de ec ion is p o ided by de ec o based on phaso
ans o m, and sequence o RR in e als is compu ed. In
he second pa , he aw RR sequence is ans o med in o a
sequence o speci ic symbols and subsequen ly in o a wo d
sequence. Finally, Shannon en opy o he wo d sequence
is calcula ed. Acco ding o he alue o Shannon en opy,
i is decided, whe he AF is p esen in he cu en ca diac
bea .
2.1. QRS complex de ec ion
Fi s ly, signal is il e ed by bandpass il e wi h cu -o
equencies 12 and 19 Hz. In his equency ange lies he
mos o QRS complex ene gy. Using his il e supp esses
P and T wa es and also high equency a i ac s. On he
o he hand, QRS complexes a e highligh ed.
A e ha , phaso ans o m (PT) is applied. PT
ans o ms each sample o he signal in o a complex alue
p ese ing he signal in o ma ion [2].
Con e ing each ECG sample in o a phaso enhances
changes in he ECG signal ( he wa es). The deg ee wi h
which ECG wa es a e enhanced in phaso signal is
de e mined by alue RV. The alue o RV is always wi hin
he in e al 0-1. A cons an alue RV is conside ed as a eal
pa , whe eas he imagina y componen is he o iginal
alue o he ECG sample:
𝑦(𝑛)= 𝑅𝑉+𝑗𝑥(𝑛), (1)
whe e y(n) is he phaso ial signal and x(n) is he o iginal
sample o signal. The magni ude M(n) is compu ed as
𝑀(𝑛)= √𝑅𝑉
2+𝑥(𝑛)2, (2)
and phase (phaso ) 𝜑(𝑛) is compu ed as
𝜑(𝑛)= 𝑡𝑎𝑛−1 (𝑥(𝑛)
𝑅𝑉). (3)
Compu ing in Ca diology 2020; Vol 47 Page 1 ISSN: 2325-887X DOI: 10.22489/CinC.2020.335
In phaso signal 𝜑(𝑛), he QRS complexes ha e in all
cases highe ampli ude han he o he ECG componen s.
This applies also in a case o o iginal ECG signals wi h
smalle ampli ude o QRS complex han T wa e. Due o
his ac , he QRS complexes in phaso signal a e easie
de ec able [2].
In he case o QRS de ec ion, phaso ans o m o ECG
signal wi h RV = 0.001 is pe o med. The example o
phaso ans o m (g ey cu e) o ECG signal (black cu e)
p epa ed o QRS de ec ion is in Fig. 1. Than we sea ch o
maxima in sliding window wi h 300 ms size. The nex s ep
is a check, whe eas he ound maxima a e highe han used
adap i e h eshold. A he end i is checked, whe he he
in e al be ween wo subsequen QRS complexes (RR
in e al) is 1.75x highe han p e ious one. I i is
accomplished, backwa d sea ching is pe o med. This
de ec o was used and es ed also in ou p e ious s udies
[3], [4], [5].
The example o phaso ans o m o ECG signal is
shown in Fig. 1. In phaso signal 𝜑(𝑛), he QRS complexes
ha e in all cases highe ampli ude han he o he ECG
componen s. This applies also in a case o o iginal ECG
signals wi h smalle ampli ude o QRS complex han T.
Figu e 1 An example o (a) an o iginal ECG signal; (b) phase
signal φ(n); (c) de ail o he op pa o he phase signal
(illus a ed by ed box in (b)), he g een line ep esen s he
h eshold o QRS de ec ion. [3]
2.2. Symbolic dynamic and Shannon en opy
The pu pose o using symbolic dynamics (symbols and
wo ds) is o desc ibe he dynamic o hea a e. Du ing
a ial ib illa ion, high a iabili y o RR in e als is p esen
and hus also high alue o Shannon en opy [6].
Fi s ly, hea a e h (n) is de i ed om RR in e als
(RR(n)). RR(n) a e compu ed om leng h wo consecu i e
hea bea s (R(n)). The sequence o aw RR in e als is
ans o med in o he hea a e (h (n)) acco ding o he eg.
(4) and hen quan i ied in o symbol sequence (Sy(n)) [6]
acco ding o he equa ion (4)
ℎ𝑟(𝑛)=60/𝑅𝑅(𝑛), (4)
𝑆𝑦(𝑛)= { 63 𝑖𝑓 ℎ𝑟(𝑛)>315 ⌊ℎ𝑟(𝑛)
5⌋ 𝑜𝑡ℎ𝑒𝑟 ,
(5)
The sequence o symbols Sy(n) ep esen ins an aneous
s a e o hea a e ans o med in o he 64 possible symbols.
