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This chapter delves into the neuronal responses to both negative and positive pulses during high-frequency stimulation (HFS), focusing on the activation effects of these pulses on neuronal membranes. It reveals that, contrary to conventional beliefs, positive pulses can match or even exceed the activation efficiency of negative pulses during sustained HFS. The study investigates the mechanisms behind these findings, including the role of extracellular potassium concentration and the inactivation of sodium channels. Additionally, it explores the potential applications of these insights in neuromodulation therapies, suggesting that alternating opposite-polarity pulses could enhance the excitatory effects of stimulation while maintaining the axonal block effect. The chapter also discusses the potential of this stimulation paradigm in neural prostheses, offering a new dimension to neural coding. The findings challenge the traditional view of pulse efficiency and provide valuable insights into improving the efficacy and safety of electrical stimulation techniques in various therapeutic applications.
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Abstract
This chapter presents our findings that challenge the conventional view—that negative pulses are more effective than positive pulses in extracellular stimulations. During sustained high-frequency stimulations (HFS) with alternating monophasic pulses of opposite polarities, the firing induced by positive pulses became comparable to that induced by negative pulses. Furthermore, the two types of pulses activated different subpopulations of neurons. For neurons that responded to both types of pulses at baseline, positive pulses actually surpassed negative pulses during HFS. Our computational simulations revealed complex interactions between the two pulse types in their activation mechanisms on axonal membrane.
In extracellular electrical stimulations, negative pulses can activate neuronal membranes more effectively than positive pulses. A negative pulse depolarizes the membrane near the stimulation site while hyperpolarizing it at a distance by returning current. Conversely, a positive pulse hyperpolarizes the membrane nearby while depolarizing it at a distance. As the electrical field from the stimulation site diminishes rapidly with distance, the depolarization produced by a positive pulse at a distance is much weaker than that produced by a negative pulse near the stimulation site. This makes negative pulses more efficient for activation. In clinical neuromodulation applications, single-phase pulses are rarely used because they may cause tissue damage and electrode corrosion (refer to Sect. 1.4.4). Instead, charge-balanced biphasic pulses—consisting of a preceding negative phase followed by a positive phase—are commonly used. The negative phase provides activation while the positive phase balances the charges.
The positive phase in biphasic pulses can potentially weaken the effect of the preceding negative phase. If the depolarization caused by the negative phase has not fully initiated an action potential before the positive phase begins, the resulting hyperpolarization may interrupt the action potential generation (Cappaert et al. 2013). To eliminate this impact, asymmetric charge-balance waveforms have been developed, including smaller and wider square or non-square waveforms for positive phases (Montgomery 2017; Foutz and McIntyre 2010; Haji Ghaffari et al. 2020). Additionally, adding a short interphase gap (IPG) between the negative and positive phases can provide sufficient time for the negative phase-induced depolarization to initiate an action potential, thereby reducing the impact of positive phase (Gorman and Mortimer 1983; Weitz et al. 2014; Carlyon et al. 2005; Deprez et al. 2018). However, previous studies have shown that for myelinated nerve fibers in the brain, the “vulnerable window” of hyperpolarization interference is only about 100 μs. Furthermore, under the super-threshold activation from a negative pulse with sufficient intensity and width, this vulnerable window can virtually disappear. Therefore, the immediately following positive phase likely has no significant effect on the activation of preceding negative phase (van den Honert and Mortimer 1979). Our experimental results from stimulations on axonal fibers in the rat hippocampus CA1 region support this point. Using a pulse width of 100 μs per phase with sufficient intensities, the activation effect of the biphasic pulses was similar to that of single-phase negative pulses (Hu et al. 2015). In some cases, the following positive phase may even enhance the activation effect of the preceding negative phase (Zheng et al. 2022). Additionally, the IPG effect can depend on whether unipolar or bipolar stimulation is used. In our bipolar stimulation experiments (a method commonly used in clinic), adding an IPG did not improve the efficiency of preceding negative phase and sometimes even weakened it, consistent with other report (Eickhoff and Jarvis 2021). Therefore, the positive phase in biphasic pulses does not necessarily reduce stimulation efficiency.
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Nevertheless, the addition of balance phase can double electric energy consumption, regardless of its possible adverse effect. Could the positive phase be beneficial in specific stimulation situations? Particularly, during sustained HFS such as in neuromodulation therapies, the efficiencies of positive and negative phases could change. On slender neuronal axons, a positive pulse can hyperpolarize the axonal membrane near the stimulation electrode while depolarizing the membranes on both flanks. These depolarizations can produce action potentials that propagate bidirectionally—a phenomenon known as “virtual cathode” activation (Ranck 1975; Rattay 1989; Basser and Roth 2000). Although positive pulses typically show much lower activation efficiency than negative pulses, our experiments with axonal HFS on CA1 pyramidal neurons revealed surprising results: During intermittent axonal block induced by sustained HFS, the activation effect of positive pulses can match or even exceed that of negative pulses (Feng et al. 2022; Hu et al. 2023), as presented below.
7.1 Neuronal Responses to A-HFS with Alternating Opposite-Polarity Pulses
7.1.1 Effect of Positive Pulses During the Steady Period of A-HFS with Alternating Pulses
To investigate the effects of monophasic pulses with opposite polarities during HFS, we separated the negative and positive phases of biphasic pulses by adding an IPG between them to create a stimulation sequence with alternating negative and positive pulses. We applied this sequence as A-HFS at alveus, using a bipolar concentric electrode (Mode CBCSG75, refer to Sect. 3.4) with the diameters of inner and outer poles of 75 and 250 μm respectively, and both poles having a height of 100 μm with a separation distance of 100 μm (Fig. 7.1A). The 16-channel recording array (Mode A1 × 16-Poly2-5 mm–50 s-177) positioned at ~ 1.3 mm upstream of the stimulation site. We still analyzed the APS signal recorded in the CA1 pcl to evaluate neuronal responses. During baseline tests, the APS┬ induced by a single negative pulse (denoted as ┬) was much larger than the APS┴ induced by a positive pulse (denoted as ┴) (Fig. 7.1A, left), indicating a higher activation efficiency of the ┬ pulse.
