Slow Conduction in Cardiac Tissue, II

Effects of Branching Tissue Geometry

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 rohr{at}pyl.unibe.ch

	Abstract

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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 [K⁺]_o (5.8 and 14.8 mmol/L, respectively; in the latter case, propagation was carried by the L-type Ca²⁺ 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 44.9±3.4 to 16.7±1.0 cm/s) and by 93% in elevated [K⁺]_o (from 15.7±2.3 to 1.1±0.2 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.

Key Words: discontinuous conduction • impedance mismatch • voltage-sensitive dye • atrioventricular node • myocardial infarction

	Introduction

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It 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 (I_Ca)–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 6 7 8 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 () 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 current-to-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 18 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 conduction^{10 20} in addition to action potentials carried by the Ca²⁺ 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 ("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

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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 µm wide, 10 mm long) releasing 2 branches (80 µm 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 µm wide, 10 mm long) releasing multiple branches (n>30; 80 µm wide) at equidistant intervals ([I], 150 or 300 µm) along the entire length of the strand ("multiple branch points"). In both types, branch length was varied from 60 to 1960 µm. Each coverslip carried, in addition to the test patterns, linear unbranched cell strands (80 µm wide, 10 mm long) that served as controls (Figure 1C).

View larger version (18K): [in this window] [in a new window]   Figure 1. Growth patterns. A, Pattern with a single branch point: two 80-µm–wide branches emerge from the strand (identical width) at right angles. Branch length (L) varied between 60 and 1960 µm. 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 µm, and the inter-branch distance (I) was either 150 or 300 µm. C, Unbranched, 80-µm-wide cell strand used as control in all experiments.

Optical Recording of Electrical Activation Patterns
As described previously,^{12 22} impulse propagation in the patterned growth cultures was followed optically using the fast voltage–sensitive dye di-8-ANEPPS (Molecular Probes; 135 µmol/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 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 20x objective (Fluar, Zeiss; NA 0.75), resulting in a spatial resolution of 50 µm.

Experimental Protocol
After mounting the preparations in the temperature-controlled experimental chamber (36±0.4°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 [K⁺]_o=5.8 mmol/L). Subsequently, the preparation was superfused for at least 5 min with HBSS containing elevated [K⁺]_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 µmol/L; Calbiochem), nifedipine (5 µmol/L; Sigma), or palmitoleic acid (20 µmol/L; Sigma) was delivered to the preparation in a spatially controlled manner by a local superfusion device^{24 25} : briefly, the drug-containing solution was delivered to the preparation using a syringe pump connected to an extruded polyethylene tube (diameter, 200 µm), 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 [K⁺]_o. The signal amplitudes obtained under control conditions were set to 100%. The measurements in elevated [K⁺]_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/dt_max) 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, s were determined by linear regression.

Statistics
Data are given as mean±SD. Data sets were compared using the Student t test (2-tailed), and differences were considered significant at P<0.05.

	Results

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Control Experiments With Linear Cell Strands
Each patterned growth culture contained, in addition to the specific patterns under investigation, 80-µm-wide linear and unbranched cell strands (Figure 1C) serving as controls. In these strands, propagation was assessed routinely at the beginning of each experiment. An example of such a measurement is shown in Figure 2. Under control conditions ([K⁺]_o=5.8 mmol/L), propagation was fast (=45.4 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 [K⁺]_o (14.8 mmol/L, mainly I_Ca-dependent propagation),¹² fell to 19.8 cm/s, and upstrokes were substantially slowed.

View larger version (51K): [in this window] [in a new window]   Figure 2. Impulse propagation along a linear cell strand. A, Phase-contrast videomicrograph of the preparation (80-µm-wide strand). White circles indicate the optical recording sites (distance between sites, 50 µm); , direction of propagation. B, Superimposed action potential upstrokes obtained from all sites (1 to 19) under control conditions ([K+]o=5.8 mmol/L; top) and in elevated [K+]o (14.8 mmol/L; bottom). The similar shapes and the regular spacings of the upstrokes indicate uniform propagation. APAs in elevated [K+]o were reduced by 30%, and upstroke velocities were slowed by 85%. C, Activation profiles under control conditions () and in elevated [K+]o (). 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 [K+]o (r=0.999; =45.4 cm/s) and elevated [K+]o (r=0.994; =19.8 cm/s).

Summarizing all control measurements with linear cell strands (n=15), elevation of [K⁺]_o from 5.8 to 14.8 mmol/L reduced from 44.9±3.4 to 15.7±2.3 cm/s. At the same time, dV/dt_max fell from 97±13 to 15±2 %APA/ms. The absence of a significant rundown of the preparations during the experiments was assessed by reexamining at the end of each experiment. The measurements showed a nonsignificant decrease of by 4±5%. 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-µm-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 µm from the branch ends).

View larger version (32K): [in this window] [in a new window]   Figure 3. Propagation across a single branch point. A, Videomicrograph of the preparation consisting of a cell strand (horizontal) releasing two 460-µm-long branches. 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 ([K+]o=5.8 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). 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 [K+]o. C, Plot of activation times along the strand (, ) and branches (, ) under control conditions (, ) and in elevated [K+]o (14.8 mmol/L; , ). Activation delays at the branch point amounted to 1.5 ms under control conditions and to 4.7 ms in elevated [K+]o (for mode of calculation, see Results).

