Interactions between cathodic- and anodic-pulses during high-frequency stimulations with the monophasic-pulses alternating in polarity at axons—experiment and simulation studies

Background. Electrical neuromodulation therapies commonly utilize high-frequency stimulations (HFS) of biphasic-pulses to treat neurological disorders. The biphasic pulse consists of a leading cathodic-phase to activate neurons and a lagging anodic-phase to balance electrical charges. Because both monophasic cathodic- and anodic-pulses can depolarize neuronal membranes, splitting biphasic-pulses into alternate cathodic- and anodic-pulses could be a feasible strategy to improve stimulation efficiency. Objective. We speculated that neurons in the volume initially activated by both polarity pulses could change to be activated only by anodic-pulses during sustained HFS of alternate monophasic-pulses. To verify the hypothesis, we investigated the interactions of the monophasic pulses during HFS and revealed possible underlying mechanisms. Approach. Different types of pulse stimulations were applied at the alvear fibers (i.e. the axons of CA1 pyramidal neurons) to antidromically activate the neuronal cell bodies in the hippocampal CA1 region of anesthetized rats in-vivo. Sequences of antidromic HFS (A-HFS) were applied with alternate monophasic-pulses or biphasic-pulses. The pulse frequency in the A-HFS sequences was 50 or 100 Hz. The A-HFS duration was 120 s. The amplitude of antidromically-evoked population spike was measured to evaluate the neuronal firing induced by each pulse. A computational model of axon was used to explore the possible mechanisms of neuronal modulations. The changes of model variables during sustained A-HFS were analyzed. Main results. In rat experiments, with a same pulse intensity, the activation volume of a cathodic-pulse was greater than that of an anodic-pulse. In paired-pulse tests, a preceding cathodic-pulse was able to prevent a following anodic-pulse from activating neurons due to refractory period. This indicated that the activation volume of a cathodic-pulse covered that of an anodic-pulse. However, during sustained A-HFS of alternate monophasic-pulses, the anodic-pulses were able to prevail over the cathodic-pulses in activating neurons in the overlapped activation volume. Model simulation results show the mechanisms of the activation failures of cathodic-pulses. They include the excessive membrane depolarization caused by an accumulation of potassium ions, the obstacle of hyperpolarization in the conduction pathway and the interactions from anodic-pulses. Significance. The study firstly showed the domination of anodic-pulses over cathodic-pulses in their competitions to activate neurons during sustained HFS. The finding provides new clues for designing HFS paradigms to improve the efficiency of neuromodulation therapies.


Introduction
Functions of nervous system are fundamentally realized through the generation and conduction of neuronal APs.Theoretically, abnormal neural activity in neurological disorders can be controlled by modulating neuronal firing artificially.Extracellular stimulation of electrical pulses is a direct and efficient way to activate neuronal membranes and to change the firing of neuronal populations.For instance, in the central nervous system, neuromodulation therapies such as DBS and SCS utilize HFS of electrical pulses to treat Parkinson's disease, epilepsy and chronic pain (Grider et al 2016, Sivanesan et al 2019, Frey et al 2022).In the peripheral nervous system, VNS, CIs and SNM employ electrical pulses to treat epilepsy, hearing loss and overactive bladder (Noblett and Buono 2018, Naples and Ruckenstein 2020, Wang et al 2021a).
To ensure a balance in opposite electrical charges to minimize possible damages to neural tissues, biphasic-pulses with a leading cathodic-phase and a lagging anodic-pulse are commonly used in sustained extracellular stimulations (Merrill et al 2005, Brocker and Grill 2013, Voigt and Kral 2019).The lagging anodic-phase (i.e.anodic-pulse) usually serves as a balance phase without any activation effect.However, either cathodic-pulse or anodic-pulse can activate neurons by depolarizing neuronal membranes.A cathodic-pulse can directly depolarize the membrane immediately adjacent to the SE.In contrast, an anodic-pulse can hyperpolarize the adjacent membrane but depolarize the membrane at slightly distant sites through a return current (Ranck 1975, Rattay 1989).The smaller current efflux to depolarize membrane by an anodic-pulse makes it less efficient than a cathodic-pulse in activating neurons (Volkmann et al 2006, Zhang and Grill 2010, Bower and McIntyre 2020).Nevertheless, splitting biphasicpulses into cathodic-and anodic-pulses could be a feasible strategy to improve stimulation efficiency by exerting the activation effect of anodic-pulses in sustained stimulations.
In neuromodulations, besides those with a stimulation target originally at axon of neurons (e.g.SCS, VNS, CI and SNM), even in DBS, the stimulationinduced AP usually initiates at axon not soma.It is because the axonal membrane has the shortest chronaxie among the neuronal elements and can been firstly activated by the narrow pulses used in DBS (Ranck 1975, Nowak and Bullier 1998, Buzsáki 2006, Brocker and Grill 2013).During sustained HFS of pulses in DBS, axonal membranes can be excessively depolarized, resulting in an intermittent block at axons (Jensen and Durand 2009, Zheng et al 2011, Feng et al 2013, 2014).Under the situation of partial axon block, we recently found that the activation of anodic-pulses was not weaker than that of cathodicpulses during a type of HFS with alternate cathodicand anodic-pulses (Feng et al 2022).In addition, the two types of monophasic pulses were found to activate distinct sub-populations of neurons, respectively.Furthermore, this type of HFS did not cause obvious damage to the stimulated neurons.The neuronal activity was able to return to baseline level in a couple of minutes after the end of HFS (figure 3 in Feng et al 2022).It is a meaningful finding to show that both polarity pulses can exert such activation effects in neuromodulations.However, the underlying mechanisms of the activations of opposite pulses remain unclear.
We speculated that the axons in the volume initially activated by both polarity pulses could be activated only by anodic-pulses rather than cathodicpulses during sustained HFS, because cathodic-pulses could induce a more severe axonal block.To test this hypothesis, we applied axonal stimulations in rat experiments in-vivo and investigated neuronal responses to pulses of different combinations and different HFS sequences.The experiment results revealed the activation volumes of and the competitions between the pulses of opposite polarities.In addition, the limitations in current techniques of experiments prevent multiple electrophysiological recordings in a thin axon in-vivo to track its AP propagation directly (Radivojevic et al 2017, Tovar et al 2018, Broussard et al 2021).Therefore, we utilized a computational model to simulate axonal conduction and to analyze the underlying mechanisms of interactions between the two types of monophasic-pulses.The results can reveal the mechanisms of the activations of neuron sub-populations.They can also provide clues for developing new stimulation paradigms for neuromodulation therapies.

