6. Neuronal Responses to Axonal HFS with Time-Varying Parameters

Figures 5.2 and 5.7 in Chap. 5 show the changes in the APSs induced by antidromic activation of CA1 pyramidal neurons during constant A-HFS applied at alveus. The initial APS amplitude at the onset of 100 Hz A-HFS was approximately 5 times its steady amplitude in the late A-HFS period. To prevent the large initial APSs, we used a modified A-HFS train including an initial 10 s ramp-up pulse intensity linearly from 0.02 to 0.2 mA before remaining constant at 0.2 mA for 50 s until the end of stimulation (Fig. 6.1A). The small 0.02 mA initial intensity hardly induced any APSs. As the intensity gradually increased, the evoked APS gradually appeared with increasing amplitude. However, no large APS appeared throughout the entire 1 min A-HFS. The peak APS (only ~ 3 mV) appeared at ~ 6 s when the intensity increased to ~ 0.13 mA (Fig. 6.1B). During the late 40 s period with the fixed 0.2 mA intensity, the APS amplitudes matched those evoked by the control A-HFS with a fixed 0.2 mA intensity from beginning to end, in the same rat experiment. But, the initial APS evoked in the control A-HFS exceeded 10 mV (Fig. 6.1B).

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While the duration of ramp-up transition period in Fig. 6.1 was set as 10 s, shortening this duration could speed up the extension of stimulated area to a desired range. We compared the changes in APS amplitudes with three different transition periods of 1, 5 and 10 s (Fig. 6.2A). With a 1 s transition, the peak APS only decreased to ~ 90% of the control, significantly greater than with 5 s (~ 60%) and 10 s (~ 40%) transitions (Fig. 6.2B). While merely shortening the transition caused large APS to reappear, simultaneously increasing pulse frequency could suppress the APSs. With a 1 s transition, increasing the pulse frequency from 100 to 400 Hz resulted in significantly smaller peak APS than that of 100 and 200 Hz (Fig. 6.2C and D). Therefore, we next tested a paradigm using higher pulse frequency and ramp-up intensity in a shortened transition period at the beginning of A-HFS.

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As shown in Fig. 6.3, we designed a 100 s A-HFS train where the first 10 s used a 400 Hz frequency with a ramp-up intensity from 0.03 to 0.3 mA, followed by 90 s at constant 100 Hz and 0.3 mA. No large APS appeared during the initial 10 s period. However, when the frequency dropped suddenly from 400 to 100 Hz at 0.3 mA intensity, a large APS occurred due to the abrupt IPI change from 2.5 to 10 ms. This APS reached approximately half the baseline amplitude. Then the evoked APS gradually decreased to a steady level.

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To prevent the large APSs triggered by the abrupt frequency change, we designed an A-HFS train with three distinct periods: an initial 1 s period at 400 Hz with intensity ramping up from 0.03 to 0.3 mA, followed by a 10 s period at 0.3 mA with frequency ramping down from 400 to 100 Hz (using a reciprocal frequency decay curve from linearly increasing IPIs, as detailed in Cai et al. 2018), and a final 49 s period of constant stimulation at 0.3 mA and 100 Hz—completing a total 60 s A-HFS train.

Figure 6.4A shows an example of neuronal responses to this A-HFS paradigm. During the initial 1 s period, the maximum APS amplitude was only 3.2 mV. In the subsequent 10 s period, as frequency gradually decreased, the APS amplitude increased slightly. During the final 49 s period with constant stimulation parameters, the APS amplitude remained small (the black scatter plot in Fig. 6.4B). In contrast, the control A-HFS with constant parameters of 0.3 mA and 100 Hz produced a maximum APS amplitude of 10.3 mV at onset (the grey scatter plot in Fig. 6.4B). The late 49 s period showed no significant difference between control and varying A-HFS. Statistical results showed that during the initial 11 s transition period, the varying A-HFS induced a maximum APS amplitude of only 33 ± 5.0% (n = 7 rats) of the value of constant A-HFS (0.3 mA, 100 Hz). The mean APS amplitudes during the late 49 s period (from 11 to 60 s) were similar between both paradigms (Fig. 6.4C). The APS recovered quickly within 2 min after A-HFS ended, indicating that the 400 Hz transition period stimulation is safe, despite requiring higher electrical power consumption.

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The above results indicate that using ramped intensity and frequency during the initial A-HFS period can reshape the neuronal responses, preventing synchronous firing of large neuronal populations at stimulation onset. During the transition period with ramp-up intensity, the initial weak intensity activated too few axons to generate large APSs. As intensity increased, the stimulated area gradually expanded and more axons were activated. However, even when the intensity reached that of constant A-HFS, the evoked APS remained much smaller than that at the onset of constant A-HFS. Additionally, the peak APS amplitude was smaller with either a slower intensity increase (Fig. 6.2A and B) or a higher pulse frequency (Fig. 6.2C and D). These responses can be explained by HFS-induced axonal block. By the time pulse intensity reaches and maintains its upper level, axonal block has already developed in the early stimulated axons. Each pulse can then only activate a subset of stimulated axons, keeping the APS amplitude well below baseline level. While a slower ramp-up intensity can provide sufficient time for more axons to gradually enter block states, it also slows the stimulation to reach the desired action area. Higher pulse frequencies can enable axons to enter their block states more quickly (refer to Sect. 5.2). Therefore, using a higher frequency can allow to shorten the initial transition period of ramped intensity. Adding a subsequent period with ramp-down frequency can reduce the frequency to the desired level. This approach—combining two transition periods with varying parameters—can quickly achieve a sufficiently large stimulated area while preventing synchronous firing of large neuronal populations (Fig. 6.4).

Similar stimulation paradigms have been used in peripheral nerve stimulations to minimize onset responses (Bhadra et al. 2009; Bhadra and Kilgore 2005; Miles et al. 2007; Gerges et al. 2010). However, this approach has not been applied to clinical brain stimulations like DBS therapy. The highly synchronized neuronal firing produced by HFS resembles epileptiform activity that could be harmful to the brain. Clinical observations have shown that frequent ON/OFF stimulations at intervals shorter than one minute can reduce DBS efficacy in controlling the symptoms of Parkinson’s disease (Khandhar et al. 2005). Similarly, periodic DBS is less effective at relieving patient tremors compared to conventional DBS (Kuncel et al. 2012). While the mechanisms behind these phenomena remain unclear, the onset response may be a contributing factor. If this is true, addressing the onset responses can be crucial for improving adaptive stimulation treatments that require frequent ON/OFF switching.

To investigate how changes in pulse intervals affect neuronal population responses, we still examined the neuronal responses to antidromic stimulations (Fig. 6.5A). As controls, we first evaluated the APS amplitude ratios (APS₂/APS₁) produced by paired-pulses with various IPIs (Fig. 6.5B). With IPIs ranging in 5–50 ms and an identical 0.3 mA pulse intensity, both pulses in the pairs produced large APSs of similar amplitude. Even with an IPI as short as 5 ms, the amplitude of the second APS (APS₂) was above 85% of the first APS (APS₁), indicating minimal impact of APS₁ on APS₂. When the IPI exceeded 12 ms, the APS₂/APS₁ ratio approached 100%, showing no effect of APS₁ on APS₂. This occurred because the refractory period of CA1 pyramidal neurons is shorter than 5 ms under baseline conditions. Additionally, the activation of neuronal soma through antidromic stimulation on its own axon does not involve synaptic integration. As a result, antidromic activation is hardly affected by local inhibitory circuits. The antidromic response thus differs from the orthodromic response of paired-pulse stimulation applied at the Schaffer collaterals, which is strongly affected by inhibitory circuits (refer to Sect. 2.3).