Fig. 7.1
Neuronal responses to A-HFS┬┴ with alternating negative and positive pulses at 100 and 200 Hz in the rat hippocampal CA1 region. A Schematic diagram showing the electrode positions in the CA1 region, along with APS waveforms induced by single ┬ and ┴ pulses (left). A histological picture of sagittal slice shows the SE trace to the alveus, indicated by a bloodstain trail through cortex to the dorsal hippocampus (right). B Typical APS signal during 2-min 100 Hz A-HFS with alternating ┬ and ┴ pulses. C For 100 Hz A-HFS (n = 15 rats): typical scatter plot of APS amplitudes induced by each pulse (C1), comparisons of initial APS amplitudes (A┬init vs. A┴init, C2) and steady APS amplitudes (A┬end vs. A┴end, C3), as well as typical scatter plot of APS latencies (C4), and comparisons of initial APS latencies (L┬init vs. L┴init, C5) and steady APS latencies (L┬end vs. L┴end, C6). The A┬end, A┴end, L┬end and L┴end were averages from the final second of A-HFS. D For 200 Hz A-HFS (n = 13 rats): comparisons of initial (D1) and steady (D2) APS amplitudes, as well as initial (D3) and steady (D4) APS latencies. *P < 0.05, **P < 0.01, paired t-test, n = 15 or 13.
In a sequence of 100 Hz monophasic A-HFS with alternating negative and positive pulses (denoted as A-HFS┬┴), the occurrence frequencies of both ┬ and ┴ pulses were 50 Hz. At the onset of 2-min A-HFS┬┴, the two types of pulses alternately produced larger APS┬ and smaller APS┴, respectively (Fig. 7.1B), similar to the single-pulse stimulations at baseline. As the A-HFS┬┴ continued, the APS amplitudes decreased rapidly. Interestingly, the APS┴ first decreased to almost disappearance before returning to a steady level, while the APS┬ decreased monotonically to a steady level. After approximately 40 s stimulation, the amplitudes of APSs produced by both types of pulses became similar (Fig. 7.1B, C1). In the experiments with 100 Hz A-HFS┬┴, the amplitudes between the initial APS┬ and APS┴ (A┬init and A┴init) differed significantly (Fig. 7.1C2), with the mean A┴init being only about half of the mean A┬init. However, the mean amplitudes of steady APSs (A┬end and A┴end) were similar (Fig. 7.1C3). The A┬end and A┴end were ~ 20% and ~ 40% of A┬init and A┴init, respectively (Fig. 7.1C2, C3), indicating different suppression ratios of APSs generated by the two types of pulses.
In addition, during A-HFS┬┴, the latencies of all APSs gradually increased, with the mean APS┴ latency being shorter than the mean APS┬ latency (Fig. 7.1C4), which persisted throughout the entire A-HFS┬┴ period (L┴init vs. L┬init in Fig. 7.1C5 and L┴end vs. L┬end in Fig. 7.1C6). The latencies of both APS types nearly doubled from their initial to steady levels. After the end of A-HFS┬┴, the APSs induced by single-pulse test stimulations returned to baseline level within about 2 min (Fig. 7.1B, upper right).
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When the pulse frequency of A-HFS┬┴ was increased from 100 to 200 Hz, the change of APS amplitudes showed similar patterns (Fig. 7.1D1 and D2), with the steady values decreasing to below ~ 10% of the initial value for APS┬s and below ~ 20% for APS┴s, approximately half of the ratios observed at 100 Hz A-HFS┬┴. The mean APS┴ latency was significantly shorter than that of APS┬s (Fig. 7.1D3, D4).
These results indicated that despite the significant differences in their initial activations, the ┴ pulse activation was not weaker than that of ┬ pulses during sustained A-HFS┬┴ when the induced APSs were suppressed. We then compared APS changes between monophasic-pulse A-HFS┬┴ and biphasic-pulse A-HFS (denoted as A-HFS┼┼), using identical pulse frequency and intensity but different consumptions of electric energy.
2.
Comparison of APS signals during monophasic-pulse A-HFS┬┴and biphasic-pulse A-HFS┼┼
The neuronal responses to A-HFS┼┼ have been described in details in Chap. 5, simplified as A-HFS. For comparison, an example of 100 Hz A-HFS┼┼ is shown in Fig. 7.2A again. Each pulse of the A-HFS┼┼ produced an APS, denoted as APS┼. During the steady period of A-HFS┼┼, the APS┼ amplitude decreased to a level similar to that of A-HFS┬┴ (Fig. 7.2B1). Meanwhile, the APS┼ latency gradually increased to a steady level, falling between the latencies of APS┴ and APS┬ during A-HFS┬┴ (Fig. 7.2B2).
Fig. 7.2
Comparisons of APS amplitudes and latencies between A-HFS┬┴ and A-HFS┼┼. A Typical APS┼ signal during 2-min 100 Hz A-HFS┼┼. B Scatter plots showing APS amplitude (left) and latency (right) induced by each biphasic-pulse (green) during the A-HFS┼┼ shown in (A), along with corresponding data from APS┬ and APS┴ (blue and orange, respectively) during A-HFS┬┴ in the same rat experiment. C Comparisons of initial and steady values of APS amplitudes (C1 and C2) and latencies (C3 and C4) among APS┬, APS┴ and APS┼ induced during 100 Hz A-HFSs. (C1) and (C2) also include comparisons between the APS┼ values and the average values of APS┬ and APS┴ (rightmost two-colored bar). D Corresponding comparisons for 200 Hz A-HFS. *P < 0.05, **P < 0.01, two-way ANOVA with post-hoc Bonferroni tests, n = 8. #P < 0.05, ##P < 0.01, paired t-test, n = 8. From Feng et al. (2022)
Statistical data showed that at the onset of A-HFSs, the mean amplitudes of A┼init and A┬init showed no significant difference, and both were significantly greater than A┴init (Fig. 7.2C1). This difference disappeared during the steady period (Fig. 7.2C2). Additionally, the mean latencies of the three types of APSs showed significant differences in both initial and steady periods of A-HFSs. Biphasic-pulses produced APS latencies (L┼init and L┼end) significantly longer than those by positive-pulses (L┴init and L┴end), but shorter than those by negative-pulses (L┬init and L┬end) (Fig. 7.2C3, C4). When the pulse frequency was increased from 100 to 200 Hz, similar results were observed, except that the mean latency L┼end was significantly shorter than both L┬end and L┴end (Fig. 7.2D).
