Probing Field-Induced Tissue Polarization Using Transillumination Fluorescent Imaging
Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.
Probing Field-Induced Tissue Polarization Using Transillumination
Bryan J. Caldwell,
* Marcel Wellner,
Bogdan G. Mitrea,
Arkady M. Pertsov,
and Christian W. Zemlin
Department of Pharmacology, State University of New York Upstate Medical University, Syracuse, New York; and
Syracuse University, Syracuse, New York
ABSTRACT Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart,
recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of
negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock elec-
trodes. There is little consensus as to whether these differences result from deﬁciencies of experimental techniques, artifacts of
tissue damage, or deﬁciencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensi-
tive dyes and transillumination optical imaging to perform, for the ﬁrst time that we know of, noninvasive probing of ﬁeld effects
deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental
studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce
considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold
diastolic ﬁeld stimulation produces activation of deep myocardial layers 2–6 mm away from the cathodal surface, contrary to
theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We
show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous
The effects of electrical ﬁelds on tissue have been attracting
signiﬁcant theoretical and experimental interest due to their
wide-ranging applications. The most important and best
studied application is deﬁbrillation, where strong ﬁeld
shocks restore normal electrical activity and synchronized
contractions in a ﬁbrillating heart, enabling resuscitation
of patients from sudden cardiac death. More recent applica-
tions use strong ﬁelds as a tool to deliver genetic material
into cells (1,2) or for the targeted treatment of cancerous
Sophisticated biophysical theories have been developed
that predict the distribution of the transmembrane and extra-
cellular potentials inside the heart during electrical shocks.
Major successes were the prediction of the dog-bone-shaped
polarization in anisotropic myocardial tissue (5–7), the
formation of quatrefoil reentry (8), and qualitative patterns
of surface polarization during deﬁbrillation shocks in the
whole heart (9). However, recent optical imaging studies
utilizing voltage-sensitive dyes have revealed several major
discrepancies between theory and experiment that cannot
readily be resolved.
One of these discrepancies is the presence of negative
bulk polarization recorded during strong shocks (10) despite
theoretical prediction of near-zero bulk polarization. A
second discrepancy is the unexpectedly low degree of
surface polarization (11) under the shock electrodes. The
depth-averaging effect of optical mapping techniques (12)
was shown to mask the degree of surface polarization.
However, the masking effect cannot explain recently re-
ported activation patterns during near-threshold diastolic
ﬁeld stimulation (13). Rather than emerging at the cathodal
surface, where the magnitude of depolarization should be
maximal (11,14–18), the early activation consistently
occurs away from the cathode (12,13). This leads to the
paradoxical conclusion that surface polarization during ﬁeld
stimulation may be less than intramural polarization.
The major obstacle to resolving these discrepancies was
the lack of adequate techniques for assessing intramural
polarization, or so-called virtual electrodes. Until recently,
the degree of intramural polarization was assessed using
measurements from the epicardial surface (19) or, more
often, from the transmural cut edge of wedge preparations
(10). Limitations of these approaches, in particular,
unavoidable tissue damage characteristic of the cut-edge
approach, have been a source of concern and controversy
in the interpretation of experimental data (20).
The goal of this study is to explore noninvasively the
effects of electrical ﬁelds deep inside the ventricular wall.
To achieve this goal, we take advantage of near-infrared
voltage-sensitive dyes (21) and transillumination imaging
techniques (22,23) recently developed in our laboratory.
Here, we carry out the ﬁrst, to our knowledge, noninvasive
measurements, of intramural bulk polarization during strong
and weak electrical shocks. We also use the new technique
to track early intramural activation during near-threshold
diastolic ﬁeld pacing. Finally, we use computer modeling
to explore the possibility of reconciling current models
with experimental observations.
Submitted December 23, 2009, and accepted for publication July 28, 2010.
Editor: Randall L. Rasmusson.
Ó 2010 by the Biophysical Society
2058 Biophysical Journal Volume 99 October 2010 2058–2066
Right ventricle slab preparation
All experimental protocols conformed to institutional and National Insti-
tutes of Health guidelines. Pigs of either sex (12–30 kg, n ¼ 4) were intra-
venously anesthetized with sodium pentobarbital (35 mg/kg) and
heparinized (500 IU). The heart was rapidly removed and chilled with
C cardioplegic solution. The right ventricle (RV) was quickly excised
and the right coronary artery cannulated. Nonperfused tissue was removed,
and the preparation was stretched on a plastic frame and mounted in a glass
perfusion chamber. Preparations were perfused and superfused with warm
C) oxygenated Tyrode solution with 0.04 g/L albumin at a constant
pressure of 80 mm Hg. After 30 min equilibration, 10–15 mmol/L of
2,3,-butanedione monoxime was added to extinguish contractions, and
the preparation was stained with the near-infrared dye DI-4-ANBDQBS
The preparation was continually paced at 508-ms base cycle length from
two 50 50-mm silver mesh electrodes (6 12 mm spacing) oriented
parallel to the epi- and endocardial surfaces. The ﬁeld electrodes were
placed 32 mm apart and ~11 mm from the respective surfaces. This insured
that the electric ﬁeld was near uniform across the surface (variation of
<10% measured in the bath). The amplitude was set at 2 threshold
(1.2–1.8 V/cm, 5 ms). This was sufﬁcient to provide near-simultaneous
transmural activation and uniform phase distribution during a 10-ms shock
applied 50 ms after the pacing stimulus. Shock strength was monitored in
the tissue using two resin plunge needles with two bipolar electrodes
(0.5 mm spacing). For near-threshold diastolic ﬁeld pacing, the ﬁeld ampli-
tude was reduced to within 5–10% of the lowest voltage (0.6–1.1 V/cm,
5 ms) that sustained capture.
