Modeling the response of small myelinated axons in a compound nerve to kilohertz frequency signals

The interplay between pulse width and activation depth in TENS: a computational study

Background

Transcutaneous electrical nerve stimulation (TENS) has been a commonly used modality to relieve aches and pain for over 40 years. Commercially available devices provide multiple therapy modes involving a different combination of frequency and pulse width with intensity. While frequency sets sensation, intensity helps determine tolerability, longer pulse width is reported to induce a feeling of deeper stimulation. In fact, longer pulse width has been empirically shown to deliver current into deeper tissues, but in context of other electrical stimulation modalities. The goal of this study was to unpack the relationship between pulse width and activation depth in TENS.

Methods

A highly realistic, anatomically-based, 3D finite element model of the forearm was used to simulate the electric field (E-field) distribution, as the pulse width is varied. A typical titration-guided mechanism was used to obtain the strength-duration (S-D) curves of a sensory McIntyre-Richardson-Grill (MRG) axonal model simulating the pain-transmitting A-delta fibers. The pulse widths tested ranged from 30 μs to 495 μs.

Results

As expected, shorter pulse widths required more current to achieve activation, resulting in a larger E-field. The S-D curve of the target median nerve indicates a rheobase of 1.75 mA and a chronaxie of 232 µs. When the applied currents are the same, shorter pulse widths result in a smaller volume of tissue activated (VTA) compared to the longer pulse widths. A 21 fold difference in VTA was found between the longest and shortest pulse widths considered. For the conditions tested in the study, an increase in pulse width resulted in an increase in activation depth, exhibiting a linear relationship.

Conclusion

Our findings highlight the impact of pulse width on activation depth. While choice of a given therapy mode is usually based on an ad-hoc desirable sensation basis, medical professionals may consider advocating a certain therapy mode based on the depth of the intended target nerve.

Recommendations for the Safe Application of Temporal Interference Stimulation in the Human Brain Part I: Principles of Electrical Neuromodulation and Adverse Effects

Temporal interference stimulation (TIS) is a new form of transcranial electrical stimulation (tES) that has been proposed as a method for targeted, non-invasive stimulation of deep brain structures. While TIS holds promise for a variety of clinical and non-clinical applications, little data is yet available regarding its effects in humans and its mechanisms of action. In order to inform the design and safe conduct of experiments involving TIS, researchers require quantitative guidance regarding safe exposure limits and other safety considerations. To this end, we undertook a two-part effort to determine frequency-dependent thresholds for applied currents below which TIS is unlikely to pose risk to humans in terms of heating or unwanted stimulation. Part I of this effort, described here, comprises a summary of the current knowledge pertaining to the safety of TIS and related techniques. Specifically, we provide: i) a broad overview of the electrophysiological impacts neurostimulation, ii) a review of the (bio-)physical principles underlying the mechanisms of action of transcranial alternating/direct stimulation (tACS/tDCS), deep brain stimulation (DBS), and TIS, and iii) a comprehensive survey of the adverse effects (AEs) associated with each technique as reported in the scientific literature and regulatory and clinical databases. In Part II, we perform an in silico study to determine field exposure metrics for tDCS/tACS and DBS under normal (safe) operating conditions and infer frequency-dependent current thresholds for TIS that result in equivalent levels of exposure.

High-frequency epidural electrical stimulation reduces spasticity and facilitates walking recovery in patients with spinal cord injury

Spinal cord injury (SCI) causes severe motor and sensory deficits, and there are currently no approved treatments for recovery. Nearly 70% of patients with SCI experience pathological muscle cocontraction and spasticity, accompanied by clinical signs such as patellar hyperreflexia and ankle clonus. The integration of epidural electrical stimulation (EES) of the spinal cord with rehabilitation has substantial potential to improve recovery of motor functions; however, abnormal muscle cocontraction and spasticity may limit the benefit of these interventions and hinder the effectiveness of EES in promoting functional movements. High-frequency excitation block introduced in peripheral nerve stimulation could reduce abnormal activity and lead to more physiological activation patterns. Here, we evaluated the application of high-frequency EES (HF-EES) in alleviating undesired muscular cocontraction and spasticity in two patients with motor incomplete SCI implanted with a commercial 32-channel EES paddle commonly used for pain therapy. To design custom HF-EES protocols, we first mapped the muscles targeted by different EES configurations. Our results showed that HF-EES substantially reduced patellar reflex in one participant and eliminated both patellar reflex and ankle clonus in the other participant. By combining HF-EES and low-frequency EES (LF-EES) to enhance functional movements with intensive rehabilitation, we observed notable improvements in lower limb kinematics, muscle strength, and clinical lower limb motor assessments over the trial period. This study suggests that HF-EES could be an important supplementary tool in SCI treatment, emphasizing the importance of personalized rehabilitation approaches and advanced tools to optimize EES treatments and offering hope for individuals with SCI-related motor deficits.

Activation thresholds for electrical phrenic nerve stimulation at the neck: evaluation of stimulation pulse parameters in a simulation study

Objective.Phrenic nerve stimulation reduces ventilator-induced-diaphragmatic-dysfunction, which is a potential complication of mechanical ventilation. Electromagnetic simulations provide valuable information about the effects of the stimulation and are used to determine appropriate stimulation parameters and evaluate possible co-activation.Approach.Using a multiscale approach, we built a novel detailed anatomical model of the neck and the phrenic nerve. The model consisted of a macroscale volume conduction model of the neck with 13 tissues, a mesoscale volume conduction model of the phrenic nerve with three tissues, and a microscale biophysiological model of axons with diameters ranging from 5 to 14 µm based on the McIntyre-Richardson-Grill-model for myelinated axons. This multiscale model was used to quantify activation thresholds of phrenic nerve fibers using different stimulation pulse parameters (pulse width, interphase delay, asymmetry of biphasic pulses, pulse polarity, and rise time) during non-invasive electrical stimulation. Electric field strength was used to evaluate co-activation of the other nerves in the neck.Main results.For monophasic pulses with a pulse width of 150 µs, the activation threshold depended on the fiber diameter and ranged from 20 to 156 mA, with highest activation threshold for the smallest fiber diameter. The relationship was approximated using a power fit functionx-3. Biphasic (symmetric) pulses increased the activation threshold by 25 to 30 %. The use of asymmetric biphasic pulses or an interphase delay lowered the threshold close to the monophasic threshold. Possible co-activated nerves were the more superficial nerves and included the transverse cervical nerve, the supraclavicular nerve, the great auricular nerve, the cervical plexus, the brachial plexus, and the long thoracic nerve.Significance.Our multiscale model and electromagnetic simulations provided insight into phrenic nerve activation and possible co-activation by non-invasive electrical stimulation and provided guidance on the use of stimulation pulse types with minimal activation threshold.

Highly efficient modeling and optimization of neural fiber responses to electrical stimulation

Peripheral neuromodulation has emerged as a powerful modality for controlling physiological functions and treating a variety of medical conditions including chronic pain and organ dysfunction. The underlying complexity of the nonlinear responses to electrical stimulation make it challenging to design precise and effective neuromodulation protocols. Computational models have thus become indispensable in advancing our understanding and control of neural responses to electrical stimulation. However, existing approaches suffer from computational bottlenecks, rendering them unsuitable for real-time applications, large-scale parameter sweeps, or sophisticated optimization. In this work, we introduce an approach for massively parallel estimation and optimization of neural fiber responses to electrical stimulation using machine learning techniques. By leveraging advances in high-performance computing and parallel programming, we present a surrogate fiber model that generates spatiotemporal responses to a wide variety of cuff-based electrical peripheral nerve stimulation protocols. We used our surrogate fiber model to design stimulation parameters for selective stimulation of pig and human vagus nerves. Our approach yields a several-orders-of-magnitude improvement in computational efficiency while retaining generality and high predictive accuracy, demonstrating its robustness and potential to enhance the design and optimization of peripheral neuromodulation therapies.

NRV: An open framework for in silico evaluation of peripheral nerve electrical stimulation strategies

Electrical stimulation of peripheral nerves has been used in various pathological contexts for rehabilitation purposes or to alleviate the symptoms of neuropathologies, thus improving the overall quality of life of patients. However, the development of novel therapeutic strategies is still a challenging issue requiring extensive in vivo experimental campaigns and technical development. To facilitate the design of new stimulation strategies, we provide a fully open source and self-contained software framework for the in silico evaluation of peripheral nerve electrical stimulation. Our modeling approach, developed in the popular and well-established Python language, uses an object-oriented paradigm to map the physiological and electrical context. The framework is designed to facilitate multi-scale analysis, from single fiber stimulation to whole multifascicular nerves. It also allows the simulation of complex strategies such as multiple electrode combinations and waveforms ranging from conventional biphasic pulses to more complex modulated kHz stimuli. In addition, we provide automated support for stimulation strategy optimization and handle the computational backend transparently to the user. Our framework has been extensively tested and validated with several existing results in the literature.