Animal surgery and electrode implantation
Adult male Sprague-Dawley rats (300 ± 50 g, n = 33) were anesthetized by urethane (1.25 g kg −1 ) and placed in a stereotaxic apparatus (Stoelting Co, USA) to perform acute experiments.The details of surgical procedures were similar to our previous reports (Feng et al 2013(Feng et al , 2014)).
A SE and a RE were inserted into the left hippocampal CA1 region.The SE was a bipolar concentric electrode (#CBCSG75, FHC, Inc., Bowdoin, ME, USA) with an inner pole: platinum-iridium, diameter 75 µm, height 100 µm; an outer pole: stainless steel, diameter 250 µm, height 100 µm; and a 100 µm space between the two poles.The inner pole of SE acted as a working pole to activate the alvear fibers, i.e. the axons of CA1 pyramidal neurons (figure 1(A)).The location of SE tip was anteroposterior −4.8 mm, mediolateral 2.7 mm and dorsoventral ∼2.0 mm to bregma.The RE was a 16channel electrode array (#Polytrode, A1x16-Poly2-5 mm-50 s-177, NeuroNexus Technologies Inc., USA).It was placed perpendicularly across the CA1 region with a location at anteroposterior −3.5 mm, mediolateral 2.7 mm and dorsoventral ∼2.5 mm to bregma.Both the typical waveforms of evoked APS and the spontaneous firing of unit spikes appearing along the 16 channels of RE were used to judge the correct positions of the electrodes (Kloosterman et al 2001).After the experiments, the locations of electrodes were confirmed further on brain slices (Wang et al 2021b).

Recording and stimulating
Electrical potentials collected extracellularly by the RE were amplified ×100 and band-pass filtered (0.3-5000 Hz) by a 16-channel amplifier (Model 3600, A-M System Inc., USA).The amplified signals were then sampled by a Powerlab data acquisition system (Model PL3516, ADInstruments Inc., Australia) with a 20 kHz sampling rate per channel.
Stimulation pulses were rectangular waveforms of electrical current and were generated by a programmable stimulator (Model 3800, A-M System Inc., USA).The pulse polarity was defined as the polarity of current flowing through the inner pole of the concentric bipolar electrode.The following types of pulses were used: biphasic-pulse (┼) always with a cathodic-phase first, monophasic cathodic (⊤) and anodic (⊥) pulses, as well as pseudo-monophasic cathodic (⊤ B ) and anodic (⊥ B ) pulses with a balance phase to avoid charge accumulation.The pulse width was always 100 µs per phase except balance phases.The pulse intensity was ±0.3 mA to evoke an APS ┼ with an ∼75% maximal amplitude at baseline, except where specifically noted.
A-HFS formed by ┼, alternate ⊤ and ⊥, alternate ⊤ B and ⊥ B or pure ⊥ B was respectively applied at the alvear fibers.The duration of A-HFS was 120 s.The pulse frequency of A-HFS was 50 or 100 Hz.For clarity in illustrations, the artifacts of stimulation pulses in A-HFS recordings were all removed by a custommade MATLAB program using a linear interpolation method (Yu et al 2016).

Computational modeling
A model of myelinated axon was established in the NEURON simulation environment (Hines and Carnevale 1997).The axon consists of 21 Ranvier nodes (Node 0 to Node 20 ) and 20 myelinated internode segments.The model parameters were similar to the previous study (Guo et al 2018), including morphologic parameters, passive electrical parameters and active electrical properties of the axon and its membrane, as well as the accumulation and clearance mechanisms of K + in the narrow periaxonal space.The maximum conductance of voltagegated channels of Na + on axonal nodes was modified to 0.6 S cm −2 , according to the range of measurements from previous study (Lorincz and Nusser 2010).
The electrical field potential of A-HFS delivered by the SE was calculated 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 tip center of SE was located above the center node (Node 10 ) of the axon.To analyze the mechanisms of axonal responses to A-HFS sequences with alternate ⊤ and ⊥ pulses, the following model variables at each node of the axons were recorded and analyzed: the membrane potential (V m ), the h_Na and the K + concentration in the narrow peri-axonal space ([K + ] o ).

Data analysis
As an integrated potential of the synchronous firing of a population of CA1 pyramidal neurons (Anderson et al 1971), the APS recorded in the somatic layer of CA1 region was used to evaluate the responses of neurons under axonal stimulations.The amplitude of APS was measured as the potential drop of the falling phase of APS waveform to evaluate the amount of neuronal firing evoked by a pulse (Theoret et al 1984, Kloosterman et al 2001).
All statistical data were represented as mean ± standard deviation.'n' is the number of rats for data collection.T-test or one-way ANOVA with post hoc Bonferroni tests were used to assess the statistical significances of the differences between or among data groups.