Alternating transillumination optical mapping
Fig. 1 shows the optical imaging system. Each surface of the preparation was
alternately illuminated (compare Fig. 1, A and B) with one of two 600-mW,
660-nm lasers (Shanghai Dream Laser Technology, Shanghai, China). The
laser beams were expanded by a holographic diffuser and directed onto the
heart surface by a long-pass dichroic mirror (680DCLP, Chroma Technology,
Rockingham, VT). Fluorescence images of the same (30 30 mm) area were
simultaneously recorded from opposite sides of the preparation with two
CCD cameras (Lil’Joe, Scimeasure Analytical Systems, Decatur, GA) at
80 80-pixel, 2-kHz, 14-bit resolution. The ﬂuorescent light was isolated
using 715-nm interference ﬁlters (Chroma Technology).
For each shock strength and ﬁeld orientation, four movies (Fig. 1, PP, PN,
NP, and NN) were recorded. The ﬁrst letter refers to the position of the light
source and the second to the position of the camera with respect to the
ePicardium (P) and eNdocardium (N). The PP and PN movies were re-
corded when the light was directed to the epicardial (P) surface so that
charge-coupled device camera CCD-1 recorded epiﬂuorescence from the
epicardium and CCD-2 simultaneously recorded transillumination from
the endocardium (Fig. 1 A). When the excitation light was switched to
the endocardial (N) surface (Fig. 1 B) and the shock was repeated,
CCD-1 recorded transillumination from the epicardium (NP) and CCD-2
recorded epiﬂuorescence from the endocardium (NN).
PP, PN, NP, and NN images contain different contributions from the
layers across the ventricular wall, as quantiﬁed by the weighting functions
presented in Fig. 2 (see Derivation in the Supporting Material). The weight-
ing functions for the epiﬂuorescence images PP and NN are largest in the
2 mm below the surface (~70% cumulative weight). In contrast, the trans-
illumination images NP and PN are largest in the deep intramural layers
(2–6 mm, ~70% cumulative weight). The NP and PN weighting functions
have similar shape, but the epicardial subsurface layers (0–1 mm)
contribute substantially more to NP than to PN, whereas the deeper layers
(1–4 mm) contribute up to 15% more to PN than to NP. On the endocardial
side, the roles are reversed. Note that the weighting functions in Fig. 2
describe planar sources induced by a uniform ﬁeld that changes only trans-
murally (they are 1D weighting functions). For point sources of excitation
(see Fig. 6), we use 3D weighting functions described elsewhere (23). We
generally displayed the four images according to the depth at which the
weighting function has its maximum; for 1D weighting functions, this is
PP, PN, NP, NN, and for 3D weighting functions, it is PP, NP, PN, NN.
Temporal and spatial averaging ﬁlters (diameters 2.5 ms and 3.4 mm for
plateau shock, 1.5 ms and 1.9 mm for diastolic ﬁeld pacing) were applied
to all frames. These ﬁlter parameters have been shown to improve signal/
noise ratio with little effect on action potential (AP) morphology (24).
Shock-induced transmembrane voltage (DV
)(Fig. 3 A) was estimated at
shock end by subtracting the ensemble-averaged AP (12–16 beats) generated
by ﬁeld pacing in the absence of the shock (Fig. 3 B). If DV
was less than the
mean peak noise amplitude, it was set to zero. Activation time was estimated
of the AP upstroke, and referenced to the stimulus onset.
A bidomain model was used to simulate electrical activity in response to
uniform ﬁeld stimulation inside an 8-mm slab of myocardial tissue. To
reduce computation to 1D, ﬁbers were assumed parallel to the epicardium,
FIGURE 1 Alternating transillumination map-
ping system. The RV preparation is mounted in
a glass perfusion chamber between two CCD
cameras. For each shock strength and ﬁeld orien-
tation, four movies (PP, PN, NP, and NN) were
recorded. The ﬁrst letter refers to the position
of the light source and the second letter to the
position of the camera with respect to the ePicar-
dium (P) and eNdocardium (N). (A) Light from
a single 600-mW, 660-nm laser is expanded by
a holographic diffuser (1) and directed to the
epicardial surface (P) via a dichroic mirror (2).
Fluorescent emission is long-pass ﬁltered at
715 nm (3) and recorded by CCD-1 as epiﬂuor-
escence (PP) and by CCD-2, from the endocar-
dial surface (N), as transillumination (PN).
(B) Laser light is now directed toward the endo-
cardial surface (N), where CCD-1 records
transillumination (NP) and CCD-2 records epi-
ﬂuorescence (NN). Field electrodes are shown superimposed on the tissue surfaces at the bottom of the ﬁgure, red corresponding to epiﬂuorescence
and black to transillumination. (Insets) Camera views showing DV
for a ﬁeld (E) oriented from N to P.
