Control of spatiotemporal activation of organ-specific fibers in the swine vagus nerve by intermittent interferential current stimulation

Rossetti, Nicolò; Song, Weiguo; Schnepel, Philipp; Jayaprakash, Naveen; Koutsouras, Dimitrios A.; Fichman, Mark; Wong, Jason; Levy, Todd; Elgohary, Mohamed; Qanud, Khaled; Giannotti, Alice; Barbe, Mary F.; Chen, Frank Liu; Langereis, Geert; Datta-Chaudhuri, Timir; Mihajlović, Vojkan; Zanos, Stavros

doi:10.1038/s41467-025-59595-4

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Published: 13 May 2025

Control of spatiotemporal activation of organ-specific fibers in the swine vagus nerve by intermittent interferential current stimulation

Nature Communications volume 16, Article number: 4419 (2025) Cite this article

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Abstract

Vagus nerve stimulation (VNS) is emerging as potential treatment for several chronic diseases. However, limited control of fiber activation, e.g., to promote desired effects over side effects, restricts clinical translation. Towards that goal, we describe a VNS method consisting of intermittent, interferential sinusoidal current stimulation (i²CS) through multi-contact epineural cuffs. In experiments in anesthetized swine, i²CS elicits nerve potentials and organ responses, from lungs and laryngeal muscles, that are distinct from equivalent non-interferential sinusoidal stimulation. Resection and micro-CT imaging of a previously stimulated nerve, to resolve anatomical trajectories of nerve fascicles, demonstrate that i²CS responses are explained by activation of organ-specific fascicles rather than the entire nerve. Physiological responses in swine and activity of single fibers in anatomically realistic, physiologically validated biophysical vagus nerve models indicate that i²CS reduces fiber activation at the interference focus. Experimental and modeling results demonstrate that current steering and beat and repetition frequencies predictably shape the spatiotemporal pattern of fiber activation, allowing tunable and precise control of nerve and organ responses. When compared to equivalent sinusoidal stimulation in the same animals, i²CS produces reduced levels of a side-effect by larger laryngeal fibers, while attaining similar levels of a desired effect by smaller bronchopulmonary fibers.

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Introduction

Neural signaling through the vagus nerve is essential for physiological homeostasis through autonomic reflexes¹ and is implicated in the pathogenesis of several chronic brain, cardiopulmonary, gastrointestinal, and inflammatory diseases². For those reasons, the vagus nerve has emerged as a target for therapeutic neuromodulation, with vagus nerve stimulation (VNS) therapies approved for epilepsy, depression and stroke rehabilitation^3,4,5,6, Alzheimer’s disease⁷, pain⁸, anxiety⁹, tinnitus¹⁰, rheumatoid arthritis¹¹, inflammatory bowel disease¹², heart failure¹³, diabetes¹⁴, obesity¹⁵, and pulmonary hypertension^16,17.

VNS is typically delivered through epineural cuff electrodes implanted around the cervical nerve trunk (Fig. 1B), where sensory and motor fibers travel inside nerve fascicles¹⁸. Stimulating smaller vagal fibers, such as those innervating the heart, lungs or abdominal viscera may elicit clinically beneficial, desired effects¹⁹. However, currently used bipolar VNS devices strongly activate larger fibers, some of which innervate organs like the larynx and pharynx and result in side effects, e.g., coughing and voice hoarseness, which may lead to sub-optimal dosing and reduced therapeutic efficacy²⁰. Spatially selective VNS, comprising rectangular pulses delivered through multi-contact cuff electrodes (MCEs) has been shown to activate organ-specific fibers asymmetrically and differentially in swine (Fig. 1C)^21,22,23. To the extent that the fascicular and functional organization of the human vagus nerve shares similarities with that of the swine vagus nerve^{24,25,26,27,28}, spatially focused stimulation may be a viable strategy for more selective VNS. However, even with MCEs, functional selectivity of rectangular pulse stimulation is limited: larger fibers are still activated before smaller fibers, due to their lower activation threshold^21,22, and fibers located at the periphery of the trunk are activated before those at the interior of the trunk, due to closer proximity to stimulating contacts²⁹. Despite its potential translational significance, spatial and temporal control of activation of vagal fibers, i.e., fibers mediating specific desired effects vs. side effects, is currently not feasible.

**Fig. 1: Anatomical basis for control of spatiotemporal activation of fibers by vagus nerve stimulation using intermittent, interferential current stimulation (i²CS).**

Interferential current stimulation (iCS) was introduced in the 1950s to facilitate muscle strengthening in athletes^30,31 and has recently regained attention as a method for targeted neuromodulation^32,33. iCS of the brain uses separate electrical sources generated from scalp electrodes, with slightly different, high frequencies (in the order of kHz) that, through temporal interference, give rise to lower frequency amplitude modulations (AMs); AMs produce spatially focused activation of neurons located deeper in the brain^34,35. The potential of iCS for targeted stimulation of peripheral somatic nerves was recently demonstrated in small animals, both non-invasively³⁶ and using invasive cuff electrodes³⁷. In addition to continuous iCS, recent work demonstrated the use of short bursts, e.g., consisting a few AM cycles, to entrain low frequency activity in deeper brain regions³⁸.

Whether invasive iCS through cuff electrodes has a role in selective stimulation of nerves with complex fascicular structure in general, and of the vagus nerve in particular, is not known. In this paper, we report a method for VNS, termed intermittent interferential current stimulation (i²CS) that delivers short pulses (< 1 ms) of high-frequency stimulation (around 20 kHz), resulting in AMs in the low kHz range. Through a combination of in vivo experiments in anesthetized swine and in silico computational modeling of an anatomically realistic vagus nerve obtained through fascicle tracking, we uncover working principles of the method and demonstrate that i²CS activates organ-specific fibers in a predictable, spatially focused and temporally precise manner. In animal experiments, i²CS has improved selectivity for a desired effect over a side effect compared to equivalent, non-interfering sinusoidal stimulation.

Results

Bronchopulmonary- and laryngeal-specific fascicles progressively merge, resulting in a bimodal anatomical organization at the cervical vagus nerve of a swine

Use of spatially selective VNS to preferentially activate a desired effect, e.g., from the lungs, over a side effect, e.g., from laryngeal muscles, relies on anatomical separation between bronchopulmonary- and laryngeal-specific vagal fibers at the site of electrode implantation. Separation of organ-specific fibers inside fascicles at the cervical vagus nerve of a swine has been qualitatively demonstrated²² but has not been quantified, and therefore anatomical constraints on spatially selective VNS are unknown. To quantify the anatomical separation of fibers, we tracked the longitudinal trajectories of bronchopulmonary (BP) and recurrent laryngeal (RL) fascicles from the level of branch emergence to the cervical region, identified merges and splits of fascicles, and estimated mixing of fibers inside fascicles at different levels (Fig. 2). At branch emergence, and for a few millimeters in the rostral direction, BP- and RL-specific fascicles are spatially almost completely separated from other fascicles (4 mm for BP; 4.6 mm for RL; Fig. 2B, C, respectively). However, at more rostral levels, BP, RL and other fascicles progressively merge, and no fascicles at the cervical region project solely to branches innervating a single organ; instead, fascicles contain a mix of BP, RL and other fibers (Fig. 2D). Despite significant merging of fascicles, BP and RL fiber percentage estimates show a distinct spatial arrangement: BP-rich fascicles occupy one area of the nerve and RL-rich fascicles a different area (Fig. 2D3, D4). The result is a bimodal distribution of fibers along a transverse axis, with most RL and BP fibers located at approximately 1 mm on either side of the axis mid-point and about 2 mm away from the nerve periphery (Fig. 2D5).

**Fig. 2: Bronchopulmonary- and recurrent laryngeal-specific fascicles progressively merge and give rise to a bimodal anatomical organization at the cervical level.**

Using quantitative anatomical tracking, we document bimodal anatomical organization of organ-specific fibers in the cervical vagus nerve of a swine, suggesting that focal stimulation along a transverse direction could improve selectivity of VNS.