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As shown in Fig. 6.6A, during 1 min A-HFS with a fixed frequency of 66.7 Hz, large APSs appeared only at onset, despite the IPI being as long as 15 ms. After ∼ 1 s A-HFS, the APS amplitudes decreased markedly, and after∼10 s A-HFS, they declined to ∼ 25% of the initial amplitude (Fig. 6.6B). Interestingly, during the 1-10 s A-HFS period when APS amplitudes decreased substantially, a bifurcation emerged between adjacent APSs. Larger (∼ 4 mV) and smaller (∼ 1 mV) APSs appeared alternatively, despite the constant IPI. In the study of 16 rats applied with mono-IPI A-HFS at 66.7 Hz, such APS bifurcation appeared in 6 (38%) rats and lasted only several seconds, after which the evoked APSs became uniformly small. During the steady A-HFS period, the mean APS amplitudes were similar in groups both with and without bifurcation.

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When a 1 min bi-IPI A-HFS was applied with alternating IPI of 12 and 18 ms (ΔIPI = 6 ms), the mean pulse frequency remained at 66.7 Hz. Large APSs appeared at onset with similar amplitudes despite the alternating IPIs (Fig. 6.6C), similar to the APSs induced by paired-pulses (IPI = 12 or 18 ms) at baseline (Fig. 6.5B). However, after 1 to 2 s, as APS amplitude decreased, a bifurcation appeared and persisted until the end of A-HFS (Fig. 6.6D). During the steady A-HFS period, the mean APS amplitude following the shorter IPI = 12 ms (denoted as APS_S) was only 14.8 ± 9.1% of that following the longer IPI = 18 ms (APS_L). The APS_S/APS_L ratio was far smaller than the IPI ratio of 12/18 = 67%. Additionally, the APS_L amplitude was significantly greater than the APS amplitude induced by mono-IPI A-HFS at 66.7 Hz (Fig. 6.6E). However, the average APS amplitude in bi-IPI A-HFS was similar to that of mono-IPI A-HFS, indicating that both types of A-HFS produced similar levels of neuronal firing given the same number of applied pulses.

These results indicated that even with A-HFS at a constant IPI, a brief period of APS bifurcation can occur during the APS decay phase before stabilization—characterized by alternating larger and smaller amplitudes. Such brief bifurcation in constant A-HFS often appeared at pulse frequencies between 50 and 70 Hz, but not at higher frequencies (e.g., 100 or 200 Hz) or lower frequencies (e.g., 20 or 10 Hz). During bi-IPI A-HFS, the bifurcation persisted until the end of A-HFS, suggesting a gradual transfer of firing from following the shorter IPI to the longer IPI. The APS attenuation during A-HFS results from intermittent axonal block, with the degree of attenuation depending on pulse frequency (see Sect. 5.2). Therefore, we next examined how neuronal populations respond to bi-IPI A-HFS across various mean pulse frequencies.

In the 1 min bi-IPI A-HFS, we fixed the ratio of the shorter IPI (IPI_S) to longer IPI (IPI_L) at 2/3, corresponding to a ΔIPI ratio (ΔIPI/mean IPI) of 40%. We varied the mean A-HFS frequency in a range of 16–200 Hz, corresponding to a ΔIPI range of 25–2 ms. Here, we tentatively use “HFS” to refer to all these stimulations, although neuromodulation stimulations at 50 Hz and above are commonly referred to as HFS (Durand and Bikson 2001). As shown in Fig. 6.7A, during the onsets of bi-IPI A-HFS with various ΔIPI, each pulse consistently induced a large APS with similar amplitude despite the alternating IPIs. The APS amplitudes then decreased as A-HFS progressed, with higher average pulse frequencies leading to more rapid decreases. The mean APS amplitudes at the end of A-HFS were always significantly smaller than their initial values (Fig. 6.7B).

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At a lower mean frequency of 16 Hz, the APS amplitudes decreased slightly and slowly, maintaining more than 50% of the initial amplitude until the end of stimulation. No bifurcation appeared during the entire 16 Hz A-HFS, even with a ΔIPI as long as 25 ms. When the mean pulse frequency increased to 50 Hz and above (including 66.7, 100, 133 and 200 Hz), the APS amplitudes decreased more and quickly. The decrease speed was frequency-dependent. The half-amplitude time—the duration until APS amplitude decreased to half its initial value—dropped significantly from ∼ 20 s at 50 Hz to ∼ 0.2 s at 200 Hz (Fig. 6.7C). A bifurcation appeared along with the APS attenuation and persisted to the end of A-HFS (Fig. 6.7A, right). Higher pulse frequencies triggered earlier bifurcation, with initial times ranging from ∼ 6 s at 50 Hz to ∼ 0.1 s at 200 Hz (Fig. 6.7D). As the mean pulse frequency increased, a greater proportion of APS_S shifted to APS_L. At 133 Hz and above, the APS_S almost disappeared. Only the pulses following IPI_L induced APS, despite the IPI_S/IPI_L ratio remaining at 2/3 (Fig. 6.7A and E).

These results indicate that when the mean pulse frequency is sufficiently high, even a tiny ΔIPI in bi-IPI A-HFS can induce a bifurcation in neuronal responses. Since clinical DBS typically uses pulse frequencies between 100 and 200 Hz—particularly around 130 Hz—we set the mean pulse frequency to 133 Hz (with a mean IPI of 7.5 ms) to determine the minimum ΔIPI needed to induce a bifurcation. Figure 6.8A shows examples of APS signals in different periods of bi-IPI A-HFS with ΔIPI of 0, 0.2, 1 and 3 ms, respectively. The scatter plots of APS amplitudes are shown on the right side of the figure. At ΔIPI = 0 ms (mono-IPI A-HFS as control), no bifurcate appeared in the APS amplitudes (Fig. 6.8A1). However, with the other three ΔIPIs, a bifurcation began shortly after A-HFS onset and persisted until the end of A-HFS (Fig. 6.8A2–A4). In the final second of 1 min A-HFS, the amplitude of APS_L following the longer IPI was significantly greater than the amplitude of APS_S following the shorter IPI (Fig. 6.8B). Especially, when the two IPIs were 7.4 and 7.6 ms with a ΔIPI of only 0.2 ms and a ratio ΔIPI/mean IPI = 2.7%, about 20% of neuronal firing transferred from APS_S to APS_L. When ΔIPI increased to 3 ms or above (ΔIPI/mean IPI ≥ 40%), APS_S almost disappeared (Fig. 6.8A and B).

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With similar APS amplitudes (APS_S/APS_L ≈ 1.0) at the onset of A-HFS, the APS_S/APS_L ratios fell significantly below 1 in the final second of the A-HFS with the non-zero ΔIPI values (0.2, 1, 3 and 5 ms). The APS_S/APS_L ratios decreased exponentially as ΔIPI increased, with a determination coefficient R² = 0.99 (Fig. 6.8C). Additionally, in the final second of A-HFS with different ΔIPI, the mean APS amplitudes (sum of APS amplitudes/pulse number) showed no significant differences (Fig. 6.8D). This indicated that at a same mean frequency of 133 Hz, these A-HFS trains generated similar levels of neuronal firing in the steady period. However, the temporal structure of the pulse trains (the different IPIs) altered the timing of neuronal responses by redistributing firing between IPI pairs.

Furthermore, when the order of the IPI pairs in an A-HFS train switches from shorter-longer to longer-shorter, the APS amplitudes can quickly adapt to the change. Figure 6.9 shows an example of this change in a bi-IPI A-HFS with a 133 Hz mean frequency at 0.3 mA. Initially, the A-HFS ran with IPI pairs of 7.4 ms followed by 7.6 ms for 30 s. During the steady period, the APS amplitude after the longer IPI (7.6 ms) was approximately double that following the shorter IPI (7.4 ms). At 30 s, the order of IPI pairs switched to 7.6 ms first then 7.4 ms, resulting in two consecutive 7.6 ms IPIs at the switching point. Following the second 7.6 ms IPI (marked by the red arrow in the figure), the induced APS was smaller, indicating a delay in neuronal response to the IPI change. Within several IPIs, the neuronal responses adjusted to produce a larger APS following the longer IPI. The scatter plot shows that the APS amplitudes following odd pulses (blue dots) and even pulses (orange dots) exhibit an “X” pattern around the IPI switch, as one APS group decreasing while the other increasing.

