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

Ramped kilohertz-frequency signals produce nerve conduction block without onset response

Objective.Reversible block of peripheral nerve conduction using kilohertz-frequency (KHF) electrical signals has substantial potential for treating diseases. However, onset response, i.e. KHF-induced excitation en route to producing nerve block, is an undesired outcome of neural block protocols. Previous studies of KHF nerve block observed increased onset responses when KHF signal amplitude was linearly ramped for up to 60 s at frequencies up to 30 kHz. Here, we evaluated the onset response across a broad range of ramp durations and frequencies.Approach. In experiments on the rat tibial nerve and biophysical axon models, we quantified nerve responses to linearly ramped KHF signals applied for durations from 16 to 512 s and at frequencies from 10 to 83.3 kHz. We also investigated the role of slow inactivation on onset response during linear ramps by using lacosamide to enhance slow inactivation pharmacologically and by introducing a slow inactivation gating variable in computational models.Main results. In experiments, sufficiently high frequencies (⩾20.8 kHz) with amplitudes that were ramped sufficiently slowly (4.4-570μA s-1) generated conduction block without onset response, and increasing frequency enabled shorter ramps to block without onset response. Experimental use of lacosamide to enhance slow inactivation also eliminated onset response. In computational models, the effects of ramp duration/ramp rate on onset response only occurred after introducing a slow inactivation gating variable, and the models did not account for frequency effects.Significance. The results reveal, for the first time, the ability to use charge-balanced linearly ramped KHF signals to block without onset response. This novel approach enhances the precision of neural blocking protocols and enables coordinated neural control to restore organ function, such as in urinary control after spinal cord injury.

Bridging macroscopic and microscopic modeling of electric field by brain stimulation

Background

Modeling the electric field (E-field) on the microscopic scale improves our understanding of brain stimulation modalities and modeling methods but requires careful consideration of the conductivity values and correction of the field amplitudes to match conventional models on the macroscopic scale.

Objective

We analyze the correction step and discuss its relevance and implications for E-field modeling efforts bridging the macroscopic and microscopic scales.

Methods

We provide the theoretical framework for comparing microscopic and macroscopic models and describe approaches for effectively and efficiently matching the E-field amplitude and tissue conductivity.

Results

Consistent results can be obtained for brain stimulation models on different scales with appropriately selected conductivity and E-field amplitudes.

Conclusion

Microscopic E-field models enable numerical estimation of conductivity of macroscopic homogenous neural tissue from microscopically realistic brain samples and exploration of the effect of microscopic E-field perturbations on neural activation threshold by brain stimulation, therefore improving modeling accuracy.

Enabling electric field model of microscopically realistic brain

BACKGROUND

Modeling brain stimulation at the microscopic scale may reveal new paradigms for various stimulation modalities.

OBJECTIVE

We present the largest map to date of extracellular electric field distributions within a layer L2/L3 mouse primary visual cortex brain sample. This was enabled by the automated analysis of serial section electron microscopy images with improved handling of image defects, covering a volume of 250 × 140 × 90 μm³.

METHODS

The map was obtained by applying a uniform brain stimulation electric field at three different polarizations and accurately computing microscopic field perturbations using the boundary element fast multipole method. We used the map to identify the effect of microscopic field perturbations on the activation thresholds of individual neurons. Previous relevant studies modeled a macroscopically homogeneous cortical volume.

RESULT

Our result shows that the microscopic field perturbations - an 'electric field spatial noise' with a mean value of zero - only modestly influence the macroscopically predicted stimulation field strengths necessary for neuronal activation. The thresholds do not change by more than 10 % on average.

CONCLUSION

Under the stated limitations and assumptions of our method, this result essentially justifies the conventional theory of "invisible" neurons embedded in a macroscopic brain model for transcranial magnetic and transcranial electrical stimulation. However, our result is solely sample-specific and is only relevant to this relatively small sample with 396 neurons. It largely neglects the effect of the microcapillary network. Furthermore, we only considered the uniform impressed field and a single-pulse stimulation time course.

Characterization of Machine Learning-Based Surrogate Models of Neural Activation Under Electrical Stimulation

Electrical stimulation of peripheral nerves via implanted electrodes has been shown to be a promising approach to restore sensation, movement, and autonomic functions across a wide range of illnesses and injuries. While in principle computational models of neuromodulation can allow the exploration of large parameter spaces and the automatic optimization of stimulation devices and strategies, their high time complexity hinders their use on a large scale. We recently proposed the use of machine learning-based surrogate models to estimate the activation of nerve fibers under electrical stimulation, producing a considerable speed-up with respect to biophysically accurate models of fiber excitation while retaining good predictivity. Here, we characterize the performance of four frequently employed machine learning algorithms and provide an illustrative example of their ability to generalize to unseen stimulation protocols, stimulating sites, and nerve sections. We then discuss how the ability to generalize to such scenarios is relevant to different optimization protocols, paving the way for the automatic optimization of neuromodulation applications.