Interferential stimulation (IS) elicits distinct nerve and organ responses that are different than those of equivalent, non-interfering sinusoidal stimulation

Interfering current sources give rise to electric fields and amplitude modulations at distinct spatial locations that are different than those with equivalent non-interfering stimulation (Suppl. Fig. S1)³³. To test whether interferential VNS activates different areas inside the vagal trunk, thereby engaging different fiber populations, i²CS was delivered through pairs of contacts of an MCE (see Methods for detailed stimulation parameters); then, evoked compound action potentials (eCAPs) and physiological responses from the lungs and laryngeal muscles were measured in anesthetized swine. i²CS with uneven stimulus intensities results in AM on one side of the nerve (negative steering ratio, expressed as the ratio in amplitude of the left current source with respect to the total current, mapped to a −1 to +1 range for illustration purposes; i.e., 0.9 = −1, 0.7 = −0.5, 0.5 = 0, 0.3 = 0.5, 0.1 = 1; Fig. 3A). The fast-fiber eCAP and the respective, fast-fiber-mediated, laryngeal electromyography (EMG) signal (Fig. 3A1, A2, respectively; Suppl. Fig. S2) are smaller than those in response to i²CS with the opposite steering ratio (Fig. 3B1, B2, respectively; Suppl. Fig. S2). Slow eCAP and respective breathing responses follow the opposite pattern (Fig. 3A3 vs. B3). To test the hypothesis that differential responses depend on interference rather than solely on activation of nearby vagal fibers by the two sinusoidal sources, sinusoidal stimulation with the same frequency and steering ratio was delivered through the same contacts, resulting in large, fast eCAP and EMG responses in both steering conditions (Fig. 3C1–2 and D1–2). On the other hand, breathing responses in the two steering conditions were similar to those with i²CS (Fig. 3, C3, D3, see also Suppl. Fig. S3 for single contact stimulation).

**Fig. 3: i²CS elicits distinct experimental nerve and organ responses that are different than those to equivalent, non-interfering sinusoidal current stimulation.**

Experimental results suggest that interferential stimulation elicits specific nerve responses that depend on current steering and are different than those elicited by equivalent, non-interfering, sinusoidal stimulation delivered through the same contacts.

Interferential stimulation elicits reduced fiber activation at the focus of interference, in an anatomically realistic, physiologically validated model of the swine vagus nerve

To demonstrate interference at a focal area of the nerve, fiber activity within anatomically characterized organ-specific fascicles needs to be recorded. Because recording from single fibers was not available to us, we used a recently developed modeling framework³⁹ to compile an anatomically realistic neuro-electric model of a micro-CT-imaged and anatomically quantified swine vagus nerve (Fig. 4A–C). Because the same nerve was stimulated in in vivo experiments, we were able to compare modeled and experimentally measured responses to the same interferential stimuli. For example, the magnitude of the breathing response and the activity of modeled fibers in BP fascicles both change as a function of steering ratio, in a highly correlated manner (Fig. 4D). RL-mediated EMG responses and activity of modeled RL fibers are similarly correlated (Fig. 4E). Significant correlations between measured physiological responses and modeled fiber responses are found across steering ratios (Fig. 4F), in line with significant correlations between experimental eCAPs and physiological responses, also across steering ratios (Suppl. Fig. S2).

**Fig. 4: An anatomically realistic, physiologically validated biophysical model of the nerve-electrode interface predicts that i²CS produces reduced activation of fibers at the focus of interference.**

Using the model, we estimated the magnitude of the interferential electric potential (Fig. 4G), the amplitude modulation (AM, Fig. 4H) and the activation thresholds of fibers (Fig. 4I and Suppl. Figs. S4, S21, and S22), within different fascicles. Activation thresholds of fibers located inside fascicles experiencing maximum AM with i²CS are greater than with non-interferential sinusoidal stimulation, indicating reduced fiber activation at the focus of interference (Fig. 4I, left panel). In contrast, for fascicles closer to the nerve periphery, where non-interferential sinusoidal stimulation dominates, activation thresholds are similar for the two stimulation conditions (Fig. 4I, right panel).

Results from anatomically realistic, physiologically validated biophysical models of a swine vagus nerve indicate that i²CS results in increased fiber activation threshold at the focus of interference, compared to equivalent non-interferential stimulation, potentially providing an anatomical basis for selective VNS.

Interferential stimulation activates vagal fibers in a specific spatiotemporal pattern, in experimental recordings and in swine vagus nerve models

The time course of the AM generated with i²CS depends on the difference between the two carrier frequencies, e.g., carrier frequencies of 20 and 22 kHz generate half beats with 0.25 ms duration (Fig. 1D). In principle, the slower rise of AM at the focus of maximum interference should result in gradual depolarization of fibers and a delay in the onset of i²CS-elicited responses, compared to the faster onset responses to sinusoidal stimulation (Fig. 1E). To test this hypothesis, we recorded laryngeal EMG and eCAPs in response to i²CS and sinusoidal stimulation, at different steering ratios and beat durations (Fig. 5A and Suppl. Fig. S6). While sinusoidal stimulation elicits EMG responses with the same short latencies independently of steering ratio, i²CS elicits EMG responses with longer, steering ratio-dependent latencies (Fig. 5A), consistent with a shifting focus of interference. In addition, i²CS with different beat durations elicits EMG responses with different latencies, all of which are longer than the latency of sinusoidal stimulation-elicited responses (Fig. 5B), consistent with slower activation of fibers by the rising AM at the focus of interference.

**Fig. 5: Interferential stimulation activates vagal fibers in a specific spatiotemporal pattern, in experiments in swine and in swine vagus nerve models.**

To establish a single fiber basis for these effects, we modeled action potentials (APs) in response to i²CS in a deep-located RL fascicle (inset); we found that APs occur at different latencies, depending on steering ratio, with slower onset of APs at fibers inside vs. outside of the interference focus (Fig. 5C). This finding agrees with experimental results obtained with i²CS-elicited eCAPs (Suppl. Fig. S6). Similarly, modeled APs elicited by i²CS with longer beat durations occur at longer latencies than those elicited by shorter-beat i²CS or with sinusoidal stimulation (Fig. 5C), a difference that holds across all fascicles with a preponderance of RL fibers (Fig. 5D). In modeled fibers, increasing the beat duration of i²CS increases the latency of activation of fibers at the focus of interference (Fig. 5E); the same dependency holds for a second interference focus, defined by a different steering ratio (Fig. 5F).

Experimental and modeling results indicate that i²CS confers control of spatial and temporal aspects of activation of vagal fibers through selection of current steering and beat duration, respectively.

Intermittent interferential stimulation controls precise timing of action potentials in modeled nerve fibers

Because interference produces a specific spatiotemporal pattern of fiber activation, the choice between continuous or intermitted stimulation may differentially impact generation of action potentials in nerve fibers. With i²CS, fascicles experience a range of AM levels, from minimal AM in superficial fascicles right next to contacts, to maximal AM in deeper fascicles (Fig. 6i1). Modeled responses to continuous interferential stimulation, with the same carrier frequency as i²CS used in the in vivo experiments (Fig. 1D), span a variety of profiles after initial onset response, depending on AM at the respective fascicle, e.g., phasic activation followed by a block (Fig. 6A1, A2, and A5), regular tonic (Fig. 6A3) or irregular tonic activation (Fig. 6A4), substantially differing from activation profiles obtained via pure sinusoidal stimulation (Fig. S20), in agreement with previous reports³³. In contrast, i²CS with the same carrier frequencies and a pulse duration below the fibers’ refractory period (<2 ms), results in a predictable, regular temporal profile of fiber activation characterized only by the onset response, across all fascicles regardless of their location, with an inter-spike-interval (ISI) determined by the pulse repetition frequency (33 Hz; Fig. 6B). Across all nerve fascicles experiencing different levels of AM (Fig. 6i2), the temporal precision of fiber activation, quantified by the variance of ISI distributions, is relatively low for interferential stimulation and depends on the location of the fascicle (Fig. 6C1–C3), whereas it is consistently high for intermittent i²CS, independently of the level of AM at the respective fascicle (Fig. 6C4).