Activations of cathodic-and anodic-pulses with an identical intensity in A-HFS
An electrical pulse applied at alvear fibers of the pyramidal neurons in rat hippocampal CA1 region can antidromically activate the neuronal somata to generate APs, thereby forming an APS in the extracellular recording (figure 1(A)).To compare the activations of different single-pulses, the APS ┼ , APS ⊥ and APS ⊤ evoked respectively by biphasic-(┼), anodic-(⊥) and cathodic-(⊤) pulses were analyzed at baseline (figure 1(B, left)).With an identical pulse intensity of 0.3 mA, the mean amplitude of APS ┼ was similar to that of APS ⊤ (figure 1(B)), indicating a similar activation ability of ┼ and ⊤ pulses.However, the mean amplitude of APS ⊥ was significantly smaller than APS ┼ and APS ⊤ , indicating a weak activation of the ⊥ pulses.
To evaluate the relationship between the activation volumes of two pulses, paired-pulse stimulations with different IPI were applied.If the activation volumes of two pulses are overlapped, with a sufficiently short IPI, the APS evoked by the second pulse (APS test ) should be suppressed by the APS evoked by the first pulse due to the effect of refractory period.The APS test would be smaller than its baseline value (APS control ).With an identical pulse intensity 0.3 mA, for a short IPI = 1 ms, the second pulse of both '┼ ┼' and '⊤ ⊥' paired-pulses failed to evoke an APS (the first and second rows in figure 1(C)), while the second pulse of a '⊥ ⊤' paired-pulse was able to evoke a decreased APS test (the third row in figure 1(C)).This small APS test was generated from the neurons in the ⊤ activation volume beyond the range overlapped by the ⊥ activation volume.These results verified that the activation volume of a ⊤ pulse was greater than and included that of a ⊥ pulse.As IPI increased, in all the three types of paired-pulses, the APS test increased (figures 1(C) and (D)), indicating a decrease of the effect of refractory period.
The statistical data showed that with IPI = 2.5 ms, in both '┼ ┼' and '⊤ ⊥' paired-pulses with the activation volume of second pulse covered by the first pulse, the mean amplitude ratios of APS test /APS control were greater than 50%.With IPI = 17.5 ms, the ratios increased to ∼100% (figure 1(D)).The results indicated that with an IPI greater than 2.5 ms, the effect of refractory period had decayed significantly.To investigate the changes of neuronal responses during sustained A-HFS, we set A-HFS sequences by repeating these paired-pulses (IPI = 2.5 ms) at 50 Hz for 120 s.That is, the IPIs of A-HFS pulses were alternated between 2.5 and 17.5 ms.The A-HFS with '┼ ┼' paired-pulses was denoted as A-HFS ┼ ┼ , and A-HFS with '⊤ ⊥' as A-HFS ⊤⊥ (figure 2).
Similar to the responses of paired-pulse stimulations (figures 1(C) and (D)), at the onset of A-HFS ┼ ┼ (figure 2(A1)), the normalized amplitude of APS 2.5 (following the IPI 2.5 ms) was significantly smaller than that of APS 17.5 (following the IPI 17.5 ms, figure 2(A2)).Subsequently, the APSs gradually decreased due to the HFS-induced axonal block (Jensen et al 2009, Feng et al 2013).The APS 2.5 disappeared after ∼1.5 s of A-HFS (figure 2(A1)) due to the extension of refractory period by A-HFS (Feng et al 2014).During the steady period of A-HFS, i.e. the late 60 s of A-HFS, the amplitude of APS 2.5_steady was 0, while the mean amplitude of APS 17.5_steady was ∼22% of control level (figure 2(A2)).
For the A-HFS ⊤⊥ (figure 2(B1)), at its onset, the normalized amplitude of APS ⊥ was significantly smaller than that of APS ⊤ (figure 2(B2)).Then, the APS ⊥ disappeared for a while in the period of ∼0.6-17 s (figure 2(B1), the expanded insets in the middle).However, the APS ⊥ reappeared later.During the steady period of A-HFS ⊤⊥ , the normalized amplitude of APS ⊥steady /APS ⊥control was even significantly greater than that of APS ⊤steady /APS ⊤control (figure 2(B2)).The persistent appearance of APS ⊥steady following APS ⊤steady with the short IPI 2.5 ms indicated that the APS ⊥steady was not affected by the refractory period of the preceding APS ⊤steady .The result further verified the finding in previous report (Feng et al 2022) that the alternate monophasic ⊤ and ⊥ pulses in A-HFS ⊤⊥ can separately activate different sub-populations of neurons (Feng et al 2022), which is different from the situation of A-HFS ┼ ┼ .
Furthermore, here we hypothesized that the neurons within the overlapped activation volume of ⊤ and ⊥ pulses could be only activated by ⊥ pulses during the steady period of A-HFS ⊤⊥ .If so, the APS ⊥steady should be a fraction of APS ⊥control , while the APS ⊤steady should be generated by the neurons within the volume only activated by the ⊤ pulses.At baseline, the number of neurons activated only by the ⊤ pulses can be approximately evaluated by the amplitude: APS ⊤only = APS ⊤control − APS ⊥control (figure 3(A1)).In this case, with an identical pulse frequency in A-HFS, the ratios APS ⊤steady /APS ⊤only , APS ⊥steady /APS ⊥control and APS ┼steady /APS ┼control should be in a similar level.To verify the hypothesis, we next compared these ratios.
To make equal conditions for ⊤ and ⊥ pulses, a constant IPI 10 ms was set in A-HFS ⊤⊥ with the frequency of ⊤ and ⊥ pulses still at 50 Hz (figure 3(A2)).An A-HFS ┼ ┼ with a same frequency 50 Hz (i.e.IPI = 20 ms) was used as a control (figure 3(B)).The mean amplitude ratios of APS ⊥steady /APS ⊥control , APS ⊤steady /APS ⊤only and APS ┼steady /APS ┼control were not significantly different (figure 3(C)), which supported the above hypothesis.To verify the hypothesis further directly, we next decreased the intensity of ⊤ pulses in the A-HFS ⊤⊥ to make a similar activation volume for ⊤ and ⊥ pulses.