Computational modeling of autonomic nerve stimulation: Vagus et al

Computational models of electrical stimulation, block and recording of autonomic nerves enable analysis of mechanisms of action underlying neural responses and design of optimized stimulation parameters. We reviewed advances in computational modeling of autonomic nerve stimulation, block, and recording over the past five years, with a focus on vagus nerve stimulation, including both implanted and less invasive approaches. Few models achieved quantitative validation, but integrated computational pipelines increase the reproducibility, reusability, and accessibility of computational modeling. Model-based optimization enabled design of electrode geometries and stimulation parameters for selective activation (across fiber locations or types). Growing efforts link models of neural activity to downstream physiological responses to represent more directly the therapeutic effects and side effects of stimulation. Thus, computational modeling is an increasingly important tool for analysis and design of bioelectronic therapies.

A finite element model for biomechanical characterization of ex vivo peripheral nerve dysfunction during stretch

Peripheral nerve damage can cause debilitating symptoms ranging from numbness and pain to sensory loss and atrophy. To uncover the underlying mechanisms of peripheral nerve injury, our research aims to develop a relationship between biomechanical peripheral nerve damage and function through finite element modeling. A noncontact, ex vivo electrophysiology chamber, capable of axially stretching explanted nerves while recording electrical signals, was used to investigate peripheral nerve injury. Successive stretch trials were run on eight sciatic nerves (four females and four males) excised from Sprague-Dawley rats. Nerves were stretched until 50% compound action potential (CAP) amplitude reduction was obtained. A constitutive model developed by Raghavan and Vorp was suitable for rat sciatic nerves, with an average α and β of 0.183 MPa and 1.88 MPa, respectively. We then generated 95% confidence intervals for the stretch at which specific CAP amplitude reductions would occur, which compares well to previous studies. We also developed a finite element model that can predict stretch-induced signaling deficits, applicable for complex nerve geometries and injuries. This relationship between nerve biomechanics and function can be expanded upon to create a clinical model for peripheral nerve dysfunction due to stretch.

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuromodulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g. Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

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.

Harnessing the Potential of Self-Assembled Peptide Hydrogels for Neural Regeneration and Tissue Engineering

Spinal cord injury, traumatic brain injury, and neurosurgery procedures usually lead to neural tissue damage. Self-assembled peptide (SAP) hydrogels, a type of innovative hierarchical nanofiber-forming peptide sequences serving as hydrogelators, have emerged as a promising solution for repairing tissue defects and promoting neural tissue regeneration. SAPs possess numerous features, such as adaptable morphologies, biocompatibility, injectability, tunable mechanical stability, and mimicking of the native extracellular matrix. This review explores the capacity of neural cell regeneration and examines the critical aspects of SAPs in neuroregeneration, including their biochemical composition, topology, mechanical behavior, conductivity, and degradability. Additionally, it delves into the latest strategies involving SAPs for central or peripheral neural tissue engineering. Finally, the prospects of SAP hydrogel design and development in the realm of neuroregeneration are discussed.

Selective intrafascicular stimulation of myelinated and unmyelinated nerve fibers through a longitudinal electrode: A computational study

Carbon nanotube (CNT) fiber electrodes have demonstrated exceptional spatial selectivity and sustained reliability in the context of intrafascicular electrical stimulation, as evidenced through rigorous animal experimentation. A significant presence of unmyelinated C fibers, known to induce uncomfortable somatosensory experiences, exists within peripheral nerves. This presence poses a considerable challenge to the excitation of myelinated Aβ fibers, which are crucial for tactile sensation. To achieve nuanced tactile sensory feedback utilizing CNT fiber electrodes, the selective stimulation of Aβ sensory afferents emerges as a critical factor. In confronting this challenge, the present investigation sought to refine and apply a rat sciatic-nerve model leveraging the capabilities of the COMSOL-NEURON framework. This approach enables a systematic evaluation of the influence exerted by stimulation parameters and electrode geometry on the activation dynamics of both myelinated Aβ and unmyelinated C fibers. The findings advocate for the utilization of current pulses featuring a pulse width of 600 μs, alongside the deployment of CNT fibers characterized by a diminutive diameter of 10 μm, with an exclusively exposed cross-sectional area, to facilitate reduced activation current thresholds. Comparative analysis under monopolar and bipolar electrical stimulation conditions revealed proximate activation thresholds, albeit with bipolar stimulation exhibiting superior fiber selectivity relative to its monopolar counterpart. Concerning pulse waveform characteristics, the adoption of an anodic-first biphasic stimulation modality is favored, taking into account the dual criteria of activation threshold and fiber selectivity optimization. Consequently, this investigation furnishes an efficacious stimulation paradigm for the selective activation of touch-related nerve fibers, alongside provisioning a comprehensive theoretical foundation for the realization of natural tactile feedback within the domain of prosthetic hand applications.

