Virtual Sources and Sinks During Extracellular Field Shocks in Cardiac Cell Cultures:

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1 Virtual Sources and Sinks During Extracellular Field Shocks in Cardiac Cell Cultures: Effects of Source-Sink Interactions Between Adjacent Tissue Boundaries Running title: Kondratyev et al.; Membrane Potential and Extracellular Shocks Aleksandar A. Kondratyev, MD, PhD 1 ; Jean-Philippe Didon, PhD 2 ; Helene Hinnen-Oberer 1 ; Mathieu Lemay, PhD 1 ; Jan P. Kucera, MD 1 ; André G. Kléber, MD 1 1 Dept. of Physiology, University of Bern, Bern, Switzerland; 2 Schiller Inc. Laboratory, Wissembourg, France Corresponding author: André G. Kléber, MD Department of Pathology Beth Israel Deaconess Medical Center, DANA 752 Harvard Medical School 330 Brookline Avenue Boston, Massachusetts Tel: Fax: akleber@bidmc.harvard.edu Journal Subject Codes: [130] Animal models of human disease, [132] Arrhythmias-basic studies 1

2 Abstract: Background - One mechanism by which extracellular field shocks (ECFSs) defibrillate the heart is by producing changes in membrane potential (V m ) at tissue discontinuities. Such virtual electrodes may produce new excitation waves or affect locally propagating action potentials. The rise time of (V m ) determines the required duration of a single defibrillation pulse to reach a critical threshold for activation or for the modification of ion channel function and depends on the electrical and micro-structural characteristics of the tissue. Methods and Results - We used optical mapping of V m in patterned cultures of neonatal rat ventricular myocytes to assess the relationship between cardiac structure and the early time course of V m during ECFSs. At monolayer boundaries, the time course of V m showed a close fit to the theoretical change predicted by theory, with a membrane time constant of 2.65±0.19 ms (n=13) and a length constant of 159±6 μm (n=10). Experiments in patterned strands, mimicking the resistive boundaries which occur naturally in the heart, explained the observation that the rate of rise and the maximal amplitudes of the V m changes are inversely related because of electrotonic interactions between structural boundaries. Interrupting ECFSs by very short intervals diminished V m but did not cause major changes in its overall time course. Conclusions - Interaction between virtual sinks and sources decreases the magnitude of the changes in V m but accelerates its time course. For efficient defibrillation, short ECFSs are needed, with an amplitude adapted to match the boundary interaction. m Key words: electrophysiology, defibrillation, electrical mapping 2

3 Introduction Cardiac cells form a network that allows rapid propagation of the electrical impulse and coordinated mechanical contraction. This process is determined by the electrical properties of the cells, the extracellular space and the architecture of the cellular network. 1 The same factors also determine how the tissue reacts to an electrical field shock applied between extracellular electrodes. Such shocks are used to defibrillate the heart and to measure the passive electrical properties of the tissue itself. 2-4 The effect of extracellular field shocks (ECFSs) on cardiac tissue is complex and depends on the field strength of the shock, the tissue structure, the bidomain nature of cardiac tissue and the electrical properties of the cardiac cells. 2,5 The introduction of optical mapping pi of transmembrane potential (V whole hearts 6,7 m ) has enabled the direct measurement of V m in and tissue cultures 8 without interference from stimulation artifacts. Early work using this technique has shown that an ECFS can produce either membrane depolarization or hyperpolarization. Thus changes of opposite polarity have been observed within very short distances (~1mm) in perfused rabbit hearts. 7 Recent studies on the effect of short defibrillation pulses have demonstrated the importance of intramyocardial virtual electrodes caused by the coronary vasculature. 9 While membrane potential sources close to the extracellular electrodes are mostly produced by the macroscopic boundaries of the heart itself, 10 far-field virtual sources 11,12 are most likely caused by the bidomain nature of cardiac tissue 5,13 and the structural organization of myocardial tissue 14,15 Theoretically, structural discontinuities may occur in both intra- and extracellular domains. In a tissue culture model, we have shown that such histological boundaries form major sources for transmembrane current flow and that they represent 3

