Download Slow Conduction in Cardiac Tissue, II

Slow Conduction in Cardiac Tissue, II
Effects of Branching Tissue Geometry
Jan P. Kucera, André G. Kléber, Stephan Rohr
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Abstract—In cardiac tissue, functional or structural current-to-load mismatches can induce local slow conduction or
conduction block, which are important determinants of reentrant arrhythmias. This study tested whether spatially
repetitive mismatches result in a steady-state slowing of conduction. Patterned growth of neonatal rat heart cells in
culture was used to design unbranched cell strands or strands releasing branches from either a single point or multiple
points at periodic intervals. Electrical activation was followed optically using voltage-sensitive dyes under control
conditions and in elevated [K1]o (5.8 and 14.8 mmol/L, respectively; in the latter case, propagation was carried by the
L-type Ca21 current). Preparations with multiple branch points exhibited discontinuous and slow conduction that became
slower with increasing branch length and/or decreasing inter-branch distance. Compared with unbranched strands,
conduction was maximally slowed by 63% under control conditions (from 44.963.4 to 16.761.0 cm/s) and by 93% in
elevated [K1]o (from 15.762.3 to 1.160.2 cm/s). Local activation delays induced at a single branch point were
significantly larger than the delays per branch point in multiple branching structures. Also, selective inactivation of
inward currents in the branches induced conduction blocks. These 2 observations pointed to a dual role of the branches
in propagation: whereas they acted as current sinks for the approaching activation thus slowing conduction (“pull”
effect), they supplied, once excited, depolarizing current supporting downstream activation (“push” effect). This “pull
and push” action resulted in a slowing of conduction in which the safety was largely preserved by the “push” effect.
Thus, branching microarchitectures might contribute to slow conduction in tissue with discontinuous geometry, such as
infarct scars and the atrioventricular node. (Circ Res. 1998;83:795-805.)
Key Words: discontinuous conduction n impedance mismatch n voltage-sensitive dye n atrioventricular node
n myocardial infarction
I
t has been shown both experimentally and in computer
simulation studies that slowing of conduction in cardiac
tissue is governed by any (or a combination) of the following
3 mechanisms: (1) reduction of excitability1 and calcium
inward current (ICa)– dependent propagation,2 (2) reduction of
intercellular coupling,1,3,4 and (3) impedance mismatch and
wavefront curvature caused by specific tissue structures or
occurring in continuous excitable media.5–9 These mechanisms were used to explain the occurrence of slow conduction
under both physiological (eg, atrioventricular [AV] node)10
and pathophysiological (eg, ischemia and infarction)11 conditions. Whereas it was shown experimentally in another
study12 that a reduction of gap-junctional coupling in linear
tissue structures can decrease overall conduction velocity (u)
to a much greater extent than a reduction of excitability, the
present study focused on the third mechanism: induction of
slow conduction by specific tissue architectures that confront
the propagating activation with a single or repetitive currentto-load mismatches. Such mismatches can be expected to
occur in elderly myocardium, in which sheets of connective
tissue disrupt the myocardial tissue,13,14 or in infarct scars, in
which the surviving tissue forms cell islands interconnected
by cell strands.15,16 Finally, the presence of repetitive current-
to-load mismatches might be relevant for propagation
through the AV node, where so-called “dead-end” pathways
have been functionally identified in mapping studies.17–19
These pathways appear as “strand-like” zones that activate
almost simultaneously with the N zone of the node. It
therefore has been questioned whether these pathways could
contribute to slow conduction10,20 in addition to action potentials carried by the Ca21 inward current and to decreased
intercellular coupling.
In the present study, patterned growth of neonatal rat heart
cells in culture was used to produce precisely defined
branching structures of cardiac tissue. In these preparations,
the characteristics of activation were determined at high
spatio-temporal resolution using multiple-site optical recording of transmembrane voltage. By virtue of representing
repetitive current-to-load mismatches, multiple branch points
induced slowing of conduction. Maximal conduction slowing
induced by the combination of branching tissue geometry
with a reduction in excitability (few centimeters per second)
was close to the range of velocities obtained in unbranched
strands by partial gap-junctional uncoupling (,1 cm/s).12
Importantly, the branches acted not only as current loads
(“pull” effect) but, on activation, also as current sources
Received January 14, 1998; accepted August 7, 1998.
From the Department of Physiology, University of Bern, Switzerland.
Correspondence to Stephan Rohr, MD, Department of Physiology, University of Bern, Bühlplatz 5, CH-3012 Bern, Switzerland. E-mail [email protected]
© 1998 American Heart Association, Inc.
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Slow Conduction in Branching Tissue
selected according to the shape of a given preparation and were
connected to individual photodiodes. The resulting photocurrents
were converted to voltages, amplified, and simultaneously digitized
at 20 kHz. Experiments were performed with a 203 objective (Fluar,
Zeiss; NA 0.75), resulting in a spatial resolution of 50 mm.
Experimental Protocol
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Figure 1. Growth patterns. A, Pattern with a single branch
point: two 80-mm–wide branches emerge from the strand (identical width) at right angles. Branch length (L) varied between 60
and 1960 mm. B, Pattern with multiple branch points: sequentially arranged branches (n.30) emerge at right angles from the
strand. The branch length was varied between 60 and 1960 mm,
and the inter-branch distance (I) was either 150 or 300 mm. C,
Unbranched, 80-mm-wide cell strand used as control in all
experiments.