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization 2059
so there is no epiparallel component of the electrical ﬁeld. Intracellular
transmural conductivity (gi) and interstitial transversal conductivity (ge)
were set so that the ge/gi ratio is 2.5, as is generally accepted (25,26),
and the transmural conduction velocity was 34 cm/s (27). This led to
ge ¼ 0.8 S/m and gi ¼ 0.32 S/m. To incorporate the layered structure of
the myocardium, which is oriented at a mean angle of 25
to the transmu-
ral z axis (27,28), intracellular coupling was reduced to 0.1 gi randomly
every 2–8 cells, corresponding to layer thicknesses of 30–120 mm. These
reductions of gi reﬂect the discontinuity of the intracellular domain in the
transmural direction. The surface/volume ratio was set to 2700/cm, corre-
sponding to a cylindrical cell geometry with a radius of 7.5 mm. Transmem-
brane currents were computed using the Luo-Rudy II dynamic model (29).
In some simulations, the model was augmented for high ﬁeld strengths by
incorporating an additional outward current (I
) activated at large depolariz-
ing voltages (30).
We used a time step of 1 ms during shocks and 5 ms for propagation, and
a space step of 17 mm. An AP was initiated by 5-ms stimulus current to all
model cells simultaneously, and a 10-ms-duration 30 V/cm shock was
applied after 50 ms during the plateau phase. Near-threshold diastolic ﬁeld
pacing was evaluated by varying the amplitude of a 5-ms-duration stimulus
from 0.9 to 6.3 V/cm.
To model the effect of a shock on the optical signal, model results were
convolved with the optical weighting functions shown in Fig. 2.
The experiments were conducted for two shock strengths:
weak shocks of ~3 V/cm and strong shocks of ~30 V/cm.
To achieve uniformity of AP phase throughout the wall
during the p lateau shock, we generated a uniform ﬁeld
pacing stimulus at two times threshold (1.2–1.8 V/cm).
Fig. 4 A shows typical activation maps of the epicardial
(PP), endocardial (NN), and transmural (PN and NP) layers
after that ﬁeld stimulus. Although the amplitude of the stim-
ulus is relatively small (1.5 V/cm), the spatial dispersion of
FIGURE 4 Activation during uniform ﬁeld pacing at twice the excitation
threshold (1.5 V/cm). (A) Activation maps superimposed with isochrones at
2-ms intervals. Mean activation time and SD is displayed below the respec-
tive map. The ﬁeld direction (E) is indicated at the top of the ﬁgure. PP, PN,
NP, NN are deﬁned in Fig. 1 legend. (B) Normalized AP averaged over all
pixels from each optical movie are superimposed. (C) Close-up of the AP
upstrokes from B. The stimulus markers for both B and C are shown at
FIGURE 2 Weighting functions for epiﬂuorescence and transillumina-
tion images. Attenuation lengths (mm) are a ¼ 2.56 for diffuse photons,
b ¼ a/4 for ballistic photons, and f ¼ 3.3 for near-infrared dye emission.
PP, PN, NP, and NN are deﬁned in Fig. 1 legend.
FIGURE 3 Measurement of DV
.(A) A typical ensemble-averaged optical
AP is overlain with the AP showing the response to strong shock during the
plateau phase. The AP amplitude (APA) is normalized. S1 pacing and S2
shock markers are depicted at base line. (B) Result of subtracting the APs in A.
is measured at S2 end and presented as a percentage of the APA (% APA).
Biophysical Journal 99(7) 2058–2066
2060 Caldwell et al.
activation time in any image had a standard deviation of
<1.6 ms. This means that all cells across the entire wall
are practically in the same state at the time of the plateau
shock. This is further highlighted in Fig. 4, B and C, which
shows the average APs from all pixels in each layer, with the
full APs and a close-up of the upstroke, respectively. In each
panel, it is clear that activation is near-simultaneous in all
layers, with a slight delay (~2 ms) at the endocardial surface
(NN). This is a signiﬁcant improvement over commonly
used point-stimulus pacing (10).
The results for weak shock strengths (3.6 V/cm) are illus-
trated in Fig. 5 A. At the cathode (NN), polarization is
uniformly positive (yellow to red, 3.1 5 0.7% AP amplitude
(APA)), whereas at the anode (PP) it is uniformly negative
(green, 5.3 5 1.2% APA). The shock response in PN
and NP transillumination images, representing bulk polari-
zation in deep myocardial layers, is near zero (predomi-
nantly white, 1.0 5 1.2 and 0.1 5 0.4% APA,
respectively). The APs benea th the color panels are the
average APs from all pixels in each panel. They highlight
the very weak response to the shock both at the surfaces
and in intramural layers. Our analysis shows that even
taking into account depth-averaging effects of optical
recordings, the observed surface polarization is still much
smaller than can be explained by existing theories.
