Examination of stimulation mechanism and strength-interval curve in cardiac tissue

Veniamin Y. Sidorov, Marcella C. Woods, Petra Baudenbacher, Franz Baudenbacher


Understanding the basic mechanisms of excitability through the cardiac cycle is critical to both the development of new implantable cardiac stimulators and improvement of the pacing protocol. Although numerous works have examined excitability in different phases of the cardiac cycle, no systematic experimental research has been conducted to elucidate the correlation among the virtual electrode polarization pattern, stimulation mechanism, and excitability under unipolar cathodal and anodal stimulation. We used a high-resolution imaging system to study the spatial and temporal stimulation patterns in 20 Langendorff-perfused rabbit hearts. The potential-sensitive dye di-4-ANEPPS was utilized to record the electrical activity using epifluorescence. We delivered S1-S2 unipolar point stimuli with durations of 2–20 ms. The anodal S-I curves displayed a more complex shape in comparison with the cathodal curves. The descent from refractoriness for anodal stimulation was extremely steep, and a local minimum was clearly observed. The subsequent ascending limb had either a dome-shaped maximum or was flattened, appearing as a plateau. The cathodal S-I curves were smoother, closer to a hyperbolic shape. The transition of the stimulation mechanism from break to make always coincided with the final descending phase of both anodal and cathodal S-I curves. The transition is attributed to the bidomain properties of cardiac tissue. The effective refractory period was longer when negative stimuli were delivered than for positive stimulation. Our spatial and temporal analyses of the stimulation patterns near refractoriness show always an excitation mechanism mediated by damped wave propagation after S2 termination.

  • cardiac excitability
  • cathodal stimulation
  • anodal stimulation
  • damped wave
  • optical mapping

earlier studies of excitability during the cardiac cycle demonstrated that recovery of excitability is not a smoothly progressive process but has an interval of increased excitability or period of superexcitability (1, 24). In the S-I curve, this interval appears as a “dip,” and in the family of strength-duration curves, the period of increased excitability is manifested as displacement of the curves under stimulation during the relative refractory period (RRP) (25, 36). Investigations of unipolar cathodal and anodal stimulation of the heart with short pulses revealed that periods of superexcitability are characteristic of positive (anodal) stimulation, whereas the S-I curve for negative (cathodal) stimulation is close to a hyperbolic shape (13, 32).

Cranefield (9, 13) showed in 1957 that during stimulation by a pair of separated electrodes in diastole, the excitation originates from the site of cathodal stimulation starting with the beginning of the pulse, indicating cathodal make stimulation, but for stimulation in the RRP, the excitation occurs at the location of the anode after stimulus termination, indicating anodal break stimulation. In 1970, Dekker (14) established the heart's ability to respond to all four modes of direct current activation: anodal make, anodal break, cathodal make, and cathodal break. He also demonstrated the composite nature of the anodal and cathodal S-I curves. He showed that because of differences in threshold for make and break stimulation, the S-I curve for short stimuli includes the most effective portions of the curves created individually for make and break stimulation.

A theoretical framework for these observations was first established in 1996 with the use of the bidomain model (38, 47). During unipolar myocardial stimulation, both regions of negative and positive polarizations are present. These depolarized and hyperpolarized regions are called the virtual cathode (VC) and virtual anode (VA), respectively (29, 33, 50). The difference in the ratios of electrical conductivities parallel and perpendicular to the fiber direction in the intracellular and interstitial spaces, also called “unequal anisotropy ratios,” causes the formation of virtual electrodes (39, 48). The bidomain model incorporates this feature of cardiac tissue explicitly (37, 41, 42, 47). During anodal stimulation, a dog bone-shaped region of hyperpolarization, oriented transverse to the fiber direction, arises centrally around the stimulating electrode. This hyperpolarized area is flanked by two regions of depolarization in the convex portions of the dog bone. During cathodal stimulation, the tissue polarization has similar geometry but opposite polarity. In make stimulation, the excitation originates in the depolarized region (VC) at the onset of the stimulus. In break stimulation, the wave front originates in the hyperpolarized area (VA) because of charge diffusion from the VC to the VA area after termination of the stimulus. Bidomain model simulations have demonstrated the importance of virtual electrodes in the complexity of S-I curve shape (38). Specifically, the dip results from an interaction between the VC and VA areas. The plateau is caused by break stimulation, whereas the abrupt descent of the plateau phase at the end of the RRP is associated with the change of the stimulation mechanism from break to make.

Although a number of prior studies have explored excitability through the cardiac cycle, this work is the first attempt of a systematic investigation of the role of virtual electrodes in excitability at different S1-S2 coupling intervals. The goal of our study was to investigate experimentally the spatiotemporal effects underlying the mechanism of the S-I relation for unipolar cathodal and anodal stimulation.


Experimental Preparation

All experiments followed the guidelines of the National Institutes of Health for the ethical use of animals in research and were approved in advance by the Vanderbilt Institutional Animal Care and Use Committee.