(“push” effect) during impulse propagation by supplying
depolarizing current for downstream activation. This dual
action resulted in very slow but safe conduction. As both slow
and safe conduction are crucial for the function of the AV
node, it therefore might be argued that the previously described “dead-end” pathways fulfill a similar role.
Materials and Methods
Patterned Growth Cell Cultures
Cell cultures from neonatal rat hearts (Wistar) exhibiting defined
growth patterns were prepared according to published procedures.12,21 As illustrated schematically in Figure 1, the growth
patterns consisted of 2 types of branched structures. The first type
(Figure 1A) consisted of a strand (80 mm wide, 10 mm long)
releasing 2 branches (80 mm wide) of a predefined length from a
common branch point at an angle of 90° (“single branch point”). The
second type (Figure 1B) consisted of a strand (80 mm wide, 10 mm
long) releasing multiple branches (n.30; 80 mm wide) at equidistant
intervals ([I], 150 or 300 mm) along the entire length of the strand
(“multiple branch points”). In both types, branch length was varied
from 60 to 1960 mm. Each coverslip carried, in addition to the test
patterns, linear unbranched cell strands (80 mm wide, 10 mm long)
that served as controls (Figure 1C).
Optical Recording of Electrical Activation Patterns
12,22
As described previously,
impulse propagation in the patterned
growth cultures was followed optically using the fast voltage–
sensitive dye di-8-ANEPPS (Molecular Probes; 135 mmol/L for 3 to
4 min).23 Emitted fluorescence from the preparation was projected
onto a hexagonal array of 379 closely packed optical fibers with a
diameter of 1 mm each. From the entire array, #80 fibers were
After mounting the preparations in the temperature-controlled experimental chamber (3660.4°C), control superfusion was started
(HBSS containing [in mmol/L]: NaCl 137, KCl 5.4, CaCl2 1.3,
MgSO4 0.8, NaHCO3 4.2, KH2PO4 0.5, NaH2PO4 0.3, and HEPES
10, which was titrated to pH 7.40 with NaOH). The preparations
were stimulated at a basic cycle length of 500 ms with an extracellular pipette electrode (rectangular impulses, duration 1 ms; twice
threshold intensity) placed at sufficient distance from the site of
measurement to exclude electrotonically mediated stimulation artifacts and permit propagation to reach steady-state conditions. The
preparations were stimulated for at least 10 seconds before a given
optical recording.
During each experiment, optical recordings first were obtained
under control conditions (HBSS, control [K1]o55.8 mmol/L). Subsequently, the preparation was superfused for at least 5 min with
HBSS containing elevated [K1]o (14.8 mmol/L), and a second
recording was performed at the same sites. At the end of each
experiment, absence of significant phototoxic effects was assured by
reassessing impulse propagation after washout.
In some experiments, tetrodotoxin ([TTX], 22 mmol/L; Calbiochem), nifedipine (5 m mol/L; Sigma), or palmitoleic acid
(20 mmol/L; Sigma) was delivered to the preparation in a spatially
controlled manner by a local superfusion device24,25: briefly, the
drug-containing solution was delivered to the preparation using a
syringe pump connected to an extruded polyethylene tube (diameter,
200 mm), the tip of which was placed over the target location. A
second extruded tube, facing the first tube, was connected to a
vacuum pump and served to remove the superfusate. At the end of an
experiment, phase-contrast videomicrographs of the regions of
interest were recorded with a monochrome video camera (XC-77;
Sony Corp), which was connected to a framegrabber card (DT 3152;
Data Translation).
Data Analysis
The raw data were analyzed by a program written in Interactive Data
Language ([IDL]; Creaso GmbH). The traces were passed through a
digital low-pass filter with a corner frequency of 1.5 kHz for
measurements under control conditions and a corner frequency of 0.5
kHz for measurements in elevated [K1]o. The signal amplitudes
obtained under control conditions were set to 100%. The measurements in elevated [K1]o were scaled to this data set. Assuming an
average action potential amplitude (APA) of 100 mV under control
conditions,21 the scaled values given as %APA translate directly into
APA given in millivolts. Values for maximal upstroke velocities
(dV/dtmax) were scaled correspondingly and are given as %APA/ms
(average APA, 100 mV; %APA/ms corresponds to volts per second).
Activation times for each recording site were determined at 50% of
the APA.22 From these values, us were determined by linear
regression.
Statistics
Data are given as mean6SD. Data sets were compared using the
Student t test (2-tailed), and differences were considered significant
at P,0.05.
Results
Control Experiments With Linear Cell Strands
Each patterned growth culture contained, in addition to the
specific patterns under investigation, 80-mm-wide linear and
unbranched cell strands (Figure 1C) serving as controls. In
these strands, propagation was assessed routinely at the
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Figure 2. Impulse propagation along a
linear cell strand. A, Phase-contrast
videomicrograph of the preparation (80mm-wide strand). White circles indicate
the optical recording sites (distance
between sites, 50 mm); 3, direction of
propagation. B, Superimposed action
potential upstrokes obtained from all sites
(1 to 19) under control conditions
([K1]o55.8 mmol/L; top) and in elevated
[K1]o (14.8 mmol/L; bottom). The similar
shapes and the regular spacings of the
upstrokes indicate uniform propagation.