Nonbinary 2D Distribution Tool Maps Autonomic Nerve Fiber Clustering in Lumbosacral Ventral Roots of Rhesus Macaques

Neuromodulation of the peripheral nervous system (PNS) by electrical stimulation may augment autonomic function after injury or in neurodegenerative disorders. Nerve fiber size, myelination, and distance between individual fibers and the stimulation electrode may influence response thresholds to electrical stimulation. However, information on the spatial distribution of nerve fibers within the PNS is sparse. We developed a new two-dimensional (2D) morphological mapping tool to assess spatial heterogeneity and clustering of nerve fibers. The L6-S3 ventral roots (VRs) in rhesus macaques were used as a model system to map preganglionic parasympathetic, γ-motor, and α-motor fibers. Random and ground truth distributions of nerve fiber centroids were determined for each VR by light microscopy. The proposed tool allows for nonbinary determinations of fiber heterogeneity by defining the minimum distance between nerve fibers for cluster inclusion and comparisons with random fiber distributions for each VR. There was extensive variability in the relative composition of nerve fiber types and degree of 2D fiber heterogeneity between different L6-S3 VR levels within and across different animals. There was a positive correlation between the proportion of autonomic fibers and the degree of nerve fiber clustering. Nerve fiber cluster heterogeneity between VRs may contribute to varied functional outcomes from neuromodulation.

Computational models of compound nerve action potentials: Efficient filter-based methods to quantify effects of tissue conductivities, conduction distance, and nerve fiber parameters

BACKGROUND

Peripheral nerve recordings can enhance the efficacy of neurostimulation therapies by providing a feedback signal to adjust stimulation settings for greater efficacy or reduced side effects. Computational models can accelerate the development of interfaces with high signal-to-noise ratio and selective recording. However, validation and tuning of model outputs against in vivo recordings remains computationally prohibitive due to the large number of fibers in a nerve.

METHODS

We designed and implemented highly efficient modeling methods for simulating electrically evoked compound nerve action potential (CNAP) signals. The method simulated a subset of fiber diameters present in the nerve using NEURON, interpolated action potential templates across fiber diameters, and filtered the templates with a weighting function derived from fiber-specific conduction velocity and electromagnetic reciprocity outputs of a volume conductor model. We applied the methods to simulate CNAPs from rat cervical vagus nerve.

RESULTS

Brute force simulation of a rat vagal CNAP with all 1,759 myelinated and 13,283 unmyelinated fibers in NEURON required 286 and 15,860 CPU hours, respectively, while filtering interpolated templates required 30 and 38 seconds on a desktop computer while maintaining accuracy. Modeled CNAP amplitude could vary by over two orders of magnitude depending on tissue conductivities and cuff opening within experimentally relevant ranges. Conduction distance and fiber diameter distribution also strongly influenced the modeled CNAP amplitude, shape, and latency. Modeled and in vivo signals had comparable shape, amplitude, and latency for myelinated fibers but not for unmyelinated fibers.

CONCLUSIONS

Highly efficient methods of modeling neural recordings quantified the large impact that tissue properties, conduction distance, and nerve fiber parameters have on CNAPs. These methods expand the computational accessibility of neural recording models, enable efficient model tuning for validation, and facilitate the design of novel recording interfaces for neurostimulation feedback and understanding physiological systems.

NRV: An open framework for in silico evaluation of peripheral nerve electrical stimulation strategies

Electrical stimulation of peripheral nerves has been used in various pathological contexts for rehabilitation purposes or to alleviate the symptoms of neuropathologies, thus improving the overall quality of life of patients. However, the development of novel therapeutic strategies is still a challenging issue requiring extensive in vivo experimental campaigns and technical development. To facilitate the design of new stimulation strategies, we provide a fully open source and self-contained software framework for the in silico evaluation of peripheral nerve electrical stimulation. Our modeling approach, developed in the popular and well-established Python language, uses an object-oriented paradigm to map the physiological and electrical context. The framework is designed to facilitate multi-scale analysis, from single fiber stimulation to whole multifascicular nerves. It also allows the simulation of complex strategies such as multiple electrode combinations and waveforms ranging from conventional biphasic pulses to more complex modulated kHz stimuli. In addition, we provide automated support for stimulation strategy optimization and handle the computational backend transparently to the user. Our framework has been extensively tested and validated with several existing results in the literature.

Adaptive octree meshes for simulation of extracellular electrophysiology

Objective.The interaction between neural tissues and artificial electrodes is crucial for understanding and advancing neuroscientific research and therapeutic applications. However, accurately modeling this space around the neurons rapidly increases the computational complexity of neural simulations.Approach.This study demonstrates a dynamically adaptive simulation method that greatly accelerates computation by adjusting spatial resolution of the simulation as needed. Use of an octree structure for the mesh, in combination with the admittance method for discretizing conductivity, provides both accurate approximation and ease of modification on-the-fly.Main results.In tests of both local field potential estimation and multi-electrode stimulation, dynamically adapted meshes achieve accuracy comparable to high-resolution static meshes in an order of magnitude less time.Significance.The proposed simulation pipeline improves model scalability, allowing greater detail with fewer computational resources. The implementation is available as an open-source Python module, providing flexibility and ease of reuse for the broader research community.

Modulating individual axons and axonal populations in the peripheral nerve using transverse intrafascicular multichannel electrodes

Objective.A transverse intrafascicular multichannel electrode (TIME) may offer advantages over more conventional cuff electrodes including higher spatial selectivity and reduced stimulation charge requirements. However, the performance of TIME, especially in the context of non-conventional stimulation waveforms, remains relatively unexplored. As part of our overarching goal of investigating stimulation efficacy of TIME, we developed a computational toolkit that automates the creation and usage ofin siliconerve models with TIME setup, which solves nerve responses using cable equations and computes extracellular potentials using finite element method.Approach.We began by implementing a flexible and scalable Python/MATLAB-based toolkit for automatically creating models of nerve stimulation in the hybrid NEURON/COMSOL ecosystems. We then developed a sciatic nerve model containing 14 fascicles with 1,170 myelinated (A-type, 30%) and unmyelinated (C-type, 70%) fibers to study fiber responses over a variety of TIME arrangements (monopolar and hexapolar) and stimulation waveforms (kilohertz stimulation and cathodic ramp modulation).Main results.Our toolkit obviates the conventional need to re-create the same nerve in two disparate modeling environments and automates bi-directional transfer of results. Our population-based simulations suggested that kilohertz stimuli provide selective activation of targeted C fibers near the stimulating electrodes but also tended to activate non-targeted A fibers further away. However, C fiber selectivity can be enhanced by hexapolar TIME arrangements that confined the spatial extent of electrical stimuli. Improved upon prior findings, we devised a high-frequency waveform that incorporates cathodic DC ramp to completely remove undesirable onset responses.Conclusion.Our toolkit allows agile, iterative design cycles involving the nerve and TIME, while minimizing the potential operator errors during complex simulation. The nerve model created by our toolkit allowed us to study and optimize the design of next-generation intrafascicular implants for improved spatial and fiber-type selectivity.

Modulating functionally-distinct vagus nerve fibers using microelectrodes and kilohertz frequency electrical stimulation

Modulation of functionally distinct nerve fibers with bioelectronic devices provides a therapeutic opportunity for various diseases. In this study, we began by developing a computational model including four major subtypes of myelinated fibers and one unmyelinated fiber. Second, we used an intrafascicular electrode to perform kHz-frequency electric stimulation to preferentially modulate a population of fibers. Our model suggests that fiber physical properties and electrode-to-fascicle distance severely impacts stimulus-response relationships. Large diameter fibers (Aα- and Aβ-) were only minimally influenced by the fascicle size and electrode location, while smaller diameter fibers (Aδ-, B- and C-) indicated a stronger dependency.Clinical Relevance- Our findings support the possibility of selectively modulating functionally-distinct nerve fibers using electrical stimulation in a small, localized region. Our model provides an effective tool to design next-generation implantable devices and therapeutic stimulation strategies toward minimizing off-target effects.

Validated computational models predict vagus nerve stimulation thresholds in preclinical animals and humans

Objective.We demonstrated how automated simulations to characterize electrical nerve thresholds, a recently published open-source software for modeling stimulation of peripheral nerves, can be applied to simulate accurately nerve responses to electrical stimulation.Approach.We simulated vagus nerve stimulation (VNS) for humans, pigs, and rats. We informed our models using histology from sample-specific or representative nerves, device design features (i.e. cuff, waveform), published material and tissue conductivities, and realistic fiber models.Main results.Despite large differences in nerve size, cuff geometry, and stimulation waveform, the models predicted accurate activation thresholds across species and myelinated fiber types. However, our C fiber model thresholds overestimated thresholds across pulse widths, suggesting that improved models of unmyelinated nerve fibers are needed. Our models of human VNS yielded accurate thresholds to activate laryngeal motor fibers and captured the inter-individual variability for both acute and chronic implants. For B fibers, our small-diameter fiber model underestimated threshold and saturation for pulse widths >0.25 ms. Our models of pig VNS consistently captured the range ofin vivothresholds across all measured nerve and physiological responses (i.e. heart rate, Aδ/B fibers, Aγfibers, electromyography, and Aαfibers). In rats, our smallest diameter myelinated fibers accurately predicted fast fiber thresholds across short and intermediate pulse widths; slow unmyelinated fiber thresholds overestimated thresholds across shorter pulse widths, but there was overlap for pulse widths >0.3 ms.Significance.We elevated standards for models of peripheral nerve stimulation in populations of models across species, which enabled us to model accurately nerve responses, demonstrate that individual-specific differences in nerve morphology produce variability in neural and physiological responses, and predict mechanisms of VNS therapeutic and side effects.