New Zealand White rabbits of either sex weighing 2.2–2.5 kg were first preanesthetized with ketamine (50 mg/kg), then heparinized (1,000 units) and anesthetized by pentobarbital sodium injection (60 mg/kg) into an ear vein. After a midsternal incision was made, the heart was removed and placed onto a Langendorff apparatus, where it was retrogradely perfused via the coronary arteries with oxygenated (95% O2-5% CO2) Tyrode's solution of the following composition (in mM): 133 NaCl, 4 KCl, 2 CaCl2, 1 MgCl2, 1.5 NaH2PO4, 20 NaHCO3, and 10 glucose. The excitation-contraction uncoupler 2,3-butanedione monoxime (BDM; Sigma-Aldrich, St. Louis, MO) was added to the perfusate (15 mM) to eliminate contractile artifacts in the optical recordings. The temperature and pH were continuously maintained at 37°C (SD 0.5) and 7.4 (SD 0.05), respectively. Coronary perfusion pressure was regulated to 50 mmHg. The hearts were exposed to air during the experiments. A 30-min stabilization period followed the staining of the heart with 200 μl of di-4-ANEPPS (Molecular Probes, Eugene, OR) stock solution (0.5 mg/ml dimethyl sulfoxide) administered via a bubble trap above the aorta.

Experimental Protocol

In all experiments the anterior left ventricle (LV) was mapped. The heart was continuously paced at a cycle length of 300 ms via a bipolar Teflon-coated platinum electrode (0.125 mm in diameter, 1 mm distance between poles) placed on the right ventricle close to the septum, 8–9 mm from the unipolar testing electrode. The pacing stimulus strength was adjusted to twice the diastolic threshold of excitation. The unipolar testing electrode (delivering S1 and S2 stimuli), made from platinum wire (0.25-mm diameter), was placed on the center of the anterior LV. The camera field of view was centered with respect to the testing electrode. For S1 stimuli (4-ms duration), the current strength was set slightly above diastolic threshold. A piece of titanium mesh against the posterior LV served as the reference electrode for the S1 and S2 stimuli.

S2 pulses of 20-ms duration for both negative and positive polarities were examined. To test the excitability of the myocardium through the cardiac cycle, we decremented the S1-S2 interval in 20-ms steps beginning at 270 ms. When approaching refractoriness, the testing interval was progressively shortened in 5- to 10-ms steps until S2 no longer produced a propagating wave in response to currents as large as 10 mA. To measure the threshold current, we progressively decreased the S2 pulse in amplitude in 0.1-mA steps for anodal stimulation and 0.05-mA steps for cathodal stimulation for each examined S1-S2 interval. After the stimulation protocol was completed, the stability of the diastolic threshold was additionally verified. The electrical stimuli in the experiments were provided by computer-controlled current sources (Bloom Associates, Narberth, PA). The light-emitting diode (LED) was placed in the right upper corner of the imaged area to indicate the time of S2 application. Electrograms were continuously monitored using two Ag-AgCl pellet electrodes (EP8; World Precision Instruments) placed on opposite sides of the heart.

Imaging System and Data Acquisition

A high spatial and temporal resolution imaging system was utilized. The main components of the optical system are a Coherent diode-pumped, solid-state Verdi laser (532 nm), bundles of optical fiber for illumination delivery, and a high-speed DALSA 12-bit digital camera with spatial resolution of 128 × 128 pixels and temporal resolution of 490 frames/s (model CA D1–0128T; Dalsa, Waterloo, ON, Canada). The faceplate of the camera was cooled via a 15°C refrigerated bath. The fluorescence emitted from the imaged area of the heart was collected by a 52-mm lens (+4; Tiffen) and passed through a cutoff filter (no. 25 red, 607 nm; Tiffen). The magnification was adjusted to focus on a 12 × 12-mm area.

The camera was connected to a Bitflow R3-DIF image acquisition board (Boston, MA) in a Dell 650 Pentium IV/2 GHz Precision workstation equipped with 2 GB of random access memory. Custom data acquisition software written in LabView (National Instruments, Austin, TX) recorded the ∼12 MB/s data stream. After acquisition, data were visualized with a custom MATLAB viewer.

Data Processing and Analysis

Data were first spatially filtered with an 8 × 8 Gaussian filter and then normalized pixel by pixel according to fluorescence changes during the last pacing response. Voltage calibration was performed according to our previous microelectrode measurements: the resting membrane potential is −85 mV, and the action potential (AP) amplitude is 112 mV (44). To illustrate the net effect of the S2 stimulation on the transmembrane potential (Vm) distribution, we subtracted the previous S1 response from the S2 response for some analyses. We refer to this potential distribution as ΔVm.

To study the development of the cardiac electrical response during stimulation and immediately after termination of the stimulus, we utilized time-space plot (TSP) analysis (44). TSPs were constructed for lines along and transverse to the fiber direction. The intersection of these two lines roughly coincided with the position of the pacing (S1 and S2) electrode.

To visualize damped propagation after break stimulation, we used three-dimensional stack plots. For this purpose, data were additionally preprocessed by employing a 5 × 5 Gaussian spatial filter and a five-point mean temporal filter; two-dimensional plots of dVm/dt were then sequentially stacked, yielding the isosurface plot.