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These results indicate that at a sufficiently high mean frequency, even a sub-millisecond difference in IPI can lead to a bifurcation in the neuronal population responses to bi-IPI A-HFS. Besides IPI, we hypothesized that small changes in other A-HFS parameters might also generate similar bifurcations in neuronal responses. Therefore, we investigated the neuronal responses to bi-intensity A-HFS.

We set three bi-intensity pairs with small differences: 0.10 and 0.11 mA, 0.30 and 0.31 mA and 0.60 and 0.62 mA. In baseline single-pulse stimulations at these intensities, the APS amplitude increased with pulse intensity (Fig. 6.10A). In separated paired-pulse stimulations (IPI = 7.5 ms) at these bi-intensity pairs (Fig. 6.10B), the weaker intensity pair (0.10 and 0.11 mA) produced an APS₂ amplitude that was slightly greater than the APS₁ amplitude, resulting in an APS₂/APS₁ ratio above one (Fig. 6.10C). With the other two stronger bi-intensity pairs, the APS₂/APS₁ ratios were both below one, indicating a slight inhibitory effect of APS₁ on APS₂ at the 7.5 ms IPI.

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We created 1 min A-HFS trains respectively using the three bi-intensity sets to form stimulations with alternating intensities at a constant 133 Hz (IPI = 7.5 ms). As shown in Fig. 6.10D, the APS amplitudes decreased rapidly during initial A-HFS periods, with stronger bi-intensity causing faster decreases. The half-amplitude times of APS attenuation differed significantly among stimulations with different bi-intensity sets (Fig. 6.10E). As APS amplitude decreased, a bifurcation appeared during all the bi-intensity A-HFS trains—smaller APSs followed weaker pulses while larger APSs followed stronger pulses (Fig. 6.10D). This bifurcation response contrasted with both the baseline situation and the initial response to the first pulse pair at A-HFS onset, where the weaker pulse induced a larger APS at the stronger bi-intensities of 0.30 and 0.31 mA and 0.6 and 0.62 mA. When we swapped the order of two intensities in bi-intensity A-HFS, the APS bifurcation still appeared, maintaining larger APS following stronger pulses. The APS₂/APS₁ amplitude ratio increased from ∼ 1 at onset to ∼ 3 during the final second of A-HFS (Fig. 6.10F), reaching nearly triple the intensity ratios of 1.1 (0.11/0.10) and 1.03 (0.31/0.30 and 0.62/0.60). This showed that a mere 3–10% difference in pulse intensities produced a ∼ 200% difference in APS amplitudes, indicating nonlinear neuronal responses to the intensity changes.

The results demonstrate that while small differences in bi-intensity A-HFS cannot produce substantial changes in baseline neuronal responses, they can generate substantial bifurcation in neuronal responses during sustained stimulations, similar to bi-IPI A-HFS.

As described above, during sustained A-HFS with either bi-IPI or bi-intensity (referred to as bi-pulse A-HFS), APS bifurcations caused neurons to fire mostly following every other pulse. This produced an APS sequence similar to the pattern induced by mono-IPI or mono-intensity A-HFS (referred to as mono-pulse A-HFS) at half frequency. It raised a question: what were the effects of those pulses that rarely produced APS in bi-pulse A-HFS? To address this question, we next compared neuronal excitability between bi-pulse A-HFS and mono-pulse A-HFS at half frequency by inserting test pulses into the A-HFS trains.

As shown in Fig. 6.11A–C, we compared the A-HFS of bi-IPI (5 and 10 ms) with the A-HFS of mono-IPI (15 ms). During the steady period of the 133 Hz bi-IPI A-HFS, only pulses following the longer IPI (10 ms) induced an APS, while pulses following the shorter IPI (5 ms) induced no obvious APS (Fig. 6.11A upper). The mean APS amplitude following the longer IPI was similar to that induced by mono-IPI A-HFS pulses at 66.7 Hz (Fig. 6.11A and B). The test pulse inserted in the middle of the longer IPI in bi-IPI A-HFS induced an APS that was much smaller than the corresponding APS induced in mono-IPI A-HFS (Fig. 6.11A). Although the preceding APSs were similar (A_Bi/A_Mono ≈ 100%), the mean APS amplitude induced by the test pulses during bi-IPI A-HFS (A_Bi-test) was only ∼50% of those during mono-IPI A-HFS (A_Mono-test). Across all six insertions spaced 9 s apart during 1 min A-HFS, the A_Bi-test/A_Mono-test ratios were significantly smaller than the A_Bi/A_Mono ratios (Fig. 6.11C). This indicates that neurons had lower excitability during pulse intervals of higher-frequency bi-IPI A-HFS.

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Similarly, we compared bi-intensity 133 Hz A-HFS (at an average pulse intensity of 0.3 mA) with mono-intensity 66.7 Hz A-HFS at 0.3 mA (Fig. 6.11D–F) using test pulses. Both A-HFS modes had mono-IPI of 7.5 and 15 ms respectively, with a test pulse inserted every 9 s. In the bi-intensity (0.29 and 0.31 mA) A-HFS, the test pulse was inserted at 11.5 ms after the stronger pulse (i.e., at the middle between 0.29 and 0.31 mA pulses). In the mono-intensity A-HFS, the test pulse was inserted at the same timing of 11.5 ms after an A-HFS pulse (Fig. 6.11D). The mean APS amplitude induced by weaker pulses in bi-intensity A-HFS was significantly smaller than those induced both by stronger pulses and in mono-intensity A-HFS (Fig. 6.11E). Test pulses in bi-intensity A-HFS hardly induced APS (A_Bi-test). Across all six insertions during 1 min A-HFS, the APS ratios of A_Bi-test/A_Mono-test ≈ 10% were significantly smaller than the preceding APS ratios of A_Bi/A_Mono ≈ 80% (Fig. 6.11F). Again, this result confirms that neuronal excitability during the pulse interval was lower in higher-frequency A-HFS.

The experiments shown in Fig. 6.11 indicate that the neuronal excitability in the pulse interval can weaken during bi-pulse A-HFS trains with twice the pulse number, even though their APS sequences are similar to mono-pulse A-HFS trains. This means that the additional pulses in the higher-frequency A-HFS create a deeper axonal block, despite similar firing levels. This finding is consistent with the results showing similar neuronal firing levels during steady periods of A-HFS at different frequencies ranging in 50–200 Hz, as described in Sect. 5.2.2 (see Fig. 5.7G).

Bifurcation refers to a radical change in the rate and/or timing pattern of neuronal firing caused by small alterations in external inputs when nonlinear neurons are unstable near a bifurcation point. While previous studies focused mainly on bifurcations in individual neurons, our study explored this phenomenon in neuronal populations. We showed that small changes in both the IPI and intensity of bi-pulse A-HFS can lead to bifurcation in population-level neuronal responses. Additionally, our study was conducted in the intact brain in-vivo, making the results more clinically relevant than in-vitro studies. The mechanism of intermittent axonal block produced by A-HFS suggests that the stimulation-induced depolarization may bring the axonal membrane near a bifurcation point, where sodium and potassium channels can change more rapidly and sensitively than at rest (Hodgkin and Huxley 1952; Kocsis et al. 1983; Zheng et al. 2020). Consequently, tiny changes in stimulation excitatory inputs from varying parameters—such as IPI and pulse intensity—can result in neuronal firing bifurcation, whereas such small changes cannot make substantial difference under baseline conditions.

In addition, a single pulse applied extracellularly at the alveus of hippocampal CA1 region can activate a bundle of axons simultaneously. The coupling between adjacent axons may also contribute to firing bifurcation in neuronal populations. Previous studies have shown that electrical coupling between axons in the hippocampal region can lead to extremely rapid synchronous activity in neuronal populations (Blankenship and Feller 2010; Molchanova et al. 2016; Schmitz et al. 2001). During sustained A-HFS, this coupling mechanism may cause axonal firing to increasingly follow longer IPI or stronger pulses due to their facilitation effects. This firing convergence can amplify the firing difference between pulses with slightly different parameters, resulting in bifurcation.