4 preferential sites for the initiation of propagated excitation, 16 whereas resistive barriers formed by individual cell borders play only minor roles. 8 The time course of V m in response to an ECFS is important because it will determine the time needed by an ECFS to produce biologically relevant changes of membrane potential. These changes include the initiation, prolongation or shortening of action potentials, which may interrupt fibrillation. Work in cell cultures using high resolution optical mapping of V m has shown that, depending on pulse strength, the responses of V m to ECFS exhibit 3 typical phases. 17 The very early phase produces symmetrical hyper- and depolarization at the respective anodal and cathodal boundaries. This symmetry suggests that it can be attributed to the passive linear electrical properties of the myocyte network. The second phase, which is superimposed on the first phase at intermediate ediate levels of shock strength, is most likely due to a change in the timeand voltage-dependent ent properties of ion channels. The third phase, observed at high field strengths is characterized rized by a decrease in the V m response and is probably associated with m electroporation. 8,18-20 A relatively fast initial change in membrane potential may increase the efficiency of short defibrillation pulses to excite tissue at the sites of intramyocardial virtual sources, and it has been recently suggested that repetitive short pulses (requiring less energy) can be efficient in defibrillation. 9,21 In the present study we used the experimental model of patterned cardiac cell cultures to assess the time course of the first, very early phase of V m changes after application of an ECFS. Whereas the tissue culture model is limited and cannot asses the full spectrum of variables determining the effect of ECFSs attributable to the bidomain nature of cardiac tissue such as anisotropy, fiber curvature, heterogeneous extracellular resistance and heterogeneous extracellular fields, it is nevertheless ideally suited for the reproducible control of the 4

5 architecture of the cellular network. 22 The time dependence of V m during an ECFS reflects the charge and discharge of the myocyte membrane capacitance, because the extracellular and intracellular spaces have no major capacitive elements. Therefore use of the cell culture model devoid of the features playing a role in a bidomain model (as mentioned above) seems appropriate to test the specific effect of local tissue boundaries, which are present in the myocardium in vivo, 14, 23 on the time dependence of ECFS. In order to provide a mechanistic explanation for the observed interrelation between V m and structure, we compared the experimental with theoretical results derived using a 1-dimensional model of cardiac tissue. 4,24 Methods Production of Patterned Cell Cultures The production of patterned cell cultures from neonatal rat heart cells has been described in detail. 8,16,22 In brief, hearts from neonatal rats were excised, enzymatically digested to form a cell suspension, preplated to eliminate fibroblasts and seeded on coverslips at a density of 0.5x10 6 cells per ml. Before seeding, defined fibronectin patterns were produced by microphotolithography to determine cell attachment and thus to produce well defined cell culture boundaries. After seeding, the cultures were kept in an incubator for 6 to 8 days at 35 o C. For experiments, two types of patterns were used, as illustrated in Figure 1. For the determination of passive cable properties, patterns were constructed in the shape of a half disk with a sharp rectilinear boundary. For the investigation of the interactions between adjacent boundaries, linear strands were patterned with a width of 200 m (interboundary distance). In all cultures the arrangement and shape of the myocytes was isotropic. 8 Stimulation and Optical Mapping of Transmembrane Potential 5

6 Transmembrane potential (Vm) was recorded by multisite optical mapping of transmembrane potential, as described in detail previously 8,16 (see on-line supplement). The change in transmembrane potential was expressed in % of action potential amplitude (%APA). 25 Application of Extracellular Field Shocks (ECFS) Propagated action potentials were elicited via electrical stimulation using a bipolar electrode at a basic (S1-S1) interval of 500ms. ECFS s were applied via 2 platinum electrodes placed in the tissue bath (Figure 1). The electrical field produced in this way was homogeneous, as previously shown. 8 ECFS s were produced by a custom-built device. This device produced single or repetitive rectangular voltage pulses that could be varied with respect to field strength, number, interpulse interval, polarity, duration and latency after the basic stimulus us (S1-S2 interval). Computation of Time Dependent Changes in Transmembrane Potential (V m ), Determination of the Space Constant and the Membrane Time Constant, In our experiments we consistently applied ECFS exactly perpendicular to the tissue boundaries. We have previously shown that such an arrangement produces changes in V m with isopotential lines parallel to the boundaries (Figure 1S, on-line supplement). This relationship between the patterned tissue boundary and the extracellular field facilitates the computation of the change in V m, because a 1-dimensional model can be used. The linear equivalent circuit illustrated in Figure 1C comprises the intercellular resistance per unit length, r i, the resistance of the cell membrane, r m, and membrane capacitance c m. The membrane time constant, and length constant, are defined in their usual way ( 2 =r m /r i ; = r m * c m ). 24 For L>>, which corresponds to the single boundary case in the cell culture (Fig. 2A), can be obtained from the exponential decay of V m along the cable at the end of a long ECFS (t ): 2-4,24 6

