1"
"
Spa io empo al Model-Based Es ima ion o High-Densi y A ial Fib illa ion Ac i a ion 1"
Maps 2"
Running i le: Spa io empo al Es ima ion o A ial Fib illa ion Ac i a ion Maps 3"
Alejand o Alcaine1,2, Na asja M. S. de G oo 3, Pablo Laguna1,2, 4"
Juan Pablo Ma ínez1,2, Richa d P. M. Houben4 5"
1BSICoS G oup, A agón Ins i u e o Enginee ing Resea ch (I3A), IIS A agón, Uni e sidad de 6"
Za agoza, 50018, Za agoza, Spain; 2CIBER en Bioingenie ía, Bioma e iales y Nanomedicina 7"
(CIBER-BBN), 28029, Mad id, Spain; 3T ansla ional Elec ophysiology Uni , Depa men o 8"
Ca diology, E asmus Medical Cen e ,"PO Box 2040, 3000 CA, Ro e dam, The Ne he lands; 9"
42BMedical B.V., 6226 NA, Maas ich , The Ne he lands. 10"
Co espondence: 11"
Richa d P. M. Houben 12"
2BMedical B.V. 13"
Be ge s aa 2, 6226 NA, Maas ich , The Ne he lands. 14"
Phone: 0031 6 397 666 70 15"
E-Mail: [email p o ec ed] 16"
Documen o al wo ds: 8578 (F om Abs ac o Re e ence sec ion: 6534) 17"
18"
2"
"
Abs ac : 19"
Examina ion o ac i a ion maps using mul i-elec ode a ay (MEA) senso s can help o 20"
unde s and he mechanisms unde lying a ial ib illa ion (AF). Classically, c ea ion o 21"
ac i a ion maps s a s wi h de ec ion o local ac i a ion imes (LAT) based on eco ded 22"
unipola elec og ams. LAT de ec ion has a limi ed obus ness and accu acy, and gene ally 23"
equi es manual edi ion. In gene al, LAT de ec ion igno es spa io empo al in o ma ion o 24"
ac i a ion embedded in he ela ion be ween elec ode signals on he MEA mapping senso . 25"
In his wo k, a uni ied app oach o cons uc ac i a ion maps by simul aneous analysis o 26"
ac i a ion pa e ns om o e lapping clus e s o MEA elec odes is p oposed. An ac i a ion 27"
model i s on he measu ed da a by i e a i e op imiza ion o he model pa ame e s based on a 28"
cos unc ion. The accu acy o he es ima ed ac i a ion maps was e alua ed by compa ison 29"
wi h audi ed maps c ea ed by expe elec ophysiologis s du ing sinus hy hm (SR) and AF. 30"
Du ing SR eco dings, 25 ac i a ion maps (3100 LATs) we e au oma ically de e mined 31"
esul ing in an a e age LAT es ima ion e o o -0.66 ± 2.00 ms and a co ela ion o 32"
98.0=
s
compa ed o he expe e e ence. Du ing AF eco dings (235 maps, 28226 LATs), 33"
he es ima ion e o was -0.83 ± 6.02 ms wi h only a sligh ly lowe co ela ion (
93.0=
s
). In 34"
conclusion, complex spa ial ac i a ion pa e ns can be decomposed in o local ac i a ion 35"
pa e ns de i ed om i ing an ac i a ion model, allowing he c ea ion o smoo h and 36"
comp ehensi e high-densi y ac i a ion maps. 37"
38"
Keywo ds: Ac i a ion Mapping, A ial Fib illa ion, Mul i-Elec ode A ay Senso s, No mal 39"
Sinus Rhy hm, Solid Angle, Uni o m Double Laye , Unipola Elec og ams.40"
3"
"
1. In oduc ion: 41"
A ial ib illa ion (AF) is one o he mos common a hy hmias, esponsible o one hi d o 42"
all hospi aliza ions a ca diac a hy hmia uni s [1], wi h an inc easing p e alence due o aging 43"
o he popula ion[2,3]. Moe e al. [4] i s p oposed he wa ele hypo hesis unde lying he 44"
ini ia ion and pe pe ua ion o AF, desc ibing he p esence o mul iple p opaga ing wa ele s 45"
sus aining he ib illa ion p ocess, alida ed la e by Allessie e al. [5,6]. O he p oposed 46"
mechanisms include d i ing oci, mainly loca ed a he pulmona y eins [7], e-en an 47"
ci cui s, o o s [8,9] and ans-mu al conduc ion o ib illa ion wa es be ween epica dial and 48"
endoca dial a ial laye s [10,11]. Howe e , mechanisms unde lying he ini ia ion and 49"
pe pe ua ion o AF a e no ye ully unde s ood [8], limi ing he op imal ea men o pa ien s. 50"
Ac i a ion mapping is he mos commonly used me hod o isualiza ion and s udy o 51"
ca diac a hy hmias [12]. Du ing hemodynamically s able and egula achyca dia, ac i a ion 52"
maps can be c ea ed a e sequen ial eco ding o elec og ams (EGM) and de ec ed local 53"
ac i a ion imes (LAT) can be e e ed agains a iducial poin in a simul aneously eco ded 54"
su ace o in aca diac signal [13]. Howe e , du ing i egula achyca dia like AF, 55"
simul aneous mapping is needed due o he non- epe i i e na u e and complexi y o he 56"
a hy hmia [8]. Mul i-elec ode mapping ca he e s such as Pen aRay and Lasso (Biosense 57"
Webs e , Inc. Diamond Ba , CA, USA) o he Cons ella ion ull con ac baske ca he e 58"
