Enhancing the selective electrical activation of human vagal nerve fibers: a comparative computational modeling study with validation in a rat sciatic model

Objective. Vagus nerve stimulation (VNS) is an emerging treatment option for a myriad of medical disorders, where the method of delivering electrical pulses can vary depending on the clinical indication. In this study, we investigated the relative effectiveness of electrically activating the cervical vagus nerve among three different approaches: nerve cuff electrode stimulation (NCES), transcutaneous electrical nerve stimulation (TENS), and enhanced TENS (eTENS). The objectives were to characterize factors that influenced nerve activation and to compare the nerve recruitment properties as a function of nerve fiber diameter. Methods. The Finite Element Model, based on data from the Visible Human Project, was implemented in COMSOL. The three simulation types were compared under a range of vertical and horizontal displacements relative to the location of the vagus nerve. Monopolar anodic stimulation was examined, along with latency and activation of different fiber sizes. Nerve activation was determined via the activating function and McIntyre-Richardson-Grill models, and activation thresholds were validated in an in-vivo rodent model. Results. While NCES produced the lowest activation thresholds, eTENS generally performed superior to TENS under the range of conditions and fiber diameters, producing activation thresholds up to three times lower than TENS. eTENS also preserved its enhancement when surface electrodes were displaced away from the nerve. Anodic stimulation revealed an inhibitory region that removed eTENS benefits. eTENS also outperformed TENS by up to four times when targeting smaller diameter nerve fibers, scaling similar to a cuff electrode. In latency and activation of smaller diameter nerve fibers, eTENS results resembled those of NCES more than a TENS electrode. Activation threshold ratios were consistent in in-vivo validation. Significance. Our findings expand upon previously identified mechanisms for eTENS and further demonstrate how eTENS emulates a nerve cuff electrode to achieve lower activation thresholds. This work further characterizes considerations required for VNS under the three stimulation methods.


Introduction
Vagus nerve stimulation (VNS) refers to the therapeutic delivery of electrical pulses to the vagus nerve, most commonly in the cervical region using a surgically implanted device.VNS has received regulatory approval (e.g.US FDA, Health Canada) for treating epilepsy, depression, migraines, and cluster headaches [1][2][3], and there is ongoing research for new indications such as rheumatoid arthritis, heart failure and gastrointestinal disorders [4][5][6].Although implanted stimulators enable highly selective (as in, activating the desired nerves while eliminating or minimizing off-target effects) activation of a targeted nerve, studies show that for the vagus and other neuromodulation targets, this approach entails potentially complex surgical procedures, high cost, possible postoperative complications and revision surgeries, and uncertain long-term clinical efficacy [7][8][9].In this paper, we compared different nerve stimulation modalities to assess the advantages/disadvantages of using less invasive methods to selectively activate the cervical vagus nerve.
Non-invasive VNS, commonly referred to as transcutaneous (tVNS) or transcutaneous auricular (taVNS), is an alternative to surgically implanted stimulators and has demonstrated certain degrees of effectiveness in reducing pain and headaches [10,11].tVNS stimulates the vagus nerve by means of surface electrodes placed on the neck, whereas taVNS applies electrical stimulation on the outer ear.Both modalities have been investigated for a range of conditions including depression, irritable bowel syndrome, gastroparesis, and opioid withdrawal [12][13][14][15].Of note, GammaCore is the first FDA approved device for non-invasively delivering cervical tVNS for headache and migraine [16].Despite the many advantages of non-invasive tVNS, the presence of multiple muscle and tissue layers between the skin and the cervical vagus nerve raises the potential for off-target effects, resulting in poor overall effectiveness despite a low risk of adverse effects and high patient adherence [17].Selective non-invasive activation of the cervical vagus nerve remains a challenge.
The need to address a trade-off between invasiveness and selectivity has led to the exploration of alternative stimulation paradigms, such as percutaneous stimulation [18], the stimulus router system [19], and enhanced transcutaneous electrical nerve stimulation (eTENS).eTENS is a recently developed method that aims to achieve selective nerve activation without the need of an implanted nerve cuff electrode (NCE), battery, or lead wire.In eTENS, conventional transcutaneous electrical nerve stimulation (TENS) electrodes are used in conjunction with an electrically conductive element (e.g. a platinum nerve cuff) placed around the target nerve.This idea was initially investigated in a small animal model of tibial nerve stimulation, where a finite-element model (FEM) was used to determine the size of conductive nerve cuffs suitable for rodent experiments [20].A more recent computational study of tibial nerve stimulation in a human leg model showed that the lower nerve activation threshold achieved by eTENS (compared to TENS) was a result of the voltage difference that is generated between the isopotential nerve cuff and the surrounding tissue [21].The longitudinal current within the nerve cuff is redirected in the radial direction, thereby creating a 'virtual bipole' similar to that of a bipolar stimulating NCE.
The purpose of this study was to investigate eTENS within the context of electrically stimulating the cervical vagus nerve.We constructed an anatomically realistic FEM of the human neck region to compare VNS delivered by three different stimulation approaches: TENS, eTENS and NCE stimulation (NCES).A quantitative analysis of the nerve activation thresholds and fiber recruitment properties was performed to assess and compare the functional differences among the nerve stimulation modalities.We followed the computational study with in-vivo validation in an anesthetized rat model.