APAs in elevated [K1]o were reduced by
'30%, and upstroke velocities were
slowed by '85%. C, Activation profiles
under control conditions (▫) and in elevated [K1]o (n). Relative activation times
(time set to 0 at site 1) are plotted vs distance. Conduction was uniform, as indicated by a close linear fit of the data for
conditions of both control [K1]o (r50.999;
u545.4 cm/s) and elevated [K1]o
(r50.994; u519.8 cm/s).
beginning of each experiment. An example of such a measurement is shown in Figure 2. Under control conditions
([K1]o55.8 mmol/L), propagation was fast (u545.4 cm/s)
and uniform, as indicated by the regular spacing between the
action potential upstrokes (Figure 2B) and by the linear
increase of activation times along the preparation (Figure
2C). In elevated [K1]o (14.8 mmol/L, mainly ICa-dependent
propagation),12 u fell to 19.8 cm/s, and upstrokes were
substantially slowed.
Summarizing all control measurements with linear cell
strands (n515), elevation of [K1]o from 5.8 to 14.8 mmol/L
reduced u from 44.963.4 to 15.762.3 cm/s. At the same
time, dV/dtmax fell from 97613 to 1562 %APA/ms. The
absence of a significant rundown of the preparations during
the experiments was assessed by reexamining u at the end of
each experiment. The measurements showed a nonsignificant
decrease of u by 465%. These results are in close agreement
with results obtained in another study,12 indicating a high
degree of functional consistency among the patterned growth
cell cultures.
Impulse Propagation Across Single Branch Points
The characteristics of propagation along a preparation with a
single branch point is shown in Figure 3. The videomicrograph (Figure 3A) shows the pattern consisting of a strand
(horizontal) releasing two 460-mm-long branches (vertical).
Activation of the preparation from the left was characterized
by a local slowing of the action potential upstroke as
propagation crossed the branch point (recording sites 4 to 9).
Moreover, action potentials recorded in the vicinity of the
branch point were notched. This finding is typical for electrotonic interactions in the situation of a current-to-load
mismatch as represented by the branch point: the initial
depolarization phase occurs during charging of the load
(branches), and the second phase occurs at the moment during
which the branches are activated and the load is released.5,26
In the branches, action potential upstrokes became smooth
and rapidly rising as activation approached their ends (sites D
and H located '150 mm from the branch ends).
An overview of the activation patterns across the branch
point under control conditions and in elevated [K1]o is
depicted in Figure 3B. As indicated by the 3-dimensional
plots, the branch point induced a local activation delay that
became highly prominent in elevated [K1]o. As illustrated in
Figure 3C, activation times of the branches in control [K1]o
showed a slight increment within the first 300 mm, whereas
the remainder of the branches were activated almost simultaneously. In elevated [K1]o, the distal parts of these relatively
short branches tended to be activated earlier than did the
proximal parts.
Quantitative aspects of the activation of the preparation
and the mode of calculation of the conduction delay at the
branch point are illustrated in Figure 3C. As indicated by ▫
and n (activation times along the strand), the branch point
induced a delay that was highly accentuated in elevated [K1]o.
This delay was quantified by first fitting a line with a slope
corresponding to the average u measured in control unbranched strands to the first 3 data points in front of the
branch point to obtain an estimate for the activation profile in
the absence of branches. The conduction delay (arrow)
caused by the branch point was then calculated as the time
difference between this line and the measured activation
times obtained after the branch point. In this experiment, the
delay amounted to 1.5 ms under control conditions and to 4.7
ms in elevated [K1]o. Whereas the activation profile of the
branches (E, F) under control conditions was similar to that
of the strand (▫, n), activation of the relatively short branches
in elevated [K1]o was distinctly different, because distal parts
of the branches were activated earlier than proximal parts.
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Slow Conduction in Branching Tissue
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For branch lengths of up to 3 multiples of the space
constant (l5360 mm),27 activation of the branches was
consistently faster than activation along the main strand
because of the presence of a sealed end within electrotonic
reach of the branch point. However, for the longest branches
(length, 1960 mm), the activation profiles of the branches
matched the activation profile of the main strand, as expected
for this structure that was, in electrotonic terms, symmetrical
in respect to the branch point.
The relationship between activation delays and branch
lengths was investigated in a total of 14 different preparations
(2 experiments with branch lengths of 60 mm, 3 experiments
each with branch lengths of 160, 260, 360, and 460 mm). As
summarized in Figure 4, the delays increased with increasing
branch length. Under control conditions, the maximal delays
observed were 1.560.4 ms (length, 460 mm; n53), whereas
in elevated [K1]o, they amounted to 4.561.0 ms (length,
460 mm; n53). Both values were significantly different from
those of control strands (P,0.05).
