DOI: 10.1161/CIRCEP.114.002661
Cardiac Response to Low Energy Field Pacing Challenges the
Standard Theory of Defibrillation
Running title: Caldwell et al.; Cardiac response to electrical field pacing
Bryan J. Caldwell, PhD1,3; Mark L. Trew, PhD2; Arkady M. Pertsov, PhD1
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
1
SUNY
NY
YU
Upstate
p ta
ps
t tee Medical
Medical University, Syracuse,
Syrac
acus
ac
u e, NY;
NY 2Auckla
Auckland
A
kland
nd Bioengineering
Bi
i
i
te, Auckland,
te
Aucklandd, New
New Ze
Z
a an
al
and; 3C
Current
urrrentt A
Address:
ddr
dresss: Institute
Inst
s ituutee forr T
st
Translational
ran
ansslattio
an
iona
nall Sc
na
S
Sciences,
iennce
ie
Institute,
Zealand;
UTMB,
UTMB
UT
B, Ga
G
Galveston,
l es
lv
e to
on,
n TX
TX
Correspondence:
Mark L. Trew, PhD
Auckland Bioengineering Institute
The University of Auckland
Private Bag 92019
Auckland 1142
New Zealand
Tel: +64 9 923 5114
Fax: +64 9 367 7157
E-mail: [email protected]
Journal Subject Codes: [104] Structure, [106] Electrophysiology, [157] Quantitative modeling
1
DOI: 10.1161/CIRCEP.114.002661
Abstract:
Background - The electrical response of myocardial tissue to periodic field stimuli has attracted
significant attention as the basis for low-energy anti-fibrillation pacing (LEAP), potentially more
effective than traditional single high-energy shocks. In conventional models, an electric field
produces a highly non-uniform response of the myocardial wall, with discrete excitations, or “hot
spots” (HS), occurring at cathodal tissue surfaces or large coronary vessels. We test this
prediction using novel 3D tomographic optical imaging.
Methods and Results - Experiments were performed in isolated coronary perfused pig
ventricular wall preparations stained with near-infrared voltage-sensitive fluorescent dye
y DI-4Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
ANBDQBS. The 3D coordinates of HS were determined using alternating
transillumination.
attin
ingg tr
tran
ansi
an
sill
si
llum
ll
umin
um
in
nattion
ion To
relate HS formation with myocardial structures we used ultra-deep confocal
imaging
nfocaal im
imag
agin
ag
ingg
in
(interrogation
distribution
wall
i n depths
ion
dep
e th
hs >4
> mm).
mm). The peak HS distribu
buti
bu
tion is locatedd deep
ti
ep inside the heart wa
a and
the depth iss not
Wee di
strong
noot significantly
significa
canttly
ca
y affected
aff
ffec
ff
ecte
ec
tedd by field
te
fie
ielld polarity.
pollaritty. W
ddid
d not
not observe
obbseervve th
thee st
stro
rong
ongg cocolocalizationn of
of HS
H with
wiith
t major
ma r coronary
coroona
nary
y vessels
v ss
ve
ssel
e s anticipated
annticcip
patted from
frroom theory.
th
heory
ry. Yet,
Y t,
Ye
t wee observed
obseerved
ob
ed
considerable
lateral
displacement
field
polarity
Models
that
deemphasized
l la
le
ateeral di
disp
splace
sp
ceme
ce
m nt of HS with fi
fiel
e d po
pola
larity
y rreversal.
eversal. Mo
M
dels
lss tha
haat deemph
p as
lateral intracellular
resistive
a llular coupling
acel
coup
upli
up
lingg and
li
andd accounted
accountted
d ffor
or resi
istiv
i e he
hheterogeneity
t roge
te
g ne
n it
i y in
n the
the extracellular
extraceelllullar sspace
showed similar
milar
m
ilar
il
ar HS
HS distributions
disttribu
riibuti
t ons
onns to
to the
thhee experimental
exp
xper
erim
imen
enta
t l observations.
ta
obbse
serv
rvat
atio
at
i ns
io
ns..
Conclusions - The HS distributions within the myocardial wall and the significant lateral
displacements with field polarity reversal are inconsistent with standard theories of defibrillation.
Extended theories based around enhanced descriptions of cellular scale electrical mechanisms
may be necessary. The considerable lateral displacement of HS with field polarity reversal
supports the hypothesis of biphasic stimuli in LEAP being advantageous.
Key words: optical imaging, pacing, myocardial structure, modeling, field stimuli
2
DOI: 10.1161/CIRCEP.114.002661
Introduction
The response of heart tissue to low-energy electrical field stimuli has attracted significant interest
in the search for alternative, more efficient therapies against life-threatening cardiac
arrhythmias.1, 2 While conventional high-energy shocks restore orderly cardiac contractions by
resetting irregular electrical activity of cardiac myocytes, low-energy shocks can also be used to
achieve a similar result. Commonly referred to as low-energy anti-fibrillation pacing (LEAP),
these produce multiple simultaneously firing excitation centers, or “hot spots” (HS), which
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
gradually take control over the entire heart until it beats normally.3, 4
Understanding the nature of HS and their connection with the anatom
anatomical
omic
icall oorganization
rg
gan
aniz
izaati
iz
ati of
tis
issu
ssuue iss critical
cri
r tiica
cal for understanding the de
defi
f brillation me
fi
m
ch
han
anisms and efficacy of
o
myocardiall tissue
defibrillation
mechanisms
LEAP. There
ere is a consen
er
consensus
nsuus th
that H
HS
S gene
generated
n raated by
y low
low-energy
ow-en
nerrggyy el
electrical
lecctrica
cal fi
field
iel
e d st
stimuli
tim
i ulii repr
represent
press
pr
t max
th
axim
ax
imum memb
im
brane de
dep
po izaati
polari
tion
ion.3 Ac
According
A
cord
rdiing
rd
ing to ttheory,
heory,55,, 6 th
he
thee majo
majority
j riity
t off H
HS
regions with
maximum
membrane
depolarization.
should emerge
e ge at the
erg
h tissue
tiissuue surface
surfface nearest the
th
he negative
nega
g tive
i field
fiield
ld electrode
ellectr
trrodde (cathode)
( atho
(c
th de) an
and
nd mi
m
migrate
igr
g a to
77-9
9
the opposite
polarity.
ttee surface
s rface
fa with
ith
ith changing
ch
h gii fi
field
eld
ld polarit
larit
it 33,, 7Alternative
Alternati
Alt
Al
te ati
ti e llocalizations
locali
o li ations
ti
off HS
HS predicted
predic
edi
dic
by models are the cathodal boundaries of major coronary vessels,1-3, 10 with migration to the
opposite side of the vessel with changing field polarity.
Here we test these predictions in the intact pig ventricular wall using a novel tomographic
optical imaging technique, enabling 3D localization of HS during field stimulations while
preserving tissue integrity. Near-threshold field pacing of quiescent tissue is used to ensure a
small number of solitary HS form that do not coalesce into regional activation, masking the onset
and location of local activation. In this lowest energy field, HS will form only on the largest
discontinuities. To establish the anatomical correlation between HS and myocardial vasculature,
the macroscopic functional imaging was complemented with ultra-deep 3D confocal imaging.
3
DOI: 10.1161/CIRCEP.114.002661
Methods
All data are expressed as mean ± SD.