(Bos on Scien i ic, Inc. Na ick, MA, USA) lack spa ial esolu ion du ing mo e complex 59"
ac i a ion o he a ium due o elec ode spa si y and bad wall con ac [14]. Fo high-densi y 60"
mapping o mo e complex AF, a high-densi y mul i-elec ode a ay (MEA) mapping senso 61"
will be needed [8]. 62"
In his s udy, unipola elec og ams (u-EGM) we e eco ded using a MEA mapping 63"
senso in di ec con ac o he epica dial wall o he a ium du ing open ches su ge y. The 64"
4"
"
eco ded signals a e displayed in a ma ix ela ed o he loca ion o he elec odes on he 65"
MEA senso . This will allow cons uc ing ac i a ion maps which show he p opaga ion o 66"
ca diac ac i a ion [6,8]. 67"
The cons uc ion o ac i a ion maps in ol es se e al p ocessing s eps including 68"
denoising, baseline co ec ion, a ield R-wa e cancela ion and de ec ion o ac i a ion imes 69"
ollowed by an e o ejec ion p ocess. De ec ion o LATs is ela ed o he u-EGM s eepes 70"
nega i e slope (
d dV
) as a esul o an ac i a ion wa e unde -passing he eco ding 71"
elec ode [15,16]. Ac i a ion maps a e cons uc ed by combining LATs de ec ed om each o 72"
he elec odes on he mapping a ay. Howe e , his p ocedu e igno es he in o ma ion 73"
embedded in he mo phology o he u-EGM signal, hence no used o he c ea ion o high-74"
densi y ac i a ion maps. 75"
De ailed ca diac elec ophysiological modelling p o ides insigh in he physiology 76"
unde lying ca diac a hy hmias and se es as a ool o a be e diagnosis and in e p e a ion o 77"
expe imen al da a [17]. Those models desc ibe he ion cu en s lowing h ough he 78"
myoca dial cell memb ane (e.g.[18,19]) embedded in ealis ic s uc u es and geome ies o 79"
he human hea [17]. Less de ailed models o ca diac p opaga ion p o ide a less ime-80"
consuming al e na i e o ep esen he ca diac ac i a ion p opaga ion. Equi alen sou ce 81"
model uses cu en sou ces and densi ies o calcula e he po en ials, hence desc ibing he 82"
ac i a ion p opaga ion as a uni o m double laye (UDL) model [20]. 83"
In his pape , a uni ied spa io empo al app oach o es ima ion and cons uc ion o 84"
high-densi y ac i a ion maps is p esen ed. The p oposed me hod i s an ac i a ion pa e n 85"
model o acqui ed ca diac ac i i y in o de o econs uc he comple e ac i a ion map as he 86"
combina ion o con ibu ions om di e en iso opic ocal ac i a ion sou ces. The 87"
con ibu ion o each o he sou ces was de e mined by an i e a i e op imiza ion p ocess 88"
5"
"
modi ying he UDL p opaga ion model a e compa ing he modelled signals agains u-EGM 89"
signals acqui ed du ing epica dial a ial mapping in sinus hy hm (SR) and AF. Finally, he 90"
comple e ac i a ion map was econs uc ed by combining indi idual solu ions. P elimina y 91"
analysis o his app oach has been epo ed in [21]. 92"
2. Ma e ials and me hods: 93"
2.1. High-densi y a ial epica dium eco dings: 94"
The clinical da a used in his s udy was ob ained om a 61 yea s-old male pa ien wi h 95"
co ona y a e y disease, wi hou a his o y o AF which echoca diog aphic examina ion 96"
e ealed a no mal le en icula ejec ion ac ion and no mal a ial dimensions. The pa ien 97"
was admi ed o open ches su ge y a E asmus Medical Cen e Ro e dam (Ro e dam, The 98"
Ne he lands) in whom an in aope a i e elec ophysiological s udy was pe o med. The 99"
pa ien was in o med and signed he consen o m. Du ing he in e en ion, a cus om made 100"
high-densi y MEA mapping senso (Applied Biomedical Sys ems B.V., Maas ich , The 101"
Ne he lands) was posi ioned on he epica dial wall o he le and igh a ium ollowing a 102"
sequence o epica dial loca ions, as illus a ed in Fig. 1(a). Da ase s o high-densi y u-EGMs 103"
signals we e acqui ed du ing SR and AF. 104"
Figu e 1 he e 105"
Fig. 1: Schema ic o he mapping p ocedu e in pos e io iew: (a) Ana omical loca ion o he 106"
MEA senso in he a ium and (b) MEA senso used o mapping p ocedu e. CS: Co ona y 107"
Sinus, CT: C is a Te minalis, IVC: In e io Vena Ca a, LA: Le Appendage, LBB: Le 108"
Bachmann Bundle, LPV: Le Pulmona y Vein, RA: Righ Appendage, RBB: Righ 109"
Bachmann Bundle, RPV: Righ Pulmona y Vein, SVC: Supe io Vena Ca a. 110"
6"
"
The cus om MEA senso measu es 3.0×1.4 cm, is composed by 128 ci cula gold 111"