The duration of the effective refractory period (ERP) was defined as the minimal S1-S2 interval under which the threshold excitation current exceeded 10 mA. To estimate the relative refractory period (RRP), we determined the maximal S1-S2 interval (Tmax) for threshold current of 0.1 mA higher than diastolic threshold current. Thereafter, we defined RRP as the difference between Tmax and ERP.

Because excitation of cardiac tissue can originate from either the VC (make stimulation) or the VA (break stimulation), four spatial locations were examined in the analysis: two points in the central VA and one in each of the adjacent VC regions for anodal stimulation, or two points in the central VC and one in each of the flanking VA areas for cathodal stimulation. We refer to these locations as VA1, VA2, VC1, and VC2. Although stimulation at threshold intensity does not always yield obvious positive or negative virtual electrode polarizations, for convenience and consistency in analyzing each data set, we will refer to these areas as VC or VA as indicated by the stimulus polarity.

Statistical Analysis

Nine rabbit hearts were used to study cathodal stimulation, and 11 hearts were used for examining anodal stimulation. In addition, three experiments were conducted without BDM in the perfusate. Group data are presented as mean values (SD). Statistical analysis was accomplished using the unpaired t-test. Differences were considered significant if P < 0.05.


Experimental Cathodal and Anodal Strength-Interval Curves

Figure 1 shows the variation of cathodal (Fig. 1A) and anodal (Fig. 1B) S-I curves from different rabbit hearts. Despite some variability, common trends inherent in the cathodal and anodal S-I curves are evident. Anodal S-I curves (Fig. 1B) always contain a dip under stimulation close to the ERP, followed by a plateau, and then abruptly fall off at the end of the RRP. These characteristics are not as evident in the cathodal S-I curves (Fig. 1A).

Fig. 1.

Typical cathodal (A) and anodal (B) experimental S-I curves illustrating the variability in the measurements among 6 rabbit hearts. The S2 stimulus duration was 20 ms. D, dip under stimulation close to the effective refractory period (ERP); P, plateau; F, falloff at the end of the relative refractory period (RRP).

For anodal stimulation, the dip was located at an S1-S2 interval of 136.4 ms (SD 13; n = 11) with current magnitude of 1.6 mA (SD 0.7; n = 11). The local maximum for the plateau phase was 2.3 mA (SD 0.8; n = 11) at an S1-S2 interval of 176.4 ms (SD 9.2; n = 11). The subsequent decrease to a constant diastolic threshold was observed at S1-S2 coupling intervals ranging between 178 (SD 7.0) and 183 ms (SD 7.0; n = 9) for cathodal stimulation and between 185 (SD 8.4) and 190 ms (SD 8.4; n = 11) for anodal stimulation. The mean values of threshold current in diastolic tissue were 0.15 mA (SD 0.09; n = 9) and 1.05 mA (SD 0.36; n = 11) for cathodal and anodal stimulation, respectively. The experimentally measured RRP was longer under anodal stimulation (62.3 ms, SD 12.1; n = 11) than under cathodal stimulation (49.4 ms, SD 5.8; n = 9) (P < 0.01). However, the duration of the ERP was not significantly longer for cathodal (134.4 ms, SD 5.8; n = 9) than for anodal testing (129.5 ms, SD 13.3; n = 11).

To determine whether BDM affects the S-I curve shape, we conducted control experiments without BDM. Figure 2, A and B, illustrates cathodal and anodal S-I curves for stimulus durations of 20, 10, 5, and 2 ms. The measurements for each polarity were attained in two separate experiments. Figure 2C shows the 20-ms cathodal and anodal S-I curves measured in one heart. The shortening of the plateau phase and the increase of the ERP can be seen as the S2 duration decreases. In addition, the 20-ms S-I curves reproduce all of the characteristic phases observed in Fig. 1 when BDM was used. Because some of these characteristic properties of S-I curves are not apparent for stimuli of shorter durations, the S-I curves constructed for 20-ms pulses were chosen for analysis.

Fig. 2.

Variation of S-I curves as a function of S2 duration obtained without the use of 2,3-butanedione monoxime (BDM). Cathodal (A) and anodal (B) S-I curves have been constructed with S2 durations of 2, 5, 10, and 20 ms. C: cathodal and anodal 20-ms S-I curves measured in 1 heart.

In terms of stimulation mechanism, every curve can be divided into make and break portions (Fig. 3). The transition between these two segments is illustrated in the following sections.

Fig. 3.

Experimental cathodal (A) and anodal (B) S-I curves consisting of 2 sections: make and break stimulation. The vertical dashed line corresponds to the S1-S2 interval of the transition from the make to break stimulation mechanism. The points of the curves corresponding to the shortest interval for make stimulation and the longest interval for break stimulation are depicted by the numbers 1 and 2, respectively. The number 3 corresponds to the S1-S2 interval close to the ERP when the S2 pulse initiates damped waves. The S2 stimulus duration was 20 ms.

Stimulation at End of RRP: Transition of Stimulation Mechanism From Make to Break

Cathodal stimulation.

