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Am J Physiol Heart Circ Physiol 297: H1521–H1534, 2009.
First published August 21, 2009; doi:10.1152/ajpheart.01066.2008.
Experimental and theoretical ventricular electrograms and their relation to
electrophysiological gradients in the adult rat heart
Rodrigo Weber dos Santos,1 Anders Nygren,2,3,4 Fernando Otaviano Campos,1,5 Hans Koch,6 and
Wayne R. Giles2,7
1
Department of Computer Science, Universidade Federal de Juiz de Fora, Juiz de Fora, Brazil; 2Department of Physiology
and Biophysics, 3Department of Electrical and Computer Engineering, 4Centre for Bioengineering Research and Education,
and 7Faculty of Kinesiology, University of Calgary, Calgary, Alberta, Canada; 5Institute of Biophysics, Medical University of
Graz, Graz, Austria; and 6Department of Biosignals, Physikalisch-Technische Bundesanstalt, Berlin, Germany
Submitted 2 October 2008; accepted in final form 18 August 2009
cardiac electrophysiology; electrocardiogram; potassium currents;
mathematical models; voltage-sensitive dyes
many different genetically altered mouse
models of known defects in the human cardiovascular system
has created a strong demand for a more quantitative understanding of murine cardiovascular physiology (8, 15, 25, 36,
41– 43, 57, 58). In addition, the recent completion of the rat
genome (22) and improvements in methods for genetically
modifying rat progeny (1) have provided a need for improved
cardiovascular measurements in the rat. Within the past five
years, significant advances have been made in adapting existing electrophysiological recording techniques for application to
the mouse and rat heart. Important examples include recordings and analyses of the electrocardiogram (ECG) (4, 13, 18,
37, 61) and monophasic action potential (MAP) recordings (18,
32, 34).
However, a quantitative analysis and a mechanistic interpretation of the repolarization phase (or T wave) of the rodent
THE AVAILABILITY OF
Address for reprint requests and other correspondence: R. Weber dos
Santos, Dept. of Computer Science, Univ. Federal de Juiz de Fora, Juiz de
Fora, Brazil (e-mail: [email protected]).
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ECG and surface electrograms remain very difficult, in part
because of the high heart rate and very brief action potential
(AP) duration (APD) in mice and rats compared with those of
larger mammals including humans (27, 51, 53, 60). The ventricular APs in both mice and rats lack the distinct plateau
phase that is characteristic of the mammalian ventricular AP.
Instead, ventricular APs in mouse and rat have a triangular
shape due to a very rapid phase of repolarization that almost
immediately follows the initial depolarization. The lack of a
plateau phase between depolarization and repolarization results
in the absence of an isoelectric S-T segment, which separates
the QRS complex from the T wave in the ECG of larger
mammals. In the lead I ECG of the adult rat or mouse, the QRS
complex is followed immediately by a positive deflection that
is generated mainly by what in larger mammals would be
termed early repolarization. Late or final repolarization of the rat
or mouse AP gives rise to a smaller, longer-lasting, and usually
negative deflection of the ECG in distinction to the positive T
wave of the mammalian ECG. In this article, we have used the
notation Tp for the early, positive deflection and Tn for the later,
negative deflection to clearly identify these two separated deflections related to repolarization in the rat or mouse ECG.
Recently, the repolarization phase of the adult mouse ECG,
and in particular its relationship to repolarization of the AP as
measured by the MAP, has been the focus of a number of
studies (13, 18, 27). Danik et al. (18) examined the relationship
between MAP duration [at 50% (APD50) or 90% (APD90)
repolarization] and the Q-T interval of the surface ECG. Their
recordings revealed only a very weak correlation between any
of these parameters; accordingly, they concluded that an accurate measurement of the repolarization of the murine ventricle
could not be obtained from surface ECG recordings. In contrast, the study of Liu et al. (34), which was based on measurements of the epicardial and endocardial MAPs and included comparison to simultaneous recordings of limb lead
ECGs, suggested that there may be a close correlation between
the end of the T wave and the onset of the short plateau phase
of the epicardial MAP. Liu et al. (34), in fact, concluded that
the Tp of the ECG corresponded to the J wave of the ECG in
larger mammals. Interestingly, in the Liu et al. (34) study, the
MAP recordings exhibited a short but distinct plateau phase.
The similarity between the J wave in mammals and early
repolarization had been pointed out previously with respect to
the rat ventricular AP and ECG by Gussak et al. (27). In
agreement with Danik et al. (18), Liu et al. (34) concluded that
the slow final phase of repolarization could not be detected in
the adult mouse ECG.
0363-6135/09 $8.00 Copyright © 2009 the American Physiological Society
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Weber dos Santos R, Nygren A, Campos FO, Koch H, Giles
WR. Experimental and theoretical ventricular electrograms and their
relation to electrophysiological gradients in the adult rat heart. Am J
Physiol Heart Circ Physiol 297: H1521–H1534, 2009. First published
August 21, 2009; doi:10.1152/ajpheart.01066.2008.—The electrical
activity of adult mouse and rat hearts has been analyzed extensively,
often as a prerequisite for genetic engineering studies or for the
development of rodent models of human diseases. Some aspects of the
initiation and conduction of the cardiac action potential in rodents
closely resemble those in large mammals. However, rodents have a
much higher heart rate and their ventricular action potential is triangular and very short. As a consequence, an interpretation of the
electrocardiogram in the mouse and rat remains difficult and controversial. In this study, optical mapping techniques have been applied to
an in vitro left ventricular adult rat preparation to obtain patterns of
conduction and action potential duration measurements from the
epicardial surface. This information has been combined with previously published mathematical models of the rat ventricular myocyte to
develop a bidomain model for action potential propagation and
electrogram formation in the rat left ventricle. Important insights into
the basis for the repolarization waveform in the ventricular electrogram of the adult rat have been obtained. Notably, our model demonstrated that the biphasic shape of the rat ventricular repolarization
wave can be explained in terms of the transmural and apex-to-base
gradients in action potential duration that exist in the rat left ventricle.
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METHODS
Experimental Preparation
The experimental protocol used in the study was reviewed and
approved by the University of Calgary Health Sciences Animal Care
Committee to ensure that all experiments followed the guidelines of
the Canadian Council for Animal Care. Rat hearts were isolated using
a procedure similar to one published previously (46). Male SpragueDawley rats (250 –300 g) were injected with 300 units of heparin (ip)
15 min before the heart was isolated. The animals were anaesthetized
with pentobarbital sodium and euthanized by cervical dislocation,
after which the heart was immediately excised and placed in ice-cold
Krebs-Henseleit solution. Following the removal of extraneous tissues, the aorta was cannulated and perfusion with Krebs-Henseleit
solution (37°C) was started at a constant flow rate of 13 ml/min. The
Krebs-Henseleit buffer consisted of (in mM) 118.0 NaCl, 4.7 KCl, 1.2
KH2PO4, 1.2 MgSO4, 1.0 CaCl2, 25.0 NaHCO3, and 11.1 glucose. It
was bubbled with 95% O2-5% CO2 in a 37°C water bath for a pH of
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7.4. This solution passed through a glass heating coil (Radnoti Glass
Technology, Monrovia, CA) immediately before entering the aorta.
The heart was immersed in solution in a water-jacketed chamber
throughout these recordings. The heating coil and water-jacketed
chamber were warmed using a thermocirculator (Harvard Apparatus,
Saint Laurent, QC, Canada). The temperature in the bath near the
heart was monitored using a thermocouple device (Harvard Apparatus) and recorded throughout each experiment. With this setup, the
heart temperature could be controlled to within 1°C of the desired
recording temperature (37°C). 4-Aminopyridine (4-AP) was prepared
as a 1 M stock solution in distilled water. The pH of the 4-AP stock
solution was adjusted to 7 by titration with HCl.