Methods
Computational simulation of human VNS involved multiple steps (figure 1): (1) construction of a realistic model using computer aided design (CAD) software; (2) translation of the CAD model into a finite element modeling (FEM) software; (3) solving for the electric field; and (4) prediction of nerve fiber activation.

CAD model construction
Transverse cross-sectional images of a 39 year old human male were acquired from the Visible Human Project [22].A total of 37 images were digitally cropped to a common size of 1601 × 901 pixels, where spatial resolution within each slice was 0.33 mm pixel -1 and the distance between slices was 5 mm.The digitized slices spanned from the T4 vertebra up to the base of the cerebellum (distance = 18 cm).
A complete CAD model was created by manually segmenting tissues within the digitized slices (Autodesk Inventor Professional 2023, Autodesk Inc., San Rafael, CA), with the exception of the vagal neurovascular bundle, which was positioned based on literature as the carotid sheath and the vagus nerve could not be resolved in the images [23].The left vagus nerve was modeled with a single myelinated axon embedded with a monofascicular nerve trunk, which included an endoneurium, perineurium, and an epineurium with outer diameter of 0.32 cm [24].Preliminary simulations showed that certain anatomical components (e.g.bones, muscles and soft tissues) located posterior to the trachea did not have a significant impact on the accuracy of the predicted nerve activation threshold and unnecessarily increased computational time.These components were excluded in the final FEM.Once all segmented features were lofted into 3D objects, the CAD model was exported into COMSOL Multiphysics (v5.6, COMSOL Inc., Stockholm, Sweden) using the CAD Import Module.

Translation into a FEM
Within COMSOL, the model was automatically repaired and smoothed using built-in tools to correct irregularities in the CAD-generated anatomy.The connective tissue was generated by geometrically downscaling a copy of the subcutaneous fat to 87.5% of its initial size.This resulted in a skin layer (thickness = 0.2 cm to 0.6 cm), a fatty layer of subcutaneous tissue (thickness = 0.6 cm to 2.7 cm), and connective tissue that filled the space between objects.The perineurium of the vagus nerve was defined as a 50 µm layer surrounding the endoneurium using the contact impedance-thin layer option in COMSOL.
Electrodes were constructed to simulate TENS, NCES, or eTENS.Based on values from literature [21], TENS electrodes were modeled as a pair of thin disks placed on the ventral neck surface, with a radius of 0.75 cm and thickness of 0.3 cm.As illustrated in figure 2, the electrodes were separated by 1 cm and centered along the left vagus nerve.The nerve was located at an approximate depth of 2.3 cm relative to the skin surface at the stimulation site.A bipolar NCE was constructed to fit around the cervical vagus nerve, where the insulating cuff had a length of 1 cm, an external diameter of 0.36 cm and an internal diameter of 0.32 cm.Two platinum ring contacts (length = 0.1 cm, inter-contact distance = 0.6 cm) were placed on the inner surface of the cuff.Finally, eTENS was implemented by aligning a platinum nerve cuff (dimensions equal to the insulating cuff of the NCE) with the 1 cm gap between the TENS electrodes (figure 2).Electrical conductivity values of the FEM are provided in table 1 [22,25].

Simulation protocols for VNS
VNS was compared among three different stimulation methods: NCE, TENS, and eTENS.In each case, electrical stimulation was approximated within the FEM software by a quasi-static current applied in a bipolar configuration: rostral anode (1 mA) and caudal cathode (1 mA).An electrical ground was defined by a point located on the latero-caudal edge of the right shoulder.Using a single 10 µm fiber positioned along the center of the vagus nerve trunk, the nerve activation threshold was initially investigated at the position indicated in figure 2. Subsequently: • [Helical electrode]: Nerve stimulation with a helical electrode was approximated by removing the insulating silicone material between the two platinum contacts of the NCE.• [TENS vs. eTENS]: simulations were performed where the pair of surface electrodes was displaced along the rostro-caudal (superior-inferior) and medio-lateral axes (±2 cm, 0.5 cm intervals).• [eTENS]: the location of the surface electrodes was fixed at (0,0) and the platinum cuff was displaced (rostro-caudally) along the nerve.• [Monopolar eTENS]: the cathodic TENS electrode was removed and the return was defined by the electrical ground.The cuff was shifted in intervals  the post-stimulus latency-time between the beginning of a stimulus pulse and initiation of an action potential (AP).

Analysis of neural activation
The extracellular potential along a single axon located at the center of the nerve was sampled at intervals corresponding to the internodal distance for the axon diameters listed above.These values were exported from COMSOL to MATLAB (r2022b, Mathworks Inc., Natick, MA) where further analysis of neural activation was performed by computing the activating function (AF) and determining the nerve activation threshold current as predicted by the McIntyre-Richardson-Grill (MRG) model.The AF provides a relative measure of peripheral nerve fiber activation without determining the actual threshold current amplitude.It is quantitatively defined as the second spatial difference of the extracellular voltage along the nerve, where positive AF values correlate with nerve membrane depolarization (i.e.closer to reaching the fiber activation threshold) [25].The MRG model, previously implemented in MATLAB, predicts the threshold amplitude for activating nerve fibers by using a series of differential equations to model individual nodes of Ranvier, as well as at paranodal and internodal sections [27,28].The MRG model takes the given extracellular voltages at known positions along the nerve at an initial simulated current (from COMSOL) and scales these values to determine membrane voltages at any other stimulation current, which allow for prediction of AP initiation [29].By conducting repeated MRG simulations, the minimum current (within a margin of 0.01 mA) required to activate the nerve was determined.The MRG model assumed monophasic current pulses, with pulse duration = 500 µs and simulation time = 3 ms.A measure of relative excitability was defined by the ratio of nerve activation thresholds (TENS/eTENS), where a unity value indicated that eTENS did not enhance neural activation.