For strong shocks (35.1 V/cm) (Fig. 5 B), polarization
was strongly negative everywhere in epiﬂuorescence (PP
and NN) and transillumination (PN and NP) images and it
was maximal at the anode (PP, deep blue, 64.6 5 5.1%
APA). We also observed negative polarization at the cathode
(NN, deep green to blue, 30.5 5 5.7% APA). Unlike weak
shocks, strong shocks produced signiﬁcant negative bulk
polarization, as seen in the transillum ination images (NP
and PN, blue, 43.7 5 1.9 and 46.5 5 2.4% APA,
respectively). These observations are consistent with early
observations by the Fast group (10) but contradict conven-
tional theory (see Bidomain simulations, below, and
The effects of both weak and strong shocks under the
anode and cathode are reproduced after the reversal of shock
polarity (see Fig. S5 in the Supporting Material). Shock data
are summarized in Table 1. Independent of shock polarity, in
all but one recording, the amplitude of response was larger
at the epicardial than at the endocardial surface (see
Near-threshold diastolic shocks
According to classical bidomain theories, a diastolic ﬁeld
shock just above the excitation threshold should activate
only a thin layer of tissue under the cathode. This activated
layer should give rise to an activation wave propagating
transmurally from cathode to anode. However, this is not
what we observe experimentally. Analysis of our transillu-
mination data shows that diastolic shocks <10% above
the excitation threshold induce activation not only at the
cathodal surface but also at the anodal surface and within
An example of such multisite activation produced by
a 0.9 V/cm, 5-ms diastolic shock is shown in Fig. 6.
Fig. 6 A shows the PP, PN, NP, and NN snapshots 17 ms
after the onset of shock. Small circles show the x,
s of the centers of early activated regions (labeled
1–3). The time-dependent signals in the respective locations
are shown below the snapshots. The analysis of these signals
implies that regions 1 and 2 are located near the endocar-
dium (anode), whereas region 3 spans almost the entire
Indeed, at region 1, the NN signal appears ﬁrst, 1–2 ms
after the end of the shock. It is followed 4 ms later by the
rise in PN and NP and 10 ms later by the PP signal. This
indicates that the excitation starts near the endocardium
(anode) and subsequently propagates toward the epicar-
dium. Region 2 is activated a little later than region 1
(5 ms after the shock end). Again, as in region 1, the NN
signal appears ﬁrst, which indicates that the activation
source is located closer to the endocardium. Unlike in
region 1, however, the increase in the NN signal is almost
FIGURE 5 DV
during weak shock (3.6 V/cm) (A) and strong shock
(35.1 V/cm) (B) applied during the plateau phase of optical APs generated
by uniform ﬁeld pacing (see Fig. 4). DV
is displayed as % APA in the
color maps, with the corresponding preshock (black), and during-shock
(blue) normalized AP averaged over all pixels displayed below. S1 pacing
and S2 shock markers are depicted at base line. DV
, expressed as mean 5
SD, is shown below each map.
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization 2061
immediately followed by an increase in PP, PN, and NP
signals, suggesting that region 2 spans almost the entire
thickness of the wall. Region 3 is activated almost simulta-
neously with region 2. Similar to region 2, it is also very
large, as indicated by almost simultaneous intramural and
Note that the sites of early activation feature a slow rising
phase (foot) that starts immediately after the stimulus. The
foot of the optical AP is >5 ms, which is very slow
compared to what would be observed in electrical record-
ings. This is a consequence of spatial integration resulting
from light-scattering and depth-averaging effects intrinsic
to optical recordings (31) and most likely reﬂects an incre-
mental increase in the volume of tissue activated during the
In Fig. 6 B, we present conventional isochronal maps
derived from PP, PN, NP, and NN recordings in the same
experiment. The activation time was determined from the
time of dF/dt
. In all four maps, the earliest activation
contours are 23 ms (18 ms after shock end). This clearly
shows that weak shocks do not produce propagation from
cathodal to anodal surface as predicted by theory.
Similar multisite activation with early activation sites
scattered throughout the ventricular wall was observed in
all experiments. It is interesting that reversal of ﬁeld polarity
did not always preserve the location of the early activation
sites. Fig. S6 shows the effect of the reversal of ﬁeld polarity
in the experiment illustrated in Fig. 6. It also shows multiple
activation sites spread across the entire thickness of the
To compare our experimental observations with theoretical
predictions, we simulated optical action potentials and
shock responses for all types (PP, PN, NP, and NN) of
FIGURE 6 Intramural activation
initiated by near-threshold diastolic
ﬁeld pacing (0.9 V/cm). The cathode
is at the epicardial surface (PP). (A)
Normalized AP 17 ms after stimulus
onset (see color bar at right). The three
earliest activating regions (1–3) corre-
spond to the close-up of AP upstrokes
in insets 1–3. Upstroke line thickness
corresponds to the optical plane in A,
with PP represented by the thinnest
line, NP and PN by lines of interme-
diate thickness, and NN by the thickest
line. The gray vertical line marks the
17-ms interval shown in A. The dura-
tion of the stimulus is shown at the
beginning of the plots. (B) Activation
contour maps are colored according to
the color bar at right, with 2-ms contour
TABLE 1 Mean % APA across all experiments for weak and strong shocks
Mean V/cm PP PN NP NN Field polarity
2.6 5 0.4 5.8 5 2.5 0.8 5 1.3 0.5 5 1.1 3.8 5 1.4 Cathode P
2.8 5 0.7 6.1 5 1.7 1.0 5 1.5 0.2 5 0.7 3.1 5 0.7 Anode P
34.2 5 0.8 24.2 5 7.1 33.7 5 3.6 35.4 5 4.5 42.3 5 4.6 Cathode P
34.0 5 1.2 56.8 5 7.3 42.2 5 4.7 39.0 5 4.2 25.2 5 6.6 Anode P
% APA is expressed as the mean 5 SD for all shocks. Weak shocks were 2–4 V/cm and strong shocks were 32–35 V/cm.