In summary, with the combined effects of intermittent depolarization block and axonal coupling, even small changes can alter the firing patterns of neuronal populations during sustained bi-pulse A-HFS. Additionally, although the pulses with weaker parameters in bi-pulse A-HFS cannot directly produce substantial neuronal firing, they can maintain the depolarization block on neuronal membrane, preventing neurons from responding to additional activations between pulses (see Fig. 6.11).

In the experiments with inserted test pulses shown in Fig. 6.11A and D, we observed that a pulse insertion produced a series of firing changes in the subsequent A-HFS period that differed from the pre-insertion firing. This implied that a single pulse insertion could generate substantial changes in neuronal responses well beyond the immediate pulses. During high-frequency stimulations, axons may behave like taut strings—a strike can produce a period of vibrations. This led us to investigate the effects of deleting and inserting pulses during HFS with constant parameters as shown below.

During the steady period of 100 Hz A-HFS, we deleted a pulse to extend a 10 ms IPI to a 20 ms gap (Fig. 6.12A1). We labeled the APS evoked by the first A-HFS pulse as APS_init, the APS evoked by the pulse preceding the gap (P₀) as APS₀, and the APS that would have been evoked by the deleted pulse (P₁) as APS₁. For the pulses following the gap, we labeled their evoked APSs sequentially as APS₂, APS₃, …, APS_k, with their corresponding pulses labeled as P_k. The APS₁ amplitude was zero due to the absence of P₁ (Fig. 6.12A1 and A2). The 20 ms gap caused the APS₂ amplitude to increase significantly—reaching approximately 3 times the APS₀ amplitude and half of the APS_init amplitude (Fig. 6.12A3). However, the following APS₃ was small again. Subsequently, the evoked APSs alternated between large and small amplitudes for a period (Fig. 6.12A2, top).

The increase in APS₂ amplitude resulted from more neuronal recovery in the prolonged gap interval (refer to Sect. 5.2.2). By this logic, shortening the interval by inserting a pulse should decrease the subsequent APS. Indeed, inserting a pulse in the middle of 10 ms IPI hardly produced an APS (APS₁) following the subsequent pulse P₁ (Fig. 6.12B1 and B2). The inserted pulse itself neither produced an APS. However, the APS₂—produced by the second pulse P₂ after the insertion—increased significantly to ∼ 2 times the APS₀ amplitude and∼1/3 of APS_init amplitude (Fig. 6.12B3). Subsequently, an oscillation between larger and smaller APSs appeared (Fig. 6.12B2, top), resulting in an APS pattern similar to that produced by the opposite manipulation of deleting a pulse—an unexpected result.

After normalization by APS₀ amplitude, the mean amplitudes of APS₁ through APS₈ following the deleted or inserted pulse showed clear changes: significant decreases in APS₁, APS₃, APS₅ and APS₇, alongside significant increases in APS₂, APS₄, APS₆ and APS₈ (Fig. 6.12C1 and C2). Additionally, the mean normalized APS₂ amplitude was significantly greater following the deleted pulse (3.0 ± 0.38, n = 7) than following the inserted pulse (2.0 ± 0.22, n = 7; t-test, P < 0.001). The APS latencies showed no substantial changes following both the deleted and inserted pulse (Fig. 6.12D). These results showed that during the steady period of 100 Hz A-HFS, both shortening the IPI by inserting an pulse and extending it by deleting a pulse can produce similar oscillations in the subsequent APSs.

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To investigate how the timing of inserted pulse affects responses, we inserted pulses at nine different time points during the steady period of late 60 s in 2 min A-HFS. The pulses were inserted at 1, 2, … and 9 ms (denoted as Δt = 1, 2, …, 9 ms) within the 10 ms IPI. We performed these nine insertions in each A-HFS in random order, spacing them 5 s apart (Fig. 6.13A). At Δt ≤ 7 ms, the inserted pulse hardly produced APS, while the APS₁ evoked by the subsequent pulse (P₁) gradually decreased to a disappearance as Δt increased. At Δt = 8 and 9 ms, the inserted pulse produced an APS (also denoted as APS₁), but P₁ produced no APS.

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When the inserted pulse occurred around the middle of 10 ms IPI (e.g. Δt = 6 ms), the oscillations of subsequent APSs were greater. As shown in the bottom of Fig. 6.13B, two indices were used to evaluate the oscillation in the normalized APS amplitudes. The first was oscillation magnitude, defined as the difference between the maximum and minimum APS following the insertion, i.e., the difference between the normalized amplitude of APS₂ and APS₁. The second was oscillation duration, defined as the period during which the larger APSs (those with even subscripts) monotonically decreased. Both indices changed non-monotonically with insertion time Δt, showing a pattern of slower increase followed by rapider decrease (Fig. 6.13C). The indices peaked around Δt = 6 ms. At Δt = 1 and 9 ms, both the mean oscillation magnitudes and durations were minimal. However, at Δt = 1 ms, the APS₁ was produced by the A-HFS pulse, whereas at Δt = 9 ms, it was produced by the inserted pulse.

The APS oscillation produced by the inserted pulse suggested a redistribution of neuronal firing. For example, when inserting a pulse at Δt = 6 ms, the APS_k alternated between smaller and larger amplitudes, yet the average amplitudes of adjacent APS pairs remained similar to the APS₀ amplitude (Fig. 6.13D). This pattern indicated that the insertion did not significantly change the total neuronal firing but shifted the firing from APS₁ to APS₂, thereby creating a damped oscillation in the subsequent APSs.

To investigate whether more neuronal firing could be postponed through repeated insertions, we added four pulses respectively in four successive IPIs at Δt = 6 ms, and applied this four-pulse insertion at 60, 80 and 100 s of A-HFS repeatedly (Fig. 6.14A, top). The inserted pulses were labeled as p₁, p₂, p₃ and p₄. Neither p₁ nor its immediately subsequent A-HFS pulse produced an APS, which was consistent with the results of single-pulse insertion. The inserted pulses p2, p3 and p4 produced small APSs (shown as red dots in Fig. 6.14A bottom), while none of the four A-HFS pulses following the inserted pulses produced any obvious APS (shown as green dots). After the insertion completed, the APS sequence (APS₁, ₂ …… _k) showed temporary amplitude oscillations, similar to the pattern observed with single-pulse insertion (Fig. 6.14B). Both the mean magnitude and duration of the APS oscillations after the four-pulse insertion showed no significant difference from those following single-pulse insertion (Fig. 6.14C).

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The mean duration from the beginning of the four-pulse insertion to the end of APS oscillation was approximately 0.24 s, including a 0.04 s insertion period and a 0.20 ± 0.07 s oscillation period (Fig. 6.14C2). The corresponding duration for the single-pulse insertion was approximately 0.25 s, including a 0.01 s insertion period and a 0.24 ± 0.10 s oscillation period. To compare neuronal firing levels, we calculated the sums of APS amplitudes (normalized by APS₀) over a 0.25 s period for both single- and four-pulse insertions, as well as for the steady period of A-HFS immediately before the insertions. The comparison showed no significant difference in APS amplitude sums among these three periods (Fig. 6.14D).

These results showed that pulse insertion only temporarily redistributed evoked neuronal firing without changing the total firing amount during the transient phases. In addition, multiple pulse insertions in successive IPIs neither postponed more neuronal firing nor produced greater APS oscillation than single-pulse insertion.

The above results of antidromically evoked APS were generated by A-HFS applied directly to the axons of recorded CA1 pyramidal neurons without involving synaptic transmissions. We also investigated the effects of the same pulse insertions in the O-HFS at the Schaffer collaterals to orthodromically activate the post-synaptic CA1 pyramidal neurons through monosynaptic transmissions (Fig. 6.15A).