Optical Fluorescence Imaging
All experimental protocols conformed to institutional and National Institutes of Health
guidelines. Seven right ventricular (RV) and three left ventricular (LV) pig preparations were
used in this study. The preparations were perfused through respective coronary arteries, mounted
between mesh field electrodes, and stained with the near-infrared dye DI-4-ANBDQBS (40 μM)
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
as described previously.11 Figure 1a shows a schematic of the experimental
mental setup
setup.
p. A pu
puls
pulsed
lsed
ls
e
ed
electric field was applied transmurally from planar mesh electrodes, sufficiently
ufficiien
entl
tly
tl
ly sp
spar
sparse
arse
s ffor
or
or
passage of both
bot
othh illumination
ot
illu
il
lu
umi
minaatiion light and voltage-sensitive
voltage-senssitiv
ittiv
i e fluorescence
fluorescen
nce signals.
signals. The field intensity
intee
was 3-5% aabove
bove the exci
bo
excitation
itaatio
on capture
capptu
ture tthreshold
hres
eshold (0.41
4 ± 0.31
0.31
.33 V/cm,
V//cm, 5 mss duration).
durattio
on)). The
Th
he
preparation
n wass co
cont
continually
n inuall
nt
lly paced
ll
pa
in the
the
he range
ran
nge
g 3358-508
58-5508 m
58
mss BC
BCL,
L w
with
i h both
it
both
h positive
positive andd negative
ne
field orientations.
tations. This
Thi produced
producedd 1-3
1 3 ddiscrete
1iscrete H
HS
S in
i the
h opt
optical
ptic
pt
i al viewing
vieewi
wing
ing frame,
frame, comm
commencing
men
encingg soon
after pulse ttermination
termination.
e inati
tion Hi
Higher
gh
h field
field
ld strengths
tr gth
ths make
ke HS llocalizations
locali
ali
li ati
ations
tio ambig
ambiguous
bi o s as the
the HS
HS form
at a range of discontinuity scales and they coalesce into regional activations. Control point
stimulation pacing was applied to the surfaces of two RV and one LV preparation. The 3D
optical imaging system has been described in full previously.12
To localize the HS in 3D, we used alternating transillumination with rapid switching of
the illumination from the epicardium (P) to endocardium (N) and syncronous recording using
two high-speed CCD cameras, labeled P and N, respectively. Camera recordings were
demultiplexed into four quasi-simultaneous movies: PP, PN, NP and NN. (The letters indicate
the position of the light source and the camera respectively). The HS depths from the epicardium
(Z) were determined by comparing integral intensities in PP, PN, NP, and NN images over the
4
DOI: 10.1161/CIRCEP.114.002661
areas containing the respective HS.
Structural Imaging
After HS detection experiments, four RV preparations (40 x 40 x 10 mm) were subjected to
ultra-deep confocal imaging using an optical clearing technique.13 Confocal imaging (Zeiss LSM
510 system, 10x objective) used the fluorescent properties of DI-4-ANBDQBS which remained
during the clearing process. The dye was excited at 633 nm and recorded using a 650-715 nm IR
bandpass filter. Voxel resolution was isotropic (32 or 83 μm).
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
Data Analysis
The coordinates of the earliest activation “hot-spots” (HS) were determined
mineed us
usin
using
ingg a pr
ppreviously
ev
vio
iou
1
m
thod
th
od.14
od
To
T
o ac
account for simultaneous m
multiple
ultiple sites off activation,
ul
acttiv
i ation, we adapted th
the
h
described meth
method.
original algorithm
gorithm
gor
oriithm by subdividing
or
subd
bdivid
idiing th
id
the
he op
optical
ptica
cal reco
recording
ordin
ing im
imag
images
agees into
ag
int
nto smaller
nt
sm
malle
leer re
regions
regi
giions
onss contain
ccontaining
onnt
ntain
only one source.
o e
ource.
Optical
t l reco
tical
recordings
rddin
ings
g were regi
gs
registered
gisttered
gi
d wi
with
ithh 2D
D surfa
surface
f ce iimages
mage
g s andd cconfocal
ge
onffocall ima
images
age
g s byy
matching structural
segmented
ttrr ctt rall llandmarks
andd rkk such
s ch
h as vessel
essel
ell bbranching
hi and
ndd ttrabeculae.
trabec
be llae
a V
Vessels
ls were
ere segm
from confocal images in LabVIEW© (National Instruments Inc.) and co-localized with the sites
of early activation in Voxx (Indiana University). The mean radius R of the three largest coronary
vessels was estimated by taking an axial line through three straight segments (~2 mm length) of
each vessel and sectioning the vessel normal to this line. R was estimated from the area of an
ellipse fitted to each cross-section using ImageJ and averaged across vessel cross-sections. The
minimum distance (d) of the HS to the surface of the three largest coronary vessels was
calculated using MATLAB (Mathworks).
Modeling
Computer modeling was used to interpret our experimental observations. We constructed a 15 ×
5
DOI: 10.1161/CIRCEP.114.002661
10 mm2 bidomain15 model of electrical activity in a cross-section of cardiac tissue surrounded on
two sides by a 5 mm bath. The electrical conductivities varied spatially in the tissue. Discrete
structural features at multiple scales were included in the model and are shown in Figure 2. Key
features distinct from previous models of field stimulation are discrete cell-scale lateral
discontinuities and boundary layers on extracellular conductivity transitions at myocardial edges.
The experimental electrical field stimulus was orthogonal to the epicardium (Fig. 1a), and
primarily oriented across the short axes of myocytes.16 Consequently, we assumed the
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
experimental problem could be modeled as a 2D curvilinear surface off cell cross–sectio
cross–sections
ons
orthogonal to the transmurally rotating myocyte long axis.16 This also
o miti
mitigated
tiiga
g te
tedd th
thee
o al complexity
ona
c mp
co
ple
lexity
ty of incorporating anisotropic
anisotro
opi
p c intracellular
intracellula
laar el
lectrical conductivity and
computational
electrical
variable cell
lll to
topology.
opology.
nsm
smuural ddimension
imension
i off ou
our 2D
Dm
oddell was ddivided
ivid
iv
id
ded iinto
nto three
nt
th st
tru
ructurall regions
regiion
Thee tran
transmural
model
structural
1
based on a visuall iinterpretation
nterppreetati
tion
i off th
the
he work
workk off P
Pope
ope
p et al.:
l 17
ssub-epicardium
ubb-eepi
p card
rddium (2
(25%),
25%
%),
) m
midwall
id
dwall
(50%) and ssub-endocardium
b endocardi
do rdi
di m (2
(25%
(25%).
(25%)
5%)) L
Laminar
in clefts
left
ft 7 iin the
th sub-epicardial
s b epicardial
ic diall and
ndd sub–endocardial
s b endocard
do rdd
regions are orthogonal to the epicardium, while those in the midwall region are at an angle of 70ͼ
to the epicardium (Fig. 2). The lengths of the laminar clefts were varied randomly. Lengths in the
sub-epicardium were 0.16 ± 0.016 mm, in the midwall 0.54 ± 0.23 mm and the sub-endocardium
0.11 ± 0.022 mm. The ratio of laminar cleft length to the end-to-end distance between the clefts
is 1:2 in the sub-epicardium and sub–endocardium regions and 1:3 in the midwall region. Two
vessels of diameter 1.2 mm, consistent with expected sizes,1 were placed in the sub-epicardium.
The vessels have a wall thickness of 0.04 mm.10 The model was discretized into finite volumes
of edge length 20 μm and solved using previously described techniques.15, 18
To construct cell-scale cross sections around the intramural features, transmural strips 60
6
DOI: 10.1161/CIRCEP.114.002661
μm apart and one finite volume wide were populated with a cell height varying randomly
between 40-80 μm. The cell strips were then grown volume-by-volume left and right until they
abutted with cells from adjacent strips (Fig. 2 – inset). Single finite volume holes between the
cells and the laminar clefts were assigned characteristics of connective tissue. The randomly
generated cell cross-sections were 3215.7 ± 1160.6 μm2 (8 ± 3 finite volumes); an approximation
of actual cardiac ventricular cell shapes.19
Membrane currents were modeled using a dynamic Luo-Rudy20 model with Rush-Larsen
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
approximations.21 The membrane capacitance was set to 0.01 μF/mm2 and the cell surfa
surface
faace tto
volume ratio for a typical problem varied spatially with cell discretization
tion as 2223
23 ± 112
2 mm--1.
n a- and
ntra
a d extra-cellular
an
e traa-ccellular conductivities were
ex
weere based on prev
e io
ous studies22 and were 0.15
Isotropic intraprevious
and 0.05 mS
m
mS/mm
S/mm respectively.
respecttiv
velyy. Thee bath
bathh and
an
nd perf
perfused
rffused
ed ves
vessel
esse
es
seel cconductivities
onndu
nductivi
vities
es were
ree assigned
asssiigneed a
typical value
ue fo
fforr Ty
Tyrodes solution
solu
l ti
tion
i off 2 mS/m
mS/mm,
/m
mm,
m, connective
connectiv
ivee tissue
iv
tisss
ti
ss e (including
ssue
(inclluddingg the
th interlamin
interlaminar
intterllamiin
2
clefts) 1 mS/mm
S
S/mm
and
d th
the
he vess
vessel
ell llumen
umen 0.0
0.01
01 mS
mS/mm.