Quasistatic approximation in neuromodulation

We define and explain the quasistatic approximation (QSA) as applied to field modeling for electrical and magnetic stimulation. Neuromodulation analysis pipelines include discrete stages, and QSA is applied specifically when calculating the electric and magnetic fields generated in tissues by a given stimulation dose. QSA simplifies the modeling equations to support tractable analysis, enhanced understanding, and computational efficiency. The application of QSA in neuro-modulation is based on four underlying assumptions: (A1) no wave propagation or self-induction in tissue, (A2) linear tissue properties, (A3) purely resistive tissue, and (A4) non-dispersive tissue. As a consequence of these assumptions, each tissue is assigned a fixed conductivity, and the simplified equations (e.g., Laplace's equation) are solved for the spatial distribution of the field, which is separated from the field's temporal waveform. Recognizing that electrical tissue properties may be more complex, we explain how QSA can be embedded in parallel or iterative pipelines to model frequency dependence or nonlinearity of conductivity. We survey the history and validity of QSA across specific applications, such as microstimulation, deep brain stimulation, spinal cord stimulation, transcranial electrical stimulation, and transcranial magnetic stimulation. The precise definition and explanation of QSA in neuromodulation are essential for rigor when using QSA models or testing their limits.

AxoDetect: an automated nerve image segmentation and quantification workflow for computational nerve modeling

Objective.Bioelectronic treatments targeting near-organ innervation have unprecedented clinical applications. Particularly in the spleen, the inhibition of the cholinergic inflammatory response by near-organ nerve stimulation has potential to replace pharmacological treatments in chronic and autoimmune diseases. A caveat is that the optimization of therapeutic stimulation parameters relies onin vivoexperimentation, which becomes challenging due to the small nerve diameters (2 μm), complex anatomy, and mixed axon type composition of the autonomic nerves. Effective development ofin silicomodels requires tools which allow for fast and efficient quantification of axonal composition of specific nerves. Current approaches to generate such information rely on manual image segmentation and quantification.Approach.We developed a combined image-segmentation and model-generation software called AxoDetect: a target- and format-agnostic computer vision algorithm which can segment myelin, endo/epineurium, and both myelinated and unmyelinated fibers from a nerve image without training.Main results.AxoDetect is over 10 times faster on average when compared with current automatic methods while maintaining flexibility through the use of tunable pixel threshold filters to detect different types of tissue. When compared to a distribution-based and a manually segmented model of the splenic nerve terminal branch 1, the model generated with AxoDetect had comparable threshold prediction and was able to accurately detect an increase in activation threshold caused by the addition of surrounding fat tissue to the modeled nerve.Significance.AxoDetect contributes to the acceleration of neuromodulation treatment development through faster model design and iteration without requiring training. Furthermore, the computer vision approach and tunable nature of the filters in our method allow for its use in a variety of histological applications. Our approach will impact not only the study of nerves but also the design of implantable neural interfaces to enhance bioelectronic therapeutic options.

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.

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

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

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.

Design of an adaptable intrafascicular electrode (AIR) for selective nerve stimulation by model-based optimization