Spatiotemporal parameters for energy efficient kilohertz-frequency nerve block with low onset response

BACKGROUND

Electrical nerve conduction block has great potential for treatment of disease through reversible and local inactivation of somatic and autonomic nerves. However, the relatively high energy requirements and the presence of undesired excitation at the onset of the kilohertz-frequency (KHF) signals used for block pose obstacles to effective translation. Frequency, electrode geometry, and waveform shape are known to influence block threshold and onset response, but available data provide a limited understanding of how to select these parameters to optimize nerve block.

METHODS

We evaluated KHF nerve block in rat tibial nerve across frequencies (5-60 kHz), electrode geometries (monopolar, bipolar, and tripolar), and waveform shapes. We present a novel Fourier-based method for constructing composite signals that systematically sample the KHF waveform design space.

RESULTS

The lowest frequencies capable of blocking (5-16 kHz) were not the most energy-efficient among the tested frequencies. Further, bipolar cuffs required the largest current and power to block, monopolar cuffs required the lowest current, and both tripolar and monopolar cuffs required the lowest power. Tripolar cuffs produced the smallest onset response across frequencies. Composite signals comprised of a first harmonic sinusoid at fundamental frequency (f0) superposed on a second harmonic sinusoid at 2f0 could block at lower threshold and lower onset response compared to the constituent sinusoids alone. This effect was strongly dependent on the phase of the second harmonic and on the relative amplitudes of the first and second harmonics. This effect was also dependent on electrode geometry: monopolar and tripolar cuffs showed clear composite signal effects in most experiments; bipolar cuffs showed no clear effects in most experiments.

CONCLUSIONS

Our data provide novel information about block threshold and onset response at the boundary of frequencies that can block. Our results also show an interaction between spatial (cuff geometry) and temporal (frequency and waveform shape) parameters. Finally, while previous studies suggested that temporal parameters could reduce onset response only in exchange for increased block threshold (or vice versa), our results show that waveform shape influences KHF response in ways that can be exploited to reduce both energy and onset responses.

Deep-learning segmentation of fascicles from microCT of the human vagus nerve

Introduction

MicroCT of the three-dimensional fascicular organization of the human vagus nerve provides essential data to inform basic anatomy as well as the development and optimization of neuromodulation therapies. To process the images into usable formats for subsequent analysis and computational modeling, the fascicles must be segmented. Prior segmentations were completed manually due to the complex nature of the images, including variable contrast between tissue types and staining artifacts.

Methods

Here, we developed a U-Net convolutional neural network (CNN) to automate segmentation of fascicles in microCT of human vagus nerve.

Results

The U-Net segmentation of ~500 images spanning one cervical vagus nerve was completed in 24 s, versus ~40 h for manual segmentation, i.e., nearly four orders of magnitude faster. The automated segmentations had a Dice coefficient of 0.87, a measure of pixel-wise accuracy, thus suggesting a rapid and accurate segmentation. While Dice coefficients are a commonly used metric to assess segmentation performance, we also adapted a metric to assess fascicle-wise detection accuracy, which showed that our network accurately detects the majority of fascicles, but may under-detect smaller fascicles.

Discussion

This network and the associated performance metrics set a benchmark, using a standard U-Net CNN, for the application of deep-learning algorithms to segment fascicles from microCT images. The process may be further optimized by refining tissue staining methods, modifying network architecture, and expanding the ground-truth training data. The resulting three-dimensional segmentations of the human vagus nerve will provide unprecedented accuracy to define nerve morphology in computational models for the analysis and design of neuromodulation therapies.

Fibers in smaller fascicles have lower activation thresholds with cuff electrodes due to thinner perineurium and smaller cross-sectional area

Objective. In nerve stimulation therapies, fibers in larger fascicles generally have higher activation thresholds, but the mechanisms are not well understood. We implemented and analyzed computational models to uncover the effects of morphological parameters on activation thresholds.Approach. We implemented finite element models of human vagus nerve stimulation to quantify the effects of morphological parameters on thresholds in realistic nerves. We also implemented simplified models to isolate effects of perineurium thickness, endoneurium diameter, fiber diameter, and fascicle location on current density, potential distributions (Ve), and activation thresholds across cuff geometries and stimulation waveforms. UsingVefrom each finite element model, we simulated activation thresholds in biophysical cable models of mammalian axons.Main results. Perineurium thickness increases with fascicle diameter, and both thicker perineurium and larger endoneurial diameter contributed to higher activation thresholds via lower peak and broader longitudinal potentials. Thicker perineurium caused less current to enter the fascicle transversely, decreasing peakVe. Thicker perineurium also inhibited current from leaving the fascicle, causing more constant longitudinal current density, broadeningVe. With increasing endoneurial diameter, intrafascicular volume increased faster than surface area, thereby decreasing intrafascicular current density and peakVe. Additionally, larger fascicles have greater cross-sectional area, thereby facilitating longitudinal intrafascicular current flow and broadeningVe. A large neighboring fascicle could increase activation thresholds, and for a given fascicle, fiber diameter had the greatest effect on thresholds, followed by fascicle diameter, and lastly, fascicle location within the epineurium. The circumneural cuff elicited robust activation across the nerve, whereas a bipolar transverse cuff with small contacts delivering a pseudo-monophasic waveform enabled more selective activation across fiber diameters and locations.Significance. Our computational studies provide mechanistic understanding of neural responses across relevant morphological parameters of peripheral nerves, thereby informing rational design of effective therapies.

Asynchronous axonal firing patterns evoked via continuous subthreshold kilohertz stimulation

Objective.Transcutaneous electrical stimulation of peripheral nerves is a common technique to assist or rehabilitate impaired muscle activation. However, conventional stimulation paradigms activate nerve fibers synchronously with action potentials time-locked with stimulation pulses. Such synchronous activation limits fine control of muscle force due to synchronized force twitches. Accordingly, we developed a subthreshold high-frequency stimulation waveform with the goal of activating axons asynchronously.Approach.We evaluated our waveform experimentally and through model simulations. During the experiment, we delivered continuous subthreshold pulses at frequencies of 16.67, 12.5, or 10 kHz transcutaneously to the median and ulnar nerves. We obtained high-density electromyographic (EMG) signals and fingertip forces to quantify the axonal activation patterns. We used a conventional 30 Hz stimulation waveform and the associated voluntary muscle activation for comparison. We modeled stimulation of biophysically realistic myelinated mammalian axons using a simplified volume conductor model to solve for extracellular electric potentials. We compared the firing properties under kHz and conventional 30 Hz stimulation.Main results.EMG activity evoked by kHz stimulation showed high entropy values similar to voluntary EMG activity, indicating asynchronous axon firing activity. In contrast, we observed low entropy values in EMG evoked by conventional 30 Hz stimulation. The muscle forces evoked by kHz stimulation also showed more stable force profiles across repeated trials compared with 30 Hz stimulation. Our simulation results provide direct evidence of asynchronous firing patterns across a population of axons in response to kHz frequency stimulation, while 30 Hz stimulation elicited synchronized time-locked responses across the population.Significance.We demonstrate that the continuous subthreshold high-frequency stimulation waveform can elicit asynchronous axon firing patterns, which can lead to finer control of muscle forces.

Organ- and function-specific anatomical organization of vagal fibers supports fascicular vagus nerve stimulation

Vagal fibers travel inside fascicles and form branches to innervate organs and regulate organ functions. Existing vagus nerve stimulation (VNS) therapies activate vagal fibers non-selectively, often resulting in reduced efficacy and side effects from non-targeted organs. The transverse and longitudinal arrangement of fibers inside the vagal trunk with respect to the functions they mediate and organs they innervate is unknown, however it is crucial for selective VNS. Using micro-computed tomography imaging, we tracked fascicular trajectories and found that, in swine, sensory and motor fascicles are spatially separated cephalad, close to the nodose ganglion, and merge caudad, towards the lower cervical and upper thoracic region; larynx-, heart- and lung-specific fascicles are separated caudad and progressively merge cephalad. Using quantified immunohistochemistry at single fiber level, we identified and characterized all vagal fibers and found that fibers of different morphological types are differentially distributed in fascicles: myelinated afferents and efferents occupy separate fascicles, myelinated and unmyelinated efferents also occupy separate fascicles, and small unmyelinated afferents are widely distributed within most fascicles. We developed a multi-contact cuff electrode to accommodate the fascicular structure of the vagal trunk and used it to deliver fascicle-selective cervical VNS in anesthetized and awake swine. Compound action potentials from distinct fiber types, and physiological responses from different organs, including laryngeal muscle, cough, breathing, and heart rate responses are elicited in a radially asymmetric manner, with consistent angular separations that agree with the documented fascicular organization. These results indicate that fibers in the trunk of the vagus nerve are anatomically organized according to functions they mediate and organs they innervate and can be asymmetrically activated by fascicular cervical VNS.

