The International Association for the Study of Pain (IASP) defines pain as an unpleasant sensory and emotional experience associated with, or resembling that associated with, actual or potential tissue damage (1). The Centers for Disease Control and Prevention (CDC) estimates that 20.4% (50 million) of American adults suffer from chronic pain and, of which 8% (19.6 million) live with high-impact chronic pain (2). Chronic pain is further defined by IASP to be pain persisting beyond typical tissue healing time, which is generally considered to be 3 months (3). Common types of chronic pain include back, headache, joint, neck, hip, and osteoarthritis pain (4). Although treatment typically includes pharmacological approaches, one non-pharmacological and non-invasive option recommended by some clinicians for its convenience and effectiveness is Transcutaneous electrical nerve stimulation (TENS) therapy (5).

Studies suggest that TENS helps reduce pain via peripheral and central mechanisms. Conventional TENS activates large diameter afferent fibers which is then sent to the central nervous system to activate descending inhibitory systems to reduce hyperalgesia (6). Specifically, the potential main pathways activated by TENS include projections from the ventrolateral periaqueductal gray (PAG) sending input to the rostroventral medial medulla (RVM), which consequently, projects to the spinal cord to produce analgesia (6, 7). In parallel, studies in fibromyalgia suggest that TENS can restore central pain modulation. Using small battery-powered devices, TENS typically delivers biphasic, symmetric or asymmetric, rectangular or square pulses through cutaneous electrodes positioned near the painful area (6). They can be applied with varying frequencies, from low (<10 Hz) to high (>50 Hz), or mixed frequencies (8). In general, higher-frequency stimulation is delivered at sensory intensity, and low-frequency stimulation is delivered at motor intensity (6). At sensory intensity, patients may experience strong but comfortable sensations without contractions, whereas at high intensity they can feel painless motor contraction (6).

The early evolution of TENS has been characterized by a faster rate of development of clinical applications rather than determining optimal parameters (9). This has been compounded by the fact that use for low back pain was “grandfathered” in the United States. As TENS for low back pain was marketed prior to the 1976 medical device regulation act (10), it was allowed to stay in commerce, and therefore TENS efficacy for low back pain was never “premarket approved”. Newer devices could thereby, obtain marketing “clearance” based on demonstrating equivalence to prior devices based on technology (stimulation parameter) comparison. Given no incentive for device manufacturers to develop proper clinical utility and generate high quality efficacy data, clinical evidence has continued to be debated (4, 5). Newer indications such as TENS for migraine and sinus pain have however demonstrated definitive clinical utility (11–13). TENS devices are considered medium risk (Class 2) devices and are available for both prescription and OTC use.

Commercially available TENS devices for peripheral pain provide multiple therapy modes with each mode delivering a different combination of frequency and pulse width with intensity. The intended use of such devices varies from symptomatic relief of chronic pain associated with sore and aching muscles in the shoulder, waist, back, neck, arm, and leg and/or adjunctive treatment in the management of post-surgical and post-traumatic acute pain. Users are asked to screen through available modes and settle on the mode that provides the “most desirable sensation/comfort”. While frequency selection allows to set desired sensory or motor contraction, intensity generally maps to tolerability, longer pulse width is suggested to induce a feeling of deeper stimulation.

Studies exploring the effects of pulse width/duration over the years, have mostly studied physiological responses and not the exact relationship to activation depth in TENS. Li and Bak 1976 (14) showed that isolated excitation of different nerve groups (motor, sensory, pain-conducting fibers) in adult cats may be easier with a short duration pulse. Effects on pulse width on the arm have reproduced basic relationships between pulse duration and current intensity found in prior literature (15, 16). Specifically, Alon et al. (9) demonstrated that pain thresholds mediated by pain-conducting fibers in healthy subjects resulted in reducing thresholds (350 mA—30 mA) as pulse duration was increased (5 μs—1,000 μs). Further, stimulus pulse width may also be used to selectively recruit fibers of different sizes (17). Some efforts do however come close in context of other electrical stimulation modalities. For instance, increasing pulse width was empirically shown to improve current penetration by reaching distant muscles from surface electrodes in neuromuscular electrical stimulation (NMES) (18). In the context of invasive deep brain stimulation (DBS), increasing pulse width has been shown to lead to activation at greater distances from electrode center (or deeper stimulation) (19, 20). Further, long pulse width stimulation has been shown to penetrate and activate deeper muscles in functional electrical stimulation (FES) (21, 22).