For cathodal stimulation, the duration of the RRP was 49.4 ms (SD 5.8; n = 9). Figure 4 demonstrates the analysis of the tissue response to stimulation of −0.4 mA in magnitude with an S1-S2 coupling interval of 185 ms. The corresponding point on the S-I curve in Fig. 3A is indicated by the number 1. The images of Vm distribution at 4-ms intervals after the onset of S2 are presented in Fig. 4A. Excitation originates in the center of the mapped region, which coincides with the point electrode location and forms the spreading wave of elliptical shape. The image of ΔVm corresponding to the 8-ms image in Fig. 4A is shown in Fig. 4B. Negative polarization in the regions flanking the central VC area is not revealed. In addition, because of stimulation of threshold intensity, the dog bone contour of the VC is not as evident as for stimulation with larger currents (49). Four superimposed calibrated optical signals from the VC (red) and VA (blue) regions are demonstrated in Fig. 4C. The VC APs initiated before S2 termination. The falling of the VA traces during S2 indicates tissue repolarization at these regions. Figure 4, D and E, illustrates the TSPs for lines longitudinal and transverse to the fiber direction. These lines are depicted in Fig. 4B as white and black dashed lines. Activation is shown to start simultaneously at the same location for both longitudinal (Fig. 4D) and transverse directions (Fig. 4E). This location corresponds to the VC area. The origination of the excitation at the VC indicates cathodal make stimulation.

Fig. 4.

Cathodal make response to threshold stimulation at the end of the RRP using an S1-S2 interval of 185 ms. A: images of transmembrane potential (Vm) distribution as a function of time. The numbers at upper right in each image represent the elapsed time (ms) since S2 onset. The stimulation electrode is located at the center of the images. The bright blue spot in the upper right corner during the first 20 ms is a light-emitting diode artifact. B: image of ΔVm during S2. C: 4 traces recorded within the virtual cathode (VC; red) and virtual anode (VA; blue) areas. D and E: time-space plots (TSPs) for lines longitudinal and transverse to the fiber direction (white and black dashed lines in B, respectively). The red and blue arrows indicate the location of the pixels depicted by the black and white dots in B. The white horizontal isochronal line corresponds to 13 ms after S2 onset. The white slanted lines in D and E demonstrate propagation velocity along and transverse to the fiber direction, respectively.

Figure 5 illustrates the tissue response to stimulation of −0.8 mA in magnitude. The S1-S2 interval of 180 ms was 5 ms shorter than in the above-described recording. The corresponding position on the S-I curve in Fig. 3A is indicated by the number 2. Figure 5B illustrates the distribution of ΔVm at 8 ms after the S2 onset. No prominent VA hyperpolarization can be observed. However, after S2 termination (20-ms frame, Fig. 5A), charge diffusion is shown to occur from the central VC area into the adjacent VA region, which serves as the origin for the later excitation (36-ms frame). In Fig. 5C, the optical signals reveal depolarization in the VC region during S2, whereas the VA signals exhibit continuation of the recovery from S1. After S2 termination, the VC traces reveal negative polarization, whereas the VA2 signal exhibits depolarization. After intersecting with the VC traces, the VA2 trace shows activation before the traces from the VC region. Although VC depolarization is very noticeable in Fig. 5, D and E, the TSP for the longitudinal direction displays an asymmetric activation pattern, suggesting excitation from the VA2 region. In addition, the horizontal isochronal line indicates activation of the VC area (Fig. 5E) after VA stimulation (Fig. 5D) with a delay of 15 ms after S2 termination. The origination of excitation from the VA region after termination of the stimulus indicates cathodal break as the stimulation mechanism.

Fig. 5.

Cathodal break response to threshold stimulation at the end of the RRP. The S1-S2 coupling interval is 180 ms. For detailed description, refer to the legend for Fig. 4. The white horizontal isochronal line in D and E corresponds to 28 ms after the onset of S2.

The Vm distribution around the stimulating electrode (1 × 1-mm2 area) at the beginning of S2 was −69.8 mV (SD 2.0; 121 pixels) for make stimulation and −60.7 mV (SD 2.1;121 pixels) for break stimulation.

Figure 6 shows the mean (n = 9) ΔVm profiles (10 ms after S2 onset) along the fiber direction for both make (Fig. 6A) and break (Fig. 6B) cathodal stimulation. The maximal VC depolarization was +16.1 mV and +22.5 mV for make and break stimulation, respectively. No obvious hyperpolarization was detected in the regions flanking the VC.

Fig. 6.

ΔVm profiles during S2 of cathodal make (A), break (B), and damped wave-mediated responses (C). The repolarization of the previous S1 wave was subtracted, and then ΔVm profiles were extracted for an 8-mm segment along the fiber direction 10 ms after S2 onset. Data are represented as means (SD), as indicated by the error bars (n = 9). The stimulation site is located at the middle (4 mm) of the segment. Asterisks in B indicate significant difference (P < 0.05) between the make (A) and break (B) profiles, and those in C indicate significant difference (P < 0.05) between the break (B) and damped wave (C) profiles. The S2 strengths were 0.6 mA (SD 0.4) for make (A), 1.2 mA (SD 0.7) for break (B), and 2.6 mA (SD 0.6) for damped waves (C).