Optical Mapping
After perfusion was begun and the pacing and electrogram
electrodes were attached, the heart was immersed in the waterjacketed recording chamber and maintained at 37°C. A 30-min
stabilization period followed, during which the perfusion pressure
and electrogram were monitored and recorded. The solution was
then switched to one containing 1 ␮M 4-{␤-[2-(di-n-butylamino)6-naphthyl]vinyl}pyridinium (di-4-ANEPPS; Molecular Probes,
Portland, OR) for a period of 5 min. Di-4-ANEPPS was prepared as
10 mM stock solution in DMSO (stored frozen) and added to the
standard Krebs-Henseleit solution (0.01% DMSO in the final solution). After the dye-loading procedure had been completed, the heart
was perfused with the standard Krebs-Henseleit solution for the
remainder of the experiment unless otherwise noted. To reduce the
influence of motion artifacts on our recordings, the heart was positioned and stabilized in the chamber using adjustable supports on
either side. In addition, for short periods of time (⬇10 s) during each
recording, the heart was gently pressed against the front glass of the
chamber using a remotely operated paddle behind the heart to immobilize it and to obtain a relatively flat surface for imaging. The motion
blocker cytochalasin D (3 ␮M; Sigma-Aldrich, Oakville, ON, Canada) was added to the perfusate to reduce the contractile force
sufficiently that APDs could be measured reliably (29). The imaging
system has been described in detail elsewhere (46).
As explained in the next section, the optical maps were processed
to produce activation and APD maps of the epicardial surface.
Recordings of the activation sequence were carried out in sinus
rhythm. However, recordings aimed at measuring APDs were carried
out using pacing from the base to ensure that the rate of activation was
consistent across preparations.
Data Processing
Data were processed off-line using software developed in the IDL
development environment (Research Systems, Boulder, CO) with
external routines written in C⫹⫹ (Visual C⫹⫹, Microsoft, Redmond,
WA) for the most computationally demanding tasks. The data recorded for each individual pixel were processed as follows: 1) the
background fluorescence level was subtracted from the signal, 2) any
linear trend in the data was removed, and 3) the sign of the data was
changed so that a depolarization corresponded to a positive change in
the signal. Areas of the field of view not covering the preparation were
manually masked and excluded from further analysis. The activation
time for each pixel was detected as the time of the maximum rate of
rise of the fluorescence signal. Activation maps were computed for
individual cycles with activation times referenced to the stimulus
pulse (paced rhythms) or the R (or S) wave of the electrogram (sinus
rhythm). Signal-averaged activation maps were then computed by
averaging the activation times for individual pixels over all cycles.
The activation maps used in this study are signal averaged over 5 s of
recording (20 –25 cycles).
Repolarization times were detected as the time of crossing a level
corresponding to 80% repolarization. This detection was done using
lowpass filtered (5-point moving average smoothing) and signal-
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A very significant contribution to the present understanding
of the J and T wave of the mammalian ECG has been made by
Antzelevitch and colleagues (26, 65, 66). They have developed
a novel preparation consisting of a perfused “wedge” of the
canine left ventricle (LV) and published extensive data based
on microelectrode impalements and simultaneous transmural
electrogram recordings. Their findings relate both the J and T
waves of the ECG to the transmural gradient of AP waveforms
and heterogeneous expression of underlying K⫹ and Ca2⫹
currents. Based, in part, on these findings, Gima and Rudy (23)
developed a one-dimensional mathematical model to simulate
many of the important features of the electrogram of this
transmural wedge preparation. Recently, Bondarenko and Rasmusson (5) have also developed a similar one-dimensional
mathematical model for the mouse (6) that reproduced in silico
important mechanisms related to cardiac arrhythmia, such as
AP alternans and Ca2⫹ concentration transients. In that work,
the computer simulations have also suggested that mouse heart
should be able to sustain substantial molecularly based heterogeneity of repolarization.
The present study extends the Gima and Rudy (23) work by
developing a 2-D model of a significant fraction of the LV of
the adult rat heart. Recent studies suggest that T-wave intervals
do not correlate with a transmural dispersion of repolarization
but rather with a whole heart dispersion of repolarization (47,
63). Accordingly, our computational model contributes to the
understanding of how nontransmural gradients of repolarization, in particular, apex-to-base gradients, are related to the T
wave of the rat ECG.
Many of the most important parameters of our model are
based on our experimental recordings using voltage-sensitive
dye methods (3, 21, 38, 44 – 46) of apex-to-base conduction
times and gradients in epicardial APD. Optical data were
combined with recordings of the extracellular electrogram and
computations of the analogous signals in the extracellular
space. We have focused on the rat heart because detailed
models of the cellular electrophysiology of ventricular myocytes from the endocardium and epicardium are available (49)
and because the Langendorff-perfused rat heart is used routinely for voltage-sensitive dye recordings in our laboratory
(46). The availability of the rat genome and the very common
use of the adult rat in Safety Pharmacology provided additional
motivations for this study.
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Electrogram Recordings
Langendorff-perfused rat heart preparations used for electrogram
recordings were prepared in the same way as for optical mapping,
except that no dye (di-4-ANEPPS) or motion blocker (cytochalasin D)
was added to the perfusate. Electrograms were recorded using AgAgCl electrodes in the form of small loops sutured onto the surface of
the heart for epicardial recordings. Endocardial recordings were obtained using an Ag-AgCl “hook” electrode (Teflon insulated, except at
the tip), which was inserted through the wall using a needle and then
pulled back to make contact with the endocardial surface. Figure 1A
shows the electrode arrangement. Note that recordings were made
with the heart intact and in sinus rhythm. The preparation shown in
Fig. 1A has been cut open after the completion of the study to examine
the position of the endocardial electrode. Electrograms were recorded
using an alternating current-coupled differential amplifier (model
1700, A-M Systems, Carlsborg, WA) with a highpass cutoff of 0.1 Hz.
Signals were lowpass filtered at 500 Hz and acquired at the same
sampling rate as the optical mapping data (950 Hz). Electrogram
signals shown in this article were signal averaged over 20 s of
recordings.
Mathematical Simulations
We have developed a mathematical model for the purpose of
simulating electrophysiological phenomena arising from a segment of
rat LV that is assumed to be in a perfusion medium or bath (a passive
and isotropic conductor). The size of this ventricular tissue was
chosen to be ⬃4 mm (endo- to epicardium) by 12 mm (apex to base).
As shown in Fig. 1B, both endocardium and epicardium surfaces
interface with a 4 ⫻ 12-mm bath, yielding an overall tissue-bath
dimension of 12 ⫻ 12 mm. The mathematical model includes the
formulation of a passive and isotropic conductor that interfaces with
cardiac tissue, as to capture the experimental preparations where the
hearts were immersed in a perfusing solution.
Our simulations are based on the bidomain equations to account for
both the intracellular and extracellular domains of this cardiac tissue.
The functional coupling of these two domains is accomplished using
nonlinear sets of equations that describe the transmembrane ionic
currents, which are expressed in the sarcolemma of the rat ventricular
myocyte as described in detail by Pandit et al. (49). In fact, two
distinct ventricular myocyte models were used in these calculations:
the first depicts myocytes within the epicardium, and the second
simulates electrophysiological processes in endocardial myocytes.
