Rela ionship Be ween A ial Oscilla o y Ace ylcholine Release Pa e n and
-wa e F equency Modula ion: a Compu a ional and Expe imen al S udy
Chia a Celo o1,2, Ca los S´
anchez1,2,3, Kons an inos A. Moun is1,2, Mos a a Abdollahpu 4, F ida
Sandbe g4, Pablo Laguna1,2, Es he Pueyo1,2
1A agon Ins i u e o Enginee ing Resea ch, Uni e si y o Za agoza, Spain
2CIBER in Bioenginee ing, Bioma e ials and Nanomedicine, Za agoza, Spain
3De ence Uni e si y Cen e, Gene al Mili a y Academy, Za agoza, Spain
4Uni e si y o Lund, Lund, Sweden
Abs ac
The equency o ib illa o y wa es ( -wa es), F , ex-
hibi s signi ican a ia ion o e ime, and p e ious s udies
sugges ha some o his a ia ion is ela ed o espi a o y
modula ion h ough he au onomic ne ous sys em. In his
s udy, we es ed he hypo hesis ha his a ia ion (∆F )
could be ela ed o ace ylcholine concen a ion ([ACh]) e-
lease pa e n.
Elec oca diog ams we e eco ded om se en pa ien s
du ing con olled espi a ion be o e and a e ull agal
blockade, om which -wa e equency modula ion was
cha ac e ized. Compu a ional simula ions in human a ial
issues we e pe o med o assess he e ec s o [ACh] e-
lease pa e n on F and compa ed o expe imen al e-
sul s in humans. A c oss-s imula ion p o ocol was applied
on o he issue o ini ia e a o o while cyclically a ying
[ACh] ollowing a sinusoidal wa e o m o equency equal
o 0.125 Hz. Di e en mean le els (0.05, 0.075 µM/l) and
peak- o-peak anges (0.1, 0.05, 0.025 µM/l) o [ACh] a i-
a ion we e es ed.
In all pa ien s, an -wa e equency modula ion could be
obse ed. In 57% o he pa ien s, his modula ion was sig-
ni ican ly educed a e agal blockade. Simula ions con-
i med ha o o equency a ia ions ollowed he induced
[ACh] pa e ns. Mean F was dependen on mean [ACh]
le el, while ∆F was dependen on [ACh] a ia ion ange.
1. In oduc ion
The au onomic ne ous sys em (ANS) plays a majo
ole in he genesis and main enance o a ial ib illa ion
(AF). S imula ion o he agus ne e and, on he con a y,
agal dene a ion ha e been p o en o espec i ely acili-
a e and supp ess AF [1]. Fu he mo e, agal s imula ion,
by sho ening AF cycle leng h, has been pos ula ed o in-
c ease he le a ial mean dominan equency [1]. The
pa asympa he ic neu o ansmi e ace ylcholine (ACh), in
ac , sho ens ac ion po en ial (AP) du a ion (APD) and
hype pola izes he es ing memb ane po en ial (RMP) in
a dose dependen manne . Hype pola iza ion o he RMP
b ings o a educ ion in he maximum ups oke eloci y
(UV) o he AP [2], which can slow conduc ion eloci y
(CV). These e ec s acili a e AF by sho ening he wa e-
leng h o een y (WL), which is de ined as he dis ance
a eled by he depola iza ion wa e du ing he e ec i e e-
ac o y pe iod (ERP) and is compu ed as CV imes ERP.
In AF pa ien s, he dominan -wa e equency (F ) ex-
hibi s signi ican a ia ion o e ime and p e ious s udies
ha e sugges ed ha his a ia ion is ela ed o espi a o y
modula ion h ough he pa asympa he ic ne ous sys em
[3,4]. In ou s udy, we es ed he hypo hesis ha such a i-
a ion could be ela ed o he elease pa e n o ACh o e
ime.
We i s analyzed clinical da a om se en ch onic AF
(cAF) pa ien s, om which elec oca diog ams (ECGs)
we e eco ded du ing baseline and con olled espi a ion,
be o e and a e ull agal blockade by a opine injec ion.
Nex , we pe o med in silico modeling and simula ion o
wo-dimensional cAF human a ial issues o assess he e -
ec s o ACh concen a ion ([ACh]) pa e n on F . The
ad an age o his in silico app oach, a e con i ma ion o
ag eemen wi h clinical ou comes, is ha i allows dissec -
ing he in luence o ACh elease on -wa e equency mod-
ula ion independen ly o o he ac o s.