To compare the mean firing levels produced by A-HFS┬┴ and A-HFS┼┼, the amplitudes of APS┬ and APS┴ induced by A-HFS┬┴ were averaged (shown by the rightmost two-colored bar in Fig. 7.2C1, C2, D1, D2). For both 100 and 200 Hz A-HFSs, at onset, the average amplitudes (A┬init + A┴init)/2 were significantly smaller than the amplitude A┼init (Fig. 7.2C1, D1). During the steady period, the (A┬end + A┴end)/2 became similar to the A┼end (Fig. 7.2C2, D2), indicating similar neuronal firing levels for both types of A-HFS. However, A-HFS┼┼ consumed twice the electric energy of A-HFS┬┴.
3.
Safety of Monophasic-pulse A-HFS┬┴
During A-HFS┬┴, a gap existed between the negative and positive pulses—10 ms at 100 Hz and 5 ms at 200 Hz. Could this gap disrupt the charge balance between positive and negative pulses and cause neuronal damage? To address this concern, we compared the recovery of neuronal activity after A-HFS┬┴ versus A-HFS┼┼. Single test pulses with parameters identical to A-HFS pulses were applied at ~ 30 s intervals after A-HFS ended. Both types of A-HFS showed over 90% recovery in APS amplitudes and latencies within ~ 2 min after A-HFS, indicating no obvious neuronal damages caused by either A-HFS (Fig. 7.3).
Fig. 7.3
Recoveries of neuronal responses after A-HFS with alternating monophasic-pulses and A-HFS with biphasic-pulses. A Typical APSs to single-pulse tests before and after both types of A-HFS. B and C Changes in the mean APS amplitudes normalized to baseline values for both A-HFS types. The shadow denotes the A-HFS period during which the first data point was from the single APS induced by the first A-HFS pulse, while each subsequent data point represented an average APS value from the last second of each 5-s interval. Post-A-HFS data points were from single-pulse tests at 30-s intervals. D Comparison of mean recovery times for APS amplitudes to reach 90% of baseline value (T90%) calculated by linear interpolation as illustrated in (B) and (C). E–G APS latency data corresponding to the APS amplitude data in (B–D). The recovery time of APS latency was measured when the increased latency returned to 110% of baseline value (T110%).
7.1.2 Opposite-Polarity Pulses Activate Different Subpopulations of Neurons During A-HFS┬┴
The above results showed that despite significant differences in the initial APSs, the steady-state APSs during both A-HFS┬┴ and AHFS┼┼ were suppressed to a similar level. This suppression indicated that each pulse activated only a small portion of the neuronal population that was originally responsive during baseline and at A-HFS onset. Since the ┬ and ┴ pulses activate different sites along an axon (Brocker and Grill 2013; Ranck 1975; Rattay 1999), we hypothesized that the suppressed APSs induced by the two types of pulses during A-HFS┬┴ could be generated by distinct subpopulations of neurons.
To test this hypothesis, we utilized the refractory period following APSs to determine whether the two opposite pulses activated the same neuronal population. As shown in Fig. 7.4A, in baseline conditions, pairs of biphasic-pulses were applied with progressively shortened IPIs. The first pulse was designated as the control pulse and the second as the test pulse. At an IPI of 1.5 ms, the test pulse induced a smaller APS (denoted as A┼test). When the IPI decreased to 0.8 ms, no A┼test was induced, indicating a baseline refractory period of ~ 1 ms. However, during sustained 100 Hz A-HFS┼┼ with identical parameters, an additional pulse inserted 5 ms after an A-HFS pulse induced no APS (denoted as A┼ins in Fig. 7.4B), indicating that A-HFS prolonged the refractory period to longer than 5 ms (refer to Sect. 5.2.2).
Fig. 7.4
Different activation patterns during sustained A-HFS┼┼ and A-HFS┬┴. A Examples of the control APS (A┼control) induced by a single biphasic-pulse (left) and the APSs induced by paired biphasic-pulses with IPI of 1.5 and 0.8 ms (right) under baseline conditions. B During 2 min 100 Hz A-HFS┼┼, test pulses inserted at ~ 105 and ~ 115 s in the middle of 10 ms IPIs produced no APS (A┼ins = 0). C Examples of the control APS (A┴control) induced by a single ┴ pulse and the APSs induced by paired ┬ and ┴ pulses with IPI of 1.5 and 0.8 ms in baseline conditions. D During 2 min 100 Hz A-HFS┬┴, test-pulses inserted at ~ 100, ~ 105, ~ 110 and ~ 115 s in the middle of 10 ms IPI formed four types of tests (orange boxes in D1–D4): ┬ after ┬, ┴ after ┴, ┬ after ┴ and ┴ after ┬. E Amplitude ratios between the APSs induced by the inserted test pulses and those induced by the preceding A-HFS┬┴ pulses of the same polarity.
Pairs of monophasic-pulses were applied with a leading ┬ pulse followed by a ┴ pulse in baseline conditions (Fig. 7.4C). At an IPI of 1.5 ms, the ┴ pulse induced only a smaller APS (denoted as A┴test). When the IPI decreased to 0.8 ms, no A┴test was induced due to the refractory period. This suggested that the neuronal population activated by the ┴ pulse was fully included within the population activated by the ┬ pulse. With an IPI shorter than the refractory period, the subsequent ┴ pulse could not reactivate the neurons that had just fired in response to the leading ┬ pulse.
During sustained 100 Hz A-HFS┬┴, an additional pulse of ┬ or ┴ was inserted in the middle of the 10 ms IPI—5 ms after an A-HFS┬┴ pulse (Fig. 7.4D). These insertions generated different APSs. When the polarity of the inserted pulse was same as the preceding A-HFS┬┴ pulse, it induced no APS (Fig. 7.4D1, D2), similar to the results during A-HFS┼┼ (Fig. 7.4B). However, when the inserted pulse had opposite polarity to the preceding pulse, it induced a substantial APS (Fig. 7.4D3, D4) with a mean amplitude of 60%–70% of the APS induced by the last previous pulse with the same polarity (Fig. 7.4E). Meantime, the inserted pulse prevented any APS following the subsequent A-HFS┬┴ pulse of the same polarity (denoted by the hollow triangles in Fig. 7.4D3, D4), which further demonstrating the effect of extended refractory period.