Biophysical Journal 99(7) 2058–2066
2062 Caldwell et al.
recordings and experimental protocols. We calculated the
transmural distributions of V
using a bidomain model
with Luo-Rudy (LRd) membrane kinetics. To simulate
optical responses, we convolved these voltage distributions
with the optical weighting functions derived from the real-
istic light transport model of myocardial tissue (see the Sup-
Fig. 7 shows simulated optical responses to weak
(3 V/cm) and strong (30 V/cm) shocks applied during the
plateau phase of the AP for standard and augmented models.
Fig. 7 A shows the simulations utilizing the standard LRd
model. Fig. 7 B shows the results for the augmented LRd
model with added asymmetric negative current (I
vated at high transm embrane voltages (see Methods).
For weak shocks (3 V/cm), the simulated responses are
practically identical for both models (compare Fig. 7, A
and B, upper rows). The predicted surface polarization is
positive under the cathode and negative under the anode,
which is consistent with our experimental observations
(see Fig. 5). It should be noted, however, that the amplitudes
of the simulated surface responses (PP ¼9.6 and NN ¼
11.1% APA) are approximately two to three times larger
than those recorded experimentally (PP ¼5.8 and
NN ¼ 3.1% APA). This discrepancy is not likely to be
rooted in the optical model, but rather reﬂects a fundamental
problem of existing electrical models (see Discussion).
For strong shocks (30 V/cm), the predictions of the stan-
dard and augment ed models diverge signiﬁcantly (Fig. 7 A).
The standard LRd model predicts signiﬁcant depolarization
(129.4% APA) at NN under the cathode, whereas experi-
mentally we observe hyperpolarization of 30.5% APA
(Fig. 5 B). The model also fails to predict the correct sign
of the optical responses in the intramural PN and NP layers
as well. Final ly, the biphasic responses apparent in simu-
lated PP, PN, NP, and NN recordings are largely absent in
real experimental data .
Using the augmented model (Fig. 7 B) considerably
improves the agreement between theory and experiment
for strong shocks. The augmented model not only accu-
rately predicts the sign of responses in all recording modes
(50.4, 20.1, 22.2, 35.1% APA for PP, PN, NP, and
NN, respectively), but also more accurately reproduces
their magnitude and kinetics, bringing the model predic-
tions closer to experimental observations (compare with
Fig. 5 B).
Simulation results of diastolic near-threshold ﬁeld stimu-
lation are illustrated in Fig. 8 . Fig. 8 A shows time-space
plots indicating the changes in spatial distribution of the
transmembrane voltage across the myocardial wall during
and after the shock for four different ﬁeld strengths. Fig. 8 A
(left) shows the time-space plot for the threshold shock
(0.9 V/cm). The color scale (lower right ) indicates the trans-
membrane potential. The excitation starts near the depolar-
ized cathodal surface (white arrows) and propagates toward
the opposite surface. The characteristic alternating blue
(hyperpolarization) and red (depolarization) stripes, visible
on each plot between 1 and 6 ms during the stimulus, repre-
sent intramural virtual electrodes, also known as a sawtooth
pattern. In our model, these electrodes represent boundaries
between myocardial bundles. The same pattern of excitation
with the origin at the cathodal surface is preserved as the
shock amplitude increases up to 4.5 V/cm (ﬁve thresholds).
The characteristics of the response change when the
shock strength reaches 6 V/cm. At this voltage, in addition
to the surface source of excitation we see the emergence of
an intramural excitation source. Indeed, one of the intramu-
ral virtual electrodes located >6 mm away from the cath-
odal surface (gray arrow) gives rise to an expanding
excitation wave. At the end of the 4.5-V/cm stimulus, one
can also see a local transient depolarization at the same
site, although the depolarization is too weak to initiate
a propagating wave. The position of the secondary excita-
tion site is random and is determined by the initial distribu-
tion of heterogeneities (in our case, boundaries between
myocardial bundles). Further increase in shock strength
from 6 V/cm to 7.5 V/cm produces multiple excitation
centers all the way across the thickness of the myocardial
wall, causing almost simultaneous ventricular excitation.
Fig. 8 B shows the PP, PN, NP, and NN simulated optical
responses for all ﬁeld strengths. The left three panels, corre-
sponding to lower shock strengths, show that the cathodal
upstroke occurs ﬁrst, the intramural upstroke after a delay,
the anodal upstroke after an even longer delay. This
characteristic sequence reﬂects the intramural activation
sequence shown in Fig. 8 A. Our experimental recordings,
however, do not follow this sequence. For both weak shocks
FIGURE 7 Simulated optical APs of
during the plateau
phase for different electrophysiological
models. The shock-affected AP (thick
line) is superimposed on the standard
LRd AP (thin line). The effects of
a weak (3 V/cm) and a strong shock
(30 V/cm) are shown for the standard
LRd II dynamical model (LRd)(A),
and the modiﬁed model with I
The cathode is at the endocardial
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization 2063
(Fig. 4 C) and near-threshold stimulation (Fig. 6 and
Fig. S6), the upstroke sequences are more similar to multi-
site responses, which occur in the model at much larger
(6.0 V/cm) ﬁeld strengths.