7 V m = V 0 + V amplitude* exp( x/ ) eq. 1 and the is obtained from the change in V m close to the boundary by: V m = V 0 + V amplitude* erf( (t/ )) eq. 2 Mathematically, changes in amplitude and shape of V m during an ECFS due to interactions between boundaries can be derived from the 1-dimensional cable equation corresponding to the equivalent circuit described in Figure 1C, and the application of the so-called superimposition and reflexion principles (equation 1S, on-line supplement). 24 Computations and fitting algorithms were implemented in MatLab ab and the exponential fit (eq. 1) needed for the determination of was programmed in LabView (National a Instruments). Statistics Experimental values were compared using the non-paired t-test where appropriate. Differences were considered significant at p<0.05. Unless specified otherwise, values are expressed as mean±s.d.. Results Early Time Course of the Change in V m During Application of an ECFS The time course of V m during application of an ECFS during phase 4 and the plateau phase of the action potential was determined at the border of a dense culture of myocytes (Figure 2A). Selection of this single boundary geometry represents the extreme case where interaction between boundaries is excluded (L ). Figure 2A shows 5 signals from measuring sites close to the culture border during a hyperpolarizing ECFS applied 30ms before an S1 stimulus. 7

8 Superimposition of the signals reflects the homogeneity of the electrical field and V m and at the culture border. The change in V m produced by the field pulse is depicted in Figure 2B. The red line in Figure 2B corresponds to the fit with eq. 2 and shows that V m during the ECFS follows closely the time course predicted by eq. 2 with a membrane time constant of 3.08ms. Approximately 90% of maximal hyperpolarization was achieved after about 4ms. In each experiment, the membrane time constant was obtained as the average from the fit of eq. 2 to 5 signals located at the culture boundary. In 13 different cultures, the mean value of amounted to 2.70±0.19ms. During phase 4, determination of following depolarizing ECFS was not possible, because action potentials were elicited close to the boundary, which h precluded an appropriate fit with eq. 2 in most experiments. V m elicited by an EPFS of 6 8ms during the plateau phase of the action potential is depicted in Figure 3A. Similarly to a hyperpolarizing pulse during phase 4, theree was an accurate fit to eq. 2 that yielded ed a membrane time constant of 3.24ms. At the boundary, 90% hyperpolarization was reached after approximately 5ms. The mean was 3.57±0.47ms (n=8). As shown previously 17 and illustrated in Figure 3A, the time course of hyperpolarizing pulses during the plateau was different from depolarizing pulses. Hyperpolarization produced an initial change in V m symmetrical to depolarization, and after the initial pulse segment of approximately 0.5ms duration, a subsequent rapid repolarization was observed, probably corresponding to so-called all-or-nothing repolarization, 17,26 caused by activation of repolarizing ion currents. This precluded the determination of for hyperpolarizing pulses. The Effect of Adjacent Tissue Boundaries on the Time Course of ECFS s In order to assess the effect of interaction of virtual electrodes at tissue boundaries on the time course and amplitude of V m during an ECFS (during phase 4 of the action potential), we applied 8

9 ECFS s perpendicular to 200 m wide strands (Figure 1B). Figure 4A illustrates the peak deflection of V m (measured at the end of the pulse) in response to a single ECFS of 4ms, as a function of position across the strand (from the border adjacent to the anode to the border adjacent to the cathode; mean±s.e., n=5, field-strength 6.36V/cm). The interaction of the virtual electrodes at tissue boundaries is reflected in the shape of the peak V m deflection profile. The linear aspect of the profile is in agreement with previous observations in cell cultures. 8 The maximal amplitude measured at the cathodal boundary of a strand of 200 m in width amounted to 23±2 %APA (n=5). In contrast, at a single boundary, the same field strength produced a significantly larger depolarization (filled rectangle with asterisk), of 38±4 %APA (n=7, p<0.05, non-paired t-test), demonstrating experimentally that the proximity ity of tissue sue boundaries decreases the maximal mal deflection of V m induced by an ECFS. m Figure 4B illustrates V m at various distances from the middle axis of the strand (-103 m m to 103 m) in the same experiments shown in Figure 4A. The ECFS resulted in an initial rapid change of V m reaching a plateau level at approximately 2ms, i.e. earlier than in the presence of a single boundary, i.e. in the absence of virtual source interaction (Figures 2 and 3). The red curve shows the comparison with the theoretical prediction (eq. 1 in the on-line supplement). Altogether Figure 4 demonstrates that the interaction of virtual sources at resistive boundaries has two major effects on V m during an ECFS: (1) A decrease of the maximal change in V m, and (2) an increase in the relative rate of change in V m (see discussion). Comparison of the effects of single versus multiple pulses Modifying the time course of ECFS pulses and thus influencing V m changes may be useful to optimize the delivered energy during electrical pulses and thus important for the design of defibrillation devices. Figure 5A shows optical signals depicting V m changes caused by a 9

