Experimental Model for an Ectopic Focus Coupled to Ventricular Cells
Background We used a mathematical model of a sinoatrial nodal cell (SAN model) electrically coupled to real ventricular cells (VCs) to investigate action potential conduction from an automatic focus.
Methods and Results Since input resistance of a VC is less than that of an SAN cell, coupling of the SAN model, with a size factor of 1, to a VC produced either (1) spontaneous pacing at the slower rate of the SAN model but without driving (activation) of the VC for lower values of coupling conductance (Gj) or (2) inhibition of pacing of the SAN model by electrical coupling to the VC for higher values of Gj. When the SAN model was adjusted in size to be 3 to 5 times larger than a sinoatrial nodal cell, thus making effective SAN model capacitance 3 to 5 times larger and input resistance 3 to 5 times smaller, the SAN model propagated activity to the coupled VC for Gj above a critical value. When the VC was paced at 1 Hz, the coupled cell pair demonstrated a stable rhythm of alternating cycle lengths and alternating conduction directions. By increasing pacing frequency to 2 Hz, we converted this rhythm to a regular 2-Hz frequency in which each action potential originated in the VC. More complex periodic interactions were observed at intermediate cycle lengths and lower or higher values of Gj.
Conclusions The phenomena we observed demonstrate the critical role of the size of an automatic focus as well as the coupling in the propagation of activity from the focus into surrounding myocardium.
The complex interactions among heart cells with spatial variability in action potential properties and intercellular coupling are poorly understood in the normal heart, and the additional spatial variability induced by ischemia leads to a plethora of proposals for the mechanisms and treatment of cardiac arrhythmias. As recently reviewed by Curtis et al,1 ischemia induces the accumulation or depletion of a large number of chemical mediators in addition to the loss of oxygen and metabolic substrates. These mediators induce cellular electrophysiological dysfunction (in both the membrane properties of individual cells and the intercellular coupling), which then induces the syncytial electrophysiological dysfunction we call arrhythmias. The cellular electrophysiological dysfunction may lead to conduction slowing and/or block, which can then lead to the development of a reentrant arrhythmic pattern. Alternatively, the cellular electrophysiological dysfunction may lead to one or more localized areas of ectopic spike generation (either as automaticity or as triggered activity), which, if conducted out to the surrounding myocardium, act as an ectopic focus to generate a nonreentrant arrhythmia. We have developed an experimental technique that allows the study of interactions between a cell (or group of cells) with spontaneous activity and another cell (or group of cells) that are quiescent, but excitable, in terms of the relative sizes of the cells and the coupling conductance between the cells. In this technique, the cell with spontaneous activity is represented by a “real-time” simulation of a mathematical model of the rabbit sinoatrial node cell2 that is electrically coupled to an isolated GP ventricular myocyte. Although the actual membrane properties of the cells within an ectopic focus with automaticity are not known, many studies have been done on membrane properties of cells within the sinoatrial or atrioventricular node, in which cells normally have a depolarized membrane potential, show automaticity, and are able to propagate to quiescent excitable cells to which they are electrically coupled. This technique also allows a systematic variation in the effective size of the focus region as well as that of the coupled excitable cell to examine some of the effects of geometrical factors on the interactions between the automaticity of the focus region and the periodic excitation of the real cardiac cell.
The common feature of all nonreentrant arrhythmias is the localized nature of the initiation event, whether it is automaticity from phase 4 depolarization or localized production of early afterdepolarizations or delayed afterdepolarizations. The conduction of the initiating activation out into the surrounding myocardium demands that a sufficient amount of tissue (the “liminal length,” as expressed in cable terminology) be activated for further conduction to occur. The demonstration that a particular intervention can produce automaticity or triggered activity in an isolated cell does not prove that such activity in a single cell, or even a small group of cells, can actually conduct activity out into the myocardium when the cell is in situ. We previously studied this phenomenon with evaluations of the refractory period both in normal Tyrode's solution and with elevated potassium3 4 in comparative studies of isolated rabbit VCs versus the intact rabbit papillary muscle. The electrotonic influences of surrounding cells within the syncytium abolished the period of supernormal excitability we demonstrated for the isolated cells and greatly extended the functional refractory period for depolarized tissue versus depolarized isolated cells. The critical size of an automatic focus region was the subject of theoretical studies5 in which we simulated a two-dimensional sheet of atrial tissue with a centrally located sinoatrial node area of variable size and showed that a partial electrical uncoupling between the automatic area and the quiescent area was required for the automatic area to maintain automaticity and still drive the quiescent area. The hybrid cell pair system we have developed combines a mathematical representation of an ectopic focus with actual recordings from isolated GP VCs to determine how the size of the focus with respect to the quiescent cell, the amount of electrical coupling, and the rate of direct stimulation of the quiescent cell all combine to produce a particular pattern of electrical interactions.