The goal of this computational study was to investigate the effect of the pulse width in TENS on the arm. A high anatomically realistic finite element model was used to simulate the induced electric field (E-field) distribution. The E-field is then coupled to a sensory neuron model given TENS's efficacy is predicated on providing pain relief by exciting sensory nerves. We evaluated strength-duration (S-D) curve and volume of tissue activated (VTA). The VTA map was related to pulse width to provide insight on the effect of pulse width on activation depth.

The central aim of this study was to unpack the relationship between pulse width and activation depth during TENS on the arm. Prior electrical stimulation studies using other modalities have empirically shown that wider pulses can recruit deeper targets. Using a highly detailed 3D model, we provide enhanced visualization of available geometry, induced E-field profile, VTA maps, and relationship to activation depth, for the first time.

The S-D curves for nerve stimulation have clearly established its shape over numerous investigations dating back to the 30's (42–45). Given the dominant electrical capacitance of the neural membrane, S-D curves expectedly follow a capacitor discharge curve. A TENS practitioner can therefore readily use the inverse relationship between intensity and pulse width to make an informed stimulation strategy choice. Now longer pulse widths at the same current would lead to more charge delivered across the membrane- presumably translating to deeper stimulation. However, the exact relationship has not been explored previously in TENS. Further for non-invasive electrical nerve stimulation applications, lowering pulse width in order to deliver higher current intensity is limited to the intensity at which the user can comfortably receive stimulation (46). This restriction is however not applicable for invasive delivery (20) as stimulation does not have to navigate superficial cutaneous sensation.

The linear relationship between VTA and pulse width observed in our simulations indicates that longer widths would lead to deeper activation. We note that our observations are restricted to only the pulse widths and the concomitant geometry (forearm) considered here. We expected the relationship to asymptote at higher pulse widths as the excitability threshold reaches rheobase. While the excitability threshold in the S-D curve (Figure 4) follows a hyperbolic or exponential decay similar to classical equations [Weiss-Lapique and Lapique-Blair (44, 45)], the VTA expands with a similar convexity resulting in a net linear VTA—pulse width relationship. We suspect this is due to (1) volume being cubic and (2) the Hessian of voltage dropping exponentially away from the electrodes. There are several limiting assumptions to the plot. We are considering only the magnitude of the Hessian, which does not account for orientation/alignment with any possible axon. The AF thresholds were calibrated for the median nerve A-delta fiber running along the length of the arm; other nerve orientations and fiber types would be expected to respond differently. Further, heterogeneous tissues cause spikes in E-field and AF at material boundaries. Additionally, the MRG model is a simplification of real nerves (i.e., devoid of complex morpho-electric properties) and does not incorporate all ion channel sub-types. It is therefore possible that the lack of model complexity masks non-linearities.

TENS efficacy is likely predicated upon a net effect of stimulating multiple underlying nerves of various types including discharge frequencies. We note that we simply used the median nerve in this study as a test nerve to explore relationships between E-field, strength, duration, activation depth, etc. However, the choice of A-delta fiber is rational as nociceptors generally transmit noxious stimuli through A-delta and C-fiber nerves (47). Further, it is known that the C-fiber afferents carry slow sensations associated with aches, whereas the A-delta afferents are associated with fast sensations such as sharp pain. Given the type of pain felt and if one were to know underlying nerve depth (47), one could potentially start with a suitable pulse width. In reality however, pre-programmed therapy modes (combination of pre-set frequency and pulse width) are provided in TENS devices for pain relief, limiting full flexibility to the user in parameter selection. Therefore, the best approach continues to be to try all modes first, and in each case, titrating intensity to the strongest possible but at a level that is comfortable. If deeper pain relief is desired, patients may consider picking the next mode with longer pulse width while maintaining the frequency and intensity from the prior mode. The caveat however, is that overall pain relief is contingent not only on pulse width parameter of TENS but other factors including discharge frequency, temporal and spatial summation of signals, segmental and central pain mechanisms should also be accounted.