10 continuous ECFS (control) and an ECFS interrupted 3 times (I = 0.5ms). The changes in V m during a train of 4 pulses of 0.5ms duration, interrupted by 3 intervals I are shown in Panels B D (Panel B: I=0.1ms, total duration 2,3ms; Panel C: I=0.2ms, total duration 2.6ms; Panel D: I=0.5ms, total duration 3.5ms). These 3 protocols correspond to a decrease of delivered energy by 13%, 23% and 43%, with respect to control pulses of the same total duration. Data are represented as mean±s.e immediately before each interruption (n=6 for Panels B and D, n=5 for Panel C). For each series, the corresponding changes in V m recorded during control experiments without pulse interruption (blue) are superimposed on the changes measured with pulse interruption (red). The computed changes (equation 1, on-line supplement) (solid curves) are superimposed on the experimentally determined values (circles connected nect cted by dotted lines). Comparison of Figures 5B 5D shows that increasing I from 0.1ms to 0.5ms with a pulse duration of 0.5ms lowers the level of the maximal deflection of V m but does not affect the general time course of the voltage change. The curves computed from equation 1 confirm this general behavior, but show a faster rise in V m during control and test interventions at all intervals I. At I = 0.1ms, V m at the end of the interruption and the plateau level are not significantly different from control (Fig. 5B). The plateau level amounts to 77% of control (simulated value 91%) with I = 0.2ms (Fig. 5C), and to 70% of control (simulated value 85%, Fig. 5D). Comparison of the Time Course of V m During Different Phases of the Action potential and Determination of the Length Constant, In order to simulate the changes in V m during the early phase of an ECFS, it was necessary to determine the length constant Based on experimental measurements. The length constant was determined from the decay of the steady-state V m at the end of a sufficiently long (8 10ms) hyperpolarizing pulse applied during the phase 4 of the action potential. V m from up to 48 sites 10

11 was recorded in each experiment and plotted as a function of distance from the boundary (Figure 6). The exponential fit (equation 2) in the experiment illustrated in Figure 6B produced a value of = 152 m. The mean value of amounted to 159±6 m (n= 10). During the plateau phase of the action potential, the well-known 27 relative increase in membrane resistance was responsible for the increase in. The associated increase in produced a very flat profile of steady state V m along the optically mapped distance x, which rendered an exponential fit analogous to Figure 6B inaccurate. Therefore, the value for plateau was calculated from equations 1 and 2, using plateau, plateau and phase4 ; it amounted to 188 m. Discussion A major purpose of this study was the determination of the time course of the early change in V m induced by an extracellular field shock (ECFS) and its dependence on tissue boundaries. Application of a homogeneous extracellular field shock perpendicular to a single tissue boundary produced virtual sources with isopotential lines parallel to the tissue boundary. This made it possible to apply a relatively simple one-dimensional model for the computation of the theoretical predictions and comparison with the experimental results. Because in one dimension, the monodomain and bidomain formulations are equivalent, this one-dimensional simplification permitted us to apply a monodomain approach. The quality of the fit suggests that our experimental model is well represented by the electrical circuit shown in Figure 1C. The effect of strand boundaries on the size and time course of virtual sources One of the major advantages of recording V m using voltage-sensitive dyes is the absence of stimulation artifacts during the application of ECFS s. In experiments in situ, this made it possible to detect the virtual sources on the epicardial surface and at intramural sites. 2,6,7,9,11,28 It 11