To acili a e he analysis o Sy(n) is used 3-symbol
empla e o examina ion o en opic p ope ies o
sequence. This ans o ma ion is compu ed acco ding o
he eg. (6) and a e ha we ob ain sequence o wo d
(w (n)) [7]. Each wo d akes in o accoun 3 successi e
symbols (3 hea bea s).
𝑤𝑣(𝑛)=(𝑠𝑦(𝑛 −2).212)+(𝑠𝑦(𝑛 −1).26)+
𝑠𝑦(𝑛), (6)
Finally, Shannon en opy (SH) is compu ed (7). SH is a
s a is ical ool ha quan i ies a ime se ies (in ou case
leng h o hea bea s) in e ms o he in o ma ion size [8].
A i s , we de ine he disc e e p obabili y space o a
dynamic sys em as A = (A|P). A ep esen se o
cha ac e is ic elemen s A = {a1, · · · , ak}, and P = {p1, · · ·
, pk}(1≤ k ≤N) is ele an p obabili y. Each elemen a(i) has
p obabili y p(i) = N(i)/N (0<p(i)<1,∑𝑘
𝑖=1 𝑝(𝑖)= 1
whe e N is numbe o all elemen in A and N(i) is o al
numbe o elemen a(i) in A. Thus, he SH o A is de ined
as [26],
𝑆𝐻(𝐴)= − 𝑘
𝑁.𝑙𝑜𝑔2∑𝑘
𝑖=1 𝑝(𝑖)𝑙𝑜𝑔2𝑝(𝑖) (7)
In ou wo k, he dynamic sys em A consis s o 95
consecu i e wo d elemen s om w (n-47) o w (n+47).
The alue o SH lies in in e al <0,1>. I means ha on
compu ing o SH o R(n) is needed in o ma ion o RR(n)
o 95 consecu i e hea bea s. Acco ding o he alue o SH
is de e mined i a ial ib illa ion is p esen o no in ac ual
hea bea s. In ou wo k, we ound ha he bes h eshold
he alue o disc imina ion be ween AF and non AF is
T=0.733.
In Figu e 2 p ocess o classi ica ion is illus a ed.
Subg aph b) shows alues o Shannon en opy ans o med
om leng h o RR in e als and also h eshold (blue line)
o decision o p esence o a ial ib illa ion (o e line) o
o he hy hm (below line). I is clea isible ha alue o
Shannon en opy co ela ed wi h anno a ion o a ial
ib illa ion c) ( alue 1 ep esen s AF, alue 0 ep esen s no
AF).
Page 2
Figu e 2 a) Leng h o RR in e als, b) Shannon en opy o RR
in e als – blue line is eeshold o decision o p esence AF, c)
annno a ion – alue 1 ep esen s AF, 0 ep esen s nonAF
3. Resul s
We used ou publicly a ailable da abases o es ing o
ou algo i hm. The esul s a e summa ized in Table 1. The
exac alues o ue posi i e (TP), ue nega i e (TN), alse
posi i e (FP), alse nega i e (FN) a e epo ed in Table 2.
We achie ed sensi i i y Se=96.32% and speci ici y
Sp=98.61% on MIT-BIH A ial Fib illa ion da abase,
Se=91.30% and Sp=90.80% on MIT-BIH A hy hmia
da abase, Se=95.6% and Sp=80.27% o Long Te m A ial
Fib illa ion da abase and Se=93.04% and Sp=87.30% o
CinC Challenge da abase 2020.
Table 1 The pe o mance o AF de ec ion algo i hm signals om MIT-
BIH a hy hmia da abase, MIT-BIH a ial ib illa ion da abase, CinC
chalange da abase (1s ed) and Long e m a ial ib illa ion da abase (Se –
sensi i i y; PP – posi i e p edic i i y).
Da abase
SE [%]
PP [%]
MIT-BIH AF
96,32
98,61
MIT-BIH AR
98,42
90,78
CinC Ch. (1s ed)
93,04
87,30
Long Te m AF
95,60
80,27
Table 2 The alues o ue posi i e (TP), ue nega i e (TN), alse posi i e
(FP), alse nega i e (FN) hea bea s o AF de ec ion algo i hm on signals
om MIT-BIH a hy hmia da abase, MIT-BIH a ial ib illa ion da abase,
CinC chalange da abase (1s ed) and Long e m a ial ib illa ion da abase.