The strength of our modeling process in simulating TENS on the arm is the usage of a highly realistic model. Previous 3-D FEM approaches have either used idealized geometries such as a cylindrical arm (48–50) or derived from 2-D anatomical images by extruding geometry (37) and limiting to certain cross sections (34). The modeling methodology applied here, from the geometry, applying EM simulations into a dynamic Neuron solver, using the modified MRG model, and subsequently using titration analysis, mimics the one employed in the context of magnetic stimulation (MS) (24). The simulation setup used in the aforementioned MS study has been further validated using clinical experiments. Specifically, numerically estimated latencies and waveforms were in agreement with the empirical measurements on subjects undergoing MS on the arm (25). The only difference to our simulation is the application of electrical stimulation and thereby, related governing equation. However, the governing equation is a standard equation used to predict induced current in volumetric media and has been validated in other applications (51, 52). Further, the MRG model has been shown to generate accurate predictions for TENS specifically, compared to active cable and mammalian nerve models (29, 37). Taken together, we expect the main conclusions of this study to be robust.

We specifically isolated the effects due to pulse width given the main aim of our study. In reality, pulse widths are associated with pulse repetition frequency and it is well known that frequency also allows for selective nerve activation. However, this isolation was needed to unpack the relationship of pulse width to activation depth.

It is further meaningful to compare our simulation results to previous experimental attempts. When Kuhn et al., (48) tested three volunteers using 5 × 5 cm electrodes placed on Flexor Digitorum Superficialis and on the wrist, the S-D curve at 0.5 ms indicated a corresponding intensity of ∼5 mA. Goffredo and colleagues tested direct stimulation of the median nerve at the biceps brachii level using a pair of round electrodes (1.5 cm diameter) on six subjects (49). The S-D curve based on experiments indicated intensities of ∼16 mA and ∼9 mA at pulse widths of 200 μs and 500 μs respectively. When considering smaller diameter A-beta fibers to study tactile sensation and 9 mm diameter electrodes on forearm (separation = 12 mm) on six subjects, S-D curve indicated a ∼1.7 mA multiples of rheobase at 200 μs pulse width (50). Finally, Gaines and colleagues report good agreement with historical experimental data with multiples of rheobase of ∼6 V and a chronaxie of 230 μs for a sensory axon (10 μm diameter) (34). The region of interest was the arm near the elbow. We note that a one-to-one comparison across aforementioned efforts and our simulations is non-trivial due to several differences—from geometry (3D forearm is different to 3D upper arm), specific stimulation electrode montage (size and separation)/induced E-field distribution, nerve fiber/related properties considered, etc. Notwithstanding, our predictions of 1.75 mA (rheobase) and 232 μs (chronoaxie) considering the median nerve in the forearm are in the range of experimentally shown values. For similar reasons, extrapolating our predictions to other body parts is not possible due to geometrical, electrode placement, and nerve fiber differences.

There are practical limitations to increasing the pulse width at the same current intensity to increase activation depth, namely battery life. The chronaxie is usually considered the most efficient pulse width choice for conserving the pulse generator's battery life and is naturally a key factor in invasive applications (53). With modern day TENS devices powered by high capacity small rechargeable batteries, this is not much of a concern. However, as mentioned above, we expect the linear relationship to ultimately change and plateau. Promising solutions such as coupling TENS with a nerve cuff to facilitate activation of deeper nerves has been proposed (37). However, nerve cuff involves surgery and moreover, such solutions are still being developed and not currently available to the practitioner or the patient.

Computational modeling and simulation such as the one reported here is now increasingly used across a range of stimulation modalities, from optimizing delivery, performing safety analysis, to supporting device design/development (31, 41, 54–57). Furthermore, these predictions have helped in elucidating stimulation parameter choices, understanding mechanism of action, explaining stimulation outcome, and thereby advancing stimulation administration in general (13, 58–62). We expect this study on the arm to guide researchers in performing future explorations on other body parts, determine ideal pulse width range for target nerve of interest, attempt validation using TENS like the one performed in MS (25), and investigate new TENS delivery approaches (63). One could screen across different electrode montages (i.e., electrode separation, size, and shape) to optimally deliver stimulation to a desired target. Modalities such as interferential (IF)/temporal interference stimulation is now being studied in brain using high resolution anatomical models (64), but it has existed in peripheral stimulation since the 50s (65). Our simulations could be further expanded to study IF stimulation for specific peripheral targets.

Stimulation parameter selection during TENS programming for pain relief is typically based on an ad-hoc sensation basis. Using a highly detailed and realistic 3D arm model, we demonstrate a linear relationship between commonly available pulse width settings and activation depth for TENS on the forearm. While multiple factors impact overall pain relief, once frequency and intensity are set, medical professionals may consider choosing a certain pulse width setting based on the depth of pain relief desired. One can expect a 21 fold difference in volume of tissue activated across the range of pulse width settings available in commercially available devices.