12 has been shown that virtual sources and sinks coexist within distances of < 1mm. 7 A similar close association between local hyper- and depolarizations has more recently been described in isolated perfused rabbit hearts by Mowrey et al. 28 Interestingly, these authors found a strict inverse relationship between the maximal amplitude of a virtual source caused by an ECFS and the rate of rise, in correspondence with our results. This inverse correlation was proposed as a general principle of tissue behavior and independent of the application of drugs that inhibited ion channels, suggesting indirectly that it might be related to the intrinsic passive electrical properties of the tissue. The mechanistic explanation for this inverse relation is provided in this work. Figure 7 depicts the theoretical changes in the maximal amplitude and the time course of V m during an ECFS in absence and presence of interactions between adjacent acen boundaries. It can be seen that the V m perpendicular to the border of the obstacle shows an exponential n decay in the absence of interaction between the virtual source and virtual sink at the boundaries (blue line), in accordance with the experimental results (Figure 6). 2-5 If the length L of the excitable structure (corresponding to the strand width in Figure 1B) decreases, the profile of V m during an ECFS assumes an increasingly linear shape (red curve) and the absolute values of the amplitude maxima or minima of V m decrease, due to the electrical interaction between the strand borders. Concomitant with the decrease in amplitude, source-sink interaction produces a more rapid change in the transmembrane potential during the shock (Panel B). Interruption of ECFS by short intervals Changing the time course of ECFS of a given duration may be useful to reduce the delivered energy, and it may be important for the design of the charge-delivering device. The effect of complex pulse forms on the efficiency of defibrillation was investigated in detail by Malkin et al. 19 These authors made the empirical observation that the defibrillation efficiency of an ECFS 12

13 was highest in presence of a short initial peak in the defibrillation pulse form. In our study, the maximal V m deflection in 200 μm wide strands was changed only to a minor extent (<10%) if pulses of 2-3 ms in duration were interrupted by 3 short ( ms) intervals, corresponding to a decrease of the delivered energy by up to 23% (see the online supplement for the calculation). Thus, in terms of energy expenditure, the interrupted pulse represents an advantage. These experimental results and theoretical simulations taken together suggest that the interactions between boundaries, producing a very rapid initial change in V m, should be taken into account when optimizing ECSF pulse forms. Malkin et al. 19 attributed the observation that a short initial peak in the defibrillation pulse form increases the efficiency of defibrillation to the possible occurrence of electroporation. We have previously shown that electroporation ectrop or (which manifests itself by an internalization of the dye Lucifer yellow 8 or by a decrease in the amplitude of V m late during an ECFS 17 ) occurs only at relatively high field strengths (> 20V/cm) in our experimental model (see online supplement). A contribution of electroporation to the observed changes in V m in the present experimental setting is therefore unlikely. Limitations and Validity of the Cell Culture Model The present study focuses specifically on the interaction between virtual sources and sinks cause by the vicinity of resistive boundaries during a single ECFS and on the theoretical basis underlying the observed V m changes. Multiple important variables in defibrillation were not assessed, such as the effect of (1) shape and the polarity of the shocks, (2) the anisotropic architecture of cardiac tissue, (3) the possibility that inhomogeneities in extracellular space resistance create virtual sources, and (4) multiple pulses with longer interpulse intervals. Indeed, such repetitive pulses with intervals in the order of the defibrillation cycle length have been efficiently used to sequentially interrupt reentrant circuits. 9, 21 A further aspect relates to the 13

14 question of the validity of the cell culture model for representing the cellular network in vivo. It has been shown that the interplay between the resistive properties of the extra- and intracellular spaces are important for the formation of virtual electrodes in the myocardium. 5,13,29 Cultures from neonatal rat myocytes have passive electrical properties different from adult tissue in vivo. The most important difference is probably cell size Decreasing cell size will decrease the spacing between cell borders, and consequently, increase intracellular resistance, r i (cytoplasmic and intercellular resistance in series). This most likely explains the observation that the length constant in rat neonatal cultures is significantly smaller than in adult hearts (for extensive discussion and summary of values see 34, 35 ). Other factors, such as effects of the extracellular space resistance, r o, and ion channel expression (affecting membrane resistance stan r m ) will additionally affect.. Thus far, only one study dealt specifically with the determination of cable properties in cell cultures of rat cardiomyocytes. 34 Irrespective of these considerations, an important property of our experimental model is that it consists of a cell monolayer and not of a multi-layered preparation, and there is therefore no ambiguity in our optical measurements that might arise because of voltage-dependent fluorescence emitted from deeper tissue layers. Potential Importance of Virtual Source-Sink Interactions for Defibrillation Work in cell cultures and in whole hearts has demonstrated the importance of intramyocardial virtual sources as site of excitation waves, which may interrupt reentrant circuits during defibrillation. 9 The presence of resistive boundaries caused by the myocardial architecture, blood vessels and bidomain tissue properties are important causes for the formation of virtual sources. In larger mammals the space constant, reflecting the degree of electrical interaction between adjacent myocardium, is larger than in murine hearts (see 1,35 for review). Therefore, source-sink interaction of virtual sources as shown in the present study is expected to occur between sources 14