S/mm.10 F
Following
olllowingg Krassowska
Krasssowskka & Neu
Neu23
a ce
celle
dimension boundary
bo
b
o ndar
da layer
lla er or ttransition
r siti
iti in
i extracellular
e ttracell
r ell
ll llar
a conductivity
cond
ndd cti
ti iitt was
as applied
lied
d att myocardium
m ocard
d
to non-myocardium (bath, vessels and laminar clefts) boundaries. A smooth extracellular
conductivity transition distance of 0.1 mm was used at the tissue-bath interface (Fig. 2 - inset)
and a transition distance of 0.04 mm was used at the tissue-laminar cleft interface. Consequently,
the extracellular conductivities through the myocardial region were highly heterogeneous.
Lateral cell-to-cell connectivity was modeled for the following cases: (a) fully connected cells
(standard model), (b) fully disconnected cells, (c) cells disconnected in the direction of the
electric field, and (d) cells disconnected in the direction orthogonal to the electric field. The fully
disconnected cells are influenced by the extracellular potential but do not directly interact with
each other.
7
DOI: 10.1161/CIRCEP.114.002661
The model was stimulated on the top and bottom edges using a 5 ms oriented field
stimulus (capture at 0.72 V/cm). Six structural model variations with differing discontinuities
were investigated. Three had different random distributions of cell-level cross-section areas and
shapes (Models 1-3), two had different proportional thickness of sub-endocardial region (Model
4 – 20%, Model 5 – 30%) and one had an alternative random distribution of midwall laminar
cleft lengths (Model 6).
Results
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
7-99
Our experiments show that HS do not cluster at surfaces, as predicted by
models,
b mo
mode
dels
de
ls,,7ls
butt are
bu
are
distributed across
ss tthe
h tthickness
he
hiick
ckness of the heart wall. Figu
Figure
gure 1b illustratess HS
gu
H in a RV preparati
preparation 22
ms after field
eld pulse termi
el
termination
m nati
mi
tiion w
tion
with
itth an
n eendocardial
ndoocarrdial catho
nd
cathode.
hode
ho
de. Th
de
The
he av
average
ver
eraagee wa
w
wall
ll tthickness
hick
hi
ck
kne
n ss
s (L
((L)
L of
this preparation
a ion w
ati
was
as 88.6
.66 ± 00.9
.99 m
mm.
m. T
Three
hrree
e H
HS
S (1
(1-3)
3 aare
3)
ree aapparent
ppar
pp
aren
ar
ent
en
nt in NN aand
nd NP
N iimages
m gees with
ma
with 1 and
2 bright in NN
faint
with
mm)) and
HS2
N and
and vvery
eryy fa
er
fain
intt in PP iimages.
in
mage
ges.
ge
s. This
Thi
h s iss consistent
connsiistten
nt wi
w
th
h HS1
HS11 (Z=5.5
(Z=5.
Z=5.
Z=
5.55 mm
m
an
nd H
(Z=5.2 mm)
m)) be
beingg cl
clos
closer
oser
e to
to the
the endocardial
e ddooca
en
card
rdia
rd
diall ((N)
N) th
than
a tthe
hhee eepicardial
ppi
pica
card
rddia
i l ((P)
P) su
surf
surface.
rffac
ace.
e. H
HS3
S33 ((Z=4.3
S
Z=4..3 mm)
is clearly visible in all four images indicating a midwall location. Figure 1c and 1d shows the
localization of HS with respect to coronary vessels and the endocardial surface for opposing field
polarities in a different RV preparation. With field reversal the HS depth and lateral locations
changed, but not toward the surfaces.
Figure 3a shows the depth distribution of HS in left and right ventricular wall
preparations (n = 10) for opposing field polarities. In all but three experiments (4/37 HS)
excitation emerged more than 3.2 mm from the cathodal surface; two standard deviations greater
than the detection algorithm error.14 To ensure the total lack of cathodal surface activation was
not an artifact of our depth detection algorithm, we applied a point stimulus directly onto the
surfaces using a unipolar electrode (Fig. 3a control). In these experiments, our algorithm
8
DOI: 10.1161/CIRCEP.114.002661
consistently detected the origin of excitation immediately under the stimulated surface (Z=1.2 ±
0.6 mm, Z/L = 11 ± 3%), providing a positive control.
For opposing field polarities, the distribution of HS depths (Fig. 3b) remains largely
unchanged with the maximum around Z/L = 50-70%. This is dramatically different from
predictions by a conventional bidomain model where cells are fully coupled as a functional
syncytium (Fig. 3c) and HS always form adjacent to the cathodal surface.
We also found, contrary to recent predictions,10 that the HS did not co-localize with the
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
largest coronary vessels. Models suggest that the relatively large spatial
al scale of coronary
coronaary vessels
v
should make them a main mediator of HS formation.1-3, 10 However, this
his was
was nnot
ott the
the
h case
casse in
in our
ts. Figures
Fig
i ur
ures
e 1c
es
1c and
an 1d show HS mapped on
onto 3D imagess of the
th vascular tree for bboth
experiments.
field polarities
itiess in one expe
it
experiment.
perime
ment. Re
R
Reversed
veers
r ed
d fiel
field
ld po
polarity
olaaritty ch
changes
han
ngees thee llocation
occattion ooff th
the
he HS
S ac
across
c
w
butt th
bu
they
y are nnot
ott co-loca
cali
ca
lizedd with
li
with maj
ajjor ve
ves
ssel
elss in
el
n eeither
itthe
h r case
e.
the heart wall,
co-localized
major
vessels
case.
To correl
correlate
late th
the
he lo
location
ocatiion off the
th
he HS
S with
wiithh the coronary
y vesse
vessels
els iin
n di
diff
different
f erent expe
ff
experiments,
experimen
peri
pe
r men we
ri
assessed the
hhee minimum
minim
iniim m distance
distta
off each
h HS ffrom th
the th
three llargest
a
t vessels
essels
ell ((Fig
(Fig.
Fi 44)
4).
) Th
The radii
diii of
di
the largest coronary vessels ranged in size from 0.2 - 1.5 mm. Figure 4 shows the results of this
analysis in four preparations with 3D vessel reconstructions. (A total of 21 HS for two field
polarities were evaluated). The majority of HS were located far away from the largest vessels,
with an average distance of 4.9 ± 1.8 mm. Those few HS with a minimum distance similar or
smaller than the lateral error (3 mm) of the periodic wave localization error,14 were still detached
from the vessel surface when the depth error bounds (1.3 mm) were taken into account as shown
in the projections of minimum distance, d, in Figure 4. This is further corroborated by significant
shifts of HS in the plane orthogonal to the field, following polarity reversal (Fig. 5). On average
the minimal lateral shift was 12.7 ± 10.7 mm. If vessels were a primary origin of the HS, we
9
DOI: 10.1161/CIRCEP.114.002661
would have observed a shift in the field direction only with practically no lateral displacement.10
Hence, it is unlikely that the large vessels have a significant effect on promoting HS formation.
Although the 3D co-localizations in Figure 4 show HS located near small vessels, the projections
of minimum distance, d, suggests this is not a causal link for the same reasons as the major
vessels.
The data of Figures 3 through 5 show significant discrepancies between our experimental
observations and the predictions of conventional bidomain models (Fig. 3c and references1-3,7-10)
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
for the depth distribution of the HS and the role of major coronary vessels.
sels. These discre
discrepancies
epa
pann
can be reconciled by accounting for the discontinuity at the cellular length
ngth scales.
scal
sc
alles
es. Such
S ch
Su
h
discontinuities
i es are
itie
are absent
ar
abssent
ab
ntt iin
n the conventional models
model
e s of cardiac exc
el
excitation
x itat
atio
at
i n and electrical
defibrillation
highly
coupled
and
on where
where cellss are
are hi
ighly
ly
y cou
upled
ed electrically
eleectriccallly an
nd ffunction
unncttion as a uunit
nit rrather
atheer than
at
an
individually.
y
y.
Wee developed
devellope
p d a mo
m
more
re detailed
detaiile
l d bidomain
bido
d maiin model
moddell which
whhich
h inclu
included
lu
ude
d d di
discon
discontinuities
tiinuiitie
iess aatt va
various
a
spatial scales
lles
es ((Fig
(Fig.