This study explores the effects of electrical ﬁelds deep
inside the ventricular wall using recently developed nonin-
vasive transillumination imaging techniques (22,23) and
near-infrared voltage-sensitive dyes (21). With this what
we believe is a novel approach, we obtain a direct view of
the effects of electrical ﬁelds on deep intramural myocardial
tissue not previously available, to our knowledge.
Negative bulk polarization
As mentioned in the introduction, one of the discrepancies
of ﬁeld-induced myocardial tissue polarization is negative
bulk polarization spanning almost the entire thickness of
the myocardial wall and changing sign only at the very
vicinity of the cathodal surfaces. This effect has been
observed during strong shocks (>25 V/cm) applied during
the plateau phase of the AP (10,19,32–34) and is attributed
to some asymmetric negative current I
, which shifts the
inherent positive bias in the LRd model to a negative bias
during such shocks (35). The existence of I
is inf erred
from ﬂuorescence imaging experiments, but its ionic nature
remains poorly understood. An experimental study by
Cheek et al. (36) suggests that I
may ﬂow through the
channel. However, the measurements of I
have yet to be corroborated by direct voltage-clamp experi-
In previous simulations in continuous bidomain models
did introduce a negative bias, but qualitative
differences with experimental data remained. In particular,
the simulations still predicted a positive shock-induced
deﬂection in the cathodal epiﬂuorescence signal. This led
some researchers to question the validity of the experimen-
tally observed negative bulk polarization (20). Their
concern was that negative polarization in the cathodal epi-
ﬂuorescence signal might be the consequence of tissue
damage inﬂicted by the cut-edge technique.
In this study, we use a different experimental approach,
which enables us to determine bulk intramural polarization
noninvasively. By using transillumination imaging tech-
niques and near-infrared voltage-sensitive dyes, we assess
the intramural polarization in intact cardiac tissue far from
the boundaries, which eliminates possible effects of tissue
damage. We show (see Fig. 5 and Fig. S5) that negative
bulk polarization is equally strong in both transillumination
images (NP and PN) that represent mid-myocardium. We
also observe signiﬁcant hyperpolarization under the cathodal
surface. Our ﬁndings are consistent with earlier experimental
reports and provide unequivocal evidence that negative bulk
polarization is not an artifact of tissue damage.
Here, we demonstrate that negative bulk polarization can
be largely reproduced computationally in a discontinuous
rather than continuous bidomain model (see Fig. 7). Despite
the presence of a negative bias produced by I
, in continuous
bidomain models (20,35), a substantial volume underneath
the cathode is depolarized. In contrast, in the discontinuous
gives rise to negatively biased polarization
patterns at every discontinuity, even in the direct vicinity
of the cathode. As a result, we see negative polarization
throughout the wall and achieve good agreement with our
FIGURE 8 Simulated V
threshold to six-times-threshold dia-
stolic shocks (0.9–6.0 V/cm). (A)
Time-space plot of Vm across the
myocardial wall. The standard LRd
model was modiﬁed with I
. The shock
duration is apparent from 1 to 6 ms as
an alternating polarized band. Field
polarity for each plot is indicated
above and below the band in the left-
most plot. Resting membrane potential
(~89 mV) is colored white with depo-
larization red and hyperpolarization
blue (see color bar at lower right).
Surface activation (white arrow) occurs
at 0.9 V/cm and intramural activation
(gray arrow) at 6.0 V/cm. (B) Close-
up of the upstroke of simulated optical
APs of the time-space plots above.
Colors are deﬁned in panel B.
Biophysical Journal 99(7) 2058–2066
2064 Caldwell et al.
Weak plateau-phase shocks
Our experiments show that weak 2- to 3-V/cm plateau-phase
shocks produce very little bulk polarization, which is consis-
tent with bidomain simulations. Indeed, simulated optical
responses to weak shocks look very similar to real experi-
mental recordings (compare Fig. 7 with Fig. 5).
It should be noted, however, that the amplitudes of simu-
lated surf ace optical responses are 2–3 times larger than
those recorded experimentally. Considering that our compu-
tational light transport model uses Dirichlet boundary
conditions (see the Supporting Materials), and therefore
has a tendency to under estimate the contribution of surface
layers, the discrepancy between theory and experiments is
likely to be even larger. This means that at weak shocks,
the real ﬁeld-induced surface polarization is signiﬁcantly
smaller than that predicted by theory. This conclu sion is
further corroborated by the results of near-threshold dia-
stolic ﬁeld stimulation (see next section).
Near-threshold diastolic shocks
Current bidomain models (11,14–18) predict that shock-
induced surface potential s are much larger than intramural
virtual electrode potentials and that during near-threshold
diastolic ﬁeld stimulation, activation originates in a thin
layer under the cathode and then propagates toward the
anode. In theory, the activation of intramural layers requi res
much larger ﬁeld strengths that exceed several times the
activation threshold (see Fig. 8).
In contrast, during near-threshold ﬁeld stimulation, our
experiments show, for the ﬁrst time that we know of, the
location of multisite activation patter ns spanning the entire
thickness of the wall. We show examples in which early
activation occurs in deep myocardial layers (2–6 mm) far
from the cathodal surface, as well as cases of anodal excita-
tion. The cathodal surface is typically not activated directly,
but signiﬁcantly after the end of the shock. This ﬁn ding has
been reported previously from optical recordings taken only
from the ventricular surface (12,13,33,37 ).