**Fig. 6: Repetition frequency of intermittent interferential stimulation controls timing of evoked action potentials in a temporally precise manner, in models of nerve fibers.**

Neural modeling results indicate that intermittent interferential stimulation precisely controls the timing of elicited action potentials in fibers across the entire nerve, with ISIs determined by the pulse repetition frequency.

Interferential stimulation has improved functional selectivity for a desired effect over a side effect compared to equivalent, non-interfering sinusoidal stimulation, in experiments in anesthetized swine

The spatial distributions of RL and BP fibers along a transverse axis of swine vagus nerve show separate peaks at deeper-located fascicles rather than at the nerve periphery (Fig. 2D5). We therefore hypothesized that interferential stimulation producing maximum AM in deeper fascicles on the “RL side” of the nerve would result in reduced activation of an RL-mediated side-effect (laryngeal muscle contraction) over a BP-mediated desired effect (breathing response), compared to equivalent, non-interfering sinusoidal current stimulation. We recorded nerve potentials (eCAPs) in response to i²CS and to sinusoidal stimulation, at different steering ratios; while slow eCAPs, corresponding to the (smaller fiber-mediated) desired effect, are similar in both conditions, i²CS elicits smaller fast eCAPs, that correspond to the (larger fiber-mediated) side effect (Fig. 7A, B, respectively). Compared to sinusoidal stimulation, i²CS is associated with both greater selectivity and greater range for slow eCAPs across several steering ratios (Fig. 7C), resulting overall in greater selectivity for smaller fibers (Fig. 7D). Furthermore, i²CS elicits the same level of breathing response (Fig. 7E), but with smaller magnitude of laryngeal EMG (Fig. 7F), resulting in greater selectivity for desired effect over side effect, both in individual animals and on the population level (Fig. 7D, H, Suppl. Figs. S7, S14–19). Selectivity depends on stimulus intensity: higher stimulation amplitudes tend to reduce selectivity, due to increased fiber recruitment across all fascicles (Suppl. Figs. S30 and 31). When compared with physiological responses to rectangular pulse stimulation, collected in previously described experiments²², i²CS tends to attain greater selectivity, even though the comparison is not parametric nor systematic and therefore can only be taken as suggestive (Suppl. Fig. S8, note that the experimental design and cuff electrode geometry was different in these experiments).

Fig. 7: Interferential stimulation of the swine vagus nerve attains increased selectivity of a desired effect, mediated by smaller BP fibers, over a side effect, mediated by larger RL fibers, compared to equivalent sinusoidal stimulation.

Consistent with experimental results, recruitment of modeled smaller fibers inside BP fascicles (desired effect) and of larger fibers inside RL fascicles (side effect) depends on steering ratio for i²CS and sinusoidal stimulation (Fig. 7I–K), resulting in different recruitment profiles (Fig. S21) which are consistent with the mechanism of reduced activation at the focus of interference. This is particularly evident for a steering ratio of −0.5, where the two selectivity profiles are very different from each other, with i²CS being able to achieve better selectivity of BP fibers. This difference results in higher BP fiber selectivity of i²CS over sinusoidal stimulation for a stimulation amplitude of 1.5 mA (Fig. 7L). For high amplitude values, the two waveforms tend to provide similar activation profiles (Suppl. Fig. S21), which is expected due to the increased fiber recruitment at high currents which overcomes the selective steering effect of interference. For reference, computational modeling results obtained with single contact biphasic rectangular wave stimulation delivered close to the BP center (Fig. S23) present a similar selectivity index profile as obtained via i²CS with a steering ratio of −1.

In a series of experiments in swine, i²CS with interference focus on RL fascicles has improved selectivity for a desired effect, mediated by smaller BP fibers, over a side-effect, mediated by larger RL fibers, compared to equivalent non-interfering sinusoidal stimulation; results are corroborated by modeling studies.

Discussion

Significance of spatially focused and temporally precise control of vagal fiber activation with i²CS

Our study demonstrates that interferential stimulation is a viable method for tunable and precise, spatially focused VNS. Selection of the 2 contact pairs of the MCE defines the steering axis on the radial plane, and of the 2 stimulus intensities (steering ratio) defines the maximum AM site along that axis (Figs. 3–5). To the best of our knowledge, ours is the first demonstration, both in principle and in practice, of precise control of the spatial focus at which the maximum AM of the electric field is generated. To the extent that the vagus nerve in humans has a functional fascicular organization that has similarities with that of the swine vagus nerve, e.g., heart-specific fascicles²⁶, spatial focusing may be a viable strategy for selective VNS¹⁹. This has implications for the future design of more selective VNS devices, since attaining tunable focusing of the electric fields with rectangular pulses delivered through cuff is less feasible. With rectangular pulses, spatial focusing and fiber recruitment depends on the position of stimulated contacts with respect to the underlying spatial distribution of fibers, i.e., the closer the fibers are to the electrode, the lower the activation threshold^22,40. Consequently, the only way to improve spatial selectivity of rectangular pulse stimulation is the repositioning of the multi-channel cuff electrodes on the nerve or mechanical deformation of neural tissue to redistribute fiber locations and better expose certain areas in the nerve trunk^41,42.

In addition to reducing side effects, more selective VNS may permit testing of a wider range of stimulus intensities for calibration of the desired effect (Fig. 7), potentially resulting in improved dose titration and therapeutic efficacy⁴³. For example, even though VNS in epilepsy is generally safe and well tolerated in the long-run, titration of therapy is performed progressively, over repeated office visits, to minimize side effects like cough and voice alteration, arising from activation of large, low threshold laryngeal and pharyngeal fibers⁴⁴; rapid titration could significantly accelerate clinical response, as reported in a recent meta-analysis⁴⁵. Similarly, in clinical studies of VNS in heart failure, laryngeal and pharyngeal side effects prevented clinicians from adequately dosing VNS to a level required to activate smaller, higher threshold cardiac fibers mediating the desired effect of cardio-inhibition, possibly contributing to the failure of clinical trials⁴⁶.

Our study also demonstrates that intermittent delivery of short ‘pulses’ of interfering stimuli results in temporally precise activation of vagal fibers, with the timing of elicited APs controlled by the amplitudes and frequencies of the 2 interfering sources (Fig. 5), and ISIs controlled by the pulse repetition frequency (Fig. 6). To the best of our knowledge, i²CS is the first paradigm that combines spatial focusing with temporal precision. Contrary to conduction block observed with continuous kHz stimulation^47,48, control of fiber activation is achieved here via an onset response^49,50. Conventional, rectangular pulse VNS elicits temporally precise action potentials, time-locked to the stimulus onset, but spatial focusing is limited. Suprathreshold^51,52 or subthreshold high-frequency stimulation⁵³ attains improved fiber selectivity but elicits asynchronous action potentials in nerve fibers, with limited temporal precision.

Temporally precise stimulation of vagal fibers may be useful when fiber activation needs to be tightly controlled relative to a dynamically changing physiological state. For example, respiratory-gated auricular nerve stimulation is thought to control hypertension by eliciting afferent volleys at specific phases of the respiratory cycle, i.e., when sensory brainstem neurons involved in the baroreflex are more excitable^54,55. Likewise, delivering stimuli to the vagus nerve at specific phases of the cardiac pacemaker cells during the cardiac cycle may differentially impact the risk of vagally-induced sinus, atrial, sinoatrial or ventricular arrhythmias^{56,57,58,59,60}. Finally, closed-loop VNS to control blood pressure⁶¹, treat arrhythmias⁶², modulate gastric sphincter function in gastrointestinal disorders⁶³ or regulate inflammation-related functions of the vagus nerve⁶⁴ relies on delivering responsive stimulation precisely triggered from the detection of a relevant physiological event, a scenario feasible with i²CS.

