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(Circulation Research. 1996;79:115-127.)
© 1996 American Heart Association, Inc.

Articles

Anisotropic Activation Spread in Heart Cell Monolayers Assessed by High-Resolution Optical Mapping

Role of Tissue Discontinuities

Vladimir G. Fast, Bruce J. Darrow, Jeffrey E. Saffitz, Andre G. Kleber

the Department of Physiology (V.G.F., A.G.K.), University of Berne (Switzerland), and the Department of Pathology (B.J.D., J.E.S.), Washington University, St. Louis, Mo.

Correspondence to V.G. Fast, PhD, or A.G. Kleber, MD, Department of Physiology, University of Berne, Buhlplatz 5, CH-3012, Berne, Switzerland. E-mail fast@pyl.unibe.ch. E-mail kleber@pyl.unibe.ch.

	Abstract

Top Abstract Introduction Materials and Methods Results Discussion References

 
The role of tissue discontinuities in anisotropic impulse propagation was assessed in two-dimensional anisotropic monolayers of neonatal rat myocytes cultured on a growth-directing substrate of collagen. Activation spread and distribution of maximal upstroke rate of rise (V_max) of the action potential were measured with an optical system using a voltage-sensitive fluorescent dye (RH-327) and a 10x10 photodiode array with a spatial resolution ranging from 7 to 15 µm. Activation maps were compared with the cellular architecture and the distribution of gap junctions obtained from immunostaining the gap junction protein connexin43 (Cx43). Four types of structures were studied: (1) dense cell cultures, (2) cultures with anisotropic intercellular clefts of variable size, (3) discontinuities created by inclusion of nonmyocyte cells, and (4) discontinuities resulting from nonuniform expression of gap junctions. In dense monolayers, activation spread was continuous with microinhomogeneities in both longitudinal and transverse directions. The average cell dimensions in such monolayers were smaller than in adult canine myocardium. However, the degree of cellular anisotropy (length-to-width ratio of 5.3±1.4) and connectivity were similar. The presence of small intercellular clefts (less than one cell in length) did not disturb the general pattern of transverse or longitudinal activation spread, but it was associated with wave front microcollisions during transverse propagation and a concomitant increase of V_max beyond the cleft. Long intercellular clefts caused discontinuous transverse propagation. Conduction velocity and V_max decreased significantly at narrow isthmuses formed by closely apposed clefts, rendering such sites susceptible for conduction block. In contrast, V_max increased when the wave front faced the borders of the clefts. Nonmyocyte cells were electrically connected to myocytes and served as sinks for electrotonic currents, thereby producing localized conduction slowing and a decrease in V_max. Localized inhomogeneity in Cx43 distribution correlated accurately with circumscribed conduction block and changes in V_max. Our results provide direct experimental evidence that the cellular structure and gap junction distribution correlate with action potential propagation and distribution of V_max. We suggest that in tissue with a nonuniform anisotropy, connective tissue separating fiber bundles or sites of inhomogeneous connexin distribution may represent predilective sites for block in transverse direction.

Key Words: cell culture • ventricular myocytes • anisotropy • collagen • voltage-sensitive dyes

	Introduction

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Propagation of activation waves in heart muscle depends on the excitable properties of the cardiac membranes and on the passive electrical properties, which are determined by tissue microanatomy and the distribution and function of intercellular connections. Two properties of ventricular myocardium are believed to be especially important for impulse conduction: structural anisotropy and the discrete architecture of cardiac tissue. It is well established that conduction velocity is greater in the direction parallel to fiber orientation than in the direction perpendicular to the fiber axis (functional anisotropy).^{1 2 3 4 5 6 7 8} The directional differences in velocity of propagation are believed to be due to the higher resistivities in the intracellular and extracellular compartments in the transverse direction compared with the longitudinal direction and can be modeled by using continuous cable theory.² The question of how other parameters of activation spread are affected by structural anisotropy has not been fully clarified. In atrial and ventricular tissue, it has been reported that V_max of the action potential is larger in the transverse than in the longitudinal direction.^{9 10 11 12 13} This difference is associated with a higher margin of safety of transverse versus longitudinal conduction. The higher margin of safety has been used to explain the generation of circus movement and reentry in anisotropic tissue with depressed excitable properties.^{9 14}

Continuous cable theory, as well as its extension to two dimensions, is unable to explain directional dependence of V_max because it predicts no changes in action potential waveshape upon changing the direction of impulse spread. Therefore, it has been suggested that in addition to the structural anisotropy, per se, the discrete structure of cardiac muscle and the resulting discontinuities of axial resistance play a major role in impulse conduction.^{9 14} These discontinuities in myocardial structure exist on several levels. On the smallest scale, they are related to the intercellular borders and nonuniform distribution of gap junctions. Discontinuities of larger dimensions are imposed by connective tissue sheets and the vasculature separating cells and cell bundles.¹⁵ The relation between microscopic tissue structure and impulse conduction has been investigated in computer models of anisotropic conduction.^{16 17 18 19 20} However, only a few experimental studies on a microscopic level have been performed so far. This task demands recording of anisotropic activation spread with high spatial and temporal resolution and correlation of electrophysiological measurements with tissue microstructure. To this aim, we have recently developed an experimental model of anisotropic tissue using two-dimensional monolayers of neonatal rat ventricular myocytes cultured on a growth-directing substrate of collagen.²¹ This model allows for high-resolution recordings of action potentials at multiple sites and correlation of activation spread with tissue microarchitecture. Using a method of optical recording of action potentials with a voltage-sensitive dye, we have characterized impulse conduction in monolayers with dense cell growth, where discontinuities in axial resistance are produced by cell borders alone. In this preparation, no directional differences in V_max were found.²¹

The present study was designed to assess the effects of discontinuities in tissue architecture on impulse conduction in anisotropic cell monolayers by using an optical mapping technique. Three types of discontinuities found in cell cultures were investigated: (1) The first type of discontinuities corresponded to anatomic clefts. Depending on cell density and cell growth, clefts of different length are found in anisotropic monolayers. These discontinuities simulate resistive obstacles in intact myocardium. Such obstacles may be created by connective tissue sheets or blood vessels.²² (2) The second type of discontinuities was created by inclusion of nonmyocyte cells. In cell cultures, fibroblasts and epithelioid cells have been reported to be electrically connected to myocytes.^{23 24} The influence of this interaction on impulse propagation has not been established so far. (3) The third type of discontinuities resulted from nonuniform expression and distribution of gap junctions. To this aim, maps of activation spread were correlated with the pattern of gap junction distribution obtained by immunostaining cells with antibodies against the major cardiac gap junction protein Cx43.²⁵