Cell Isolation and Electrodes
Single ventricular myocytes were prepared from adult GPs weighing 300 to 500 g anesthetized with 50 mg/kg pentobarbital sodium and 500 U heparin IP. The heart was rapidly removed via thoracotomy with artificial ventilation, and the aorta was cannulated for Langendorff perfusion. Single cells were isolated according to the method described in our recent publications.6 7 Briefly, the isolated heart was mounted on a Langendorff apparatus and perfused sequentially with normal Tyrode's solution for 5 minutes, with nominally Ca2+-free Tyrode's solution for 6 to 7 minutes, with nominally Ca2+-free Tyrode's solution containing collagenase and protease for 8 to 12 minutes, and with storage solution for 5 minutes at a rate of 3 to 4 mL·g−1·min−1 at 35°C to 36°C. For VC isolation, the enzyme-perfused left ventricle was cut into small pieces, stirred in storage solution, and filtered through nylon mesh. The resulting suspension of cells was kept in storage solution at room temperature. The isolated cells were transferred to an experimental chamber containing normal Tyrode's solution. The chamber was continuously perfused with normal Tyrode's solution at 2 mL/min, and the temperature was maintained at 35±0.5°C. Only cells that were quiescent and rod-shaped were used in this study. The pipettes were pulled from borosilicate glass and, after fire polishing, had resistances of 4 to 6 MΩ when filled with the internal solution. High-resistance seals were formed with the cell membrane by light suction, and the membrane was disrupted by a transient suction. The junctional potential was corrected by zeroing of the potential before the surface of the cell was touched by the pipette tip. Series resistance was carefully compensated for each cell by a calibrated internal circuit of the amplifier used (Axoclamp, Axon Instruments). Repetitive stimulation of the GP VC was produced by depolarizing current pulses of 2-ms duration applied via the patch pipette.
Normal Tyrode's solution contained (in mmol/L) NaCl 148.8, KCl 4.0, CaCl2 1.8, MgCl2 0.53, NaH2PO4 0.33, HEPES 5, glucose 5, pH adjusted to 7.4 with NaOH. The composition of Ca2+-free solution was the same as that of normal Tyrode's solution, except that the CaCl2 was omitted. The enzyme solution contained 4 to 6 mg/100 mL collagenase (Yakult) and 0.5 mg/100 mL protease (type XIV, Sigma Chemical Co) in Ca2+-free solution. The storage solution contained (in mmol/L) potassium glutamate 120, MgCl2 5, taurine 20, EGTA 0.5, glucose 10, HEPES 10, pH adjusted to 7.4 with KOH. The composition of the internal pipette solution was KCl 145, Mg-ATP 5, sodium creatine phosphate 5.0, HEPES 5.0, pH adjusted to 7.2 with KOH. The external solution was normal Tyrode's solution.