Peripheral nerve stimulation is being investigated as a therapeutic tool in several clinical scenarios. However, the adopted devices have restricted ability to obtain desired outcomes with tolerable off-target effects. Recent promising solutions are not yet employed in clinical practice due to complex required surgeries, lack of long-term stability, and implant invasiveness. Here, we aimed to design a neural interface to address these issues, specifically dimensioned for pudendal and sacral nerves to potentially target sexual, bladder, or bowel dysfunctions. We designed the adaptable intrafascicular radial electrode (AIR) through realistic computational models. They account for detailed human anatomy, inhomogeneous anisotropic conductance, following the trajectories of axons along curving and branching fascicles, and detailed biophysics of axons. The model was validated against available experimental data. Thanks to computationally efficient geometry-based selectivity estimations we informed the electrode design, optimizing its dimensions to obtain the highest selectivity while maintaining low invasiveness. We then compared the AIR with state-of-the-art electrodes, namely InterStim leads, multipolar cuffs and transversal intrafascicular multichannel electrodes (TIME). AIR, comprising a flexible substrate, surface active sites, and radially inserted intrafascicular needles, is designed to be implanted in a few standard steps, potentially enabling fast implants. It holds potential for repeatable stimulation outcomes thanks to its radial structural symmetry. When compared in-silico, AIR consistently outperformed cuff electrodes and InterStim leads in terms of recruitment threshold and stimulation selectivity. AIR performed similarly or better than a TIME, with quantified less invasiveness. Finally, we showed how AIR can adapt to different nerve sizes and varying shapes while maintaining high selectivity. The AIR electrode shows the potential to fill a clinical need for an effective peripheral nerve interface. Its high predicted performance in all the identified requirements was enabled by a model-based approach, readily applicable for the optimization of electrode parameters in any peripheral nerve stimulation scenario.

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.

Measuring and modeling the effects of vagus nerve stimulation on heart rate and laryngeal muscles

BACKGROUND

Reduced heart rate (HR) during vagus nerve stimulation (VNS) is associated with therapy for heart failure, but stimulation frequency and amplitude are limited by patient tolerance. An understanding of physiological responses to parameter adjustments would allow differential control of therapeutic and side effects. To investigate selective modulation of the physiological responses to VNS, we quantified the effects and interactions of parameter selection on two physiological outcomes: one related to therapy (reduced HR) and one related to side effects (laryngeal muscle EMG).

METHODS

We applied a broad range of stimulation parameters (mean pulse rates (MPR), intra-burst frequencies, and amplitudes) to the vagus nerve of anesthetized mice. We leveraged the in vivo recordings to parameterize and validate computational models of HR and laryngeal muscle activity across amplitudes and temporal patterns of VNS. We constructed a finite element model of excitation of fibers within the mouse cervical vagus nerve.

RESULTS

HR decreased with increased amplitude, increased MPR, and decreased intra-burst frequency. EMG increased with increased MPR. Preferential HR effects over laryngeal EMG effects required combined adjustments of amplitude and MPR. The model of HR responses highlighted contributions of ganglionic filtering to VNS-evoked changes in HR at high stimulation frequencies. Overlap in activation thresholds between small and large modeled fibers was consistent with the overlap in dynamic ranges of related physiological measures (HR and EMG).

CONCLUSION

The present study provides insights into physiological responses to VNS required for informed parameter adjustment to modulate selectively therapeutic effects and side effects.

Exploring the Physicochemical, Electroactive, and Biodelivery Properties of Metal Nanoparticles on Peripheral Nerve Regeneration

Despite the advances in the regeneration/rehabilitation field of damaged tissues, the functional recovery of peripheral nerves (PNs), especially in a long gap injury, is considered a great medical challenge. Recent progress in nanomedicine has provided great hope for PN regeneration through the strategy of controlling cell behavior by metal nanoparticles individually or loaded on scaffolds/conduits. Despite the confirmed toxicity of metal nanoparticles due to long-term accumulation in nontarget tissues, they play a role in the damaged PN regeneration based on the topography modification of scaffolds/conduits, enhancing neurotrophic factor secretion, the ion flow improvement, and the regulation of electrical signals. Determining the fate of neural progenitor cells would be a major achievement in PN regeneration, which seems to be achievable by metal nanoparticles through altering cell vital approaches and controlling their functions. Therefore, in this literature, an attempt was made to provide an overview of the effective activities of metal nanoparticles on the PN regeneration, until the vital clues of the PN regeneration and how they are changed by metal nanoparticles are revealed to the researcher.

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.

Imaging peripheral nerve micro-anatomy with MUSE, 2D and 3D approaches

Understanding peripheral nerve micro-anatomy can assist in the development of safe and effective neuromodulation devices. However, current approaches for imaging nerve morphology at the fiber level are either cumbersome, require substantial instrumentation, have a limited volume of view, or are limited in resolution/contrast. We present alternative methods based on MUSE (Microscopy with Ultraviolet Surface Excitation) imaging to investigate peripheral nerve morphology, both in 2D and 3D. For 2D imaging, fixed samples are imaged on a conventional MUSE system either label free (via auto-fluorescence) or after staining with fluorescent dyes. This method provides a simple and rapid technique to visualize myelinated nerve fibers at specific locations along the length of the nerve and perform measurements of fiber morphology (e.g., axon diameter and g-ratio). For 3D imaging, a whole-mount staining and MUSE block-face imaging method is developed that can be used to characterize peripheral nerve micro-anatomy and improve the accuracy of computational models in neuromodulation. Images of rat sciatic and human cadaver tibial nerves are presented, illustrating the applicability of the method in different preclinical models.