These results showed that monophasic-pulses of opposite polarities controlled distinct neuronal subpopulations during sustained A-HFS┬┴, although initially a ┴ pulse only controlled a subset of neurons responding to a ┬ pulse. The following additional experiment further verified this finding. We set an A-HFS┬┴ train by repeating a paired-pulse (IPI = 2.5 ms) at 50 Hz for 2 min (Fig. 7.5A). This resulted in the IPIs of A-HFS┬┴ alternating between 2.5 and 17.5 ms—with each ┴ pulse following the shorter 2.5 ms IPI and each ┬ pulse following the longer 17.5 ms IPI. At the A-HFS┬┴ onset, due to the refractory period, the induced APS┴ following the shorter IPI was significantly smaller than both its baseline control (APS┴control) and the APS┬ following the longer IPI (Fig. 7.5B, left). The APS┴ then almost disappeared in the period of 0.6–17 s before reappearing with an increasing amplitude until it reached the APS┬ level. During the steady period of A-HFS┬┴, the amplitude ratio of APS┴steady/APS┴control was significantly greater than that of APS┬steady/APS┬control (Fig. 7.5B, right). The APS┴ showed a smaller suppression rate (~ 65%) than that of APS┬ (~ 81%). In contrast, when the same alternating IPI sequence (2.5 and 17.5 ms) was applied to A-HFS┼┼, the APS following shorter IPIs disappeared completely (refer to Sect. 6.2.1). The persistent APS┴steady following APS┬steady with the short 2.5 ms IPI demonstrated that APS┴steady was unaffected by the refractory period of the preceding APS┬steady. The result again confirmed that A-HFS┬┴ pulses of opposite polarities activated different subpopulation neurons. Then, which subset of neurons was activated by each type of pulses?
Fig. 7.5
Neuronal responses to A-HFS┬┴ with alternating IPIs of 2.5 and 17.5 ms. A Typical APS signal during 2 min 100 Hz A-HFS┬┴ with alternating IPIs. APS┬control and APS┴control, induced by single ┬ and ┴ pulses in baseline, are shown in the upper left. B Comparison of the normalized amplitudes of APS┬ and APS┴ at the onset and steady period of A-HFS┬┴. ***P < 0.001, paired t-test, n = 8 rats.
As described in Sect. 5.2.1, during the steady period of 50 Hz biphasic-pulse A-HFS┼┼, the suppression rate of APS┼ was approximately 60%. Similarly, in the 100 Hz A-HFS┬┴, where the ┴ pulses also had a frequency of 50 Hz, the suppression rate of APS┴ during the steady period was approximately 60%, too (Fig. 7.5B). Based on this, we inferred that the neuronal population originally activated by both ┬ and ┴ pulses could become responsive only to the ┴ pulses—not the ┬ pulses—during the steady period of A-HFS┬┴. At baseline, the activation area of ┬ pulse was larger than and encompassed that of ┴ pulse. Could sustained A-HFS┬┴ have made the activation capability of ┴ pulses to surpass that of ┬ pulses? To test this hypothesis, we designed the following experiment to make identical activation areas for both pulse types at baseline, then compared the neuronal responses to them during the steady period of A-HFS┬┴.
7.1.3 Only Positive Pulses Can Activate Neurons Initially Responsive to Both Pulse Types
At an identical intensity, the activation area of a ┬ pulse was larger than that of a ┴ pulse. To equalize the activation areas, we reduced the ┬ pulse intensity. However, using different intensities while keeping the same 100 μs pulse width would disrupt the charge balance during A-HFS┬┴. To preserve this balance, we added an opposite phase with 1/40 intensity and 40 × width immediately following each ┬ and ┴ pulse, creating quasi-monophasic-pulses (denoted as ┬Q and ┴Q). Their corresponding APSs were denoted as APS┬Q and APS┴Q (Fig. 7.6A1). Under baseline conditions, these pulses produced activation effects similar to those without a balance phase, as verified by comparable APS amplitudes (Fig. 7.6A2). This indicated that the balance phase did not substantially affect the action of the leading phase.
Fig. 7.6
Responses of neurons within the shared area activated by quasi-monophasic negative- and positive-pulses. AA1: Schematic diagram showing the creations of quasi-monophasic-pulses with a balance phase, denoted as ┬Q and ┴Q (left), along with typical APSs induced by these pulses (right). A2: Comparison of APS amplitudes induced by negative- and positive-pulses with and without a balance phase. BB1: APSs induced by single-pulses of 0.3–0.1 mA ┬Q and 0.3 mA ┴Q. B2: Comparison of the APS amplitudes induced by ~ 0.1 mA ┬Q and ~ 0.3 mA ┴Q. C APSs produced by paired-pulse stimulations of “┬Q┴Q” and “┴Q┬Q” (0.1 mA ┬Q and 0.3 mA┴Q) with short IPIs of 1, 1.5 and 2.5 ms. DD1: Typical APS signal during 100 Hz A-HFS┬Q┴Q alternating between 0.1 mA ┬Q and 0.3 mA ┴Q. D2: Comparison of APS┬Q and APS┴Q amplitudes in the steady period of A-HFS┬Q┴Q. EE1: Typical APS signal during 50 Hz A-HFS┴Q with mere 0.3 mA ┴Q pulses. E2: Comparison of mean amplitude ratios APS┴Q_steady/APS┴Q_control between A-HFS┬Q┴Q (shown in D1) and A-HFS┴Q (shown in E1). In A2, B2, and D2: n.s. P > 0.05, **P < 0.01, paired t-test. In E2: n.s. P > 0.05, t-test, n = 7.