Impulse Propagation Along Periodically
Branching Structures
The effect of repetitive branching on propagation and the
possibility of interactions between neighboring branch sites
were investigated in preparations exhibiting multiple branch
points. In general, these preparations consisted of 80-mmwide cell strands releasing branches of identical width and of
defined length at regular intervals. Figure 5A shows an
example of activation obtained under control conditions in
such a preparation (length, 360 mm; I5300 mm). In contrast
to the notched upstrokes observed in preparations with a
single branch point (Figure 3A), action potential upstrokes in
multiple branching preparations were rather smooth. Along
the strand, there was a decrease of dV/dtmax immediately
before the first and the second branch points (recording sites
2 to 3 and 7 to 9). Whereas no clear decrease was observed
before the third branch point in this particular experiment,
spatial averaging of dV/dtmax over all experiments involving
the same geometry (length, 360 mm; I5300 mm) showed
a clear periodical pattern with minimal dV/dt max
(6267 %APA/ms; n55) of 50 mm in front of the branch
points and a significantly larger maximal dV/dtmax (89610
Figure 3. Propagation across a single branch point. A, Videomicrograph of the preparation consisting of a cell strand (horizontal) releasing two 460-mm-long branches. 3 indicates the direction of propagation; white circles, recording sites from which the
signals displayed below and to the right of the videomicrograph
were obtained; V, action potential upstrokes; and dV/dt, time
derivatives (corresponding numbering). The signals recorded
under control conditions ([K1]o55.8 mmol/L) showed, near the
branch point, typical notched upstrokes and a local depression
of dV/dtmax. B, Plot of activation times determined at the sites
indicated in (A). 3 indicates the direction of propagation along
the strand. The activation delay present under control conditions
in front of the branch point became accentuated during elevation of [K1]o. C, Plot of activation times along the strand (▫, n)
and branches (E, F) under control conditions (▫, E) and in elevated [K1]o (14.8 mmol/L; n, F). Activation delays at the branch
point amounted to 1.5 ms under control conditions and to 4.7
ms in elevated [K1]o (for mode of calculation, see Results).
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were activated virtually simultaneously. Overall u in this
preparation was 28.7 cm/s under control conditions and 8.9
cm/s at [K1]o514.8 mmol/L.
The degree of conduction slowing associated with increasing branch lengths was assessed in preparations with different
branch lengths for 2 different inter-branch distances (300 mm,
Figure 6A; 150 mm, Figure 6B). In both cases, lengthening of
the branches from 60 to 260 mm led to a progressive
reduction of u. Beyond 500 to 1000 mm, no further major
slowing was obtained. As expected, maximal conduction
slowing was observed in the preparations with a narrow
inter-branch distance (I5150 mm): under control conditions,
u was reduced by 63% to 16.761.0 cm/s (length, 960 mm;
n54), whereas in elevated [K1]o, u fell by 93% to 1.160.2
cm/s (length, 1960 mm; n53). These minimal velocities were
significantly different from velocities in control strands
(P,0.05). Whereas irrespective of the branch lengths, conduction blocks never occurred under control conditions, a few
preparations with very long branches showed intermittent 2:1
blocks under conditions of elevated [K1]o (length, 960 or
1960 mm; n56 of 17).
Dual Effects of Multiple Branches: “Pull and
Push” Effect
Figure 4. Conduction delays across a single branch point as a
function of branch length. A, Under control conditions
([K1]o55.8 mmol/L), activation delays at the branch point displayed a trend to increase up to the third branch length tested
(260 mm) before leveling off (mean6SD; n53 for each data
point, except for branch lengths of 60 mm; n52). B, Same as (A)
but for measurements obtained in elevated [K1]o (14.8 mmol/L).
Gray bands depict variations of conduction times (SD) in
unbranched strands at either [K1]o (n515). *Significantly
increased delays vs control strands (n515; P,0.05).
%APA/ms; n56) of 100 mm thereafter (P,0.05). Within the
branches, dV/dtmax increased to steady values within 250 to
300 mm from the branch point (sites C, D, G, and H).
Figure 5B shows 3-dimensional plots illustrating the general characteristics of activation along the preparation at both
[K1]o. In contrast to the isolated large activation delay
observed in preparations with a single branch point (Figure
3B), activation delays per branch point in periodically
branching preparations were smaller, giving the overall impression of a rather uniform type of propagation. As shown in
more detail in Figure 5C, activation exhibited a staircase-like
profile that was pronounced especially under conditions of
elevated [K1]o. As in the case of a single branch point,
activation of the branches was relatively fast under control
conditions, whereas in elevated [K1]o, the short branches
Comparison of the activation delay occurring in preparations
with a single branch point with the individual delay induced
by each branch point in preparations with repetitive branchings showed, as illustrated in Figure 7, that the delay per
branch point was smaller in the case of periodically branching
preparations. In control [K1]o, the average delays were 32%
(I5300 mm) and 18% (I5150 mm) of the average delay
across a single branch point. In elevated [K1]o, this change
was less pronounced, as the average delays were 77%
(I5300 mm) and 48% (I5150 mm) of the average delay
across a single branch point. This observation is in contrast to
the concept that the current-to-load mismatch is the only
determinant of propagation at a branch point. If it were,
adding additional branches within a distance permitting
electrotonic interactions among adjacent branch points would
be expected to increase the mismatch, thus resulting in an
increased, or at least unchanged, delay per branch point.
These findings, together with the observation that the cells in
the branches were activated almost simultaneously, suggested
that the branches might have 2 functions: (1) slowing of
conduction because of the current-to-load mismatch as described above (“pull” effect) and (2) boosting of conduction
toward the next branch point after activation of the branches
(“push” effect).