Anodal stimulation.

The RRP for the anodal stimulation was estimated as 62.3 ms (SD 12.1; n = 11). Analysis of the tissue response to stimulation of +1.3 mA in magnitude with an S1-S2 coupling interval of 185 ms is presented in Fig. 7. The point on the S-I curve in Fig. 3B that corresponds to the stimulus under consideration is indicated by the number 1. Two distinguishable VC depolarizations can be seen during S2 in both the set of consecutive Vm distributions, starting with the 12-ms frame (Fig. 7A), and the image of ΔVm (Fig. 7B). The VA hyperpolarization is not visible in Fig. 7B. At the termination of S2, Vm in the lower right VC achieves threshold and thereafter produces the asymmetric pattern of activation. The time traces in Fig. 7C demonstrate delay in excitation between the two VC regions. Activation is first observed in the VC2 area (Fig. 7B), and then the wave propagates into the VA area (Fig. 7C, blue traces). VC1 activation occurs last. The TSPs in Fig. 7, D and E, show the activation begins in the VC2 area, followed by activation in the VA region. Both the succession of Vm images (Fig. 7A) and the longitudinal TSP (Fig. 7D) demonstrate asymmetric anodal make stimulation.

Fig. 7.

Anodal make response to threshold stimulation at the end of the RRP using an S1-S2 interval of 185 ms. For detailed description, refer to the legend for Fig. 4. The white horizontal isochronal line in D and E corresponds to 18 ms after the onset of S2.

Figure 8 illustrates the tissue response to stimulation of +2.3 mA in magnitude with an S1-S2 coupling interval of 180 ms. The corresponding location on the S-I curve in Fig. 3B is indicated by the number 2. The central region of negative polarization and the adjacent areas of more prominent positive polarization can be observed in Fig. 8, A and B. Despite the more distinctive positive polarization compared with Fig. 7A, the activation does not happen at the VC regions; instead, charge diffusion occurs from the VC to the VA area (interval between 24 and 32 ms) after S2 termination. As a result, after the Vm reaches threshold at the VA site, the excitation initiates and propagates in a similar manner as the cathodal make stimulation in Fig. 4A. Four representative VC and VA optical APs in Fig. 8C also indicate that excitation occurs first at the VA region. Two areas of depolarization corresponding to VCs are very distinguishable in Fig. 8D during S2. However, the horizontal white isochronal line reveals that activation occurs at the same time in the two TSPs: 10 ms after S2 termination, originating at the VA. The initiation of excitation at the central VA area with delay after S2 termination is characteristic of the anodal break stimulation mechanism.

Fig. 8.

Anodal break response to threshold stimulation in the RRP. The S1-S2 coupling interval is 180 ms. For detailed description, refer to the legend for Fig. 4. The white horizontal isochronal line in D and E corresponds to 28 ms after S2 onset.

The Vm distribution over the stimulation site (1 × 1 mm2) at the time of S2 application was −71.2 mV (SD 2.0) (121 pixels) for make stimulation and −60 mV (SD 2.4) (121 pixels) when stimulation occurred via the break mechanism.

Although VA hyperpolarization is not obvious in Fig. 7B, small negative polarization can be observed in Fig. 9A. The VC depolarization is stronger than VA hyperpolarization and displays maximums of +6.5 mV for the VC1 region and +6.1 mV for VC2 region vs. the VA minimum of −4.7 mV. In break stimulation, the stronger S2 strength induces a larger ΔVm (Fig. 9B). However, the difference in ΔVm between make and break stimulation is more prominent for the VCs than for the VA area and is statistically significant.

Fig. 9.

ΔVm profiles during S2 of anodal make (A), break (B), and damped wave (C) stimulation. Data are represented as means (SD) (n = 11). Asterisks in B indicate significant difference (P < 0.05) between the make (A) and break (B) profiles, and those in C indicate significant difference (P < 0.05) between the break (B) and damped wave (C) profiles. The mean values of the anodal S2 current were 1.48 mA (SD 0.5) for make (A), 2.1 mA (SD 0.7) for break (B), and 1.6 mA (SD 0.7) for damped waves (C).

Stimulation Close to ERP: Damped Wave Mediated Response

Cathodal stimulation.