Augmented Transcutaneous Stimulation Using an Injectable Electrode: A Computational Study

Minimally invasive neuromodulation technologies seek to marry the neural selectivity of implantable devices with the low-cost and non-invasive nature of transcutaneous electrical stimulation (TES). The Injectrode® is a needle-delivered electrode that is injected onto neural structures under image guidance. Power is then transcutaneously delivered to the Injectrode using surface electrodes. The Injectrode serves as a low-impedance conduit to guide current to the deep on-target nerve, reducing activation thresholds by an order of magnitude compared to using only surface stimulation electrodes. To minimize off-target recruitment of cutaneous fibers, the energy transfer efficiency from the surface electrodes to the Injectrode must be optimized. TES energy is transferred to the Injectrode through both capacitive and resistive mechanisms. Electrostatic finite element models generally used in TES research consider only the resistive means of energy transfer by defining tissue conductivities. Here, we present an electroquasistatic model, taking into consideration both the conductivity and permittivity of tissue, to understand transcutaneous power delivery to the Injectrode. The model was validated with measurements taken from (n = 4) swine cadavers. We used the validated model to investigate system and anatomic parameters that influence the coupling efficiency of the Injectrode energy delivery system. Our work suggests the relevance of electroquasistatic models to account for capacitive charge transfer mechanisms when studying TES, particularly when high-frequency voltage components are present, such as those used for voltage-controlled pulses and sinusoidal nerve blocks.

Human organ donor-derived vagus nerve biopsies allow for well-preserved ultrastructure and high-resolution mapping of myelinated and unmyelinated fibers

The vagus nerve provides motor, sensory, and autonomic innervation of multiple organs, and electrical vagus nerve stimulation (VNS) provides an adjunctive treatment option for e.g. medication-refractory epilepsy and treatment-resistant depression. The mechanisms of action for VNS are not known, and high-resolution anatomical mapping of the human vagus nerve is needed to better understand its functional organization. Electron microscopy (EM) is required for the detection of both myelinated and unmyelinated axons, but access to well-preserved human vagus nerves for ultrastructural studies is sparse. Intact human vagus nerve samples were procured intra-operatively from deceased organ donors, and tissues were immediately immersion fixed and processed for EM. Ultrastructural studies of cervical and sub-diaphragmatic vagus nerve segments showed excellent preservation of the lamellated wall of myelin sheaths, and the axolemma of myelinated and unmyelinated fibers were intact. Microtubules, neurofilaments, and mitochondria were readily identified in the axoplasm, and the ultrastructural integrity of Schwann cell nuclei, Remak bundles, and basal lamina was also well preserved. Digital segmentation of myelinated and unmyelinated axons allowed for determination of fiber size and myelination. We propose a novel source of human vagus nerve tissues for detailed ultrastructural studies and mapping to support efforts to refine neuromodulation strategies, including VNS.