Fi 2):
2): (a)
(a)) cell-scale
cell
ll scale
le discontinuities,
ddiscontin
is nti
tin iities
ti (b)
(b) laminar
lamii
clefts
clleft
fts off both
both
th varying
ar iing llength
gth
th and
increased extracellular conductivity, that were oriented according to transmural location, and (c)
cell-scale extracellular conductivity boundary layers across transitions between the myocardium
and non-myocardium. These features, except for laminar clefts,7 have typically not been
incorporated in conventional activation models.
Figure 6a shows simulation results for geometric Model 1 where we assumed full lateral
coupling of cells (a standard defibrillation model or control). In this case, HS formed exclusively
under the cathodal surface and transitioned from one surface to another with the change of field
polarity. The situation changed dramatically when we included cell-scale uncoupling in the
transmural (field) direction (Fig. 6b). Similar to the experimental studies, HS are now mostly
10
DOI: 10.1161/CIRCEP.114.002661
distributed within the tissue. A change in field polarity produced a different distribution of HS,
which is consistent with the experimental observations. Finally, like in the experiments, HS do
not co-localize with large coronary vessels (large cicles) and show significant lateral
displacements. A similar result was obtained when we completely eliminated lateral coupling in
the intracellular domain (Fig. 6c). Note that the field activation threshold increased moving from
the fully coupled model (0.35 V/cm) to lateral uncoupling in the field direction (0.47 V/cm) to
the fully uncoupled model (0.72 V/cm). For completeness, we also considered the case of lateral
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
uncoupling orthogonal to the electric field (Fig. 6d). This case shared HS distribution
characteristics of both fully coupled and fully uncoupled cells, with HS
forming
S for
rmiing bboth
otth inn the
oth
the
he
midwall and
results
n on cathodal
nd
cat
atho
hoda
ho
d l tissue
t ssue and vessel surfacess ((Fig.
ti
F g. 6d). The resul
Fi
ultts shown in Figure 6
ul
suggest that
field
required
at att a minimum,
at
m lateral
laateeral uncoupling
uncouuplin
ing inn thee direction
direc
ecti
ec
tion
ti
on off the
th
he electric
eleectr
tric
tr
i fie
ic
eld
l iss a re
equui
feature for mode
model
consistency
observations.
dell co
de
consis
o i tencyy with tthe
h experimental
he
exper
errim
imen
e tall ob
bseerv
rvat
attio
atio
ionss.
Figure
summarizes
the
HS
perturbations
u 7 summar
ure
riz
izes th
he H
S di
ddistributions
striibutiions predicted
p edic
pr
di tedd ffrom
rom tthe
h six
he
ix
x ge
ggeometric
ometric
i pe
pert
r urbaa
rt
from the base
cell-scale
ase model,
model
dell bboth
oth
th with
iith
th cell
ell
ll scale
all lateral
latte l uncoupling
nco pling
li in
i the
th field
field
ld direction
di cti
tio (Figs.
((Figs
Fi 7a-c)
77aa and
lateral uncoupling in both directions (Figs. 7d-f). The combined HS distributions for both field
orientations are shown in Figures 7a and 7d. Predictions of HS distributions for the individual
models are shown in the Data Supplement. For all models, most HS form in the midwall. The
variation of HS with relative transmural distance from the epicardium is shown in Figures 7b and
7e. These figures are directly comparable to Figure 3a. Likewise, the histograms of depth
distributions in Figures 7c and 7f are directly comparable to Figure 3b. These data are consistent
with the experimental observations. Also noteworthy, Figure 7b (and the Data Supplement)
clearly shows that different HS distributions are excited for each field polarity. This is also
consistent with the experimental observations summarized in Figure 5.
11
DOI: 10.1161/CIRCEP.114.002661
The physical mechanisms that made aspects of these models consistent with the
experimental observations were as follows. Lateral cell uncoupling emphasized cell-scale
discontinuities. This shifted the length scales driving the intra- and extracellular current
redistributions responsible for HS formation away from the tissue surfaces and the laminar clefts.
Under this condition any intramural region is as likely as any other to be a HS.
The simulations with lateral cell uncoupling alone (not shown), gave unrealistically high
excitation thresholds as the imposed field gradient had to depolarize membranes of cell-scale
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
dimension. The incorporation of extracellular resistive heterogeneities increased localiz
localized
zed
potential gradients and reduced the field threshold for HS formation in
model
n the mo
mode
dell to
to 00.47
.447 V/cm
V
for lateral unco
V/cm
lateral
uuncoupling
coup
co
u li
up
ling
n in the
ng
th
he field direction and 0.722 V
/cm for late
eral un
uuncoupling
coupling in both
directions. Both
comparable
mean
threshold
V/cm
Bo of these are
are co
omp
parab
ble
l too the m
eaan thre
resh
shhoolld of 0.44 ± 00.31
.33 V/
.31
/cm
m measured
meaasuuree in
the experiment.
model,
clefts
low-resistance
m t. In our
ment
our m
oddell, the
th
h intramural
intr
tram
tr
amural
am
al llaminar
amiinar cle
am
l ft
ftss functioned
f ncti
fu
tiion
oned
d as low
w-rresisttance
extracellular
mechanism
a pa
ar
ppathways
th
hways
y aand
n were a mechani
nd
ism ffor
or llocal
ocall pe
pperturbations
rtu
t rbattio
ons of
of the
th
he electric
ellectriic ffield
i ld att their
ie
endpoints (this
Supplement).
realistic
(thi
(t
hi is
is illustrated
iill
ll strated
tratted
d in
i the
th Data
Datta S
pplement)
pll
t) This
Thiis was
Th
as critical
iti l for
fo achieving
achie
hi iing
n a reali
ali
li
excitation threshold.
The introduction of the extracellular conductivity boundary layers on the myocardium to
non-myocardium interfaces23 removes sudden depolarisation-inducing jumps in extracellular
conductivity and mitigates HS formation on the valley surfaces when the cathode is located at
the endocardium. This component ensures the midwall distribution of HS remains independent
of field polarity.
The assumption of lateral cell-scale uncoupling in our modified models, which is
sufficient for replicating the HS distribution at the time of field application, compromises lateral
propagation following cardiac excitation. There is no conduction velocity when the cells are fully
12
DOI: 10.1161/CIRCEP.114.002661
uncoupled, and the conduction velocity is approximately 50% of the fully coupled case when the
cells are uncoupled in the field direction (see the Data Supplement).
Discussion
For the first time, depth distributions of HS through the heart wall following weak electrical field
stimuli have been measured non-invasively using a novel tomographic imaging technique
developed in our lab. Our most striking findings were that at near-threshold field strengths HS
were scattered across the wall and not clustered near the cathodal surface as ppredicted by
y models.
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
Also, contrary to recent predictions,10 the HS location is not determined
ed
d by
by coronary
coro
co
rona
ro
nary
na
ry vvessels.
esse
es
sell
se
According
cording
cordin
ingg to Luther
in
L ther
Lu
th
h et al,
al 1 vessels are substrates
substrrat
ates ffor maximum
m polarization and the
selss should ggenerate
se
e er
en
erat
atee th
at
thee la
larg
ges
est po
ppolarizations
olari
r zation
ons an
aand
d be
bbecome
co
ome ssites
ites for
for earliest
earrli
l es
estt excitation.
exci
ex
citaa
ci
largest vessels
largest
To test this,
s we used
s,
use
sedd near-threshold
neear
a -th
thrre
th
resh
sholdd fi
fiel
field
elld st
strengths
tre
r ng
ngth
th
hs to
t iisolate
solaate the
so
h ssites
he
ites
it
ess off ma
maxi
maximal
xima
xi
mall po
ma
ppolarization
laariizaati
ti
which manifest
nifest
s as
st
as sources
sour
so
urce
ur
cees for
f r di
fo
disc
discrete
scre
sc
rete
re
te H
HS.
S If
S.