To separate the role of the branches as current sources
(“push” effect) from their role as current sinks (“pull” effect),
2 types of additional experiments were carried out in which
the branches were either rendered inexcitable (Figure 8) or
were electrically uncoupled (Figure 9), using a local superfusion containing appropriate drugs. For these experiments, a
modified version of the “single branch point” pattern was
used, which consisted of a strand releasing 2 branches to 1
side only (I5150 mm; length, 960 mm; Figures 8A and 9A).
This modification was technically necessary to permit the
local superfusion to reach both branches simultaneously.
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Irrespective of [K1]o, activation of these patterns before local
superfusion of the branches was qualitatively similar to the
single branch point pattern; ie, the branches induced a local
activation delay.
In the first type of experiment, the “push” effect was
eliminated by rendering the branches inexcitable with TTX
and nifedipine. A typical experiment is shown in Figure 8.
Before the local application of the ion channel blockers,
conduction along the strand was successful at either concentration of [K1]o (Figure 8B and 8C). In elevated [K1]o
(14.8 mmol/L), local superfusion of the branches with TTX
(22 mmol/L) and nifedipine (5 mmol/L) resulted in failure of
conduction along the strand, as indicated by decremental
signal amplitudes (Figure 8D). This effect was fully reversible, as shown in Figure 8E. Thus, excitability of the
branches, underlying the “push” effect, seemed to be of
crucial importance for successful conduction along the strand
in elevated [K1]o. Similar results were obtained in all preparations subjected to this experimental protocol, ie, blocking
the inward currents in the branches induced conduction
blocks in elevated [K1]o (n58; 5 full blocks, 3 intermittent
2:1 blocks). Conversely, under conditions of control [K1]o, no
conduction blocks were observed, but the delay induced by
the branches rose significantly from 0.760.4 to 1.260.7 ms
(n55; P,0.05).
In the second type of experiment, the “pull” effect was
suppressed by electrical uncoupling of the branches with the
gap-junctional uncoupler palmitoleic acid.12,28 The results of
such an experiment are illustrated in Figure 9. In elevated
[K1]o, the propagation delay induced by the 2 branches
amounted to 13 ms (Figure 9B). Local superfusion of the
branches with palmitoleic acid (20 mmol/L), TTX (22
mmol/L), and nifedipine (5 mmol/L) for 6 min reduced this
delay by '60% to 5 ms. A similar reduction of the delay was
obtained in another experiment. These findings illustrate that
(1) in accordance with the proposed “pull” effect, a reduction
of the load by the complete electrical uncoupling of the
branches resulted in a reduction of the local activation delay,
and (2) diffusion of drugs from the local superfusion toward
the strand was, in accordance with previous determinations of
the border zone width of an identical local superfusion system
(20 mm),24 negligible because this would have resulted in an
increase of the activation delay. The fact that the delay was
not completely suppressed by the electrical uncoupling of the
Figure 5. Propagation across multiple branch points. A, Videomicrograph of the preparation showing the cell strand (horizontal) releasing 360-mm-long branches every 300 mm. 3 indicates
the direction of propagation; overlaid solid white circles, recording sites from which the signals displayed below and to the right
of the videomicrograph were obtained (control conditions,
[K1]o55.8 mmol/L; V, action potential upstrokes; and dV/dt, time
derivatives (corresponding numbering). B, Plot of activation
times determined from the sites indicated in (A) (solid and
dashed circles). 3 indicates the direction of propagation along
the strand. Whereas, under control conditions, propagation is
close to uniform along the strand, it progresses staircase-like in
elevated [K1]o (14.8 mmol/L) with single steps coinciding with
the branch points. C, Plot of activation times along the strand
(▫, n) and along the central branches (E, F; denoted with asterisks in [B]) under control conditions (▫, E) and during elevation
of [K1]o (n, F). The locations of the branch points are indicated
by vertical dotted lines. Under control conditions, only small discontinuities in the activation profile were visible with a slight
slowing of conduction in front and an acceleration after the
branch points. In elevated [K1]o, these discontinuities were
enhanced. Overall us determined from these activation profiles
were 28.7 cm/s under control conditions and 8.9 cm/s in elevated [K1]o. Note that the activation of the branches occurred
virtually simultaneously in elevated [K1]o.
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Figure 6. u in preparations with multiple branch points. A, u as a function of branch length and [K1]o (5.8 and 14.8 mmol/L) for preparations with an inter-branch distance (I) of 300 mm (mean6SD; n52 to 4 for each branch length). B, same analysis as in (A) for preparations with an inter-branch distance of 150 mm (mean6SD; n52 to 4 for each branch length). Gray bands depict mean6SD of u
obtained in unbranched strands at either [K1]o (n515).
branches is explained by the circumstance that the load was
not completely eliminated, because the border of the local
superfusion was kept '100 mm away from the main strand
(arrows, Figure 9A). Finally, the finding that there was no
diffusion of drugs toward the main strand24,28 rules out that the
diffusion of TTX and nifedipine toward the main strand
might have contributed to the induction of blocks in the
experiments in which only ion channel blockers were present
in the local superfusion (Figure 8).