	Materials and Methods

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Cell Culture
Anisotropic Cell Growth
The method for production of anisotropic cell monolayers has been reported previously in detail.²¹ In brief, the extracellular matrix protein collagen type IV from human placenta (Sigma Chemical Co) was dissolved in phosphate-buffered solution at a concentration of 20 to 50 µg/mL. Two milliliters of the solution was applied to one side of glass coverslips (diameter, 22 mm; thickness, 0.14 mm; Haska) for 1 hour at room temperature. The coverslips were then rinsed with distilled water and air-dried. Subsequently, a growth-directing substrate was obtained by gently rubbing the collagen coat with a fine brush. This mechanical treatment produced an adhesion matrix leading to parallel alignment of the cultured cells (Fig 1). Myocytes were isolated from neonatal Wystar rats (2 days old) using a procedure reported elsewhere.²⁶ The ventricles of the excised hearts were dissociated with trypsin (0.1%). The dispersed cells were suspended in medium M199 (GIBCO) with an ionic composition of (mmol/L) NaCl 137, KCl 5.4, CaCl₂ 1.3, MgSO₄ 0.8, NaHCO₃ 4.2, KH₂PO₄ 0.5, and NaH₂PO₄ 0.3, along with 20 U/mL penicillin, 20 µg/mL vitamin B12, and 10% neonatal calf serum. The cell suspension was preplated to reduce the fibroblast content and then diluted to 3x10⁵ cells per milliliter. Two milliliters of cell suspension was placed into a well containing the collagen-coated coverslip. The cultures were incubated in medium M199 containing 5% serum at 37°C in a humidified atmosphere containing 1.5% CO₂. Medium was changed every second day. Measurements were made between culture days 4 and 12. Typically, regions with dense anisotropic growth, regions with intercellular clefts, and regions containing few interspersed nonmyocytes were observed on the same monolayer.

View larger version (180K): [in this window] [in a new window]   Figure 1. A, Schematic presentation of technique used for anisotropic cell growth showing the essential steps in the preparation of glass coverslips covered by a growth-directing matrix. B, Phase-contrast image of anisotropic cell monolayer.

Voltage-Sensitive Dye Staining
Coverslips were transferred to the experimental chamber mounted on a vibration-free table. Cells were superfused at a rate of 2 mL/min with a solution composed of (mmol/L) NaCl 150, KCl 5, CaCl₂ 1.2, MgCl₂ 1, NaHCO₃ 5.8, HEPES 5, and glucose 5. pH was 7.4; temperature was 34°C to 35°C. The voltage-sensitive dye RH-237 (Molecular Probes) was used to measure transmembrane potential changes. The dye was stored in a 2 mmol/L stock solution of dimethyl sulfoxide and diluted to yield a final dye concentration of 2 µmol/L in Tyrode's solution (final dimethyl sulfoxide concentration, 0.1%). Cells were superfused with the dye solution for 4 to 6 minutes.

Optical Recording of Impulse Conduction
Optical Setup
The experimental setup for optical recording of action potential upstrokes using 12 recording channels has been described in detail previously.^{21 27 28} In the present system, the number of channels was increased from 12 to 96. The system includes an inverted Axiovert 35M microscope with x40, x63, or x86 objectives (Zeiss) and a filter set with a band-pass–exciting filter (530 to 585 nm), a dichroic mirror (600 nm), and a low-pass–emitting filter (>615 nm) (Fig 2). Cells were exposed to excitation light for 50 ms. The fluorescence emitted by the dye was measured using a 10x10 photodiode array (Centronic) located in the image plane of the microscope. A square with a side-length of 14, 8.9, or 6.5 µm corresponded to the recording area of each photodiode at magnifications of x40, x63, or x86, respectively. The photocurrents from 96 diodes were converted to voltage and fed into second-stage amplifiers containing a sample-and-hold circuit for subtraction of DC signals. The signals were multiplexed with a custom-made multiplexer into 12 channels and digitized using three ADC cards (four channels, 1 MHz each; National Instruments) installed in a Quadra 840av computer (Apple). The sampling rate was 25 kHz per channel at a resolution of 12 bits. High-frequency noise was eliminated by digital filtration with a cutoff frequency of 1.5 to 2 kHz.²⁷ The specific cutoff frequency was selected to provide maximal noise reduction without modifying the overall shape of action potential upstrokes and without introducing a significant error in determination of local activation time. The activation times were determined at the level of the 50% change of optical upstroke.²⁸ This level was obtained by linear interpolation between the nearest sampling points. Activation maps were built using linear interpolation between neighboring diodes. To calculate V_max, filtered signals were scaled to a 100-mV amplitude and digitally differentiated. The assumption was made that the APA was constant throughout the mapping area and did not depend on the direction of propagation. The existence of APA gradients on the microscopic scale (less than the electrotonic space constant, 350 µm)²⁹ is highly unlikely, taking into account the flow of local axial currents that would neutralize such gradients. The lack of directional differences in APA is corroborated by theoretical as well as experimental data: (1) No direction-dependent changes of APA and no spatial gradients were found in anisotropic computer models of both ventricular myocardium¹⁹ and cultured cell monolayers³⁰ within a wide range of conditions. (2) Experiments on isolated preparations of atrial and ventricular muscle revealed no significant directional differences of APA.^{9 10 11 12} (3) In the present experiments, the amplitude of optical upstrokes was not significantly different in longitudinal versus transverse directions (see "Results").

View larger version (19K): [in this window] [in a new window]   Figure 2. A, Schematic diagram of the optical setup. The exciting light emitted from the mercury lamp is filtered and sent to the objective and the cell preparation via a dichroic mirror. The light emitted from the preparation is filtered and split into a beam recorded by a CCD camera and processed to a picture and a beam falling on an array of light-sensitive diodes. The electrical currents from the diodes are converted to voltage, amplified (sample-and-hold amplifier [S&H Amp]), multiplexed (into 12 channels [ch]), and sent to A/D converters (ADC). Subsequently, the digital information is stored and processed in a Quadra 840av computer (Apple). B, Fluorescent optical recording of cell transmembrane potential with a single photodiode. The upper two traces show the whole of the optical signal and stimulator output. The first negative deflection of the signal corresponds to the opening of the shutter; the second deflection represents the upstroke of the action potential evoked by the stimulation pulse. The two bottom traces show the enlarged portion with the action potential upstroke (F) and the first time derivative (dF/dt).

Measurements of activation times and V_max were affected by optical noise and were dependent on S/N_rms. The noise-induced error was estimated using a method described previously.²⁷ It included summation of a simulated action potential with experimental noise. Both signal and noise were sampled at a rate of 25 kHz, the same rate as used for optical recordings. The noise was scaled with respect to the action potential to give a specified S/N_rms. The mixed signal was filtered (cutoff, 1.5 kHz) and processed to determine activation time and V_max. By repeating this procedure several times (n=14), parameter distributions were obtained, and their standard deviations were taken as experimental errors. At S/N_rms=58, which was typical for our measurements, the error (standard deviation) in activation was 9 µs, and error in V_max was 6.5 V/s.