Coupling a GP VC to a Computed SAN Model
The Wilders et al2 SAN model has been published in detail. This model includes mathematical representations of sarcolemmal ionic channel currents and pump currents as well as a representation of intracellular calcium ion concentration and the release and uptake of calcium by the sarcoplasmic reticulum. The coupling circuit we used for coupling a VC to a resistance/capacitance circuit or to another VC has been described.6 We now extend this method to couple a GP VC to a simulated cell model with a sampling rate of 10 kHz and thus a time step for the model of 100 μs. Briefly, we are recording from a real isolated cell in the “current clamp” mode with the ability to pass a computed time-varying current into the cell on the basis of the coupling current that would have been present if the cell were actually coupled by a given conductance to the SAN model cell. Simultaneously, the computed coupling current is applied to the SAN model computations. All of our records then are recordings from the real cell, with simultaneously generated model solutions. Fig 1⇓ illustrates the method used. In Fig 1A⇓, we diagram the overall paradigm used in these experiments. We are creating a model system to represent the situation in which a cell (or a region of cells) with properties of depolarization and automaticity is connected through a conductance, Gj, to a cell (or a region of cells) with properties of normal polarization, quiescence, and excitability. As shown in Fig 1B⇓, the depolarized, automatic cell is represented by a real-time simulation of the Wilders et al2 model of a sinoatrial nodal cell by a 90-MHz Pentium processor Gateway 2000 computer. The quiescent, excitable cell is an experimentally recorded GP VC. At each time step, the computer samples the membrane potential of the real cell (through an analog-to-digital converter) and then uses this potential (V2) and the membrane potential of the SAN model cell (V1) to compute the value of coupling current (Ij) from the equation Ij=(V1–V2)×Gj, where Gj is the value of coupling conductance previously selected. A voltage proportional to the coupling current is sent to the experimental setup by a digital-to-analog converter and is then converted to a current of appropriate value by an amplifier with gain Z2 and a voltage-to-current converter for passage into the cell through the recording pipette. Also during the 100-μs time step, the computer solves for the new value of membrane potential for the SAN model, using the computed coupling current as an outward current for the membrane model scaled by the parameter Z1. The parameters Z1 and Z2 thus allow the effective sizes of the model cell and the real cell, respectively, to be adjusted during the experiment to examine the effects of geometrical changes in the coupled cell system. Thus, a doubling of the size of either the model cell or the real cell is accomplished by setting Z1 or Z2, respectively, equal to 0.5. For these particular experiments, a doubling of the size of the model cell effectively creates a larger ectopic focus, since the mathematical model used is for a spontaneously pacing cell, while a doubling of the size of the real cell increases the current threshold of the GP VC by a factor of two and lowers its input resistance by a factor of two, thus producing a greater electrotonic load on the model cell at any given value of coupling conductance. Our experiments used two different protocols. For the first protocol (n=5), we varied the size of the model cell and the coupling conductance to examine the interactions between a spontaneously pacing model cell and a quiescent or repetitively stimulated GP VC to determine the phenomena produced under a variety of conditions, as shown in Figs 2 through 7⇓⇓⇓⇓⇓⇓. In these experiments, we made no adjustments in the size of the GP VC. For the second protocol (n=10), we fixed the size of the pacing model cell with a size factor of 5 (Z1=0.2) and adjusted, for each cell studied, the size of the VC such that the current threshold of the VC for direct application of a 2-ms-duration current pulse was 2.6 nA. The value of 2.6 nA was chosen as the value required for a similar stimulation of the GP VC model of Luo and Rudy.8 The actual values of current threshold for these 10 cells was 2.53±0.21 nA (mean±SEM) before normalization of the cell size. Results with this second protocol are included in Figs 8 and 9⇓⇓.
The SAN model has spontaneous activity at a BCL of 388 ms with a prominent diastolic depolarization and a slow rate of rise of the action potential. In this model, the membrane capacitance is 32 pF and the effective input resistance during the diastolic period is ≈500 MΩ (2 nS input conductance), much higher than for typical VCs (10 to 20 MΩ). When we coupled the SAN model cell with a size factor of 1 (Z1=1) to isolated GP VCs, we found that the presence of electrical coupling slowed the spontaneous pacing of the SAN model, as illustrated in Fig 2⇑. In Fig 2A, 2B, and 2C⇑⇑⇑, the solution of the SAN model is shown as a dotted line and the recording from the isolated VC is shown as a solid line. Coupling is established at 1, 2, or 5 nS for Fig 2A, 2B, and 2C⇑⇑⇑, respectively, after the third spontaneous action potential of the SAN model. This particular VC had an input resistance of 17.9 MΩ (55.9 nS input conductance) and a resting membrane potential of −88.5 mV. At a coupling conductance of 1 nS, there is a slowing of activation of the SAN model to a cycle length of 570 ms, and each activation of the SAN model produces only a 1.9-mV depolarization in the VC. When the coupling conductance was raised to 2 nS, the slowing of the SAN model was more dramatic and led to complete cessation of SAN model activity. At a coupling conductance of 5 nS, the coupling to the VC nearly completely suppresses the electrical activity of the SAN model. When the coupling is removed, for Fig 2A, 2B, and 2C⇑⇑⇑, the SAN model instantly resumes spontaneous activity.
