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‡Physics Department,
Syracuse University, Syracuse, New York
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
Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart,
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.
? 2010 by the Biophysical Society
2058Biophysical JournalVolume 99October 20102058–2066
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
4?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
(37?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
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
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).
Foreach shock strength and fieldorientation, fourmovies (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 (DVm) (Fig. 3 A) was estimated at
from dF/dtmaxof 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,
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
transillumination (NP) and CCD-2 records epi-
Alternating transillumination map-
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 DVmfor 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
incorporatingan additionaloutwardcurrent (Ia) 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 plateau 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
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
Activation during uniform field pacing at twice the excitation
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.
Weighting functions for epifluorescence and transillumina-
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.
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% APamplitude
(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 beneath 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). Unlikeweak
shocks, strong shocks produced significant negative bulk
polarization, as seen in the transillumination 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,y coordi-
nates 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
(35.1 V/cm) (B) applied during the plateau phase of optical APs generated
by uniform field pacing (see Fig. 4). DVmis 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. DVm, expressed as mean 5
SD, is shown below each map.
DVmduring weak shock (3.6 V/cm) (A) and strong shock
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization2061
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/dtmax. 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
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/cmPP PNNPNNField polarity
2.6 5 0.4
2.8 5 0.7
34.2 5 0.8
34.0 5 1.2
5.8 5 2.5
?6.1 5 1.7
?24.2 5 7.1
?56.8 5 7.3
0.8 5 1.3
?1.0 5 1.5
?33.7 5 3.6
?42.2 5 4.7
?0.5 5 1.1
0.2 5 0.7
?35.4 5 4.5
?39.0 5 4.2
?3.8 5 1.4
3.1 5 0.7
?42.3 5 4.6
?25.2 5 6.6
% 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
2062Caldwell et al.
recordings and experimental protocols. We calculated the
transmural distributions of Vm 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 (Ia), acti-
vated at high transmembrane 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 ¼ ?9.6 and NN ¼
11.1% APA) are approximately two to three times larger
than those recorded experimentally (PP ¼ ?5.8 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 augmented 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. Finally, 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,
and 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
shock-induced Vmduring 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 Ia(B).
The cathode is at the endocardial
Simulated optical APs of
Biophysical Journal 99(7) 2058–2066
Field-Induced Tissue Polarization2063
(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 Ia, which shifts the
inherent positive bias in the LRd model to a negative bias
during such shocks (35). The existence of Iais inferred
from fluorescence imaging experiments, but its ionic nature
remains poorly understood. An experimental study by
Cheek et al. (36) suggests that Iamay flow through the
L-type Ca2þchannel. However, the measurements of Ia
have yet to be corroborated by direct voltage-clamp experi-
In previous simulations in continuous bidomain models
(20,35), Iadid 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
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 Ia, in continuous
bidomain models (20,35), a substantial volume underneath
the cathode is depolarized. In contrast, in the discontinuous
model, Ia 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
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 Ia. 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.
Simulated Vm for near-
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 produceverylittle bulkpolarization, 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 surface 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 underestimate 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 conclusion 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 potentials 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 requires
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 patterns 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 finding 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
(e.g., Ia) is insufficient, because even in such an augmented
model, surface polarization still exceeds intramural polari-
zation (20,35). 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 evenfor weak shocks (13), butthe
distributions used in this study were not based on experi-
mental measurement, and it is unclear whether similar
distributions underlie 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 possibility 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.
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