Neurons within the overlapped activation volume of cathodic-and anodic-pulses can be only activated by anodic-pulses during steady period of A-HFS ⊤ ⊥
With an identical intensity, the activation volume of a ⊤ pulse is greater than a ⊥ pulse (figure 1(B)).To make a similar range of activation volumes for the two types of pulses, the intensity of ⊤ pulse was reduced.To keep charge balance in the A-HFS ⊤⊥ , a balance phase (i.e.opposite phase) with a 1/40 intensity and a 40-fold width was added immediately following each ⊤ and ⊥ pulse to form pseudo-monophasic cathodic (⊤ B ) and anodic (⊥ B ) pulses (figure 4(A1)).The activation effects of these pulses were similar to those without a balance phase, indicated by the similar amplitudes of APSs induced by the pulses with and without balance-phase (figure 4(A2)).Therefore, the balance phase did not affect the action of leading phase obviously.
Keep the intensity of ⊥ B and reduce the intensity of ⊤ B gradually to titrate the APS ⊤B to an amplitude similar to the APS ⊥B (figure 4 pulses evoked obvious APS ⊥B (figure 4(D2)).In addition, we removed all the ⊤ B pulses in the 100 Hz A-HFS ⊤B⊥B to set an A-HFS ⊥B with pure ⊥ B pulses at 50 Hz (figure 4(E1)).The ratio of APS ⊥B_steady /APS ⊥B_control in the A-HFS ⊤B⊥B was not significantly different from that in the A-HFS ⊥B (figure 4(E2)).The results indicated that during the steady period of A-HFS ⊤B⊥B , only ⊥ B pulses were able to elicit APs in the neurons within the overlapped activation volume of both polarity pulses, just as the ⊥ B pulses did in the A-HFS ⊥B without ⊤ B pulses.Furthermore, statistical data showed that before APS ⊤B decreased to smaller than APS ⊥B in the late period of A-HFS ⊤B⊥B , in an early period from ∼2 to ∼15 s, the mean amplitude of APS ⊤B was greater than that of APS ⊥B (figure 5).The result indicated that during the transition period, the activation of ⊥ B was firstly lower than and subsequently rebounded to higher than that of ⊤ B .To further investigate the underlying mechanisms, we next utilized a computational model of axon to simulate the changes in neuronal activation by cathodic-and anodic-pulses during A-HFS ⊤⊥ .