The initial conditions used were those obtained after pacing the
myocyte models at 1 Hz until steady state was reached.
The numerical solution of the large nonlinear partial differential
system yields spatial distributions and temporal characteristics of the
extracellular potential (␾e), intracellular potential (␾i), and transmembrane potential. All bidomain parameters were based on those reported in previous experimental work (39). A three-dimensional (3-D)
orthotropic conductivity tensor was used to replicate the laminar fiber
structure of the heart: higher conduction velocity occurs along fibers,
medium conduction velocity across fibers in the same sheet, and
lowest conduction velocity is across sheets in the tissue. The cardiac
tissue conductivity values from the literature (39) have been uniformly rescaled to match the reported apex-to-base (70 cm/s) and
transmural conduction velocities (45 cm/s) in the mammalian ventricles. The bath conductivity was set to 20 mS/cm. The capacitance per
unit area and the surface area-to-volume ratio are set to 1 ␮F/cm2 and
2,000/cm, respectively. Table 1 summarizes the parameters used for
the bidomain equations.
The interface between the cardiac tissue and the bath is modeled as
described previously (33). All the other boundaries are assumed to be
electrically insulated. The spatial and temporal discretization steps of
the numerical model are set to 50 ␮m and 5 ␮s, respectively. All
simulations were carried out for a minimum of 500 ms after a single
current stimulus was introduced at a selected endocardial site. The
fiber-laminar structure of the heart can be represented by a local tensor
Fig. 1. Diagram illustrating the experimental recording configuration with corresponding 2-dimensional (2-D) model of adult rat left ventricle (LV) and recording
electrodes. A: electrode locations for transmural ECG recordings in Langendorff-perfused rat hearts. The epicardial electrodes consisted of Ag-AgCl loops sutured
to the surface of the LV. The endocardial “hook” electrode was inserted through the wall using a needle and then pulled back to establish contact with the
endocardial surface. Note that the preparation shown was cut open after the completion of the experiment to verify electrode locations. All recordings were made
with the heart intact. B: geometrical parameters of our mathematical model of the “wedge” preparation for the rat LV, corresponding to the experimental setup
described in A. This model consists of a rectangular 2-D slice of LV tissue, surrounded by bath solution (black) on both the endocardial and epicardial sides.
The color map on the ventricular tissue shows a typical transmembrane potential (mV) distribution obtained during repolarization. The electrode locations used
in the simulations are shown as yellow circles.
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averaged data to avoid spurious detections due to remaining noise.
APs at individual pixel locations affected by remaining motion artifact
or having unusually low signal-to-noise ratio were excluded based on
the following heuristic criteria, applied to the signal-averaged but
unfiltered signal: 1) the signal must remain below 15% of the maximum amplitude until 15 ms before the detected activation (maximum
rate of rise) time (to exclude signals with unstable baseline and/or
large noise), 2) the signal must reach above 90% of the maximum
amplitude within 20 ms after the activation time (to exclude signals
with very slow upstrokes), and 3) the signal must return (and remain)
below 15% of the maximum amplitude by 100 ms after the activation
time (to exclude signals with unstable baseline, large noise, or very
long apparent APDs due to motion artifacts). APDs were then computed as the intervals between the activation time, and the repolarization time was detected for each pixel. The field of view was divided
into three equal parts (base, middle, and apex), and summary statistics
(means ⫾ SE) of the APD were computed for each region to quantify
the apex-to-base APD gradient.
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Table 1. Parameters of the bidomain model
Parameter
Value
Capacitance per unit area, ␮F/cm2
Surface area-to-volume ratio, /cm
Bath conductivity, mS/cm
Intracellular conductivity along fibers, mS/cm
Intracellular conductivity across fibers, mS/cm
Intracellular conductivity across sheets, mS/cm
Extracellular conductivity along fibers, mS/cm
Extracellular conductivity across fibers, mS/cm
Extracellular conductivity across sheets, mS/cm
1
2,000
20
6.2
1.3
0.5
4.1
3.6
2.1
Parameter values of the bidomain equations.
RESULTS
Optical Mapping of Activation and Measurement of APD
Optical mapping experiments were carried out on seven
Langendorff-perfused rat hearts. Motion artifacts were minimized by using cytochalasin D (3 ␮M) in combination with a
mechanical restraint of the preparation. Isochronal activation
maps were constructed from data collected in sinus rhythm, as
described in METHODS. Figure 2A shows a typical pattern of the
activation sequence. Note that the first detectable activation
(epicardial breakthrough) occurred at a site near the apex. The
activation wave was then moved approximately uniformly
toward the base of the LV, and activation was completed in 2
to 3 ms.
APDs were measured at sites across the epicardium from
these recordings. To ensure that the heart rate was consistent
across all preparations (to avoid any influence of rate dependence of the APD), APDs were measured from recordings
made during fixed rate pacing. The pacing electrode was
positioned at the base of the LV of each preparation. The
average APDs at the base, midregion, and apex of the LV were
measured. Figure 2B shows a summary of these results. Note
Fig. 2. Optical mapping data. A: a typical 2-D activation
map. The activation map was recorded in sinus rhythm (no
pacing applied; the heart is controlled by the sinus node).
Zero time on the time scale is defined as the peak of the R
wave in the electrogram. Note that early epicardial activation produces a “breakthrough” location near the LV apex.
Epicardial activation thus begins near the LV apex and
proceeds toward the base. Activation of the entire LV
epicardium is completed over 2 to 3 ms. B: average
epicardial action potential durations (APDs) at 80% repolarization (APD80) obtained from the optical mapping data.
C: optical action potentials in selected locations across the
LV epicardium in a representative preparation. These data
have been signal averaged over 20 –25 cycles to improve
signal-to-noise ratio. Note that APDs gradually shorten
toward the apex as indicated by the summary data in B.
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that is based on information denoting myocardial fiber orientation,
sheet direction of the myocardial laminae, and normal direction of the
overall sheet structure. Jiang et al. (30) have recently examined the
distribution of myocardial fiber and sheet orientation in normal
murine hearts based on diffusion tensor magnetic resonance imaging.
In such measurements, each direction parameter was converted to a
pair of angles in a local cylindrical coordinate system composed of
three orthogonal references. In our simulations, fiber direction is
represented by a fiber angle, whereas sheet angle attains information
specifying sheet direction. The exact definition of these angles can be
found in our previous work (19).
Fiber and sheet angles have both been shown to vary in the
transmural and apex-to-base aspects of the LV wall of adult rats (12,
13). For simplicity, our computer model incorporates only transmural
changes in these fiber and sheet angles. The fiber angle was set to
progress (change) linearly from 60° at the endocardium to ⫺60° at the
epicardium. The sheet angle was assumed to change linearly from 30°
at the endocardium to ⫺10° at subepicardium. At a point that
corresponds to 10% of the transmural distance from the epicardial
surface, we have introduced a break in this continuity. At this point,
the sheet angle changes from ⫺10° to ⫺60°. In this 10% region
closest to the epicardial border, the sheet orientation does not change:
it is kept at ⫺60°. This distribution of angles was chosen to reproduce
the pattern of orientation obtained from the histological data and
analysis by Yan and Antzelevitch (66).
In our mathematical model, for every anatomical point on the
ventricular wall, the corresponding fiber and sheet angles were used to
compute the 2-D projection of the 3-D conductivity tensor of the
bidomain mathematical formulation.
Signals that would be sensed by transmural electrogram leads were
calculated by taking the difference of the simulated ␾e at the endocardial and epicardial boundary points. This is illustrated in Fig. 1.