Responses of model cortical neurons to temporal interference stimulation and related transcranial alternating current stimulation modalities

Objective.Temporal interference stimulation (TIS) was proposed as a non-invasive, focal, and steerable deep brain stimulation method. However, the mechanisms underlying experimentally-observed suprathreshold TIS effects are unknown, and prior simulation studies had limitations in the representations of the TIS electric field (E-field) and cerebral neurons. We examined the E-field and neural response characteristics for TIS and related transcranial alternating current stimulation modalities.Approach.Using the uniform-field approximation, we simulated a range of stimulation parameters in biophysically realistic model cortical neurons, including different orientations, frequencies, amplitude ratios, amplitude modulation, and phase difference of the E-fields, and obtained thresholds for both activation and conduction block.Main results. For two E-fields with similar amplitudes (representative of E-field distributions at the target region), TIS generated an amplitude-modulated (AM) total E-field. Due to the phase difference of the individual E-fields, the total TIS E-field vector also exhibited rotation where the orientations of the two E-fields were not aligned (generally also at the target region). TIS activation thresholds (75-230 V m-1) were similar to those of high-frequency stimulation with or without modulation and/or rotation. For E-field dominated by the high-frequency carrier and with minimal amplitude modulation and/or rotation (typically outside the target region), TIS was less effective at activation and more effective at block. Unlike AM high-frequency stimulation, TIS generated conduction block with some orientations and amplitude ratios of individual E-fields at very high amplitudes of the total E-field (>1700 V m-1).Significance. The complex 3D properties of the TIS E-fields should be accounted for in computational and experimental studies. The mechanisms of suprathreshold cortical TIS appear to involve neural activity block and periodic activation or onset response, consistent with computational studies of peripheral axons. These phenomena occur at E-field strengths too high to be delivered tolerably through scalp electrodes and may inhibit endogenous activity in off-target regions, suggesting limited significance of suprathreshold TIS.

Selective electrical stimulation of low versus high diameter myelinated fibers and its application in pain relief: a modeling study

Electrical stimulation of peripheral nerve fibers has always been an attractive field of research. Due to the higher activation threshold, the stimulation of small fibers is accompanied by the stimulation of larger ones. It is therefore necessary to design a specific stimulation theme in order to only activate narrow fibers. There is evidence that stimulating Aδ fibers can activate endogenous pain-relieving mechanisms. However, both selective stimulation and reducing pain by activating small nociceptive fibers are still poorly investigated. In this study, using high-frequency stimulation waveforms (5-20 kHz), computational modeling provides a simple framework for activating narrow nociceptive fibers. Additionally, a model of myelinated nerve fibers is modified by including sodium-potassium pump and investigating its effects on neuronal stimulation. Besides, a modified mathematical model of pain processing circuits in the dorsal horn is presented that consists of supraspinal pain control mechanisms. Hence, by employing this pain-modulating model, the mechanism of the reduction of pain by activating nociceptive fibers is explored. In the case of two fibers with the same distance from the point source electrode, a single stimulation waveform is capable of blocking one large fiber and stimulating another small fiber. Noteworthy, the Na/K pump model demonstrated that it does not have a significant effect on the activation threshold and firing frequency of fiber. Ultimately, results suggest that the descending pathways of Locus coeruleus may effectively contribute to pain relief through stimulation of nociceptive fibers, which will be beneficial for clinical interventions.

Fascicles split or merge every ∼560 microns within the human cervical vagus nerve

Objective.Vagus nerve stimulation (VNS) is Food and Drug Administration-approved for epilepsy, depression, and obesity, and stroke rehabilitation; however, the morphological anatomy of the vagus nerve targeted by stimulatation is poorly understood. Here, we used microCT to quantify the fascicular structure and neuroanatomy of human cervical vagus nerves (cVNs).Approach.We collected eight mid-cVN specimens from five fixed cadavers (three left nerves, five right nerves). Analysis focused on the 'surgical window': 5 cm of length, centered around the VNS implant location. Tissue was stained with osmium tetroxide, embedded in paraffin, and imaged on a microCT scanner. We visualized and quantified the merging and splitting of fascicles, and report a morphometric analysis of fascicles: count, diameter, and area.Main results.In our sample of human cVNs, a fascicle split or merge event was observed every ∼560µm (17.8 ± 6.1 events cm-1). Mean morphological outcomes included: fascicle count (6.6 ± 2.8 fascicles; range 1-15), fascicle diameter (514 ± 142µm; range 147-1360µm), and total cross-sectional fascicular area (1.32 ± 0.41 mm2; range 0.58-2.27 mm).Significance.The high degree of fascicular splitting and merging, along with wide range in key fascicular morphological parameters across humans may help to explain the clinical heterogeneity in patient responses to VNS. These data will enable modeling and experimental efforts to determine the clinical effect size of such variation. These data will also enable efforts to design improved VNS electrodes.

kHz-frequency electrical stimulation selectively activates small, unmyelinated vagus afferents

BACKGROUND

Vagal reflexes regulate homeostasis in visceral organs and systems through afferent and efferent neurons and nerve fibers. Small, unmyelinated, C-type afferents comprise over 80% of fibers in the vagus and form the sensory arc of autonomic reflexes of the gut, lungs, heart and vessels and the immune system. Selective bioelectronic activation of C-afferents could be used to mechanistically study and treat diseases of peripheral organs in which vagal reflexes are involved, but it has not been achieved.

METHODS

We stimulated the vagus in rats and mice using trains of kHz-frequency stimuli. Stimulation effects were assessed using neuronal c-Fos expression, physiological and nerve fiber responses, optogenetic and computational methods.

RESULTS

Intermittent kHz stimulation for 30 min activates specific motor and, preferentially, sensory vagus neurons in the brainstem. At sufficiently high frequencies (>5 kHz) and at intensities within a specific range (7-10 times activation threshold, T, in rats; 15-25 × T in mice), C-afferents are activated, whereas larger, A- and B-fibers, are blocked. This was determined by measuring fiber-specific acute physiological responses to kHz stimulus trains, and by assessing fiber excitability around kHz stimulus trains through compound action potentials evoked by probing pulses. Aspects of selective activation of C-afferents are explained in computational models of nerve fibers by how fiber size and myelin shape the response of sodium channels to kHz-frequency stimuli.

CONCLUSION

kHz stimulation is a neuromodulation strategy to robustly and selectively activate vagal C-afferents implicated in physiological homeostasis and disease, over larger vagal fibers.

Vagus nerve stimulation drives selective circuit modulation through cholinergic reinforcement

Vagus nerve stimulation (VNS) is a neuromodulation therapy for a broad and expanding set of neurologic conditions. However, the mechanism through which VNS influences central nervous system circuitry is not well described, limiting therapeutic optimization. VNS leads to widespread brain activation, but the effects on behavior are remarkably specific, indicating plasticity unique to behaviorally engaged neural circuits. To understand how VNS can lead to specific circuit modulation, we leveraged genetic tools including optogenetics and in vivo calcium imaging in mice learning a skilled reach task. We find that VNS enhances skilled motor learning in healthy animals via a cholinergic reinforcement mechanism, producing a rapid consolidation of an expert reach trajectory. In primary motor cortex (M1), VNS drives precise temporal modulation of neurons that respond to behavioral outcome. This suggests that VNS may accelerate motor refinement in M1 via cholinergic signaling, opening new avenues for optimizing VNS to target specific disease-relevant circuitry.

HFAC Dose Repetition and Accumulation Leads to Progressively Longer Block Carryover Effect in Rat Sciatic Nerve

This paper describes high-frequency nerve block experiments carried out on rat sciatic nerves to measure the speed of recovery of A fibres from block carryover. Block carryover is the process by which nerve excitability remains suppressed temporarily after High Frequency Alternative (HFAC) block is turned off following its application. In this series of experiments 5 rat sciatic nerves were extracted and prepared for ex-vivo stimulation and recording in a specially designed perfusion chamber. For each nerve repeated HFAC block and concurrent stimulation trials were carried out to observe block carryover after signal shutoff. The nerve was allowed to recover fully between each trial. Time to recovery from block was measured by monitoring for when relative nerve activity returned to within 90% of baseline levels measured at the start of each trial. HFAC block carryover duration was found to be dependent on accumulated dose by statistical test for two different HFAC durations. The carryover property of HFAC block on A fibres could enable selective stimulation of autonomic nerve fibres such as C fibres for the duration of carryover. Block carryover is particularly relevant to potential chronic clinical applications of block as it reduces power requirements for stimulation to provide the blocking effect. This work characterizes this process toward the creation of a model describing its behavior.