In-vivo validation
All surgical procedures were approved by the University of Toronto Animal Care Committee in accordance with the regulations of the Ontario Animal Research Act (Toronto, ON, Canada, Protocol #20012656).In acute experiments, male Sprague-Dawley rats (n = 8, 598-705 g, mean: 655 g) were anesthetized with 5% isoflurane (induction chamber) and maintained with a gas mask (2%-3%).
Heart rate and blood O 2 level were monitored via pulse-oximeter.Animals were euthanized at the end of each experiment via intra-cardiac injection of T61 (0.3 ml kg −1 , Merck., Inc) and thoracotomy.
The sciatic nerve was chosen because it provided a better approximation to the human VN (nerve diameter and subcutaneous depth), when compared to the rat VN.Animals were placed in a prone position; the lower back and legs were shaved and treated with a commercial depilator cream (n = 6, n = 2 conducted without cream, both left and right legs for a total of 16 data points).Wire electrodes were implanted in the foot to record electromyogram (EMG) signals with a ground needle electrode placed subcutaneously in the upper back [20].The EMG was conditioned (gain = 20x, bandpass filter = 100 Hz to 3 kHz, SR560 Stanford Research Systems, Sunnyvale, CA, USA) and stored digitally (sampling rate = 10 kHz, Powerlab 16/35, ADInstruments, Inc., Colorado Springs, CO, USA).
TENS stimulation was delivered by a pair of selfadhesive round surface electrodes (1.5 cm diameter, 1 cm separation) placed dorsally over the biceps femoris muscle and in alignment with the sciatic nerve (one proximal to spine, one distal).The location of the electrodes was marked; the electrodes were replaced at the same position for eTENS.The nerve was surgically exposed by making a dorsal incision and separating the biceps femoris and vastus lateralis muscles.eTENS was implemented by wrapping gold foil (thickness 0.25 µm, length = 1.0 cm) around the sciatic nerve and replacing the surface electrodes at the marked locations.NCES was performed by implanting a bipolar flat-interface nerve electrode (FINE) on the sciatic nerve.The FINE was 10 mm long and 5 mm wide, with two 1 mm wide platinum electrodes separated by 3 mm.In all three configurations, trains of biphasic pulses were delivered (duration 5 s, frequency 2 Hz, 500 µS pulse width) via an electronic stimulator (Model 2100, AM Systems Inc., Carlsborg, WA).EMG responses were visually confirmed in real time using an oscilloscope (TDS 2024 C, Tektronix, Beaverton, OR), where the stimulation amplitude was adjusted until the stimulation threshold was reached, to the nearest 0.1 mA for TENS/eTENS, and 1 µA for NCES.
The stimulation protocol involved determining the nerve activation threshold by using the stimulation methods in the following order: (1) TENS (presurgical), (2) NCES, (3) eTENS (post-surgical), and (4) TENS (post-surgical).Following completion of finding the nerve activation threshold by TENS, a dorsal incision allowed the implantation of the stimulating bipolar FINE electrode on the sciatic nerve.Once the NCES threshold was determined, the FINE was replaced with the gold foil and the skin was sutured closed.Using the same surface electrodes as the TENS protocol, the eTENS threshold was determined.Finally, the gold foil was surgically removed and the skin was re-sutured such that the TENS protocol could be repeated.In each animal, the stimulation protocol was performed on both legs.
Although the nerve activation threshold values for the four different stimulation conditions were averaged across all experiments, the effect of eTENS was assessed by directly comparing the eTENS threshold to that of the post-surgical TENS.This was primarily due to changes in the underlying tissue that resulted from surgically dissecting the sciatic nerve.Validation of the computational modeling data was also assessed by calculating the ratio of nerve activation threshold values obtained post-surgically (NCE:eTENS:TENS), where values were normalized with respect to the NCE threshold and subsequently averaged across all experiments.It is noted that statistical analysis showed no significant difference in nerve activation thresholds achieved on either leg, with or without the depilator cream, so all results were analyzed in aggregate.

VNS at the initial position
NCES resulted in the lowest nerve activation threshold for a 10 µm fiber (I = 0.10 mA), followed by eTENS (6.50 mA) and TENS (13.30 mA).Simulations showed that eTENS exhibited a virtual bipole (figure 3), which resulted in a relative excitability of 2.05, indicating TENS required twice as much current to activate the same nerve fiber.The virtual bipole is absent during TENS (figure 3(A)) as well as for monopolar anodic eTENS (figure 3(C)).Approximating VNS with a helical NCE yielded a nerve activation threshold of 0.13 mA for the same 10 µm fiber.Analysis of the FEM revealed there was approximately 13% less current density in the region of the nerve between the two electrode contacts, which suggests a notable degree of current leakage.