Discussion
It is well established that very slow conduction (,10 cm/s)2
plays a pivotal role both under physiological conditions (slow
conduction in the AV node) and in reentrant excitation.
Slowing of conduction has been shown to be induced by the
following mechanisms: (1) reduction of excitability and
ICa-dependent propagation (“slow response”),2 (2) reduction
of electrical coupling,4 (3) impedance mismatch and wavefront curvature occurring in specific tissue structures or in
continuous excitable media,5–7,9 and (4) zig-zag activation of
fibrotic myocardium.13,14,16 It was the aim of this study to
investigate the possibility that yet another mechanism might
underlie slow conduction, namely the presence of multiple
current-to-load mismatches being lined up along a given
pathway of activation.
Conduction Slowing in Branched Structures
Figure 7. Dependence of conduction delays per branch point
on the spatial frequency of branch points. A, Compared with the
delays observed in preparations with a single branch point (normalized to 100%), delays measured in preparations with multiple branch points were significantly reduced under control conditions ([K1]o55.8 mmol/L). This effect was enhanced with
increasing spatial frequency of the branches (reduction of interbranch distance from 300 to 150 mm). B, In elevated [K1]o
(14.8 mmol/L), qualitatively similar results were obtained. However, the change was quantitatively less pronounced.
Local slowing of conduction at sites of discontinuities in
tissue structures representing a current-to-load mismatch is a
well-known phenomenon.26 It has been reported to affect
conduction in branching atrial tissue,7 at the Purkinje fiber–
ventricular junction,6 and in patterned growth cell cultures.25,28
In all of these structures, electrotonic current provided by
excited cells in front of the discontinuity disperses into a
larger cell mass, thus giving rise to a local conduction delay
or conduction block. The occurrence of blocks indicates that
current-to-load mismatch is associated with a reduction of
propagation safety.
In the present study, multiple current-to-load mismatches
consisting of many branches attached at regular intervals to a
linear cell strand were used to slow conduction along the
entire length of the preparation. As expected, an increase in
the length of the branches and/or a decrease in the interbranch distance was accompanied by a decrease of u. Compared with unbranched strands, the maximal reduction of u in
control [K1]o in periodically branched strands was 263% (17
802
Slow Conduction in Branching Tissue
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Figure 8. Inhibition of inward currents in the branches. A,
Videomicrograph of the preparation, showing a strand that
released two 960-mm-long branches to 1 side only (I5150 mm).
White circles indicate the recording sites; solid arrow, direction
of propagation; and open arrows, the lower border of the local
superfusion used during the measurement shown in (D). B,
Action potential upstrokes recorded along the preparation under
control conditions ([K1]o55.8 mmol/L); overall u540.2 cm/s. C,
During elevation of [K1]o to 14.8 mmol/L, action potential
upstroke velocities decreased and u fell to 4.5 cm/s. D, Same
as (C), but the branches were rendered inexcitable by local
superfusion with 22 mmol/L TTX and 5 mmol/L nifedipine for 2
min. The lower border of the superfusion was kept at a distance
$100 mm from the cell strand. As indicated by the decremental
signal amplitudes, this intervention caused conduction block. E,
Control recordings obtained 5 min after washout
([K1]o55.8 mmol/L). Overall u returned to 38.5 cm/s.
cm/s). This reduction was in the same range as that observed
in unbranched strands during a marked elevation of [K1]o
(14.9 cm/s at [K1]o530.0 mmol/L; conduction based primarily on ICa12) and in intact cardiac tissue exposed to moderately
increased [K1]o (12 mmol/L; 19 cm/s; transverse conduction).29 When the effects of branching were combined with a
reduction of excitability ([K1]o514.8 mmol/L), u was reduced by 293% (1.1 cm/s) compared with values obtained in
unbranched control strands at the same [K1]o. Thus, the
combination of branching tissue geometry with ICa-based
conduction induced very slow and safe conduction, which
was almost an order of magnitude slower than that obtained
with either mechanism alone. Furthermore, the lowest us
obtained in the branched preparations in elevated [K1]o were
close to the velocities measured during gap-junctional uncoupling in unbranched strands.12
Activation Patterns at the Branching Sites
In all preparations with multiple branchings, activation of
individual branch sites followed a common pattern: (1)
propagation was delayed in front of a given branch point, and
(2) the proximal regions of the branches were activated
before the main strand.
Figure 9. Simultaneous inhibition of inward currents and uncoupling of gap junctions in the branches. A, Videomicrograph of
the preparation consisting of a strand that released two 960mm-long branches to 1 side only (I5150 mm). White circles indicate the recording sites; solid arrow, direction of propagation;
and open arrows, the lower border of the local superfusion containing TTX, nifedipine, and palmitoleic acid. B, Plot of activation
times along the strand in elevated [K1]o (14.8 mmol/L) before
(gray squares) and during (black squares) local superfusion of
the branches with 22 mmol/L TTX, 5 mmol/L nifedipine, and
20 mmol/L palmitoleic acid. Vertical dotted lines indicate the
positions of branch points; solid line, the expected activation
profile in the absence of branching. During the intervention, activation was substantially accelerated, which suggests that gapjunctional uncoupling induced a substantial reduction of the current load exerted by the branches.
