RESEARCH ARTICLE
Dynamic App oxima e En opy
Elec oana omic Maps De ec Ro o s in a
Simula ed A ial Fib illa ion Model
Juan P. Uga e
1
*, And e´s O ozco-Duque
1
, Ca alina Tobo´n
2
, Vacla K emen
3,4
,
Daniel No ak
3
, Ja ie Saiz
5
, Tobias Oes e lein
6
, Clauss Schmi
7
, A min Luik
7
,
John Bus aman e
1
1. Cen o de Bioingenie ı´a, Uni e sidad Pon i icia Boli a iana, Medellı´n, Colombia, 2. GI
2
B, Ins i u o
Tecnolo´gico Me opoli ano, Medellı´n, Colombia, 3. Czech Ins i u e o In o ma ics, Robo ics and Cybe ne ics,
Czech Technical Uni e si y in P ague, P ague, Czech Republic, 4. Depa men o Cybe ne ics, Facul y o
Elec ical Enginee ing, Czech Technical Uni e si y in P ague, P ague, Czech Republic, 5. I3BH, Uni e si a
Poli e`cnica de Vale`ncia, Valencia, Spain, 6. Ins i u e o Biomedical Enginee ing, Ka ls uhe Ins i u e o
Technology (KIT), Ka ls uhe, Ge many, 7. Medizinische Klinik IV, S aed isches Klinikum Ka ls uhe, Ka ls uhe,
Ge many
*[email p o ec ed].edu.co
Abs ac
The e is e idence ha o o s could be d i e s ha main ain a ial ib illa ion.
Complex ac iona ed a ial elec og ams ha e been loca ed in o o ip a eas.
Howe e , he concep o elec og am ac iona ion, de ined using ime in e als, is
s ill con o e sial as a ool o loca ing a ge si es o abla ion. We hypo hesize ha
he ac iona ion phenomenon is be e desc ibed using non-linea dynamic
measu es, such as app oxima e en opy, and ha his ool could be used o
loca ing he o o ip. The aim o his wo k has been o de e mine he ela ionship
be ween app oxima e en opy and ac iona ed elec og ams, and o de elop a new
ool o o o mapping based on ac iona ion le els. Two episodes o ch onic a ial
ib illa ion we e simula ed in a 3D human a ial model, in which o o s we e
obse ed. Dynamic app oxima e en opy maps we e calcula ed using unipola
elec og am signals gene a ed o e he whole su ace o he 3D a ial model. In
addi ion, we op imized he app oxima e en opy calcula ion using wo eal mul i-
cen e da abases o ac iona ed elec og am signals, labeled in 4 le els o
ac iona ion. We ound ha he alues o app oxima e en opy and he le els o
ac iona ion a e posi i ely co ela ed. This allows he dynamic app oxima e en opy
maps o localize he ips om s able and meande ing o o s. Fu he mo e, we
assessed he op imized app oxima e en opy using bipola elec og ams gene a ed
o e a icini y enclosing a o o , achie ing o o de ec ion. Ou esul s sugges ha
high app oxima e en opy alues a e able o de ec a high le el o ac iona ion and
OPEN ACCESS
Ci a ion: Uga e JP, O ozco-Duque A, Tobo´n C,
K emen V, No ak D, e al. (2014) Dynamic
App oxima e En opy Elec oana omic Maps De ec
Ro o s in a Simula ed A ial Fib illa ion
Model. PLoS ONE 9(12): e114577. doi:10.1371/
jou nal.pone.0114577
Edi o : Alexande V. Pan ilo , Gen Uni e si y,
Belgium
Recei ed: June 13, 2014
Accep ed: No embe 11, 2014
Published: Decembe 9, 2014
Copy igh : ß2014 Uga e e al. This is an open-
access a icle dis ibu ed unde he e ms o he
C ea i e Commons A ibu ion License, which
pe mi s un es ic ed use, dis ibu ion, and ep o-
duc ion in any medium, p o ided he o iginal au ho
and sou ce a e c edi ed.
Da a A ailabili y: The au ho s con i m ha all da a
unde lying he indings a e ully a ailable wi hou
es ic ion. The da a a e a ailable a h ps://gi hub.
com/and es od/A ial_Elec og ams_ApEn.