Lead I equals ␾e at the epicardium base minus ␾e at the endocardium.
APD90 was calculated for every discretized point of the LV tissue,
using the difference between the activation time and the repolarization
time to 90% relaxation. Activation times were obtained as the time of
the maximum rate of rise of the simulated transmembrane potentials.
Repolarization times were calculated as the time of crossing a level
corresponding to 90% of repolarization to the transmembrane resting
potential.
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that there is a distinct APD gradient in the rat LV: the
epicardial APD is shorter at the apex than at the base (Fig. 2C).
Recording of Surface Electrograms
Modeling of the LV Wedge Preparation
Requirements for a positive T wave. Recorded LV electrograms and the average distributions of the activation sequences
and APD data from the optical maps obtained on the epicardial
surface were used to guide our computer simulations. However, some other important information necessary to develop a
realistic computational LV wedge is not available in the literature. In particular, although it is known that the AP shapes of
endo- and epicardial myocytes in the rat heart are different
Fig. 3. Lead I electrogram records from 5 Langendorff-perfused rat hearts. Note that during
repolarization, lead I shows a prominent early
positive T-wave deflection (Tp) followed by a
smaller negative T-wave deflection (Tn). These
recordings were obtained in separate studies
from the optical mapping experiments. These
preparations were not perfused with either
4-{␤-[2-(di-n-butylamino)-6-naphthyl]vinyl}
pyridinium (di-4-ANEPPS) or cytochalasin D
(see METHODS). A: records under control conditions. B: lead I electrogram records of 3 rat
hearts after perfusion with 4-aminopyridine
(4-AP, 5 mM). The Tp shifts to the right, i.e.,
QT interval lengthens as expected in these
hearts. The amplitude of the Tp wave increases for 2 rat hearts and decreases for the
third one. Note that a brief isoelectric ST
segment appears in the record for rat 3 as the
repolarization wave separates from the QRS
complex.
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Surface electrograms were recorded from five Langendorffperfused rat heart preparations. Each of these hearts was
prepared in the same way as for the optical mapping studies.
However, no dye (di-4-ANEPPS) was added, and the perfusate
did not contain cytochalasin D. The recording electrodes were
positioned with one epicardial electrode located near the base
of the LV and an endocardial electrode located near the base of
the LV. The experimental results for lead I configuration were
consistent across all five preparations, as shown in Fig. 3A.
To verify that the QT interval in these recordings reflected
the APDs in this preparation, additional measurements were
carried out in three hearts in the presence of 5 mM 4-AP. This
large concentration of 4-AP produces a substantial block of the
transient outward K⫹ current (Ito) and therefore a large prolongation of the AP. As seen in Fig. 3B, 4-AP application
prolonged the QT interval and began to separate the Tp wavefrom the depolarization (QRS) complex. In one case (rat 3),
4-AP application even resulted in a brief isoelectric ST segment, similar to that observed in larger mammals. These results
clearly show that the QT interval (Q-to-Tp interval) in these
recordings is directly related to APD.
(49), little information is available about the relative amount of
endo- and epicardial myocytes across the ventricular wall.
Accordingly, we made use of the information provided by the
experiments as a basis for a plausible computational model of
the LV wedge preparation from the adult rat. After validating
the basic properties of this model, we used it to quantify the
influence of some important variables we did not have control
of during the experiments. Our main goals were to evaluate the
influence of the distribution of endo- and epicardial myocytes,
the transmural activation sequence, the transmural APD distribution, and the Ito distribution.
There is no complete set of experimental data that specifies
in required detail the numbers or the relative distributions of
the two different types of myocytes (epi- and endocardial) that
comprise the rat LV wall. We therefore simulated a number of
different fractions of epicardial and endocardial myocytes in
our model. Activation was initiated with a current stimulus on
the endocardial surface, therefore initiating a strictly transmural AP propagation. Figure 4A illustrates how different ratios of
epicardial to endocardial myocytes affect the computed transmural electrogram. A consistent finding was that wedges having a high percentage of epicardial myocytes generated electrograms with positive T waves. Moreover, as the ratio of
epicardial to endocardial myocytes decreased progressively,
the amplitude of the computed T waves gradually decreased,
flattened, and finally reversed polarity to become weakly negative. This dependency of T-wave amplitude (and polarity) on
the percentage of epicardial myocytes is mainly due to electrotonic effects and can be better understood by transmembrane
potential maps taken at 30 ms and presented in Figs. 4, B–D.
As presented by Fig. 4B, with no epicardial myocytes at all,
there is a weak repolarization gradient from right to left (i.e., the
endocardium is more repolarized than the epicardium). This
weak reverse gradient, caused by the propagation delay
through the wall, gives rise to the weak negative T wave seen
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in Fig. 4A (0% epi). On the other hand, in a case with 50% of
epicardial myocytes (Fig. 4D), the two halves of the tissue have
significantly different repolarization time courses, which give
rise to a strong repolarization gradient from left to right (i.e.,
epicardium is more repolarized than endocardium) and to a
substantial positive T-wave amplitude (Fig. 4A). Thus propagation delays through the wall can, in principle, result in a
negative T-wave deflection, but not in the presence of a
significant endo-epi APD gradient. Since the existence of the
endocardial-epicardial gradient is well established (49), the
negative deflection in the biphasic rat T wave cannot be
explained by transmural propagation delays.
The ratio of maximum QRS amplitude to maximum T-wave
amplitude in the experimentally recorded transmural electrograms (Fig. 3) was around 10%. To simulate this waveform
characteristic, our model required that at least 25% of the
transmural wall consisted of epicardial myocytes. Therefore,
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Fig. 4. A: simulated transmural electrograms (lead I) for in silico rat LV
wedges for systematic changes in the relative amounts of endocardial and
epicardial (epi) myocytes. Note that wedges having a small percentage of
epicardial myocytes generate electrograms with low-amplitude T waves. As
the relative amount of epicardial myocytes increases, the T-wave amplitude
increases. B: transmembrane potential map taken at 30 ms for the case of a
model consisting exclusively of endocardial myocytes. Note the weak reverse
gradient of repolarization, with the epicardium less repolarized than the
endocardium (see text). C: transmembrane potential map taken at 30 ms for the
case of 25% of epicardial myocytes. Note the normal gradient of repolarization, with the epicardium more repolarized than the endocardium. D: transmembrane potential map taken at 30 ms for the case of 50% of epicardial
myocyte. Note that the transmural gradient of transmembrane potential during
repolarization is very substantial for this phenotype distribution.
all subsequent simulation results that are presented in this
section are based on computational wedges with a transmural
phenotype distribution of 75% of endocardial and 25% of
epicardial myocytes.