Effect of surface electrode location (TENS vs. eTENS)
Simulation of TENS at different locations on the neck surface showed that the lowest nerve activation  thresholds occurred when the electrodes were aligned with the vagus nerve (figure 4(A), see figure 2 for relative positions).With a platinum nerve cuff placed at (0,0), eTENS was able to achieve lower nerve activation thresholds than TENS if the (rostral) anodic surface electrode did not overlap with the cuff.As depicted in figure 4(B), enhanced nerve activation occurred when the (caudal) cathodic surface electrode overlapped with the nerve cuff, with maximum relative excitability (3.02) achieved when the surface electrodes were displaced (up to 1 cm) medial to the vagus nerve (figure 4(B)).Outside of the anodal region, eTENS achieves both a lower mean and standard deviation of nerve activation thresholds when .This suggests eTENS is both more efficient at activating the nerve, and less sensitive to changes in surface electrode position.When comparing eTENS and TENS at their relative optimal locations, the relative excitability value is 2.4; thus, even when TENS is optimally positioned, eTENS outperforms TENS by a factor greater than 2:1.
Simulations confirmed that TENS initiated APs near the horizontal edge of the surface electrode; whereas AP initiation by eTENS occurred at the cathodic edge (i.e.virtual bipole) of the nerve cuff.If the eTENS nerve cuff is located underneath the anode, AP initiation occurs at the cathodic surface electrode, just as in regular TENS (figure 5(A)).There was also a narrow region (dashed line, figure 4(A)) where activation occurred at both the eTENS nerve cuff and the cathodic surface electrode, generating two simultaneous APs (figure 5(B)).

Interaction between platinum cuff and stationary surface electrodes (eTENS)
Vertical displacement of the eTENS cuff alone showed similar results to vertical displacement of the surface electrodes.Rostral displacement of the cuff towards the anodic surface electrode reduced the enhancing effect of eTENS (figure 6).Conversely, moving the cuff towards the cathode (between −0.5 and −1.5 cm), showed a further decrease in the activation threshold with relative excitability reaching 2.49.This is consistent with results in section 3.2.
Simulations where the platinum cuff was displaced relative to a monopolar anodic surface electrode showed (1) eTENS is ineffective when the cuff is located under the anode (figure 7(A)) and ( 2) neural excitation is enhanced when current can flow longitudinally inside the cuff (larger virtual bipole, figure 7(B)).A comparison between monopolar anodic eTENS and bipolar anodic eTENS, where the cuff is located at the caudal edge of the anodic surface electrode, showed that the cathodic surface electrode (bipolar eTENS) amplifies the effects of the nerve cuff (larger virtual bipole, figure 8(A)).As shown in figure 8(B), eTENS enhancement can occur in a region that is depolarized by a monopolar cathode, but not within the hyperpolarized region of a monopolar anodic surface electrode.

Nerve fiber recruitment properties
At the nerve activation threshold for a 10 µm fiber (T 10 ), eTENS exhibited significantly shorter poststimulus latencies for initiating an AP than that for TENS: 0.74 ± 0.03 ms vs 0.94 ± 0.04 ms, respectively (p < 0.01, Wilcoxon signed-rank test).The latency exhibited by NCES at this amplitude was 0.64 ms.As the stimulation amplitude was increased from 2 to 6 times T 10 (figure 9(A)), there was little difference in the post-stimulus latencies between NCES and eTENS.A similar trend was observed in the nerve recruitment properties (figure 9(B)), where electrical activation of the 5.7 µm fibers by NCES and eTENS was achieved at amplitudes that were 2.6 and 3.1 times the threshold for activating a 16 µm fiber (T 16 ), respectively.In contrast, TENS required markedly larger amplitudes (12 times T 16 ) to electrically recruit 5.7 µm fibers.

In-vivo validation
In vivo experiments confirmed the ratios of nerve activation thresholds obtained in our computational Figure 6.Nerve activation thresholds and relative excitability of eTENS with cuff-only displacement.The cuff was displaced along the rostro-caudal axis in 0.5 cm intervals while the surface electrodes remained centered at the (0,0) position.The activation threshold increases as the cuff is moved in the rostral direction (underneath the anode) and decreases as the cuff is moved caudally (underneath the cathode).The relative excitability, compared to TENS, is shown on the secondary vertical axis.model (figure 10).The measured depth of the sciatic nerve (mean ± SD) was 1.55 ± 0.20 cm, compared to 2.3 cm in our human model.Interestingly, there was no correlation between the relative excitability (TENS:eTENS threshold ratio) and nerve depth; indicating that other factors may be more relevant in predicting eTENS enhancement.Overall, the in vivo nerve activation thresholds were lower than our computational model at baseline position.The mean nerve activation thresholds are plotted in figure 10: NCE at 0.06 mA (vs 0.1 mA), eTENS at 3.76 mA (vs 6.5 mA) and TENS at 3.06 mA pre-surgical and  (long-dash), both NCES (solid-line) and eTENS (short dash) exhibited post-stimulus latencies that were shorter by 0.09 ± 0.07 ms (range = 0.04-0.27ms).This was consistent across stimulation amplitudes that reached 6 times the activation threshold of a 10 µm fiber (T10).A post-stimulus latency below 0.5 ms indicated that the action potential occurred during the 500 µs stimulus pulse.(B) The fiber recruitment properties of NCES and eTENS were very similar, where activation of small myelinated fibers (5.7 µm) required at least 3.8 times less current when compared to TENS.The stimulation amplitudes were normalized to the threshold for activating a large (16 µm) fiber.NCES, eTENS, and TENS 16 µm fibre thresholds were 0.08, 4.83, and 5.28 mA respectively, while 5.7 µm fiber thresholds were 0.22, 15.15, and 63.55 mA respectively.4.81 mA post-surgical (vs 13.3 mA).There was a 1.57x increase in the TENS threshold between the pre and post surgical conditions (3.06 mA vs. 4.81 mA, p < 0.05).The mean TENS:eTENS threshold ratio across all experiments was 1.3:1 and the eTENS activation thresholds exhibited lower standard deviation than TENS (0.49 vs 1.06).Overall, NCE:eTENS:TENS ratio was 1:73:99, which was relatively close to the computational ratio of 1:65:130.