1. Initially, the approaching activation was delayed in
front of a given branch point (Figure 5). This delay was
induced by the current load represented by (1) the
branches and (2) the downstream portions of the preparation situated within electrotonic reach of the branch
point. The contribution of the branches to the current
load was directly demonstrated by the finding that
electrical uncoupling of the branches led to a significant
reduction of the local activation delay (Figure 9). Also,
as expected for branches acting as current loads, increasing the size of the load by increasing the length of
the branches resulted in an enhancement of the activation delay. This effect showed a tendency to plateau at
branch lengths of 500 to 1000 mm (Figure 6), which is
readily explained by the fact that these lengths correspond to 2 to 3 multiples of the space constant
(l5360 mm in cardiac monolayer cultures).27 At these
larger distances, a further increase of branch length
therefore is not expected to increase the load to any
additional significant extent.
2. Subsequent to the delay, it was consistently observed
that the proximal regions of the branches were activated
before propagation continued downstream beyond the
branch point. For the case of branch lengths ,2 to 3 l,
Kucera et al
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this observation primarily is explained by the wellknown reflection of depolarizing subthreshold current at
the branch endings, contributing to a nearly simultaneous activation of these short branches. This is analogous to findings of previous computer simulations, in
which raising the resistive barriers between groups of
excitable elements induced a quasi-simultaneous activation of such groups.3 Interestingly, activation of the
proximal regions of the branches preceded activation of
the main strand beyond the branch point also in preparations where the branches were very long (1960 mm;
.5 l). In this situation, the explanation of branch
activation by reflection of local electrotonic current at a
“sealed end” no longer can be invoked. Instead, the
phenomenon is likely to be explained by the following
hypothesis: from the geometry of the preparations, it is
easily recognized that the current load exerted by the 2
branches connected to a given branch point is always
smaller than the load imposed by the main strand. This
is because further branches are attached to the main
strand within the distance of electrotonic interaction. As
a consequence of this unequal distribution of the current
loads in respect to a given branch point, it is to be
expected that, during depolarizing current flow, the
regions with the lesser load reach threshold first, ie, the
proximal regions of the branches are activated first.
This hypothesis also predicts that, with decreasing
inter-branch distance (enhancement of the “downstream
load” at constant “branch load”), increasingly longer
segments of the branches adjacent to the branch point
should activate before activation invades the main
strand, because the imbalance of the loads is accentuated. This was confirmed by the analysis of activation
patterns in the preparations with long branches (length,
1960 mm; control [K1]o): when the lengths of the
proximal segments of the branches, which were activated before downstream activation of the main strand
occurred, were compared for the 2 different interbranch distances, a significant difference could be
observed. Whereas, at an inter-branch distance of
300 mm, the average length of these “preactivated”
segments was 94659 mm (n554), it increased to
131684 mm (n5130; P,0.05) for an inter-branch
distance of 150 mm as predicted for the increased
“downstream load.”
Although activation generally invaded the side branches in
a proximal-to-distal direction, it could be observed in some
preparations with short branches (,400 mm) and in the
presence of elevated [K1]o (Figure 5) that activation of the
distal sites of the branches actually preceded activation of the
proximal sites (Figure 3C). This is analogous to findings
obtained in computer simulations of cardiac fibers in which
the introduction of a critically high resistive barrier within
electrotonic reach of the sealed end (1 to 2 l) induced
initiation of excitation a certain distance away from the
barrier.30 In this simulation, the phenomenon was explained
by partial inactivation of sodium channels in the close
proximity of the barrier due to the slow subthreshold depolarization. Whether a similar mechanism involving L-type
calcium channels contributed to the observed “reversed”
activation of short branches in elevated [K1]o remains to be
shown.
October 19, 1998
803
Theoretically, factors such as local changes in cellular
architecture and inhomogeneous expression of gap junctions
might have affected the generation of local activation delays
at the branch points. However, results of experiments with
patterned growth neonatal rat cardiomyocytes are not in
accordance with any major involvement of these factors.
(1) Whereas the cells were aligned largely in parallel in the
strands and the branches, they were oriented randomly at the
branch points. It previously has been shown that such a
change in the cell arrangement affects propagation velocities12,23,31 with maximal effects found in anisotropically grown
cell monolayers (longitudinal-to-transverse velocity ratios of
1.9).31 Based on this ratio, the highest possible contributions
from a change in cellular layout at the branch point can be
calculated as 0.16 ms (control [K1]o), which is only a small
fraction of the delays actually observed. (2) The preparations
consisted of uniformly and densely packed cardiomyocytes,
which rules out the possibility that the occurrence of large
intercellular clefts could have contributed to local activation
delays. (3) It could be speculated that a change in the
distribution of gap junctions at the branch points could
influence the size of the activation delays. Although the
distribution of gap junctions was not investigated in the
preparations used in the present study, the finding of spatially
uniform distributions of connexin 43 at the sites of abrupt
tissue expansions suggests that this was most likely not the
case (S.R. et al, unpublished data, 1997).