pla ed elec odes (2 mm in e -elec ode dis ance, 1 mm diame e ) o ganized in an 8×16 112"
ec angula g id. Elec ode channels co esponding o each co ne o he mapping a ay we e 113"
no a ailable o mapping and we e ese ed o s o ing su ace ECG, e e ence and 114"
calib a ion signals, esul ing in 124 u-EGM signals a ailable o analysis (Fig. 1(b)). The 115"
acqui ed u-EGM signals we e band-pass il e ed (1-500 Hz) sampled and digi ized a 1 kHz. 116"
The eco ding leng h du ing SR episodes was 5 s and 10 s du ing AF episodes. 117"
Au oma ic LAT de ec ion was pe o med o -line a e he p ocedu e using a wa ele -118"
based algo i hm [22] and subsequen ly audi ed by an expe elec ophysiologis blind o he 119"
de ec ion ou come o his wo k. The e o e, he esul ing LATs we e conside ed as “g ound 120"
u h” o pe o mance e alua ion o he p oposed algo i hm. 121"
2.2. Algo i hm o e iew and no a ion: 122"
Be o e algo i hm s a s, a 100 ms signal exce p ha includes a comple e ac i a ion 123"
ac oss he MEA senso is selec ed and he mapping a ay is segmen ed in 44 o e lapped 124"
g oups o 5×5 elec odes (a ea 64 mm2), being his he size o he analysing mask in his 125"
wo k. A comp ehensi e low o he p ocessing s eps is desc ibed below: 126"
L1: Fo each 5×5 g oup o elec odes: 127"
1. Es ima e conduc ion eloci y and ini ial ocus loca ion, 128"
which is conside ed he sou ce o his es ima ion. 129"
2. Gene a e ac i a ion pa e n and modelled u-EGMs. 130"
3. Compa e measu ed agains modelled u-EGMs. 131"
7"
"
L2: While he simila i y is below a gi en h eshold o he 132"
maximum numbe o i e a ions is no eached: 133"
a) Compu e new ocus loca ion o nex i e a ion. 134"
b) Gene a e new ac i a ion pa e n and modelled u-EGMs. 135"
c) Compa e measu ed agains modelled u-EGM signals. 136"
End o loop L2. 137"
End o loop L1. Go o s ep 1 unless all 5x5 g oups ha e been 138"
al eady analysed. 139"
4. Ac i a ion map econs uc ion. 140"
Fo no a ion,
][nsi
s ands o he eco ded u-EGM signal co esponding o he
i
h 141"
elec ode,
25...1=i
, om he 5×5 g oup unde analysis and
][
ˆnsi
deno es he modelled u-142"
EGM signal co esponding o he same elec ode loca ed in he ca diac issue model. 143"
2.3. Ac i a ion pa e n and issue model: 144"
The basic ac i a ion pa e n can be gene alized as a single ocal poin gene a ing an 145"
ac i a ion wa e on concen ically sp eading wi h a uni o m conduc ion eloci y. In a 2-146"
dimensional plane, he wa e on coo dina es
T
,]],[],,[[],[
qqq
nwnwn yx =
w
c ea ed by a 147"
ci cula ac i a ion pa e n wi h cen e ocus loca ion
[ ]
T
,yx =
a a ime ins an
n
; can be 148"
desc ibed by he pa ame ic o m: 149"
ú
û
ù
ê
ë
é
××+
ú
û
ù
ê
ë
é
=
ú
û
ù
ê
ë
é
=
)sin(
)cos(
],[
],[
],[
,
q
q
q
q
q
n
nw
nw
n
y
x
y
x
w
, (1) 150"
whe e
[
)
pq
2,0=
and
s ands o he conduc ion eloci y o he medium. No e ha 151"
8"
"
],[
,
q
n
w
is he exp ession o a ci cum e ence o adius
n ×
cen ed a
. Hence, (1) de ines 152"
a ci cula ac i a ion pa e n om a single ocus, becoming a plana wa e when he ocus is 153"
loca ed a away om he obse e scope. 154"
The ac i a ion pa e n was in oduced in o a UDL model using he bounda y elemen 155"
me hod [20]. The UDL models a squa e plana slice o a ial issue o 12×12 mm and 2 mm 156"
hick con o m o he a e age hickness o he human a ia [23]. Since no EGMs om he 157"
endoca dial wall we e eco ded, epica dial and endoca dial conduc ion eloci y was assumed 158"
o be equal [24]. Consequen ly, he modelled ac i a ion p opaga es in pa allel and a he same 159"
eloci y in bo h endoca dial and epica dial side o he UDL model. 160"
2.4. EGM signal modelling: 161"
A i ual MEA senso ( -MEA) wi h 5×5, 2 mm spaced, ci cula elec odes was placed on 162"
he epica dial side o he UDL enabling calcula ion o elec ical ac i i y du ing ac i a ion. 163"
Each
i
h i ual elec ode o he -MEA has a spa ial loca ion
T
],[ iii yx=e
. The in ini e 164"
medium po en ial gene a ed by a UDL a ime ins an
n
and posi ion
i
e
is gi en by [20]: 165"
][
4
][
ˆn
V
ns
i
d
ie
W-=
p
, (2) 166"
whe e
d
V
s and o a cons an alue called double laye s eng h o he UDL [20] and
][n
i
e
W
167"
s ands o he solid angle o he su ace c ea ed by he ac i a ion wa e on
],[
,
q
n
w
and 168"
sub ended wi hin he UDL a
i
e