In terms of hardware viability of i²CS, recent reports have demonstrated feasibility of dedicated, miniaturized and low-power integrated circuits capable of delivering iCS to peripheral nerves⁶⁵ and of methods to efficiently capture and read out neural responses to stimulation⁶⁶. Furthermore, due to intermittent charge delivery, power consumption of i²CS is similar to standard biphasic current stimulators, i.e., i²CS is more power efficient than its continuous counterpart, a property favorable to long-term implanted stimulation devices.

Sources of favorable selectivity and mechanisms of action of i²CS

Interferential stimulation attains reduced levels of a side effect (RL-mediated laryngeal EMG) for similar levels of desired effect (BP-mediated breathing response), compared to equivalent sinusoidal stimulation (Fig. 7E–H). Counterintuitively to our initial expectation that fiber activation would be increased at the focus of interference with i²CS, our experimental and modeling results indicate that i²CS’s favorable response profile is instead driven primarily by a comparatively reduced activation of fibers at the focus of interference. For example, when maximal AM is focused on RL-rich fascicles, laryngeal EMG is reduced, compared to equivalent sinusoidal stimulation, whereas breathing response is comparable (negative steering ratios, Figs. 3 and 7E–H). That is likely caused by reduced activation of larger fibers, some of which innervate the larynx, compared to activation of smaller fibers, some of which innervate the lung (e.g., Fig. 7I, J); this is also reflected in the size of fast and slow eCAPs (e.g., Fig. 7A–D). In contrast, non-interfering sinusoidal stimulation produces less graded laryngeal EMG responses along the steering axis (Fig. 7E–H), as fibers in RL fascicles are now more consistently activated in the absence of AM (Fig. 7I–L). The distribution of fibers inside fascicles can also have a role on this effect, as fascicles predominantly containing RL fibers occupy a larger area within the nerve cross section (Fig. 5 inset i1), meaning that for every steering ratio, it is more likely that several fascicles containing mainly RL fibers will experience some level of AM, which can therefore result in higher activation thresholds and lower EMG activation for i²CS as shown in Fig. 7. Recruitment curves obtained via the computational model demonstrate that i²CS achieves generally higher BP fiber selectivity at negative steering ratios, and for a wider range of stimulus intensities (Suppl. Fig. S21).

Although this study did not perform a direct and systematic experimental comparison between single contact rectangular pulse stimulation and i²CS, our analysis of historical data obtained in similar experimental conditions²² suggests that i²CS may be able to attain improved selectivity for BP-mediated over RL-mediated responses over conventional pulse stimulation (Suppl. Fig. S8). In modeling results, i²CS with a steering ratio of −0.5 and no parameter optimization attains similar (maximum) BP fiber selectivity as single contact rectangular stimulation, with 30% less total current delivered from the contact placed close to the BP-rich area (Suppl. Figs. S21 and 23), therefore i²CS provides a unique way to compensate for potential suboptimal contact placement and/or movement/drift over time. Additional studies, specifically designed to compare conventional and interferential stimulation waveforms in the same animals and with the same electrodes (shared anatomy and neural interfaces), across a range of stimulus parameters, including intensities, pulse widths, beat and pulsing frequencies, are required to establish improved selectivity of i²CS over conventional waveforms.

The different fiber activation profiles between i²CS and sinusoidal stimulation likely arise because fibers show lower activation threshold when exposed to a non-amplitude modulated sinusoidal field (20 kHz) compared to an amplitude modulated field (2 kHz beat frequency) (Fig. 4I and Suppl. Fig. S10). The effects of i²CS are consistent with a simple threshold mechanism, in which activation of a fiber takes place when the delivered charge results in membrane depolarization that overcomes the activation threshold (Suppl. Fig. S24). This mechanism explains the delayed onset of fiber activation at the focus of interference, as membrane depolarization progressively ramps up with each consecutive cycle, requiring more time to reach the threshold. This is in line with a recent report supporting that interferential stimulation does not rely on envelope extraction for activation, but rather on a simple integration mechanism³⁷.

On the other hand, in kHz-frequency sinusoidal stimulation, the symmetric current cycles, due to nonlinearities in membrane conductivity, produce depolarization cycles that are not fully counterbalanced by the hyperpolarizing periods, resulting in stimulus rectification^67,68,69. For this reason, high frequency bursts facilitate summation of subthreshold stimuli over time, resulting in lower activation thresholds as the number of cycles increases (Gildemeister-effect)^33,70,71. In the present work, we deployed a half-beat interferential waveform, which has a total cathodic net charge that is lower than the respective sinusoidal carrier, and a lower charge per cycle due to the presence of a higher frequency component at 22 kHz. This, together with the slower ramp-up of the total charge which has been linked to reduced fiber activation for a given intensity level^72,73, would result in increased activation thresholds at the point of interference as compared to the non-interferential case. It should also be noted that, in contrast to previous works that focused on continuous interferential stimulation^33,37,68, in the present work we deployed short sinusoidal bursts (≈ 250 µs), which impact the activation of fibers differently compared to continuous interferential stimulation (Fig. 6).

Importantly, our experimental and modeling results provide evidence that the anatomical substrate, i.e., organ-specific fibers, upon which spatially selective stimuli are applied, explains a significant amount of variability in the physiological responses, i.e., organ-specific effects (Fig. 4). This underlines the practical significance of resolving the functional anatomy of nerves and using anatomical constraints in the design of nerve interfaces⁷⁴. In our experiments in swine, almost no electrode pair or steering ratio was associated with perfect selectivity for the desired, BP-mediated breathing effect (Fig. 7D, H). This is likely due to the significant mixing of BP and RL fibers inside the same fascicles (Fig. 2D2–D4) despite an overall organotopic and bimodal distribution of fascicles within the swine vagus nerve^22,28, which poses fundamental anatomical limitations in the degree of functional selectivity of any stimulus targeting single fascicles or small groups of fascicles. Attaining better selectivity in the swine nerve or in the possibly less “compartmentalized” human vagus nerve, would likely require even greater stimulus resolution, e.g., by using more than 2 current sources for interference, or high-channel count intraneural electrode arrays that can target smaller sub-fascicular sectors or even single fibers⁷⁵.

Study limitations

Our study has several limitations. First, our methodology for anatomical tracking cannot reconstruct trajectories of single fibers and assumes that mixing of fibers when 2 fascicles merge into one is uniform across the resulting fascicle (Fig. 2). This assumption does not consider sub-fascicular organization of fibers²² and may result in an overestimation of the amount of fiber mixing at the cervical level of a swine. Second, although our models are anatomically realistic and experimentally validated (Figs. 4 and 5), they are not ideal. For example, the nerve in our model is deformed to a circular shape and fascicles are modeled as extrusions of a single nerve cross section instead of more complex splitting and merging structures, thereby limiting accurate modeling of electrical fields⁷⁶. Fiber populations linked to desired and side effects are simplified by modeling a single fiber inside each fascicle with one of two sizes and simplified ionic conductances, instead of modeling many fibers, with a variety of sizes, specific sub-fascicular clustering statistics and a variety of ionic conductances^22,76,77. Third, our experimental and modeling approaches do not consider current shunting and escape of current outside of the cuff, both of which are likely altering physiological responses significantly^21,29. Experiments performed in anesthetized animals offer limited time to fully explore the stimulation parameter space, hence only selected values of contact pairs, intensities and steering ratios, carrier frequencies and beat frequencies were tested (Suppl. Figs. S30 and 31), preventing us from compiling comprehensive recruitment curves for all stimulation conditions during the experiments. Finally, we did not study i²CS delivered through chronically implanted cuffs or in awake animals; stimulation responses in both these cases are likely to be different than those in acutely implanted, anesthetized animals reported here, as shown previously⁷⁸.

In conclusion, in this work, we introduce an electrical stimulation paradigm, termed intermittent interferential current stimulation (i²CS), that allows for tunable and precise spatiotemporal control of fiber activation during peripheral nerve stimulation. This paradigm has a favorable selectivity profile for a desired effect over a side effect, compared to equivalent sinusoidal stimulation. We also describe a new mechanism of action of intermittent stimulation, which involves relatively reduced and delayed fiber activation at the focus of interference. Due to its intermittent nature, i²CS may be advantageous in terms of energy efficiency, and can be readily implemented in standard implantable stimulation devices.