2. Me hods
2.1. Clinical eco dings
A g oup o se en pa ien s wi h cAF, a io en icula
block III and a pe manen pacemake we e s udied o
in es iga e modula ion o F by espi a ion h ough he
pa asympa he ic sys em. The o iginal s udy [4] included
Compu ing in Ca diology 2020; Vol 47 Page 1 ISSN: 2325-887X DOI: 10.22489/CinC.2020.303
Table 1. F and ∆F in simula ions and eal cases
SIMULATIONS EXPERIMENTS
[ACh] elease 0.125 Hz Range (peak o peak) o [ACh] Mean alues
om pa ien sMean ACh 0.0 0.025 0.05 0.1
0.05 µM/l
F 7.51 7.47 7.46 7.25 F
σ
6.82
0.59
∆F 0.02 0.18 0.44 1.21
0.83 0.94 0.95
0.075 µM/l
F 7.99 7.97 7.97 no es ed: ∆F
σ
0.15
0.01
∆F 0.02 0.14 0.35 ou o
0.88 0.95 physiol. ange
eigh pa ien s, bu he -wa e signal quali y was su icien
o analysis o espi a o y modula ion in only se en o
hese [5]. ECGs we e eco ded a es du ing baseline, du -
ing 0.125 Hz equency con olled espi a ion and du ing
con olled espi a ion a e ull agal blockade by a opine
injec ion [4].
2.2. A ial issue models
Human a ial elec ical ac i i y was simula ed in wo-
dimensional 7-by-7 cm shee s o issue. A di usion coe -
icien o 0.002 cm2/ms and a ans e sal- o-longi udinal
di usion a io o 0.5 we e conside ed. This co esponds o
a longi udinal conduc ion eloci y o 44.0 cm/s o a plana
wa e, in ag eemen wi h alues epo ed o AF pa ien s in
p e ious s udies [6].
The Cou emanche human a ial AP model was used o
ep esen cellula elec ophysiology [7]. Pa asympa he ic
e ec s we e inco po a ed in o he model by including an
ACh-ac i a ed po assium cu en , IKACh, as de ined in [8]
wi h he upda es p oposed in [6].
Elec ical emodeling associa ed wi h cAF was ac-
coun ed o by educing he maximal conduc ances o I o,
ICaL and Iku by 50%, 70% and 50%, espec i ely, as in
[9]. Rega ding cAF-induced s uc u al emodeling, a i-
ous s udies ha e epo ed pe cen ages o a ial di use i-
b osis up o 40%, wi h a mean epo ed pe cen age o ap-
p oxima ely 20% [10]. To simula e 20% di use ib osis,
20% o nodes we e andomly selec ed and assigned wi h
he MacCannell model [11], an ac i e ib oblas model ha
includes ou memb ane ionic cu en s. Myocy es we e
elec ically coupled o ib oblas s wi h a gap junc ional di -
usion coe icien o 0.0005 cm2/ms.
2.3. Simula ed ACh elease pa e ns
ACh was applied homogeneously in space while cycli-
cally a ying in ime ollowing a sinusoidal wa e o m o
equency equal o he 0.125 Hz espi a o y equency.
Di e en mean le els (0.05, 0.075 µM/l) and peak- o-peak
a ia ion anges (0.1, 0.05, 0.025 µM/l) o [ACh] we e
es ed, all wi hin epo ed physiological anges (0 - 0.1
µM/l) [12].
2.4. Nume ical me hods and simula ions
Simula ions we e un using ELECTRA, an in-house
so wa e ha implemen s he Fini e Elemen and he Mesh-
ee Mixed Colloca ion me hods o sol e he monodomain
model. In his wo k, we used he Fini e Elemen imple-
men a ion. An adap i e ime s ep anging om 0.05 o
0.005 ms and a space s ep o 0.02 cm we e conside ed.
Single cells we e paced a a ixed cycle leng h (CL) o 1000
ms o 1 minu e o each s eady-s a e. The s eady-s a e al-
ues o he cellula models’ s a e a iables we e used o
ini ializa ion o issue models. A c oss-s imula ion p o o-
col was applied on o he issue o ini ia e a o o : a i s
s imulus was applied a he bo om edge o he issue and a
second s imulus was applied on o a 3.5 by 3.5 cm squa e a
he bo om igh co ne . The simula ion ime in a ial is-
sues was 10 s. Fig. 1 illus a es ol age maps a di e en
ime ins an s.
2.5. Dominan equency cha ac e iza ion
F om he clinical ECGs, he -wa e signal was ob ained
by applying spa io empo al QRST cancella ion and F
end was es ima ed using a model-based app oach. F
was compu ed as he a e age alue o F , while ∆F , he
magni ude o -wa e equency modula ion, was compu ed
as he median o he uppe en elope o he bandpass il-
e ed F signal [5].
F om he simula ions, he ol age ime se ies om 49
e enly sampled poin s ac oss he issue (black do s in
Fig.1) we e analyzed. A comple e 8-second espi a o y pe-
iod ( om seconds 1 o 9) was conside ed. The 8-second
ol age se ies o one o he 49 poin s is illus a ed in Fig.