During baseline tests, we kept the intensity of ┴Q while gradually reduced the intensity of ┬Q to match the APS┬Q amplitude with the APS┴Q amplitude (Fig. 7.6B1). The mean APS amplitude evoked by ┬Q at ~ 0.1 mA was similar to that evoked by ┴Q at ~ 0.3 mA (Fig. 7.6B2). Additionally, in paired-pulse stimulations of both “┬Q┴Q” and “┴Q┬Q” with IPIs ranging from 1 to 2.5 ms (Fig. 7.6C), the first APS showed consistent amplitude whether evoked by ┬Q or ┴Q. The second APS was fully suppressed at 1 ms IPI and emerged progressively as IPI increased. These results indicated that ┬Q and ┴Q shared a similar activation area.
These pulses were then applied alternately to form the A-HFS┬Q┴Q with a constant 10 ms IPI (Fig. 7.6D1). Initially, the amplitudes of APS┬Q and APS┴Q were similar, though both gradually decreased. During the steady period of the A-HFS┬Q┴Q, the APS┬Q almost disappeared while ┴Q pulses continued to produce clear APS┴Q events. The mean amplitudes of the two APS types differed significantly (Fig. 7.6D2). Additionally, when we removed all ┬Q pulses from the 100 Hz A-HFS┬Q┴Q to create an A-HFS┴Q with pure ┴Q pulses at 50Hz (Fig. 7.6E1), the ratio of APS┴Q_steady/APS┴Q_control in the A-HFS┴Q was comparable to that in the A-HFS┬Q┴Q (Fig. 7.6E2). These results showed that during the steady period of A-HFS┬Q┴Q, only ┴Q pulses were able to produce APSs in neurons within the shared activation area of both polarity pulses, similar to the action of ┴Q pulses in A-HFS┴Q without ┬Q pulses.
Furthermore, statistical data showed that during the ~ 2 to ~ 15 s A-HFS┬Q┴Q period, the mean amplitude of APS┬Q exceeded that of APS┴Q before eventually decreasing to below APS┴Q in the late period (Fig. 7.7). That is, during the transition period of declining APSs, the activation of ┴Q initially dropped below that of ┬Q but later rebounded to surpass it. Since current experimental techniques cannot effectively track pulse-induced action potentials in individual neuronal axons in the brain, we employed a computational axon model to simulate neuronal responses to both ┬ and ┴ pulses during A-HFS┬┴ to investigate the possible underlying mechanisms.
Fig. 7.7
Scatter plot showing mean normalized amplitudes of APS┬Q and APS┴Q produced by each pulse of A-HFS┬Q┴Q alternating between ~ 0.1 mA ┬Q and ~ 0.3 mA ┴Q. The light-colored ranges represent ± standard deviation.
7.2 Simulation Study of Axonal Activity During HFS with Alternating Opposite-Polarity Pulses
In addition to our findings shown in Chap. 5, the experimental results in Sect. 7.1 also demonstrate that HFS-induced suppression of neuronal activations must have originated in the axons rather than the somata. Otherwise, if the suppression had originated in the somata, the action potentials (AP) initially generated on axons by the two types of pulses during A-HFS┬┴ would not have produced distinct APS┬ and APS┴ suppressions, let alone the mere APS┴Q responses during sustained A-HFS┬Q┴Q. Therefore, to focus on the axonal mechanisms, we simulated the neuronal responses to A-HFS┬┴ using the model of myelinated axons in the NEURON simulation environment (Guo et al. 2018; Hu et al. 2023).
As shown in Fig. 7.8A, the axon model consisted of 21 Ranvier nodes (denoted as Node0 to Node20) and 20 myelinated internode segments. Please refer to the literature for detailed model parameters, including morphologic parameters, passive and active electrical properties of axon membrane, as well as the accumulation and clearance mechanisms of K+ in the narrow peri-axonal space (Guo et al. 2018; Bellinger et al. 2008; Beurrier et al. 2001). The structure and materials of the stimulation electrode (SE) in the model were consistent with those used in the rat experiments (refer to Sect. 3.4.2). The electrical field potential of A-HFS┬┴, delivered by the SE, was simulated in COMSOL Multiphysics 5.3 (COMSOL Inc. Sweden) and then loaded into the NEURON to mimic the bipolar stimulation in the rat experiments (Zheng et. al. 2020). The SE tip center was positioned above the central node (Node10) of the axon. To analyze the mechanisms of axonal responses to the alternating ┬ and ┴ pulses during A-HFS┬┴, the following model variables at each axonal node were recorded and analyzed: the membrane potential (Vm), the inactivation variable of Na+ channels (h_Na), and the K+ concentration in the narrow peri-axonal space ([K+]o).
Fig. 7.8
Computational model of axons positioned at different distances from the stimulation electrode (SE) and their responses to A-HFS┬┴. A Picture of the simulated electrical field potentials generated by a ┬ pulse. B Depolarization, hyperpolarization, and AP generated by single ┬ (left) and ┴ (right) pulses at different nodes along an axon. C Membrane potentials at Node0 (Vm_Node0) generated in the three types of axons shown in (A) during the onset, intermediate and steady periods of 100 Hz A-HFS┬┴. D Schematic summary of the three firing types shown in (C). Blue and orange dots represent successful activations by ┬ and ┴ pulses respectively, while black circles represent failed activations.
The h_Na variable represents the inactivation state of Na+ channels in the HH model of neuronal membrane (refer to Sect. 1.3). When the membrane is depolarized, voltage-gated Na+ channels open, triggering an action potential. These Na+ channels then rapidly enter an inactive state, becoming unresponsive to external stimuli during their refractory period. Once the membrane potential repolarizes, the inactive Na+ channels enter a closed state, after which they can be reactivated. However, if the membrane remains depolarized, the Na+ channels stay inactive. The h_Na value ranges from 0 to 1, where smaller values indicate more severe Na+ channel inactivation, making the axonal membrane harder to trigger action potentials. Therefore, analyzing h_Na values can reveal the change of neuronal excitability caused by stimulations.