Electrical Stimulation
Electrical stimulation was performed via a bipolar electrode composed of the conducting core of a glass pipette (tip diameter, 50 to 70 µm) filled with the superfusion solution and a silver wire coiled around the pipette tip. Cells were stimulated with rectangular pulses (duration, 1 ms; double threshold strength). To ensure that electrical stimulation did not interfere with propagation measurements, the stimulation electrode was placed >1 mm from the measurement site on the extension of the line passing through the middle of the mapped area either parallel (longitudinal propagation) or perpendicular (transverse propagation) to the long cell axis. To compensate for potential phototoxic effects, the order of longitudinal and transverse stimulation was alternated from experiment to experiment as described in a previous study.²¹

Tissue Morphology and Immunostaining for Cx43
Before each recording, cell morphology was observed through a red light (filter, >630 nm), and the photodiodes were positioned over a chosen area. The bright-field illumination image of the cells and the photodiodes in each recording area as well as the phase-contrast image of cells (magnifications, x20 and x40) were obtained by a CCD video camera (Cohu 6510) and a frame-grabber of the Quadra 840av computer. This procedure avoided phototoxic damage to cells. After completion of electrophysiological recordings, cells were fixed on the collagen-coated coverslips for 30 minutes at room temperature in 4% paraformaldehyde in PBS. The fixed cells were washed three times in PBS, permeabilized in PBS containing 1% Triton X-100, and blocked in PBS containing 3% normal goat serum, 1% bovine serum albumin (globulin free), and 0.3% Triton X-100. Coverslips were exposed to bright light for 30 minutes to photobleach the remaining voltage-sensitive dye. To evaluate the effects of fixation on the monolayer structure, phase-contrast images were obtained from the same cell area before and after the fixation. Comparison of cell border outlines and locations of cell nuclei demonstrated that the fixation procedure caused no significant distortions in monolayer architecture. To delineate the microscopic distribution of gap junctions, fixed permeabilized cells were incubated for 16 hours at 4°C with a previously characterized mouse monoclonal antibody against rat Cx43 (Chemicon International Inc)³¹ diluted 1:200 in blocking buffer. Cells were then washed three times with PBS, incubated for 45 minutes with CY3-conjugated goat anti-mouse IgG (Jackson Immunolaboratories) diluted 1:400 in blocking buffer, rinsed three times in PBS, and examined with a Molecular Dynamics Sarastro 2000 laser scanning confocal microscope. The exact areas of the cultures analyzed electrophysiologically were identified under bright-field illumination, and the distribution of intercellular junctions in each region was determined by immunofluoresence microscopy.

Morphometric analysis was performed according to methods previously described.^{32 33} In addition to determining the average maximal longitudinal and transverse cell dimensions and measuring the number of cells connected to an individual myocyte in culture, the spatial orientation of each interconnection to randomly selected individual cells was characterized on the basis of its relative side-to-side or end-to-end pattern. Two classes of cell-to-cell apposition were defined: Type I included cell pairs with end-to-end contacts and up to 30% lateral border overlap. Type II included cells with >30% lateral overlap and no end-to-end contacts. Cell connectivity in cultured monolayers was compared to the adult ventricular tissue. For this purpose, 1-µm-thick sections of canine ventricular myocardium used for three-dimensional reconstruction in a previous study³³ were subjected to the two-dimensional morphometric analysis as described above.

Statistical data are expressed as mean±SD. The two-tailed paired or nonpaired Student's t tests were used for comparison where appropriate (P.05 was considered statistically significant).

	Results

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Morphology of Cell Monolayers and Immunostaining for Cx43
The number and orientation of myocyte interconnections were analyzed in eight anisotropic monolayers. Randomly selected cells were found to have connections to 5.6±0.8 (mean±SD, n=61) neighbors. This was very close to the number of contacts in two-dimensional slices of adult canine ventricular myocardium (5.5±1.1, n=38). On average, 2.5±1.1 cell connections (45%) were of type I (end-to-end with little or no side-to-side overlap), and 3.1±0.9 cell connections (55%) were of type II (side-to-side connections with >30% overlap; see "Materials and Methods"). This distribution of end-to-end and side-to-side contacts was similar to the adult ventricular muscle: 58% of cell contacts in two-dimensional tissue slices were of type I, and 42% of contacts were of type II in this tissue. The mean maximal length and width of cultured myocytes were 70.1±16.4 µm (n=63) and 13.7±3.2 µm, respectively. The anisotropic length-to-width ratio was 5.3±1.4.

To characterize the pattern of gap junction distribution in anisotropic cell cultures, four monolayers were immunostained using Cx43 antibodies. In addition to Cx43, rat ventricular myocytes in culture express a second gap junction protein, Cx45.³⁴ Because Cx45 colocalizes with Cx43 in double-labeled cultures,³⁴ the labeling of the Cx43 alone is sufficient to reveal the distribution of gap junctions. Immunolabeling showed a relatively uniform and dense distribution of gap junctions in areas with continuous cell growth in the large majority of randomly selected fields of vision. Panel A of Fig 3 shows a confocal image of Cx43 labeling in an anisotropic cell monolayer. Cell borders and small intercellular clefts are discernible on the image from background fluorescence. Typically, gap junctions were distributed in a dotted pattern along the cell perimeter. The distance between gap junctions was rather uniform. Dense bands of Cx43 immunostaining at cell ends and large intervals between junctions along lateral cell borders, as present in adult tissue,^{35 36} were rarely observed. The pattern in vitro closely resembled the gap junction distribution observed in neonatal rat hearts in vivo.³

View larger version (368K): [in this window] [in a new window]   Figure 3. Fluorescent confocal images of gap junction distribution in anisotropic cell monolayers labeled with antibodies against Cx43. A, Uniform gap junction distribution in a dense cell monolayer. B, Localized absence of Cx43 along the borders of several cells in the upper part of the image.

Sporadically, relatively large discontinuities in gap junction distribution were found in confluent regions of cell monolayers. A confocal image showing nonuniform distribution of gap junctions is presented in panel B of Fig 3. In this case, a region free of immunofluorescence is visible in the central part of the image. The region free of gap junctions consisted of three cells in the longitudinal direction and two cells in transverse orientation closely apposed to their neighbors. The cells in the Cx43-free region exhibited an obvious myocyte-like appearance showing normal shape, size, intact nuclei, and cross striations, which distinguished them from nonmyocyte cells. At least one myocyte free of gap junctions was found in 20 of 100 randomly selected observation fields (x40 magnification).

Activation Maps During Longitudinal and Transverse Conduction in Dense Monolayers
Previously, we characterized the general pattern of activation spread in confluent cell monolayers at a relatively low resolution using data acquired from 12 recording sites within an area of 150x150 µm².²¹ In order to gather information about the uniformity of conduction at the cellular level, we measured activation at high resolution from the action potential upstrokes recorded simultaneously from 96 sites within areas of 70x70 µm² (x86 magnification), 95x95 µm² (x63 magnification), or 150x150 µm² (x40 magnification).