We had to raise the effective size of the SAN model by a factor of 3 to 5 (Z1=0.33 to 0.2) to allow spontaneous activity of the model to continue and for this activity to propagate from the model cell to real VCs at some value of coupling conductance. Fig 3⇑ shows data from a different VC (input resistance, 13.8 MΩ), in which we used a size factor of 5 for the SAN model and a coupling conductance of 5 nS. For this particular cell, the critical value of coupling conductance for successful propagation from the cell model to the VC was between 5 and 10 nS. Fig 3A⇑ shows the recorded membrane potentials and coupling current when we repetitively stimulated the VC with direct current injection at a BCL of 1300 ms. We define the coupling current to be positive when it flows from the SAN model cell to the GP VC. The solid horizontal arrow indicates the time during which the coupling conductance was turned on. During the initial period of uncoupling, the action potentials of the real cell (shown as solid lines) are from direct stimulation. After coupling was established, the direct stimulation of the real cell continued, and the action potentials in the model cell produced only small depolarizations in the real cell. Nevertheless, a stable pattern of interactions between the real cell and the model cell was established, as shown at a faster sweep speed in Fig 3B⇑, showing the results of Fig 3A⇑ during the period indicated by the horizontal dashed arrow (from 15 to 19 seconds of the recording of Fig 3A⇑). The direct stimulations of the real cell during this period are indicated in Fig 3B⇑ as vertical arrows labeled A, B, and C. Just before stimulation A, the model cell has an activation that clearly does not propagate to the real cell. When the real cell is activated by stimulus A, this action potential does propagate to the model cell, since it occurs during the diastolic period of the model cell. Between stimuli A and B, there are two additional activations of the model cell, which are due to automaticity of the model cell. Note that the temporal pattern of activations of the model cell has been “entrained” to that of the directly stimulated real cell, with three activations of the model cell for every single activation of the real cell, with a repeating pattern observed for each of the stimuli A, B, and C. Although the activations of the real cell remain regular in time, with 1300 ms between each activation, the activations of the model cell are not regular in time, with a varying time between each activation but with a repetitive sequence of these activation intervals. When we then increased the pacing frequency for the same real cell, we got the results shown in Fig 4⇑ for a BCL of 600 ms. As in Fig 3⇑, the solid horizontal arrow indicates the period of coupling. During the initial period of uncoupling, the action potentials of the real cell now occur more frequently than in Fig 3⇑. The coupled system again establishes a regular pattern of interactions, as indicated in Fig 4B⇑, in which we have expanded the results for the time period from 15 to 19 seconds of Fig 4A⇑. The direct stimuli to the real cell are again indicated by the vertical arrows labeled A through G. The coupled system now shows a stable pattern of entrainment, in which the real cell has a regular activation sequence determined by the BCL of the direct stimuli. However, the waveform of the action potentials in the real cell now alternates between a pattern with a smooth repolarization and a pattern with a secondary rise in potential during the plateau period produced by electrotonic interactions with the model cell. Note that the pattern is a regular alternans, with the two-phase plateau action potential for stimuli A, C, E, and G and a single-phase plateau for stimuli B, D, and F. The activations of the model cell also follow a regular alternating pattern, with spontaneous activity occurring before each direct stimulation of the real cell. However, the time delay between the spontaneous activity of the model cell and the direct activation of the real cell alternates, producing two activations of the model cell for stimuli A, C, E, and G, while there is a nearly synchronous activation of the model cell and the real cell for stimuli B, D, and F. The resulting pattern of activations of the model cell is three activations for every two stimuli to the real cell. The overall pattern of the results of Figs 3 and 4⇑⇑ shows unidirectional block of conduction. The SAN model cell is able to sustain spontaneous activity, but this activity has an “exit block” in terms of propagation to the GP VC. The combination of progressive slowing of the automatic activity by the electrotonic loading and the repetitive “resetting” of the SAN model cell by conduction from the repetitively activated GP VC leads to a stable pattern in which the automatic activity is strongly modulated without any effect on the firing frequency of the GP VC but with significant alterations in the action potential waveform of the GP VC.