Generation-failure and conduction-failure of APs in the axons under A-HFS ⊤⊥ due to the interaction effects of cathodic-and anodic-pulses
The above experimental results and our previous study (Feng et al 2022) have shown that the A-HFS ⊤⊥ -induced suppression of the neuronal activations must have generated at the axons instead of the somata.Otherwise, the somata would not have distinguished the APs induced initially on axons by the two types of pulses and made distinct suppressions of APS ⊤ and APS ⊥ .Therefore, to focus on the axonal mechanisms, here we simulated the neuronal responses to A-HFS ⊤⊥ base on the previous model of myelinated axons (Guo et al 2018).
In the computational model (figure 6(A)), the central node (Node 10 ) of axon is located immediately under the SE.Consequently, a ⊤ pulse can initiate an AP at Node 10 by a depolarization, while simultaneously hyperpolarizes the adjacent nodes in the two flanking regions (e.g. in Node 8 , denoted by the blue ◀ in figure 6(B, left)).Conversely, a ⊥ pulse can initiate an AP at the flanking nodes (e.g.Node 8 ) by a depolarization and simultaneously hyperpolarize Node 10 (figure 6(B, right)).In the case of a single-pulse stimulation, the AP initiated by a ⊤ or ⊥ pulse can successfully propagate to the end of axon (e.g.Node 0 ), provided that the ⊤ pulse-induced AP at Node 10 is great enough to overcome the obstacle of hyperpolarization at Node 8 (Kiernan and Bostock 2000, Van de Steene 2020, Zheng et al 2022).Here, a successful activation is defined as a successful conduction of a pulse-induced AP to the end of axon, i.e. the Node 0 ; and vice versa a failed activation.A failed activation may be caused by either a failure of AP initiation or a failure in AP conduction.
During A-HFS ⊤⊥ , the recordings of membrane potentials at the Node 0 (V m _Node 0 , figure 6  (figure 7(D)).Similar axonal block should have also appeared in the activations of ⊥ pulses that initiate AP at the Node 8 .However, ⊥ pulses can always generate successful AP on some axons (figure 6(D)).As shown in the following simulation results, the interactions between the effects of ⊤ and ⊥ pulses play a crucial role on the generations of the Firing-A and Firing-B that only succeed at ⊥ pulses during the steady period of A-HFS ⊤⊥ .
For an axon with Firing-A (figure 8), at the onset of A-HFS ⊤⊥ (figure 8(A)), the axon follows each ⊤ and ⊥ pulse to initiate an AP at Node 10 and Node 8 respectively.The APs can successfully conduct to the Node 0 .During the intermediate period of the A-HFS ⊤⊥ (figure 8(B)), as h_Na_Node 10 gradually decreases, the amplitude of initial AP at Node 10 by a ⊤ pulse also decreases.Consequently, the axonal ability for AP conduction decreases, eventually resulting in a conduction failure due to the obstacle posed by the strong hyperpolarization at the Node 8 and so on (highlighted by the ◀s within the blue shadow in figure 8(B)).However, the attenuation of AP conduction to Node 8 is beneficial for the recovery of h_Na at Node 8 .This results in a small increase of the h_Na_Node 8 when the next ⊥ pulse arrives (denoted by the orange arrow line on h_Na_Node 8 ).Thus, the ⊥ pulse initiates an AP at Node 8 with an increased amplitude instead.The Node 8 -AP can propagate successfully to Node 0 (denoted by the green shadow in figure 8(B)).Simultaneously, the Node 8 -AP propagates in the opposite direction to Node 10 and induces an AP (denoted by the red ▲ on V m _Node 10 ) which is even greater than the AP induced by the previous ⊤ pulse.This Node 10 -AP causes a further decrease of h_Na_Node 10 when the next ⊤ pulse arrives.Repeatedly, due to the effect of ⊥-induced AP on Node 10 , the h_Na_Node 10 decreases further with the arrival of each subsequent ⊤ pulse until the ⊤ pulses are no longer able to initiate any AP at Node 10 , resulting in a generation failure of AP (figure 8(C)).Therefore, once a ⊤ pulse fails to make a successful AP, the following ⊤ pulses can never induce a propagable AP again.
During the steady period of A-HFS ⊤⊥ (figure 8(C)), the decrease of h_Na at each node of the axon is steady.When a ⊤ pulse arrives, the h_Na_Node 10 is too small to initiate an AP.Instead, a ⊥ pulse can still initiate a propagable AP at Node 8 .Although the amplitude of Node 8 -AP decreases obviously due to the decreased h_Na_Node 8 , the AP is able to propagate successfully because no hyperpolarization prevents its conduction in the pathway.
For an axon with Firing-B (figure 9), at the onset of A-HFS ⊤⊥ (figure 9(A)), the induced firing is similar to that of type Firing-A.However, in the intermediate period of A-HFS ⊤⊥ (figure 9(B)), along with the decrease of h_Na, the conduction failure firstly appears at the AP induced by a ⊥ pulse (the orange shadow in figure 9(B, left)), instead of a ⊤ pulse.The reason is that this axon locates farther from the SE than the axon with Firing-A.The activation of ⊥ pulses at Node 8 is relatively weak.Meanwhile, the hyperpolarization induced by a ⊤ pulse at the flanking region of this axon is also relatively weak.The hyperpolarization is too weak to prevent the conduction of AP initiated by a ⊤ pulse at the Node 10 , even though the initial AP has already decreased due to a decrease of h_Na_Node 10 .Therefore, the ⊥ pulse, which is less efficient in depolarizing neuronal membrane, causes an AP conduction failure before the ⊤ pulse.
Nevertheless, after ∼1.2 s stimulation, with a further decrease of the h_Na_Node 10 , the further attenuated AP initiated by a ⊤ pulse at the Node 10 fails to overcome the hyperpolarization in its conduction pathway, resulting in a conduction failure finally (the blue shadow in figure 9(B, right)).Once a ⊤ pulse fails to generate a propagable AP, the failure will facilitate the recovery of h_Na_Node 8 to enable a ⊥ pulse to induce a successful AP again (see the orange arrow line on h_Na_Node 8 and the green shadow in figure 9(B, right)).This successful AP results in a further decrease of h_Na_Node 10 when a ⊤ pulse arrives, which prevents the ⊤ pulse from inducing a successful AP.Consequently, the neuronal response switches from a transition period with only ⊤-induced AP to that with only ⊥-induced AP (indicated by the red line at V m _Node 0 in figure 9(B, bottom)).Then, the following process is a duplication of that appears in Firing-A, except for the periodical conduction failures of AP initiated by ⊥ pulses (the orange shadows in figure 9(C)).No more propagable AP is induced by ⊤ pulses.
In summary, the conduction failure of ⊤induced AP will occur sooner or later on axons with either Firing-A or Firing-B.Once the failure occurs, the subsequent ⊤ pulses will never induce a successful AP again.Therefore, during the steady period of A-HFS ⊤⊥ , it is always only the ⊥ pulses to induce successful AP in the overlapped activation volume of both polarity pulses.

Discussion
The novel finding of the present study is that anodic-pulses, commonly less efficient than cathodicpulses in activating neurons, can prevail over the cathodic-pulses during the sustained axonal A-HFS ⊤⊥ .In addition, with the computational model, we propose the possible mechanisms of ⊤ pulse failures: HFS-induced attenuation of membrane excitability on axons, together with the obstacle of hyperpolarization in the AP conduction pathway and the interaction effects from ⊥ pulses.