Strategies for precision vagus neuromodulation

The vagus nerve is involved in the autonomic regulation of physiological homeostasis, through vast innervation of cervical, thoracic and abdominal visceral organs. Stimulation of the vagus with bioelectronic devices represents a therapeutic opportunity for several disorders implicating the autonomic nervous system and affecting different organs. During clinical translation, vagus stimulation therapies may benefit from a precision medicine approach, in which stimulation accommodates individual variability due to nerve anatomy, nerve-electrode interface or disease state and aims at eliciting therapeutic effects in targeted organs, while minimally affecting non-targeted organs. In this review, we discuss the anatomical and physiological basis for precision neuromodulation of the vagus at the level of nerve fibers, fascicles, branches and innervated organs. We then discuss different strategies for precision vagus neuromodulation, including fascicle- or fiber-selective cervical vagus nerve stimulation, stimulation of vagal branches near the end-organs, and ultrasound stimulation of vagus terminals at the end-organs themselves. Finally, we summarize targets for vagus neuromodulation in neurological, cardiovascular and gastrointestinal disorders and suggest potential precision neuromodulation strategies that could form the basis for effective and safe therapies.

The model of litter size reduction induces long-term disruption of the gut-brain axis: An explanation for the hyperphagia of Wistar rats of both sexes

The gut microbiota affects the host's metabolic phenotype, impacting health and disease. The gut-brain axis unites the intestine with the centers of hunger and satiety, affecting the eating behavior. Deregulation of this axis can lead to obesity onset. Litter size reduction is a well-studied model for infant obesity because it causes overnutrition and programs for obesity. We hypothesize that animals raised in small litters (SL) have altered circuitry between the intestine and brain, causing hyperphagia. We investigated vagus nerve activity, the expression of c-Fos, brain-derived neurotrophic factor (BDNF), gastrointestinal (GI) hormone receptors, and content of bacterial phyla and short-chain fatty acids (SCFAs) in the feces of adult male and female Wistar rats overfed during lactation. On the 3rd day after birth, litter size was reduced to 3 pups/litter (SL males or SL females) until weaning. Controls had normal litter size (10 pups/litter: 5 males and 5 females). The rats were killed at 5 months of age. The male and female offspring were analyzed separately. The SL group of both sexes showed higher food consumption and body adiposity than the respective controls. SL animals presented dysbiosis (increased Firmicutes, decreased Bacteroidetes) and had increased vagus nerve activity. Only the SL males had decreased hypothalamic GLP-1 receptor expression, while only the SL females had lower acetate and propionate in the feces and higher CCK receptor expression in the hypothalamus. Thus, overfeeding during lactation differentially changes the gut-brain axis, contributing to hyperphagia of the offspring of both sexes.

High-throughput segmentation of unmyelinated axons by deep learning

Axonal characterizations of connectomes in healthy and disease phenotypes are surprisingly incomplete and biased because unmyelinated axons, the most prevalent type of fibers in the nervous system, have largely been ignored as their quantitative assessment quickly becomes unmanageable as the number of axons increases. Herein, we introduce the first prototype of a high-throughput processing pipeline for automated segmentation of unmyelinated fibers. Our team has used transmission electron microscopy images of vagus and pelvic nerves in rats. All unmyelinated axons in these images are individually annotated and used as labeled data to train and validate a deep instance segmentation network. We investigate the effect of different training strategies on the overall segmentation accuracy of the network. We extensively validate the segmentation algorithm as a stand-alone segmentation tool as well as in an expert-in-the-loop hybrid segmentation setting with preliminary, albeit remarkably encouraging results. Our algorithm achieves an instance-level [Formula: see text] score of between 0.7 and 0.9 on various test images in the stand-alone mode and reduces expert annotation labor by 80% in the hybrid setting. We hope that this new high-throughput segmentation pipeline will enable quick and accurate characterization of unmyelinated fibers at scale and become instrumental in significantly advancing our understanding of connectomes in both the peripheral and the central nervous systems.

ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds): A pipeline for sample-specific computational modeling of electrical stimulation of peripheral nerves

Electrical stimulation and block of peripheral nerves hold great promise for treatment of a range of disease and disorders, but promising results from preclinical studies often fail to translate to successful clinical therapies. Differences in neural anatomy across species require different electrodes and stimulation parameters to achieve equivalent nerve responses, and accounting for the consequences of these factors is difficult. We describe the implementation, validation, and application of a standardized, modular, and scalable computational modeling pipeline for biophysical simulations of electrical activation and block of nerve fibers within peripheral nerves. The ASCENT (Automated Simulations to Characterize Electrical Nerve Thresholds) pipeline provides a suite of built-in capabilities for user control over the entire workflow, including libraries for parts to assemble electrodes, electrical properties of biological materials, previously published fiber models, and common stimulation waveforms. We validated the accuracy of ASCENT calculations, verified usability in beta release, and provide several compelling examples of ASCENT-implemented models. ASCENT will enable the reproducibility of simulation data, and it will be used as a component of integrated simulations with other models (e.g., organ system models), to interpret experimental results, and to design experimental and clinical interventions for the advancement of peripheral nerve stimulation therapies.

Despite promising results from preclinical studies, novel therapies using electrical stimulation of peripheral nerves often fail to produce successful clinical outcomes due to differences in neural anatomy across species. These differences often require different electrodes to interface with the nerves and/or different stimulation parameters to achieve equivalent nerve responses. Further, differences in nerve anatomy across a population contribute to differences in nerve responses to stimulation. These inter-species and inter-individual differences can be studied using computational modeling of individual-specific peripheral nerve morphology and biophysical properties. To accelerate the process of computational modeling of individual nerve anatomy, we developed ASCENT, a software platform for simulating the responses of sample-specific nerves to electrical stimulation with custom electrodes and stimulation parameters. ASCENT automates the complex, multi-step process required to build computational models of preclinical and clinical studies and to design novel stimulation protocols using biophysically realistic simulations. The ASCENT pipeline will be used to develop technologies that increase the selectivity and efficiency of stimulation and to accelerate the translation of novel peripheral nerve stimulation therapies to the clinic.

Both high fat and high carbohydrate diets impair vagus nerve signaling of satiety

Obesity remains prevalent in the US. One potential treatment is vagus nerve stimulation (VNS), which activates the sensory afferents innervating the stomach that convey stomach volume and establish satiety. However, current VNS approaches and stimulus optimization could benefit from additional understanding of the underlying neural response to stomach distension. In this study, obesity-prone Sprague Dawley rats consumed a standard, high-carbohydrate, or high-fat diet for several months, leading to diet-induced obesity in the latter two groups. Under anesthesia, the neural activity in the vagus nerve was recorded with a penetrating microelectrode array while the stomach was distended with an implanted balloon. Vagal tone during distension was compared to baseline tone prior to distension. Responses were strongly correlated with stomach distension, but the sensitivity to distension was significantly lower in animals that had been fed the nonstandard diets. The results indicate that both high fat and high carbohydrate diets impair vagus activity.

Kilohertz-frequency stimulation of the nervous system: A review of underlying mechanisms

BACKGROUND

Electrical stimulation in the kilohertz-frequency range has gained interest in the field of neuroscience. The mechanisms underlying stimulation in this frequency range, however, are poorly characterized to date.

OBJECTIVE/HYPOTHESIS

To summarize the manifold biological effects elicited by kilohertz-frequency stimulation in the context of the currently existing literature and provide a mechanistic framework for the neural responses observed in this frequency range.

METHODS

A comprehensive search of the peer-reviewed literature was conducted across electronic databases. Relevant computational, clinical, and mechanistic studies were selected for review.

RESULTS

The effects of kilohertz-frequency stimulation on neural tissue are diverse and yield effects that are distinct from conventional stimulation. Broadly, these can be divided into 1) subthreshold, 2) suprathreshold, 3) synaptic and 4) thermal effects. While facilitation is the dominating mechanism at the subthreshold level, desynchronization, spike-rate adaptation, conduction block, and non-monotonic activation can be observed during suprathreshold kilohertz-frequency stimulation. At the synaptic level, kilohertz-frequency stimulation has been associated with the transient depletion of the available neurotransmitter pool - also known as synaptic fatigue. Finally, thermal effects associated with extrinsic (environmental) and intrinsic (associated with kilohertz-frequency stimulation) temperature changes have been suggested to alter the neural response to stimulation paradigms.

CONCLUSION

The diverse spectrum of neural responses to stimulation in the kilohertz-frequency range is distinct from that associated with conventional stimulation. This offers the potential for new therapeutic avenues across stimulation modalities. However, stimulation in the kilohertz-frequency range is associated with distinct challenges and caveats that need to be considered in experimental paradigms.