As shown in Fig. 7.8B, since the central node (Node10) of the axon is located directly under the SE, a ┬ pulse can depolarize and initiate an AP at Node10 while simultaneously hyperpolarizing the nodes in the two flanking regions (e.g. Node8, denoted by the blue ◄ in the left column of Fig. 7.8B). In contrast, a ┴ pulse can depolarize and initiate APs at the flanking nodes (e.g. Node8 and Node12) while simultaneously hyperpolarizing Node10 (Fig. 7.8B, right column). With single-pulse stimulations, the AP initiated by either a ┬ or ┴ pulse can successfully conduct to the end of axon (e.g. Node0), provided that the ┬ pulse-induced AP at Node10 is strong enough to overcome the hyperpolarization at flanking nodes (Kiernan and Bostock 2000; van de Steene et al. 2020; Zheng et. al. 2022). We define an activation that can successfully conduct to Node0 as a successful activation; otherwise, it is a failed activation.
During A-HFS┬┴, membrane potentials at the Node0 (Vm_Node0, Fig. 7.8C) show three types of firing (denoted as Firing-A, -B and -C) on axons at varying distances from the SE (Fig. 7.8A). Firing-A and -B occur on axons within the activated area of both ┬ and ┴ pulses, while Firing-C appears only on axons activated by ┬ pulses. The axons showing Firing-A are closest to the SE, while those showing Firing-C are farthest away. As shown in Fig. 7.8C, in the onset period, the Firing-A axon follows each ┬ and ┴ pulse to fire an AP and successfully conducts it. However, during intermediate and steady periods, this axon fails at ┬ pulses while succeeding only at ┴ pulses. The Firing-B axon initially behaves like Firing-A but during the intermediate period, it succeeds only at ┬ pulses. Later, it switches to succeeding at ┴ pulses through the steady period. The Firing-C axon responds exclusively to ┬ pulses throughout the entire A-HFS┬┴.
The schematic summary of the three firing types (Fig. 7.8D) shows how their integration reproduces the observations from rat experiments (Fig. 7.7). The axons initially activated by both ┬ and ┴ pulses respond only to ┴ pulses during the steady period of A-HFS┬┴. Even when ┬ pulses temporarily dominate in the intermediate period, successful activations eventually switch to ┴ pulses alone. These simulation results are consistent with the experimental data, challenging the conventional view that ┬ pulses are more effective than ┴ pulses at activation. To reveal the underlying mechanisms, we next examine the dynamic changes in the axonal membrane from our simulation results.
The simulation shows that increased [K+]o in the peri-axonal space plays a critical role in generating axon activation failures during A-HFS┬┴ (Fig. 7.9). At Node10, where ┬ pulses initiate AP, sustained A-HFS┬┴ increases [K+]o_Node10 (Fig. 7.9A), leading to partial inactivation of Na+ channels. The inactivation variable of Na+ channels at Node10 (h_Na_Node10) decreases (Fig. 7.9B), resulting in reduced amplitude of the initial AP with ┬ pulses (Fig. 7.9C). These decreased APs at Node10 fail to propagate to Node0, causing activation failures (axonal block) at the ┬ pulses (Fig. 7.9D). A similar axonal block should occur in the activations of ┴ pulses that initiate APs at Node8. However, ┴ pulses can still generate successful AP in some axons (Firing-A and Firing-B in Fig. 7.8D). The following simulation results show how interactions between ┬ and ┴ pulses affect the generations of Firing-A and Firing-B, which succeed only at ┴ pulses during the steady period of A-HFS┬┴.
Fig. 7.9
Increased [K+]o generating axonal block during A-HFS┬┴. A [K+]o in the peri-axonal space near Node10 ([K+]o_Node10). B Inactivation variable of Na+ channels at Node10 (h_Na_Node10). In A and B, black dots on the curves mark the values when ┬ pulses arrive. C Membrane potential at Node10 (Vm_Node10). The APs initiated by ┬ pulses at Node10 are indicated by blue boxes. D Membrane potential at Node0 (Vm_Node0). Blue shadows denote the failures of AP conduction to Node0, representing axonal block.
Figure 7.10 illustrates an axon with Firing-A, showing the simulation data from Node10 to Node0 (top to bottom). At the onset of A-HFS┬┴ (Fig. 7.10A), the axon responds to each ┬ and ┴ pulses to initiate an AP at Node10 and Node8, respectively. These APs can successfully conduct to Node0. During the intermediate period (Fig. 7.10B), as h_Na_Node10 gradually decreases, the amplitude of APs initiated by ┬ pulses at Node10 also decrease. This reduces the AP conduction ability, eventually leading to conduction failure due to the strong hyperpolarization at Node8 (highlighted by the blue ◄ within the blue shadow in Fig. 7.10B). However, the attenuation of AP conduction to Node8 allows h_Na at Node8 to recover, resulting in increased h_Na_Node8 when the next ┴ pulse arrives (denoted by the orange arrow line on h_Na_Node8). The ┴ pulse then initiates an increased AP at Node8, which successfully conducts to Node0 (shown in green shadow in Fig. 7.10B). Simultaneously, this Node8-AP propagates in the opposite direction to Node10, inducing an AP (denoted by the red ▲ on Vm_Node10) larger than the AP induced by the previous ┬ pulse. This Node10-AP further decreases h_Na_Node10 before the next ┬ pulse. Repeatedly, the ┴-induced AP on Node10 causes the h_Na_Node10 to decrease progressively by the arrival of each subsequent ┬ pulse until the ┬ pulses can no longer initiate APs at Node10, resulting in generation failure of AP (Fig. 7.10C). In this process, once a ┬ pulse fails to make a successful AP, subsequent ┬ pulses cannot induce any propagable APs again.
Fig. 7.10
Changes in membrane potential (Vm) at each axon node during onset (A), intermediate (B) and steady (C) periods of A-HFS┬┴ in a Firing-A neuron. The h_Na curves at Node10 (h_Na_Node10) and at Node8 (h_Na_Node8) are shown below their corresponding Vm curves. Small squares on h_Na_Node10 and h_Na_Node8 respectively highlight the values when the ┬ and ┴ pulses arrive.
During the steady period of A-HFS┬┴ (Fig. 7.10C), the decreased h_Na at each axon node is steady. When a ┬ pulse arrives, h_Na_Node10 is too small to initiate an AP. However, a ┴ pulse can still initiate a propagable AP at Node8. Although the amplitude of Node8-AP decreases obviously due to the decreased h_Na_Node8, the AP is still able to propagate successfully since no hyperpolarization blocks its conduction pathway.