In vivo Visualization of Pig Vagus Nerve "Vagotopy" Using Ultrasound

Background: Placement of the clinical vagus nerve stimulating cuff is a standard surgical procedure based on anatomical landmarks, with limited patient specificity in terms of fascicular organization or vagal anatomy. As such, the therapeutic effects are generally limited by unwanted side effects of neck muscle contractions, demonstrated by previous studies to result from stimulation of (1) motor fibers near the cuff in the superior laryngeal and (2) motor fibers within the cuff projecting to the recurrent laryngeal. Objective: Conventional non-invasive ultrasound, where the transducer is placed on the surface of the skin, has been previously used to visualize the vagus with respect to other landmarks such as the carotid and internal jugular vein. However, it lacks sufficient resolution to provide details about the vagus fascicular organization, or detail about smaller neural structures such as the recurrent and superior laryngeal branch responsible for therapy limiting side effects. Here, we characterize the use of ultrasound with the transducer placed in the surgical pocket to improve resolution without adding significant additional risk to the surgical procedure in the pig model. Methods: Ultrasound images were obtained from a point of known functional organization at the nodose ganglia to the point of placement of stimulating electrodes within the surgical window. Naïve volunteers with minimal training were then asked to use these ultrasound videos to trace afferent groupings of fascicles from the nodose to their location within the surgical window where a stimulating cuff would normally be placed. Volunteers were asked to select a location for epineural electrode placement away from the fascicles containing efferent motor nerves responsible for therapy limiting side effects. 2-D and 3-D reconstructions of the ultrasound were directly compared to post-mortem histology in the same animals. Results: High-resolution ultrasound from the surgical pocket enabled 2-D and 3-D reconstruction of the cervical vagus and surrounding structures that accurately depicted the functional vagotopy of the pig vagus nerve as confirmed via histology. Although resolution was not sufficient to match specific fascicles between ultrasound and histology 1 to 1, it was sufficient to trace fascicle groupings from a point of known functional organization at the nodose ganglia to their locations within the surgical window at stimulating electrode placement. Naïve volunteers were able place an electrode proximal to the sensory afferent grouping of fascicles and away from the motor nerve efferent grouping of fascicles in each subject (n = 3). Conclusion: The surgical pocket itself provides a unique opportunity to obtain higher resolution ultrasound images of neural targets responsible for intended therapeutic effect and limiting off-target effects. We demonstrate the increase in resolution is sufficient to aid patient-specific electrode placement to optimize outcomes. This simple technique could be easily adopted for multiple neuromodulation targets to better understand how patient specific anatomy impacts functional outcomes.

Computational modelling of nerve stimulation and recording with peripheral visceral neural interfaces

Objective.Neuromodulation of visceral nerves is being intensively studied for treating a wide range of conditions, but effective translation requires increasing the efficacy and predictability of neural interface performance. Here we use computational models of rat visceral nerve to predict how neuroanatomical variability could affect both electrical stimulation and recording with an experimental planar neural interface.Approach.We developed a hybrid computational pipeline,VisceralNerveEnsembleRecording andStimulation (ViNERS), to couple finite-element modelling of extracellular electrical fields with biophysical simulations of individual axons. Anatomical properties of fascicles and axons in rat pelvic and vagus nerves were measured or obtained from public datasets. To validate ViNERS, we simulated pelvic nerve stimulation and recording with an experimental four-electrode planar array.Main results.Axon diameters measured from pelvic nerve were used to model a population of myelinated and unmyelinated axons and simulate recordings of electrically evoked single-unit field potentials (SUFPs). Across visceral nerve fascicles of increasing size, our simulations predicted an increase in stimulation threshold and a decrease in SUFP amplitude. Simulated threshold changes were dominated by changes in perineurium thickness, which correlates with fascicle diameter. We also demonstrated that ViNERS could simulate recordings of electrically-evoked compound action potentials (ECAPs) that were qualitatively similar to pelvic nerve recording made with the array used for simulation.Significance.We introduce ViNERS as a new open-source computational tool for modelling large-scale stimulation and recording from visceral nerves. ViNERS predicts how neuroanatomical variation in rat pelvic nerve affects stimulation and recording with an experimental planar electrode array. We show ViNERS can simulate ECAPS that capture features of our recordings, but our results suggest the underlying NEURON models need to be further refined and specifically adapted to accurately simulate visceral nerve axons.

Translating node of Ranvier currents to extraneural electrical fields: a flexible FEM modeling approach

Simulations of electroneurogram recording could help find the optimal set of electrodes and algorithms for selective neural recording. However, no flexible methods are established for selective neural recording as for neural stimulation. This paper proposes a method to couple a compartmental and a FEM nerve model, implemented in NEURON and COMSOL, respectively, to translate Node of Ranvier currents into extraneural electric fields. The study simulate ex-vivo experimental conditions, and the method allows flexibility in electrode geometries and nerve topologies. This model has been made available in a public repository⁴. So far, the model behavior complies with available experimental results and expectations from literature. There is good agreement in terms of signal amplitude and waveform, and computational times are acceptable, leaving room for flexible simulation studies complementary to animal tests.

Self-Assembling Hydrogel Structures for Neural Tissue Repair

Hydrogel materials have been employed as biological scaffolds for tissue regeneration across a wide range of applications. Their versatility and biomimetic properties make them an optimal choice for treating the complex and delicate milieu of neural tissue damage. Aside from finely tailored hydrogel properties, which aim to mimic healthy physiological tissue, a minimally invasive delivery method is essential to prevent off-target and surgery-related complications. The specific class of injectable hydrogels termed self-assembling peptides (SAPs), provide an ideal combination of in situ polymerization combined with versatility for biofunctionlization, tunable physicochemical properties, and high cytocompatibility. This review identifies design criteria for neural scaffolds based upon key cellular interactions with the neural extracellular matrix (ECM), with emphasis on aspects that are reproducible in a biomaterial environment. Examples of the most recent SAPs and modification methods are presented, with a focus on biological, mechanical, and topographical cues. Furthermore, SAP electrical properties and methods to provide appropriate electrical and electrochemical cues are widely discussed, in light of the endogenous electrical activity of neural tissue as well as the clinical effectiveness of stimulation treatments. Recent applications of SAP materials in neural repair and electrical stimulation therapies are highlighted, identifying research gaps in the field of hydrogels for neural regeneration.