Influence of the activation sequence on the T-wave morphology. The activation sequence obtained from the epicardial
surface (Fig. 2) started near the apex and proceeded to the base
of the LV over a total of 2 to 3 ms. However, these experiments
provide no information about the transmural activation sequence. We therefore used our model to evaluate the influence
of the activation sequence on the morphology of the T-simulated wave. Three different activation sequences were considered: one in which activation proceeds entirely from apex to
base with no transmural component (act 1), one in which
activation proceeds entirely from endocardium to epicardium
with no apex-base component (act 2), and one in which
activation proceeds in both directions with the earliest epicardial breakthrough at the apex (act 3). As illustrated in Fig. 5A,
these activation sequences were produced by simultaneously
stimulating either a small area at the apex across the entire wall
(act 1), a thin endocardial layer from apex to base (act 2), or an
endocardial layer that reached further through the wall near the
apex (act 3). Figure 5B shows the simulated epicardial activation sequence resulting from stimulating the model according
to act 3. Initiating the computer simulation with the act 3
stimulus resulted in a simulated epicardial activation sequence
that is similar to experimental observations, i.e., epicardial
activation starts at the apex and is complete in 2 to 3 ms. (see
Fig. 2). The other two stimulation protocols resulted in highly
unrealistic epicardial activation sequences: epicardial activation in response to act 1 proceeded from apex to base over a
time period of 20 ms, whereas epicardial breakthrough in
response to act 2 occurred simultaneously across the entire
preparation. Figure 5C shows how the different activation
sequences affect the transmural electrogram. Note that there is
very little difference between the electrograms resulting from
the strictly transmural activation (act 2) and the more realistic
activation sequence obtained with the act 3 stimulation protocol. Thus, as long as activation proceeds mainly in the transmural direction, our model produces a relatively consistent
T-wave morphology. Based on this observation, we made no
further attempts to exactly match experimental data for epicardial activation. In the simulations that follow, act 3 was
adopted as the standard stimulation protocol for activating our
model.
Adjustment of Q-Tp interval duration. Xia et al. (63) have
shown experimentally that the peak of the T wave and the end
of the T wave coincide with the shortest end of repolarization
(EOR) on the epicardial surface and the longest EOR on the
endocardial surface, respectively. In our experimentally recorded electrograms, the peak of the Tp wave and the end of the
Tn wave occur around 20 and 60 ms after the onset of the QRS
complex, respectively. This is not in agreement with the APDs
of epicardial and endocardial myocyte models of Pandit et al.
(49), which are considerably longer. This discrepancy is primarily due to differences in temperature between the model
and experiments. The mathematical formulations of Pandit et
al. (49) were based on patch-clamp experiments mainly recorded at 23°C. In contrast, the experimental measurements in
this article are based on the Langendorff setup and were made
at 37°C. In this study we have chosen to adjust our model to
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match the APD in the experiments by adjusting the maximal
conductivity of Ito of the Pandit et al. (49) model. Our rationale
for this choice is presented in DISCUSSION.
Figure 6 presents simulated transmural electrograms (lead I)
following homogeneous changes in the maximum conductance
of the Ito current in both endocardial and epicardial regions.
The solid line shows the simulated results under control con-
Fig. 6. Simulated transmural electrograms (lead I) generated by the in silico
rat LV wedge model following changes in the density of transient outward K⫹
current (Ito) channel of both endocardial and epicardial myocytes. The solid
line shows the results under control conditions with Ito as reported in the
original Pandit et al. (see Ref. 49), assuming that 25% of the transmural wedge
consists of epicardial myocytes. Note that following an increase of Ito density,
the QT interval shortens. However, the dependence of the T-wave amplitude
on the density of Ito is more complex. Following small changes in Ito, the
amplitude of the T wave increases. However, further increasing Ito (beyond
150%) results in a reduced T-wave amplitude. Note that at 150% of control Ito
density, the Q-Tp interval duration corresponds approximately to that obtained
in our experimental records (Fig. 3).
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ditions with Ito as reported in the original Pandit et al. (49)
article and assuming that 25% of the transmural wall consists
of epicardial myocytes. Note that following an increase of Ito,
the QT interval shortens. However, the dependence of the
T-wave amplitude on the density of Ito is more complex.
Following small changes in Ito density, the amplitude of the T
wave increases. However, further increasing the amount of Ito
beyond 150% results in a decreased T-wave amplitude. An
increase in Ito density of ⬃50% compared with the original
Pandit model parameters is necessary to reproduce the mean of
the experimentally recorded Q-Tp interval of 19 ms. This
homogenous 50% increase in Ito density was used as a baseline
for all subsequent simulations presented in this article. However, it is important to note that this simulated waveform does
not reproduce the biphasic (Tp ⫹ Tn) shape of the repolarization waveform in the experimental records (Fig. 3A).
Requirements for a biphasic T wave. The optical mapping
data (Fig. 2) show that the APDs in adult rat LV epicardium are
heterogeneously distributed, with the APD being longest near
the base of the LV. This is in agreement with the recent
findings of Brunet et al. (9) in the LV of mouse hearts. In this
preparation, rapidly inactivating transient outward K⫹ current
densities were found to be significantly higher in apex than in
base myocytes, whereas rapidly activating, slowly inactivating
outward K⫹ current and steady-state outward K⫹ current (Iss)
densities in the apex and base cells were similar. In an attempt
to simulate this pattern of heterogeneous distributions of APD,
the following simplified approach was used. The maximum
conductance of Ito was reduced in the basal half of the epicardial layer (see Fig. 7A) to increase epicardial APD in this area.
Figure 7, B and C, shows the resulting transmural electrograms
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Fig. 5. Simulations illustrating the effects of
initiating action potential propagation (activation) from different endocardial regions. A: areas
of the model preparation stimulated to produce
the 3 different activation sequences considered
(see text). B: epicardial activation sequences
resulting from the act 3 activation sequence.
Note that activation proceeds from apex to
base over ⬃2 ms, consistent with our experimental observations (Fig. 2). C: lead I electrograms resulting from the 3 activation sequences considered. Note that the 2 transmural
activation sequences (acts 2 and 3) produce
very similar repolarization waves.
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REPOLARIZATION IN RAT VENTRICLE
(lead I) and epicardial APD gradients for selected degrees of Ito
density reduction in this area. A reduction of Ito density in the
basal epicardium region decreases the positive T-wave amplitude and results in a biphasic T wave.
In addition, this reduction of Ito in the basal epicardium
region results in an apex-to-base APD gradient that is similar
to that observed experimentally. The average APD80 distribution obtained from our optical mapping data is also shown in
Fig. 7C. Note the different scales for the simulations and
Fig. 7. Transmural electrograms (lead I) and APD gradient on the epicardium
generated by simulated rat LV wedges following changes in the density of Ito
in epicardial myocytes near the LV base. Ito was reduced in the basal
epicardium (region marked “Epicardium Base”; A) to reproduce the apex-base
gradient in APD observed with optical mapping and the apex-base gradient in
Ito density reported in the literature. B: transmural electrograms obtained from
these simulations. Reduction of Ito in the basal region decreased the Tp wave
amplitude and results in a biphasic repolarization wave. C: epicardial APD90
distributions calculated from these simulations. Reduction of Ito in the basal
region increased the apex-to-base APD gradient. The average APD80 values
obtained from optical mapping data are also shown for comparison. (Note the
different scales for the simulations and experimental values.) The experimentally measured APD80 values are longer than those of the simulations primarily
due to the use of cytochalasin D (see text). At 45% Ito reduction in the basal
epicardium, the relative APD gradient in the simulation is similar to the
average relative APD gradient observed experimentally. In addition, under
these conditions, our model generates a biphasic T wave similar to our
experimental records.
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experimental values. The calculated APD80 values from the
optical mapping are longer than those of the simulations. This
is a known artifact of using cytochalasin D to reduce motion
artifacts (44). At 55% Ito reduction in the basal epicardium
region, the relative APD gradient in the simulation is similar to
the relative average APD gradient observed in the experiments
(Fig. 7C). Furthermore, the simulation generates a biphasic
repolarization wave (Fig. 7B), which is characteristic of the
lead I ECG from adult mice and rats (27). This biphasic T wave
is characterized by a Tp, followed by a Tn.
