Excitation properties of computational models of unmyelinated peripheral axons

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.

Laterality, sexual dimorphism, and human vagal projectome heterogeneity shape neuromodulation to vagus nerve stimulation

Neuromodulation by vagus nerve stimulation (VNS) provides therapeutic benefits in multiple medical conditions, including epilepsy and clinical depression, but underlying mechanisms of action are not well understood. Cervical vagus nerve biopsies were procured from transplant organ donors for high resolution light microscopy (LM) and transmission electron microscopy (TEM) to map the human fascicular and sub-fascicular organization. Cervical vagal segments show laterality with right sided dominance in fascicle numbers and cross-sectional areas as well as sexual dimorphism with female dominance in fascicle numbers. The novel and unprecedented detection of numerous small fascicles by high resolution LM and TEM expand the known fascicle size range and morphological diversity of the human vagus nerve. Ground truth TEM quantification of all myelinated and unmyelinated axons within individual nerve fascicles show marked sub-fascicular heterogeneity of nerve fiber numbers, size, and myelination. A heuristic action potential interpreter (HAPI) tool predicts VNS-evoked compound nerve action potentials (CNAPs) generated by myelinated and unmyelinated nerve fibers and validates functional dissimilarity between fascicles. Our findings of laterality, sexual dimorphism, and an expanded range of fascicle size heterogeneity provide mechanistic insights into the varied therapeutic responses and off-target effects to VNS and may guide new refinement strategies for neuromodulation.

Reverse-engineered models reveal differential membrane properties of autonomic and cutaneous unmyelinated fibers

Unmyelinated C-fibers constitute the vast majority of axons in peripheral nerves and play key roles in homeostasis and signaling pain. However, little is known about their ion channel expression, which controls their firing properties. Also, because of their small diameters (~ 1 μm), it has not been possible to characterize their membrane properties using voltage clamp. We developed a novel library of isoform-specific ion channel models to serve as the basis functions of our C-fiber models. We then developed a particle swarm optimization (PSO) framework that used the isoform-specific ion channel models to reverse engineer C-fiber membrane properties from measured autonomic and cutaneous C-fiber conduction responses. Our C-fiber models reproduced experimental conduction velocity, chronaxie, action potential duration, intracellular threshold, and paired pulse recovery cycle. The models also matched experimental activity-dependent slowing, a property not included in model optimization. We found that simple conduction responses, characterizing the action potential, were controlled by similar membrane properties in both the autonomic and cutaneous C-fiber models, but complicated conduction response, characterizing the afterpotenials, were controlled by differential membrane properties. The unmyelinated C-fiber models constitute important tools to study autonomic signaling, assess the mechanisms of pain, and design bioelectronic devices. Additionally, the novel reverse engineering approach can be applied to generate models of other neurons where voltage clamp data are not available.

Towards enhanced functionality of vagus neuroprostheses through in silico optimized stimulation

Bioelectronic therapies modulating the vagus nerve are promising for cardiovascular, inflammatory, and mental disorders. Clinical applications are however limited by side-effects such as breathing obstruction and headache caused by non-specific stimulation. To design selective and functional stimulation, we engineered VaStim, a realistic and efficient in-silico model. We developed a protocol to personalize VaStim in-vivo using simple muscle responses, successfully reproducing experimental observations, by combining models with trials conducted on five pigs. Through optimized algorithms, VaStim simulated the complete fiber population in minutes, including often omitted unmyelinated fibers which constitute 80% of the nerve. The model suggested that all Aα-fibers across the nerve affect laryngeal muscle, while heart rate changes were caused by B-efferents in specific fascicles. It predicted that tripolar paradigms could reduce laryngeal activity by 70% compared to typically used protocols. VaStim may serve as a model for developing neuromodulation therapies by maximizing efficacy and specificity, reducing animal experimentation.

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.

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.

A modelling study to dissect the potential role of voltage-gated ion channels in activity-dependent conduction velocity changes as identified in small fiber neuropathy patients

Objective

Patients with small fiber neuropathy (SFN) suffer from neuropathic pain, which is still a therapeutic problem. Changed activation patterns of mechano-insensitive peripheral nerve fibers (CMi) could cause neuropathic pain. However, there is sparse knowledge about mechanisms leading to CMi dysfunction since it is difficult to dissect specific molecular mechanisms in humans. We used an in-silico model to elucidate molecular causes of CMi dysfunction as observed in single nerve fiber recordings (microneurography) of SFN patients.