, as illus a ed in Fig. 2. This solid angle
][n
i
e
W
can be 169"
compu ed nume ically by di iding he wa e on su ace in o iangula elemen s and 170"
summing he solid angles sub ended by each su ace elemen , using he plane iangle 171"
o mula [25]. 172"
Figu e 2 he e 173"
9"
"
Fig. 2: Schema ic in: (a) pe spec i e iew and (b) la e al iew, o he solid angle
][n
i
e
W
174"
ob ained a elec ode posi ion
i
e
om a ci cula ac i a ion pa e n
],[
,
q
n
w
sub ended 175"
wi hin a UDL shown as a closed g ey s ip. 176"
Equa ion (2) desc ibes he elec ophysiological beha iou o local u-EGMs eco ded 177"
om he myoca dium. The po en ial
][
ˆnsi
inc eases when he ac i a ion wa e on 178"
app oaches he eco ding elec ode, shows a as downwa d slope when he wa e unde passes 179"
he elec ode and goes back o baseline when he wa e passes away [13,15,20]. The 180"
ampli ude o his as downwa ds slope is p opo ional o he double laye s eng h
d
V
[20], 181"
hence i can be es ima ed om he measu ed u-EGM signals as he mean alue o all 182"
ampli ude di e ence be ween he posi i e and nega i e de lec ion (i.e., he R-wa e and S-183"
wa e, espec i ely). This cons an alue does no a ec he spa io empo al ea u es o
][
ˆnsi
184"
(i.e., he LAT and wa e mo phology) hence ha ing been se a bi a ily in his wo k o
1=
d
V
. 185"
2.5. Es ima ion o issue conduc ion eloci y: 186"
To use he p opaga ion model (1), he conduc ion eloci y o he ca diac issue
needs o be 187"
es ima ed om eco ded u-EGMs. Es ima ion o conduc ion eloci y om in asi e da a is an 188"
al eady add essed p oblem (e.g. in [6,26–28]), al hough di icul due o he spa io empo al 189"
changes o ca diac issue p ope ies, especially du ing i egula achyca dias [26]. 190"
Es ima ion o conduc ion eloci y based on LATs can be sensi i e o de ec ion e o s. 191"
The e o e, an al e na i e app oach is used in his wo k inspi ed in ha p esen ed by 192"
Fi zge ald e al. [27]. The ime delay
i
d
be ween each u-EGM
][nsi
and he cen al elec ode 193"
o he 5×5 g oup being analysed
][ns
is ob ained by maximizing he no malized c oss-194"
co a iance unc ion: 195"
16"
"
ime is no conside ed in he compu a ion o (19). The alue 0.55 is se empi ically as a 309"
minimum alue o
Q
o conside a eliable LAT solu ion. 310"
2.9. E alua ion p o ocol: 311"
The e alua ion o he p oposed algo i hm is pe o med by a compa ison o he es ima ed 312"
LATs wi h hose audi ed by an expe elec ophysiologis showing his compa ison e o as 313"
mean ± SD. 314"
Figu e 5 he e 315"
Fig. 5: Rep esen a i e examples o he a ial ac i i y complexi y classi ica ion p oposed in 316"
his pape . Re e ence agains es ima ed ac i a ion maps we e shown in: (a) No mal sinus 317"
hy hm (NSR) ac i i y (e o : -0.31 ± 0.93 ms, a ea: 100 %), (b) abno mal sinus hy hm 318"
(ASR) ac i i y (e o : -0.23 ± 3.5 ms, a ea: 100 %), (c) single a ial ib illa ion wa e on 319"
(SAFW) ac i i y (e o : -0.03 ± 2.96 ms, a ea: 100 %), (d) b eak h ough (BT) ac i i y (e o : 320"
-0.27 ± 2.59 ms, a ea: 100 %), (e) a ial ib illa ion wa e usion (AFWF) ac i i y (e o : -0.12 321"
± 1.73 ms, a ea: 100 %), ( ) dissocia ed a ial ac i i y due o a line o block (LB) (e o : 0 ± 322"
13.52 ms, a ea: 95.97 %) and (g) complex a ial ib illa ion (CAF) ac i i y (e o : -5.3 ± 323"
10.55 ms, a ea: 80.17 %). LATs a e colo -coded om ed (ea lies ) o pink (la es ) in 10 ms 324"
isoch ones. In case o no LAT could be iden i ied a one elec ode loca ion, a c oss is used. 325"
Ac i a ion maps we e s udied in unc ion o he ac i a ion pa e n complexi y and 326"
classi ied in o one o he ollowing 7 deg ees, illus a ed in Fig. 5: 327"
1. No mal sinus hy hm (NSR): No mal p opaga ion o a single wa e on wi hin he 328"
mapping ca he e du ing SR. 329"
2. Abno mal SR (ASR): Abno mal p opaga ion o one o mo e wa e on s wi hin he 330"
mapping ca he e du ing SR. 331"
17"
"
3. Single a ial ib illa ion wa e on (SAFW): Single AF wa e on p opaga ing wi hin 332"
he mapping ca he e whose o igin is loca ed ou side he mapping a ay. 333"
4. B eak h ough (BT): Concen ic AF p opaga ion wa e on whose ocus is loca ed 334"
wi hin he mapping a ay [11]. 335"
5. A ial ib illa ion wa e usion (AFWF): Two sepa a ed wa e on s collide and use 336"
in o a single wa e on . 337"