15 and sinks located more than 1mm apart in these species. The interaction between physiological boundaries represented by normal transmural architecture and blood vessels is therefore likely to affect the maximal value of virtual sources and the rate of rise of V m. Moreover, the experimentally demonstrated dependence of the time course and amplitude of V m on source-sink interaction is expected to occur independently of the mechanism causing virtual source formation. Finally, the inverse relationship between the maximal V m deflections caused by sources and loads and the rate of rise of V m during the ECFS may have implications regarding the effect of defibrillation shocks: First, single pulses of a duration shorter than the membrane time constant are likely to produce excitation at sites of source-sink interaction. tion Second, to reach the threshold for excitation ion at such a site, increasing the amplitude of a short ECFS will be more efficient than increasing its duration for an equal amount of energy delivered. Funding Sources This study was supported by the Swiss National Science Foundation (grant to AGK) and by a grant from Schiller Inc., Wissembourg, France (to AGK). Conflict of Interest Disclosures: AGK is recipient of a research grant from Schiller Inc., Wissembourg, France. JPD is an employee of Schiller Inc., Wissembourg, France. References: 1. Kleber AG, Rudy Y. Basic mechanisms of cardiac impulse propagation and associated arrhythmias. Physiol Rev. 2004;84: Dosdall DJ, Fast VG, Ideker RE. Mechanisms of defibrillation. Annu Rev Biomed Eng. 2010;12:

16 3. Kleber AG, Riegger CB. Electrical constants of arterially perfused rabbit papillary muscle. J Physiol.1987;385: Weidmann S. Electrical constants of trabecular muscle from mammalian heart. J Physiol. 1970;210: Basser PJ, Roth BJ. New currents in electrical stimulation of excitable tissues. Annu Rev Biomed Eng. 2000;2: Dillon SM. Optical recordings in the rabbit heart show that defibrillation strength shocks prolong the duration of depolarization and the refractory period. Circ Res. 1991;69: Zhou X, Ideker RE, Blitchington TF, Smith WM, Knisley SB. Optical transmembrane potential measurements during defibrillation-strength shocks in perfused rabbit hearts. Circ Res. 1995;77: Gillis AM, Fast VG, Rohr S, Kleber AG. Spatial changes in transmembrane potential during extracellular electrical shocks in cultured monolayers of neonatal rat ventricular myocytes. Circ Res. 1996;79: Luther S, Fenton FH, Kornreich BG, Squires A, Bittihn P, Hornung D, Zabel M, Flanders J, Gladuli A, Campoy L, Cherry EM, Luther G, Hasenfuss G, Krinsky VI, Pumir A, Gilmour RF, Jr., Bodenschatz E. Low-energy control of electrical turbulence in the heart. Nature. 2011;475: Chen PS, Wolf PD, Claydon FJ, Dixon EG, Vidaillet HJ, Jr., Danieley ND, Pilkington TC, Ideker RE. The potential gradient field created by epicardial defibrillation electrodes in dogs. Circulation. 1986;74: Fast VG, Sharifov OF, Cheek ER, Newton JC, Ideker RE. Intramural virtual electrodes during defibrillation shocks in left ventricular wall assessed by optical mapping of membrane potential. Circulation. 2002;106: Sharifov OF, Fast VG. Optical mapping of transmural activation induced by electrical shocks in isolated left ventricular wall wedge preparations. J Cardiovasc Electrophysio.l 2003;14: Wikswo JP, Jr., Lin SF, Abbas RA. Virtual electrodes in cardiac tissue: A common mechanism for anodal and cathodal stimulation. Biophys J.1995;69: Le Grice IJ, Smaill BH, Chai LZ, Edgar SG, Gavin JB, Hunter PJ. Laminar structure of the heart: Ventricular myocyte arrangement and connective tissue architecture in the dog. Am J Physiol. 1995;38:H571-H