Advantage of anodic-pulses over cathodic-pulses and its possible mechanisms
It is common sense that a cathodic-pulse has a greater activation effect than an anodic-pulse (Ranck 1975,  Basser and Roth 2000, Volkmann et al 2006, Zhang and Grill 2010, Soh et al 2019, Bower and McIntyre 2020).Just as the baseline situation in the present study, with an identical intensity, a single cathodicpulse was able to activate more neurons in a greater volume than an anodic-pulse (figure 1).However, during sustained A-HFS ⊤⊥ , the normalized amplitude of APS ⊥steady /APS ⊥control was significantly greater than that of APS ⊤steady /APS ⊤control regardless of the effect of refractory period (figure 2).This indicates an increase in the proportion of anodic-pulse-induced firing.Also, it indicates that two distinct populations of neurons were activated by the two types of pulses respectively.Furthermore, both the approximate estimation by A-HFS ⊤⊥ (figure 3) and the direct demonstration by A-HFS ⊤B⊥B (figures 4 and 5) showed an interesting result: the anodic-pulses were able to prevail over the cathodic-pulses in activating neurons in the volume covered by both polarity pulses.The model simulations showed that the sub-population of neurons closer to the SE (i.e. in the overlapped activation volume) were only activated by anodic-pulses during steady A-HFS ⊤⊥ , while those farther from the SE were only activated by cathodic pulses all the time (figure 6).
The model of individual axons includes a mechanism of K + accumulation and has been used to simulate HFS-induced axonal block previously (Guo et al 2018, Zheng et al 2020).Increase of [K + ] o in the narrow peri-axonal space can elevate the membrane potential of axon and cause partial inactivation of Na + channels (Poolos et al 1987, Beurrier et al 2001, Bellinger et al 2008, Lowet et al 2022).Since the activations of voltage-gated Na + channels are essential for generating an AP, their inactivation attenuates the evoked AP and finally results in the failures of AP conductions, i.e. an axonal block (figure 7).Different from the previous simulations with a point source (Guo et al 2018) or with biphasic-pulses (Zheng et al 2020), here the stimulations are monophasic-pulses alternating in polarity and are applied by a bipolar electrode.The three types of axonal firing in simulation results (figure 6) can fit the responses of a population neurons (i.e. the changes of APS) in rat experiments through the A-HFS ⊤⊥ , including its transition period (figure 5).
The modeling results show that the decline of axonal responses to A-HFS ⊤⊥ is due to two types of failure with gradual AP attenuations: the AP conduction failure and the AP generation failure.Both failures are caused by HFS-induced increase of [K + ] o and inactivation of Na + channels.Because of the obstacle of hyperpolarization in the conduction pathway, a conduction failure of AP will occur upon a cathodic-pulse sooner or later.Once the failure occurs, the following cathodic-pulses will never succeed again, because the AP induced by the subsequent anodic-pulses will always suppress the activation of Na + channels when a cathodic-pulse arriving.An AP conduction failure may firstly occur on an anodicpulse-induced AP (figure 9), thereby resulting in a transition period with APS ⊤ > APS ⊥ as showed in figure 5.However, the transition period cannot prevent a late occurrence of conduction failure of cathodic-pulse-induced AP.Ultimately, no cathodicpulse but anodic-pulses can elicit AP successfully in the overlapped activation volume of both polarity pulses.Therefore, the interaction effects between the pulses with opposite polarities and among their evoked-APs result in the advantage of anodic-pulses (figures 8 and 9).
In summary, both the animal experiments and the computational simulations show an unexpected result that the anodic-pulses can prevail over cathodicpulses during sustained HFS.

Implications
It has great prospects to adjust waveform parameters to improve stimulation efficiency and to expand applications in therapeutic neurostimulations (Gilbert et al 2023).The present study provides clues for the waveform adjustments.Conventionally, cathode-leading biphasic-pulses have been used in neurostimulations to prevent possible damage of neural tissues.The second anodic-phase only acts as a balance phase (Merrill et al 2005, Brocker andGrill 2013).To avoid a repolarization effect of the anodic-phase to counteract the preceding depolarization of cathodic-phase, an inter-phase gap may be added in some applications (Gorman and Mortimer 1983, Weitz et al 2014, Luna et al 2017, Eickhoff and Jarvis 2021).However, in the present study, in the A-HFS ⊤⊥ with an inter-phase gap as the IPI between the split cathode-and anodic-pulses, both polarity pulses can activate distinct sub-populations of neurons respectively.The discharge of the two relatively separated groups of neurons can get rid of the constraint of refractory period.This finding opens a way to design new stimulation paradigms for therapeutic neuromodulations.
First, activating two sub-populations of neurons with merely a short IPI by HFS ⊤⊥ (figure 2(B1)) indicates a magnification of excitation effect through spatial and temporal summations at synaptic transmissions in neuronal projection pathways.Given that one of the main mechanisms of DBS therapy is to excite neural activity or to overwrite pathologic activity with an artificial activity induced by HFS (Chiken and Nambu 2016, Lee et al 2019).The magnified activation of HFS ⊤⊥ on the post-synaptic neurons in projection regions may enhance the efficiency of neuromodulation.Actually, previous studies on the thresholds and loudness of CI in patients have shown that HFS trains with monophasic-pulses alternating in polarity at fixed intervals were more effective than biphasic-pulses (Van Wieringen et al 2005, 2006).The activation mechanisms of HFS ⊤⊥ found in the present study provide insights into the phenomenon observed in the previous CI studies.In addition, the HFS ⊤⊥ is also a power-saving paradigm, since it only consumes a half of the electrical power by a HFS of biphasic-pulses with an identical pulse frequency (figure 2).
Second, the applications of certain neural prosthetics may get benefits from utilizing the features of HFS ⊤⊥ to activate two relatively separated populations of neurons by a single electrode contact.Many implanted neural prosthetics are realized by multiple micro-stimulation contacts (or an electrode array) to provide encoded information, such as auditory midbrain implant (Lim et al 2015), visual cortical implant (Fernández et al 2021), tactile implant in somatosensory cortex (Hughes et al 2021) and so on.An HFS ⊤⊥ sequence may encode the activations at each single contact/site to some extent.The encoding may be fulfilled by varying the parameters of the two polarity pulses, such as the interval between adjacent opposite pulses, the intensity and/or frequency ratios of opposite pulses.The time varying parameters may generate various combinations of the activations of two sub-population neurons to form encoded information.
Finally, the finding of the present study is relatively essential and universal.It was obtained from the neuronal responses to antidromic stimulations on the axonal fibers of rat hippocampal CA1 region.The direct reactions of axons immediately under stimulations involve neither synaptic transmissions nor interactions of neuronal networks.Therefore, they are the essential reactions being commonly applicable to axons in either normal or pathological nervous system providing normal axonal functions.The finding is meaningful for the neuromodulation therapies involving axonal activations in deep brain or peripheral nerves, such as DBS, SCS, VNS and SNM.