6. Line o Block (LB): A line o block is p esen in he p opaga ion pa e n o he 338"
mapping ca he e c ea ing longi udinal dissocia ion o wa e on s a eling a 339"
di e en eloci ies and/o di ec ions [10]. 340"
7. Complex AF (CAF): Chao ic ac i a ion wi h wa e in e up ion and mul iple lines o 341"
block. 342"
Since LATs ha e an o de ed na u e (i.e., om ea lies ac i a ed o la es ac i a ed 343"
elec ode), Spea man's ank co ela ion
s
has been compu ed o assessing he pe o mance 344"
o he p oposed me hod. Addi ionally, Lin's conco dance co ela ion ac o
c
[29] and 345"
Bland-Al man analysis we e used o assess ag eemen be ween he measu emen s. A
p
- alue 346"
05.0£
was equi ed o conside ing s a is ical signi icance. Sensi i i y
Se
and posi i e 347"
p edic i e alue
+
P
o he de ec ion ha e been compu ed as: 348"
FNTP
TP
Se
+
=
, (20) 349"
FPTP
TP
P
+
=
+
, (21) 350"
whe e
TP
s ands o he numbe o ue de ec ions,
FN
s ands o he numbe o missed 351"
18"
"
de ec ions and
FP
s ands o he numbe o alse de ec ions. A ole ance o ± 5 ms espec o 352"
he expe e e ence LATs was used o conside a ue de ec ion. 353"
3. Resul s: 354"
3.1. Analysis o SR eco dings: 355"
Table 1 summa izes he esul s ob ained du ing SR. No e ha in con as o eco dings a RA1 356"
o RA3, eco ding a RA4 shows abno mal SR ac i i y sugges ing a s able unc ional e-357"
en an ci cui (illus a ed in Fig. 5(b)) which is p esen du ing he comple e eco ding ime. 358"
Table 1 he e 359"
Table 1: De ec ion e o (mean ± SD), sensi i i y and posi i e p edic i e alue o compa ing 360"
es ima ed LATs wi h he manual e e ence in SR eco dings. N/A s ands o No Applicable. 361"
The global e o ob ained wi h he p oposed me hod is -0.66 ± 2.00 ms ac oss 3100 362"
LAT measu emen s, hus co e ing he 100 % o he senso a ea. A high le el o ag eemen is 363"
con i med by high Spea man’s co ela ion (
98.0=
s
,
01.0<p
) and high Lin's conco dance 364"
co ela ion ac o (
98.0=
c
,
01.0<p
) as shown in Fig. 6. Bland-Al man analysis shows 365"
(Fig. 6(b)) no end in LAT es ima ion (Pea son's
01.0-=
,
73.0=p
). Mo eo e , he 366"
de ec ion pe o mance is also high wi h
100=Se
% and
84.97=
+
P
%. Those obse a ions 367"
con i m he high ag eemen be ween measu emen s du ing SR as illus a ed by ac i a ion 368"
maps shown in Fig. 5(a)-(b). 369"
Figu e 6 he e 370"
Fig. 6: Ag eemen e alua ion be ween e e ence and es ima ed LATs du ing SR: (a) 371"
Re e ence s. es ima ed LATs plo o Lin's conco dance co ela ion ac o
c
whe e pink 372"
19"
"
line indica es he uni slope and (b) Bland-Al man plo whe e ed solid line indica es mean 373"
e o and ed dashed lines show mean ± 2SD o he e o . 374"
3.2 Analysis o AF eco dings: 375"
Table 2 summa izes he esul s ob ained using he p oposed me hod du ing AF. No e ha LB 376"
and CAF complexi y le els we e only p esen a eco ding RA1. The global e o ob ained by 377"
e alua ing a o al o 28226 di e en LATs is -0.83 ± 6.02 ms co e ing almos he comple e 378"
MEA senso a ea (97.99 ± 7.66 %) ha ing high ag eemen wi h manual anno a ions indica ed 379"
by Spea man's
93.0=
s
and Lin's conco dance co ela ion ac o
90.0=
c
(
01.0<p
bo h). 380"
On he o he hand, he de ec ion pe o mance is also high wi h
80.97=Se
% and 381"
36.88=
+
P
%. The Bland-Al man analysis (Fig. 7( )) illus a es his ag eemen and shows a 382"
sligh end o he p oposed me hod owa ds o e -es ima ion o ea ly LATs and sub-383"
es ima ion o la e LATs (Pea son's
21.0=
,
01.0<p
). Rep esen a i e examples o 384"
ac i a ion map econs uc ion du ing AF a e shown in Fig. 5(c)-(g). 385"
Table 2 he e 386"
Table 2: De ec ion e o (mean ± SD), sensi i i y and posi i e p edic i e alue o compa ing 387"
es ima ed LATs wi h he manual e e ence pe AF eco ding a di e en le els o AF 388"
complexi y. N/A s ands o No Applicable. 389"
Figu e 7(a)-(e) shows indi idual LATs ag eemen analysis o each AF complexi y le el 390"
p oposed in his pape . A high le el o ag eemen is ound o SAFW, BT and AFWF. 391"
Howe e , LB and CAF show lowe le el o ag eemen (Fig. 7(d)-(e)). 392"
Figu e 7 he e 393"
20"
"
Fig. 7: Ag eemen e alua ion be ween e e ence and es ima ed LATs du ing AF a di e en 394"
complexi y le els including (a) SAFW, (b) BT, (c) AFWF, (d) LB (e) CAF and ( ) all LATs 395"