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We inserted single pulses at 60, 80 and 100 s during the steady period of 100 Hz O-HFS at Δt = 6 ms in IPIs by using the identical pulse sequence as A-HFS (Fig. 6.15A). The O-HFS pulses immediately following the insertion pulse were sequentially labeled as P₁, P₂, P₃, etc. The pulse insertion produced a large OPS, denoted as OPS₂ because it followed the second pulse (P₂). No more OPS appeared after OPS₂. The OPS₂ waveforms from the three insertions at 60, 80 and 100 s of O-HFS were superimposed and averaged. The mean amplitude of the averaged OPS₂ was significantly smaller than that of OPS_init induced by the first O-HFS pulse (Fig. 6.15B1). Similarly, in the responses of A-HFS with identical pulse insertion, the mean amplitude of APS₂ was significantly smaller than that of APS_init (Fig. 6.15B2). However, the amplitude ratio OPS₂/OPS_init ≈ 2/3 was significantly greater than the corresponding ratio APS₂/APS_init ≈ 1/3 (Fig. 6.15B3).

A notable observation concerned the timing of OPS₂ occurrence. The OPS₂ appeared following the second pulse (P₂) after the insertion, with a mean latency of 9.8 ± 1.6 ms measured from P₂, indicating that P₂, not P₁, produced the OPS₂. Additionally, the OPS₂ latency was significantly longer than the OPS_init latency of 4.2 ± 0.83 ms (Fig. 6.15C1), which was consistent with the prolonged latency of APSs in A-HFS with single-pulse insertions (Fig. 6.15C2).

To further verify that P₂ produced the OPS₂, we deleted P₂ from the O-HFS train. This resulted in no OPS appearing in the virtual interval between P₂ and P₃ (see the blue shade in Fig. 6.15D). However, a new OPS (labeled as OPS₃) appeared following P₃, with a mean amplitude significantly greater than the OPS₂ induced in the O-HFS with P₂ (Fig. 6.15E1). The mean OPS₃ latency was slightly shorter than that of OPS₂ (Fig. 6.15E2). This experiment confirmed that P₂—not the preceding pulses—produced OPS₂. These results were consistent with the A-HFS results, indicating that the inserted pulse delayed the P₁-induced activation and merged it into the P₂-induced activation. This increased activation generated OPS₂. When P₂ was deleted, the longer IPI allowed more recovery of axonal excitability, thereby resulting in a larger OPS₃.

To investigate the effects of multiple-pulse insertions, the same sequence used in A-HFS with four-pulse insertions was applied as O-HFS (Fig. 6.16A). No OPS occurred during the 40 ms insertion period (dashed boxes in Fig. 6.16A), while the second pulse (P₂) after the insertions induced a large OPS₂. The mean amplitude of OPS₂ was not significantly smaller than that of OPS_init (Fig. 6.16B1), while the mean latency of OPS₂ was significantly longer than that of OPS_init (Fig. 6.16B2).

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These results showed that both single-pulse and four-pulse insertions produced large OPS during steady O-HFS period originally without obvious OPS. The OPS was induced by the second pulse (P₂) after the end of both types of insertions, with an extended latency.

The experiment results of pulse deletion and insertion indicate that during steady HFS periods with constant IPI, altering a single pulse can change the neuronal response in a subsequent period, leading to larger population potentials. When axonal fibers undergo sustained HFS, they experience intermittent depolarization block with extended refractory periods. Under this situation, each axon can only fire action potentials in response to some HFS pulses (refer to Sect. 5.2). Through the antidromic pathway without involving synaptic transmissions, the intermittent activation can produce soma APSs with reduced amplitudes. Deleting a pulse to extend an IPI can provide additional time to allow more axons to recover from depolarization block, resulting in increased APS amplitude (i.e., the APS₂ in Fig. 6.12A).

Interestingly, inserting a pulse to shorten an IPI can produce a similar APS sequence including larger APSs (Fig. 6.12B, C). This result can also be explained by the mechanism of intermittent depolarization block. The activation of the inserted pulse can deepen the depolarization block in the membranes, causing the axon firing that would have followed pulse P₁ to be postponed until after pulse P₂, thereby generating an increased APS₂ (Fig. 6.12B). In addition, the increase of APS₂ correlated with the timing of pulse insertion (Fig. 6.13), with substantial increased APS appearing only when the insertion occurred around the middle of IPI. Presumably, when the additional pulse is inserted closer to the preceding A-HFS pulse (P₀ in Fig. 6.13A), it cannot affect the neuronal firing already triggered by P₀. When the pulse is inserted late near the next A-HFS pulse (P₁ in Fig. 6.13A), it can replace P₁ to trigger neuronal firing itself. Therefore, only a pulse inserted in the middle of IPI can optimally delay the recovery process of ongoing axonal block, postponing the neuronal firing from following P₁ to P₂. This firing redistribution can result in a damped oscillation of smaller and larger APSs (Fig. 6.13B). The unchanged total evoked firing, shown by the sum of APS amplitudes, supports the redistribution hypothesis for both single- and four-pulse insertions (Fig. 6.14D). In addition, the four-pulse insertion did not accumulate more firing to make a larger APS₂ than the single-pulse insertion, likely due to the released neuronal firing during the multi-pulse insertion period (see the small APSs induced by the inserted pulses p₂, p₃ and p4 in Fig. 6.14A).

Similarly, the redistribution of axonal firing through pulse insertions can occur during O-HFS at the Schaffer collaterals, which orthodromically activates the CA1 pyramidal neurons through monosynaptic transmissions. A large OPS₂ was induced by the second pulse (P₂) rather than the first pulse (P₁) after both single- and four-pulse insertions (Figs. 6.15A and 6.16A). This timing matched the appearance of APS₂ during A-HFS (Figs. 6.13 and 6.14). The parallel changes in both amplitudes and latencies of the OPS₂ and APS₂ further supported the hypothesis (Fig. 6.15B, C).

However, the activation pathway of O-HFS includes both axonal conduction and synaptic transmission (Fig. 6.15A). It may be argued that HFS-induced synaptic failures, such as transmitter depletion, could explain our observations, as suggested in previous studies (Anderson et. al. 2006; Iremonger et. al. 2006; Rosenbaum et. al. 2014). This would suggest that synaptic failures, rather than axonal blocks, can cause the absence of OPS events during sustained O-HFS. Thus, the large OPS₂ after the inserted pulse might result from enhanced synaptic transmission due to the additional pulse. However, if this were true, the large OPS should have appeared immediately after the inserted pulse or P₁, not after P₂. The temporal distance (> 20 ms) from the OPS₂ to the inserted pulse was too long to benefit from synaptic transmissions generated by the inserted pulse, because the baseline OPS latency (OPS_init latency, partly caused by the delay of monosynaptic transmission) was only about 5 ms (Figs. 6.15C1 and 6.16B2). In addition, in the experiments with P₂ deleted, the appearance of OPS₃ after pulse P₃ cannot be explained by synaptic failure correction by the inserted pulse, since the temporal distance (>30 ms) from OPS₃ to the inserted pulse was even longer (Fig. 6.15D). Instead, the deletion of P₂ can provide an additional recovery period for the HFS-induced axonal block. Meantime, the inserted pulse can postpone firing. Together, the effects of pulse insertion and P₂ deletion can result in an OPS₃ greater than OPS₂ (Fig. 6.15E1).

While the neuronal responses to pulse insertions during both A-HFS and O-HFS can be explained by intermittent axonal block, the synaptic transmission in the O-HFS pathway does create notable differences. First, the insertion-induced OPS₂ was greater than the APS₂ (Fig. 6.15B3). However, during the steady O-HFS period before insertion, there was no OPS, whereas small APS continued to follow each pulse during the steady A-HFS period. These differences can stem from the threshold effect of synaptic transmission (Spruston 2008), as shown by the S-shape amplitude curve of single-pulse induced OPS versus stimulus intensity (Fig. 2.7 in Sect. 2.3). After insertion, the axonal activation induced by P₂ in O-HFS should have reached a maximum (corresponding to APS₂ with the greatest increased amplitude during the insertion-induced APS oscillation in A-HFS). This P₂ activation exceeded the thresholds of many synaptic transmissions, thus inducing a large OPS₂ from absence. This threshold effect led to the more pronounced change in neuronal responses during O-HFS than during A-HFS. Additionally, the orthodromic activation from each afferent axon of Schaffer collaterals can innervate many post-synaptic neurons through its axonal terminations, while the antidromic activation from each efferent axon can activate only one neuronal soma. This difference also contributed to the larger amplitude of insertion-induced OPS₂ than APS₂.