17 15. Hsu EW, Muzikant AL, Matulevicius SA, Penland RC, Henriquez CS. Magnetic resonance myocardial fiber-orientation mapping with direct histological correlation. Am J Physiol. 1998;274:H Fast VG, Rohr S, Gillis AM, Kleber AG. Activation of cardiac tissue by extracellular electrical shocks: Formation of 'secondary sources' at intercellular clefts in monolayers of cultured myocytes. Circ Res. 1998;82: Tung L, Kleber AG. Virtual sources associated with linear and curved strands of cardiac cells. Am J Physiol Heart Circ Physiol.2000;279:H Kodama I, Shibata N, Sakuma I, Mitsui K, Iida M, Suzuki R, Fukui Y, Hosoda S, Toyama J. Aftereffects of high-intensity dc stimulation on the electromechanical performance of ventricular muscle. Am J Physiol. 1994;267:H Malkin RA, Guan D, Wikswo JP. Experimental evidence of improved transthoracic defibrillation with electroporation-enhancing pulses. IEEE Trans Biomed Eng. 2006;53: Krassowska W. Effects of electroporation ti on transmembrane m potential induced by defibrillation shocks. s. Pacing Clin Electrophysiol.1995;18: Gray RA, Wikswo JP. Cardiovascular disease: Several small shocks beat one big one. Nature. 2011;475: Rohr S, Scholly DM, Kleber AG. Patterned growth of neonatal rat heart cells in culture. Morphological and electrophysiological characterization. Circ Res. 1991;68: Pope AJ, Sands GB, Smaill BH, LeGrice IJ. Three-dimensional transmural organization of perimysial collagen in the heart. Am J Physiol Heart Circ Physiol. 2008;295:H1243-H Jack J, Noble D, Tsien R. Electric current flow in excitable tissues. Clarendon Press - Oxford; Fast VG, Kleber AG. Microscopic conduction in cultured strands of neonatal rat heart cells measured with voltage-sensitive dyes. Circ Res. 1993;73: Noble D, Hall AE. The conditions for initiating "all-or-nothing" repolarization in cardiac muscle. Biophys J. 1963;3: Weidmann S. Effect of current flow on the membrane potential of cardiac muscle. J Physiol. 1951;115: Mowrey KA, Efimov IR, Cheng Y. Membrane time constant during internal defibrillation strength shocks in intact heart: Effects of na+ and ca2+ channel blockers. J Cardiovasc Electrophysiol. 2009;20:

18 29. Sobie EA, Susil RC, Tung L. A generalized activating function for predicting virtual electrodes in cardiac tissue. Biophys J. 1997;73: Fast VG, Darrow BJ, Saffitz JE, Kléber AG. Anisotropic activation spread in heart cell monolayers assessed by high-resolution optical mapping. Role of tissue discontinuities. Circ Res. 1996;79: Rohr S, Kleber AG, Kucera JP. Optical recording of impulse propagation in designer cultures. Cardiac tissue architectures inducing ultra-slow conduction. Trends Cardiovasc Med. 1999;9: Saffitz JE, Kanter HL, Green KG, Tolley TK, Beyer EC. Tissue-specific determinants of anisotropic conduction velocity in canine atrial and ventricular myocardium. Circ Res. 1994;74: Spach MS, Heidlage JF, Dolber PC, Barr RC. Electrophysiological ogical effects of remodeling cardiac gap junctions and cell size: Experimental and model studies of normal cardiac growth. Circ Res. 2000;86: Jongsma HJ, van Rijn HE. Electronic spread of current in monolayer cultures of neonatal rat heart cells. J Membr Biol. 1972;9: Kléber AG, Janse MJ, Fast VG. Normal and abnomal conduction in the heart. In: Page E, Fozzard H, Solaro R, eds. The Handbook of Physiology. New York: Oxford University Press; 2002: Figure Legends: Figure 1: Schematic illustration of the experimental setup. A: Schematic of a cell culture dish showing a continuous layer of cultured neonatal rat heart cells patterned in the shape of half a disk (black). A bipolar electrode was used to stimulate the culture at an S1-S1 interval of 500ms. Two platinum electrodes (grey) were arranged in such a way to produce a homogenous electrical field (arrows) oriented perpendicular to the linear border of the cell culture. B: Schematic of a cell culture dish showing the culture pattern used to assess the effects of boundaries on the time 18

