Field Induced Responses at Rest

When a cell is stimulated at rest with field pulses of increasing amplitude, it elicits an action potential once the pulse amplitude exceeds a threshold.16'18 Figure 4 shows the response of a cell stimulated at rest with a 2 ms duration pulse of suprathreshold amplitude (labeled as S1). The cell polarizes rapidly at the onset of the field pulse with the speed of polarization limited by the bandwidth of the setup electronics (rise time of ~0.3ms). The cell end facing the anode (site 1) undergoes maximum negative polarization, the cell end facing the cathode undergoes maximum positive polarization (Fig. 4b), and polarization varies linearly along the cell length (Fig. 4c). During the pulse the polarization is not constant, but exhibits a gradual positive shift. This spatially linear pattern for the field-induced AVm with a nonconstant value during the field pulse is reminiscent of theoretical responses of an active cell (Fig. 2). The positive shift in Vm responses is indicative of the fact that there is a net inward current during the field pulse that facilitates cell excitation by elevating membrane potential toward the excitation threshold. We will examine the source of this net current in more detail below. In the above example the cell fired an action potential following the termination of the pulse. However, this is not a typical scenario, and often the excitation occurs during the S1 pulses (e.g., refer to Figs. 7 and 8). Several factors intrinsic (e.g., cell length and excitability) and extrinsic (e.g., pulse parameters) to the cell seem to play a role in determining the early (during S1) versus late (after S1) pattern of excitation.

The excitation of an isolated cell at rest exhibits an interesting pattern when stimulated with a field pulse of short duration and increasing amplitude.19 For a pulse < 1ms in duration, the cell is excited normally at lower amplitudes once above a lower threshold for

Figure 4: Field-induced responses at rest. (a) Shows a cell stimulated with a 2ms, 4.1 V/cm S1 pulse. (b) Shows the field-induced change in Vm (AVm) normalized to action potential amplitude from eight sites on the cell. (c) plots the AVm responses measured 0.3 and 2 ms [AVm(i = 0.3) and AVm(t = 2.0), respectively] from the onset of S1 pulse along the cell length. AVm has been normalized to the action potential amplitude

Figure 4: Field-induced responses at rest. (a) Shows a cell stimulated with a 2ms, 4.1 V/cm S1 pulse. (b) Shows the field-induced change in Vm (AVm) normalized to action potential amplitude from eight sites on the cell. (c) plots the AVm responses measured 0.3 and 2 ms [AVm(i = 0.3) and AVm(t = 2.0), respectively] from the onset of S1 pulse along the cell length. AVm has been normalized to the action potential amplitude excitation. However, as the field amplitude is gradually raised, it reaches a threshold at which the excitation is suppressed (Fig. 5). This loss of excitation is reversible and hence not associated with cell damage (e.g., resulting from membrane electroporation).20'21 The excitation is restored upon lowering the pulse amplitude or increasing the pulse duration while maintaining the pulse amplitude at the level of paradoxical unexcitation.

One approach to understand the mechanism of paradoxical unexcitation at higher amplitudes is to resort to computer modeling. A convenient model to use is phase 1 Luo-Rudy model22 with description of six major cardiac membrane currents. Although there

Figure 5: Paradoxical loss of excitation at rest with short-duration high amplitude pulses. (a) Shows a cell stimulated successively with three S1 pulses of 50, 55, and 50V/cm. (b) Shows the responses corresponding to the three S1 pulses. (c) Shows the pattern of excitation with S1 amplitude fixed at 55V/cm, and the S1 duration increased from 0.5 to 1, 5, and 10 ms. The circled numbers next to each set of traces indicate sequence of stimulation. The recordings corresponding to sites 1 and 8 have also been numbered