An overview of the activation patterns across the branch point under control conditions and in elevated [K⁺]_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 [K⁺]_o. As illustrated in Figure 3C, activation times of the branches in control [K⁺]_o showed a slight increment within the first 300 µm, whereas the remainder of the branches were activated almost simultaneously. In elevated [K⁺]_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 (activation times along the strand), the branch point induced a delay that was highly accentuated in elevated [K⁺]_o. This delay was quantified by first fitting a line with a slope corresponding to the average 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 [K⁺]_o. Whereas the activation profile of the branches (, ) under control conditions was similar to that of the strand (, ), activation of the relatively short branches in elevated [K⁺]_o was distinctly different, because distal parts of the branches were activated earlier than proximal parts.

For branch lengths of up to 3 multiples of the space constant (=360 µm),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 µm), 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 µm, 3 experiments each with branch lengths of 160, 260, 360, and 460 µm). As summarized in Figure 4, the delays increased with increasing branch length. Under control conditions, the maximal delays observed were 1.5±0.4 ms (length, 460 µm; n=3), whereas in elevated [K⁺]_o, they amounted to 4.5±1.0 ms (length, 460 µm; n=3). Both values were significantly different from those of control strands (P<0.05).

View larger version (22K): [in this window] [in a new window]   Figure 4. Conduction delays across a single branch point as a function of branch length. A, Under control conditions ([K+]o=5.8 mmol/L), activation delays at the branch point displayed a trend to increase up to the third branch length tested (260 µm) before leveling off (mean±SD; n=3 for each data point, except for branch lengths of 60 µm; n=2). B, Same as (A) but for measurements obtained in elevated [K+]o (14.8 mmol/L). Gray bands depict variations of conduction times (SD) in unbranched strands at either [K+]o (n=15). *Significantly increased delays vs control strands (n=15; 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-µm-wide 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 µm; I=300 µm). 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/dt_max 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/dt_max over all experiments involving the same geometry (length, 360 µm; I=300 µm) showed a clear periodical pattern with minimal dV/dt_max (62±7 %APA/ms; n=5) of 50 µm in front of the branch points and a significantly larger maximal dV/dt_max (89±10 %APA/ms; n=6) of 100 µm thereafter (P<0.05). Within the branches, dV/dt_max increased to steady values within 250 to 300 µm from the branch point (sites C, D, G, and H).

View larger version (33K): [in this window] [in a new window]   Figure 5. Propagation across multiple branch points. A, Videomicrograph of the preparation showing the cell strand (horizontal) releasing 360-µm-long branches every 300 µm. 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, [K+]o=5.8 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). 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 [K+]o (14.8 mmol/L) with single steps coinciding with the branch points. C, Plot of activation times along the strand (, ) and along the central branches (, ; denoted with asterisks in [B]) under control conditions (, ) and during elevation of [K+]o (, ). 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 [K+]o, these discontinuities were enhanced. Overall s determined from these activation profiles were 28.7 cm/s under control conditions and 8.9 cm/s in elevated [K+]o. Note that the activation of the branches occurred virtually simultaneously in elevated [K+]o.

Figure 5B shows 3-dimensional plots illustrating the general characteristics of activation along the preparation at both [K⁺]_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 [K⁺]_o. As in the case of a single branch point, activation of the branches was relatively fast under control conditions, whereas in elevated [K⁺]_o, the short branches were activated virtually simultaneously. Overall in this preparation was 28.7 cm/s under control conditions and 8.9 cm/s at [K⁺]_o=14.8 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 µm, Figure 6A; 150 µm, Figure 6B). In both cases, lengthening of the branches from 60 to 260 µm led to a progressive reduction of . Beyond 500 to 1000 µm, no further major slowing was obtained. As expected, maximal conduction slowing was observed in the preparations with a narrow inter-branch distance (I=150 µm): under control conditions, was reduced by 63% to 16.7±1.0 cm/s (length, 960 µm; n=4), whereas in elevated [K⁺]_o, fell by 93% to 1.1±0.2 cm/s (length, 1960 µm; n=3). 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 [K⁺]_o (length, 960 or 1960 µm; n=6 of 17).

View larger version (22K): [in this window] [in a new window]   Figure 6. in preparations with multiple branch points. A, as a function of branch length and [K+]o (5.8 and 14.8 mmol/L) for preparations with an inter-branch distance (I) of 300 µm (mean±SD; n=2 to 4 for each branch length). B, same analysis as in (A) for preparations with an inter-branch distance of 150 µm (mean±SD; n=2 to 4 for each branch length). Gray bands depict mean±SD of obtained in unbranched strands at either [K+]o (n=15).

Dual Effects of Multiple Branches: "Pull and Push" Effect
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 [K⁺]_o, the average delays were 32% (I=300 µm) and 18% (I=150 µm) of the average delay across a single branch point. In elevated [K⁺]_o, this change was less pronounced, as the average delays were 77% (I=300 µm) and 48% (I=150 µm) 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).