Non-monotonic kilohertz frequency neural block thresholds arise from amplitude- and frequency-dependent charge imbalance

Reversible block of nerve conduction using kilohertz frequency electrical signals has substantial potential for treatment of disease. However, the ability to block nerve fibers selectively is limited by poor understanding of the relationship between waveform parameters and the nerve fibers that are blocked. Previous in vivo studies reported non-monotonic relationships between block signal frequency and block threshold, suggesting the potential for fiber-selective block. However, the mechanisms of non-monotonic block thresholds were unclear, and these findings were not replicated in a subsequent in vivo study. We used high-fidelity computational models and in vivo experiments in anesthetized rats to show that non-monotonic threshold-frequency relationships do occur, that they result from amplitude- and frequency-dependent charge imbalances that cause a shift between kilohertz frequency and direct current block regimes, and that these relationships can differ across fiber diameters such that smaller fibers can be blocked at lower thresholds than larger fibers. These results reconcile previous contradictory studies, clarify the mechanisms of interaction between kilohertz frequency and direct current block, and demonstrate the potential for selective block of small fiber diameters.

The Phantom Satiation Hypothesis of Bariatric Surgery

The excitation of vagal mechanoreceptors located in the stomach wall directly contributes to satiation. Thus, a loss of gastric innervation would normally be expected to result in abrogated satiation, hyperphagia, and unwanted weight gain. While Roux-en-Y-gastric bypass (RYGB) inevitably results in gastric denervation, paradoxically, bypassed subjects continue to experience satiation. Inspired by the literature in neurology on phantom limbs, I propose a new hypothesis in which damage to the stomach innervation during RYGB, including its vagal supply, leads to large-scale maladaptive changes in viscerosensory nerves and connected brain circuits. As a result, satiation may continue to arise, sometimes at exaggerated levels, even in subjects with a denervated or truncated stomach. The same maladaptive changes may also contribute to dysautonomia, unexplained pain, and new emotional responses to eating. I further revisit the metabolic benefits of bariatric surgery, with an emphasis on RYGB, in the light of this phantom satiation hypothesis.

Limited Sensitivity of Hippocampal Synaptic Function or Network Oscillations to Unmodulated Kilohertz Electric Fields

Understanding the cellular mechanisms of kilohertz (kHz) electrical stimulation is of broad interest in neuromodulation including forms of transcranial electrical stimulation, interferential stimulation, and high-rate spinal cord stimulation (SCS). Yet, the well-established low-pass filtering by neuronal membranes suggests minimal neuronal polarization in respond to charge-balanced kHz stimulation. The hippocampal brain slice model is among the most studied systems in neuroscience and exhaustively characterized in screening the effects of electrical stimulation. High-frequency electric fields of varied amplitudes (1–150 V/m), waveforms (sinusoidal, symmetrical pule, asymmetrical pulse) and frequencies (1 and10 kHz) were tested. Changes in single or paired-pulse field EPSPs (fEPSP) in CA1 were measured in response to radial-directed and tangential-directed electric fields, with brief (30 s) or long (30 min) application times. The effects of kHz stimulation on ongoing endogenous network activity were tested in carbachol-induced γ oscillation of CA3a and CA3c. Across 23 conditions evaluated, no significant changes in fEPSP were resolved, while responses were detected for within-slice control direct current (DC) fields; 1-kHz sinusoidal and pulse stimulation (≥60 V/m), but not 10 kHz, induced changes in oscillating neuronal network. We thus report no responses to low-amplitude 1-kHz or any 10-kHz fields, suggesting that any brain sensitivity to these fields is via yet to be-determined mechanism(s) of action which were not identified in our experimental preparation.

Biophysics of Temporal Interference Stimulation

Temporal interference (TI) is a non-invasive neurostimulation technique that utilizes high-frequency external electric fields to stimulate deep neuronal structures without affecting superficial, off-target structures. TI represents a potential breakthrough for treating conditions, such as Parkinson's disease and chronic pain. However, early clinical work on TI stimulation was met with mixed outcomes challenging its fundamental mechanisms and applications. Here, we apply established physics to study the mechanisms of TI with the goal of optimizing it for clinical use. We argue that TI stimulation cannot work via passive membrane filtering, as previously hypothesized. Instead, TI stimulation requires an ion-channel mediated signal rectification process. Unfortunately, this mechanism is also responsible for high-frequency conduction block in off-target tissues, thus challenging clinical applications of TI. In consequence, we propose a set of experimental controls that should be performed in future experiments to refine our understanding and practice of TI stimulation. A record of this paper's transparent peer review process is included in the Supplemental Information.

Quantified Morphology of the Cervical and Subdiaphragmatic Vagus Nerves of Human, Pig, and Rat

It is necessary to understand the morphology of the vagus nerve (VN) to design and deliver effective and selective vagus nerve stimulation (VNS) because nerve morphology influences fiber responses to electrical stimulation. Specifically, nerve diameter (and thus, electrode-fiber distance), fascicle diameter, fascicular organization, and perineurium thickness all significantly affect the responses of nerve fibers to electrical signals delivered through a cuff electrode. We quantified the morphology of cervical and subdiaphragmatic VNs in humans, pigs, and rats: effective nerve diameter, number of fascicles, effective fascicle diameters, proportions of endoneurial, perineurial, and epineurial tissues, and perineurium thickness. The human and pig VNs were comparable sizes (∼2 mm cervically; ∼1.6 mm subdiaphragmatically), while the rat nerves were ten times smaller. The pig nerves had ten times more fascicles-and the fascicles were smaller-than in human nerves (47 vs. 7 fascicles cervically; 38 vs. 5 fascicles subdiaphragmatically). Comparing the cervical to the subdiaphragmatic VNs, the nerves and fascicles were larger at the cervical level for all species and there were more fascicles for pigs. Human morphology generally exhibited greater variability across samples than pigs and rats. A prior study of human somatic nerves indicated that the ratio of perineurium thickness to fascicle diameter was approximately constant across fascicle diameters. However, our data found thicker human and pig VN perineurium than those prior data: the VNs had thicker perineurium for larger fascicles and thicker perineurium normalized by fascicle diameter for smaller fascicles. Understanding these differences in VN morphology between preclinical models and the clinical target, as well as the variability across individuals of a species, is essential for designing suitable cuff electrodes and stimulation parameters and for informing translation of preclinical results to clinical application to advance the therapeutic efficacy of VNS.

Quantitative comparisons of block thresholds and onset responses for charge-balanced kilohertz frequency waveforms

OBJECTIVE

There is growing interest in delivering kilohertz frequency (KHF) electrical signals to block conduction in peripheral nerves for treatment of various diseases. Previous studies used different KHF waveforms to achieve block, and it remains unclear how waveform affects nerve block parameters.

APPROACH

We quantified the effects of waveform on KHF block of the rat tibial nerve in vivo and in computational models. We compared block thresholds and onset responses across current-controlled sinusoids and charge-balanced rectangular waveforms with different asymmetries and duty cycles.

MAIN RESULTS

Sine waves had higher block thresholds than square waves, but used less power at block threshold. Block threshold had an inverse relationship with duty cycle of rectangular waveforms irrespective of waveform asymmetry. Computational model results were consistent with relationships measured in vivo, although the models underestimated the effect of duty cycle on increasing thresholds. The axonal membrane substantially filtered waveforms, the filter transfer function was strikingly similar across waveforms, and filtering resulted in post-filtered rms block thresholds that were approximately constant across waveforms in silico and in vivo. Onset response was not consistently affected by waveform shape, but onset response was smaller at amplitudes well above block threshold. Therefore, waveforms with lower block thresholds (e.g. sine waves or square waves) could be more readily increased to higher amplitudes relative to block threshold to reduce onset response. We also observed a reduction in onset responses across consecutive trials after initial application of supra-block threshold amplitudes.

SIGNIFICANCE

Waveform had substantial effects on block thresholds, and the amplitude relative to block threshold had substantial effects on onset response. These data inform choice of waveform in subsequent studies and clinical applications, enhance effective use of block in therapeutic applications, and facilitate the design of parameters that achieve block with minimal onset responses.

Sacral nerve stimulation for refractory OAB and idiopathic urinary retention: Can phenotyping improve the outcome for patients: ICI-RS 2019?

AIMS

Sacral nerve stimulation (SNS) is widely used to treat refractory idiopathic overactive bladder (OAB) and idiopathic urinary retention. However, clinical outcomes are variable and understanding predictive factors for success or side-effects would enable personalization of therapy and optimization of outcomes. At the International Consultation on Incontinence-Research Society meeting 2019, a Think Tank was convened to discuss how advances in the basic science study of SNS may be translatable into clinical practice to improve outcomes of patients undergoing SNS treatment.

METHODS

We conducted a literature review and expert consensus meeting focusing on current methods of phenotyping patients and specifically, how advances in basic science research of the mechanism of action of SNS can be translated into clinical practice to improve patient selection for therapy.

RESULTS

The terms "Idiopathic OAB" and "idiopathic urinary retention" encompass several underlying pathophysiological phenotypes. Commonly, phenotyping is based on clinical and urodynamic factors. Animal studies have demonstrated that high-frequency stimulation can produce rapid onset, reversible conduction block in peripheral nerves. Altering stimulation parameters may potentially enable personalization of therapy depending upon the clinical indication in the future. Similarly, advances in conditional and closed-loop stimulation may offer greater efficacy for certain patients. Phenotyping based on psychological comorbidity requires further study to potentially optimize patient selection for therapy.