The ERP measured for cathodal stimulation was 134.4 ms (SD 5.8; n = 9). Figure 10 illustrates the analysis of the tissue response to stimulation −2.3 mA in amplitude and 145 ms for the S1-S2 coupling interval. The corresponding point on the S-I curve in Fig. 3A is indicated by the number 3. At the time of S2 delivery, the Vm around the electrode is −21.2 mV (SD 1.2) (1 × 1 mm2, 121 pixels). However, 16 ms after S2 onset, the negative polarizations at VA1 and VA2 have magnitudes of −47.4 mV (SD 1.9) and −43.5 mV (SD 1.7) (1 × 1 mm2, 121 pixels), accordingly. The depolarization at the VC at this time is elevated to −10.4 mV (SD 3.4) (1 × 1 mm2, 121 pixels). Similar to the previously described episode of cathodal break stimulation (Fig. 5A, 24-ms through 32-ms frames), charge diffusion from the VC to VA regions occurs after S2 termination (Fig. 10A, 24-ms through 32-ms frames). However, charge diffusion does not successfully generate full-amplitude APs at the VA regions but initiates low-amplitude damped waves (Fig. 10A, 36-ms through 56-ms frames), that develop into regenerative responses at 6.6 and 6.2 mm from the stimulation site. The dog bone-shaped VC and two VAs are very prominent in Fig. 10B. Figure 10C shows that immediately after S2 termination the voltage at the VC decreases, whereas voltage at the VAs increases, indicating charge diffusion from the VC to VA areas. About 35 ms after S2 onset, the voltage at the VC and VA regions is almost equal. Thereafter, the VC and VA time traces do not intersect as Vm at the VA increases, which takes place for break stimulation (Fig. 5C). In this situation, the VA optical signals first exhibit decreasing voltage and then subsequent activation ∼65 ms after S2 onset. The failure of the S2 stimulus to initiate full-amplitude responses at VA areas is obvious in the TSPs (Fig. 10, D and E). After S2 termination, Vm immediately spreads out from the VC region ∼2.5 mm and dissipates. Afterward, longitudinal and transverse TSPs reveal the excitation occurs ∼45 ms after S2 termination.

Fig. 10.

Damped wave-mediated response as a result of cathodal threshold stimulation close to the ERP using an S1-S2 interval of 145 ms. A: Vm distribution after S2 onset as a function of time. B: ΔVm during S2. C: 4 VC and VA traces. D and E: TSPs along and transverse to the fiber direction. The white horizontal isochronal line in D and E corresponds to 56 ms after the start of S2.

Because of color saturation, it is difficult to show clearly both large and small Vm deflections with the same color scale in Fig. 10A. To demonstrate that depolarization does not disappear between 36 and 56 ms, we further analyzed the movie of this time interval. The images of ΔVm distribution as a function of time are displayed in Fig. 11A. The detailed evolution of the wave front beginning at 28 ms is presented in Fig. 11, B and C. The dVm/dt dynamics show decreasing amplitude between 28 and 36 ms, followed by propagation to the upper left and lower right corners of the image. The isosurface plot in Fig. 11C was constructed using a threshold of −0.2 mV/ms. Two knobs reflect the charge diffusion to the VAs, and two isthmuses represent damped waves that eventually develop into the regenerative response.

Fig. 11.

Damped wave propagation after cathodal stimulation near refractoriness. A: successive images of ΔVm computed by subtracting the previous S1 action potential (AP) from the S2 response. The numbers at upper right in each image represent the time (ms) since S2 onset. B: images of dVm/dt as a function of time. C: isosurface plot of signal upstroke, constructed by sequential stacks of dVm/dt contours, using −0.2 V/s as the threshold. Arrows at top indicate damped waves, and double arrow at bottom shows the fiber direction (FD).

The mean ΔVm profile during stimulation early in the RRP, when excitability sharply decreases with shortening of the S1-S2 interval, is shown in Fig. 6C. Compared with break stimulation at the end of RRP (Fig. 6B), the most important difference between the two profiles is the increased negative polarization that occurs when the stronger S2 stimulus is applied. The differences in the minimum areas between the two profiles are 4.7 mV (VA1) and 4.2 mV (VA2). There is also a difference in the positive deflection (VC): this difference is smaller, however, at 3.7 mV.

Anodal stimulation.

The ERP for anodal stimulation was 129.5 ms (SD 13.3; n = 11). Figure 12 represents the response of the tissue to a stimulus +1.4 mA in amplitude applied at a 130-ms S1-S2 coupling interval. The corresponding point in Fig. 3B is indicated by the number 3 and is located in the dip of the S-I curve. Before S2 application, Vm in the vicinity of the stimulation electrode was −11.7 mV (SD 4.8) (1 × 1 mm2, 121 pixels). During S2, the polarization at VC1 and VC2 was −22.8 (SD 1.7) and −26 mV (SD 1.3), respectively; the Vm at the VA was −41.8 mV (SD 5.2) (16 ms, 1 × 1 mm2, 121 pixels). After S2 termination, charge diffusion to the VA region can be observed (Fig. 12A, 24-ms through 42-ms frames), but this voltage elevation fails to initiate a full-amplitude AP at the VA area. The regenerative response occurs below the VA region with considerable delay, ∼52 ms after S2 termination (Fig. 12A, 72-ms frame). Although positive polarization is barely observed during S2 in Fig. 12A, it is visible after S1 subtraction (Fig. 12B). The VA traces presented in Fig. 12C intersect the VC optical signals around the time interval of 35–40 ms but then do not elevate to become regenerative APs as for anodal break stimulation shown in Fig. 8C; instead, the VA signals decrease in amplitude to −50 mV. Successive activation of the VC and VA regions occurs in the range of 70–78 ms. TSPs along and transverse to fiber direction in Fig. 12, D and E, demonstrate an increase of the Vm in the central hyperpolarized area after stimulus termination, but no activation occurs immediately afterward. The horizontal isochronal line shows the initiation of excitation at a delay ∼50 ms after S2 termination. The site of origination of activation in Fig. 12E is spatially shifted from the center compared with the TSP in Fig. 8E, suggesting the stimulation occurs outside of the VA area.