For an axon with Firing-B (Fig. 7.11), at the onset of A-HFS┬┴ (Fig. 7.11A), its firing resembles Firing-A, with successful AP reaching Node0 following each pulse. However, during the intermediate period (Fig. 7.11B), as h_Na decreases, the first conduction failure occurs with the AP induced by a ┴ pulse (shown in the orange shadow in the left of Fig. 7.11B), not by a ┬ pulse. This occurs because this axon locates farther from the SE than the axon with Firing-A, resulting in a weaker activation of ┴ pulses at Node8. Similarly, a ┬ pulse produces weaker hyperpolarization at the flanking regions of this axon. The hyperpolarization is insufficient to block the conduction of AP initiated at Node10, despite the initial AP having decreased due to decreased h_Na_Node10. Consequently, the ┴ pulse, being less effective at depolarizing the neuronal membrane, causes AP conduction failure before the ┬ pulse does.
Fig. 7.11
Changes in membrane potential (Vm) at each axon node during onset (A), intermediate (B) and steady (C) periods of A-HFS┬┴ in a Firing-B neuron. The h_Na_Node10 and h_Na_Node8 curves are shown below their corresponding Vm curves. Small squares on h_Na_Node10 and h_Na_Node8 respectively highlight the values when the ┬ and ┴ pulses arrive.
Nevertheless, after about 1.2 s of stimulation, as h_Na_Node10 continues to decrease, the further decreased AP—initiated by a ┬ pulse at Node10—fails to overcome the hyperpolarization in its conduction pathway, resulting in a conduction failure (shown in the blue shadow in the right of Fig. 7.11B). Once a ┬ pulse fails to generate a propagable AP, the failure facilitates h_Na_Node8 to recover, allowing a ┴ pulse to induce a successful AP (indicated by the orange arrow line on h_Na_Node8 and the green shadow in the right of Fig. 7.11B). This successful AP results in a further decrease in h_Na_Node10 when a ┬ pulse arrives, preventing the pulse from inducing a successful AP. Consequently, the neuronal response switches from a transition period with only ┬-induced APs to one with only ┴-induced APs (indicated by the red line at Vm_Node0 in the bottom of Fig. 7.11B). The subsequent process is similar to that of Firing-A, but with periodic conduction failures of APs initiated by ┴ pulses (indicated by the orange shadows in Fig. 7.11C). ┬ pulses no longer generate propagable APs due to failure at Node10.
In summary, the simulation results show that axonal responses to A-HFS┬┴ decline due to two failures: AP conduction failure and AP generation failure. Both failures originate from the HFS-induced increase of [K+]o in the narrow peri-axonal space, which elevates the axonal membrane potential and then inactivates Na+ channels partially. Due to hyperpolarization in the conduction pathway, an AP conduction failure eventually occurs upon a ┬ pulse. Once this occurs, subsequent ┬ pulses cannot succeed again due to the effect of ┴ pulse-induced APs. Additionally, AP conduction failure can first occur with a ┴ pulse-induced AP, resulting in the transition period where APS┬ > APS┴, as showed in Fig. 7.7. The transition period cannot prevent the eventual conduction failure of ┬ pulse-induced AP. Ultimately, no ┬ pulse but ┴ pulses can elicit AP successfully in the shared activation area of both polarity pulses. Therefore, the interactions among the neuronal responses to the opposite pulses result in the advantage of ┴ pulses.
Nevertheless, this simulation model only includes axons without other neuronal structures. While this simplification helps highlight axonal mechanisms in the stimulations, it may introduce bias by neglecting the influence of other structures. Additionally, besides the depolarization block at stimulated axons caused by increased [K+]o, the neuronal responses to A-HFS┬┴ could also involve more mechanisms or a combination of multiple mechanisms—all of which require further investigations.
7.3 Neuronal Responses to O-HFS with Alternating Opposite-Polarity Pulses
The above results indicate that opposite-polarity pulses can activate distinct subpopulations of neuronal axons when applied alternately in sustained A-HFS. If these pulse sequences were used as O-HFS to orthodromically activate downstream neurons through synaptic transmissions, the alternately activated axon subpopulations could produce strong excitatory inputs to postsynaptic neurons through numerous axonal terminals. Since these axonal activations occurred within a 10 ms or shorter IPI, the spatial and temporal integration of these synaptic inputs (refer to Sect. 2.2.3) could amplify these activations, enhancing the responses of postsynaptic neurons. To test this hypothesis, we applied the pulse sequences used in the A-HFS┬┴ to the Schaffer collaterals of rat hippocampal CA1 region as O-HFS┬┴.
We conducted the O-HFS┬┴ at three pulse frequencies (100, 133, and 200 Hz) and compared them with biphasic-pulse O-HFS┼┼ at the same frequencies. Figure 7.12A shows an example of 2 min O-HFS┬┴ at 133 Hz. In the early stimulation period, OPSs continuously occurred. The synchronous firing of neuronal populations resembled epileptiform discharge and lasted about 43 s. We termed this the “OPS period”. In the later O-HFS┬┴ period, no obvious OPSs appeared (though occasional OPSs reappeared in some rats). Figure 7.12B shows O-HFS┼┼ applied to the same rat for comparison. The OPS1 induced by the first pulse showed similar amplitude to that in O-HFS┬┴, but the OPS period lasted less than 10 s. No obvious OPSs appeared in the later O-HFS┼┼ period. At all three frequencies, O-HFS┬┴ consistently produced longer mean OPS periods than O-HFS┼┼ (Fig. 7.12C). The durations of OPS periods for both types of O-HFS decreased as pulse frequency increased. This result was consistent with the changes in the durations of initial OPS periods during O-HFS┼┼ at 50, 100 and 200 Hz (refer to Sect. 5.3.1).