Funding: JPU, CT, and JB we e pa ially
suppo ed by Depa amen o Adminis a i o de
Ciencia, Tecnologı´a e Inno acio´n de la Republica
de Colombia (www.colciencias.go .co), p ojec
#121056933647; AO was suppo ed by he
P og ama de Fo macio´n de In es igado es
F ancisco Jose de Caldas (www.colciencias.go .
co); VK and DN we e pa ially suppo ed by
esea ch p ojec #MSM6840770012
In e disciplina y Biomedical Enginee ing Resea ch
II om he Minis y o Educa ion (www.msm .cz),
You h and Spo s o he Czech Republic, and VK
was pa ially suppo ed by pos -doc o al esea ch
p ojec GACR #P103/11/P106 o he Czech
Science Founda ion (www.gac .cz). The unde s
had no ole in s udy design, da a collec ion and
analysis, decision o publish, o p epa a ion o he
manusc ip .
Compe ing In e es s: The au ho s ha e decla ed
ha no compe ing in e es s exis .
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 1/19
o loca e o o ips in simula ed a ial ib illa ion episodes. We sugges ha dynamic
app oxima e en opy maps could become a ool o a ial ib illa ion o o mapping.
In oduc ion
Ca he e abla ion based on mapping p ocedu es has e olu ionized he ea men
o a ial ib illa ion (AF). Elec oana omical mapping o guided AF abla ion
p o ides a 3D econs uc ion o he ca diac chambe s oge he wi h elec ical
in o ma ion ob ained om elec og ams (EGM). Mappings o ac i a ion wa es,
ol age, dominan equency and complex ac iona ed a ial elec og ams (CFAE)
a e used o localize a ge si es o abla ion. Howe e , he e a e limi a ions wi h
hese echniques, which depend hea ily on he expe ise o he elec ophysiologis
[1].
CFAE mapping is s ill a deba ed echnique [2]. CFAE is a physiopa hological
concep ha was in oduced by Nademanee [3]. Howe e , his concep is b oadly
and unclea ly de ined, and in ol es inhe en subjec i i y [4]. This can lead o
inco ec de ec ion o a ge si es o abla ion, mis aking EGM ha a e
ac iona ed and unc ional in na u e [5]. I also makes s udies di icul o
compa e. While he concep o CFAE has made a ele an con ibu ion o he
s udy o AF, i may ail o desc ibe he wide ange o EGM ac iona ion ha
occu s in speci ic cases. In addi ion, inconsis en esul s ha e been ound using he
CFAE concep . Taking his in o accoun , ecen s udies ha e helped o unde s and
he concep o CFAE as a nonlinea phenomenon o quan i ying a ious CFAE
pa e ns, wi hou using cycle leng h c i e ia [6–8].
S udies ha e shown ha si es ep esen ing AF subs a es a e cha ac e ized by a
high deg ee o diso ganiza ion in EGM [9], and, acco dingly, me hods o EGM
signal p ocessing a e being designed o quan i y he deg ee o ac iona ion o
EGM [7,8]. The ela ionship be ween CFAE and he o o ip has been epo ed in
ecen s udies [7,10–13], bu au oma ic o o mapping me hods ha e no been
ully es ablished.
The o o hypo hesis desc ibed in [14] p oposes ha in a signi ican numbe o
pa ien s, a o o o a small numbe o o o s a e d i e s which main ain he
a hy hmia. A o o is a o ex o a spi al wa e o a ing a ound an unexci able
co e. Na ayan e al ha e p o ided e idence ha human AF can be sus ained by
localized o o s [15,16].
Based on he o o hypo hesis, which su mises ha sus ained AF depends on
unin e up ed pe iodic ac i i y o he disc e e een an si e, and on e idence ha
a high deg ee o i egula i y is p esen in EGM signals a he o o ip, we
hypo hesized ha 1) he le el o ac iona ion on EGM can be measu ed using a
non-linea index such as App oxima e En opy (ApEn), and 2) high le els o
ApEn can be used o localize he o o ip.
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 2/19
Ma e ials and Me hods
We p esen dynamic ApEn maps as a new ool o o o de ec ion. ApEn alues
o each EGM eco ded om he a ial su ace a e used o cons uc a colo map.