Methods

Physiology experiments

Animals and surgery

The experimental protocol used in this study has been described in detail earlier²². In brief, the effects of i²CS on physiological and neural response were examined in 7 male Yucatan swine (30–54 kg). All animal protocols and surgical procedures were reviewed and approved by the animal care and use committee of Feinstein Institutes for Medical Research and New York Medical College. Animals were sedated with a mixture of Ketamine (10–20 mg/kg) and Xylazine (2.2 mg/kg) or Telazol (2–4 mg/kg). Propofol (4–6 mg/kg, i.v.) was used to induce anesthesia, and following intubation, the anesthesia was maintained with isoflurane (1.5–3%, ventilation). Body temperature was maintained at 38 and 39 °C using a heated blanket. Blood pressure and blood oxygen level were monitored with a cuff and a pulse oximeter sensor. All surgeries were performed using sterile techniques.

Cervical vagus and laryngeal muscle implants

The right cervical vagus nerve was exposed, and 2 MCEs (Cortec GmbH) were placed on the nerve. The MCE for stimulation (custom AirRay spiral, 18 contacts, see Suppl. Fig. S11) was placed rostrally, ~2 cm away from the nodose ganglion. The design of stimulation MCE aimed at facilitating targeted delivery of IS through minimizing electrode contact size and optimizing its location, which is in accordance with recent recommendation for selective PNS electrode design²¹. A second recording MCE (AirRay helix cuff, 8 recording contacts and 2 ring-shaped reference electrodes) was placed 5-6 cm caudally from the stimulation MCE to record eCAP waveforms. Electrode impedances at a frequency of 1 kHz were measured in vivo using an IMP-2A impedance tester (Microprobe) to verify good contact with the tissue. For laryngeal muscle recordings, Teflon-insulated single or multi-stranded stainless-steel wires were de-insulated at the tip for about 1 mm and inserted in the thyroarytenoid laryngeal muscle with a needle. In 2/7 animals, the laryngeal EMG signal deteriorated and was lost over the course of the experiment, preventing the calculation of physiological selectivity indices (cf. Fig. 7H).

Electrical nerve stimulation

The experimental setup as described in Suppl. Fig. S12 was deployed for in-vivo VNS. Stimulation waveforms and digital signals for timing pulses and stimulation trains were designed using Python 3.9⁷⁹ using a sampling frequency of 1 MHz and transmitted from a PC to a data acquisition (DAQ) board (NI-PCIe6363, National Instruments) via serial communication. The parameters of the two types of stimulation waveforms (sinusoidal and i²CS) are listed in Table 1. Stimuli were presented for 20 s, with a pulse repetition frequency of 33 Hz which was chosen to avoid noise at harmonic multiples of the power line frequency (60 Hz), and low enough to avoid muscle fatigue (cf. Suppl. Fig. S13). Stimulus presentation was randomized and interstimulus interval was 60 s. Stimulation contacts for steering experiments were selected based on an initial functional mapping by stimulating each contact separately at a few amplitudes ranging from 0.5 to 3 mA (Fig. 1C2) using a bipolar configuration. From this mapping, the contact with the lowest threshold for eliciting breathing reduction and an opposing contact were selected. The currents for the steering experiments were chosen around a threshold value (‘medium’ current, see Table 2) that provided an increase in breathing interval (BI) without causing apnea (Table 2). The ‘high’ current condition could, in some cases, still lead to apnea. The ‘steering ratio’ describes the ratio in amplitude of the left current source with respect to the total current as described in Eq. (1), mapped to a −1 to +1 range for illustration purposes; i.e., 0.9 = −1, 0.7 = −0.5, 0.5 = 0, 0.3 = 0.5, 0.1 = 1.

$${current\; ratio}=\frac{{I}_{1}}{{I}_{{\rm{tot}}}},{with}\,{I}_{1}+{I}_{2}={I}_{{tot}}$$

(1)

Table 1 Stimulation waveforms for in vivo experiments and computational models

Full size table

Table 2 Currents used in steering experiments for all animals

Full size table

The choice of a 2 kHz beat frequency for the main comparison with sinusoidal stimulation is related both to the idea of using i²CS as a pulsed technique and to practical setup constraints. One of the main challenges of deploying continuous IS is related to the long (seconds) stimulus durations that are required to generate multiple low frequency beats. This can be a challenge both on the energy consumption in the context of an implant but also on the safety aspects due to the prolonged stimulation. To address these limitations, we have deployed a beat frequency resulting in a total stimulus duration (250 µs) that is comparable to standard rectangular wave pulses (hundreds of µs). Moreover, recording eCAPs requires the stimulus to be shorter than the arrival time of the eCAPs at the recording electrode to avoid stimulation artefact contamination. In our setup, with a typical distance between stimulation and recording electrodes of 5-6 cm, the arrival time of fast eCAPs is around 500 µs after the stimulus onset. Therefore, to keep the stimulation artefact duration less than 500 µs, we used a half-beat of 2 kHz.

The choice of the 20 kHz carrier frequency was driven by the need of having multiple sinusoid cycles within one beat to achieve a good AM of the final interferential signal. In the case of a 250 µs beat, this results in 5 carrier cycles, which creates a well-represented amplitude-modulated interferential signal. On the other hand, choosing a lower carrier frequency, would cause “down sampling” of the final amplitude modulated signal.

The stimulation waveforms were used as input for the DAQ to generate analog output waveforms, and voltage to current conversion was performed via custom-made dual differential Howland current pumps with 1 V: 10 mA conversion factor and power supply of +15/−15 V. To ensure that the stimulation sources were isolated from the rest of the hardware, the Howland current pumps were powered using a 22.5 W, 20000 mAh battery power bank (INIU) and the two outputs of the Howland current source were connected to the stimulation cuff via a custom analog multiplexer designed to allow each independent current source to be routed to any of the electrode channels. The channel selection was controlled digitally using the DAQ system. The connection from the multiplexer to the spiral stimulation cuff was implemented via a micro 360 plastic circular straight tail connector (Omnetics Connector Corporation). DC blocking capacitors were placed at the output of each current pump, and it was verified experimentally using both a resistor network (Fig. S26) and a saline solution (Fig. S27) that no low frequency components were present at the output signal. It was also verified that no electrode polarization occurred at the output electrodes by inspecting the voltage transient during in vitro saline stimulation (Fig. S28), which was also supported by no changes in electrode impedance over repeated experiments (Fig. S29) and no eCAP response changes over the 20 s stimulation period (Fig. S13).

Two additional digital signals were generated by the DAQ: one pulsed digital line whose value was set to 5 V during each stimulation burst and −5 V otherwise, and a stimulation train line whose value was set to 5 V during the whole duration of the stimulation train and 0 otherwise. The two digital lines were directly connected to the digital input ports of the recording instrumentation for synchronization during data acquisition.

Recording of physiological and neural signals

All physiological signals were continuously sampled at 1 kHz (PowerLab 16/35, ADI) and visualized using LabChart (ADI). We monitored heart rate (HR) by recording ECG in a 3-lead patch electrode configuration from the wrist of the animal. Signals were amplified using a commercial bio-amplifier (FE238, ADI). Breathing rate was monitored via a respiratory belt transducer (TN1132/ST) connected to a bridge amplifier (FE221, ADI). The train digital line from the DAQ was used to identify the stimulation windows for post-processing.

Neural and EMG signals were sampled at 30 kHz using a second data acquisition system including an amplification and digitization head-stage and controller unit (RHS-32, Intan Tech). The train digital line from the DAQ was used to trigger the start and stop of the recording, and the pulse digital signal was used to identify single burst stimulation windows for post-processing.