Gima and Rudy (23) have demonstrated that the T-wave/
repolarization complex in mammalian ventricles can be
strongly modulated by interactions between two or three different transmembrane ionic currents, particularly when they
are expressed in a spatially heterogeneous fashion across the
transmural aspect of the LV. In part, this is due to distinct types
of myocytes within the ventricular wall of mammals: the
so-called M cell, as well as the endocardial and epicardial
myocytes. At present, there is little information concerning the
presence or functional role of M cells in the rat ventricle.
However, our results consistently demonstrate significant
apex-to-base APD gradients on the epicardium of the rat LV.
Thus the functional interactions between these regions of the
LV were explored in our simulations. Figure 8 illustrates how
the transmural gradient caused by the epicardial region having
short APD (near the apex) contributes significantly to the
generation of the Tp of the simulated ventricular electrogram
during early repolarization. Moreover, Fig. 8 also demonstrates
that the transmural gradient caused by epicardial regions having longer APD (near the base) contributes to the Tn. In
summary, therefore, this combination of two different electrophysiological “gradients” (transmural and apex to base) can
give rise to the observed biphasic rat ventricular repolarization
wave or the Tp ⫹ Tn complex.
Parameter sensitivity analysis. The computational model
developed here has nearly one hundred parameters. Some of
them are related to the tissue model, whereas others are part of
the myocyte mathematical models of the three different regions
identified in this work: endocardium, epicardium base, and
epicardium apex. It is well known that with enough free
parameters, one can have a model fit almost any data. For this
reason we have chosen to adjust very few parameters and have
taken all the other values from the previous works where the
original models were proposed and validated. The tissue model
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Table 2. Parameters of the myocyte model
Phenotype
Maximum Conductance (in ␮S) of
Ito in the Original Pandit et al.
Model (See Ref. 49)
Maximum Conductance (in
␮S) of Ito in the Final
Wedge Model
Endocardium
Epicardium
Epicardium-base
0.016
0.035
—
0.024
0.052
0.029
Parameter values for the maximum conductance of transient outward K⫹
current (Ito) for the different phenotypes in the computational model of the rat
left ventricular wedge. In the final model the value presented for the epicardium was used for the epicardim-apex phenotype as shown in Fig. 7A. The
formulations and all other parameters of the model for the endocardium
phenotype are those presented as Model formulation for the endocardial
ventricular cell in Ref. 49. The formulations and all other parameters of the
models for the epicardium-base and epicardium-apex phenotypes are those
presented as Model formulation for the epicardial ventricular cell in Ref. 49.
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Fig. 8. Comparison of simulated LV action potentials and simulated lead I
electrogram illustrating the origin of the Tp and Tn of the repolarization phase of
the rat ECG. A: simulated lead I electrogram showing the Tp and Tn waves
(indicated by the vertical markers). B: simulated action potentials for 3 recording
electrode positions [endocardium (endo), epicardium near apex (epi apex), and
epicardium near base (epi base)]. Note that because of the apex-to-base difference
in APD, the repolarization gradient between the endocardial electrode and the
epicardial electrode at the base (endo base) is of opposite polarity to that between
the endocardial electrode and the epicardial electrode at the apex (endo apex).
Early in repolarization (first vertical marker), the transmural APD gradient is
largest near the apex. This results in a net positive deflection in the electrogram.
Later in repolarization (second marker), the transmural APD gradient is largest
near the base, resulting in a net negative deflection. Thus Tp reflects repolarization
of the epicardium near the apex area, whereas Tn reflects repolarization of the
epicardium near the base. C: the mechanism described in B can be illustrated by
plotting the difference between the action potentials at the chosen 3 electrode
positions. The APD difference between the endocardium and the epicardium near
apex generates a positive repolarization wave (apex), whereas the difference
between endocardium and the epicardium near base generates a negative repolarization wave (base). A waveform that is very similar to the simulated electrogram
signal can be generated by taking the difference between the endocardium action
potential and the average of the base and apex epicardium action potentials (mid).
was based on the bidomain formulation with parameters (see
Table 1) taken from Muzikant and Henriquez (39), and conductivities were adjusted to reproduce the conduction velocities as reported previously (34). The relative size of each
region that composes the computational wedge was adjusted
with one single parameter, the ratio of epicardial to endocardial
myocytes. As presented by Fig. 7A, the final model has 25% of
epicardial myocytes . This value was chosen to reproduce the
relative T-wave peak to QRS peak obtained in the experiments.
Propagation was initiated by stimulating different sites of the
tissue. The stimulus site named act 3 in Fig. 5A was chosen
since it better reproduced the activation sequence observed in
the experiments. Finally, rat ventricular myocytes were modeled as described in detail by Pandit et al. (49). In fact, the
original model proposes two distinct ventricular myocyte models: the first depicts myocytes within the epicardium, and the
second simulates electrophysiological processes in endocardial
myocytes. Two modifications were performed to the original
models: we have chosen to increase the maximum conductance
of Ito by 50% in both epicardial and endocardial models to
reproduce the QT interval observed in the experiments, and we
generated a third phenotype, epicardium base, by reducing Ito
expression to 55% of that of the epicardium apex. With the
three phenotypes described in Table 2, we were able to reproduce the apex-to-base APD gradient observed in the experiments and the Ito density gradient reported previously (9).
The parameter values of the final model may not be optimal
in the sense that different sets of parameters may exist that
better reproduce the experiments. Nevertheless, a more important question is how sensitive the final model and results are to
each of the adjusted parameters. Figure 9A presents the sensitivity of the waveform of the transmural electrogram to the
percentage of epicardial myocytes. The T-wave amplitude
decreases with small percentages of epicardial myocytes. Nevertheless, even with only 10% of epicardial myocytes, the T
wave is clearly biphasic and not flat as in the case of Fig. 4.
Figure 9B presents the sensitivity of the transmural electrogram to the activation sequence. As before there is very little
difference between the electrograms resulting from the strictly
transmural activation (act 2) and the more realistic activation
sequence obtained with the act 3 stimulation protocol (see Fig.
5). Nevertheless, T waves are clearly biphasic for all three
activation sequences.
Figure 9C presents the sensitivity of the waveform of the
transmural electrogram to the adjustment performed on Ito
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REPOLARIZATION IN RAT VENTRICLE
Figure 7B presents the sensitivity of the waveform of the
transmural electrogram to the adjustment performed on Ito in
the region we called the epicardium base. This is the only
parameter that, if altered, can eliminate the biphasic nature of
the T wave of the final computational model. Therefore, the
parameter sensitivity analysis performed here confirms that the apexto-base repolarization gradient is the key element for the
generation of a biphasic T wave in our computational model.
DISCUSSION
Activation and Repolarization of the Rat LV
maximum conductance as a simplified mechanism to shorten
the QT interval duration to reproduce the values observed by
the experiments. As before, following an increase of Ito conductance, QT interval shortens. Nevertheless, T waves are still
biphasic for any scaling factor introduced in Ito maximum
conductance. In particular, this is also true when Ito is not
altered (control case in the figure), i.e., when the values for Ito
maximum conductance are the original ones presented previously (49).
The sensitivity analysis presented by Fig. 9 suggests that
from all the parameters we have chosen to adjust, only one
really contributes to the biphasic waveform of the simulated T
wave: the Ito, maximum conductance of the epicardium base.
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Distribution of Endocardial and Epicardial Myocytes
A previous one-dimensional model of the dog ventricle (23)
that was developed to mathematically reconstruct important
features of the mammalian ECG assigned 35% of the transmural ventricular volume to epicardial myocytes. Measurements
obtained from human ventricles (20) have suggested that epicardial cells constitute only ⬃10% of the transmural thickness.