Fig 4 demonstrates an example of impulse propagation in a dense anisotropic cell culture. The photodiode array occupied an area of 95x95 µm² crossing borders of eight cells in the transverse direction and two or three cells in the longitudinal direction. Panels A and B show isochronal maps of activation spread during longitudinal and transverse propagation, respectively. Isochronal lines were drawn at an interval of 100 µs and overlaid on the pattern of cell borders. Values for conduction velocities averaged over the whole mapping area were 30.6 and 9.4 cm/s in longitudinal and transverse directions, respectively. Longitudinal spread was nonuniform at this level of resolution. In the longitudinal direction, two large cells in the middle of the mapping area (indicated by asterisks) were excited both by the longitudinally propagating wave front and by current flowing laterally between cells, as indicated by the arrows depicting the direction of activation spread. Transverse propagation was consistently more uniform than longitudinal spread in all experiments. This does not rule out longitudinal microcollisions during transverse propagation (see Fig 6 and "Discussion").

View larger version (78K): [in this window] [in a new window]   Figure 4. Activation spread in a dense anisotropic cell monolayer. Isochronal activation maps during longitudinal (right to left, A) and transverse (bottom to top, B) propagation. Isochrones are drawn at an interval of 100 µs. Arrows depict the direction of activation spread. White lines show cell borders redrawn from the phase-contrast picture. Asterisks indicate two large cells in the middle of the mapping area. The quadrangle with cutoff edges overlaid on cell pattern corresponds to the area covered by the diode array containing 96 measuring points. Dots indicate centers of photodiodes. Note inhomogeneities during longitudinal propagation with localized lateral conduction compared with more homogeneous alignment of isochrones during transverse propagation.

View larger version (402K): [in this window] [in a new window]   Figure 6. Anisotropic activation spread in a region with a small intercellular cleft. A, Phase-contrast image of the cell culture with overlaid photodiode array mask. Note the small intercellular cleft in the upper half of the image. B, Isochronal map during transverse activation spread overlaid on the cell pattern. Isochrones (black) are presented with an interval of 50 µs. C, Distribution of Vmax (upper graph) and activation times (lower graph) along the row of photodiodes located in two cells above the cleft. Relative activation times (in microseconds) are given from the earliest activation moment within the photodiode row. Note that the highest value of Vmax within the cell corresponds to the position of latest activation and indicates local collision.

Because of limitations in spatial resolution, activation maps did not allow for precise and consistent determination of the localization of conduction pathways between individual cells. However, at some recording sites, such pathways were suggested from the comparison of transverse and longitudinal activation maps, as shown in Fig 5, which depicts high-resolution maps of activation spread (7-µm spacing of measuring points, x86 magnification) and selected recordings of action potentials in an area encompassing four cells. During longitudinal spread (panels A and C), the left end of the cell in the middle-right part marked with an asterisk was excited from above (site 4), in addition to longitudinal activation from the right (site 1). The site of breakthrough from the upper cell likely corresponded to a low-resistance pathway. This was substantiated by the transverse activation map shown in panel B. At the same location on the upper cell border, the isochronal line shows a bulge into the upper cell, again indicating local acceleration of conduction by the presence of a low-resistance pathway.

View larger version (69K): [in this window] [in a new window]   Figure 5. Microscopic activation spread recorded at high magnification (interdiode interval, 7 µm). Panels A and B depict activation maps of longitudinal (A) and transverse (B) propagation. Panels C and D show selected recordings of action potential upstrokes during longitudinal and transverse conduction, respectively. During longitudinal propagation, the cell marked with an asterisk is activated from the right as well as from above (vertical arrow). During transverse propagation, the isochrones show a forward curvature at the same site (vertical arrow), indicating that there is preferential conduction through a low-resistance pathway in the cell border at this location. Cell borders are drawn in white. Dots in panels A and B indicate centers of photodiodes; large dots in panels C and D correspond to activation times.

Directional differences in conduction velocity and V_max were evaluated in nine dense monolayers. Conduction velocity averaged 35.2±5 cm/s in the longitudinal direction and 15.8±7 cm/s in the transverse direction (n=9). The anisotropic velocity ratio was 2.5±0.8. Amplitudes of optical upstrokes were not significantly different in the two directions (paired t test): the transverse-to-longitudinal ratio of optical amplitudes amounted to 0.93±0.11. There was significant variability of V_max during both longitudinal and transverse conduction. This variability exceeded the variability caused by optical noise and is likely due to a microscopic variability of electrical load.²⁰ However, no directional difference was present between mean values, as previously reported.²¹ In the experiment shown in Fig 4, average longitudinal and transverse V_max values were 87±13 and 102±14 V/s, respectively (averaged on all 96 diodes). In all experiments (n=9), average V_max was 110±18 V/s during longitudinal versus 108±11 V/s during transverse propagation (P=NS, paired t test).

Impulse Conduction in the Presence of Small Intercellular Clefts
The degree of functional anisotropy and the pattern of gap junction distribution vary according to the cardiac region. In some regions, such as the crista terminalis, gap junctions are concentrated at end-to-end cell appositions, with lateral gap junctions being relatively scarce.³⁶ As a consequence of this distribution pattern, longitudinal microcollision of local activation waves may occur within single cells during transverse propagation. We assessed intracellular wave collision during transverse propagation in the anisotropic cell cultures in the presence of small longitudinally oriented intercellular clefts (length, 69±20 µm; n=5). In this situation, gap junctions were absent within a major segment of the lateral cell border. Fig 6 shows an example of transverse activation spread in a monolayer with a small intercellular cleft located in the upper middle part of the mapping area (panel A). The width and the length of the cleft were 5 and 50 µm, less than the dimensions of the cell located above the cleft. Panel B demonstrates the general pattern of transverse activation spread. The activation map in panel A was generated by linear interpolation between local activation times, ie, without taking into account the presence of resistive boundary imposed by the cleft. The average transverse conduction velocity across the map was 25 cm/s, and the V_max was 156±20 V/s (n=96). It can be seen that the overall spread of activation in this type of presentation appeared to be only slightly perturbed by the cleft. However, a more detailed inspection of the activation sequence and the distribution of V_max (panel C) indicated that a microcollision of two opposite excitation waves probably took place within the cell above the cleft: earliest activation occurred at the cell ends and latest activation in the middle (bottom of panel C). Also, the central cell area was associated with an increase in V_max (upper part of panel C), which is typical for wave microcollisions.¹⁸ The specific activation sequence and the increase of transverse V_max behind the cleft in its middle portion, suggesting wave microcollision during transverse propagation, were observed in another four experiments.