Discussion
Electrical stimulation of the cervical vagus nerve provides a unique approach to modulating the nervous system, while also offering promise for effectively treating a myriad of clinical indications [1,30,31].And computational modeling is widely recognized as a useful tool for investigating different approaches to delivering electrical stimulation in humans [18,[32][33][34].In this set of simulations, we directly compared three different methods of applying cervical VNS (NCES, TENS, and eTENS) by determining the nerve activation thresholds under a variety of experimental conditions.We modified the vertical and horizontal location of surface electrodes, as well as shifted the eTENS cuff along the nerve, to elucidate the effects of both parameters on nerve activation.The enhancing effects of eTENS were also shown by the improved nerve fiber recruitment properties and shorter post-stimulus delays of AP initiation, both of which were similar to those of NCES.Our simulations revealed some important considerations for the application of eTENS technology within the context of current standards of VNS.Finally, we conducted in-vivo validation of our findings in a model of the rat sciatic nerve; this is the first time eTENS has been tested in-vivo with a bipolar configuration as well as the first time eTENS performance has been compared in-vivo to direct nerve stimulation.These validation experiments confirmed the relative performance of TENS, eTENS, and NCES as presented in our simulations.
In previous work, eTENS was found to achieve significantly lower nerve activation thresholds (compared to TENS), when the implanted cuff was aligned with the edge of the cathodic stimulating electrode [21].Our simulations confirm that this enhancing effect persists even in a more complicated, heterogenous anatomical model such as the human cervical vagus nerve.Here, we further discovered that any improvements in nerve activation thresholds by eTENS were lost when the cuff was located directly under the anodic surface electrode, but re-appeared when the nerve cuff did not overlap with the hyperpolarized region under the anode (monopolar anodic eTENS, figure 7).This further highlights the role played by the electrically conductive nerve cuff.
The nerve activation thresholds predicted by our TENS and NCES model align with previous computational models.A model of the gammaCore device demonstrated activation of 10 µm fibers with a TENS current of 10 mA [34], which was implemented in a human VNS model with comparable anatomical detail to our current study.The nerve activation threshold of the gammaCore model was lower than ours by approximately 3 mA, which is likely attributed to our model characterizing the vagal nerve trunk as gradually deviating away from the skin surface as the nerve traveled along the caudal direction; whereas the gammaCore model presumed a straight nerve.Computational simulation of NCES in a VNS model also showed nerve fiber activation of myelinated fibers (diameter = 5-8 µm) at a stimulation amplitude of 0.3 mA [33], which also helps to validate the accuracy of our model predictions.
Computationally derived nerve activation thresholds for NCES in this study were relatively lower than experimental data acquired in-vivo.Human trials of direct VNS have shown thresholds in the range of 0.25-0.5 mA [35][36][37], while rat trials show activations in the range of 0.025 mA for discernable compound APs to 0.36 mA for bradycardia [38,39].A recent study of VNS for heart failure reported a threshold for laryngeal fiber activation as 0.99 ± 0.67 mA [5].This indicates that our simulations report a lower activation threshold than the smallest threshold in these studies.In an in-vivo VNS study conducted in a canine model [40], the threshold for large A fibers was found to be 0.52 ± 0.12 mA.In our model, values for the four largest fiber sizes were 0.08, 0.1, 0.12, and 0.15 mA respectively, which were lower than the in-vivo data.We propose a few possibilities for this discrepancy.First, the cited human and canine experiments employed helical electrodes, which unlike the cylindrical nerve cuffs used in our model show a greater degree of current spread and consequently higher nerve activation thresholds.Indeed, in our simulations of a helical-type NCE, we found that removing the insulating material between the electrode contacts caused a 30% increase in the nerve activation threshold.Second, the use of nerve recordings in vivo to determine the nerve activation thresholds generally relies on detecting compound nerve APs, not single fiber APs.The current thresholds for single fibers will be lower.Finally, it is worth noting that values reported in human experiments in the absence of a recording electrode are perceptual thresholds, whereas activation of individual nerve fibers can occur sub-perceptually.Indeed, subperceptual threshold VNS is beginning to be explored as an alternative to conventional VNS, which uses amplitudes titrated from perception [41,42].
Our rostral-caudal and medial-lateral displacements confirm that eTENS enhancement occurs under a range of placement conditions, dependent on the relative placement of the surface electrodes and the cuff, as well as the polarity of the surface electrodes.For example, referring to figure 4, a 1 cm, medial displacement of the surface electrodes resulted in an increase in the activation threshold by 0.6 mA for eTENS; whereas, the same displacement caused a 2.2 mA increase in TENS.On the other hand, moving the surface electrodes from the initial position along the vertical axis resulted in minimal change for TENS (0.3-0.7 mA decrease), whereas, eTENS could exhibit a 0.4 mA decrease (rostral shift) or a 6.6 mA increase (caudal shift) in the nerve activation threshold.This increase in the eTENS threshold (i.e.loss of enhancement) underscores our finding that eTENS cannot overcome the nerve hyperpolarization generated underneath the anodic surface electrode.If the current through the surface electrodes is further increased, nerve activation will occur in the region under the cathode and not at the eTENS cuff.This demonstrates that under eTENS, there is the potential for TENS cathodic activation given sufficiently high surface currents.We additionally report a transition region, where APs are initiated almost simultaneously by both the cuff and the cathodic surface electrode.However, due to the small size of this region (0.25-2.5 mm), this phenomenon is not likely to be clinically relevant.
In general, eTENS achieves nerve activation in a more consistent manner and across a broader skin area when compared to TENS, as long as the surface anode does not overlap with eTENS cuff.From a clinical perspective, the best eTENS excitation can be expected where the surface cathodic electrode is aligned with both the target nerve and the implanted cuff.Due to the wide range where eTENS excitation is observed, electrode placement need not be as strict as compared to TENS.eTENS can efficiently route current to a nerve target in the absence of direct stimulation as in NCES, or a guide wire as in the stimulus router system [19].