Second, the oscillation in APSs (Figs. 6.12, 6.13 and 6.14) was absent in OPSs (Figs. 6.15 and 6.16). This absence can be attributed to both feedforward and feedback local inhibitory circuits (refer to Sect. 2.3). The O-HFS pulses and the pyramidal neuron firing can activate the inhibitory effects of these local circuits, thereby preventing subsequent OPSs after the large OPS₂. In contrast, local inhibitions hardly affect APS generation, which does not involve synaptic integrations.

Taken together, based on the mechanism of HFS-induced intermittent axonal block, inserting pulses can redistribute axonal firing, substantially changing neuronal responses during the steady period in both A-HFS and O-HFS. This redistribution can result in increased synchronized firing of neuronal populations. In addition, in the activation pathway of O-HFS, synaptic transmissions and synaptic integrations in local neuronal circuits can nonlinearly transform activations from the afferent axons through a threshold effect. As a result, the post-synaptic neuron firing in O-HFS differs from the firing directly induced in the same neurons by antidromic activations of A-HFS. Our study provides a potential way to design HFS patterns with varying IPIs by inserting pulses into conventional HFS with a constant frequency. Clinical trials and animal experiments have shown that pulse sequences with real-time varying IPIs can produce diverse stimulation effects, offering more options for neuromodulation therapies (Brocker et al. 2013; Akbar et al. 2016; Karamintziou et al. 2016; Grill 2018; Santos-Valencia et al. 2019; Okun et al. 2022). The next section will show our investigations into the stimulation effects of randomly varying IPIs.

As shown in Fig. 6.17A, we compared varying and constant frequency stimulations within an A-HFS train, which was consisted of three periods: a 50 s period of constant 100 Hz stimulation to allow neuronal response to reach steady state, a 10 s period of varying frequencies ranging from 20 to 600 Hz, and a final 20 s period returning to constant 100 Hz. The total A-HFS duration was 80 s. During the varying-frequency period, the mean pulse frequency was maintained at 100 Hz, with IPI ranging from 1.67 to 50 ms.

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In the typical APS recording shown in Fig. 6.17A, during the initial 50 s period of 100 Hz constant A-HFS, the APS change was similar to those described previously. At onset, each pulse induced a large APS. Within seconds, the APS amplitude rapidly decreased and stabilized at about 20% of its initial amplitude by the end of the 50 s constant stimulation (Fig. 6.17B). During the subsequent 10 s period with varying frequency, the IPI randomly varied with a Poisson distribution ranging from 1.67 to 50 ms (Fig. 6.17C). The APS amplitude became unstable, fluctuating in a range of 0–4.5 mV (Fig. 6.17B and D). Once the stimulation returned to constant frequency, the APS reverted to a stable small level. Approximately 2 min after the end of A-HFS, the neuronal responses returned to baseline level, as indicated by the recovered APS (shown in the lower right corner of Fig. 6.17A).

During the 10 s A-HFS period with random IPIs, despite the mean pulse frequency remaining at 100 Hz, the APS amplitudes varied markedly and showed an overall positive correlation with the preceding IPI (Fig. 6.17D). Larger APSs (> 4 mV) followed longer preceding IPIs (25–50 ms), while smaller APSs (< 1 mV) followed shorter preceding IPIs (1.7–5 ms). This pattern reflected that longer intervals facilitated larger APS generation. However, in the 5–15 ms IPI range, the APS amplitude varied in a range of 0–4.5 mV with no clear correlation to IPI (shadow area in Fig. 6.17D). A larger APS could follow a shorter IPI, or vice versa. This result suggested that even when all IPIs were short, slight variations in the IPIs could result in irregular firing in neuronal populations with some larger APSs. To test this hypothesis, we narrowed the IPI range to 5–10 ms (equivalent to 100–200 Hz). This produced markedly different results from the consistently small APSs seen in A-HFS with a constant IPI in the same range.

As shown in Fig. 6.18A, after a 50 s 100 Hz control stimulation period, when the APSs stabilized at a small amplitude, the A-HFS switched to a 10 s period with random IPIs distributed uniformly within 5–10 ms, resulting in a mean pulse frequency of 133 Hz. Notably, no IPI in the varying period exceeded the 10 ms IPI of the constant period. However, during this varying period, many APS amplitudes exceeded those observed during the constant period. This result differed from the larger APSs induced by longer IPIs during the steady A-HFS period with constant frequency (Fig. 5.7F). Additionally, many pulses during the varying period hardly induced APSs (Fig. 6.18A, B).

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We compared the neuronal responses to A-HFS between constant and varying IPIs by analyzing APS amplitude distributions during two adjacent 10 s periods: the 40–50 s period with constant 10 ms IPI (Fig. 6.18C) and the 50–60 s period with randomly varying IPIs (Fig. 6.18D). With constant IPI, APS amplitudes showed an approximately normal distribution with a narrower range of 0.83–1.90 mV and a mean of 1.32 mV. In contrast, with varying IPIs, APS amplitudes followed a declining distribution with a wider range of 0–3.22 mV and a mean of 1.03 mV. Additionally, this declining distribution differed from the uniform distribution of varying IPIs (shown in the upper right of Fig. 6.18D), indicating a nonlinear relationship between neuronal responses and IPIs.

The mean frequency during the varying period was 133 Hz, higher than the constant 100 Hz in the control period. Increasing the control frequency to 200 Hz while keeping other parameters unchanged, we observed similar results (Fig. 6.18E–H). The higher control frequency resulted in a decrease in the steady APS amplitude with a mean of 0.64 mV and a narrower range of 0.36–1.15 mV during the 40–50 s constant period (Fig. 6.18G). However, during the 50–60 s period with randomly varying IPIs (still ranging in 5–10 ms), the APS amplitudes increased to a wider range of 0–3.38 mV with a mean of 1.17 mV (Fig. 6.18H).

Statistical data showed that while the initial APS amplitudes induced by the first pulse of A-HFS were similar (Fig. 6.19A), the mean steady APS amplitude of 200 Hz A-HFS was significantly smaller than that of 100 Hz A-HFS during the control periods of both 40–50 s and 60–70 s (the periods immediately before and after the 10 s varying period). This difference occurred because higher-frequency constant A-HFS can suppress APS more by causing deeper axonal block. However, during the 10 s varying period inserted in the middle of 200 Hz control A-HFS, both the mean and the interquartile range of APS amplitudes were not significantly different from those with 100 Hz control A-HFS (Fig. 6.19B). This result indicated that neuronal responses to the varying IPIs were independent of the preceding APS suppression level.

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Interestingly, despite the narrow range of varying IPIs in 5–10 ms (equivalent to 200–100 Hz), the amplitude ranges of APSs produced by these IPIs were far beyond the steady APS amplitudes produced by constant IPI at 100 or 200 Hz. When IPI varied randomly, the maximum APS amplitude was significantly greater than those during the preceding control periods of both 100 and 200 Hz A-HFS (Fig. 6.19C). Additionally, some pulses with varying IPIs failed to induce any APS (amplitude = 0), whereas pulses with constant IPI consistently induced APS (Fig. 6.18). As shown in Fig. 6.20A, the frequency of the constant periods was set to 133 Hz to match the mean frequency of the varying period. Using the APS area, a more accurate index reflecting the neuronal firing level (Theoret et al. 1984), the sum of APS areas per second during varying A-HFS was not significantly different from that during constant A-HFS (Fig. 6.20B). However, the interquartile range of APS area distribution was significantly larger during varying A-HFS than during constant A-HFS (Fig. 6.20C). These results showed that small random variations in IPIs generated APS amplitude changes that significantly exceeded the range of steady APS amplitudes caused by constant A-HFS. Moreover, the varying IPIs affected only the timing of neuronal firing without significantly altering the total firing level.

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Note: unless otherwise specified in this book, the pulse intensity was set to induce APS or OPS at about 3/4 of the maximum amplitude, usually around 0.3 mA. At this unsaturated intensity, the amplitude of APS or OPS correlates linearly with its area (Theoret et al. 1984). Therefore, we often used the more intuitive measure of amplitude to compare the relative number of neurons involved in firing (i.e., firing level).