If the
th
he la
largest
arg
rges
esst vessels
veesssel
elss were
weree the
the source
sou
ourc
rcee of H
rc
HS
S th
then
reversing the
hee field
fiel
e d di
ddirection
reectio
cttion co
coul
could
ulld eeither
uld
ith
ther
th
e hhave
avee li
av
litt
little
ttle
tt
l effect
le
eff
ffec
ectt on
on HS
HS location
loca
lo
cati
tion
ti
o or
or the
the HS would
wou
ould
d sshift to
a similar size vessel. However, in the preparations where one vessel was larger than the other
two, we still found lateralization away from the largest vessel, which is contradictory. In the
preparations where there were three large vessels of similar size, lateralization also occurred but
the new location was not adjacent to any of the other vessels. Furthermore, the lateral
displacement in Figure 5 also precludes the contribution of major laminar clefts to HS
formation7, since, if they were the source, HS should only purturb the short distance across the
cleft with a reversal of field orientation.Discrepancies between experimentally measured surface
polarizations and conventional model predictions have been noted before,24, 25 where the
experimentally measured surface polarization was significantly lower than theoretical
predictions. These discrepancies were attributed to the depth averaging effects of optical
13
DOI: 10.1161/CIRCEP.114.002661
mapping, which underestimates the actual degree of surface polarization.24, 25 However, other
experiments at near-threshold field strengths reported the lack of activation on the myocardial
surface under the cathode, which suggested that surface polarization was indeed very small and
could not be explained by existing models.11, 26 Nevertheless, these findings failed to attract
attention to this significant inconsistency. A major criticism of previous experimental reports
questioning the validity of the existing models27 was that the observations were likely
experimental artifacts caused by tissue damage.28 Importantly, our experimental techniques
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
enable us to preserve the integrity of the myocardial tissue, which makes
kes such criticism
m lless
es
es
relevant and indicates that the problems may not be with the experiment,
nt, bu
bbutt with
wiith the
the theory
the
heoor
itself.
Thee an
study
analysis
nalysis of this
th
his stu
tuddy suggests
suggest
stts the
th
he theory
th
heory
y cann be
be reconciled
reeco
onciled
ed with
wit
i h thee experimen
eexperimental
xpe
perime
men
me
observation
n by iincluding
nclu
nc
ludding iin
lu
n the
th
h mode
model
dell more aaccurate
de
ccuuratte ddescriptions
cc
esccri
ript
pttio
ptio
ionss of el
electrical
lectriica
call hheterogeneities
eterogeneit
it at
the cell-scale.
a By
ale.
By introducing
introd
oduucin
od
i g lateral
lateral cell-scale
cell-scalle uncoupling
uncouppli
l ngg iinn th
the
h in
intracellular
ntraccel
e lu
l la
l r ddomain
omain
in ttogether
o ett
og
with heterogeneities
ogeneities
eiti
iti off extracellular
e ttracell
r ell
ll llar
a resistivities
resisti
siisti
ti it
iti
ities
ies iinto
ntt a con
conventional
entional
ti all bidomain
bid aii model,
model
dell wee were
able to correctly reproduce the experimental observations. This was not possible in standard
models which do not include these features.
Our experimental and model findings shed new light onto the mechanism of electrical
field excitation. In particular, they expose the possible effects of macroscopic and cellular scale
heterogeneities on the distributions of potential throughout the heart wall during weak electrical
field stimuli. This understanding is central to the development of effective low-energy
defibrillation therapies. Modeling analysis shows that lateral cell-scale uncoupling, especially
uncoupling in the direction of the electrical field, significantly reduces the liklihood of tissue
surface activations, for example, at the interfaces between the myocardium and the bath and the
14
DOI: 10.1161/CIRCEP.114.002661
myocardium and vessels. Consequently, the so-called “sawtooth” alternating pattern of
depolarization and hyperpolarization predicted by bidomain models at the boundaries of
individual cardiac myocytes9 becomes more prominent, especially when coupled with local
extracellular potential gradients associated with midwall cleft spaces. These mechanisms
dramatically shift the spatial distribution of HS into the myocardial wall, which is critically
important for sucessful application of low energy electrical defibrillation. While designed to
elucidate mechanisms of electrical defibrillation, our study has broader implications for
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
understanding the biophysics of impulse propagation in the heart. Thiss combined experimental
expe
p riime
m
and theoretical analysis challenges the functional syncytium paradigm and
dm
may
ay signal
sig
i na
nall the
the need
n
m nta
men
tall ch
cchanges
a gess tto
an
o our current mechanisticc understanding
unnderstandingg off ddefibrillation
efibrillation and imp
p
for fundamental
impulse
propagationn inn the heart.
e ar
ere
re two
tw
w pr
prin
i ciipa
pall ttranslational
ransl
slat
sl
ati
at
tionall im
impl
pllicati
pli
tions
ns from
from
m our
ouur st
tuddy. Fi
irs
rstt, any mod
dels
l
There
are
principal
implications
study.
First,
models
nformin
i g device
device
i ddesign
esig
ign andd cl
ig
lin
i icall practice
practic
i e off L
EA
AP wi
will
lll need
d to account
acc
ccou
cc
ouunt ffor
developed for iinforming
clinical
LEAP
non-syncytial
ttial
iall electrical
ell triicall acti
activation
cti
ti ati
ation
tio and
d propagation.
propagation
ati
tio S
Second,
Second
e ndd it has
h been
b
speculated
spec llated
atted
d tthat
hatt th
the use of
biphasic stimuli in LEAP could be advantageous.2 Our study supports this concept as our
experimental data shows that HS translate throughout the myocardial wall with field reversal,
indicating that with biphasic stimuli more HS could be formed leading to more effective antifibrillatory pacing.
Limitations
There is a systematic bias of our depth detection method which moves HS away from the surface
towards inside the tissue.14 However, the bias is too small to mask the cathodal surface activation
if the latter were consistently present. In Figure 3a, we show the depth distributions of surface
pacing. While the HS produced by surface pacing are not placed by our algorithm directly on the
15
DOI: 10.1161/CIRCEP.114.002661
surface they are distinctly closer to the surface than the majority of HS initiated by field pacing.
The important result is that HS during field pacing are found throughout the myocardial wall.
We chose to limit our modeling analysis to a 2D model of transmural cell cross sections.
This assumption will have an impact on current loading and ideally a 3D model based on actual
tissue reconstructions would be constructed. However, not only are 3D models resolving
structures at the cellular scale computationally challenging, they are limited in the extent of
tissue that can be modeled. We are not aware of any which fully capture the transmural
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
dimension of cardiac tissue,22, 29 which would be required to address the
he pr
pproblem
oblem in qquestion.
ueest
stio
i
io
While reproducing the intramural HS distribution during field stimu
stimuls
muls
l well,
ls
welll, our
ou mo
m
model
odd
does not accurately
c ur
ccur
urat
atel
at
elly re
rreproduce
prod
odduce the transmural condu
conduction
uct
ction velocity
y30 an
and
nd will require furtherr
development.
ent. One of thee logical
en
logiicaal approaches
ap
pproaachees wo
would
ould be to
o analyse
ana
naly
ysee iitt in the
th
he range
raange ooff llow
ow bbut
ut nonn
zero laterall coupling.
coupl
plin
plin
ingg.3311 T
The
he oth
other
ther
th
h dir
direction
i ec
ir
ecttion w
would
o ld be
ou
be ttoo ac
account
acc
coun
unt fo
un
forr th
tthee epha
ephaptic
h pt
ha
ptic
i cou
ic
coupling
plin
li g
32-36
-36
3
mechanism,
m 32m,
which
whi
hich
hi
h ccould
ould
l bbecome
ecome essentia
essential
i l iin
n th
the
he abs
absence
b ence of
of,
f, or
o at re
reduced,
edu
d cedd, ga
ggap
p ju
junc
junctional
nctionn
nc
coupling. Ephaptic
Ephhapti
tic coupling
co pli
pling
lin iiss common in
in the
the central
trall nervous
ner o s system
s stem
te 33 andd most
stt effective
effecti
ff ti e where
cells are densely packed. The discussion of ephaptic coupling in cardiac propagation, which
started in the early sixties,34-36 has re-emerged recently12, 37-39 with the demonstration of electrical
propagation in knockout mice hearts lacking most of their gap junctions.38 Ephaptic coupling is
achieved exclusively through the extracellular space, and is mediated via voltage changes in
narrow intercellular clefts. Our current model does not have sufficient resolution to investigate
these two directions, but we anticipate they will be the subject of future studies.
Acknowledgments: BJC designed, carried out and analyzed all experiments, and co-wrote the
manuscript. MLT designed and implemented the model and co-wrote the manuscript. AMP
conceived the project, analyzed the data, and co-wrote the manuscript.
16
DOI: 10.1161/CIRCEP.114.002661
Funding Sources: This work was supported by NIH Grants: R01HL07162 (Pertsov) and
R03TW008039 (Pertsov).
Conflict of interest Disclosures: None.