Limitations
The results of the present study of A-HFS ⊤⊥ were only observed in rat hippocampus in-vivo.Further studies on other targets of neuromodulation therapies, such as other brain regions, spinal nerves and peripheral nerves, are needed to be investigated to verify the universality.Moreover, the effect, safety and practicality of the stimulation paradigm of alternate monophasic-HFS to treat neurological diseases need further animal studies and clinical verifications.
The experimental results presented here and in our previous studies (Feng et al 2013(Feng et al , 2022) ) have shown that the HFS-induced suppressions of neuronal activations mainly occur at axons instead of somata.Therefore, to focus on the investigation of axonal mechanisms, here we utilized an axonal model without other neuronal elements such as axonal initial segment, soma and dendrites.The simplified model may underestimate the influences of other elements on the actions of axon.A more integral model is needed to further confirm the axonal mechanisms.In addition, integrating more factors may improve the model.For instance, an increase of temperature around HFS site could induce a thermal block in axonal conduction, especially for thin axons in brain (Ford et al 2020).

Conclusion
Because of the obstacle of hyperpolarization in the conduction pathway and the suppression actions from anodic-pulses, cathodic-pulses can lose their original advantage and fail in the competition with anodic-pulses to activate neurons during sustained HFS of alternate cathodic-and anodic-pulses, an equivalent of split biphasic-pulses.The advantage of anodic-pulses in sustained HFS provides new clues for neuromodulations.

Figure 1 .
Figure 1.Determine the relationships between the ranges of activation volumes of different types of pulses.(A) Schematic diagram of the locations of recording electrode (RE) and stimulation electrode (SE) in rat hippocampal CA1 region.(B) APS waveforms evoked by the three types of single-pulse tests (left) and comparisons of their mean amplitudes (right).### P < 0.001, n.s.P > 0.05, one-way ANOVA with post hoc Bonferroni tests.(C) Typical recordings of control APSs evoked by the single-pulses (most left), together with APSs evoked by the three types of paired-pulses composed of biphasic-pulse (┼), monophasic anodic-(⊥) and cathodic-(⊤) pulses with different IPIs.(D) Changes in the mean ratios of the APS amplitudes (APStest) evoked by the second pulse of the paired-pulses to their control amplitudes (APS control ) with different IPIs.Error bars depict ± standard deviation.

Figure 2 .
Figure 2. Neuronal responses to A-HFS ┼ ┼ and A-HFS ⊤⊥ with alternate IPIs.(A) A1: typical recording of neuronal responses during an A-HFS ┼ ┼ with alternate IPI (2.5 & 17.5 ms).The expanded insets show the evoked APS waveforms at onset, ∼1.5 s and ∼100 s (steady period).A2: comparisons of the normalized amplitudes of APS17.5 and APS2.5 at the onset and steady period of A-HFS ┼ ┼ .(B) Similar to (A), the waveforms of APS ⊤ and APS ⊥ during an A-HFS ⊤⊥ with alternate IPI (B1) and comparisons of the normalized amplitudes of APS ⊤ and APS ⊥ at the onset and steady period of A-HFS ⊤⊥ (B2).In A2 and B2, the APS amplitudes were normalized by their baseline values (APS control ) and * * * P < 0.001, paired t-test.

Figure 3 .
Figure 3. Comparisons of APSs evoked by anodic-and cathodic-pulses in steady period of A-HFS ⊤⊥ .(A) A1: APS ⊤control and APS ⊥control induced by single ⊤ and ⊥ pulses together with APS ⊤only = APS ⊤control − APS ⊥control .The APS ⊤only was generated by the neurons only activated by a ⊤ pulse.A2: Typical recording of neuronal responses to A-HFS ⊤⊥ with constant IPI 10 ms.The expanded insets show the evoked APSs at onset, ∼3.5 s and ∼100 s (steady period) of A-HFS ⊤⊥ .(B) Typical recording of A-HFS ┼ ┼ with constant IPI 20 ms.(C) Comparisons of the ratios of APS amplitudes: APS ⊥steady /APS ⊥control , APS ⊤steady /APS ⊤only and APS ┼steady /APS ┼control .n.s.P > 0.05, one-way ANOVA.

Figure 4 .
Figure 4. Responses of neurons within the overlapped volume activated by pseudo-monophasic cathodic-and anodic-pulses.(A) A1: schematic diagram of the formations of pseudo-monophasic-pulses with a balance phase, denoted as ⊤B and ⊥B (left), together with the typical APSs evoked by them (right).A2: comparisons of APS amplitudes evoked by the cathodic-and anodic-pulses with and without a balance phase.(B) B1: APSs evoked by single-pulses of 0.3-0.1 mA ⊤B (left) and 0.3 mA ⊥B (most right).B2: comparison of the amplitudes of APSs evoked by ∼0.1 mA ⊤B and ∼0.3 mA ⊥B.(C) Neuronal responses to paired-pulse stimulations of '⊤B⊥B' and '⊥B⊤B' (0.1 mA ⊤B and 0.3 mA ⊥B) with a small IPI: 1, 1.5 and 2.5 ms.(D) D1: typical recording of an A-HFS ⊤B⊥B consisting of alternate 0.1 mA ⊤B and 0.3 mA ⊥B.D2: comparison of amplitudes of APS ⊤B and APS ⊥B in the steady period of the A-HFS ⊤B⊥B .(E) E1: typical recording of an A-HFS ⊥B consisting of 0.3 mA ⊥B only.E2: comparison of the mean amplitude ratios APS ⊥B_steady /APS ⊥B_control between A-HFS ⊤B⊥B (shown in D1) and A-HFS ⊥B (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.