CONCLUSIONS

Idiopathic OAB and idiopathic urinary retention are heterogenous conditions with multiple potential underlying phenotypes. Tailoring stimulation parameters to the needs of each individual according to phenotype could optimize outcomes. Assessing psychological comorbidity may improve patient selection. Areas for further research are proposed.

Unveiling Stimulation Secrets of Electrical Excitation of Neural Tissue Using a Circuit Probability Theory

Electrical excitation of neural tissue has wide applications, but how electrical stimulation interacts with neural tissue remains to be elucidated. Here, we propose a new theory, named the Circuit-Probability theory, to reveal how this physical interaction happen. The relation between the electrical stimulation input and the neural response can be theoretically calculated. We show that many empirical models, including strength-duration relationship and linear-non-linear-Poisson model, can be theoretically explained, derived, and amended using our theory. Furthermore, this theory can explain the complex non-linear and resonant phenomena and fit in vivo experiment data. In this letter, we validated an entirely new framework to study electrical stimulation on neural tissue, which is to simulate voltage waveforms using a parallel RLC circuit first, and then calculate the excitation probability stochastically.

Kilohertz waveforms optimized to produce closed-state Na+ channel inactivation eliminate onset response in nerve conduction block

The delivery of kilohertz frequency alternating current (KHFAC) generates rapid, controlled, and reversible conduction block in motor, sensory, and autonomic nerves, but causes transient activation of action potentials at the onset of the blocking current. We implemented a novel engineering optimization approach to design blocking waveforms that eliminated the onset response by moving voltage-gated Na⁺ channels (VGSCs) to closed-state inactivation (CSI) without first opening. We used computational models and particle swarm optimization (PSO) to design a charge-balanced 10 kHz biphasic current waveform that produced conduction block without onset firing in peripheral axons at specific locations and with specific diameters. The results indicate that it is possible to achieve onset-free KHFAC nerve block by causing CSI of VGSCs. Our novel approach for designing blocking waveforms and the resulting waveform may have utility in clinical applications of conduction block of peripheral nerve hyperactivity, for example in pain and spasticity.

Many neurological disorders, including pain and spasticity, are characterized by undesirable increases in sensory, motor, or autonomic nerve activity. Local application of kilohertz frequency alternating currents (KHFAC) can effectively and completely block the conduction of undesired hyperactivity through peripheral nerves and could be a therapeutic approach for alleviating disease symptoms. However, KHFAC nerve block produces an undesirable initial burst of action potentials prior to achieving block. This onset firing may result in muscle contraction and pain and is a significant impediment to potential clinical applications of KHFAC nerve block. We present a novel engineering optimization approach for designing a blocking waveform that completely eliminated the onset firing in peripheral axons by moving voltage-gated Na⁺ channels to closed-state inactivation. Our results suggest that the resulting KHFAC waveform can generate electric nerve block without an onset response. Our approach for optimizing blocking waveforms represents a novel engineering design methodology with myriad potential applications and has relevance for the conduction block of peripheral nerve hyperactivity.

Neural selectivity, efficiency, and dose equivalence in deep brain stimulation through pulse width tuning and segmented electrodes

BACKGROUND

Achieving deep brain stimulation (DBS) dose equivalence is challenging, especially with pulse width tuning and directional contacts. Further, the precise effects of pulse width tuning are unknown, and recent reports of the effects of pulse width tuning on neural selectivity are at odds with classic biophysical studies.

METHODS

We created multicompartment neuron models for two axon diameters and used finite element modeling to determine extracellular influence from standard and segmented electrodes. We analyzed axon activation profiles and calculated volumes of tissue activated.

RESULTS

We find that long pulse widths focus the stimulation effect on small, nearby fibers, suppressing distant white matter tract activation (responsible for some DBS side effects) and improving battery utilization when equivalent activation is maintained for small axons. Directional leads enable similar benefits to a greater degree. Reexamining previous reports of short pulse stimulation reducing side effects, we explore a possible alternate explanation: non-dose equivalent stimulation may have resulted in reduced spread of neural activation. Finally, using internal capsule avoidance as an example in the context of subthalamic stimulation, we present a patient-specific model to show how long pulse widths could help increase the biophysical therapeutic window.

DISCUSSION

We find agreement with classic studies and predict that long pulse widths may focus the stimulation effect on small, nearby fibers and improve power consumption. While future pre-clinical and clinical work is necessary regarding pulse width tuning, it is clear that future studies must ensure dose equivalence, noting that energy- and charge-equivalent amplitudes do not result in equivalent spread of neural activation when changing pulse width.

Vagal mechanisms as neuromodulatory targets for the treatment of metabolic disease

With few effective treatments available, the global rise of metabolic diseases, including obesity, type 2 diabetes mellitus, and cardiovascular disease, seems unstoppable. Likely caused by an obesogenic environment interacting with genetic susceptibility, the pathophysiology of obesity and metabolic diseases is highly complex and involves crosstalk between many organs and systems, including the brain. The vagus nerve is in a key position to bidirectionally link several peripheral metabolic organs with the brain and is increasingly targeted for neuromodulation therapy to treat metabolic disease. Here, we review the basics of vagal functional anatomy and its implications for vagal neuromodulation therapies. We find that most existing vagal neuromodulation techniques either ignore or misinterpret the rich functional specificity of both vagal efferents and afferents as demonstrated by a large body of literature. This lack of specificity of manipulating vagal fibers is likely the reason for the relatively poor beneficial long‐term effects of such therapies. For these therapies to become more effective, rigorous validation of all physiological endpoints and optimization of stimulation parameters as well as electrode placements will be necessary. However, given the large number of function‐specific fibers in any vagal branch, genetically guided neuromodulation techniques are more likely to succeed.

Electrophysiology equipment for reliable study of kHz electrical stimulation

Characterizing the cellular targets of kHz (1-10 kHz) electrical stimulation remains a pressing topic in neuromodulation because expanding interest in clinical application of kHz stimulation has surpassed mechanistic understanding. The presumed cellular targets of brain stimulation do not respond to kHz frequencies according to conventional electrophysiology theory. Specifically, the low-pass characteristics of cell membranes are predicted to render kHz stimulation inert, especially given the use of limited-duty-cycle biphasic pulses. Precisely because kHz frequencies are considered supra-physiological, conventional instruments designed for neurophysiological studies such as stimulators, amplifiers and recording microelectrodes do not operate reliably at these high rates. Moreover, for pulsed waveforms, the signal frequency content is well above the pulse repetition rate. Thus, the very tools used to characterize the effects of kHz electrical stimulation may themselves be confounding factors. We illustrate custom equipment design that supports reliable electrophysiological recording during kHz-rate stimulation. Given the increased importance of kHz stimulation in clinical domains and compelling possibilities that mechanisms of actions may reflect yet undiscovered neurophysiological phenomena, attention to suitable performance of electrophysiological equipment is pivotal.

Electroceutical Targeting of the Autonomic Nervous System

Autonomic nerves are attractive targets for medical therapies using electroceutical devices because of the potential for selective control and few side effects. These devices use novel materials, electrode configurations, stimulation patterns, and closed-loop control to treat heart failure, hypertension, gastrointestinal and bladder diseases, obesity/diabetes, and inflammatory disorders. Critical to progress is a mechanistic understanding of multi-level controls of target organs, disease adaptation, and impact of neuromodulation to restore organ function.

On the parameters used in finite element modeling of compound peripheral nerves

OBJECTIVE

Computational modeling is an important tool for developing and optimizing implantable neural stimulation devices, but requires accurate electrical and geometrical parameter values to improve predictive value. We quantified the effects of perineurial (resistive sheath around each fascicle) and endoneurial (within each fascicle) parameter values for modeling peripheral nerve stimulation.

APPROACH

We implemented 3D finite element models of compound peripheral nerves and cuff electrodes to quantify activation and block thresholds of model axons. We also implemented a 2D finite element model of a bundle of axons to estimate the bulk transverse endoneurial resistivity; we compared numerical estimates to an analytical solution.

MAIN RESULTS

Since the perineurium is highly resistive, potentials were approximately constant over the cross section of a fascicle, and the perineurium resistivity, longitudinal endoneurial resistivity, and fascicle diameter had important effects on thresholds. Activation thresholds increased up to ~130% for higher perineurium resistivity (~400 versus 2200 Ω m) and by ~35%-250% for lower longitudinal endoneurial resistivity (3.5 versus 0.75 Ω m), with larger increases for smaller diameter axons and for axons in larger fascicles. Further, thresholds increased by ~30%-180% for larger fascicle radii, yielding a larger increase with higher perineurium resistivity. Thresholds were largely insensitive to the transverse endoneurial resistivity, but estimates of the bulk resistivity increased with extracellular resistivity and axonal area fraction; the numerical and analytical estimates were in strong agreement except at high axonal area fractions, where structured axon placements that achieved tighter packing produced electric field inhomogeneities.