Impulse Conduction in the Presence of Large Intercellular Clefts
Large discontinuities in cellular architecture have been implicated in nonuniformities in the extracellular electrogram or the shape of the action potential upstroke during transverse propagation. Such discontinuities were defined in our preparation by the presence of large intercellular clefts (cleft length, 148±42 µm; n=6). Fig 7 shows an example of impulse conduction in a cell monolayer with several longitudinally oriented intercellular clefts (panel A). The length of the largest cleft in the middle part of the mapping area was >150 µm, and the maximal width was 30 µm, both significantly larger than the dimensions of an average myocyte. The two clefts in the middle interrupted the monolayer structure, leaving a narrow isthmus interconnecting the upper and lower parts. The width of the isthmus was 40 µm. Panels B and C demonstrate activation maps during longitudinal and transverse conduction. Since the clefts were oriented longitudinally, the longitudinal propagation was not markedly disturbed. In the transverse direction, however, the clefts produced a major deviation from normal activation spread. Above the isthmus, transverse propagation followed the sequence typical for uniform anisotropic conduction. Conduction was blocked at the clefts and passed to the lower part of the mapping area through the isthmus. From this point, activation diverged in all directions. As a result, activation of the mapping region below the isthmus propagated predominantly in a longitudinal direction from right to left. Conduction was significantly slowed near the tip of the cleft, as shown by the high density of isochronal lines in this area. Action potential upstrokes recorded at the isthmus (panel E, traces 4 through 8) exhibited a double-component shape. No double-component upstrokes were recorded during longitudinal conduction at the same points (panel D), which indicates that this phenomenon was related to the specific tissue microarchitecture of this region and not to a local inhomogeneity in excitable properties. Both the slowing of conduction and the complex upstroke shapes indicate current-to-load mismatch typical for impulse spread at an abrupt tissue expansion.²⁸

View larger version (266K): [in this window] [in a new window]   Figure 7. Activation spread in a region with several large intercellular clefts. Panel A shows a phase-contrast image of the cell culture with overlaid photodiode array mask. The numbers 1 to 10 on the diode array correspond to the locations of the signals shown in panels D and E. In panels B and C, the location of these signals is indicated by the gray area. The two clefts in the central area (white outline) form a narrow isthmus of 40 µm. Activation maps of longitudinal and transverse conduction are shown in panels B and C, respectively. Note slowing and deviation of the wave front at the isthmus. Selected recordings of action potential upstrokes during longitudinal and transverse conduction are shown in panels D and E, respectively. Note discontinuity in the action potential upstroke at the expansion site during transverse propagation only.

Alternation of the direction of activation spread produced differences in the spatial distribution of V_max, which are illustrated in Fig 8. During longitudinal spread, V_max was distributed relatively uniformly. During transverse conduction, V_max increased before the cleft up to 141 V/s and decreased beyond the isthmus to 48 V/s. The same recording sites exhibited a V_max of 95 and 86 V/s during longitudinal propagation, respectively. The initial increase in V_max in front of the cleft can be explained by the boundary effect, where the impermeable border imposed by the clefts prevented downstream flow of axial current, reduced the electrical load and, therefore, increased the amount of current available for the local depolarization. Beyond the isthmus, the activation front emerging from a relatively small tissue area faced an increased electrical load; therefore, local depolarization rate decreased. Theoretically, the V_max values beyond the isthmus may have been overestimated because of the reduced APA at these sites. However, such a reduction is likely to be minor: simulation of impulse conduction at a site of an abrupt tissue expansion showed that even with a fourfold decrease of V_max, the APA decreased by only 7.6%.²⁸

View larger version (24K): [in this window] [in a new window]   Figure 8. Distribution of maximal upstroke rate of rise, Vmax, during longitudinal (A) and transverse (B) conduction in the experiment shown on Fig 7. Dashed area depicts intercellular cleft. Arrows show the direction of activation spread. Note increase of Vmax at collision sites (cleft borders) and decrease of Vmax beyond the expansion during transverse propagation.

Longitudinal and transverse activation spread were compared in six areas containing large anatomic clefts and narrow isthmuses of tissue. In all the cases, the V_max distribution was nonuniform during transverse propagation, with a larger V_max in front of the clefts (110 to 140 V/s) and smaller V_max values beyond the isthmuses (50 to 80 V/s, reduction by 45% to 60%), similar to the experiment shown in Figs 7 and 8.

Conduction in the Presence of Nonmyocyte Cells
Nonmyocyte cells (fibroblasts and epithelioid cells) in culture can be electrotonically connected to myocytes.^{23 24} Since such cells lack excitable properties, they are expected to act as passive current sinks, reducing V_max in surrounding myocytes and rendering conduction more vulnerable to conduction block.

The effect of nonmyocyte cells in a monolayer on impulse conduction is demonstrated in Fig 9. Two fibroblasts were identified in the upper part of the mapping area by the lack of cross striation, absence of mechanical contraction, and the cell shape. Panels A and B depict the activation maps recorded during longitudinal and transverse propagation. Both maps demonstrate significant slowing of conduction in the region surrounding the fibroblasts. Since the fibroblasts were oriented longitudinally, the perturbation of activation spread was more pronounced in transverse compared with longitudinal direction. This is evident from the collision of activation during transverse propagation fronts at the center of mapping area beyond the fibroblasts. The configuration of the electrotonic potentials in the nonexcitable fibroblasts (trace with asterisk in panel B) showed a marked slowing of depolarization rate compared with the action potentials of the surrounding myocytes. The distribution of V_max during transverse propagation is illustrated in panel D. It demonstrates that V_max was significantly reduced in fibroblasts and in the surrounding myocytes, indicating that the nonexcitable fibroblasts acted as a sink for electrotonic current. The degree of slowing of conduction and changes in upstroke waveshapes caused by nonmyocyte cells varied between experiments (n=7). In five cases, slowing of conduction and V_max were similar to the experiment shown in Fig 9. In two other experiments, slowing of conduction was more pronounced, and the upstrokes exhibited biphasic shapes.

View larger version (97K): [in this window] [in a new window]   Figure 9. Effect of nonmyocyte cells on impulse conduction. Maps of activation spread in the transverse direction are shown in panel A and in the longitudinal direction are shown in panel C. The two fibroblasts are indicated with dark background shading. Borders of myocytes are delineated with white lines. Thin black lines correspond to outer limits of diode array. Conduction is locally slowed by the nonexcitable fibroblasts. Panel B shows action potential upstrokes recorded from two myocytes (top and bottom traces) and from a fibroblast (middle trace). Panel D shows the distribution of Vmax. Note the sink of Vmax within the fibroblasts and in the surrounding myocytes, indicating that local current is drained from the excitable myocytes into the nonexcitable fibroblasts. Vmax of the fibroblast was calculated in the same way as Vmax in the myocyte, ie, with the assumption of an amplitude of the electrotonic "action potential amplitude" in the fibroblasts of 100 mV. This does not account for the electrotonic decay of potential in fibroblasts, which cannot be quantified with optical signals. In reality, the sink of Vmax within the fibroblasts would therefore be even larger.