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.

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.

3D imaging of the vagus nerve fascicular anatomy with cryo-imaging and UV excitation

Vagus nerve stimulation (VNS) is a method to treat drug-resistant epilepsy and depression, but therapeutic outcomes are often not ideal. Newer electrode designs such as intra-fascicular electrodes offer potential improvements in reducing off-target effects but require a detailed understanding of the fascicular anatomy of the vagus nerve. We have adapted a section-and-image technique, cryo-imaging, with UV excitation to visualize fascicles along the length of the vagus nerve. In addition to offering optical sectioning at the surface via reduced penetration depth, UV illumination also produces sufficient contrast between fascicular structures and connective tissue. Here we demonstrate the utility of this approach in pilot experiments. We imaged fixed, cadaver vagus nerve samples, segmented fascicles, and demonstrated 3D tracking of fascicles. Such data can serve as input for computer models of vagus nerve stimulation.

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.

Quantification of clinically applicable stimulation parameters for precision near-organ neuromodulation of human splenic nerves

Neuromodulation is a new therapeutic pathway to treat inflammatory conditions by modulating the electrical signalling pattern of the autonomic connections to the spleen. However, targeting this sub-division of the nervous system presents specific challenges in translating nerve stimulation parameters. Firstly, autonomic nerves are typically embedded non-uniformly among visceral and connective tissues with complex interfacing requirements. Secondly, these nerves contain axons with populations of varying phenotypes leading to complexities for axon engagement and activation. Thirdly, clinical translational of methodologies attained using preclinical animal models are limited due to heterogeneity of the intra- and inter-species comparative anatomy and physiology. Here we demonstrate how this can be accomplished by the use of in silico modelling of target anatomy, and validation of these estimations through ex vivo human tissue electrophysiology studies. Neuroelectrical models are developed to address the challenges in translation of parameters, which provides strong input criteria for device design and dose selection prior to a first-in-human trial.

Due to the difference between rodent, porcine and human nerve morphology, Gupta et al. propose an integrative approach of computational modelling and ex vivo electrophysiology studies to identify clinically relevant optimal parameters for human peripheral nerve stimulation as a therapeutic tool. The agreement between results validate the use of computer simulations as a first step toward determining stimulation parameters to provide input criteria for device design and dose selection prior to first-in-human trials.

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.

A computational outlook on neurostimulation

Efficient identification of effective neurostimulation strategies is critical due to the growing number of clinical applications and the increasing complexity of the corresponding technology. In consequence, investigators are encouraged to accelerate translational research of neurostimulation technologies and move quickly to clinical applications. However, this process is hampered by rigorous, but necessary, regulations and lack of a mechanistic understanding of the interactions between electric fields and neural circuits. Here we discuss how computational models have influenced the field of neurostimulation for pain and movement recovery, deep brain stimulation, and even device regulations. Finally, we propose our vision on how computational models will be key to accelerate clinical developments through mechanistic understanding.

In vivo quantification of excitation and kilohertz frequency block of the rat vagus nerve

OBJECTIVE

There is growing interest in treating diseases by electrical stimulation and block of peripheral autonomic nerves, but a paucity of studies on the excitation and block of small-diameter autonomic axons. We conducted in vivo quantification of the strength-duration properties, activity-dependent slowing (ADS), and responses to kilohertz frequency (KHF) signals for the rat vagus nerve (VN).

APPROACH

We conducted acute in vivo experiments in urethane-anaesthetized rats. We placed two cuff electrodes on the left cervical VN and one cuff electrode on the anterior subdiaphragmatic VN. The rostral cervical cuff was used to deliver pulses to quantify recruitment and ADS. The caudal cervical cuff was used to deliver KHF signals. The subdiaphragmatic cuff was used to record compound action potentials (CAPs).