The timing of neuronal firing during varying A-HFS depended on both the preceding IPI and the preceding APS. As illustrated in Fig. 6.21A, we defined the following terms: current APS, preceding APS, current IPI, and preceding IPI. Using these definitions, we analyzed the relationship between APS amplitude and IPI length during varying A-HFS through scatter plots.

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During the 10-s A-HFS period with randomly varying IPIs ranging in 5–10 ms, larger APSs (> 1.8 mV) only followed longer IPIs (7.5–10 ms) rather than shorter IPIs (5–7.5 ms, Fig. 6.21B). Although smaller APSs sometimes occurred after longer IPIs, they were often preceded by larger APSs (Fig. 6.21C and D). Even when two longer IPIs occurred consecutively in the uniform distribution of varying IPIs (Fig. 6.21E), two larger APSs never appeared consecutively (the shade area in Fig. 6.21C). This indicated that a larger preceding APS prevented a second larger APS from being immediately induced by the next pulse. In other words, the neuronal firing was history-dependent. A longer IPI was necessary but not sufficient for producing a larger APS, as some longer IPIs did not induce larger APSs. This occurred because the longest IPI was only 10 ms, not long enough. As shown in Fig. 6.17D, when the IPI was sufficiently long (e.g., > 20 ms), the pulse following the long IPI consistently induced a larger APS.

Note: The range of varying IPIs was set at 5–10 ms, which exceeded the latencies of APSs induced during A-HFS (see Fig. 5.2). Therefore, each APS was produced by its immediately preceding pulse. Additionally, the APS amplitude was independent of the current IPI (Fig. 6.21F), since the APS was induced by the preceding pulse rather than the succeeding one.

These results indicate that small variations in IPI can significantly alter the firing timing of neuronal somata and increase firing randomness during sustained antidromic activation from axonal A-HFS.

The experimental data in Fig. 6.21 suggest that changing the order of an identical set of varying IPIs can affect the neuronal responses during A-HFS. For example, we compared APS signals produced by A-HFS trains with a same set of IPIs arranged in two different orders: from longest to shortest, and random. The two IPI sequences were set to a 10-s duration, with IPIs uniformly ranging in 5-10 ms. Given the 20 kHz sampling rate used in our recordings, we set the pulse time resolution to 0.05 ms. At this resolution, the 5–10 ms range yielded 101 distinct IPI lengths. To achieve a uniform distribution, we repeated each IPI length 13 times and added one extra IPI for every five IPI lengths. This yielded 1334 IPIs (101 × 13 + 21) with a total length of 10.005 ≈ 10 s. This set of IPIs was then arranged in two different ways to produce two sequences: one decreased from longest to shortest, while the other was randomized using MATLAB “randperm” function. Both sequences contained the identical set of IPIs, differing only in their order.

As shown in Fig. 6.22A1, the 10 s decreasing IPI sequence was applied following an initial 20 s pulse sequence at constant 100 Hz to form a total 30 s A-HFS. In the 10–20 s constant period, the APS amplitude stabilized at about 20% of its initial level. Based on the mean APS amplitude in this steady period, the normalized APS amplitude showed a decrease from ~ 1 to ~ 0.3 during the final 10 s period as IPI decreased from 10 to 5 ms (Fig. 6.22A2). Due to the uniform distribution of the varying IPIs, the IPI decrease over time was quasi-linear rather than exactly linear (Fig. 6.22A3). The APS amplitude showed a strong correlation with its first preceding IPI (termed as IPI₁) with a correlation coefficient of 0.94 (Fig. 6.22A4). When this stimulation was followed by a gradually increasing IPI sequence from 5 to 10 ms, the APSs exhibited a reverse change.

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When the 10 s decreasing IPI sequence was replaced by the randomly varying IPI sequence (Fig. 6.22B1), the normalized APS amplitudes fluctuated “randomly” between 0 and 2.4 (Fig. 6.22B2). Although these random IPIs came from the identical IPI set with the same range of 5–10 ms and uniform distribution (Fig. 6.22B3), the APS amplitude showed no linear correlation with IPI₁, as both larger and smaller APSs occurred following longer IPI₁ intervals (Fig. 6.22B4 upper). Nevertheless, the APS amplitude showed a positive correlation with the difference between IPI₁ and IPI₂ (ΔIPI = IPI₁-IPI₂) (Fig. 6.22B4 bottom). This indicated that a longer IPI₁ accompanied by a shorter IPI₂ (the second preceding IPI) can produce a larger APS. For detailed statistical analyses of these experiments, please refer to our paper (Zheng et al. 2020).

The HFS sequences with time-varying IPIs can generate diverse stimulation effects, thereby offering promising options for clinical applications. While the design of IPI sequences currently lacks theoretical guidance, our experimental results indicate that neuronal firing can be mainly influenced by the preceding intervals IPI₁ and IPI₂. Based on this finding, we can design pulse sequences with IPIs varying only within a small range (such as 5–10 ms) to generate various APS sequences for different effects of neural modulations. We have tested this approach, as detailed in our reports (Zheng et al. 2021; Zheng et al. 2022).

During the 10 s period of randomly varying IPIs (5–10 ms) inserted in the steady period of A-HFS (Fig. 6.23A), while the APS amplitudes changed substantialy (Fig. 6.23B1), the APS latencies remained stable, matching the constant periods before and after the varying period (Fig. 6.23B2). Similar to those described in Sect. 5.2, Fig. 6.23B shows a substantial increase in APS latency occurred in the initial 4.5 s period of A-HFS as APS amplitude decreased. The scatter plot of APS amplitude versus latency in this period showed a significant negative correlation, with a determination coefficient of R² = 0.97 (Fig. 6.23C1). However, during the 50–60 s period of A-HFS with varying IPIs, the determination coefficient fell to R² = 0.27 (Fig. 6.23C2), indicating no correlation. As described in Sect. 5.2.3, when an extended gap was inserted during the steady period of constant A-HFS, a “fast recovery” occurred in APS amplitude but not in APS latency (see Fig. 5.11). Here the stability in APS latencies with varying IPIs was consistent with the neuronal responses to the inserted gap described in Sect. 5.2.3.

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In the A-HFS with varying IPIs described above, we initiated the stimulation with a constant IPI period to allow the induced APS to reach a steady state before switching to varying IPIs. This paradigm served two purposes. First, it allowed direct comparison between varying and constant A-HFS, with the constant period serving as a control in the same A-HFS to minimize interference. Second, it brought neuronal responses to a steady state before switching to varying A-HFS, enabling comparison of steady responses. However, one may argue that the neuronal responses to varying A-HFS could simply represent a transient response caused by the transition from constant to varying periods, rather than a steady-state response. To address this concern, we next examined neuronal responses to A-HFS with varying IPIs throughout the entire stimulation period.

Figure 6.24A1 shows a typical APS signal during A-HFS with randomly varying IPIs ranging in 100–200 Hz (a mean of 133 Hz). The corresponding IPI distribution is shown in Fig. 6.22B3. As a control, Fig. 6.24A2 shows an A-HFS with a constant 133 Hz. At the onset of both A-HFS trains, each pulse induced a large APS with a similar amplitude. After ~ 4 s of A-HFS, the APS amplitude decreased to a steady state. At this period, the APSs induced by varying A-HFS showed marked variation, while those induced by constant A-HFS were uniformly small. This difference persisted until the end of A-HFS, as shown in the scatter plots of APS amplitudes (grey dots in Fig. 6.24B1 and B2). Nevertheless, their average APS amplitudes per 0.1 s followed bi-exponential fittings (brown dots and red curves in Fig. 6.24B1 and B2) and showed similar APS trends during both A-HFS trains. These average APS amplitudes decreased rapidly in the initial period, with a half-life time shorter than 1 s (0.31 s for varying A-HFS and 0.50 s for constant A-HFS). However, the half-life time of the maximum APS amplitudes per 0.1 s differed significantly between the two A-HFS trains (blue dots and curves in the Fig. 6.24B1 and B2): 3.4 s for varying A-HFS and 0.52 s for constant A-HFS. The statistical data are detailed in our report (Hu et al. 2021).