What kind of changes to current bidomain models are
needed to reproduce these experimental results? Adding
a current to continuous models that limits depolarization
) is insufﬁcient, because even in such an augmented
model, surface polarization still exceeds intramural polari-
zation (20,3 5 ). Since intramural activation results from
discontinuities on different spatial scales, accurately incor-
porating such discontinuities appears to be the most prom-
ising approach. Indeed, bidomain models that carefully
determine the extent of the intracellular domain reproduce
some aspects of the tissue response to strong shocks (38).
However, they still fail to reproduce intramural activation
during weak shocks. Instead, they show that the surface acti-
vates ﬁrst (17,18 ), with a signiﬁcant gap between surface
and intramural excitation thresholds. A recent study showed
that intramural activation can be achieved for certain distri-
butions of heterogeneities even for weak shocks (13), but the
distributions used in this study were not based on experi-
mental measurement, and it is unclear whether similar
distributions under lie intramural activation in real tissue.
It remains to be seen whether intramural activation for
near-threshold ﬁeld stimulation can eventually be repro-
duced in a bidomain model that better captures tissue
discontinuities. Another possibili ty is that the detailed
cellular structure of cardiac tissue, which is not included
in bidomain models, is crucial to correctly predict the shock
response of tissue. In this case, new types of models would
be needed to take our understanding of the effects of electri-
cal ﬁelds on tissue to the next level (39,40).
Nine equations, references, a table, and two ﬁgures are available at http://
Research in this article has been supported by R01 Grant 47268 from the
National Institutes of Health and American Heart Association Grants
0830018N and 0815731D.
1. Escoffre, J. M., D. S. Dean, ., C. Favard. 2007. Membrane perturba-
tion by an external electric ﬁeld: a mechanism to permit molecular
uptake. Eur. Biophys. J. 36:973–983.
2. Beebe, S. J., J. White, ., K. H. Schoenbach. 2003. Diverse effects of
nanosecond pulsed electric ﬁelds on cells and tissues. DNA Cell Biol.
3. Nuccitelli, R., X. Chen, ., K. H. Schoenbach. 2009. A new pulsed
electric ﬁeld therapy for melanoma disrupts the tumor’s blood supply
and causes complete remission without recurrence. Int. J. Cancer.
4. Esser, A. T., K. C. Smith, ., J. C. Weaver. 2007. Towards solid tumor
treatment by irreversible electroporation: intrinsic redistribution of
ﬁelds and currents in tissue. Technol. Cancer Res. Treat. 6:261–274.
5. Roth, B. J., and J. P. Wikswo, Jr. 1994. Electrical stimulation of cardiac
tissue: a bidomain model with active membrane properties. IEEE
Trans. Biomed. Eng. 41:232–240.
6. Wikswo, Jr., J. P., T. A. Wisialowski, ., D. M. Roden. 1991. Virtual
cathode effects during stimulation of cardiac muscle. Two-dimensional
in vivo experiments. Circ. Res. 68:513–530.
7. Sambelashvili, A. T., V. P. Nikolski, and I. R. Eﬁmov. 2003. Nonlinear
effects in subthreshold virtual electrode polarization. Am. J. Physiol.
Heart Circ. Physiol. 284:H2368–H2374.
8. Lin, S. F., B. J. Roth, and J. P. Wikswo, Jr. 1999. Quatrefoil reentry in
myocardium: an optical imaging study of the induction mechanism.
J. Cardiovasc. Electrophysiol. 10:574–586.
9. Eﬁmov, I. R., F. Aguel, ., N. Trayanova. 2000. Virtual electrode polar-
ization in the far ﬁeld: implications for external deﬁbrillation. Am.
J. Physiol. Heart Circ. Physiol. 279:H1055–H1070.
10. Fast, V. G., O. F. Sharifov, ., R. E. Ideker. 2002. Intramural virtual
electrodes during deﬁbrillation shocks in left ventricular wall assessed
by optical mapping of membrane potential. Circulation. 106:
11. Wikswo, Jr., J. P., S.-F. Lin, and R. A. Abbas. 1995. Virtual electrodes
in cardiac tissue: a common mechanism for anodal and cathodal stim-
ulation. Biophys. J. 69:2195–2210.
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization 2065
12. Sharifov, O. F., and V. G. Fast. 2006. Role of intramural virtual elec-
trodes in shock-induced activation of left ventricle: optical measure-
ments from the intact epicardial surface. Heart Rhythm. 3:1063–1073.
13. Zemlin, C. W., S. Mironov, and A. M. Pertsov. 2006. Near-threshold
ﬁeld stimulation: intramural versus surface activation. Cardiovasc.
14. Plonsey, R., and R. C. Barr. 1986. Effect of microscopic and macro-
scopic discontinuities on the response of cardiac tissue to deﬁbrillating
(stimulating) currents. Med. Biol. Eng. Comput. 24:130–136.
15. Fast, V. G., S. Rohr, ., A. G. Kle
ber. 1998. Activation of cardiac tissue
by extracellular electrical shocks: formation of ‘‘secondary sources’’ at
intercellular clefts in monolayers of cultured myocytes. Circ. Res.
16. Trayanova, N., K. Skouibine, and F. Aguel. 1998. The role of cardiac
tissue structure in deﬁbrillation. Chaos. 8:221–233.