Nonuniform Impulse Conduction in Dense Cultures
To assess the correlation between Cx43 distribution and impulse conduction at a cellular level, we scanned dense regions of cell monolayers looking for areas exhibiting conduction block. Such a block can be anticipated from the local absence of Cx43 immunostaining (Fig 3B). Localized conduction block in dense cell areas was found in six cases. In three cases of six, it was possible to identify the mapping area on the immunostained cultures, and a direct comparison of the Cx43 immunofluorescence with the propagation pattern was obtained.

Fig 10 depicts a phase-contrast image of a dense anisotropic monolayer (panel A) and the fluorescence image of the same area (panel B) labeled with antibodies against Cx43. Comparison of the two images shows that the fixation and immunostaining procedures resulted in only small distortions of cell shapes, leaving the monolayer architecture intact. Immunofluorescent staining depicts a myocyte (asterisk) in the upper third of the imaged area almost devoid of Cx43.

View larger version (611K): [in this window] [in a new window]   Figure 10. Correlation of activation spread with gap junction distribution. A and B, Phase-contrast and fluorescent images (Cx43 immunolabeling) of the same cell region. Asterisk depicts a central myocyte with almost no expression of Cx43. The only Cx43 fluorescence can be seen at the left end of this cell (arrow). C, D, and E, Isochronal activation map, selected optical recordings, and distribution of Vmax during transverse propagation. Dark area corresponds to the myocyte with no Cx43 expression. Note block of propagation at the upper cell border and excitation of the myocyte from the left end. The highest values of Vmax are recorded within this myocyte, where polarizing current cannot escape because of the lack of gap junctions.

In Fig 10, mapping of transverse activation spread (panel C) in the area imaged on panels A and B strongly suggested a local block of conduction at the upper circumference of the myocyte marked with an asterisk. Presence of block was indicated by several findings: (1) The delay across the cell border amounted to 240 to 302 µs, corresponding to an apparent conduction velocity of only 3 to 4 cm/s. (2) Despite this very low apparent velocity, action potentials on either side of the upper cell border in the central cell portion did not exhibit two components (panel D), suggesting that they were not electrotonically connected. The V_max values before this cell were high (150 V/s versus 110 to 140 V/s in the middle of the mapping area), which also indicates conduction block at a resistive boundary. (3) The cell marked with an asterisk (panel C) was first excited at its left end, indicating that this part of the cell, where connexin fluorescence was scarce but visible (arrow), carried propagation to the remainder part from left to right. The distribution of V_max within the cell was consistent with the direction of impulse spread: the left cell end where the excitation wave entered the cell was characterized by a relatively low V_max (110 V/s), whereas in the middle portion of the cell, V_max was very high (190 V/s). This is likely to be explained by the wave fronts encountering of the high-impedance cell border with only few gap junctions. Direct correlation of conduction block with inhomogeneous Cx43 distribution was obtained in two other experiments.

	Discussion

Top Abstract Introduction Materials and Methods Results Discussion References

 
Cultures of Neonatal Rat Myocytes as a Model for Studying Anisotropic Propagation
The specific aim of the present study was to assess the effect of discontinuities at a microscopic level on anisotropic impulse conduction in the heart. For this purpose, a method to culture monolayers of neonatal rat myocytes on a growth-directing substrate and to optically monitor electrical activity at high spatial and temporal resolution was developed.²¹ The three-dimensional nature of intact myocardium and limitations with recording techniques exclude such measurements in isolated cardiac tissue.

In studying the conduction properties of cultured anisotropic monolayers, it is important to keep in mind the degree to which these cultures are representative of intact myocardium. The dense monolayers of myocytes cultured on a collagen matrix retain the same general appearance as observed in sections of intact neonatal rat ventricular myocardium. Like neonatal rat myocytes in vivo, individual cultured myocytes are characteristically spindle-shaped, with a generally uniform pattern of Cx43 distribution throughout the appositional cell membrane.³⁷ There are important similarities as well as differences between the anisotropic monolayers and adult canine ventricular myocardium. Although individual adult canine myocytes are, on average, larger than cultured neonatal rat myocytes (average length, 124 µm in dog versus 70 µm in rat), the average cell length-to-width ratios are similar (5.2 in dog versus 5.3 in rat). Similar morphometric data have been reported from strands of rat neonatal cells grown in patterns by use of a photolithographic technique.^{26 27} The number of cellular contacts in thin sections of adult dog ventricle and in neonatal rat cultures is very close (5.2 in dog³⁶ versus 5.6 in rat), suggesting a similar type of connectivity in these tissues. Also, adult canine left ventricular myocytes have numerous gap junctions along both the longitudinal and transverse boundaries of the cell.^{32 33} Despite these similarities, distinct differences exist in the pattern of gap junction distribution and in the size of gap junctions. Thus, end-to-end cell connections in adult ventricular tissue have larger gap junctions than at the lateral cell border.³² This difference was considered important for defining functional anisotropy and was introduced into the computer model of Spach and Heidlage.^{20 38} Other regions of canine hearts can exhibit a significantly higher degree of anisotropy in gap junction distribution. Thus, only few lateral gap junctions are found in the atrial crista terminalis,³⁶ which explains a very large anisotropic velocity ratio in this tissue. A close similarity in patterns of Cx43 distribution exists between cultured (or in vivo) neonatal rat tissue and canine ventricular myocytes at the borders of infarcted regions.³⁵

The Role of Cell-to-Cell Connections in Activation Spread
Conduction Velocity
Because cultured rat neonatal myocytes are smaller than adult ventricular myocytes, an action potential propagating along either the longitudinal or transverse axis through a cell monolayer must encounter an increased number of cellular borders per unit distance. This is likely to be an important reason for the observation that the absolute values for longitudinal and transverse velocities are smaller in the present experiments than in adult canine or porcine ventricular tissue.^{3 4 5} Other explanations for the moderately reduced transverse and longitudinal velocity values in the cell cultures relate to the difference in surface-to-volume ratio and reduced cell-to-cell coupling (see Reference 21 for discussion). However, the two most important determinants of anisotropic conduction, the cellular morphology (ie, the ratio of the average longitudinal and transverse cell dimensions) and the intercellular connectivity (as given by the number of cells connected to an individual myocyte), are similar in the cultured anisotropic monolayers and in intact dog ventricular myocardium. This may explain why the average anisotropic velocity ratio of 2.5 in the present experiments was close to the ratios (1.7 to 3.5) reported previously in adult canine and porcine ventricles.^{3 4 5 9 10 12}

Microscopic Spread
Determination of local activation times was limited by the S/N_rms. The estimated error in measurements of activation time amounted to 9 µs (see "Materials and Methods"), which corresponds to an error of 13 µs (9 µsx2) in the measurement of the conduction delay between two points. This is considerably smaller than the average conduction delay of 23 µs along a distance of 7 µm (highest spatial resolution), occurring at an average conduction velocity of 30 cm/s. Therefore, the temporal resolution was sufficient to reveal microscopic nonuniformities of conduction. Activation maps demonstrated that both transverse and longitudinal activation spread were nonuniform in dense monolayers. Potentially, there are two explanations for electrical nonhomogeneity at the microscopic level: (1) a nonhomogeneity in distribution of membrane channels responsible for the generation of the local ionic current or (2) a nonhomogeneity or discreteness of distribution of low resistance pathways (gap junctions) between cells of varying shape. Predilective localization at gap junctions has been reported for K⁺ channels encoded by the Kv1.5 gene.³⁹ If such nonhomogeneity existed for Na⁺ or Ca²⁺ channels, it would influence both the interpretation of the present data as well as the computer modeling of cellular propagation.