Analysis of physiological and neural signals

Raw physiological signals were high-pass filtered post-hoc to remove the DC-component (4-pole Butterworth filter, cut-off frequency: 0.1 Hz) and a custom-made beat-detection algorithm was used to extract the HR and the BI. The increase in BI was used as a measure for stimulation effectiveness since stronger stimulation of the vagus nerve can sometimes lead to apnea, which cannot be quantified via breathing rate reduction. Response strength was calculated as the average BI over the stimulation window (20 s) or until the next breathing cycle in case of apnea, corrected by the average baseline BI in a 10 s window before stimulation onset.

Raw neural signals were averaged over all contacts of the recording cuff (up to 8, excluding channels with no signal/noise) and subjected to a 60 Hz notch-filter implemented either with the Intan recording software or post-hoc in MATLAB. Furthermore, signals were also band-pass filtered post-hoc (4-pole Butterworth filter, high-pass cut-off frequencies: 10 and 260 Hz for EMG and eCAP, respectively; low-pass cut-off frequency: 8000 Hz) before averaging the responses over all stimulus presentations in the train (default: 33 Hz inter-pulse-interval for 20 s, i.e., 660 pulses). EMG response strength was calculated as the peak-to-peak magnitude of the signal in a pre-defined response window after stimulation (4–12 ms). eCAP response strengths were calculated as the peak-to-peak magnitude of the signal in 2 pre-defined response windows after stimulation onset that were derived from conduction velocities of ‘fast’ and ‘slow’ A-fibers and the measured distance between the stimulation and recording electrodes (Fast: 55–96 m/s; Slow: 32–55 m/s; Average electrode distance: 5,15 cm). The onset latency of the EMG response was never below ~4 ms in any of the experiments and we limited the analysis of the eCAP response to a window with a maximum of 2 ms.

To quantify the effect of stimulation parameters on fiber and organ functional selectivity, we defined selectivity indexes as previously described⁵¹, adapted to account for the different experimental conditions. The selectivity index SI was calculated for eCAP (2) and physiological (3) responses as follows:

$${{SI}}_{{CAP}}=\frac{{{CAP}}^{{fast}}-{{CAP}}^{{slow}}}{{{CAP}}^{{fast}}+{{CAP}}^{{slow}}}$$

(2)

$${{SI}}_{{phys}}=\frac{{EMG}-{BI}}{{EMG}+{BI}}$$

(3)

To quantify the dependence of selectivity on steering, the data was fitted with a modified logistic function of the form described in Eq. (4):

$$y=a+\frac{b-a}{1+{\exp }^{-k(x-{x}_{0})}}$$

(4)

Where a, b, k, and x₀ are the minimum and maximum reachable values of the fit, the steepness of the slope and the inflection point, respectively. The Selectivity Factor SF was derived from the logistic fits to the SI-data as a product of 2 parameters as described in Eq. (5), where $\left\langle {slope}\right\rangle$ and $\left\langle {range}\right\rangle$ are the normalized slope and range of the SI sigmoidal function in Eq. (4):

$${SF}=\left\langle {slope}\right\rangle \cdot \left\langle {range}\right\rangle$$

(5)

The normalized slope is defined as the sigmoid slope converted to degrees and normalized by the maximum value of 90° (Suppl. Fig. S9A). Here, the slope value stands for the ‘cutoff sharpness’ of the change of selectivity across the nerve diameter while the range describes the maximum relative difference between the activation of one function versus the other. The values for range and slope are reported separately in Suppl. Fig. S9B.

All data analysis was performed using custom-made or publicly available scripts in MATLAB (Mathworks). If not otherwise noted, two-sided Wilcoxon rank-sum tests were used for pair-wise comparisons of means and ANOVA using Kruskal–Wallis tests with Dunn–Sidak correction were used for multiple comparisons of medians. Stars denote p-value levels according to *p < 0.05, **p < 0.01 and ***p < 0.001. Linear regression (least squares) was performed using the ‘polyfit’ function of MATLAB.

Nerve anatomy

Anatomical dissection and micro-CT imaging of nerve samples

Animals were euthanized by injection of Euthasol (1 ml/10 pounds BW, i.v.); death was confirmed using ECG and absence of arterial pulse. After euthanasia, the right cervical vagus nerve was dissected from above the nodose ganglion to the end of the thoracic region. During that time, nerve branches, still attached to the nerve trunk, were isolated using blunt dissection up to the respective end organ (heart, lung or larynx). A fine suture loop (6–0), radiopaque and therefore visible in micro-CT images, was placed on the epineurium of each branch, close to its emergence from the trunk, to label that branch and maintain a record of the innervated organ during subsequent imaging studies. The nerve trunk, along with organ-specific labels was photographed before and after extraction. The samples were fixed in 10% formalin for 24 h, then transferred to Lugol’s solution (Sigma, L6146) for five days to achieve optimal fascicular contrast for the micro-CT scan. Nerve trunks were sectioned into several 6 cm-long segments and the rostral end of each segment was marked with a suture knot, to maintain the rostral-caudal direction. Each nerve segment was scanned individually in the micro-CT scanner. Nerve segments were mounted in position on a vertical sample holder tube. The samples were scanned using Bruker micro-CT Skyscan 1172 with a voxel size of 6 μm, using the following parameters: 55 kV, 149 μA, 0.5 mm Al filter, rotation step of 0.5, and frame averaging of six.

Fascicle reconstruction and tracking

Reconstruction of images was done using cone-beam reconstruction software based on the Feldkamp algorithm (Skyscan NRecon, version 2.2.06), with the following parameters: ring artifact correction of five, beam hardening correction of 40%, followed by automatic post-alignment. Reconstructed cross-sectional image slices were saved as bitmap files.

The reconstructed image volume was used to manually track the fascicles along the cranial-caudal axis. Ellipses were aligned with the fascicular cross-sections in several image slices. These ellipses were placed on slices approximately 180 microns apart to expedite the labelling process, but this distance was reduced in areas where the fascicles had higher than normal curvature. The parameters of the ellipses were linearly interpolated on the intermediate slices. The centers of the ellipses were connected to form a directed graph where each edge points in the cranial direction, and the graph contains splits or merges where the fascicles split or merge. Because the nerve spans multiple image volumes, these graphs were independently constructed for each image volume and manually joined together.

Fiber mixing model

Each node in the graph was also assigned a tuple representing the percentage of the main trunk, the RL branch, and the BP branch. These structures were manually identified and the leaf nodes in the graph corresponding to these structures were assigned to 100% for the respective structure and 0% of the other structures. The percentages were propagated through the graph from the caudal to the cranial end based on the following rules:

(a)
If a node has only a single input connection from the previous node, then the percentages do not change. This is true even if the previous node branches into multiple nodes. This method assumes homogenous mixing.
(b)
If a node contains multiple input connections from multiple previous nodes, as is the case when merging, then the percentage in the next node is the weighted average of the percentage in the previous nodes with a normalized weighting based on the areas of the previous ellipses. This method assumes instantaneous mixing at merge locations.

Spatial distribution of fibers

The spatial distributions of RL and BP fibers was determined by projecting the centroids of each fascicle onto a line passing through the center of mass for each fiber type. The mass of each fiber type for a given fascicle is proportional to the area of the fascicle times the percentage of each fiber type, assuming a constant fiber density. Histograms of values proportional to the fiber counts for each fiber type were generated along the axis of a diagonal line corresponding to the steering axis (Fig. 2).

Computational modeling

Anatomically realistic 3D computational models were obtained via the adaptation of the ASCENT framework v1.2.2.^39,80. In this study we deployed the ASCENT framework using Python 3.9, COMSOL Multiphysics 5.6 (COMSOL Inc., Burlington, MA), and NEURON v7.6⁸¹. The framework allows to construct a 3D nerve anatomy starting from an anatomical image and extruding the nerve section over the desired length of the nerve fiber. For this purpose, a nerve cross section from a location right below the middle row of electrodes in the nerve cuff placed on an example animal was selected to generate the 3D model (Suppl. Fig. S11). Binary image inputs were obtained using ImageJ software⁸², and the nerve shape was deformed to account for circular deformation after cuff placement ensuring a minimum inter-fascicle distance and fascicle distance to the nerve perimeter of 10 µm. A scale ratio µm/pixel of 1.56 was used to account for histological tissue shrinkage and to reach a final nerve diameter of ≈3 mm as measured experimentally during the experiment. The conductivity values of all tissues and materials are reported in Table 3. The perineurium was modelled using a thin layer approximation with thickness dependent on the fascicle diameter and whose parameters were derived from pig Vagus nerve experiments²⁷. The perineurium conductivity was selected to be dependent on temperature and frequency, with values set at 37 °C and 20 kHz to account for the stimulation frequency⁸³. Each fascicle was populated with a single myelinated fiber placed in the middle and modelled using the MRG model^84,85, deploying a fiber diameter as detailed in the analysis and a fiber length equal to the nerve length (40 mm).