“Pull and Push” Effect of Branches
Because both the reduction of excitability and the presence of
a current-to-load mismatch are known to impair the safety of
propagation, the question arose as to why the combination
of both supported very slow conduction in multiple branching
structures and did not produce early conduction failure. The
explanation for this question was provided by the finding that
local activation delays not only were dependent on the size of
the current load, ie, the branch lengths, but that they were
inversely related to the inter-branch distances: going from a
single branch point to an inter-branch distance of 300 and
150 mm, the delay introduced by each branch point was
diminished. This finding suggested that the branches not only
acted to decrease u by representing repetitive current loads
(“pull” effect) but that they became, after activated, important
current sources pushing activation ahead (“push” effect). This
effect is understood readily on the basis of the specific
activation pattern of the branch sites: as outlined above, a
substantial part of the branches was fully activated at the time
when activation along the main strand had barely surpassed
the branch point. This resulted in an injection of current from
the nearly simultaneously activated proximal segments of the
branches into the main strand downstream. This “push” effect
was directly demonstrated in experiments in which the
branches were rendered inexcitable with TTX and nifedipine
(Figure 8). This intervention caused conduction to fail at the
sites of the “passive” branches, suggesting that excitation of
the branches was indispensable for sustained conduction
because they helped “pushing” activation ahead. A similar
mechanism has been suggested to underlie impulse propagation in branching axons like the Mauthner axon of the tench.32
804
Slow Conduction in Branching Tissue
Comparison With Slow Conduction Induced by
Electrical Uncoupling
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It was shown in a recent computer simulation study that
gap-junctional uncoupling induced us as low as 0.26 cm/s.1
On the other hand, slowest us demonstrated in intact tissue
during acute uncoupling were '6 cm/s before occurrence of
conduction block.4 This large difference partly might be due
to the nonhomogeneous distribution of gap junctions in intact
tissue as opposed to the homogeneous distribution in the
computer model: tissues with an inhomogeneous distribution
of gap junctions would be prone to the occurrence of
conduction blocks at the sites of lowest gap–junctional
densities well before the minimal velocities predicted by
homogenous models could be achieved. In contrast, repetitive
discontinuities in tissue geometry, as artificially constructed
in this study or present in vivo, may form an alternative
mechanism for slow conduction in the absence of uncoupling
in which, as long as tissue geometry is largely preserved,
conduction is predicted to be relatively resistant to conduction block.
Recently, it was suggested that with increasing cell-to-cell
uncoupling and concomitant conduction slowing, the safety
factor for propagation initially increases before it finally
decreases to a level at which conduction block occurs.1 The
initial increase mainly is due to the fact that the charge
provided by inward currents during activation of a given cell
increasingly accumulates in the cell membrane because less
charge is flowing downstream. This concept shares similarities with the model of repetitive current-to-load mismatches
in which the charge produced during excitation of a given
branch is probably large relative to the charge necessary for
excitation of the same branch. Accordingly, such structures
are likely to possess a high safety factor because the “push”
effect increases propagation safety.
L-Type Ca21 Current and Success of Propagation
It was shown previously that ICa is important for the success
of impulse propagation in any situation in which a large local
propagation delay is present.1,25,33 In the branching tissue
structures used in the present study, large activation delays
were observed between adjacent branches, and it is therefore
likely that ICa played an essential role in ensuring safe
propagation also under conditions in which the Na1 current
was present. Therefore, if the major inward current is ICa, a
structure like the AV node or any structure exhibiting
geometrical discontinuities or being in an advanced state of
uncoupling displays slow conduction not only because of the
fact that propagation is ICa-based, but because ICa actually
becomes a conditio sine qua non for the success of
conduction.
Relevance for the Intact Heart
Although it is tempting to speculate that a branching structure as
investigated in this study might constitute an appropriate model
underlying very slow conduction in the AV node because it
produces slow and safe conduction, 2 major caveats apply. First,
cultured ventricular myocytes differ, to a certain extent, from
AV-nodal cells in regard to their types and distributions of both
gap junctions and ion channels.34,35 Second, a detailed morpho-
logic model of the AV node, including that of the “dead-end”
pathways, is not yet available. These pathways, which might
have a similar function to the branches investigated in this
study,20 have been described only functionally so far.17–19 Nevertheless, some morphologic studies suggest that the AV node
has an elaborate branching microarchitecture,36,37 thus lending
indirect support to the idea that very slow conduction might, in
part, be mediated by multiple “dead-end” branches. Another
situation in which the multiple branching model might apply
concerns myocardial tissue surviving in infarct scars,15,16 where
complex 2- and 3-dimensional branching networks were described, which might give rise to very slow conduction favoring
reentrant excitation.
Irrespective of the speculations as to the presence or location
of multiple branched structures in the intact heart, the present
study shows that such tissue geometries can contribute to the
establishment of very slow conduction. Moreover, the findings
suggest that the classical concept of current-to-load mismatch
can be modified by the “push” effect, in which closely spaced
current loads turn into sources on activation, thus easing conduction across the next impedance mismatch in line.
Acknowledgments
This work was supported by the Swiss National Science Foundation.
We wish to thank Mrs Regula Flückiger Labrada for the preparation
of the patterned growth cell cultures.
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Slow Conduction in Cardiac Tissue, II: Effects of Branching Tissue Geometry
Jan P. Kucera, André G. Kléber and Stephan Rohr
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Circ Res. 1998;83:795-805
doi: 10.1161/01.RES.83.8.795
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