References:
1. Luther S, Fenton FH, Kornreich BG, Squires A, Bittihn P, Hornung D, Zabel M, Flanders J,
Gladuli A, Campoy L, Cherry EM, Luther G, Hasenfuss G, Krinsky VI, Pumir A, Gilmour RF,
Bodenschatz E. Low-energy control of electrical turbulence in the heart. Nature. 2011;475:235239.
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
2. Fenton FH, Luther S, Cherry EM, Otani NF, Krinsky V, Pumir A, Bodenschatz E,, Gilmour
iel
eldd st
stim
imul
im
ulat
ul
atio
at
ion.
io
n.
RF, Jr. Termination of atrial fibrillation using pulsed low-energy far-field
stimulation.
Circulation. 2009;120:467-476.
3. Pumir A, Nikolski
Niko
kols
ko
lski
ls
k V,
V, Horning
H rning M, Isomura A, Agladze
Ho
Agla
Ag
ladze K, Yoshikawa
la
Yoshikaawa
w K, Gilmour R,
Bodenschatz
Krinsky
V.. Wave emission from heterogeneities
a z E,
atz
E, Krin
nsk
s yV
hete
terogeneitiess opens
o ens a way to controllingg
op
chaos in thee hheart.
2007;99:208101.
eart. Physs Rev
Revv Lett.
Let
ettt. 20
007
07;9
;99:
;9
9 20081101.
4. Gray RA,
Wikswo
small
Nature.
2011;475:181-182.
A Wi
A,
Wiks
ksswo JJP.
P Several
P.
Sev
everral
a sma
m lll shocks
ma
sho
hock
c s beat
ck
beeatt one
one bbig
ig
g one.
one
ne. Na
Natu
t ree. 20
tu
2011
11;4
11
;4
475
7 :181
8 -182
82
5. Weidmann
S.. El
Electrical
trabecular
muscle
mammalian
heart.
Physiol.
a S
ann
E
ectr
ec
tric
tr
ical
ic
al cconstants
onssta
on
tant
ntss of
nt
o tra
rabe
ra
becu
be
cu
ula
lar mu
musc
sccle
l ffrom
room ma
mamm
m al
mm
alia
iann he
ia
ear
art.
t. J Ph
Phy
ysiol
s l
1970;210:1041-1054.
104
0411-10
1054
54.
6. Spach MS, Kootsey JM. The nature of electrical propagation in cardiac muscle. Am J Physiol.
1983;244:H3-H22.
7. Hooks DA, Tomlinson KA, Marsden SG, LeGrice IJ, Smaill BH, Pullan AJ, Hunter PJ.
Cardiac microstructure: Implications for electrical propagation and defibrillation in the heart.
Circ Res. 2002;91:331-338.
8. Trayanova N. Defibrillation of the heart: Insights into mechanisms from modelling studies.
Exp Physiol. 2006;91:323-337.
9. Plonsey R, Barr RC. Effect of microscopic and macroscopic discontinuities on the response of
cardiac tissue to defibrillating (stimulating) currents. Med Biol Eng Comput. 1986;24:130-136.
10. Bishop MJ, Boyle PM, Plank G, Welsh DG, Vigmond EJ. Modeling the role of the coronary
vasculature during external field stimulation. IEEE Trans Biomed Eng. 2010;57:2335-2345.
11. Caldwell BJ, Wellner M, Mitrea BG, Pertsov AM, Zemlin CW. Probing field-induced tissue
polarization using transillumination fluorescent imaging. Biophys J. 2010;99:2058-2066.
17
DOI: 10.1161/CIRCEP.114.002661
12. Mori Y, Fishman GI, Peskin CS. Ephaptic conduction in a cardiac strand model with 3d
electrodiffusion. Proc Natl Acad Sci U S A. 2008;105:6463-6468.
13. Smith RM, Matiukas A, Zemlin CW, Pertsov AM. Nondestructive optical determination of
fiber organization in intact myocardial wall. Microsc Res Tech. 2008;71:510-516.
14. Mitrea BG, Caldwell BJ, Pertsov AM. Imaging electrical excitation inside the myocardial
wall. Biomed Opt Express. 2011;2:620-633.
15. Trew M, Grice I, Smaill B, Pullan A. A finite volume method for modeling discontinuous
electrical activation in cardiac tissue. Ann Biomed Eng. 2005;33:590-602.
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
16. LeGrice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ. Laminar structure of the
heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am J
Physiol. 1995;269:H571-H582.
17. Pope AJ, Sands GB, Smaill BH, LeGrice IJ. Three-dimensional transmural
ansm
mur
ural
all oorganization
rgan
rg
aniz
izat
atio
at
ion of
io
perimysial collagen in the heart. Am J Physiol Heart Circ Physiol. 2008;295:H1243-H1252.
08;295
5:H
:H12
1243
12
43 H12
1252
5
18. Austin TM,
discontinuous
TM, Trew ML
ML,
L, Pull
Pu
Pullan
ull
llan
an
n AJ.
AJ. Solving
Sol
o vi
ving
n the
the cardiac
caarddiacc bidomain
bid
idom
omai
mai
ainn equations
eq
equa
qu tion
onns fo
for disc
di
discontin
isc
s onnti
tn
conductivities.
Trans
Eng.
tiess. IEEE Tra
ti
ans Biomed
Bioomed
ed
d Eng
g. 2006;53:1265-1272.
200
006;53
533:126
265-12
1 722.
12
19. Satoh H,
H Delbridge
Del
e brid
brid
br
idge
g LM,
LM,
M, Blatter
Blatter LA,
LA, Bers
Berrs DM.
DM Surface:Volume
S rfac
Su
acee:Vo
ac
Vollume
Vo
m relationship
rellations
t ns
nshi
h p in cardiac
hi
cardi
diac
di
myocytes studi
measurements:
Speciessstudied
ied
e with
wit
ithh confocal
conf
co
nffoccal microscopy
mic
icro
roscop
ro
opyy and
op
and membrane
memb
me
mb
braanee capacitance
cap
apac
a it
ac
itan
ance
an
ce m
easu
ea
sure
su
reme
re
ment
me
nts:
nt
s:: Spe
e
dependencee and ddevelopmental
effects.
Biophys
1996;70:1494-1504.
evellop
opm
mentall eff
ffectts. Bi
ff
B
opphy
hys JJ. 19
1996
966;7
70:14
1 944-1150
5044.
20. Luo CH,
potential.
Depolarization,
H Rudy
R d Y.
Y A model
dell off the
the ventricular
entric
triic llar cardiac
di action
cti
tio potential
tenti
tiall D
Depolari
oll i ati
ation
tio
repolarization, and their interaction. Circ Res. 1991;68:1501-1526.
21. Rush S, Larsen H. A practical algorithm for solving dynamic membrane equations.
Biomedical Engineering, IEEE Trans Biomed Eng. 1978;25:389-392.
22. Stinstra J, Hopenfeld B, MacLeod R. On the passive cardiac conductivity. Ann Biomed Eng.
2005;33:1743-1751.
23. Krassowska W, Neu JO. Effective boundary conditions for syncytial tissues. IEEE Trans
Biomed Eng. 1994;41:143-150.
24. Sharifov OF, Fast VG. Role of intramural virtual electrodes in shock-induced activation of
left ventricle: Optical measurements from the intact epicardial surface. Heart Rhythm.
2006;3:1063-1073.
25. Prior P, Roth BJ. Calculation of optical signal using three-dimensional bidomain/diffusion
model reveals distortion of the transmembrane potential. Biophys J. 2008;95:2097-2102.
18
DOI: 10.1161/CIRCEP.114.002661
26. Zemlin CW, Mironov S, Pertsov AM. Near-threshold field stimulation: Intramural versus
surface activation. Cardiovasc Res. 2006;69:98-106.
27. Plank G, Prassl A, Hofer E, Trayanova NA. Evaluating intramural virtual electrodes in the
myocardial wedge preparation: Simulations of experimental conditions. Biophys J.
2008;94:1904-1915.
28. Sharifov OF, Fast VG. Optical mapping of transmural activation induced by electrical shocks
in isolated left ventricular wall wedge preparations. J Cardiovasc Electrophysiol. 2003;14:12151222.
29. Stinstra J, MacLeod R, Henriquez C. Incorporating histology into a 3d microscopic computer
model of myocardium to study propagation at a cellular level. Ann Biomed Eng. 2010;38:13991414.
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
30. Caldwell BJ, Trew ML, Sands GB, Hooks DA, LeGrice IJ, Smaill BH.
BH.