s udied in his wo k. In each pai o panels, le shows e e ence s. es ima ed LAT plo o 396"
Lin's conco dance co ela ion ac o
c
(pink line indica es he uni slope) and he igh panel 397"
shows Bland-Al man plo ( ed solid line indica es mean e o and ed dashed lines show 398"
mean ± 2SD o he e o ). 399"
3.3 The “loci maps”: 400"
Aside om he ac i a ion map econs uc ion, an in e es ing esul o he p oposed me hod is 401"
he es ima ion o he ac i a ion pa e n o igin
o a gi en 5×5 g oup o elec odes o he 402"
MEA senso . The e o e, cons uc ion o “loci maps” is possible by plo ing all es ima ed 403"
ocus loca ion
ac oss he MEA senso . Fig. 8 shows examples o hese loci maps om 404"
di e en ac i a ion pa e ns me ged wi h he ac i a ion map. No e ha loci maps spa ially 405"
ollow he po en ial ac i a ion wa e on e olu ion, p o iding ex a in o ma ion o 406"
complemen he ac i a ion map. 407"
Mo eo e , hese loci maps can show di e en wa e on beha iou and p ope ies, 408"
e.g., he numbe o wa e on s coming h ough he ca he e and hei di e en di ec ions (Fig. 409"
8(e)-( )), he cu ed wa e on s due o po en ial e-en an ci cui s (Fig. 8(b)) and e en issue 410"
aniso opy explained by small g oups o clus e s coming om he same place bu mo ing in o 411"
di e en di ec ions, p esumably ollowing he ca diac ib es o ien a ion (Fig. 8(a)). 412"
Figu e 8 he e 413"
Fig. 8: Examples o loci maps me ged wi h i s es ima ed ac i a ion map: (a) NSR, (b) ASR, 414"
(c) SAFW, (d) BT, (e) AFWF and ( ) LB. LATs a e colo -coded om ed (ea lies ) o pink 415"
(la es ) in 10 ms isoch ones. Elec odes a e shown as emp y ci cles and each ocus solu ion
416"
21"
"
is shown in black do s connec ed wi h he cen e elec ode o i s co esponding 5×5 g oup. 417"
Spa ial e e ence is shown wi h a c oss. 418"
4. Discussion: 419"
Assessing LATs o ac i a ion mapping du ing AF is a common ask o s udy and unde s and 420"
i s unde lying mechanisms [12]. Au oma ic LAT de ec ion du ing AF elies in he de ec o 421"
accu acy and o en equi es manual checking. Mo eo e , LAT de ec ion educes he 422"
ac i a ion in o ma ion o jus a bina y signal which akes alues whe he an ac i a ion is 423"
ound, ejec ing he emaining spa io empo al in o ma ion embedded in he mo phology and 424"
ime ela ion wi h adjacen elec odes. 425"
In his pape , an in eg a ed ac i a ion de ec ion scheme is p oposed, which akes 426"
bene i o he ela ion be ween u-EGMs, hence p o iding a spa io empo al de ec ion o 427"
ac i a ion maps in high-densi y eco dings using MEA senso s. The a ionale behind his 428"
echnique is ha i is possible o decompose a comple e (and complex) ac i a ion pa e n in o 429"
a combina ion o simple ac i a ion pa e ns i ed o small a eas o he MEA senso . The 430"
simples ac i a ion pa e n is concen ic and iso opic, hence only depends on he loca ion o 431"
he ac i a ion o igin and he issue conduc ion eloci y. 432"
The p ocess in oduces he pa ame e s o he ac i a ion pa e n in o a UDL model o 433"
he issue, de i ing he co esponding u-EGM signals. Model pa e n pa ame e s we e 434"
modi ied i e a i ely by compa ing he esul ing u-EGM signals agains he eco ded ones in 435"
o de o each a maximum o a cos unc ion ha akes in o accoun he signal shape 436"
simila i ies and synch oniza ion. Finally, he comple e ac i a ion map is econs uc ed by he 437"
weigh ed a e age o all solu ions ob ained by unning his i e a i e p ocess o e he comple e 438"
MEA senso . 439"
22"
"
Mapping pe o mance has been e alua ed by compa ing he es ima ed LATs wi h 440"
hose ob ained manually by an expe elec ophysiologis in eco dings du ing SR and AF. 441"
Addi ionally, ac i a ion maps we e s udied and classi ied based in a complexi y scale, hence 442"
p o iding a mo e comple e iew o he me hod's beha iou and use ulness. Mo eo e , he 443"
complexi y classi ica ion used in his wo k is simila o hose ac i a ion modes ecen ly 444"
iden i ied by Kuklik and co-wo ke s in an hype ensi e sheep ca diac model [30]. 445"
Du ing SR eco dings, he ag eemen be ween manual and es ima ed LATs was 446"
p o ed o be e y high. The e o was -0.66 ± 2.00 ms wi h e y high Spea man's co ela ion 447"
and Lin's conco dance co ela ion ac o (
98.0=
s
and
98.0=
c
,
01.0<p
bo h). An 448"