A consistent observation in our experiments was the higher degree of homogeneity of the isochronal pattern during transverse than longitudinal propagation. This is partly explained by the spatial resolution of our method. In the transverse direction, there was maximally one diode per cell, which did not show overlap with the lateral cell borders at high magnification. Therefore, it was not possible to resolve intracellular transverse propagation, with the exception of the type of experiments shown in Fig 6, where a defined anatomic discontinuity was present. For longitudinal propagation, several diodes in line separated cell borders, which allowed resolution of intracellular spread of activation in this direction. Moreover, for longitudinal propagation, cell borders formed a zigzag line, whereas cell borders were more aligned for transverse propagation. This caused a larger distortion of the isochrones in the longitudinal versus the transverse direction. Modeling studies with a similar resolution (one patch per cell in the transverse direction) demonstrated the same pattern, with the transverse propagation wave front exhibiting a relatively flat profile.^{18 19} A simulation study performed at higher resolution (up to four patches in the transverse direction) unveiled distinct intracellular nonuniformities in transverse propagation.²⁰ These comparisons indicate that the question of whether propagation is a uniform or nonuniform process is a matter of the scale at which it is measured. In other words, the degree of nonuniformity depends on whether propagation is measured at the level of whole tissue, a network consisting of a group of cells, or within a single cell. Therefore, the biological importance of microscopic inhomogeneities needs to be discussed by comparing the scale of the inhomogeneity in relation to the extension of the excitatory wave front (see last paragraph).

Directional Dependence of V_max
Experimental studies of isolated preparations of adult myocardial tissue have shown that mean V_max is 30% larger in the transverse compared with the longitudinal direction when the anisotropic longitudinal-to-transverse velocity ratio is 3.^{9 10 11 13} Although computer simulations of anisotropic impulse propagation revealed a difference in longitudinal versus transverse V_max as well, the computed differences were considerably smaller.^{18 19 20} In the work of Leon and Roberge,¹⁸ there was no difference between transverse and longitudinal V_max during propagation of flat wave fronts at a longitudinal-to-transverse velocity ratio of 5.7. This is in agreement with our previously published data²¹ and the present experiments (mean longitudinal-to-transverse velocity ratios of 1.9 and 2.5, respectively). A 27% difference between transverse and longitudinal values of V_max in the model of Leon and Roberge was computed at a high anisotropic velocity ratio of 9.6. In the study by Spach and Heidlage,²⁰ the transverse versus longitudinal difference of V_max amounted to 12% when the longitudinal-to-transverse velocity ratio was 3.2. In a third modeling study by Muller-Borer et al,¹⁹ the transverse V_max was 50% larger than the longitudinal V_max at a longitudinal-to-transverse velocity ratio of 6.7. The measurements of conduction parameters during transverse propagation in their study might have been affected by boundary effects, however, because the recording sites were located at a distance <250 µm from the model borders. We have recently shown in a computer model that the difference between longitudinal and transverse depends on both the degree of cellular anisotropy and the pattern of gap junction distribution.³⁰ In agreement with the simulation studies discussed above, V_max was higher in transverse versus longitudinal directions at a high degree of anisotropy, whereas no difference was obtained at the level of conduction anisotropy present in cell cultures.

Thus, both the simulation studies of anisotropic impulse conduction and experiments on dense cell monolayers indicate that resistive discontinuities created by cell borders and by nonuniform distribution of gap junctions that correspond to the level of conduction anisotropy found in ventricular myocardium do not fully explain directional differences in V_max. Several additional mechanisms and structural elements may contribute to the stronger directional dependence of V_max measured in adult tissue. First, activation spread was typically induced by a small stimulation electrode in experiments on adult tissue. In this case, the propagated wave front had an elliptical shape with a pronounced curvature in the longitudinal direction. Dissipation of excitatory current from a curved wave front produces a slower rate of depolarization and may partially account for smaller longitudinal values of V_max.¹⁸ Second, the discussed computer models represented cardiac tissue as a monodomain structure. This assumption holds true for cultured cell monolayers, but it may not be adequate for adult ventricular myocardium. In a bidomain model with unequal anisotropic ratios of intracellular and extracellular resistivities, it has been shown that V_max can be larger in the transverse than the longitudinal direction, even with a continuous intracellular space.⁴⁰ As discussed in our previous work,²¹ a third mechanism may include the regularly spaced resistive discontinuities formed by the presence of blood vessels and connective tissue sheets.⁴¹

Immunostaining of Cx43 distribution in dense anisotropic cell monolayers demonstrated that gap junctions were narrowly spaced along the cell perimeter (Fig 3A). Because of the small separation between lateral junctions, the main portion of excitatory current flow during transverse propagation can be assumed to be directed along the transverse axis, with collision within cells in the longitudinal direction playing a minor role. As shown in computer simulations^{18 19 20} and the present experiments (Fig 6), a more complex pattern of transverse activation is expected in tissues with a lower density of lateral gap junctions and a higher degree of functional anisotropy. In this case, activation of an individual cell during transverse propagation involves entry of excitation at the input junctions and wave microcollision either with the cell border or with another excitation wave. At the entry sites, downstream electrical load faced by the excitation wave increases, which explains the decrease of V_max. By contrast, the downstream load decreases at cell borders and at collision sites (less cellular membrane needs to be recharged), which produces an increase in V_max. The greater the lateral separation of gap junctions, the more prominent the effect of wave microcollision and the increase in average V_max.³⁰ Thus, a marked lateral separation of gap junctions may be responsible for the direction-dependent difference in V_max in tissues with a very high degree of functional anisotropy (eg, crista terminalis). In tissue with a lower degree of anisotropy, other mechanisms are likely to play a major role in direction-dependent variability of V_max, as discussed above. Despite the absence of a direction-dependent change in average V_max in the present experiments, there was a substantial variability among individual V_max measurements during both longitudinal and transverse propagation. This was most likely due to local variability in electrical load brought about by the cellular architecture and is in accordance with recent computer simulations of propagation with subcellular resolution.²⁰

The dimensionality of the tissue is an additional factor that may influence the relation between the pattern of gap junction distribution and the inhomogeneity of propagation at the cellular level. In three-dimensional myocardium, a significantly larger number of gap junctions connect an individual myocyte to its neighbors than in two-dimensional slices (eg, see Fig 1 of Reference 31), in accordance with the increase in the number of connected cells. Therefore, an increased electrotonic interaction and a higher degree of homogeneity of activation pattern are to be expected in the three-dimensional cellular network.