In rat ventricle, the volume or percentage of the transmural
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Fig. 9. Sensitivity of the waveform of the transmural electrogram to different
parameters of the computational model. A: sensitivity to the percentage of
epicardial myocytes. T-wave amplitude decreases with small percentages of
epicardial myocytes but is clearly biphasic in all cases. B: sensitivity to the
activation sequence. T waves are clearly biphasic for all 3 activation sequences. C: transmural electrograms for different adjustments of Ito conductance. Increasing Ito conductance shortens QT interval. However, the resulting
T waveforms are clearly biphasic in all cases, including when the Ito conductance is unchanged from the original Pandit formulation (C, inset).
The breakthrough, or first activation on the epicardium of
the rat LV free wall, occurs at a site (or sites) near the apex, as
has been reported previously (46). The activation wavefront
then spreads toward the base of the LV. The mathematical
model that we have developed represents a significant fraction
of the LV free wall. To begin to investigate the basis of the LV
electrogram, we have adjusted the parameters in this model so
that the sequence of epicardial activation matches our voltagesensitive dye results. It is interesting to note, however, that
although a clear pattern of apex-to-base activation is observed
on the epicardial surface, the spread of the activation is primarily transmural, i.e., from endocardial to epicardial, as
suggested by the simulation results presented in Fig. 5.
Optical mapping measurements in the guinea pig (31) and
mouse (3) LV epicardium have shown that the APD in these
species exhibits a distinct gradient: it is shortest at the apex and
longest at the base. A different (sometimes opposite) APD
gradient has been reported in the LV epicardium of large
mammals (11, 28, 40, 59, 67). Figure 2B, which consists of an
optical map of the rat LV epicardium, reveals a somewhat
similar pattern of APD heterogeneity to those found in guinea
pig and mouse. The APDs observed in our optical mapping
recordings are significantly longer than those used in our
model. Note, however, that the motion blocker cytochalasin D
prolongs the AP in the mouse and rat ventricles (3, 44). In
addition, optical mapping methods are known to reduce the
rate of rise of the AP due to spatial averaging (24). For this
reason the very sharp peak of the rat ventricular AP is blunted
somewhat in optical records. Any chosen or defined repolarization level (percentage of the AP peak amplitude) of an
optical AP will therefore correspond to a less depolarized level
of the “true” AP (e.g., a microelectrode recording or, in this
case, the model-generated AP). Since we could not fit the
absolute APD values obtained from the simulations to the
observed APD values of the optical maps, we have focused on
fitting the relative apex-to-base gradient of the APD values (the
APD difference from base to apex), as shown in Fig. 7. This
ensures that our simulations exhibit an apex-to-base APD
gradient similar to that derived from our mapping data.
REPOLARIZATION IN RAT VENTRICLE
Electrotonic Effects
In formulating our model, the discrete, stepwise APD distribution suggested from isolated myocyte recordings was
adopted and used as a basis for a 2-D mathematical model.
Therefore, the models presented in this article consider abrupt
transitions from a phenotype region to another, i.e., a myocyte
in the endocardial region can have as a neighbor an epicardial
myocyte. One might expect a model that considers smooth
transitions between different phenotype regions to be more
realistic. However, our simulations show that a model with
abrupt transitions behaves, in terms of APD distribution and
electrogram waveforms, like one with smooth transitions. Despite the use of models with abrupt transitions, smooth transmural (Fig. 4) and apex-to-base APD gradients (Fig. 7C) were
observed. To further investigate this issue, we have performed
simulations (not shown in this study) considering the smooth
transitions between phenotypes. The transition was modeled as
sigmoidal changes in Ito magnitude over the tissue and considered both transmural and apex-base gradients. The case with
gradual transitions yields very similar T waves to the case with
abrupt transitions. Therefore, the exact modeling of the transition between endocardial and epicardial, as well as apical and
basal, myocyte models is of limited importance.
This phenomenon is due to cell-cell electrotonic interactions. These interactions may reduce APD dispersion and thus
prevent the occurrence or maintenance of arrhythmias (10, 52).
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Our results also agree with recent findings that demonstrate the
transmural gradient in LV can be markedly reduced by electrotonic interactions in both human and canine LV (16, 56). In
addition, our simulations demonstrate that this marked reduction in transmural APD gradient can have the effect of emphasizing other anatomical and/or electrophysiological gradients.
In particular, we have shown that apex-to-base gradients can
play an important role in the generation of biphasic T waveforms.
Relationship of the Repolarization Wave of the Rat
Transmural Electrogram to Underlying Ionic Mechanisms
The positive repolarization wave. As expected, after the
administration of a high dose (5 mM) of 4-AP, the peak of the
Tp wave was shifted to the right in all our experiments.
However, the amplitude of the T wave increased for two of the
rats and decreased for the other one (see Fig. 3). Similar
experiments using the same K⫹ channel blocker have been
performed in mouse ventricle by Danik et al. (18). A similar
pattern of results was obtained. It should be noted that in the rat
ventricle, there is a highly 4-AP-sensitive component of the
sustained outward K⫹ current, denoted Iss in the Pandit model
(2). The administration of 5 mM 4-AP would completely block
this component of Iss as well as a large fraction of Ito current.
However, sensitivity analysis (results not shown) with respect
to the partial block of Iss indicated that the T-wave shape in our
model is much more sensitive to Ito size than it is to Iss.
We have therefore focused on computations that allowed us
to better understand the role of Ito in the repolarization wave.
Xia et al. (63) have shown experimentally that the peak of the
T wave coincides with the shortest EOR on the epicardial
surface. Therefore, the right shift of the T-wave peak agrees
with the fact that the blocking of Ito significantly increases the
epicardial APD. As in the experiments, Ito blocking invariantly
shifts the peak of T wave to the right. In addition, depending on
the amount of Ito reduction, the T-wave amplitude may increase as well as decrease (see Fig. 6), which is also consistent
with our experimental observations (Fig. 3).
The biphasic repolarization wave. The majority of lead I and
lead II ECG records from adult rats (17) and mice (18) exhibit
a biphasic shape. Following the QRS complex, there is a brief,
positive deflection and this is followed by a later and much
smaller negative-going component. Our simulations provide
new insights into how these two distinct deflections can be
related to the transmural and/or apex-to-base gradients of
repolarization in the adult rat LV. In brief, the apex-to-base
APD gradient can effectively divide the LV wall in two regions
that have opposite sequences of repolarization. Specifically, in
the region of the LV near the apex, the repolarization sequence
can be opposite to that of depolarization. In this region the
epicardium repolarizes before the endocardium. This sequence
of electrophysiological changes can give rise to the Tp, which
in both rat and mouse ECGs is often denoted as the T wave but,
as noted above, has also been referred to as a J wave (26, 34).
At the peak of Tp, note that the difference in AP at the apex of
the epicardium compared with the endocardium is greater than
the AP difference between epicardium at the base and endocardium (see arrows in Fig. 8). In contrast in the LV region
near the base, longer APDs reverse the sequence of repolarization. Thus, in the basal region, the endocardium repolarizes
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wall, which has the biophysical characteristics of epicardial
myocytes (as opposed to endocardial myocytes), has not been
determined. In our model, the average APD distribution was
reproduced most accurately by assuming that this epicardial
region consisted of ⬃25% of the transmural thickness. Electrophysiological studies of single myocytes from rodent and
mammalian ventricles have consistently identified apex-tobase and epicardial-to-endocardial gradients in the densities of
K⫹ currents (14, 27, 48, 62, 64, 68). Work from the Backx’s
laboratory (62) has drawn attention to the heterogeneous distribution of ionic current densities within the LV of the rat
heart under control conditions and in the setting of altered
hormone metabolism (hypothyroidism) or heart failure (54).