We assess he me hod in a 3D compu a ional model o human a ia. Fig. 1A
schema ically illus a es he me hodology used in his wo k, as ollows. Fi s , wo
AF episodes we e simula ed: a ch onic AF episode in which wo s able o o s we e
ound, and a ch onic AF episode in which a meande ing o o was ound. Second,
ApEn measu emen s, using s anda d pa ame e s, a e calcula ed o e i ual EGM
eco ded om he 3D model o cons uc dynamic ApEn maps. Thi d, he ApEn
pa ame e s we e op imized using eal measu ed bipola EGM om mul i-cen e
da abases. Fou h, dynamic ApEn maps we e gene a ed using op imized
pa ame e s. Nex , he o o s ips a e iden i ied by analyzing local ac i a ion ime
maps and dynamic ApEn maps. The de ails o each s ep a e p esen ed in he
ollowing sec ions.
Ch onic a ial ib illa ion model
A ealis ic 3D model o human a ia including he main ana omical s uc u es,
ibe o ien a ion, elec ophysiological and conduc ion he e ogenei y and aniso-
opy, was de eloped in an ea lie wo k [17]. I includes 52906 hexahed al
elemen s and 100554 nodes. The Cou emanche-Rami ez-Na el-Knelle mem-
b ane o malism [18,19] was implemen ed o ep oduce he human a ial cellula
elec ical ac i i y. The monodomain model o he elec ical p opaga ion o he
ac ion po en ial along he issue is desc ibed by a eac ion-di usion equa ion, and
is sol ed using a ini e elemen me hod [17].
To ep oduce a ial elec ical emodeling, changes in he maximum
conduc ance and kine ics o di e en ionic channels o human a ial cells
obse ed in expe imen al s udies o ch onic AF [20–22] ha e been inco po a ed
in o he a ial cellula model. The ollowing pa ame e s we e al e ed [23]: he
maximum conduc ance o IK1was inc eased by 100%, while he maximum
conduc ance alues o ICaL and I o we e dec eased by 70% and by 50%,
espec i ely.
Simula ion p o ocol
Two AF episodes we e gene a ed by he S1–S2 p o ocol as ollows: a ain o
s imuli wi h a basic cycle leng h o 1000 ms was applied o a pe iod o 5 seconds
in he sinus node a ea o simula e he sinus hy hm (S1). A e he las bea o he
sinus s imulus, a bu s o 6 ec opic bea s (S2) o high equency we e deli e ed
in o he igh supe io pulmona y ein, o he i s AF episode; and hey we e
deli e ed in o he pos e io wall o he le a ium nea o he igh pulmona y
eins, o he second episode.
Vi ual elec og ams
Unipola EGM in di e en poin s o he a ia su ace unde condi ions o uni o m
in acellula aniso opic esis i i y was simula ed, as p e iously desc ibed [24].
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 3/19
The ex acellula po en ial (we) is gi en by he ollowing equa ion:
we( )~{
1
4p
si
seððð+Vm( ’):+1
’{

d ð1Þ
whe e +Vmis he spa ial g adien o ansmemb ane po en ial Vm,siis he
in acellula conduc i i y, seis he ex acellula conduc i i y, is he dis ance
om he sou ce poin (x,y,z) o he measu ing poin (x’,y’,z’)and d is he
di e en ial olume. EGM signals we e eco ded a 1kHz. Bipola EGM we e
calcula ed by sub ac ing wo 1-mm-spaced adjacen unipola EGM.
Nume ical and compu a ional me hods
A hexahed al mesh was buil om he h ee-dimensional ana omical model using
Femap om Siemens PLM so wa e. Equa ions we e nume ically sol ed using
EMOS so wa e [25]. EMOS is a pa allel code (mpibased) ha implemen s he
ini e elemen me hod and Ope a o Spli ing o sol ing he monodomain model.