Table 3 Conductivity values for tissues and materials used in the computational model

Full size table

A 3D model of the electrode cuff placed around the nerve was obtained starting from the electrode geometrical specifications (Suppl. Fig. S11) and placed at the midpoint of the nerve, with a rotation of 90° to replicate contact locations from the experiment. To reduce computational load, only the two pairs (four electrodes) used during the in-vivo experiment were modeled and solved for the electric potentials (Fig. 4C). Material properties were assigned to the different electrode components as follows: electrode contacts (Pt), cuff insulation (silicone), and fill medium and recess (saline). The proximal and outer medium were defined as cylinders with radius 3.5 mm and 4.3 mm respectively, and the outer surface was set to ground. The final model had a total length of 40 mm, a diameter of 8.6 mm and 69772140 mesh elements. Dimensions were deemed appropriate by verifying that doubling separately the nerve length to 80 mm and the diameter to 16 mm would result in activation threshold errors below 2%³⁹.

The voltage transient and activation threshold simulation protocols in ASCENT were used to derive fiber responses resulting from electrical stimulation. As the ASCENT pipeline does not allow to simulate multiple waveforms at the same time as required during i²CS, the framework was extended to support this use case. The extension introduces the summation of the electric potentials resulting from separate simulation waveforms. The electric potential over the 3D space resulting from the injection of a 1 mA DC current is solved separately for each electrode using Laplace’s equation, and then modulated by the stimulation waveform, which allows to obtain a temporal profile of the electric potential during stimulation. In the present work, we computed separately the modulated electric potential for each one of the current sources, and then leveraged the principle of superposition of effects to sum the two electric potential temporal profiles, which allowed to obtain a single temporal profile of the electric potential resulting from the presence of two separate current sources. The resulting potential was then used in the pipeline to derive fiber responses. We simulated different stimulation waveforms, replicating the experimental conditions as described in Table 1. For each waveform, the timestep was set to 3 µs, with stimulation starting after 1 ms and with a total stimulation duration of 91 ms.

In the case of continuous IS, the same carrier frequency used for i²CS 0.25 ms (20 kHz and 22 kHz) were used, each carrier having a total duration of 90 ms, which is equivalent to the total duration of the i²CS 0.25 ms stimulus train used for comparison.

For each waveform, a current amplitude of 1.5 mA was used as it best matched experimental data (Suppl. Fig. S25). A current of 2 mA was also used to provide fiber recruitment across all fascicles for large fibers. Moreover, for each current amplitude, five different amplitude ratios were simulated, as defined in (1). For single contact biphasic rectangular wave stimulation, we computed activation thresholds for a symmetric biphasic rectangular wave with 25 µs cathodic/anodic pulse widths delivered from a single bipolar contact pair placed close to the BP cluster as depicted in Suppl. Fig. S23.

Analysis of electric potentials

Electric potential maps were generated from COMSOL injecting a 1 mA DC current at each contact and the resulting electric potential at a nerve cross section at the location of the stimulating electrodes was used to generate amplitude maps. For the AM maps, the potential generated by each stimulation source was modulated with a sinusoidal signal with the respective carrier frequency, and the two potentials were then summed together to create a time-varying IS electric potential profile. The resulting signal at each spatial location was processed to extract the magnitude of AM. The absolute value of the Hilbert transform was used to extract the envelope of the signal, and the envelope peak-to-peak amplitude was used to quantify the magnitude of AM. To discretize the amount of AM into three levels (high, intermediate, low), the AM magnitudes at each fascicle location were extracted to generate the values distribution across the whole fascicle population. The three levels were then defined using the values quantiles as follows: low (values below quantile 0.33), intermediate (values between quantiles 0.33 and 0.66) and high (values above quantile 0.66).

Analysis of computational modeling results

The computational modeling outcomes include activation thresholds and voltage transient profiles for each fiber/stimulation parameter combination. This allows to determine the presence of an action potential as a result of electrical stimulation. All analysis on fiber activation was performed using Python 3.9.

To investigate the correlation between physiological responses and fiber activation profiles obtained using the computational model, we performed fascicle clustering based on the percentage of fiber types within each fascicle. We considered all fascicles that contained a majority of BP fibers to be BP fascicles, while fascicles that had a prevalence of RL fibers were assigned to RL.

We computed activation thresholds for fiber diameters of 5, 7, 10, and 12 µm. The threshold for detecting an action potential was set at −30 mV, the detection location was set to a point placed at 90% of the total fiber length, and the minimum number of action potentials to determine fiber activation was set to 1. We then interpolated activation thresholds using a cubic spline interpolation to obtain activation thresholds for every fiber diameter in the 5–12 µm range. Based on a distance between the recording and stimulating electrodes of 6 cm, and a time of arrival for fast and slow eCAPs of 0.9 ms and 1.45 ms respectively for the example animal, we calculated conductions speeds of 41 m/s for BP fibers and 66 m/s for RL fibers, which were linked to fiber diameters of 6.6 µm and 11 µm respectively⁸⁶. Based on these estimations, we explored fiber diameters of 6 µm and 7 µm for BP, and 10 µm and 11 µm for RL.

For each of these values and waveform types, the linear correlation with experimental data was computed using the same method described in Fig. 4F for different amplitudes. BP fascicles were populated with a single, slow A-fiber (6 or 7 μm), while RL fascicles were populated with a single, fast A-fiber (10 or 11 μm). The knowledge of the function of fibers within the nerve acquired through fiber tracking (see Fig. 2) allowed to simulate the outcome of electrical stimulation on target physiological functions. We considered the generation of an action potential (due to suprathreshold stimulation) for a fiber an indication of the effect on the respective physiological function. We computed the strength of the functional response as the percentage of relevant fibers being activated for a specific physiological function, as described in Eq. (6).

$${{Functional\; Response\; Modeling}}_{i}=\frac{\mathop{\sum }\nolimits_{j=1}^{{N}_{i}}{{fiber}}_{{ij}}}{{N}_{i}}$$

(6)

Here, i indicates the fiber population (BP or RL) with size N_i, and fiber_ij is a Boolean value indicating if an action potential was elicited (1) or not (0). The functional response (6) was computed for both sinusoidal and i²CS waveforms with a beat duration of 0.25 ms and for all steering ratios, similarly to in vivo experiments (see Fig. 3). Functional responses obtained through modeling were directly compared with the respective physiological responses obtained experimentally for the same animal during current steering. A linear least-squares regression model was computed between the normalized (min-max normalization into the range of 0 to 1) functional responses obtained through modeling and the respective normalized functional responses obtained experimentally using the linregress function from the scipy.stats module in Python⁸⁷. Values of 6 μm and 10 μm and a stimulation amplitude of 1.5 mA were finally chosen to simulate the responses of slow and fast fibers respectively, as these values provided the best match with experimental data (Suppl. Fig. S25). It should be noted that the stimulation amplitude of 1.5 mA is double the stimulation amplitude used during the experiment (0.75 mA). This disagreement in terms of current amplitudes between model and experiment can be explained by the difficulty in perfectly replicating the experimental conditions in the modelling environment, such as nerve deformation (perfectly circular in the model), distance between stimulating contacts and nerve, and contact impedance. Similar numerical offsets are reported in other modeling literature using the ASCENT framework²¹.