Our simulations also showed that eTENS is able to initiate APs at threshold with post-stimulus latencies that were comparable to NCE stimulation, and significantly shorter than TENS.This suggests that the presence of the conductive cuff in eTENS allows for more efficient activation of nerve fibers than by surface electrodes alone.The divergence in the poststimulus latencies between TENS and eTENS remains even as the stimulation amplitude is increased to six times the activation threshold.We hypothesize that the disparity in post-stimulus latencies and also in the fiber recruitment properties were due to the difference in the number of nodes of Ranvier that were depolarized by the different stimulation methods.Even at higher amplitudes, TENS caused simultaneous depolarization in a larger number of nodes, when compared to eTENS and NCES, but the poststimulus latency of APs did not change.Our current analysis shows that peripheral nerve fibers can respond differently to different types of externally applied stimulus pulses.Further work should help elucidate the nature of this phenomenon.
The clinical effects of VNS are generally considered to be correlated with the electrical recruitment of smaller diameter nerve fibers, such as Bfiber activation being used as a marker for cardiac activity during VNS or C-fiber activation for seizure suppression [43,44].It is clear that NCES can achieve fiber activation thresholds that are orders of magnitude lower than that of TENS.Our simulations confirm the efficiency of NCES in recruiting smaller diameter fibers, which was comparable to previous work showing activation of B-fibers needing amplitudes 2.5-5 times the threshold for larger Afibers.NCES in anesthetized rats also exhibit a similar fiber activation ratio of 1:3 for A-and B-fibers, respectively [45,46].
Our current model also shows that eTENS can activate 5.7 µm fibers using markedly less current than TENS requires to activate 8.7 µm fibers.From a clinical perspective, this suggests the potential for better tolerability to stimulation and more effective recruitment of smaller-diameter fibers when compared to TENS.The improved selectivity of eTENS reduces the off-target effects of TENS by minimizing the activation of adjacent nerve and muscle tissue.The noted caveat is that correct placement of the surface cathode, relative to the implanted cuff, would be required along with precise tuning of stimulation parameters (e.g.pulse duration and amplitude) to ensure controlled recruitment of different nerve fiber types.Furthermore, when the stimulation current is increased, post-stimulus latencies for eTENS are lower than TENS; this indicates that a shorter pulse width could be used for eTENS than TENS when stimulating at a given amplitude above the activation threshold, further reducing the amount of current injected.
Our in-vivo sciatic model largely confirmed our VNS simulations, with a few deviations due to anatomical differences and experimental practicalities.Absolute thresholds were lower than the computational model predicted, but this can be attributed to the narrower diameter of the rat sciatic nerve as compared to the modeled human vagus (∼1-2 mm vs 3.2 mm), its shallower depth (1.55 cm vs ∼2.3 cm), and the use of a FINE electrode, which due to its compression of the nerve allows for lower activation thresholds [47].Due to these differences, we primarily compare the ratios or relative thresholds of the three stimulation methods.The shallower depth of the nerve also accounts for the lower TENS:NCE ratio seen in the validation experiments as compared to the computational model, as it is easier for TENS to target shallower nerves [20].As in the computational model, eTENS achieved both a lower mean threshold than TENS as well as lower standard deviation, indicating more consistent performance, and we additionally demonstrate, for the first time in-vivo, that eTENS can be effective at nerve depths of up to 1.9 cm.The TENS: eTENS ratio seen in the computational model was not achieved in the in-vivo validation, but this can be attributed to ideal attributes of the eTENS computational model, such as the nervecuff interface and optimized electrode placement.In our in-vivo study, we estimated the relative alignment of the cuff and surface electrodes based on anatomical markers, so optimal eTENS positioning may not have been achieved.In addition, the gold cuff used in the study was not self-closing and had to be manually wrapped around the nerve, which may have introduced gaps along the inner surface of the cuff.eTENS still provided a statistically significantly lower threshold than TENS under the given conditions, and in two subjects did show relative TENS:eTENS thresholds of 2:1 as predicted by the computational model.Furthermore, the NCE:eTENS ratio in the model (65:1) was closely approximated in vivo (73:1), further serving to validate the computational results.Future in-vivo experiments of eTENS could use a selfclosing cuff to ensure direct contact with the target nerve and test multiple placement locations of TENS and eTENS, while future computational modeling of imperfect cuff-nerve contact (by including an air gap, for example, between the cuff and the nerve) could be conducted to predict the degree of loss of enhancement under such conditions.Additionally, we observed a significant difference in the nerve activation thresholds between TENS applied before and after surgical dissection of the sciatic nerve (figure 10(A)).Although the order in which stimulation trials were not randomized (primarily due to minimizing surgical manipulation of the nerve), further analysis of the threshold data did not suggest evidence of an order effect.We found in half of the experiments that the eTENS threshold was comparable to TENS (pre-surgical), and we also note from previous work that the enhancing effect of eTENS is observed when the order of stimulation is opposite to the current study [20].For these reasons, we compared TENS and eTENS thresholds post-surgically to ensure both approaches were tested under the same anatomical conditions.In our study, it is noted that the incision was made directly above the sciatic nerve as this enabled the most convenient access for implanting/explanting the electrodes; however, this had the effect of creating discontinuities in the skin and underlying tissue underneath the surface electrodes.Overall, while it is difficult to directly compare the results of this study with previous in-vivo testing in the rat tibial nerve (different neural target, electrode setups, stimulation parameters, etc) we note that our TENS:eTENS ratio of 1.3 is close to the previously determined ratio of 1.4 [20].
A limitation of the computational component of our study is the use of a model based on a single cadaveric data set-meaning that populationlevel conclusions cannot be drawn due to variance among individuals [24,48].Furthermore, while computational simulation of single nerve fibers can provide useful predictions of nerve activation [21,34,49], future FEM models could be expanded into a multi-fiber and or multi-fascicular model to investigate activation of specific peripheral targets.Chronic implantation can be simulated via the modeling of progressive growth of encapsulation tissue [50].Stimulation parameters can also be expanded to include variations in pulse width, waveform, and electrode polarities.This leaves many potential avenues for future studies to explore with regards to eTENS and cervical VNS.
Another minor limitation of our simulations was the necessity of estimating the position of the vagus nerve within the neurovascular bundle, which was due to the limited resolution of the images obtained from the Visible Human Project.Future histologic studies could improve the precision of the model by extracting vagus nerve position data at regular intervals along the cervical vagus nerve, and then reconstructing the nerve as in situ [51].Magnetic resonance neurography could also be performed to acquire in-vivo images of the vagus nerve within the cervical region; this could be done on multiple volunteers to allow for comparison between individuals.