19 course of V m during an ECFS. Strands of 200 m in width emerge from a bulk monolayer of cells (black). The bulk is stimulated at an S1- S1 interval of 500ms. The electrical field (arrows) produced by the platinum electrodes (grey) is oriented perpendicular to the strands. C: Electrical equivalent circuit of a passive cable of length L. L denotes the distance between resistive borders. r i, resistance of the intracellular space per unit length, r m, membrane resistance per unit length, c m, membrane capacitance per unit length (see on-line supplement for further explanation). Figure 2: Changes of V m after application of a hyperpolarizing ECFS during phase 4. A: Schematic representation of the cell culture with 5 measuring sites (circles) cles close to the culture border. The white arrow represents the extracellular field (6.36 V/cm). Superimposed p signals from the five locations ons show hyperpolarization followed by the upstroke of the action potential. B: Hyperpolarizing portion of the change in V m from the location indicated by the filled circle on Panel A. The red curve corresponds to the fit with eq. 2. m Figure 3: Changes of V m after application of an ECFS during the plateau phase of the action potential. A: Schematic representation of the cell culture with 5 measuring sites (circles) close to the culture border. The white arrow represents the extracellular field (6.36V/cm). Superimposed signals from the five locations show changes in V m following hyperpolarizing and depolarizing shocks. The black arrow marks the onset of all-or-nothing repolarization. B: Depolarizing portion of the change in V m from the location indicated by the filled circle on Panel A. The red curve corresponds to the fit with eq

20 Figure 4: A: Effect of virtual source-sink interaction on the maximal deflection of V m across a strand of 200 m in width during an ECFS (6.36V/cm) applied during the plateau phase of the action potential (filled circles). For comparison the peak change in V m at the border of a large monolayer (absence of virtual source-sink interaction) is given for the same field strength (filled square). See text for details. B: Time course of V m during an ECFS. Each data point represents the mean value from 5 experiments. The changes in V m are depicted for recording sites located at different distances from the median axis of the strand (labels). The red curve corresponds to the theoretical result (eq.1 in the on-line supplement) with = 3.5ms and = 180 m. Note that the maximal V m change is already reached at t <. Figure 5: A: Original experimental traces recorded at the border of a 200μm wide strand showing the action potential upstroke and the changes in V m induced by depolarizing ECFSs (6.36 V/cm) applied during the action potential plateau. The upper trace depicts changes induced by the control pulse (3.5 ms), the lower trace changes induced by four pulses of 0.5ms duration interrupted by I =0.5 ms. The test ECFSs are shown schematically in the inset of Panel A. B: Superimposition of computed changes in V m induced by 4 test pulses of 0.5ms duration interrupted by I = 0.1ms (solid red curve) and a control pulse of equal duration (solid blue curve). Points connected by dotted lines depict experimentally recorded values (blue: control; red: test). Panels C and D: Same as Panel B, but I = 0.2ms (Panel C), and I = 0.5ms (Panel D). Hash symbols (#) denote significant differences between test and control (non-paired t-test, p< 0.05). The values given at the 100% levels denote the absolute changes in %APA. As expected, the changes in V m decrease with increasing interpulse interval I. Of note is the observation that m 20

21 the general time course of V m (envelope) showing a rapid increase to a plateau, does not change with increasing I. Figure 6: Determination of the space constant by a hyperpolarizing ECFS. A: Array of measuring sites extending from the culture border (on the left. Two signals showing hyperpolarization during am ECFS (6.36V/cm) are shown. B: Steady-state amplitudes of hyperpolarizing voltage changes are plotted as a function of distance from the culture border. The exponential fit (red) using equation 2 yields a space constant of 152 m (red circle). Figure 7: Computation of changes in V m (equation 1 in the Online ne Supplement) plem ent) illustrating the inverse relationship between maximal amplitude and steepness of the change in V m. A: Effect of cable length on the amplitude at steady state (t ) of the V m response caused by a rectangular ECFS. With decreasing cable length, the interaction between the flow of transmembrane current at opposing ends (virtual electrodes of opposite polarity) produces a decrease in maximal amplitude. B: Time course and amplitudes of V m during ECFS in cables of 2 mm (blue) and 200 m length (red). Amplitude at L=2mm is taken as 100% ( = 188 m, = 3.57ms). C: Same computed signals as in Panel B, but with normalized amplitudes. m 21

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