The Effect of Large Intercellular Clefts on Propagation, Action Potential Shape, and V_max
In the anisotropic cell cultures the occurrence of longitudinally oriented clefts was used to mimic the effect of connective tissue sheets. Such connective tissue layers separate fiber bundles in normal ventricular tissue¹⁵ and become more prominent during aging,⁴² in ventricular hypertrophy,⁴³ and in the tissue region surrounding chronic myocardial infarction.⁴⁴ The intercellular clefts had significant effects during transverse propagation on the local activation sequence and on the shape and V_max of the transmembrane action potential. All these effects were closely similar to the events occurring at an abrupt tissue expansion^{28 45 46} or at an isthmus separating two excitable areas.⁴⁷ The wave front during transverse propagation moving toward an obstacle will produce collision at the proximal site of the cleft, as evidenced by an increase in local V_max (Fig 8). At and beyond the expansion, the excitation wave will face a large membrane area downstream. As a consequence, there will be a marked conduction delay, a change in the shape of the local action potential upstroke, and a decrease of V_max beyond the expansion (Figs 7 and 8). This predicts that zones with low and high V_max will coexist in such structures during transverse propagation. Since such clefts or connective tissue sheets are usually oriented longitudinally, their effects are strictly anisotropic. The implications of such clefts for arrhythmogenesis will be discussed below.

Myocyte/Nonmyocyte Interaction and Heterogeneity of Gap Junction Expression
The registration of electrotonic deflections in nonmyocytes (fibroblasts and mesothelial cells) during passage of an impulse suggested that there is formation of gap junctions between myocytes and nonmyocytes in cell cultures.^{23 48 49} The deviation of the propagating wave front by nonmyocytes (Fig 9) was in line with these findings. During the propagation process, the nonexcitable fibroblast drained local current from the excitable myocytes. As a consequence, V_max and propagation velocity in the surrounding myocytes decreased. Because the interpolated fibroblasts were anisotropic in shape, these effects were more marked in the transverse than in the longitudinal direction. The relevance of this finding for creating inhomogeneity of conduction in vivo is uncertain. It is not known whether myocytes and nonmyocytes are interconnected by gap junctions in vivo to the extent that they are in vitro. If so, then this may be important in pathophysiological settings involving repair processes, such as cardiomyopathy, myocardial infarction, or ventricular hypertrophy.

At some sites in myocyte cultures, circumscribed areas were found in which Cx43 was not expressed. The correlation between the Cx43 distribution, propagation pattern, and distribution of V_max underlines the close relation between functional and morphological features of the cell cultures. Lack of Cx43 expression produced localized conduction block along a single cell border and local deviation of the impulse spread (Fig 10). The cell with decreased Cx43 expression was excited from one end only. Since the local ionic current produced in this cell could not leave the cell (by virtue of lack of gap junctions), it all charged the membrane capacitance, thereby producing a very high value of V_max. Although it is not known whether inhomogeneous expression of connexins is relevant for microconduction in healthy myocardium in vivo, such a phenomenon has been described in the border zone of acute and healed infarcts.^{33 35}

Potential Implications of Microinhomogeneities in Propagation for Conduction Block and Arrhythmogenesis
In tissue with depressed excitability and a high degree of functional anisotropy,⁹ it was shown that conduction of impulses can get blocked in the longitudinal direction while still being propagated in the transverse direction. This was taken to postulate a basically different mechanism of propagation in the transverse versus the longitudinal direction, resulting in anisotropic conduction block and anisotropic reentry. It was suggested that in the transverse direction cardiac tissue behaves as loosely coupled membrane patches, with each patch being nearly isopotential and therefore having a larger V_max than during more continuous longitudinal conduction.⁹ The two-dimensional computer models of microscopic impulse conduction^{18 20} and the present experiments contemplate a more complex pattern of transverse activation spread that includes entry of excitation at the input gap junctions, lateral intracellular spread, and wave microcollisions between entry sites or at cell borders, as discussed above. The question therefore arises whether, at an equal degree of functional anisotropy (longitudinal-to-transverse velocity ratio), the difference in the pattern of gap junction distribution between the neonatal and the adult tissue would explain the different findings about average V_max in the transverse versus the longitudinal direction. In such a case, a different susceptibility to anisotropic reentry between neonatal and adult tissue could be anticipated. Although no experimental data are available at present to answer this question, recent computer simulation indicates that in dense cellular networks, ie, in the absence of connective tissue sheets and blood vessels, direction-dependent differences in average V_max are insensitive to the change in pattern of gap junction distribution at the degree of functional anisotropy measured in the present study and previously found in adult canine ventricle.³⁰

A normal wave front of propagation in heart muscle extends over 300 to 800 µm. Therefore, resistive obstacles formed by physiologically interposed connective tissue sheets and blood vessels are expected to exert larger effects on activation spread than the discontinuities at the subcellular level. As shown in the present study, large intercellular clefts forming isthmuses of excitable tissue create a substrate for nonuniform anisotropic conduction and conduction block. In this situation, nonuniform propagation associated with slowing of conduction or conduction block will occur preferentially during transverse and not during longitudinal propagation. Computer simulations have shown that conduction events at such isthmuses are defined by a complex interaction between a number of factors, including excitability, changes in electrical load, and wave-front curvature.^{46 47} Obviously, conduction of the impulse is blocked if the width of the isthmus becomes too narrow. In a state of depressed excitability, the probability of occurrence of block increases at such a site. In contrast, partial electrical cell-to-cell uncoupling decreases the occurrence of conduction block at such a geometrical transition. These findings indicate that in pathophysiological states such as chronic myocardial infarction or ventricular hypertrophy, reentrant arrhythmias associated with tissue anisotropy will depend on the interaction between remodeling at the level of membrane function and intercellular connections and remodeling of the extracellular matrix.

	Selected Abbreviations and Acronyms

 

APA = action potential amplitude Cx43, Cx45 = connexin43, connexin45 S/Nrms = signal-to-noise ratio Vmax = maximal upstroke rate of rise

	Acknowledgments

 
This study was supported by the Swiss National Science Foundation, the Swiss Heart Foundation, and the National Institutes of Health (grant HL-50598). We wish to thank Regula Fluckiger, Lilly Lehmann, and Denis de Limoges for their technical assistance.

Received September 5, 1995; accepted April 3, 1996.

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