Conclusion
Cervical VNS has the potential for effectively treating a myriad of clinical indications, but work is needed to improve the delivery of this treatment to patients.Implantable and non-invasive methods both have their benefits and limitations, and there is a growing interest in developing minimally-invasive stimulation modalities to overcome existing approaches.This study characterized the current standard methods of NCES and TENS, while also demonstrating the application of a novel eTENS approach using a realistic model of the human vagus nerve.Our results confirmed the efficiency of activating nerve fibers using NCES, but also underscored the notable advantages of using eTENS which include markedly lower nerve activation thresholds and more efficient nerve fiber recruitment characteristics, when compared to TENS.Our results provide impetus for computational modeling of eTENS in other nerve targets (e.g.median nerve or pudendal nerve), further in-vivo validation of eTENS in larger animal models, and subsequent translational testing in clinical studies.

Figure 1 .
Figure 1.Construction of the human VNS model.(A) Sample cross-sectional image with manual segmentation overlaid in light blue.(B) Ventral view of the lofted CAD model, where the subcutaneous fat and skin are rendered transparent.(C) The corresponding FEM model showing a pair of TENS electrodes and layers of subcutaneous fat and skin.Where visible, horizontal lines indicate the plane of a cross-sectional image and vertical lines represent guidelines used in the lofting process.(D) The final meshed FEM within COMSOL, where the fineness of the mesh was varied for the different components of the model.

Figure 2 .
Figure 2. Schematic of the initial position of the bipolar TENS electrodes and nerve cuff (eTENS and NCE) centered along the left vagus nerve [ventral view].Depending on the simulation, a 1 cm vertical displacement can denote a rostral or caudal shift of either the surface electrodes alone, or the cuff alone.Similarly, a horizontal displacement of 1 cm would represent a medial or lateral shift of the surface electrodes away from the nerve.[M = medial, L = lateral, R = rostral, C = caudal].