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Like constant A-HFS, varying A-HFS showed an initial transient phase before stabilizing at a steady phase. However, small IPI variations of 5–10 ms in varying A-HFS substantially delayed the decay of maximum APS. Although both A-HFS paradigms showed similar average neuronal firing levels, the larger APS occurrences during varying A-HFS indicated stronger synchronized firing with potential stronger effects in neuronal networks. Additionally, the random synchronous firing (APSs) generated by varying stimulations may eliminate pathological rhythmic activity in brain disorders.

As previously described, APSs generated by axonal A-HFS occur without synaptic transmissions. To investigate how downstream post-synaptic neurons respond to axonal O-HFS with time-varying IPIs, we applied identical pulse sequences at the Schaffer collaterals while maintaining the CA1 recording site. The orthodromic activation pathway of O-HFS involves axonal conduction, synaptic transmission, and post-synaptic integration.

Similar to the A-HFS described above, the O-HFS train combined both constant and varying IPI periods. To verify the differences in neuronal responses, we switched between the two stimulation modes twice. The O-HFS train began with a 50 s constant 100 Hz period, followed by a 10 s period with randomly varying IPIs. It then returned to the constant period and repeated this 60 s pulse sequence once again. Finally, the stimulation concluded with a 20 s constant period, resulting in a total O-HFS duration of 140 s (Fig. 6.25A). The IPIs in the two 10 s varying periods were uniformly distributed within the range of 5–10 ms (100–200 Hz), identical to that shown in Fig. 6.22B3.

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The neuronal responses to the initial 50 s constant O-HFS was similar to that described in Sect. 5.3. After the first large OPS at the onset and subsequent OPS events, the neuronal responses in the late period of 50-s constant O-HFS entered a steady state without obvious OPS (Fig. 6.25A). However, when the constant stimulation switched to varying stimulation, OPS reappeared and persisted throughout the 10-s varying period. Upon returning to 100 Hz constant stimulation, OPS disappeared again. The neuronal responses maintained consistent patterns during the second round of varying stimulation. As shown in Fig. 6.25B, when we increased the pulse frequency in constant stimulations from 100 to 200 Hz while keeping other parameters unchanged, OPS events also occurred during the two 10-s periods of varying stimulation. No obvious OPS appeared during the steady period of 200 Hz constant stimulations. The mean pulse frequency of varying stimulation was 133 Hz. Setting the constant stimulations to 133 Hz did not change the responses during varying stimulation, as detailed in our report (Hu et al. 2019). Additionally, during the varying periods, not every pulse induced an OPS—the OPS rate was much lower than the mean pulse frequency (Fig. 6.25C1), indicating that the synchronous neuronal firing (OPS) required a cumulative effect of multiple pulses. Moreover, the OPS amplitude showed considerable variation, with an average amplitude much smaller than the initial OPS induced at O-HFS onset.

To investigate the OPS pattern during varying periods, we analyzed the relationship between OPS amplitudes and preceding IPIs. As shown in Fig. 6.26A, during a 10 s varying period, OPSs appeared either separately or in bursts. We labeled the four preceding pulses before an OPS as P₁, P₂, P₃ and P₄, with their corresponding preceding IPIs as IPI₁, IPI₂, IPI₃ and IPI₄. The random IPIs uniformly distributed within the range of 5–10 ms. The distributions of OPS amplitude and occurrence probability versus the length of IPI₁ and IPI₄ were approximately uniform (Fig. 6.26B1 and B4), indicating no significant correlation between the OPSs and these IPIs. However, both the OPS amplitude and occurrence probability showed correlation with IPI₂ and IPI₃ to some extent. When IPI₂ was longer or IPI₃ was shorter, the OPS amplitude was greater and the probability of OPS occurrence was higher (Fig. 6.26B2 and B3). The three-dimensional scatter plot in Fig. 6.26C illustrates these relationships.

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We divided the IPI range equally into two sub-ranges: 5–7.5 ms (shorter) and 7.5–10 ms (longer). Statistical data showed that OPS appeared approximately twice as frequently with the longer IPI₂ compared to shorter IPI₂ (Fig. 6.26D left), while OPS appeared more frequently with shorter than longer IPI₃ (Fig. 6.26D right). This correlations between OPS occurrence and the two IPIs showed that pulses P₂ and P₃ were more likely to induce OPS than P₁ and P₄. This occurred because the synaptic transmission in the orthodromic activation pathway delayed downstream neuronal responses to stimulation activation. Under baseline situations, a single pulse typically induced an OPS with a latency of about 5 ms. Sustained axonal stimulation could extend this latency. During the varying O-HFS period, the OPS latency could exceed most of the IPIs ranging in 5–10 ms. Therefore, P₁ was unlikely to induce OPS, while P₂ or P₃ were more likely triggers. However, if P₃ induced an OPS, its latency would exceed the combined duration of IPI₁ and IPI₂ (> 10 ms). Our another study showed that during sustained axonal O-HFS, the latency of most downstream neuronal firing was shorter than 10 ms (Wang et al. 2018), making P₃ an unlikely trigger. Thus, P₂ had the highest probability of inducing OPS (Fig. 6.26A, lower left). The experimental data confirmed that a longer IPI₂ combined with a shorter IPI₃ facilitated P₂ to induce a larger OPS (Fig. 6.26).

The above experiments investigated OPS events induced during a 10-s varying period temporarily inserted into the steady period of constant O-HFS. We also explored neuronal responses to 3-min O-HFS entirely with randomly varying IPIs of 5–10 ms (Fig. 6.27A). OPSs appeared continuously during the early O-HFS period before ceasing at about 65 s. The mean OPS occurrence rate within this 65-s period was 16 count/s (Fig. 6.27B). This OPS duration was much longer than that observed during the initial period of constant O-HFS at both 100 and 200 Hz (refer to Sect. 5.3.1). During the late period of 3-min O-HFS when obvious OPSs were absent, unit spikes (MUA) exhibited higher density than the baseline level before O-HFS. With a shorter O-HFS duration (e.g., 1 min), population spikes (PS) could even continue for a while after O-HFS ended, similar to the after-discharge described in Sect. 8.1. Strong epileptiform discharges could even lead to spreading suppression (SD).

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These results indicate that small random variations in IPIs can substantially enhance the activation effect of O-HFS on post-synaptic neurons, leading to persistent synchronous discharges in downstream neurons. These discharges resemble the OPSs that appeared before axonal block during the initial O-HFS period. This means that this time-varying stimulation paradigm can overcome the activation attenuation caused by sustained constant HFS. The resulting persistent excitation may offer therapeutic benefits for certain diseases.

The activation pathways of A-HFS and O-HFS differ essentially in whether or not involving synaptic transmissions. An identical pulse sequence with time-varying IPIs can induce different neuronal responses through these distinct activation pathways with different repeatability.

As shown in Fig. 6.28A, we applied an identical 1-min pulse sequence with randomly varying IPIs (5–10 ms) as both A-HFS and O-HFS. Both stimulations continuously induced PSs (APSs or OPSs) throughout the entire 1-min period. In the six rat experiments in which we applied both stimulations once, the first pulse induced similar APS or OPS. Subsequently, the APS patterns during A-HFS were consistent across experiments, though the APS amplitudes triggered by each pulse varied markedly. The resulting APS sequence showed good repeatability (Fig. 6.28B and C, left). However, during O-HFS with the identical pulse sequence, both the timings and amplitudes of induced OPSs lacked consistency and repeatability across experiments, except for a few pulses in the initial period (Fig. 6.28B and C, right). These results indicate that time-varying stimulations can produce definite firing patterns in directly stimulated neurons. This allows for designing various pulse sequences to meet different requirements of neuronal firing patterns, as detailed in our previous report (Zheng et al. 2021). However, when synaptic transmissions are involved, post-synaptic neurons cannot precisely replicate a definite firing pattern.

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