excep ional si ua ion was ound in hose eco dings du ing SR. The c anial loca ion o he 449"
MEA senso o e he igh a ium (RA4 eco ding) shows ull abno mal a ial ac i i y du ing 450"
SR. This ac i i y sugges s he p esence o a e-en an ci cui , desc ibed by he p oposed 451"
me hod, as illus a ed in Fig. 5(b). Mo eo e , he no el p oposed loci maps show po en ial 452"
ajec o y o he ac i a ion wa e on e olu ion, sugges ing he p esence o a cu ed 453"
wa e on due o a unc ional e-en y p esen du ing SR (see Fig. 8(b)). 454"
Du ing AF eco dings, he LAT es ima ion e o was o -0.83 ± 6.02 ms wi h high 455"
ag eemen wi h manual anno a ions (
93.0=
s
and
90.0=
c
,
01.0<p
bo h). This 456"
ag eemen is e en highe conside ing he SAFW, BT and AFWF maps solely, which 457"
co espond o he 93 % o he s udied maps. Howe e , much lesse ag eemen was ound in 458"
highe complexi y maps (LB and CAF). Ne e heless, in his s udy hose ypes o pa e ns 459"
we e poo ly ep esen ed in he a ailable da a (only a eco ding loca ion RA1), limi ing he 460"
conclusions ha can be ob ained om hose classes. 461"
23"
"
Compa ing he mean e o in LAT es ima ion wi h he s anda d e o o he mean, o 462"
each a ial hy hm and a ial loca ion, i is shown ha he p oposed me hod p esen s a 463"
s a is ically signi ican bias. Howe e , in 80 % o SR maps and 66 % o AF maps, his bias is 464"
below one sampling in e al and in 100 % o SR maps and 89 % o AF maps his bias is 465"
below wo sampling in e als. Mo eo e , i mus be no ed ha ha ing a sys ema ic bias is no 466"
c ucial in ac i a ion mapping, whe e s abili y be ween he measu emen s a di e en si es is 467"
pu sued. This is quan i ied by he e o s anda d de ia ion and he co ela ion wi h he 468"
e e ence anno a ions. 469"
The p oposed algo i hm p o ides smoo he and mo e comp ehensi e ac i a ion maps 470"
han hose ob ained manually as illus a ed by Fig. 5. This ac is in conco dance wi h he 471"
smoo hing na u e o he weigh ed a e age p ocess o econs uc ing he inal ac i a ion maps. 472"
Addi ionally, he modelled ac i a ion pa e n used o LAT es ima ion also con ibu es o his 473"
smoo hness. As an addi ional ou come o he i e a i e p ocess, he loci maps appea o be an 474"
in e es ing ool o assessing he ac i a ion beha iou and ack he wa e on e olu ion in he 475"
ac i a ion map unde analysis. The p esen ed algo i hm o ac i a ion map and loci map 476"
es ima ion was possible due o he i e a i e p ocess and he small compu a ion imes o he 477"
solid angle and UDL app oaches, in con as o he high compu a ion imes o mo e classic 478"
and de ailed issue simula ion app oaches [17]. Howe e , he p oposed me hod needs manual 479"
assis ance o selec he ime in e al o analyse he ac i a ion map; he e o e, he p esen ed 480"
me hod is a semi-au oma ic app oach. 481"
The iso opic concen ic ac i a ion model used in his wo k assumes he p esence o a 482"
single wa e on a he ime o mapping wi hin each 5x5 senso s analysis mask. This 483"
assump ion is no always accomplished and may be he eason behind he lowe pe o mance 484"
obse ed in he mo e complex AF ac i i y le els. Small lines o block o high equency 485"
24"
"
(sho wa eleng h) a ial ac i i y may yield in poo es ima ion o he issue conduc ion 486"
eloci y o small alues o he cos unc ion due o he impossibili y o he ac i a ion pa e n 487"
o model he unde lying ac i a ion beha iou . One possible solu ion is o selec a smalle 488"
g oup o elec odes. Reducing he analysis mask size may allow o be e es ima e ac i a ions 489"
unde hose si ua ions bu also u ns in o a limi a ion because es ima ion o issue conduc ion 490"
eloci y could be less accu a e and/o less obus o da a acquisi ion e o s (i.e., non-con ac 491"
o elec odes) and noise. 492"
Ano he limi a ion is ela ed o he s udied da abase. Only one se o loca ions coming om 493"
he same pa ien ha e been s udied. I mus be no ed he singula i y o he da a used in his wo k, as 494"
epica dial high-densi y mapping is no pe o med du ing ou ine clinical in e en ions. Addi ionally, i 495"
mus be no ed also he ac ha manual anno a ions and/o checking du ing AF o 124 channels is a 496"
high ime-consuming ask. The e o e, hese cons ain he da abase size o his s udy. Howe e , mo e 497"