SIGNIFICANCE

We performed a systematic investigation of the effects of values and methods for modeling the perineurium and endoneurium on thresholds for neural stimulation and block. These results provide guidance for future modeling studies, including parameter selection, data interpretation, and comparison to experimental results.

Effects of vagal neuromodulation on feeding behavior

Implanted vagus nerve stimulation (VNS) for obesity was recently approved by the FDA. However, its efficacy and mechanisms of action remain unclear. Herein, we synthesize clinical and preclinical effects of VNS on feeding behavior and energy balance and discuss engineering considerations for understanding and improving the therapy. Clinical cervical VNS (≤30 Hz) to treat epilepsy or depression has produced mixed effects on weight loss as a side effect, albeit in uncontrolled, retrospective studies. Conversely, preclinical studies (cervical and subdiaphragmatic VNS) mostly report decreased food intake and either decreased weight gain or weight loss. More recent clinical studies report weight loss in response to kilohertz frequency VNS applied to the subdiaphragmatic vagi, albeit with a large placebo effect. Rather than eliciting neural activity, this therapy putatively blocks conduction in the vagus nerves. Overall, stimulation parameters lack systematic exploration, optimization, and justification based on target nerve fibers and therapeutic outcomes. The vagus nerve transduces, transmits, and integrates important neural (efferent and afferent), humoral, energetic, and inflammatory information between the gut and brain. Thus, improved understanding of the biophysics, electrophysiology, and (patho)physiology has the potential to advance VNS as an effective therapy for a wide range of diseases.

Computational motility models of neurogastroenterology and neuromodulation

The success of neuromodulation therapies, particularly in the brain, spinal cord, and peripheral nerves, has been greatly aided by computational, biophysical models. However, treating gastrointestinal disorders with electrical stimulation has been much less explored, partly because the mode of action of such treatments is unclear, and selection of stimulation parameters is often empirical. Progress in gut neuromodulation is limited by the comparative lack of biophysical models capable of simulating neuromodulation of gastrointestinal function. Here, we review the recently developed biophysical models of electrically-active cells in the gastrointestinal system that contribute to motility. Biophysical models are replacing phenomenologically-defined models due to advancements in electrophysiological characterization of key players in the gut: enteric neurons, smooth muscle fibers, and interstitial cells of Cajal. In this review, we explore existing biophysically-defined cellular and network models that contribute to gastrointestinal motility. We focus on recent models that are laying the groundwork for modeling electrical stimulation of the gastrointestinal system. Developing models of gut neuromodulation will improve our mechanistic understanding of these treatments, leading to better parameterization, selectivity, and efficacy of neuromodulation to treat gastrointestinal disorders. Such models may have direct clinical translation to current neuromodulation therapies, such as sacral nerve stimulation.

Model of Impedance Changes in Unmyelinated Nerve Fibers

OBJECTIVE

Currently, there is no imaging method that is able to distinguish the functional activity inside nerves. Such a method would be essential for understanding peripheral nerve physiology and would allow precise neuromodulation of organs these nerves supply. Electrical impedance tomography (EIT) is a method that produces images of electrical impedance change (dZ) of an object by injecting alternating current and recording surface voltages. It has been shown to be able to image fast activity in the brain and large peripheral nerves. To image inside small autonomic nerves, mostly containing unmyelinated fibers, it is necessary to maximize SNR and optimize the EIT parameters. An accurate model of the nerve is required to identify these optimal parameters as well as to validate data obtained in the experiments.

METHODS

In this study, we developed two three-dimensional models of unmyelinated fibers: Hodgkin-Huxley (HH) squid giant axon (single and multiple) and mammalian C-nociceptor. A coupling feedback system was incorporated into the models to simulate direct and alternating current application and simultaneously record external field during action potential propagation.

RESULTS

Parameters of the developed models were varied to study their influence on the recorded impedance changes; the optimal parameters were identified. The negative dZ was found to monotonically decrease with frequency for both HH and C fiber models, in accordance with the experimental data.

CONCLUSION AND SIGNIFICANCE

The accurate realistic model of unmyelinated nerve allows the optimization of EIT parameters and matches literature and experimental results.

Modeling Current Sources for Neural Stimulation in COMSOL

Background: Computational modeling provides an important toolset for designing and analyzing neural stimulation devices to treat neurological disorders and diseases. Modeling enables efficient exploration of large parameter spaces, where preclinical and clinical studies would be infeasible. Current commercial finite element method software packages enable straightforward calculation of the potential distributions, but it is not always clear how to implement boundary conditions to appropriately represent metal stimulating electrodes. By quantifying the effects of different electrode representations on activation thresholds for model axons, we provide recommendations for accurate and efficient modeling of neural stimulating electrodes. Methods: We quantified the effects of different representations of current sources for neural stimulation in COMSOL Multiphysics for monopolar, bipolar, and multipolar electrode designs. Results: We recommend modeling each electrode contact as a thin platinum domain, modeling the electrode substrate with the conductivity of silicone, and either using a point current source in the center of each electrode contact or using a boundary current source. Alternatively, to avoid possible numerical instabilities associated with a large range of conductivity values (i.e., platinum and silicone) and to eliminate the small mesh elements required for thin electrode contacts, the electrode substrate can be assigned the conductivity of platinum by using insulating boundaries between the substrate and surrounding medium, and within the substrate to isolate the contacts from each other. When modeling more than one contact, we recommend using superposition by solving the model once for each contact, leaving inactive contacts floating, and superposing the resulting potentials. We computed comparable errors in activation thresholds across the different implementations in a simplified model (electrode in a homogeneous, isotropic medium), and in realistic models of rat spinal cord stimulation (SCS) and human deep brain stimulation, indicating that the recommended approaches are applicable to different stimulation targets.

Suppression of Urinary Voiding by Conditional High Frequency Stimulation of the Pelvic Nerve in Conscious Rats

Female Wistar rats were instrumented to record bladder pressure and to stimulate the left pelvic nerve. Repeated voids were induced by continuous infusion of saline into the bladder (11.2 ml/h) via a T-piece in the line to the bladder catheter. In each animal tested (n = 6) high frequency pelvic nerve stimulation (1-3 kHz, 1-2 mA sinusoidal waveform for 60 s) applied within 2 s of the onset of a sharp rise in bladder pressure signaling an imminent void was able to inhibit micturition. Voiding was modulated in three ways: (1) Suppression of voiding (four rats, n = 13 trials). No fluid output or a very small volume of fluid expelled (<15% of the volume expected based on the mean of the previous 2 or 3 voids). Voiding suppressed for the entirety of the stimulation period (60 s) and resumed within 37 s of stopping stimulation. (2) Void deferred (four rats, n = 6 trials). The imminent void was suppressed (no fluid expelled) but a void occurred later in the stimulation period (12-44 s, mean 24.5 ± 5.2 s after the onset of the stimulation). (3) Reduction in voided volume (five rats, n = 20 trials). Voiding took place but the volume of fluid voided was 15-80% (range 21.8-77.8%, mean 45.3 ± 3.6%) of the volume expected from the mean of the preceding two or three voids. Spontaneous voiding resumed within 5 min of stopping stimulation. Stimulation during the filling phase in between voids had no effect. The experiments demonstrate that conditional high frequency stimulation of the pelvic nerve started at the onset of an imminent void can inhibit voiding. The effect was rapidly reversible and was not accompanied by any adverse behavioral side effects.

High-Resolution Multi-Scale Computational Model for Non-Invasive Cervical Vagus Nerve Stimulation

OBJECTIVES

To develop the first high-resolution, multi-scale model of cervical non-invasive vagus nerve stimulation (nVNS) and to predict vagus fiber type activation, given clinically relevant rheobase thresholds.

METHODS

An MRI-derived Finite Element Method (FEM) model was developed to accurately simulate key macroscopic (e.g., skin, soft tissue, muscle) and mesoscopic (cervical enlargement, vertebral arch and foramen, cerebral spinal fluid [CSF], nerve sheath) tissue components to predict extracellular potential, electric field (E-Field), and activating function along the vagus nerve. Microscopic scale biophysical models of axons were developed to compare axons of varying size (Aα-, Aβ- and Aδ-, B-, and C-fibers). Rheobase threshold estimates were based on a step function waveform.

RESULTS

Macro-scale accuracy was found to determine E-Field magnitudes around the vagus nerve, while meso-scale precision determined E-field changes (activating function). Mesoscopic anatomical details that capture vagus nerve passage through a changing tissue environment (e.g., bone to soft tissue) profoundly enhanced predicted axon sensitivity while encapsulation in homogenous tissue (e.g., nerve sheath) dulled axon sensitivity to nVNS.

CONCLUSIONS

These findings indicate that realistic and precise modeling at both macroscopic and mesoscopic scales are needed for quantitative predictions of vagus nerve activation. Based on this approach, we predict conventional cervical nVNS protocols can activate A- and B- but not C-fibers. Our state-of-the-art implementation across scales is equally valuable for models of spinal cord stimulation, cortex/deep brain stimulation, and other peripheral/cranial nerve models.