The ime s ep was ixed o 0.001 ms. Simula ion o 10 seconds o a ial ac i i y
ook 14 hou s on a compu ing node wi h wo 6-co e In el Xeon X5650 clocked a
2.66 GHz and 48GB DDR3 RAM.
Isoch one ac i a ion maps
A me hod was de eloped as an a angemen o he isoch one map me hod [26],
whe e he local ac i a ion imes (LAT) a e ep esen ed in a colo map. To build an
ac i a ion map, i is necessa y o de ec he local ac i a ion wa es. An algo i hm
based on he Con inuous Wa ele T ans o m was implemen ed o de ec local
ac i a ion wa es. A e a peak has been de ec ed, an isoch one map is cons uc ed
wi h he LAT in o ma ion. In o de o ensu e ha one comple e ac i a ion cycle is
scanned, i is necessa y o isualize he LAT minimum o a pe iod o 100 ms. The
Fig. 1. Expe imen al se up. A: Simula ed episode o ch onic AF in a 3D model o human a ia. A local ac i a ion ime map was cons uc ed as an al e na i e
me hod o de ec ing o o s. A pseudo-EGM signal was calcula ed om he 3D model. ApEn was calcula ed in pseudo-EGM signals eco ded o e he whole
a ial su ace. ApEn maps we e cons uc ed in o de o obse e he ela ion be ween ApEn alues and o o loca ions. B: Examples o EGM signals o DB-
CZ-DE. Rep esen a i es om he ou le els o complexi y p oposed o he pu poses o he s udy a e shown om C0 o C3. These signals we e used o
ApEn pa ame e op imiza ion.
doi:10.1371/jou nal.pone.0114577.g001
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 4/19
poin s a which he ac i a ion wa es a e spinning can be obse ed; hese poin s
co espond o he o o ip. This p ocedu e was used as a gold s anda d o
compa ison wi h ou esul s.
App oxima e en opy and pa ame e op imiza ion
App oxima e En opy (ApEn) is a nonlinea s a is ic p oposed by Pincus [27]. I
quan i ies he deg ee o complexi y o signals. The calcula ion o ApEn depends
on h ee pa ame e s: numbe o da a poin s N, embedding dimension mand
h eshold .ApEn(m, ,N)allows o measu e egula i y by calcula ing he
p obabili y ha pa e ns o leng h m emain close on nex inc emen al
compa isons wi hin a signal o leng h N, wi h m N[28].
ApEn is heo e ically de ined as he alue dependen on mand , conside ing
N??. This alue canno be eached bu can be app oxima ed. The
app oxima ion is well sui ed when a signi ican numbe o pa e ns, de e mined
by m, a e acqui ed [29]. Pincus s a ed ha small alues o ma e needed in o de
o con e ge o he eal alue o ApEn [28]. Speci ically, he sugges ed m~2,
[½0:1,0:25as s anda d pa ame e s.
We e alua e ApEn(2,0:1,1000)and ApEn(2,0:1,500) om s anda d pa ame e s.
Fu he mo e, we p opose mand alues de i ed om an op imiza ion p ocedu e
using a da ase o EGM. This da ase has al eady been applied o o he s udies
aimed a de eloping signal p ocessing ools o CFAE [30,31].
Da ase
We used wo di e en EGM da abases, independen ly eco ded om AF pa ien s,
and independen ly e alua ed. The da abases we e anked by di e en elec o-
physiology eams, wi h di e en equipmen , om wo di e en coun ies. The 542
signals in he da abases we e classi ied using he same c i e ia di ided in o ou
classes: ac iona ed signals we e ca ego ized by expe s in o h ee le els o
ac iona ion (C1, C2 and C3), and non ac iona ed EGM signals we e conside ed
as le el 0 (C0). The ou ac iona ion classes, see Fig. 1B, a e:
NC0: Non ac iona ed EGM and also high equency EGM.
NC1: F ac iona ed EGM wi h pe iodic ac i i y.
NC2: A mix u e o pe iodic ac iona ed and pe iodic non ac iona ed EGM.
NC3: High equency EGM wi h con inuous ac i i y. No egula ac i a ion can
be seen.
The en i e da abase cons i u es a e ospec i e-o line analysis. Fo u he
in o ma ion abou he acquisi ion and classi ica ion o his da abase, e e o
[32,33]. The da abase is a ailable a h ps://gi hub.com/and es od/A ial_
Elec og ams_ApEn.
Op imiza ion p ocess
ApEn pa ame e s mand we e se using eal da a om he da abase, o ob ain
op imal alues. The a ia ion o mwas limi ed o 5, as ecommended by Pincus
[27]. Pa ame e a ied om 0.02 o 0.6, inc easing in s eps o 0.02. The da abase
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 5/19

was o ganized in o ou le els o ac iona ion (C0, C1, C2 and C3). Each le el
con ains he en i e se o signals o he co esponding le el o ac iona ion. The
i s 500 and 1000 ms o each EGM we e conside ed. The numbe s o EGM signals
we e as ollows: 175 signals in C0, 117 signals in C1, 184 signals in C2, and 66
signals in C3. F om now on, we e e o his da abase o ganiza ion as DB-CZ-GE.