With a coupling conductance of <7.5 nS, the SAN model (size factor of 5) had repetitive activity but failed to drive the VC that we used for Fig 2⇑. Fig 5⇑ shows data from the same VC as Fig 2⇑ obtained with Gj=20 nS, with a size factor of 5 for the SAN model. Fig 5A⇑ shows, in the upper panel, the membrane potential of the simulated SAN model cell and the GP VC and in the lower panel, the simultaneously recorded coupling current. For this recording, we did not apply any direct stimulation to the GP VC. The coupling conductance is turned on after the first three cycles of the SAN cell model. During the period of coupling (indicated by the horizontal solid arrow), the intrinsic cycle length of the SAN model (388 ms) is slowed by the coupling, but each activation of the SAN model propagates to the VC, with a resulting regular rhythm of cycle length 835 ms. Fig 5B⇑ illustrates, at a faster time scale, the recordings indicated by the horizontal dashed arrow in Fig 5A⇑. Note that activation occurs first in the SAN model cell. When the GP VC becomes activated, the large rising phase of the action potential rises above the potential level of the SAN model cell, thus producing a reversal of the coupling current. The coupling current remains small during the action potential in the real cell and the model cell because of the similarity in shape of the two action potentials. At the end of the action potential, the coupling current again becomes positive (ie, in the direction from the SAN model cell to the GP VC) because of the intrinsic difference in diastolic potentials for the SAN model cell (which has intrinsic automaticity) and the GP VC (which does not intrinsically show phase 4 depolarization but does show phase 4 depolarization to a small extent when coupled at this level).
Fig 6⇑ shows results when we stimulated the same real cell at 1 Hz (BCL, 1000 ms) with current pulses applied through the pipette. Note that the first stimulation of the GP VC occurs during the initial period of uncoupling. After coupling was established, the first action potential occurred by spontaneous activity of the SAN model cell, and this action potential then propagated to the GP VC. The first direct stimulus to the GP VC after coupling has been established occurs during the late plateau phase of this conducted action potential. The repetitive sequence that then develops shows an alternating pattern of action potentials initiated by the SAN model cell and action potentials directly stimulated in the GP VC, for which the cycle length eventually alternates between 275 and 725 ms. Note that the direction of conduction alternates also, as can be seen clearly in the coupling current trace, with a rhythm that closely resembles fixed coupled premature excitation with an activation frequency of 2 Hz. Fig 6B⇑ shows the uncoupled action potentials recorded from the GP VC and from the SAN model cell during the period of uncoupling at the beginning of the data plotted in Fig 6A⇑ with 1-Hz direct stimulation of the GP VC. The GP VC has a stable resting potential, a fast upstroke, a duration of about 250 ms, and a prominent plateau period. The SAN model shows the expected diastolic depolarization, a slower upstroke, a lower peak amplitude, and a shorter action potential duration compared with the GP VC. Two of the alternating pairs of action potentials are shown in Fig 6C⇑. The first of each pair (marked with an asterisk) arises from the same mechanism as that shown in Fig 5⇑, with initial activation occurring in the SAN model cell, followed by activation of the GP VC. The second action potential of each pair occurs as a result of the application of the periodic direct stimulation to the GP VC, and this action potential then propagates to the SAN model cell. Note that this directly stimulated action potential has a rising phase for the GP VC, which leads the rising phase of the SAN model cell. However, compared with the uncoupled GP VC action potential (see Fig 6B⇑), the peak amplitude is decreased and there is a prominent early partial repolarization caused by the current flow from the GP VC to the SAN model cell. Note that the current flow during this action potential is quite different from the current flow for the preceding action potential, with a nearly monophasic pattern for propagation from the GP VC to the SAN model compared with the biphasic pattern for conduction, which originates in the SAN model cell and then conducts to the GP VC.
When we increased the stimulus rate to 2 Hz (Fig 7⇑) for the same GP VC, the rhythm became regular even with coupling, with all action potentials initiated in the VC and then propagated to the SAN model cell. The more rapid stimulation of the GP VC occurs at a cycle length (500 ms) that, although longer than the intrinsic cycle length of the SAN model cell, is nevertheless shorter than the modulated cycle length (as produced by electrotonic loading, as illustrated in Fig 3⇑) of the coupled SAN model cell. Fig 7B⇑ shows a portion of the data of Fig 7A⇑, as marked by the horizontal dashed arrow at a faster time scale. Note that the GP VC action potential has a prominent early partial repolarization because of the electrotonic load imposed by the current flow from the GP VC to the SAN model cell.