Figure 3 .
Figure 3. Current density plots along the surface of the endoneurium at the fiber activation thresholds of (A) TENS (B) bipolar eTENS (C) monopolar anodic eTENS.Refer to figure 2 for further context of relative electrode and cuff positions.Positive current density (red) indicates current entering the nerve; negative values indicate current exiting.The red and blue vertical bars indicate the relative positions of the anodic and cathodic surface electrodes, respectively.(A) Under TENS, regions of positive and negative current densities are broad, indicating current spread, and a peak current density 34% lower than eTENS.(B) Under eTENS, the cuff edges define a 'virtual bipole' that occurs in an orientation opposite to that of the surface electrodes.The bipole produces narrow regions of high positive and negative current density.(C) Under monopolar anodic eTENS, current travels laterally relative to the nerve cuff and does not generate a virtual bipole.

Figure 4 .
Figure 4. Heat map plots of the nerve activation thresholds for TENS ((A), left) and eTENS ((A), right), as determined by the MRG model.The relative excitation plot is shown in panel (B).The X and Y axes represent position (along the nerve) of the midpoint of the two surface electrodes, as well as horizontal displacement away from nerve alignment.The eTENS cuff is centered at (0,6.75).eTENS exhibits enhanced neural activation when the surface electrodes are displaced rostral to the nerve cuff (i.e.cuff overlaps with cathodic electrode); whereas the nerve activation thresholds resemble TENS when the electrodes are shifted caudal to the cuff.The dotted black line in A (eTENS plot) represents the region where nerve activation occurs simultaneously due to both the cuff and the cathodic TENS electrode.

Figure 5 .
Figure 5. Propagation of action potentials evoked by computationally simulated eTENS.(A) Example of eTENS, where the nerve cuff is located under the anodic surface electrode.Although nerve depolarization is observed at the nerve cuff (between 8 and 10 cm), nerve activation is elicited by the cathodic surface electrode.(B) Example of eTENS where two APs were simultaneously elicited at the cuff and the cathodic surface electrode.

Figure 7 .
Figure 7. Effects of nerve cuff position on the relative excitability during monopolar anodic eTENS.A eTENS cuff was displaced rostrally and caudally along the nerve; MRG thresholds and AFs were determined for each position.(A) The enhancing effects of eTENS are absent when the cuff is located under the anodic surface electrode (displacement = 5.5-9 cm) but emerges outside this region (relative excitability >1, MRG).The asymmetric change in relative excitability is attributed to the tissue surrounding the nerve.(B) AF for differing cuff displacements.Higher positive values indicate greater ease of nerve activation; vice-versa for negative values.The progressive increase in the peak AF values (i.e.virtual bipole) indicates more longitudinal current flowing through the cuff as it is shifted in either direction.(C) The longitudinal voltage along the nerve epineurium; the location of the isopotential induced by the cuff changes as the cuff is displaced along the nerve length.Note the isopotential occurring at areas of less hyperpolarization (i.e.lower voltage) is associated with higher activating functions.

Figure 8 .
Figure 8.Comparison among different TENS and eTENS configurations-bipolar vs. monopolar and cathodic vs. anodic.(A) Compared to monopolar anodic TENS (solid line), the presence of a nerve cuff centered at 7.3 cm generates a virtual bipole in both monopolar and bipolar eTENS.The magnitude of the bipole for bipolar anodic eTENS (dashed line) is markedly greater, where the cuff is positioned under the anode in both cases.(B) Compared to bipolar eTENS located at the initial position, implementation of eTENS with monopolar electrodes (cuff centered under electrode) has smaller (monopolar cathode) or no effects (monopolar anode) on reducing the nerve activation threshold.(C) Longitudinal voltage along the nerve epineurium; the isopotential induced by the cuff is visible.Once again note the relationship between voltage at the isopotential and the activating function.

Figure 9 .
Figure 9.Comparison of the nerve fiber recruitment properties among the three stimulation methods.(A) Compared to TENS(long-dash), both NCES (solid-line) and eTENS (short dash) exhibited post-stimulus latencies that were shorter by 0.09 ± 0.07 ms (range = 0.04-0.27ms).This was consistent across stimulation amplitudes that reached 6 times the activation threshold of a 10 µm fiber (T10).A post-stimulus latency below 0.5 ms indicated that the action potential occurred during the 500 µs stimulus pulse.(B) The fiber recruitment properties of NCES and eTENS were very similar, where activation of small myelinated fibers (5.7 µm) required at least 3.8 times less current when compared to TENS.The stimulation amplitudes were normalized to the threshold for activating a large (16 µm) fiber.NCES, eTENS, and TENS 16 µm fibre thresholds were 0.08, 4.83, and 5.28 mA respectively, while 5.7 µm fiber thresholds were 0.22, 15.15, and 63.55 mA respectively.

Figure 10 .
Figure 10.(A) Mean activation thresholds for the four stimulation conditions.(Mean ± St.Dev) NCE: 0.06 ± 0.03, Pre-surgical TENS: 3.06 ± 0.64, Post-surgical eTENS: 3.76 ± 0.49, Post-surgical TENS: 4.81 ± 1.06).All values were significantly different from each other.(B) TENS stimulation from one animal at 4.0 mA (black line: stimulation on).Only a stimulation artifact is picked up by the recording electrode (C) eTENS stimulation in the same animal, at 4.0 mA.The EMG signal is superimposed on the stimulation artifact.