2 (a). Fo each o he 49 poin s in he issue, he ime in-
s an maxUV,i co esponden o he maximum UV o bea
iwas de e mined (Fig. 2 (b)) and he ins an aneous e-
quency was compu ed as 1/( maxUV,i+1- maxUV,i) (Fig. 2 (c)),
o all bea indices iin he eco ding. Nex , a e aging (in
Page 2
Figu e 1. Vol age maps a di e en ime ins an s o [ACh] a ying a ound 0.05 µM/l wi h peak- o-peak ange o 0.1 µM/l.
A 180 ms he second s imulus applied on o he bo om- igh co ne o he issue is isible. The 49 black do s in each
snapsho ep esen he poin s used in he compu a ion o F .
Figu e 2. a) Vol age ime se ies o one poin in he issue (poin 12 ou o he 49 poin s in Fig. 1 s a ing om bo om le
and mo ing igh /up) (blue line) in ela ion o [ACh] empo al a ia ion ( ed line). b) Iden i ica ion o he ime ins an s o
maximum AP ups oke eloci y o he same indi idual spa ial poin . c) Ins an aneous equency o he same indi idual
spa ial poin (blue line) in ela ion o [ACh] a ia ion ( ed line). d) Ins an aneous equencies compu ed o all spa ial poin s
in he issue a e emo al o hose co esponden o he o o co e. e) Time se ies o he dominan equency o he issue,
F , ob ained by spa ial immed a e aging (blue line) in ela ion o [ACh] a ia ion ( ed line).
space) was pe o med o compu e he issue dominan e-
quency F along ime. Speci ically, F was compu ed as a
immed mean o he ins an aneous equencies o e he 49
poin s, disca ding he 5% ex emes o exclude he chao ic
signals ypically co esponding o he o o co e (Fig. 2 (d)
and (e)). F and ∆F we e ob ained om he es ima ed F
ime se ies using he same me hod as o he clinical sig-
nals.
3. Resul s
In all pa ien s’ ECGs, an -wa e equency modula ion
was obse ed. In 57% o he pa ien s, his modula ion
was signi ican ly educed a e he injec ion o a opine.
Mean esul s o e pa ien s in e ms o mean dominan e-
quency F , magni ude o modula ion ∆F and s anda d
de ia ion σa e epo ed in Table 1. Simula ion esul s con-
i med ha he o o equency a ia ions ollowed he in-
duced [ACh] pa e ns (Fig. 3), wi h co ela ion coe icien
abo e 0.83 in all cases, as epo ed in Table 1. Fu he -
mo e, inc eases wi h he mean le el and he a ia ion
ange o [ACh] since he dominance o he phenomenon
inc eases wi h inc easing [ACh]. The mean dominan e-
quency F was ound o be dependen on he mean [ACh]
le el, while i s peak- o-peak a ia ion ∆F was dependen
Page 3
on he [ACh] a ia ion ange, wi h inc eases in mean and
ange o [ACh] leading o inc eases in F and ∆F , espec-
i ely. An [ACh] empo al a ia ion o 0.05 µM/l mean
alue and 0.025 µM/l peak- o-peak ange equal was he
one p o iding esul s close o hose measu ed om he
pa ien s.
Figu e 3. F (blue) and [ACh] ( ed) o mean [ACh] o
0.05 µM/l (a) and 0.075 µM/l (b). Dashed/solid/do ed
lines ep esen 0.025/0.05/0.1 µM/l [ACh] a ia ion
anges. In panel (b) he maximum [ACh] a ia ion ange
o 0.1 µM/l is no ep esen ed since i is ou o he physio-
logical ange.
4. Conclusions
The pa e n o [ACh] elease could be an impo an ac-
o in ol ed in -wa e equency modula ion. Fu he s ud-
ies will help o elucida e he con ibu ion o o he ac o s
and o asce ain whe he [ACh] a ia ions could be moni-
o ed om -wa e analysis.
Acknowledgmen s
This wo k was suppo ed by he Eu opean Resea ch
Council h ough g an ERC-S G 638284, EU H2020 Ma ie
Skłodowska-Cu ie ITN g an No.766082 MY-ATRIA, by
MICINN (Spain) h ough p ojec s PID2019-105674RB-
I00 and PID2019-104881RB-I00 and by Gobie no de
A ag´
on h ough p ojec LMP124-18 and Re e ence G oup
BSICoS T39-20R co unded by FEDER 2014-2020. Com-
pu a ions we e pe o med by ICTS NANBIOSIS (HPC
Uni a Uni e si y o Za agoza).
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Add ess o co espondence:
Chia a Celo o
Uni e sidad de Za agoza, Campus R´
ıo Eb o, Edi .I+D, C/ Poe a
Ma iano Esquillo , s/n, 50018 Za agoza
chia acelo o@uniza .es
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