Da abase
TP
TN
FP
FN
MIT-BIH AF
80964655
12502921
5
1764240
3093610
MIT-BIH AR
2891746
23887217
2424716
46321
CinC Ch. 1s ed)
1145
4908
76
748
Long Te m AF
43758987
2
28439682
5
6990500
3
2014541
9
The achie ed esul s o ou one- ea u e me hod a e
compa able wi h o he au ho s o mo e complica ed and
compu a ionally expensi e me hods [9], [10]. Fas a
simplici y o ou me hod is use ul o example in
applica ion whe e he ime is limi a ion and also o mobile
de ices, whe e he low compu a ional complexi y is
impo an . Biosignals p ocessing is nowadays an ac ual
opic.
In Figu e 3, examples o e o s caused by ou de ec ion
algo i hm, a e shown. The blue lines indica e anno a ion
om da abase, g een lines indica e ou esul s, alue 1
indica es AF, alue 0 indica es nonAF. In a) is shown
mis ake caused by ea lie e mina ion AF o ou de ec o –
p obably due o he ac , ha SH is compu ed om 95 RR
in e als and ollowing RR in e als wi hou AF dec eased
alue o SH. These mis akes o inaccu a e e mina ion and
beginning o AF is ela i ely equen . In b) is shown ha
ou de ec o poin ed o he le pa o he signal, whe e
sup a en icula a hy hmia is p esen , as a ial ib illa ion,
p obably due o he ac o highe a iabili y o RR
in e als caused by his ype o a hy hmia as wi h AF is
also p esen .
Figu e 3 Examples o e o s caused by ou de ec ion algo i hm
(blue line – anno a ion, g een line - ou esul , 1-AF, 0-nonAF),
a) signal 100 om Long e m a ial ib illa ion da abase, b) signal
05261 om MIT-BIH a ial ib illa ion da abase.
4. Discu ions
Du ing ou wo k, ou ECG expe s made a e y
impo an inding. Public da abases con ain many e o s in
anno a ions (in sense o AF) and also in o he pa hologies.
I means ha esul s o all au ho s, who used hese
da abases, a e a ec ed by e o s in anno a ions. Many
e o s we e ound in Long-Te m AF, se e al also in MIT-
BIH AF da abase and also in MIT-BIH A hy hmia
da abase. Tes ing algo i hms on poo ly anno a ed
da abases canno b ing eliable esul s and algo i hms
Page 3
use ul in eal medical p ac ice. The examples o such
anno a ions a e epo ed in Figu e 4. In he le pa o
subg aph a) is p esen AF, bu in anno a ion om da abase
(blue line) is no ma ked (signal no. 05261 om MIT-BIH
a ial ib illa ion da abase), co ec anno a ion is ma ked
by ed line. In subg aph b) is p esen AF all he ime, bu
acco ding o he anno a ion is i no ue. The pa o he
signal whe e he ex asys oles a e, is no ma ked as AF.
Figu e 4 Examples o e o s in anno a ion o AF (blue -
anno a ion in da abase, ed - co ec anno a ion, , 1-AF, 0-
nonAF); a) signal 05261 om MIT-BIH a ial ib illa ion
da abase, b) signal 100 om Long e m a ial ib illa ion
da abase.
5. Conclusion
In his wo k, highly e icien single ea u e algo i hm
o a ial ib illa ion is p oposed. The achie ed esul s o
ou one- ea u e me hod a e compa able wi h o he au ho s
o mo e complica ed and compu a ionally expensi e
me hods [9], [10]. Fas a simplici y o ou me hod is use ul
o example in applica ion whe e he ime is limi a ion and
also o mobile de ices, whe e he low compu a ional
complexi y is impo an .
In addi ion, ou ECG expe s ound ha in o en used
es ing da abases o ECG signals a e e o s in anno a ion
(in sense o AF) and also in o he pa hologies. Tes ing
algo i hms on poo ly anno a ed da abases canno b ing
eliable esul s and algo i hms use ul in eal medical
p ac ice. The e is a place o hei co ec ion o c ea ion o
new ones.
Acknowledgmen s
This wo k has been unded by he Uni ed S a es O ice o
Na al Resea ch (ONR) Global, awa d numbe N62909-19-
1-2006.
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Add ess o co espondence:
Ing. Lucie Ma šáno á
Depa men o Biomedical Enginee ing
Facul y o Elec ical Enginee ing and Communica ion
B no Uni e si y o Technology
Technická 12
B no 616 00
Czech Republic.
[email p o ec ed]
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