H. Three
Thr
hree
ee ddistinct
isti
is
tinc
ti
ncct
directions of intramural activation reveal nonuniform side-to-side electrical
coupling
tricaal co
coup
upli
ling
li
ngg ooff
ventricular myocytes. Circ Arrhythm Electrophysiol. 2009;2:433-440.
31. Keenerr JJP.
effects
junctions
myocardium:
modified
P. The eff
f ec
ff
ects
ts off ga
gapp ju
junc
ncti
nc
tion
ti
ons
ns on ppropagation
r paagation
ro
onn iin
n my
myoc
o ar
oc
ardi
d um
di
m: A mo
m
difi
di
f ed
d cable
cabb
theory. Ann
Sci.
1990;591:257-277.
n N Y Acad Sc
ci. 19
9900;591
911:257
57
7-2777.
32. Arvanitaki
evoked
Neurophysiol.
t i A.
taki
A. Effects
Efffectts evok
Ef
ked
d in an axon
n by tthe
he aactivity
ctiv
ti it
ityy of a ccontiguous
onti
on
t guous on
ti
one. J Ne
N
urophy
hhy
1942;5:89-108.
-108.
8.
33. Anastassiou
CA,
Perin
s
ssiou
CA
A, Koch
Koch
h C,
C, Markram
Maark
Mark
rkra
raam H,
H, P
e in R.
er
R. Ephaptic
Epha
Ep
hapt
ha
p icc ccoupling
pt
oupl
ou
plin
pl
in
ng of cortical
cor
orti
tiicaal ne
tica
nneurons.
urons. Nat
N
Neurosci. 20
2011;14:217-223.
2011;14:217
2011
11;14
14:21
2177 223
223
34. Sperelakis N. An electric field mechanism for transmission of excitation between myocardial
cells. Circ Res. 2002;91:985-987.
35. Pertsov AM, Medvinskii AB. Electric coupling in cells without highly permeable cell
contacts. Biofizika. 1976;21:698-670.
36. Suenson M. Ephaptic impulse transmission between ventricular myocardial cells in vitro.
Acta Physiol Scand. 1984;120:445-455.
37. Rhett JM, Veeraraghavan R, Poelzing S, Gourdie RG. The perinexus: Sign-post on the path
to a new model of cardiac conduction? Trends Cardiovasc Med. 2013;23:222-228.
38. Jansen JA, van Veen TAB, de Bakker JMT, van Rijen HVM. Cardiac connexins and impulse
propagation. J Mol Cell Cardiol. 2010;48:76-82.
39. Lin J, Keener JP. Modeling electrical activity of myocardial cells incorporating the effects of
ephaptic coupling. Proc Natl Acad Sci U S A. 2010;107:20935-20940.
19
DOI: 10.1161/CIRCEP.114.002661
Figure Legends:
Figure 1: 3D mapping of “hot spots” (HS). a, The 3D optical mapping system. The ventricular
preparation is submerged in a glass chamber and stimulated by a uniform electric field (E)
between two mesh electrodes. Each surface of the preparation is alternately illuminated by
broad-field 671nm laser light (endocardial illumination is shown). The fluorescent voltagedependent signal is recorded simultaneously at > 715 nm by two fast CCD cameras on opposite
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
sides of the preparation (N and P). b, PP, NP, PN, and NN images of HS in a pig
p g right
pi
righ
g t
ventricular (RV) preparation recorded 22 ms after termination of a 0.34
V/cm
4 V/
/cm ffield
ield sstimulus.
ield
t mu
ti
mulu
lu
Three HS aree sshown
dashed
hown
ho
wnn together
tog
oget
ether with their distances ((Z)
et
Z) from the ep
epicardium
pic
i ardi
d um in mm. The dash
di
squares indicate
for
depth
detection.
reconstruction
dicaate areas usedd fo
di
or dept
pthh de
pt
ete
tecttio
on. cc,, 3D
D reco
cons
nstrrucction ooff HS
ns
S (red
d ddots),
ots)), coronary
cor
oronn
or
vessels (gold),
(blue)
with
old), and
andd the
an
t e endocardial
th
enddocardial
d surface
suurf
rface
f
(blu
(b
lue)
lu
e)) in another
anotthe
her RV ppreparation.
r pa
re
parati
t onn. E= 00.6
.66 V
V/cm
/ mw
/c
cathode on the epicardium.
epi
picarddiu
pi
ium
m. d,
d as iin
n c withh reversed
d ffield.
ield
ld.
Figure 2: Tissue model. 15 × 10 mm2 2D structural model with laminar (90º and 70º to surface)
and cell scale discontinuities (rectangular insets), and myocardium to non-myocardium
extracellular conductivity transition regions (circular inset).
Figure 3: Transmural distribution of HS. a, The distance of HS from the epicardial surface (Z)
as a proportion of mean local wall thickness (L), for all experiments (n=10) and different field
polarities (yellow – epicardial cathode; red – endocardial cathode). Left ventricular (LV) and
right ventricular (RV) preparations are experiments 1-3 and 4-10, respectively. Depths detected
during direct surface pacing (CONTROL) are shown at right. b, Histogram of HS depth
20
DOI: 10.1161/CIRCEP.114.002661
distributions over all experiments for opposite field orientations. c, Histogram of HS depth
distribution for a standard conventional model. HS appear exclusively on the epicardial and the
endocardial surfaces.
Figure 4: Co-localization of HS with coronary vessels. Coronary vessels were segmented from
confocal images of four RV preparations. 3D reconstructions are shown on left with HS
generated by epicardial (red balls) and endocardial (yellow balls) cathodal field pacing coDownloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
localized with vessels (gold) and the endocardial surface (blue). The three
largest
vessels
hree larg
gest vessel
ells are
a
ar
labeled with their mean radius (R, mm) inside or adjacent to the orangee cir
circle.
For
rclle. Fo
F
orr ea
each
ch
h ffield
iell
ie
orientation,, the
he pprojection
roje
ro
ject
je
ctio
on of the minimum distancee d,
d (mm, blue arrowed
arrow
ow
wed line) from the HS to
the nearest of the three lar
largest
coronary
shown
scale
looking
arggesst coron
onaryy vvessels
on
ess
ssels (orange
(oorang
nge ci
ccircles)
rcle
rc
les) iss sho
own to
o sca
alee lo
ookin
ng ddown
the axial length
as
circles
circles
e h of
ength
of the
th vessel.
vessell. HS
HS aree sh
shown
h
a rred
ed
d ci
ircles
l s ((epicardial
ep
pic
icarrdiall cathode)
cathode
t de
de)) or yyellow
ell
llow cir
ir
(endocardial
al cath
cathode)
hode
d ) bo
bou
bound
und by bboxes
oxes that
tha
h t delimit
deliimit the
h measurement
measuremen
en
nt error
errroor off tthe
he ddepth
ep
epth
pth
h ddetection
detec
etec
algorithm (1.3
depth,
plane).
Distances
between
(1 3 mm depth
d th 3 mm parallel
all
llell to
to the
the epicardial
pii rdi
diall pl
plane)
l e)) Di
stt
bbet
ett een vessels
essels
ell in
the projections are not to scale to aid visualization.
Figure 5: Lateral displacement of HS. The lateral displacement of HS in the epicardial plane
after reversal of field polarity (n=10). Diamonds show the minimal displacement in a given
experiment. The cross indicates zero displacement. The solid line is the mean radial shift (12.7 ±
10.7mm).
Figure 6: Formation of HS based on cell-scale uncoupling in Model 1. a, Cells are fully coupled.
The HS form on tissue surfaces at a threshold field strength of 0.35 V/cm. These data are the
21
DOI: 10.1161/CIRCEP.114.002661
foundation of Figure 3c. Epicardial HS (yellow) are the centroids of two planar activation waves.
b, Cells are uncoupled along the field direction. HS form in the midwall at a threshold field
strength of 0.47 V/cm. The solitary endocardial HS (red) forms late in the stimulus and at a
different location to the endocardial HS in a, which is located in the endocardial valley. c, Cells
are uncoupled in both directions. HS form in the midwall at a threshold field strength of 0.72
V/cm. d, Cells uncoupled across the field direction. In addition to the midwall, HS form on the
epicardial and endocardial surfaces and at the vessels for a threshold field strength of 0.47 V/cm.