Fo each combina ion o mand ,ApEn was calcula ed o each EGM om DB-
CZ-GE and a boxplo was cons uc ed, assigning a box o each le el.
In he in e es o minimizing he sca e o each class and maximizing he
dis ances be ween he ApEn measu es o he classes, wo c i e ia we e conside ed
in he op imiza ion p ocedu e: in e class pe cen ile dis ance d1and in e class
minimum-maximum dis ance d2, which we e de ined as ollows:
d1~X
3
i~1
Q1(Ciz1){Q3(Ci)½ ð2Þ
d2~X
3
i~1
min(Ciz1){max(Ci)½ ð3Þ
whe e Q1and Q3a e he i s and hi d quan ile, espec i ely.
To selec he pa ame e s o be used o ApEn, an op imiza ion unc ion Jbp was
cons uc ed by equal weigh ing o c i e ia d1and d2 om (2) and (3):
Jbp~d1zd2ð4Þ
In o de o alida e he ApEn pa ame e s ob ained in he op imiza ion
p ocedu e and o a oid o e aining, K-c oss alida ion was pe o med.
Randomly gene a ed pa i ions we e selec ed om ull DB-CZ-GE. K~10 subse s
we e o med.
Dynamic ApEn mapping
In o de o gene a e a dynamic ApEn map o e he su ace o he a ial model, he
s anda d ApEn pa ame e s m~2and ~0:1, as sugges ed by Pincus [27,28,34]
and he pa ame e s o ApEn ob ained in he op imiza ion p ocedu e, we e used.
ApEn was calcula ed o i ual unipola EGM signals, using mo ing windows o
500 and 1000 poin s, wi hou o e lapping. The ange o ApEn, o e he en i e se
o i ual EGM, was applied o a colo scale, whe e ed colo co esponds o
max (ApEn)and blue colo co esponds o 0. Each i ual EGM is ela ed o an
elemen in he model. A 1000-poin window was applied o acking s able
o o s. A 500-poin window was applied o acking meande ing o o s. Unipola
EGM o e he en i e su ace o he a ia we e analyzed, wi h he excep ion o he
meande ing o o case, in which an obse a ion a ea was selec ed in o de o
e alua e he beha io o he op imized ApEn du ing he p esence and absence o
he ip o he o o .
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 6/19
Bipola -EGM based dynamic ApEn maps we e also cons uc ed o he s able
o o case. An obse a ion a ea, in which he o o ip is ancho ed, was selec ed.
The ApEn alues o bipola EGM we e calcula ed using he op imized pa ame e s
and he 1000-poin window. Shannon En opy (ShEn) maps we e also gene a ed,
h ough a 4-second window and bins o 0.01 mV, in acco dance wi h he wo k o
Ganesan e al [7]. The ShEn pe o mance in unipola EGM was also assessed.
Resul s
CFAE mapping o s able o o s du ing AF simula ion applying
ApEn wi h s anda d pa ame e s
An AF p opaga ion pa e n o e he a ia was gene a ed in he 3D model o
human a ia, see he ac ion po en ial p opaga ion in S1 Video. Du ing AF ac i i y
ini ia ed by an ec opic ocus applied in o he igh supe io pulmona y ein, wo
s able o o s we e obse ed in he simula ion. One is loca ed in he pos e io wall
o he le a ium, nea he le pulmona y ein, named R1, and he o he is
loca ed in he supe io ena ca a, named R2. Fig. 2A shows he ac ion po en ial
wa e on s delimi ed by con ou lines om he in e al be ween 1 s and 2 s o AF
simula ion. Ro o s R1 and R2, and a block line loca ed o e he in e io igh
pulmona y ein, named B1, ha e been ma ked. 42835 EGM we e calcula ed in he
whole a ial su ace o he 3D model, o e a ou -second window.
Fo all EGM signals, he ApEn measu emen s we e calcula ed using he
s anda d pa ame e s (m~2, ~0:1). The ApEn alues we e used o gene a e a
colo map o e he ana omic s uc u e o he a ia in a 3D model. In his manne ,
a dynamic ApEn map was ob ained and he ame co esponding o he ime
in e al om 1 s o 2 s is depic ed in Fig. 2B. Red colo a eas, co esponding o
high ApEn alues (0:3285+0:0202), include B1 and he co ona y sinus (CS) and
also R1 and R2.