MAIN RESULTS

We quantified the input-output recruitment and strength-duration curves. Fits to the data using standard strength-duration equations were qualitatively similar, but the resulting chronaxie and rheobase estimates varied substantially. We measured larger thresholds for the slowest fibres (0.5-1 m s^-1), especially at shorter pulse widths. Using a novel cross-correlation CAP-based analysis, we measured ADS of ~2.3% after 3 min of 2 Hz stimulation, which is comparable to the ADS reported for sympathetic efferents in somatic nerves, but much smaller than the ADS in cutaneous nociceptors. We found greater ADS with higher stimulation frequency and non-monotonic changes in CV in select cases. We found monotonically increasing block thresholds across frequencies from 10 to 80 kHz for both fast and slow fibres. Further, following 25 s of KHF signal, neural conduction could require tens of seconds to recover.

SIGNIFICANCE

The quantification of mammalian autonomic nerve responses to conventional and KHF signals provides essential information for the development of peripheral nerve stimulation therapies and for understanding their mechanisms of action.

A computational model to design neural interfaces for lower-limb sensory neuroprostheses

BACKGROUND

Leg amputees suffer the lack of sensory feedback from a prosthesis, which is connected to their low confidence during walking, falls and low mobility. Electrical peripheral nerve stimulation (ePNS) of upper-limb amputee's residual nerves has shown the ability to restore the sensations from the missing limb via intraneural (TIME) and epineural (FINE) neural interfaces. Physiologically plausible stimulation protocols targeting lower limb sciatic nerve hold promise to induce sensory feedback restoration that should facilitate close-to-natural sensorimotor integration and therefore walking corrections. The sciatic nerve, innervating the foot and lower leg, has very different dimensions in respect to upper-limb nerves. Therefore, there is a need to develop a computational model of its behavior in response to the ePNS.

METHODS

We employed a hybrid FEM-NEURON model framework for the development of anatomically correct sciatic nerve model. Based on histological images of two distinct sciatic nerve cross-sections, we reconstructed accurate FEM models for testing neural interfaces. Two different electrode types (based on TIME and FINE) with multiple active sites configurations were tested and evaluated for efficiency (selective recruitment of fascicles). We also investigated different policies of stimulation (monopolar and bipolar), as well as the optimal number of implants. Additionally, we optimized the existing simulation framework significantly reducing the computational load.

RESULTS

The main findings achieved through our modelling study include electrode manufacturing and surgical placement indications, together with beneficial stimulation policy of use. It results that TIME electrodes with 20 active sites are optimal for lower limb and the same number has been obtained for FINE electrodes. To interface the huge sciatic nerve, model indicates that 3 TIMEs is the optimal number of surgically implanted electrodes. Through the bipolar policy of stimulation, all studied configurations were gaining in the efficiency. Also, an indication for the optimized computation is given, which decreased the computation time by 80%.

CONCLUSIONS

This computational model suggests the optimal interfaces to use in human subjects with lower limb amputation, their surgical placement and beneficial bipolar policy of stimulation. It will potentially enable the clinical translation of the sensory neuroprosthetics towards the lower limb applications.

Impact of neuroanatomical variations and electrode orientation on stimulus current in a device for migraine: a computational study

OBJECTIVE

Conventional treatment methods for migraine often have side effects. One treatment involves a wearable neuromodulator targeting frontal nerves. Studies based on this technique have shown limited efficacy and the existing setting can cause pain. These may be associated with neuroanatomical variations which lead to high levels of required stimulus current. The aim of this paper is to study the effect of such variations on the activation currents of the Cefaly neuromodulator. Also, using a different electrode orientation, the possibility of reducing activation current levels to avoid painful side-effects and improve efficacy, is explored.

APPROACH

This paper investigates the effect of neuroanatomical variations and electrode orientation on the stimulus current thresholds using a computational hybrid model involving a volume conductor and an advanced nerve model. Ten human head models are developed considering statistical variations of key neuroanatomical features, to model a representative population.

MAIN RESULTS

By simulating the required stimulus current level in the head models, it is shown that neuroanatomical variations have a significant impact on the outcome, which is not solely a function of one specific neuroanatomical feature. The stimulus current thresholds based on the conventional Cefaly system vary from 4.4 mA to 25.1 mA across all head models. By altering the electrode orientation to align with the nerve branches, the stimulus current thresholds are substantially reduced to between 0.28 mA and 15 mA, reducing current density near pain-sensitive structures which may lead to a higher level of patient acceptance, further improving the efficacy.

SIGNIFICANCE

Computational modeling based on statistically valid neuroanatomical parameters, covering a representative adult population, offers a powerful tool for quantitative comparison of the effect of the position of stimulating electrodes which is otherwise not possible in clinical studies.