Fig. 12.

Damped wave-mediated response as a result of anodal threshold stimulation close to the ERP. The S1-S2 coupling interval is 130 ms. For detailed description, refer to the legend for Fig. 4. The artifact of the stimulating electrode is marked by the green W in B. The white horizontal isochronal line in D and E corresponds to 67 ms after S2 onset.

Because the Vm deflection at the VA is too small to be distinguishable with the color scale in Fig. 12A, the movie section between 38 and 68 ms was extracted for additional analysis and is represented separately in Fig. 13. The set of ΔVm (Fig. 13A) and dVm/dt (Fig. 13B) images demonstrates that VA depolarization propagates toward the lower left corner of the image (Fig. 13B) and converts into a regenerative response 2.3 mm from the location of the stimulation electrode. The isosurface plot in Fig. 13C illustrates wave front dynamics after charge diffusion from the VCs to the central VA area. The central knob represents VA depolarization after charge diffusion, which narrows into a thin isthmus with time and then evolves in a fast propagating AP.

Fig. 13.

Damped wave propagation after anodal stimulation near refractoriness. A: successive ΔVm images created by subtracting the previous S1 AP from the S2 response. B: images of dVm/dt as a function of time. C: isosurface plot illustrating signal upstroke dynamics after S2 termination. The threshold for creating the isosurface was −0.85 V/s. Arrow at top indicates damped wave, and double arrow at bottom shows fiber direction.

Figure 9C shows the average ΔVm profile at 10 ms after S2 onset for the S1-S2 intervals corresponding to the local minima of the dips of the S-I curves for anodal stimulation, indicating damped wave-mediated excitation. Stronger central VA hyperpolarization can be seen for the damped wave-mediated mode compared with the curve shown for break stimulation in Fig. 9B.


The shape of the S-I curve depends on inherent cardiac tissue properties as well as the electrode design (32) and parameters of the stimulus pulses (3, 6, 14, 38). There is significant variability in the S-I curve appearance among different hearts even when the same electrode and stimulation protocol are used (14). However, anodal stimulation always yields more complex dynamics through the cardiac cycle than cathodal stimulation. The manifestation of supernormal excitability, wherein the excitability is higher than expected, is a more important distinction.

In Roth's theoretical study (38) using Beeler-Reuter (BR) membrane dynamics, he computed S-I curves by using stimuli durations of 2, 5, 10, and 20 ms. Our experimentally measured anodal S-I curves (Fig. 2B) have the same characteristic shape of the numerical curves: a dip, plateau phase, and descent at the end of the RRP. In the numerical cathodal S-I curves, the dip only appeared for the 20-ms duration. For the shorter stimuli, the behavior of the theoretical cathodal S-I curves is very similar to our experimentally measured S-I curves, illustrated in Fig. 2A. The difference between the cathodal numerical and experimental data for stimulation of 20-ms duration could be the result of discrepancy in repolarization dynamics between the BR model and real cardiac tissue. In addition, although the numerical model is a three-dimensional bidomain with cylindrical symmetry, it does not represent realistic anatomical structure with fiber rotation, which can affect the spatial current distribution at the stimulation location. Another discrepancy is the lower thresholds for resting tissue in Roth's simulations (0.038 mA for cathodal and 0.41 mA for anodal stimulation) compared with our experimental measurements [0.15 mA (SD 0.09; n = 9) for cathodal and 1.05 mA (SD 0.36; n = 11) for anodal stimulation]. The disparity in unipolar stimulation thresholds in numerical and experimental studies is well known and has been discussed in the literature, although a definitive explanation has not been determined (40). However, the anodal-cathodal threshold ratio for the theoretical data (factor of 10.8) is close to the ratio from our experiments (factor of 7.0). In addition, the calculated S-I curves are shifted toward longer S1-S2 coupling intervals compared with our experimentally measured curves: this is a result of the longer AP duration in the BR model (300 ms).

Roth (38) suggested three effects combined to produce the complicated shape of the S-I curve: weak active response at the VC regions, the change in membrane resistance, and depolarization of the tissue immediately before S2 application. During stimulation at the end of the RRP, when tissue is recovering from refractoriness, the weak nonpropagating VC active response can affect the threshold. Roth hypothesized that if stimulation is cathodal, the weak nonpropagating active response prolongs the refractoriness in the border region between the VC and VA. As a result, stronger stimulation is needed to overcome this refractoriness. Therefore, the weak active response increases the stimulation threshold. However, under anode break stimulation late in the RRP, the elevation of depolarization at the VC due to local weak active response causes descent of the S-I curve as the interval increases. We believe that as long as the VC weak response increases depolarization, it elevates the voltage gradient between the VA and VC area. This increased voltage gradient will facilitate excitation and decrease threshold.

It is known that a steep change of resistance during an AP coincides with a phase of faster recovery during repolarization (21). This faster recovery facilitates polarization at shorter S1-S2 intervals and decreases the threshold. However, this phenomenon does not equally affect cathodal and anodal stimulation. It has been shown that stimulation during the plateau phase induces asymmetrical changes in Vm, yielding larger negative Vm changes than positive ones (11, 19, 23, 51). The L-type Ca2+ current was suggested to underlie this nonlinear Vm change (10).