Op imiza ion o ApEn pa ame e s (mand )
The op imiza ion p ocedu e esul ed in m~3, ~0:38, o N~1000 and m~3,
~0:30, o N~500.Fig. 3A shows he boxplo s o ApEn(3,0:38,1000)and o
ApEn(3,0:30,500), espec i ely, applied o DB-CZ-GE. In addi ion, he Spea man
co ela ion coe icien Sbe ween ApEn and he co esponding le el o
ac iona ion was calcula ed.
CFAE mapping o s able o o s du ing AF simula ion applying
ApEn wi h op imized pa ame e s
A dynamic ApEn(3,0:38,1000)map was gene a ed using unipola EGM, and he
ame co esponding o he ime in e al 1 s o 2 s is depic ed in Fig. 2C, see S1
Video. The dynamic ApEn map e eals wo a eas o high ApEn alues
(0:3285+0:0202), co esponding o o o s R1 and R2. In addi ion, he hi d a ea
wi h lowe ApEn alues (0:2724+0:0238) co esponds o B1, aking in o accoun
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 7/19
ha passi e ac i a ion egions ha e ApEn alues lowe han 0.1. A ShEn map was
also gene a ed and is shown in Fig. 2D. Red colo a eas, co esponding o high
ShEn alues (8:375+0:125), include small icini ies nea o R1 and nea o B1,
along o he zones, e.g. CS, he in e io wall o he le a ia, he le and igh
appendage and he la e al wall nea o he le appendage. The LAT me hod was
applied as a e e ence me hod, see S2 Video.Fig. 3B shows isoch onic maps om
R1 and R2. The o o ip is de ined by he con e ging poin s o he colo ed wa es.
These wa es ep esen he local ac i a ion. G een colo indica es ea ly ac i a ion
poin s. Table 1 shows he spa ial loca ion o R1 and R2 ound using he LAT
me hod and he dynamic ApEn mapping me hod. The las column co esponds o
he Euclidean dis ance be ween he spa ial coo dina es om he o o ip,
iden i ied using bo h me hods. The maximum dis ance is 1.66 mm. Unipola
EGM ex ac ed om o o si es R1 and R2, and nea o block a ea B1, a e shown
in Fig. 3C. ApEn alues a e also p esen ed. The EGM co esponding o o o
ac i i y ( op) ha e low ol age and i egula mo phology. The EGM co e-
sponding o he block line (below le ) p esen s ac iona ion, bu ac i a ion
Fig. 2. Compa ison be ween ools o o o mapping. A. Ac ion po en ial wa e on delimi ed by con ou
lines o e he 3D Human A ia Model ex ac ed om he in e al be ween 1 s and 2 s o simula ion. The
spinning wa e on s a ound one poin de ine s able o o s R1 and R2. Line block B1 can be seen a he igh
in e io pulmona y ein. B. Dynamic ApEn map calcula ed using s anda d pa ame e s and unipola EGM. C.
Dynamic ApEn map calcula ed om he op imized pa ame e s ob ained in ou wo k, using unipola EGM. D.
Shannon en opy map, using unipola EGM. No e ha map C shows be e sensi i i y o localizing o o ips.
E. Dynamic ApEn map calcula ed om op imized pa ame e s using bipola EGM wi h ho izon al and e ical
o ien a ion. The egion co esponds o he icini y o o o R1. F. ShEn map calcula ed using he bipola EGM
ob ained om he icini y o o o R1.
doi:10.1371/jou nal.pone.0114577.g002
Dynamic ApEn Maps in A ial Fib illa ion
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pa e ns a e isible and hei ampli udes a e simila o non- ac iona ed EGM
(below igh ). The highes ApEn alues co espond o R1 and R2.
A ci cula a ea con aining R1 was selec ed. Bipola EGM we e calcula ed using
ho izon al and e ical bipole o ien a ion. 636 EGM we e ob ained o each
o ien a ion. Fig. 2E shows he dynamic ApEn(3,0:38,1000)maps o ho izon al
and e ical bipola o ien a ion, in he ime in e al be ween seconds 1 and 2.