The use of only two different phenotypes/models for the
murine LV (or 3 phenotypes for the case of larger mammals)
may be too simplistic and may not reproduce important features of cardiac electrophysiology. We have found that it is
necessary to introduce a third phenotype/model in our computational wedge of the rat LV to reproduce the APD gradients
observed in the rat LV epicardium. In particular, we created a
third phenotype model for the epicardial region near the base of
the LV (see Fig. 7A). In the absence of experimental data
regarding differences in ionic current densities between apical
and basal epicardium, we have modeled the APD differences
between these areas by modifying a single parameter. Myocytes in the epicardial-base region are modeled as having lower
density of Ito than myocytes in the epicardial-apex model. As
additional experimental data become available, this aspect of
our model may have to be refined. The inclusion of this third
simple phenotype/model allowed us to reproduce important
features observed in the experiments: apex-to-base APD gradients on the rat LV epicardium and electrograms with biphasic
T waveforms.
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Limitations of this Study
Although our combination of voltage-sensitive dye mapping
and bidomain theory contributes significantly to an improved
understanding of the rat ventricular electrogram, we acknowledge that some aspects of our work remain incomplete. For
example, we have chosen a 2-D rectangular geometrical configuration of the LV free wall on which to simulate the most
important aspects of the electrophysiological phenomena of rat
LV. In future work, it will be important to carry out a similar
computational analysis based on more realistic 3-D geometry.
Second, our mathematical modeling does not take explicit
account of either the LV Purkinje fiber system or the possibility
that populations of M cells are present in the midmyocardium
of LV. Since the emphasis of this study is on repolarization, the
omission of the Purkinje conduction system is unlikely to be a
significant limitation. Very little information is available about
M cells in the rat heart, making it difficult to predict their
importance to the electrogram wave shape at this time. The
fundamental theoretical basis for this study is the single myocyte models of rat endo- and epicardium developed by Pandit
et al. (49, 50). These mathematical formulations were based on
patch-clamp experiments mainly recorded at 23°C. In contrast,
the experimental measurements in this article are based on the
Langendorff setup and were made at 37°C. As a result, the APD
of the model does not agree quantitatively with the experimental
AJP-Heart Circ Physiol • VOL
measurements. This problem is not unique to this particular
modeling study, as most computational models of cellular
electrophysiology are based on data recorded at reduced temperature. Our approach to compensating for this discrepancy
by increasing the maximum conductance parameter for the Ito
current by 50% is a simplification, but one for which there is
significant experimental basis. For example, Brouillette et al.
(7) have shown that an increase in temperature increases the
maximum conductance of Ito in mouse LV myocytes and
shortens APD. Shimoni and Banno (55) studied Ito current in
rabbit ventricular myocytes and found that the amplitude of Ito
increased by a factor of 6.14 for a 10°C increase in temperature, compared with only a 2.7-fold increase for L-type Ca2⫹
current. In addition, Pandit et al. (49) have demonstrated that
Ito is the most important ionic current in determining the rat
ventricular APD. Taken together, these observations clearly
indicate that a substantial increase in Ito amplitude is likely to
be the most significant consequence (in terms of APD) of an
increase in temperature. However, a detailed analysis would of
course also have to take into account changes in other ionic
currents, as well as changes in rate constants for ion channel
gating.
The results of Shimoni and Banno (55) illustrate the difficulty of compensating for temperature differences in an ionic
model, since the temperature sensitivity of different ion channels may vary quite widely. An adjustment of an ionic model
to physiological temperature is therefore much more involved
than a simple scaling of rate constants and is perhaps best done
as part of the original model development process, as has
indeed been done in some models in the literature (35). A
thorough adjustment of the Pandit model to physiological
temperature is thus well beyond the scope of this article and
would likely require substantial new patch-clamp data.
It is also worth noting that there is substantial variability in
Ito density even in the absence of a change in temperature. Our
50% adjustment of Ito amplitude is in fact well within the 70%
range of variability in Ito amplitude observed in the LV of
mouse hearts by Brunet et al. (9).
Finally, our simulations and experiments suggested the existence of two different epicardial regions (apex and base)
giving rise to opposite transmural repolarization sequences in
the ventricular wall. It is possible, however, that other gradients arising from different regions of the myocardium may
contribute to the modulation of the rat T wave. Notwithstanding these limitations, our simulations provide an important
proof of principle: nontransmural gradients can influence and
modulate the repolarization wave of the electrogram.
In summary, a combination of voltage-sensitive dye recordings and mathematical modeling has yielded new insights into
the basis for the well-known biphasic repolarization waveforms of the rat ventricular electrocardiogram. Electrical recordings of the rat and mouse are frequently used in basic
medical research, Safety Pharmacology studies, and in the
multidisciplinary studies of the genetic basis of cardiovascular
disease. The insights resulting from our experimental and
theoretical analysis are of significant interest and potential
importance in these endeavors.
ACKNOWLEDGMENTS
W. Giles held an Endowed Chair for Cardiovascular Research sponsored by
the Heart and Stroke Foundation of Alberta and the Northwest Territories.
297 • OCTOBER 2009 •
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before the epicardium and this sequence of repolarization can
generate a small slow Tn. At the peak of the Tn wave the AP
differences between the epicardium near the base and the
endocardium are greater than the corresponding differences
between the epicardium at apex and endocardium. Timedependent or dynamic interactions between these two distinct
APD patterns of heterogeneity underlie the biphasic transmural
electrograms waves corresponding to repolarization in the rat
heart. Figure 8C shows that, in principle, the close similarity
between the weighted algebraic sums of these two APD differences (apical epicardium AP ⫺ endocardial AP and basal
epicardial AP ⫺ endocardial AP) can account for the biphasic
lead I transmural electrogram record obtained from our experimental preparation.
Interpretation of the rat T wave. Figure 8 also illustrates why
the end of T wave in the rat ventricular electrogram is poorly
defined. The APs in all three locations shown in Fig. 8B have
very long gradual “tails” of final repolarization, typical of rat
APs. As a result, although there are significant voltage gradients in early repolarization (down to about ⫺50 mV), these
gradients are less significant in late repolarization. As our
simulations show, this results in large T-wave deflections
corresponding to early repolarization but minimal ones corresponding to late repolarization. Our model predicts that the Tp
corresponds roughly to the end of early repolarization at the
epicardial apex, whereas the Tn corresponds to the end of early
repolarization at the endocardium and/or epicardial base. The
end of the T wave is difficult to define because of its very
gradual decline but indicates the onset of slow, final repolarization. In summary, the rat T wave provides useful information about the dispersion of APDs and repolarization during the
early repolarization phase (APD50 or APD60). However, it is
difficult to obtain reliable information about final repolarization (APD90).
REPOLARIZATION IN RAT VENTRICLE
GRANTS
The experimental and theoretical work in this study was supported by grants
from the Brazilian foundation Fundação de Amparo à Pesquisa do Estado de
Minas Gerais, Coordenação de Aperfeiçoamento de Pessoal de Nı́vel Superior,
and Conselho Nacional de Desenvolvimento Cientı́fico e Technológico; the
German Ministry of Research and Technology (13N8125 BMFT); the Canadian Institutes of Health Research; and the Heart and Stroke Foundation of
Alberta and Northwest Territories. An essential equipment grant was obtained
from the Alberta Heritage Foundation for Medical Research.
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