Fig. 7.12
Comparison of neuronal responses to O-HFS┬┴ and O-HFS┼┼ in the Schaffer collaterals of rat hippocampal CA1 region. A, B Typical recordings of O-HFS┬┴ and O-HFS┼┼ at 133 Hz. C Comparisons of the mean durations of OPS periods produced by O-HFS┬┴ and O-HFS┼┼ at three frequencies (100, 133, and 200 Hz). *P < 0.05, paired t-test
During O-HFS┬┴, the frequency of each pulse type was half the stimulation frequency. Therefore, we next compared 200 Hz O-HFS┬┴ with 100 Hz O-HFS┼┼ (Fig. 7.13). Although the first ┬ pulse of O-HFS┬┴ and ┼ pulse of O-HFS┼┼ produced similar OPS1 amplitudes at onset, during the initial 0.2 s period, O-HFS┬┴ produced smaller OPSs than O-HFS┼┼. However, as stimulation continued, the subsequent OPSs in O-HFS┬┴ became larger than those in O-HFS┼┼ (Fig. 7.13A, B). Additionally, the mean OPS period duration in 200 Hz O-HFS┬┴ was longer than that in 100 Hz O-HFS┼┼ (Fig. 7.13C). This indicated that when the pulse frequency of each polarity in O-HFS┬┴ is same as that of O-HFS┼┼, O-HFS┬┴ can produce stronger activation.
Fig. 7.13
Comparison between neuronal responses to O-HFS┬┴ at 200 Hz and O-HFS┼┼ at 100 Hz. A, B Typical recordings of O-HFS┬┴ at 200 Hz and O-HFS┼┼ at 100 Hz, respectively. C Comparison of the durations of OPS periods produced by the two types of O-HFS
These results indicate that the activations of distinct subpopulation neurons by the opposite-polarity pulses during O-HFS┬┴ can enhance the excitatory effect on downstream neurons in the projection regions through synaptic integrations, thereby reducing the activation attenuation caused by axonal block.
7.4 Summary
The findings presented in this chapter challenge the conventional view of negative pulses being more effective than positive pulses. Usually, in extracellular stimulations, depolarization caused by a positive pulse is much weaker than that by a negative pulse at the same intensity, because a positive pulse depolarizes the axonal membranes on flanks of the stimulation site through a “virtual cathode” mechanism. Therefore, in baseline conditions, the APS induced by a positive pulse was much smaller than that induced by a negative pulse (Fig. 7.1C2, D1). However, during sustained HFS, the firing level produced by positive pulses became similar to that of negative pulses in the directly simulated neurons. Additionally, the two types of pulses activated distinct subpopulations of neurons. For neurons responsive to both types of pulses at baseline, positive pulses became more effective than negative pulses during steady HFS periods. Furthermore, alternating HFS with opposite monophasic-pulses is equivalent to inserting a short gap between the negative and positive phases of biphasic pulses. It can achieve safety similar to biphasic-pulse stimulation (refer to Fig. 7.3).
The simulation results of our computational axon model show the possible mechanisms behind neuronal responses to alternating monophasic-pulses of opposite polarity. The actions of the two types of pulses do not cancel each other out, but rather exhibit complex interactions. During HFS, the axonal membrane initially generates continuous action potentials (AP), which increases extracellular potassium concentration ([K+]o). The elevated [K+]o raises the membrane potential and partially inactivates Na+ channels. As the stimulation sustains, both types of pulses eventually begin to fail to induce and conduct APs. However, in the shared activation area of both types of pulses, the activation effect of positive pulses surpasses that of negative pulses.
These findings provide clues for designing new stimulation patterns for neuromodulation. During sustained HFS with alternating negative- and positive-pulses, the opposite pulses activate two subpopulations of neurons, whose discharges are not constrained by the refractory period from each other’s firing (Figs. 7.4 and 7.5), resulting in enhanced activations on projection neurons (Figs. 7.12 and 7.13). The stimulation electrodes used in our experiments were coaxial bipolar electrodes with an inner polar surface area of only 0.028mm2 (see Fig. 3.13 in Sect. 3.4.2)—about one-third of the outer polar surface area. This small inner polar can create higher current density and stronger electric field near the electrode tip, making it the active electrode in the bipolar stimulation. Despite the small active region, our experimental results indicate that alternating negative- and positive-pulses can generate substantial synchronous discharge in downstream postsynaptic neurons by amplifying the activations induced in the directly stimulated axons.
This type of alternating stimulations with opposite-polarity pulses may improve the efficacy of certain neuromodulation therapies. For example, previous studies on the thresholds and loudness of cochlear implants (CI) in patients have shown that HFS with alternating monophasic-pulses of opposite polarity at specific intervals is more effective than biphasic-pulses (van Wieringen et al. 2005, 2006). The results in this chapter suggest that this improvement may be due to the enhanced HFS activations. Other studies have shown that one of the important roles of DBS therapy is to generate new neuronal activity to replace and mask pathological activity (Chiken and Nambu 2016; Lee et al. 2019). The enhanced excitatory effect from opposite pulses could therefore improve DBS efficiency. Conventional HFS used in current DBS can cause axonal depolarization block and synaptic transmitter depletion—which help block pathological activity but reduce the excitatory effect of stimulation, limiting its ability to produce new neuronal activity. Our simulation results in Sect. 7.2 show that HFS with alternating negative- and positive-pulses can maintain the axonal block effect. Rat experiments with A-HFS confirm that this stimulation paradigm can achieve comparable axonal block to biphasic-pulse HFS (Fig. 7.2). Therefore, the alternating stimulations may both enhance the excitatory effect of stimulation and prevent the spread of pathological neuronal activity. Additionally, this method consumes only half the electric energy of biphasic-pulse HFS at the same stimulation frequency, making it more energy-efficient.
Some neural prostheses that use electrical stimulations could potentially utilize this characteristic of monophasic pulses with opposite polarities to activate different neuron subpopulations. Some implanted neural prostheses use multi-contact microelectrodes or arrays to deliver stimulation pulses for neural coding, such as auditory midbrain implants (AMI) (Lim and Lenarz 2015), visual cortical prostheses (VCP) (Fernández et al. 2021), and tactile implants in the somatosensory cortex (Hughes et al. 2021). Delivering opposite-polarity pulses alternately through a stimulation contact could add a new dimension to neural coding by activating different subgroups of neurons. These neuronal responses could be fine-tuned by varying pulse parameters, including intervals between opposite polarity pulses, pulse intensity ratios, and frequency ratios, to encode neural information. However, the practical implementation of such approach requires more research.
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