17. Fenton, F. H., S. Luther, ., R. F. Gilmour, Jr. 2009. Termination of
atrial ﬁbrillation using pulsed low-energy far-ﬁeld stimulation. Circu-
18. Hooks, D. A., M. L. Trew, ., A. J. Pullan. 2006. Do intramural virtual
electrodes facilitate successful deﬁbrillation? Model-based analysis of
experimental evidence. J. Cardiovasc. Electrophysiol. 17:305–311.
19. Sharifov, O. F., V. G. Fast, V. G. Fast., 2004. Intramural virtual elec-
trodes in ventricular wall: effects on epicardial polarizations. Circula-
20. Plank, G., A. Prassl, ., N. A. Trayanova. 2008. Evaluating intramural
virtual electrodes in the myocardial wedge preparation: simulations of
experimental conditions. Biophys. J. 94:1904–1915.
21. Matiukas, A., B. G. Mitrea, . , L. M. Loew. 2007. Near-infrared
voltage-sensitive ﬂuorescent dyes optimized for optical mapping in
blood-perfused myocardium. Heart Rhythm. 4:1441–1451.
22. Baxter, W. T., S. F. Mironov, ., A. M. Pertsov. 2001. Visualizing exci-
tation waves inside cardiac muscle using transillumination. Biophys. J.
23. Mitrea, B. G., M. Wellner, and A. M. Pertsov. 2009. Monitoring intra-
myocardial reentry using alternating transillumination. Conf. Proc.
IEEE Eng. Med. Biol. Soc. 2009:4194–4197.
24. Mironov, S. F., F. J. Vetter, and A. M. Pertsov. 2006. Fluorescence
imaging of cardiac propagation: spectral properties and ﬁltering of
optical action potentials. Am. J. Physiol. Heart Circ. Physiol. 291:
25. Sepulveda, N. G., B. J. Roth, and J. P. Wikswo, Jr. 1989. Current injec-
tion into a two-dimensional anisotropic bidomain. Biophys. J. 55:
26. Roth, B. J. 1991. Action potential propagation in a thick strand of
cardiac muscle. Circ. Res. 68:162–173.
27. Caldwell, B. J., M. L. Trew, ., B. H. Smaill. 2009. Three distinct
directions of intramural activation reveal nonuniform side-to-side
electrical coupling of ventricular myocytes. Circ. Arrhythm. Electro-
28. LeGrice, I. J., B. H. Smaill, ., P. J. Hunter. 1995. Laminar structure of
the heart: ventricular myocyte arrangement and connective tissue archi-
tecture in the dog. Am. J. Physiol. 269:H571–H582.
29. Luo, C. H., and Y. Rudy. 1994. A dynamic model of the cardiac ventric-
ular action potential. I. Simulations of ionic currents and concentration
changes. Circ. Res.
Cheng, D. K., L. Tung, and E. A. Sobie. 1999. Nonuniform responses
of transmembrane potential during electric ﬁeld stimulation of single
cardiac cells. Am. J. Physiol. 277:H351–H362.
31. Hyatt, C. J., S. F. Mironov, ., A. M. Pertsov. 2005. Optical action
potential upstroke morphology reveals near-surface transmural propa-
gation direction. Circ. Res. 97:277–284.
32. Cheek, E. R., V. G. Fast, V. G. Fast., 2004. Nonlinear changes of
transmembrane potential during electrical shocks: role of membrane
electroporation. Circ. Res. 94:208–214.
33. Sharifov, O. F., R. E. Ideker, and V. G. Fast. 2004. High-resolution
optical mapping of intramural virtual electrodes in porcine left ventric-
ular wall. Cardiovasc. Res. 64:448–456 (see comment).
34. Sharifov, O. F., and V. G. Fast. 2003. Optical mapping of transmural acti-
vation induced by electrical shocks in isolated left ventricular wall
wedge preparations. J. Cardiovasc. Electrophysiol. 14:1215–1222.
35. Ashihara, T., and N. A. Trayanova. 2004. Asymmetry in membrane
responses to electric shocks: insights from bidomain simulations. Bio-
phys. J. 87:2271–2282.
36. Cheek, E. R., R. E. Ideker, and V. G. Fast. 2000. Nonlinear changes of
transmembrane potential during deﬁbrillation shocks: role of Ca
current. Circ. Res. 87:453–459 (See comment.).
37. Maleckar, M. M., M. C. Woods, ., N. A. Trayanova. 2008. Polarity
reversal lowers activation time during diastolic ﬁeld stimulation of
the rabbit ventricles: insights into mechanisms. Am. J. Physiol. Heart
Circ. Physiol. 295:H1626–H1633.
38. Hooks, D. A., K. A. Tomlinson, ., P. J. Hunter. 2002. Cardiac micro-
structure: implications for electrical propagation and deﬁbrillation in
the heart. Circ. Res. 91:331–338.
39. Stinstra, J., R. MacLeod, and C. Henriquez. 2010. Incorporating
histology into a 3D microscopic computer model of myocardium to
study propagation at a cellular level. Ann. Biomed. Eng. 38:1399–1414.
40. Roberts, S. F., J. G. Stinstra, and C. S. Henriquez. 2008. Effect of
nonuniform interstitial space properties on impulse propagation:
a discrete multidomain model. Biophys. J. 95:3724–3737.
Biophysical Journal 99(7) 2058–2066
2066 Caldwell et al.