High ApEn alues co espond wi h he ip o he o o in bo h cases. Fig. 2F
shows he ShEn maps. The e ical bipola o ien a ion map p esen s a egion o
Fig. 3. Localiza ion o s able o o s. A: Resul s o he op imiza ion p ocedu e. Boxplo s o ApEn no malized alues using op imized pa ame e s:
ApEn(1000,3,0:38)(le ) and ApEn(500,3,0:30)( igh ). The Spea man co ela ion coe icien calcula ed o e DB-CZ-GE o each boxplo is shown. B: Ac i a ion
isoch onic maps co esponding o R1 (below) and R2 ( op). The o o ip is indica ed whe e he colo s con e ge. C: EGM gene a ed by he model in he
a eas o s able o o s and he block o he ime in e al be ween 2 s and 3 s. EGM co esponding o he R1, R2, B1 and plane ac i a ion wa e on a eas. D:
Bipola EGM co esponding o R1 and plane ac i a ion wa e on a ea. ApEn alues o each EGM a e shown.
doi:10.1371/jou nal.pone.0114577.g003
Dynamic ApEn Maps in A ial Fib illa ion
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genic mechanisms besides o o s, should be s udied. In o de o ully alida e he
esul s o ou op imiza ion p ocedu e wi h DB-CZ-GE, al hough good
pe o mance has been achie ed o o o de ec ion in he 3D model, u u e s udies
should in ol e collec ing mo e AF EGM samples om o he da abases in o de o
achie e equally dis ibu ed ac iona ion le els. Addi ionally, eal unipola EGM
mus be included.
In conclusion, we ha e p o ided e idence o pos ula ing dynamic ApEn maps
as a suppo ing ool in AF abla ion p ocedu es. ApEn calcula ion o e a ial EGM
signals can be used o build an elec oana omical map wi h con inuous ApEn
alues ep esen ed in colo s ha can iden i y o o ip loca ions wi hou p e-
speci ying h esholds. This p ope y makes he me hod adap able o speci ic
elec ophysiological cases. A combina ion o all his could help o imp o e
abla ion p ocedu es. We sugges ha dynamic ApEn colo maps could become a
ool o AF o o mapping. The me hodology p oposed he e needs o be alida ed
by expe imen al models and by clinical s udies o e alua e abla ion p ocedu es
guided by dynamic ApEn maps.
Suppo ing In o ma ion
S1 Video. S able o o s. Le : Simula ion o an AF episode induced by six
ansi o y ec opic bea s applied in he os ium o he igh pulmona y ein,
sus ained by mul iple een an wa es. Two o o s can be obse ed: in he
pos e io wall o he le a ia pos e io wall, and in he supe io ca a ein. Righ :
A dynamic ApEn map using op imized pa ame e s. Red a eas co espond o he
ips o o o s R1 and R2.
doi:10.1371/jou nal.pone.0114577.s001 (MP4)
S2 Video. Isoch one map. Isoch one maps o o o s R1 and R2 o he ime
in e al be ween 1500 ms and 2000 ms.
doi:10.1371/jou nal.pone.0114577.s002 (MP4)
S3 Video. Meande ing o o . Le : Simula ion o an AF episode induced by six
ansi o y ec opic bea s applied in he pos e io wall o he le a ium nea o he
igh pulmona y eins, sus ained by mul iple een an wa es. One meande ing
o o can be obse ed in he pos e io wall o he le a ia. Righ : A dynamic
ApEn map using op imized pa ame e s. No e ha , when a plane ac i a ion
wa e on is p esen wi hin he obse a ion a ea, he dynamic ApEn map shows
low alues (g een). Red zones appea when he o o ip is wi hin he obse a ion
a ea (e.g. he ime in e al be ween 2500 ms and 3000 ms).
doi:10.1371/jou nal.pone.0114577.s003 (MP4)
Au ho Con ibu ions
Concei ed and designed he expe imen s: JPU AO CT JS JB. Pe o med he
expe imen s: JPU AO CT VK DN JB. Analyzed he da a: JPU AO CT VK DN AL
JB. Con ibu ed eagen s/ma e ials/analysis ools: VK DN JS TO CS AL. W o e he
Dynamic ApEn Maps in A ial Fib illa ion
PLOS ONE | DOI:10.1371/jou nal.pone.0114577 Decembe 9, 2014 16 / 19

pape : JPU AO CT. D a ed he a icle o e ised i c i ically o impo an
in ellec ual con en : JPU AO CT VK DN JS TO CS AL JB.
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