Downloaded from http://circep.ahajournals.org/ by guest on July 28, 2017
Figure 7: Model based analysis of experimental findings. a, Uncoupling
direction.
ng inn field
fiel
fi
eld
ld di
dire
rect
ctio
ionn.
io
n.
Intramural dis
distribution
HS
str
trib
ibut
ib
utio
tio
ionn off H
S for six different geometric
geom
met
etric models (field
(fi
f eldd sstrength
trength 0.47 V/cm) and
both field polarities.
cathode;
yellow
endocardial
Uncoupling
polarities. Redd – epicardial
po
ep
piccardi
diial cat
atho
t ode; ye
ellow
w – en
ndo
doccarrdiial ccathode.
atthod
o e. b,, Un
od
U
couppliing
g in
field direction.
proportion of
ion. Distribution
Distr
istr
is
triibuttio
i n off HS
HS wi
with
th
h distance
distaanc
n e from
from the
the epicardial
epiicaarddiaal surface
surfface (Z)
(Z) as a propor
local wall thick
numerical
Uncoupling
tthickness
kness ((L),
L), fo
L)
fforr each
h numeric
all experiment
expperim
i entt andd both
both
h ffield
ield ppolarities.
ollariitiies. c,, Un
Unc
coupp
in field direction.
Frequency
distribution
normalized
ection
ti
F
Freq
r enc di
distrib
sttrib
ib ti
tion off model
dell HS with
ith
ith normali
ali
li ed
d ddepth,
depth
th for
fo all
ll numerical
n merr
experiments (n=6) and both field polarities. d, Full uncoupling. Intramural distribution of HS for
six different geometric models (field strength 0.72 V/cm) and both field polarities. e, Full
uncoupling. Distribution of HS with distance from the epicardial surface (Z) as a proportion of
local wall thickness (L), for each numerical experiment and both field polarities. f, Full
uncoupling. Frequency distribution of model HS with normalized depth, for all numerical
experiments (n=6) and both field polarities.
22
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Cardiac Response to Low Energy Field Pacing Challenges the Standard Theory of
Defibrillation
Bryan J. Caldwell, Mark L. Trew and Arkady M. Pertsov
Circ Arrhythm Electrophysiol. published online March 15, 2015;
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Circulation: Arrhythmia and Electrophysiology is published by the American Heart Association, 7272 Greenville Avenue,
Dallas, TX 75231
Copyright © 2015 American Heart Association, Inc. All rights reserved.
Print ISSN: 1941-3149. Online ISSN: 1941-3084
The online version of this article, along with updated information and services, is located on the
World Wide Web at:
http://circep.ahajournals.org/content/early/2015/03/15/CIRCEP.114.002661
Data Supplement (unedited) at:
http://circep.ahajournals.org/content/suppl/2015/03/15/CIRCEP.114.002661.DC1
Permissions: Requests for permissions to reproduce figures, tables, or portions of articles originally published in
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SUPPLEMENTAL MATERIAL
S1. Introduction
This supplemental material presents additional modeling results showing: (a) variation in the number
and distribution of HS for specific geometric models with lateral cell-scale uncoupling in the field
direction and in both directions; (b) the intramural variability in extracellular potential field that drives
HS formation; and (c) conduction velocity distributions for different coupling scenarios.
S3. Results
Five perturbations on the basic model were considered, with each varying a structural feature of the
base model. The HS distributions for the resulting six models together with lateral uncoupling in the
direction of the applied field are shown in Figure S1. The equivalent results, but for total lateral
uncoupling are shown in Figure S2 and the results for lateral uncoupling in the direction orthogonal to
the applied field are shown in Figure S3. In both these uncoupling cases, varying the distribution and
geometry of cell-scale uncoupling has some impact on the number of HS and their distribution
(models 1-3). However, the greatest impact on HS formation and distribution comes from varying the
thickness of the sub-endocardial region (models 4-5) and alterations to the midwall clefts (Model 6).
This second group of three models alter structures that contribute to heterogeneities in the local
extracellular potential field, such as those highlighted for Model 1 with complete cell-scale
uncoupling in Figure S4. In all cases, reversing the stimulus field results in different numbers and
distributions of HS formation.
Figure S1. HS
formation in the six
different modeling
experiments used in
this work.
Uncoupling is in the
field direction.
Models 1-3 used
different random
generations of cellscale geometries.
Models 4 and 5
varied the thickness
of the subendocardial region
from 25% of the wall
thickness down to
20% and up to 30%.
Model 6 randomly
altered the lengths of
the midwall clefts. In
all cases the field
strengths were 0.47
V/cm.
Supplemental Material
Cardiac response to electric field pacing
2
Figure S2. HS
formation in the six
different modeling
experiments used in
this work.
Uncoupling is in both
directions. Models 13 used different
random generations
of cell-scale
geometries. Models 4
and 5 varied the
thickness of the subendocardial region
from 25% of the wall
thickness down to
20% and up to 30%.
Model 6 randomly
altered the lengths of
the midwall clefts. In
all cases the field
strengths were 0.72
V/cm. Model 1 is the
same data shown in
Figure S4.
Figure S3. HS
formation in the six
different modeling
experiments used in
this work.
Uncoupling is in the
direction orthogonal
to the field. Models
1-3 used different
random generations
of cell-scale
geometries. Models 4
and 5 varied the
thickness of the subendocardial region
from 25% of the wall
thickness down to
20% and up to 30%.
Model 6 randomly
altered the lengths of
the midwall clefts. In
all cases the field
strengths were 0.72
V/cm.
Laminar clefts function as preferential pathways if they have a geometric component in the direction
of the applied electrical field. When this happens, large extracellular potential gradients form at the
end points of the cleft space. These gradients drive local membrane depolarisations and in concert
with local cell membrane area are responsible for driving HS formation. This is shown for one field
stimulus in S4.
Caldwell et al.
Supplemental Material
Cardiac response to electric field pacing
3
Figure S4. Extracellular
potential gradients and HS
formation. a. Intramural
HS formation for 0.72
V/cm
electric
field
stimulation
in
both
directions. Six HS are
highlighted for the yellow
field
stimulus.
b.
Transmural potential field
at 5 ms for the yellow field
stimulus from A. The same
six HS are highlighted in
the
exploded
and
magnified view in the
right-hand-side panel. c.
Extracellular
potential
field at 5 ms for the yellow
field stimulus from A. The
six highlighed HS form
where
the
potential
gradient is high.
Figure S5 shows the equivalent data to Figure 7, but for the case where cell-scale lateral uncoupling is
in the direction orthogonal to the applied stimulus field.
Figure S5. Model HS distributions for uncoupling orthogonal to the applied field direction. a, Intramural
distribution of HS for six different numerical experiments (field strength 0.47 V/cm) and both field
polarities. Red – epicardial cathode; yellow – endocardial cathode. b, Distribution of HS with distance
from the epicardial surface (Z) as a proportion of local wall thickness (L), for each numerical experiment
and both field polarities. c, Frequency distribution of model HS with normalized depth, for all numerical
experiments (n=6) and both field polarities.
Conduction velocities (CV) were determined for the four model scenarios shown in Figure 6 at the
activation field threshold stimuli. The CV distributions are shown in Figure S6. In the case where
cells are uncoupled and the tissue is continuous at that scale, the mean CV is 0.45±0.12 m/s (Figure
S6a). There is no conduction when the cells are uncoupled in both directions. When cells are
uncoupled in the direction of the applied field the CV is 0.21±0.13 m/s (Figure S6c) and when
uncoupling is orthogonal to the field direction the CV is 0.34±0.13 m/s (Figure S6d). For each
scenario different numbers of HS or areas of the model were activated at threshold and this is
reflected in the frequency count. Consider the case where cells are uncoupled in the field direction
(Figure 6c and S6c). If the activation time gradient components parallel and orthogonal to the applied
stimulus field are inverted separately, then the mean CV parallel to the applied field is 0.25±0.18 m/s
and the mean CV orthogonal to the applied field is 0.44±0.21 m/s.
Caldwell et al.
Supplemental Material
Cardiac response to electric field pacing
4
Figure S6. Conduction
velocity (CV) distributions
for the models shown in
Figure 6. a. CV when cells
are fully coupled in both
directions
(standard
model). b. There is no
conduction and no CV
when cells are uncoupled
in both directions. c. CV
when cells are uncoupled
in the direction of the
applied electric field. d.
CV when cells are
uncoupled in the direction
orthogonal to the applied
electric field.
Caldwell et al.