Figure 5 .
Figure 5. Scatter plot of the mean normalized amplitudes of APS ⊤B and APS ⊥B evoked by each pulse of A-HFS ⊤B⊥B (n = 7) consisting of alternate ∼0.1 mA ⊤B and ∼0.3 mA ⊥B.The ranges denoted by light colors indicate ± standard deviation.
(C)) show three types of firing (denoted as Firing-A, -B and -C) on the axons locating at different distances from the SE (figure 6(A)).The Firing-A and -B appear on the axons within the overlapped activation volume of ⊤ and ⊥ pulses, while the Firing-C appears on the axons only activated by ⊤ pulses.The axons with Firing-A are closest to the SE, while the axons with Firing-C are the farthest (figure 6(A)).As shown in figure 6(C), the axon of Firing-A can follow each of the ⊤ and ⊥ pulses to fire and successfully propagate AP at the onset of A-HFS ⊤⊥ .Then, the axon fails at ⊤ pulses and only succeeds at ⊥ pulses in the intermediate and steady periods.The axon of Firing-B acts as Firing-A at the onset of A-HFS ⊤⊥ .However, in the intermediate period, the axon can only succeed at ⊤ pulses.Later, the successes switch to ⊥ pulses till the steady period.The axon of Firing-C can only respond to the ⊤ pulses throughout the A-HFS ⊤⊥ with a decreased firing rate in the steady period.The schematic summary of the three types of firing (figure 6(D)) shows that the integration of the three types of firing can reproduce the results obtained from the rat experiments (figure 5).We next analyzed the dynamics of axonal membrane to further reveal the underlying mechanisms.Similar to previous reports (Beurrier et al 2001, Shin et al 2007, Bellinger et al 2008, Guo et al 2018), in the simulation results, the increase of [K + ] o in the peri-axonal space is a critical factor responsible for the failures of axon activations during A-HFS ⊤⊥ .Take an example of [K + ] o around Node 10 where the ⊤ pulses initiate AP.The sustained stimulation of A-HFS ⊤⊥ increases [K + ] o _Node 10 (figure 7(A)), thereby causing a partial inactivation of Na + channels.The inactivation variable of Na + channels at the Node10 (h_Na_Node 10 ) decreases (figure 7(B)), thereby resulting in a decreased amplitude of the initial APs with the ⊤ pulses (figure 7(C)).The decreased AP at the Node 10 is not able to propagate successfully to Node 0 thereby causing an activation failure (i.e.axonal block) of the ⊤ pulses

Figure 6 .
Figure 6.Computational model of axons located at different distances to the stimulation electrode (SE) and their responses to A-HFS ⊤⊥ .(A) Illustration of the simulated electrical field potentials generated by a ⊤ pulse around SE and axons.(B) A ⊤ pulse (left) and a ⊥ pulse (right) generate depolarization, AP and hyperpolarization at different nodes along an axon.(C) Membrane potentials at Node0 (Vm_Node0) of 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 types of firing shown in C. The blue and orange dots represent successful activation of axon by the ⊤ and ⊥ respectively, while the black circles represent failed activation.

Figure 7 .
Figure 7. Increase of [K + ]o induces axonal block during A-HFS ⊤⊥ .(A) [K + ]o in peri-axonal space near the Node10 ([K + ]o_Node10).(B) Inactivation variable of Na + channels at the Node10 (h_Na_Node10).In A and B, the black dots on curves mark the values at the time the ⊤ pulses arriving.(C) Membrane potential at the Node10 (Vm_Node10).The APs initiated by ⊤ pulses at the Node10 are marked by the blue boxes.(D) Membrane potential at Node0 (Vm_Node0).The blue shadows denote the failures of AP conduction to Node0, i.e. occurrence of axonal block.

Figure 8 .
Figure 8. Membrane potentials (Vm) at each node of the axon generating Firing-A during onset (A), intermediate (B) and steady (C) periods of A-HFS ⊤⊥ .The h_Na curves at Node10 (h_Na_Node10) and at Node8 (h_Na_Node8) are shown below their corresponding Vm curves.The squares on the h_Na_Node10 and h_Na_Node8 respectively highlight the values when the ⊤ and ⊥ pulses arrive.In (A), the APs initiated at Node10 and Node8 can all successfully propagate to Node0, denoted by the green shadow.In (B), the blue shadow highlights the first conduction failure of AP with ⊤ pulse.The blue boxes on the Vm_Node10 curve mark the attenuated APs initiated by ⊤ pulses.The blue arrow line on the h_Na_Node10 curve marks the decreased values when ⊤ pulses arrive.And, the orange boxes on the Vm_Node8 curve mark the increased APs initiated by ⊥ pulses.The orange arrow line on the h_Na_Node8 curve marks its increased values.In (C), the blue boxes on the Vm_Node10 curve highlight that no AP is generated by ⊤ pulses in the steady period of A-HFS ⊤⊥ .

Figure 9 .
Figure 9. Membrane potential (Vm) at each node of the axon generating Firing-B during onset (A), intermediate (B) and steady (C) periods of A-HFS ⊤⊥ .The h_Na_Node10 and h_Na_Node8 are shown below their corresponding Vm curves.The squares on the h_Na_Node10 and h_Na_Node8 respectively highlight the values when the ⊤ and ⊥ pulses arrive.In (A), the APs initiated at Node10 and Node8 can all successfully conduct to Node0, denoted by the green shadow.In (B), the blue and orange boxes on the Vm curves mark the APs initiated respectively at Node10 and Node8.The orange and blue shadows show that the conduction failure firstly occurs at ⊥ and then at ⊤.The red arrow line over the Vm_Node0 highlights the switch of AP from following ⊤ to following ⊥.In (C), the orange shadows highlight the periodical conduction failures of AP initiated by ⊥ at Node8.
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