Why does a dip appear in the anodal S-I curve but not in the cathodal curve? If anodal stimulation is delivered early in the RRP, the effect of the nonlinear cardiac cell membrane behavior at the VA area overcomes the elevation of Vm due to the short S1-S2 interval and facilitates stimulation, causing the positive slope of the anodal S-I curve. When cathodal stimulation takes place early in the RRP, the spatial geometry of virtual electrode polarization dominates. Hyperpolarizing two VAs distant from the electrode requires larger current. Therefore, no dip is observed in the cathodal S-I curve.

Thus the Vm immediately before S2 application determines the membrane conductance and affects the membrane nonlinear properties. In addition, for stimulation close to the ERP, the prestimulation Vm is crucial for unstable damped waves with diminished amplitude and velocity, causing them to either dissipate or become full-amplitude, steadily propagating waves.

It has been shown that stimulation during the RRP can induce a graded response that depends on the stimulus magnitude and S1-S2 interval (16, 18, 22, 23, 26, 28). This response can be local or can propagate (28, 45), forming damped waves with diminished amplitude and velocity (43). What is the ionic mechanism of damped waves? In our study, at the time of anodal S2 onset, the mean Vm around the electrode (1 × 1 mm2) for S1-S2 intervals corresponding to the dip locations in the S-I curves is −16.1 mV (SD 6.2) (1,331 pixels, 11 experiments). During cathodal stimulation close to the ERP, when excitability sharply increases with decreasing S1-S2 intervals, this value is −17.3 mV (SD 3.9) (1,089 pixels, 9 experiments). The mean values of depolarization measured at the end of the RRP when stimulation occurs via the break mechanism are −55.7 mV (SD 4.6) (1,331 pixels) and −53.7 mV (SD 6.2) (1,089 pixels) for anodal and cathodal stimulation, respectively. The gating of activation and inactivation for the Ca2+ current is known to operate under membrane potentials more positive than −40 mV, whereas the Na+ current starts to activate at potentials higher than −70 mV and is almost completely inactivated under voltages higher than −60 mV (5). Hence, it is reasonable to expect that the Ca2+ current is the dominant current in damped propagation, whereas the composition of the current underlying the break response during stimulation at the end of the RRP is similar to the current composition of the AP during diastolic stimulation. Further studies using simultaneous Ca2+ and Vm imaging are needed to validate this hypothesis.

Nikolski et al. (35) reported about break excitation during diastole. When stimulation was of near-threshold intensity, cathodal and bipolar stimulation revealed break excitation. If stimulation was anodal, the excitation followed the make mechanism. Later, they demonstrated that anodal break excitation also can occur in diastole but is accompanied by an overshoot of the pacing current because of the half-cell double-layer discharge. The addition of a diode in the stimulation circuit eliminated both the overshoot and the break excitation (34).

Lindblom et al. (31) conducted a theoretical study of excitability and arrhythmogenesis in the pinwheel experiment using the Beeler-Reuter Drouhard-Roberge model to represent membrane kinetics. Although they examined pinwheel stimulation protocol rather than point stimulation, their results for S2 stimuli occurring after 95% repolarization were similar to Roth's simulations in diastole (38): make excitation was always observed. In our experiments, the stimulation mechanism in diastole was make for both positive and negative polarities (Fig. 3).


To eliminate the mechanical distortion of optical signals, we utilized the electromechanical uncoupler BDM. It is known that this reagent can modify ion conductances (7, 12, 46) and, hence, can affect excitability. To determine whether BDM affects the S-I curve, we conducted control measurements of excitability through the cardiac cycle without BDM. We demonstrated that all typical characteristics of the cathodal and anodal S-I curves also were observed in hearts perfused without BDM.

Optical signals are estimated to originate from depths of 300–500 μm (20, 29) up to about 1–2 mm (2, 4, 8, 15, 17). On the other hand, tissue polarization falls off over a few electrotonic space constants. The space constants follow tissue anisotropy, with the smallest being transverse to the fiber direction. As was demonstrated in dog hearts, the value of the space constant depends on the type of cardiac tissue and varies from 920 to 1,250 μm along the fiber direction and between 115 and 595 μm for the direction transverse to the fibers (30). The depth of penetration for the polarization beneath the stimulating electrode is unknown, but it is assumed that this value is a few transverse space constants. Hence, the voltage measurements at the VA and VC can be underestimated if the electrical space constant is less than the optical decay constant (27). In addition, averaging of the fluorescence over depth also can attenuate the appearance of damped propagation, causing damped waves to appear less prominent than they actually are.


This work was supported by National Heart, Lung, and Blood Institute Grant R01-HL-58241 and the Academic Venture Capital Fund of Vanderbilt University. The work of M. C. Woods was partially supported by a predoctoral fellowship from the American Heart Association (0215128B).


We thank John P. Wikswo for support and encouragement and Bradley J. Roth for comments and suggestions.


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