han 30000 LATs combining SR and AF eco dings wi h e y di e en p opaga ion pa e ns we e 498"
s udied in his wo k, hus making a high amoun o measu emen s o e alua ing he p oposed 499"
me hodology. Ne e heless, ex ension o his wo k o mo e pa ien s and mo e a ial loca ions is 500"
needed be o e clinical usage, especially including hose le a ial loca ions whe e mo e complex 501"
ac i i y can be expec ed. 502"
5. Conclusion: 503"
This pape p esen s an in eg a ed spa io empo al de ec ion app oach ha allows o ob ain 504"
smoo h and comp ehensi e high-densi y ac i a ion maps and o ack he unde lying 505"
wa e on e olu ion. Simpli ied, bu explica i e enough, ac i a ion pa e n and issue models 506"
a e used in o de o gene a e u-EGM signals ha esemble he measu ed ac i a ion map using 507"
an i e a i e p ocess. Resul s indica e high accu acy o he p oposed me hod compa ed agains 508"
audi ed anno a ions du ing SR and AF. The e o e, al hough his wo k uses in asi e da a, i 509"
25"
"
opens he possibili y o s udying high-densi y ac i a ions maps wi h obus ou comes and he 510"
de elopmen o minimally in asi e epica dial high-densi y mapping. 511"
Acknowledgemen s: 512"
This wo k is suppo ed by pe sonal g an s o A.A. e s.: BES-2011-046644 and EEBB-I-13-513"
06613, by p ojec TEC2013-42140-R om Minis e io de Economía y Compe i i idad. Also 514"
by A agón Go e nmen (Spain) and Eu opean Social Fund (EU) h ough G upo Consolidado 515"
BSICoS e .: T96 and by CIBER in Bioenginee ing, Bioma e ials & Nanomedicine (CIBER-516"
BBN) h ough Ins i u o de Salud Ca los III."The compu a ion was pe o med by he ICTS 517"
0707NAN-BIOSIS, by he High Pe o mance Compu ing Uni o he CIBER in 518"
Bioenginee ing, Bioma e ials & Nanomedicine (CIBER-BBN) a he Uni e si y o Za agoza 519"
Re e ences: 520"
[1] V. Fus e , L.E. Rydén, D.S. Cannom, H.J.G.M. C ijns, A.B. Cu is, K.A. Ellenbogen, 521"
e al., ACC/AHA/ESC 2006 Guidelines o he Managemen o Pa ien s wi h A ial 522"
Fib illa ion, J. Am. Coll. Ca diol. 48 (2006) e149–e246. 523"
[2] J. F ibe g, B. Pe nille, H. Scha ling, N. Gadsbøll, G.B. Jensen, Rising Ra es o 524"
Hospi al Admissions o A ial Fib illa ion, Epidemiology. 14 (2003) 666–672. 525"
[3] D. Moza a ian, E.J. Benjamin, A.S. Go, D.K. A ne , M.J. Blaha, M. Cushman, e al., 526"
Hea Disease and S oke S a is ics - 2015 Upda e: A Repo F om he Ame ican Hea 527"
Associa ion, Ci cula ion. 131 (2015) e29–e322. 528"
[4] G.K. Moe, J.A. Abildsko , A ial Fib illa ion as a Sel -Sus aining A hy hmia 529"
Independen o Focal Discha ge, Am. Hea J. 58 (1959) 59–70. 530"
[5] M.A. Allessie, W.J.E.P. Lamme s, F.I.M. Bonke, J. Hollen, Expe imen al E alua ion 531"
o Moe’s Mul iple Wa ele Hypo hesis o A ial Fib illa ion, in: D.P. Zipes, J. Jali e 532"
32"
"
is shown in black do s connec ed wi h he cen e elec ode o i s co esponding 5×5 g oup. 649"
Spa ial e e ence is shown wi h a c oss. 650"
651"
33"
"
Figu es 652"
Figu e 1: 653"
Au ho : Alcaine e al.(Single Column, Black and whi e) 654"
655"
656"
34"
"
Figu e 2: 657"
Au ho : Alcaine e al. (Single Column, Black and whi e) 658"
659"
660"
35"
"
Figu e 3: 661"
Au ho : Alcaine e al. (Single Column, Black and whi e) 662"
663"
664"
36"
"
Figu e 4: 665"
Au ho : Alcaine e al. (Double Column, Black and whi e) 666"
667"
668"
37"
"
Figu e 5: 669"
Au ho : Alcaine e al. (Double Column, Colou igu e on-line) 670"
671"
672"
38"
"
Figu e 6: 673"
Au ho : Alcaine e al. (Single Column, Colou igu e on-line) 674"
675"
676"
39"
"
Figu e 7: 677"
Au ho : Alcaine e al. (Double Column, Colou igu e on-line) 678"
679"
680"
40"
"
Figu e 8: 681"
Au ho : Alcaine e al. (Double Column, Colou igu e on-line) 682"
683"
684"
41"
"
Tables: 685"
Table 1: De ec ion e o (mean ± SD), sensi i i y and posi i e p edic i e alue o compa ing 686"
es ima ed LATs wi h he manual e e ence in SR eco dings. N/A s ands o No Applicable. 687"
Loc.
Maps
(#)
LATs
(#)
A ea
(%)
E o
(ms)
NSR
(#)
ASR
(#)
s
c
Se
(%)
+
P
(%)
RA1
6
744
100
-0.82 ± 1.41
6
N/A
0.99*
0.99*
100
98.66
RA2
6
744
100
-0.78 ± 0.92
6
N/A
~1*
0.99*
100
100
RA3
6
744
100
-0.44 ± 0.76
6
N/A
~1*
~1*
100
100
RA4
7
868
100
-0.62 ± 3.36
N/A
7
0.97*
0.97*
100
93.43
To al
25
3100
100
-0.66 ± 2.00
18
7
0.98*
0.98*
100
97.84
* indica es a
p
- alue < 0.01. 688"
689"