The interactions between the electrotonic loading of the SAN model cell and the periodic direct stimuli of the GP VC are systematically illustrated in Figs 8⇑ and 9, which are recordings from a single GP VC that was coupled to the SAN model at a conductance of 5 nS (Fig 8⇑) or 10 nS (Fig 9⇑). The GP VC was directly stimulated at a BCL as indicated in each part of the two figures, with each occurrence of a direct stimulation of the GP VC marked by an arrow. Before adjustment of the size of the GP VC, this cell had a current threshold of 2.8 nA (input resistance, 16.5 MΩ). To normalize the size of this cell, we thus set Z2 to 1.08 (2.8/2.6) (see “Methods”), which made the effective current threshold of this cell 2.6 nA and its input resistance 17.8 MΩ. When uncoupled, the SAN model cell has an intrinsic cycle length of automaticity of 388 ms. For this hybrid cell pair, the critical conductance above which the model cell (size factor of 5) could successfully drive the GP VC was 7.2 nS. For each part of Figs 8 and 9⇑⇑, we coupled the SAN model cell (size factor of 5) to the GP VC and allowed the hybrid cell pair to establish a periodic pattern of interactions. For Figs 8B through 8E and 9B through 9E⇑⇑, we plotted data from 1.6 seconds before to 1.6 seconds after a direct stimulus to the GP VC. For Figs 8A and 9A⇑⇑, no direct stimuli were applied to the GP VC, and the data are plotted for 1.6 seconds before and 1.6 seconds after a spontaneous activation of the SAN model cell. The stable pattern of interaction for Figs 8A and 9A⇑⇑ (no direct stimulation) is a periodic automatic pacing of the SAN model, with a resulting cycle length of 396 ms for Fig 8⇑ (Gj=5 nS) or 743 ms for Fig 9⇑ (Gj=10 nS), the major difference being that for the higher value of Gj (Fig 9A⇑), the GP VC is being successfully driven by the SAN model cell, whereas for the lower value of Gj (Fig 8A⇑), the GP VC has no electrical activity other than the small depolarizations associated with electrotonic current flow from the SAN model cell activations. Every occurrence of successful driving of the GP VC by activity originating in the SAN model cell is marked by an asterisk in each part of Figs 8 and 9⇑⇑. For Figs 8B and 9B⇑⇑, we used direct stimuli to the GP VC at a BCL of 1400 ms. For both values of Gj, the hybrid cell pair system has established a periodic pattern of interactions. For the lower value of Gj (Fig 8B⇑), the direct activations of the GP VC propagate to the SAN model, and the SAN model is able to interpolate two cycles of spontaneous activity between each successive direct activation of the GP VC, but these cycles of spontaneous activity do not propagate to the GP VC. For the higher value of Gj (Fig 9B⇑), only one spontaneous cycle of SAN model cell is interpolated between successive direct activations of the GP VC, and this spontaneous activation of the SAN model cell is able to propagate to the GP VC (indicated by asterisks). For Figs 8C and 9C⇑⇑, we used direct stimulation of the GP VC at a BCL of 800 ms. For the lower value of Gj (Fig 8C⇑), each direct activation of the GP VC produces activation of the SAN model cell, and the SAN model cell is able to interpolate one spontaneous cycle between the direct activations of the GP VC. For the higher value of Gj (Fig 9C⇑), there is also one interpolated spontaneous cycle of the SAN model cell between successive direct stimuli of the GP VC, and this spontaneous activation occurs just before each of the direct stimuli of the GP VC, producing a pattern of activation of the GP VC of closely coupled activations in which the first activation of each pair originates from the SAN model cell (indicated by asterisks) and the second originates from the direct stimulation of the GP VC (indicated by arrows). For Figs 8D and 9D⇑⇑, we used direct stimuli to the GP VC at a BCL of 750 ms. For the lower value of Gj (Fig 8D⇑), the results are very similar to those of Fig 8C⇑, with a resetting of the spontaneous activity of the SAN model cell with each successful propagation from the GP VC to the SAN model cell, producing a single interpolated spontaneous cycle between successive direct stimuli. For the higher value of Gj (Fig 9D⇑), the slower rate of diastolic depolarization of the SAN model cell, compared with the lower value of Gj (Fig 8D⇑), produces a periodic sequence such that alternating direct stimuli to the GP VC are occurring during the plateau of the GP VC action potential, which originates from the spontaneous activity of the SAN model cell. The stable pattern of activations of the GP VC thus alternates between single activations (originating from the SAN model cell, indicated by asterisks) and pairs of closely coupled activations. For Figs 8E and 9E⇑⇑, we used direct stimuli to the GP VC at a BCL of 600 ms. For the lower value of Gj (Fig 8E⇑), the stable pattern now consists of closely coupled pairs of activations of the SAN model cell, with each direct stimulation of the GP VC propagating to the SAN model cell and resetting its automaticity. For the higher value of Gj (Fig 9E⇑), the direct stimuli to the GP VC are now occurring at a BCL that is shorter than the spontaneous cycle length of the SAN model cell with this value of Gj, and thus the direct stimuli now prevent any expression of automaticity from the SAN model cell.