The functional responses derived from modeling were also used to compare the selectivity of sinusoidal stimulation and i²CS using the same approach deployed for experimental data. The functional responses as defined in Eq. (6) obtained at different steering ratios were fitted using a sigmoidal function as described in Eq. (4), and a selectivity factor was computed based on the parameters of the sigmoidal function as detailed in Eq. (5).

To study the fiber activation timing with respect to current steering and waveform type, we performed twofold analysis leveraging the ASCENT voltage transient protocol which allowed to obtain the timings of elicited action potentials. Action potentials were detected in a point located at 10% of the total fiber length and a threshold of −30 mV was selected. Firstly, we considered a single fast A-fiber (10 µm diameter) placed in a deep fascicle as displayed in Fig. 5, inset i1. A single fiber type was selected to isolate the influence of current steering and waveform type on the timing of action potential. A total stimulation current of 2 mA was selected since it resulted in the generation of an action potential at all steering/waveform combinations. This allowed to study the impact of these stimulation parameters on the timing. Secondly, we considered all the RL-rich fascicles, which were populated with a single fast A-fiber (10 µm diameter), and we evaluated the activation timing resulting from different waveforms and steering ratios. ANOVA using Kruskal–Wallis test with Dunn–Sidak correction was used for multiple comparisons of medians between waveform types (scipy stats Kruskal⁸⁷ and scikit_posthocs posthoc_dunn⁸⁸ functions in Python). Stars denote p-value levels according to *p < 0.05, **p < 0.01 and ***p < 0.001. This experiment was used to compare the laryngeal EMG responses obtained experimentally as a result of different waveforms and steering ratios with the responses obtained using the computational model for the RL-rich fascicles. A stimulation of 1.5 mA was also used to obtain a comparison of the spatiotemporal activation profiles between sinusoidal stimulation and i²CS with different beat frequencies as reported in Fig. S10.

A similar approach was used to investigate the effect of steering/waveform selection on the spatiotemporal activation patterns for all the fascicles in the nerve model. We considered a single fast A-fiber placed in each of the nerve fascicles, during electrical stimulation with a total current of 2 mA. This resulted in most of the fibers being activated at each steering/waveform combination, allowing to investigate the effects of these stimulation parameters on the timing, as shown in Fig. 5.

In the case of continuous stimulation, together with action potential timing analysis, blocking was verified using the blocking threshold protocol available in ASCENT. A 5 nA, 0.1 ms intracellular pulse was delivered after 50 ms from the beginning of the stimulation at one extremity of the nerve (second node from the origin of the nerve in the xyz plane) and the presence of an action potential was verified at the opposite end of the nerve. Blocking thresholds were iteratively searched using the same settings reported for activation thresholds, and blocking of the selected fibers was confirmed if the blocking threshold was below the selected amplitude used to compute voltage transients.

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Data availability

The processed experimental data underlying the figures has been published in this repository: https://doi.org/10.5281/zenodo.14718703. All data supporting the findings of this study are available within the article and its supplementary files. Any additional requests for information can be directed to, and will be fulfilled by, the corresponding authors. Source data are provided with this paper.

Code availability

The input parameter files and modified code for the modelling framework have been published in the same repository: https://doi.org/10.5281/zenodo.14718703.

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Acknowledgements

This work was partially supported by NIH SPARC 75N98022C00019 and NIH NINDS-1R01NS136685-01A1, both to S.Z. IMEC has been granted a patent related to this work (patent applicant: Stichting IMEC Nederland; name of inventors: Mark Fichman, Vojkan Mihajlovic; application number: 18/197,335; publication number: US 2023/0364428 A1) that describes a device for delivering i²CS patterns to the neural tissue). The authors wish to thank Patrick van Deursen and Yousef Al-Abed for supporting the collaboration between IMEC and the Feinstein Institutes for Medical Research, Evelien Hermeling for the support on data analysis, and Eva Severijnen for the support on the design of in vivo experimental protocols.

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These authors contributed equally: Nicolò Rossetti, Weiguo Song, Philipp Schnepel.

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imec, Eindhoven, Netherlands
Nicolò Rossetti, Philipp Schnepel, Dimitrios A. Koutsouras, Mark Fichman, Geert Langereis & Vojkan Mihajlović
Institute of Bioelectronic Medicine, Feinstein Institutes for Medical Research and Northwell Health, Manhasset, NY, USA
Weiguo Song, Naveen Jayaprakash, Jason Wong, Todd Levy, Mohamed Elgohary, Khaled Qanud, Timir Datta-Chaudhuri & Stavros Zanos
Sant’Anna School of Advanced Study, Pisa, Italy
Alice Giannotti
Temple University School of Medicine, Philadelphia, PA, USA
Mary F. Barbe & Frank Liu Chen
Zucker School of Medicine at Hofstra/Northwell, Hempstead, NY, USA
Timir Datta-Chaudhuri & Stavros Zanos
Elmezzi Graduate School of Molecular Medicine, Manhasset, NY, USA
Timir Datta-Chaudhuri & Stavros Zanos

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Nicolò Rossetti
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Weiguo Song
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Philipp Schnepel
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Naveen Jayaprakash
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Frank Liu Chen
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Timir Datta-Chaudhuri
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Vojkan Mihajlović
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Stavros Zanos
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Contributions

N.R., W.S., P.S., T.D.C., V.M., and S.Z. designed experiments; N.R., W.S., P.S., N.J., D.K., T.D.C., J.W., M.E., K.Q., A.G., M.F.B., and F.L.C. collected data; N.R., W.S., P.S., T.L., and T.D.C. analyzed data; N.R., M.F., T.D.C. developed hardware and/or software; N.R., W.S., P.S., T.L., M.F.B., T.D.C., S.Z., and V.M. wrote the paper; S.Z., V.M., and G.L. conceived, supervised and acquired funding for the study.

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Correspondence to Stavros Zanos.

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IMEC has been granted patents related to this work (US18511762, US0017074A1, US0364428A1, US0198109A1). IMEC and Northwell have submitted patents related to this work.

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Rossetti, N., Song, W., Schnepel, P. et al. Control of spatiotemporal activation of organ-specific fibers in the swine vagus nerve by intermittent interferential current stimulation. Nat Commun 16, 4419 (2025). https://doi.org/10.1038/s41467-025-59595-4

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Received: 10 October 2024
Accepted: 17 April 2025
Published: 13 May 2025
DOI: https://doi.org/10.1038/s41467-025-59595-4

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Abstract

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Introduction

Results

Bronchopulmonary- and laryngeal-specific fascicles progressively merge, resulting in a bimodal anatomical organization at the cervical vagus nerve of a swine

Interferential stimulation (IS) elicits distinct nerve and organ responses that are different than those of equivalent, non-interfering sinusoidal stimulation

Interferential stimulation elicits reduced fiber activation at the focus of interference, in an anatomically realistic, physiologically validated model of the swine vagus nerve

Interferential stimulation activates vagal fibers in a specific spatiotemporal pattern, in experimental recordings and in swine vagus nerve models

Intermittent interferential stimulation controls precise timing of action potentials in modeled nerve fibers

Interferential stimulation has improved functional selectivity for a desired effect over a side effect compared to equivalent, non-interfering sinusoidal stimulation, in experiments in anesthetized swine

Discussion

Significance of spatially focused and temporally precise control of vagal fiber activation with i2CS

Sources of favorable selectivity and mechanisms of action of i2CS

Study limitations

Methods

Physiology experiments

Animals and surgery

Cervical vagus and laryngeal muscle implants

Electrical nerve stimulation

Recording of physiological and neural signals

Analysis of physiological and neural signals

Nerve anatomy

Anatomical dissection and micro-CT imaging of nerve samples

Fascicle reconstruction and tracking

Fiber mixing model

Spatial distribution of fibers

Computational modeling

Analysis of electric potentials

Analysis of computational modeling results

Reporting summary

Data availability

Code availability

References

Acknowledgements

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Significance of spatially focused and temporally precise control of vagal fiber activation with i²CS

Sources of favorable selectivity and mechanisms of action of i²CS