Figure 5: Paradoxical loss of excitation at rest with short-duration high amplitude pulses. (a) Shows a cell stimulated successively with three S1 pulses of 50, 55, and 50V/cm. (b) Shows the responses corresponding to the three S1 pulses. (c) Shows the pattern of excitation with S1 amplitude fixed at 55V/cm, and the S1 duration increased from 0.5 to 1, 5, and 10 ms. The circled numbers next to each set of traces indicate sequence of stimulation. The recordings corresponding to sites 1 and 8 have also been numbered are a number of sophisticated membrane models available,23 the simple phase-1 Luo-Rudy model would suffice for our purposes. Figure 6a shows the responses of a model cell with Luo-Rudy phase-1 membrane kinetics that is stimulated with a field pulse of ~6.3V/cm. The pattern of Vm for various patches along the cell length is similar to that observed experimentally (e.g., Fig. 4). In addition the modeling experiments also reveal flow of ionic currents along the cell length. There is a large inward sodium current (INa) at the cathode facing regions of the cell that experience depolarization during the field pulse. INa gradually diminishes moving toward the anodal end of the cell and is negligible in the cell half facing

Figure 6: Field-stimulation of a model cell and pattern of INa and IK1 at low- and high-field amplitudes. (a) Shows Vm, INa, and IK1 for a Luo-Rudy phase I model cell stimulated with 5 ms, 6.3V/cm pulse in the indicated direction. (b) Shows Vm, INa, and IK1 for the model cell stimulated with two 1ms duration pulses. The first pulse (58V/cm) is just below the threshold for paradoxical unexcitation, and the second pulse is at threshold for unexcitation. Also shown in each panel is the schematic of the cell along with the flow of INa and IK1, where the lengths of various arrows signify the relative amplitudes of the corresponding currents. Note that the time bar in each panel is applicable to all sets of traces

Figure 6: Field-stimulation of a model cell and pattern of INa and IK1 at low- and high-field amplitudes. (a) Shows Vm, INa, and IK1 for a Luo-Rudy phase I model cell stimulated with 5 ms, 6.3V/cm pulse in the indicated direction. (b) Shows Vm, INa, and IK1 for the model cell stimulated with two 1ms duration pulses. The first pulse (58V/cm) is just below the threshold for paradoxical unexcitation, and the second pulse is at threshold for unexcitation. Also shown in each panel is the schematic of the cell along with the flow of INa and IK1, where the lengths of various arrows signify the relative amplitudes of the corresponding currents. Note that the time bar in each panel is applicable to all sets of traces the anode. This is consistent with the fact that any hyperpolarization of the membrane will maintain the sodium channels in an inactivated state and limit INa. In contrast to INa, inward rectifying potassium current (IK1) is maximal in the hyperpolarized regions of the cell and diminishes moving toward the opposite end of the cell. IK1 eventually reverses direction in the maximally depolarized regions, albeit it much lower in amplitude. This pattern is consistent with inward rectifying characteristics of IK1 exhibiting large inward current for membrane potentials below ~ — 85 mV, which is close to the resting potential around which the cell's Vm is perturbed spatially. Since both INa and IK1 are largely inward, they work synergistically at lower field amplitudes to bring a net inward current and depolarize the cell to its excitation threshold.24

As the pulse amplitude is increased, the positive depolarization in the cathodal regions of the cell can exceed the reversal potential of INa. Consequently, INa now counters the inward Ik1 rather than working synergistically with it. Thus, the net inward current begins to diminish with increasing field strength and is not sufficient to raise the membrane potential to the excitation threshold. The return of excitation with increasing pulse duration can occur because even at threshold amplitude for paradoxical unexcitation the cell exhibits a slow depolarizing drift during the pulse.19 Consequently, as the pulse duration is extended the portions of the cell away from the cathode that remained below INa threshold can now be triggered, bringing in net inward current and aiding in the cell depolarization. This in turn excites neighboring regions and a miniwave of INa is set in that proceeds toward the hyperpolarized regions of the cell. This additional inward current via INa is presumably sufficient to overcome paradoxical unexcitation observed with shorter duration pulses.

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