We systematically evaluated, in 10 cells, the critical coupling conductance above which activation of the GP VC by the SAN model (size factor of 5) occurred. For these cells, we adjusted the “size” of the GP VC by our coupling circuit to produce a standard value of current threshold of 2.6 nA for a depolarizing pulse of 2-ms duration (see “Methods”). The critical coupling conductance for these 10 cells, after normalization of GP VC size, was 7.29±0.37 nS.
Both the recordings of “fractionated” electrograms9 10 11 12 13 and recent histological studies14 indicate that there are discrete groups of cells in cardiac regions that have been exposed to ischemia and that these groups of cells, while composed of well-coupled cells, show poor coupling among the groups. The extension of our experimental protocol of studying two coupled cells to the situation of two coupled groups of cells is simply a matter of scaling. To the extent that one can regard all of the cells within a given group of, for instance, 100 cells, as isopotential, the group simply acts as a single cell with a size 100 times that of one cell. This does not mean that all 100 cells must be absolutely isopotential on a very short time scale. If the dispersion of activation times for cells within the group is small with respect to the conduction delay from this group to another group of cells, then they act jointly in terms of supplying current to the next group and are jointly affected by this outward current. By this analogy, a group of 100 cells coupled to a group of 50 cells by a conductance of 500 nS would have the same characteristics of electrical loading and success or failure of conduction as a single cell of twice normal size coupled to a cell of normal size by a conductance of 10 nS. One limitation of this analogy is that in intact tissue, the two groups of cells are likely to be connected to other groups in a complex spatial pattern and our present experimental model is limited to the consideration of only a single coupled pair. Another limitation is that we do not know the actual values of coupling conductance that are present in the intact heart at regions of interactions between an ectopic focus and the surrounding tissue. The value of coupling conductance between ventricular myocytes in the normal myocardium has been estimated to be as high as 1000 nS,15 although measurements from cell pairs that remain associated after dispersal of cells often show much lower values of conductance.16 In our hybrid cell pair experiments, we used values of coupling conductance of 0 to 20 nS. At significantly higher values of coupling conductance, the spontaneously pacing cell model loses its property of spontaneous activation and becomes quiescent because of the very strong electrotonic interactions during diastole, which inhibit phase 4 depolarization. The significance of the critical coupling conductance we measured (expressed in inverse units as ≈140 MΩ) can be understood from a comparison with the typical input resistance for small depolarizations of the GP VCs used (≈20 MΩ). The actual process of excitation of an isolated GP VC is more complex than that predicted by a simple “voltage-divider” effect, since the input resistance of the GP VC rectifies during the process of excitation. As we recently showed,17 the rheobasic current required for excitation of an isolated GP VC, with the size of the cell normalized as we have used here, is ≈0.7 nA. Since the voltage difference that drives this current, in the present configuration of a SAN model cell coupled to a GP VC, is the difference between the peak amplitude of the SAN model cell action potential (≈+25 mV) and the voltage threshold of the GP VC (≈−55 mV), one can predict that the critical coupling conductance would be ≈(0.7 nA)/(0.07 V)≈10 nS, which is similar to the value of 7.29 nS we actually measured. Without the rectification of the GP VC input resistance during the activation process, the achievement of 30 mV of depolarization (from −85 to −55 mV) would have required 1.5 nA and thus a coupling conductance of (1.5 nA)/(0.07 mV)=21 nS. The results for coupling the SAN model cell to a GP VC are also quite consistent with our recent results (not shown) coupling the SAN model cell (size factor of 5) to rabbit VCs, in which we found a critical coupling conductance of 7.3±0.5 nS (n=5), or with our recently published results,17 in which we directly stimulated GP VCs coupled to a real-time simulation of the Luo and Rudy8 model cell and determined a critical coupling conductance of 7.0±0.2 nS (n=8).