View larger version (35K): [in this window] [in a new window]   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 ([K+]o=5.8 mmol/L). This effect was enhanced with increasing spatial frequency of the branches (reduction of inter-branch distance from 300 to 150 µm). B, In elevated [K+]o (14.8 mmol/L), qualitatively similar results were obtained. However, the change was quantitatively less pronounced.

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 (I=150 µm; length, 960 µm; Figures 8A and 9A). This modification was technically necessary to permit the local superfusion to reach both branches simultaneously. Irrespective of [K⁺]_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.

View larger version (111K): [in this window] [in a new window]   Figure 8. Inhibition of inward currents in the branches. A, Videomicrograph of the preparation, showing a strand that released two 960-µm-long branches to 1 side only (I=150 µm). 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 ([K+]o=5.8 mmol/L); overall =40.2 cm/s. C, During elevation of [K+]o to 14.8 mmol/L, action potential upstroke velocities decreased and fell to 4.5 cm/s. D, Same as (C), but the branches were rendered inexcitable by local superfusion with 22 µmol/L TTX and 5 µmol/L nifedipine for 2 min. The lower border of the superfusion was kept at a distance 100 µm from the cell strand. As indicated by the decremental signal amplitudes, this intervention caused conduction block. E, Control recordings obtained 5 min after washout ([K+]o=5.8 mmol/L). Overall returned to 38.5 cm/s.

View larger version (69K): [in this window] [in a new window]   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 960-µm-long branches to 1 side only (I=150 µm). 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 [K+]o (14.8 mmol/L) before (gray squares) and during (black squares) local superfusion of the branches with 22 µmol/L TTX, 5 µmol/L nifedipine, and 20 µmol/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 gap-junctional uncoupling induced a substantial reduction of the current load exerted by the branches.

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 [K⁺]_o (Figure 8B and 8C). In elevated [K⁺]_o (14.8 mmol/L), local superfusion of the branches with TTX (22 µmol/L) and nifedipine (5 µmol/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 [K⁺]_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 [K⁺]_o (n=8; 5 full blocks, 3 intermittent 2:1 blocks). Conversely, under conditions of control [K⁺]_o, no conduction blocks were observed, but the delay induced by the branches rose significantly from 0.7±0.4 to 1.2±0.7 ms (n=5; 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 [K⁺]_o, the propagation delay induced by the 2 branches amounted to 13 ms (Figure 9B). Local superfusion of the branches with palmitoleic acid (20 µmol/L), TTX (22 µmol/L), and nifedipine (5 µmol/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 µm),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 branches is explained by the circumstance that the load was not completely eliminated, because the border of the local superfusion was kept 100 µm away from the main strand (arrows, Figure 9A). Finally, the finding that there was no diffusion of drugs toward the main strand^{24 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

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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 I_Ca-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 6 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
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 inter-branch distance was accompanied by a decrease of . Compared with unbranched strands, the maximal reduction of in control [K⁺]_o in periodically branched strands was -63% (17 cm/s). This reduction was in the same range as that observed in unbranched strands during a marked elevation of [K⁺]_o (14.9 cm/s at [K⁺]_o=30.0 mmol/L; conduction based primarily on I_Ca¹² ) and in intact cardiac tissue exposed to moderately increased [K⁺]_o (12 mmol/L; 19 cm/s; transverse conduction).²⁹ When the effects of branching were combined with a reduction of excitability ([K⁺]_o=14.8 mmol/L), was reduced by -93% (1.1 cm/s) compared with values obtained in unbranched control strands at the same [K⁺]_o. Thus, the combination of branching tissue geometry with I_Ca-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 s obtained in the branched preparations in elevated [K⁺]_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.

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 µm (Figure 6), which is readily explained by the fact that these lengths correspond to 2 to 3 multiples of the space constant (=360 µm 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 , this observation primarily is explained by the well-known 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 µm; >5 ). 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 µm; control [K⁺]_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 inter-branch distances, a significant difference could be observed. Whereas, at an inter-branch distance of 300 µm, the average length of these "preactivated" segments was 94±59 µm (n=54), it increased to 131±84 µm (n=130; P<0.05) for an inter-branch distance of 150 µm 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 µm) and in the presence of elevated [K⁺]_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 ) 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 [K⁺]_o remains to be shown. 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 velocities^{12 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 [K⁺]_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 µm, the delay introduced by each branch point was diminished. This finding suggested that the branches not only acted to decrease 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

Comparison With Slow Conduction Induced by Electrical Uncoupling
It was shown in a recent computer simulation study that gap-junctional uncoupling induced s as low as 0.26 cm/s.¹ On the other hand, slowest s 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 Ca²⁺ Current and Success of Propagation
It was shown previously that I_Ca 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 I_Ca played an essential role in ensuring safe propagation also under conditions in which the Na⁺ current was present. Therefore, if the major inward current is I_Ca, 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 I_Ca-based, but because I_Ca 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 morphologic 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 18 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.

Received January 14, 1998; accepted August 7, 1998.

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