Our results emphasize the interactions between the membrane properties of quiescent and automatic excitable cells, the geometric factors of relative cell size, and the junctional conductance between cells to ultimately determine the success or failure of activation by an ectopic focus. It is clear that all of these factors interact in even more complex ways when they are included within the complex and inhomogeneous distribution of cells of a cardiac syncytium. Nevertheless, we feel that it is useful to consider a simpler system in which these factors can be systematically varied and measured. These experiments were not done specifically to ask what would happen if a sinoatrial nodal cell happened to be located within the ventricular wall but rather as a beginning step in understanding how an ectopic focus of depolarized, spontaneously active cells might interact with quiescent but excitable cells of the ventricular wall. Since the input resistance of the standard SAN model cell is much higher than that of a normal VC, it is not surprising that coupling at low levels of conductance has a dramatic effect of slowing or abolishing the automaticity of the SAN model cell without producing propagation to the VC. However, when we raised the size of the SAN model by a factor of 3 to 5, we were able to demonstrate not only repetitive activation of quiescent VCs but also a complex interaction between a regular pacing stimulus to the VC and the persistent automaticity of the SAN model cell. At slow rates of direct pacing of the VC (1 Hz), the cell pair system developed a stable rhythm of alternating cycle lengths that, if expressed in the intact heart, would be described as fixed coupled premature excitation. For the same cell pairs, when we paced the VC at 2 Hz we were able to capture the SAN model cell, even though the intrinsic cycle length of the SAN model cell was only 388 ms, because the cycle length of automaticity of the SAN model cell had been slowed (“modulated”) to >500 ms by the electrotonic effects of coupling to the VC.
In summary, we have used a recent comprehensive mathematical model of a sinoatrial nodal cell (the SAN model) coupled to real GP VCs to investigate the effects of electrical loading on the conduction of activity from an automatic focus. The correspondence between the membrane properties of actual cells of an ectopic focus (which are not definitively known) and those of the SAN model we are using obviously requires some caution in interpretation. One definitive characteristic of sinoatrial nodal cells, which is represented in the SAN model, is that they have little or none of the inward rectifier potassium channels (IK1) that are responsible for the strongly negative and stable resting membrane potential of normal atrial cells and VCs. It has been shown, however, that this current is also reduced in VCs under conditions of hypoxia or decreased intracellular ATP or by the actions of lysophosphatidylcholine.18 19 20 21 22 Recent microelectrode recordings from an ectopic focus area removed from a patient with atrial tachycardia23 showed a group of depolarized, spontaneously active cells that, under the in vitro conditions of the recordings, showed considerable electrical uncoupling from the surrounding atrial cells. The phenomena we observed demonstrate the critical role of the size of an automatic focus as well as the coupling conductance between the automatic focus and the surrounding excitable cells in the propagation of activity from the focus out into the surrounding myocardium. Our results show that the actual anatomic features and electrical connectivity, combined with the presence of automaticity, of the surviving cell groups in a region of myocardial ischemia may play decisive roles in the generation of focal arrhythmias.
This work was partially supported by NIH grant HL-22562, the Georgia Affiliate of the American Heart Association, the Emory Egleston Children's Research Center, Netherlands Heart Foundation grant 92.310, and Netherlands Organization for Scientific Research grant 805-06-152.
Selected Abbreviations and Acronyms
|BCL||=||basic cycle length|
|SAN model||=||isolated sinoatrial nodal cell model|
- Received November 20, 1995.
- Revision received February 8, 1996.
- Accepted February 16, 1996.
- Copyright © 1996 by American Heart Association
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