Approach

We analyzed microneurography data from 97 CMi-fibers from healthy individuals and 34 of SFN patients to identify activity-dependent changes in conduction velocity. Using the NEURON environment, we adapted a biophysical realistic preexisting CMi-fiber model with ion channels described by Hodgkin-Huxley dynamics for identifying molecular mechanisms leading to those changes. Via a grid search optimization, we assessed the interplay between different ion channels, Na-K-pump, and resting membrane potential.

Main results

Changing a single ion channel conductance, Na-K-pump or membrane potential individually is not sufficient to reproduce in-silico CMi-fiber dysfunction of unchanged activity-dependent conduction velocity slowing and quicker normalization of conduction velocity after stimulation as observed in microneurography. We identified the best combination of mechanisms: increased conductance of potassium delayed-rectifier and decreased conductance of Na-K-pump and depolarized membrane potential. When the membrane potential is unchanged, opposite changes in Na-K-pump and ion channels generate the same effect.

Significance

Our study suggests that not one single mechanism accounts for pain-relevant changes in CMi-fibers, but a combination of mechanisms. A depolarized membrane potential, as previously observed in patients with neuropathic pain, leads to changes in the contribution of ion channels and the Na-K-pump. Thus, when searching for targets for the treatment of neuropathic pain, combinations of several molecules in interplay with the membrane potential should be regarded.

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.

The Significance of Concentration-dependent Components in Computational Models of C-Fibers

Computational models of neurons are valuable tools that allow researchers to form and evaluate hypotheses and minimize high-cost animal work. We soon plan to use computational modeling to explore the response of different sensory fiber types to long duration external stimulation to try to selectively block nociceptive C-fibers. In this work, we modified an existing C-fiber-specific axon model to additionally include concentration-dependent conductance changes, the contribution of longitudinal current flow to changes in local concentrations, and longitudinal currents generated by concentration gradients along the axon. Then, we examined the impact of these additional elements on the modeled action potential properties, activity-dependent latency increases, and concentration changes due to external stimulation. We found that these additional model elements did not significantly affect the action potential properties or activity-dependent behavior, but they did have a significant impact on the modeled response to external long duration stimulation.Clinical Relevance- This presents a computational model that can be used to help investigate and develop electrical stimulation therapies for pathological pain.

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.

Optimized Electrical Stimulation of C-Nociceptors in Humans Based on the Chronaxie of Porcine C-Fibers

Classically, to electrically excite C-nociceptors, rectangular pulses are used with a duration close to the estimated chronaxie of C-fibres (about 2 ms). Recent results using slow depolarizing stimuli suggest longer chronaxies. We therefore set out to optimize C-fiber stimulation based on recordings of single C-nociceptors in-vivo and C-fiber compound-action-potentials (C-CAP) ex-vivo using half-sine shaped stimuli of durations between 1 and 250ms. Single fiber (n = 45) recording in pigs revealed high chronaxie values for C-touch fibers (15.8 ms), polymodal- (14.2 ms) and silent-nociceptors (16.8 ms). Activation thresholds decreased 2 to 3-fold in all fibre classes when increasing the duration of half-sine pulses from 1 to 25 ms (P < .05). C-CAPs strength-duration curves of the pig saphenous nerve (n = 7) showed the highest sensitivity for half-sine durations between 10 and 25 ms. Half-maximum currents for C-CAPS were reduced 3-fold compared to rectangular pulses (P < .01) whereas the opposite was found for A-fiber compound action potentials. Psychophysics in humans (n = 23) revealed that half-sine stimulus durations >10 ms reduced detection thresholds, pain thresholds, and stimulus current amplitudes required to generate a pain rating of 3 on an 11-point Numeric Rating Scale (NRS) as compared to 1 ms rectangular pulses (P < 0.05). Increasing the duration from 1 to 25 ms led to a 4-fold amplitude reduction for pain-thresholds and stimuli caused an axon-reflex flare. Excitability of single polymodal nociceptors in animals paralleled human psychophysics and we conclude optimized half-sine pulses facilitate C-nociceptor activation. PERSPECTIVE: Electrical stimulation with longer lasting half-sine wave pulses preferentially activates C-nociceptors and changes in the strength duration curve may identify nociceptor hyperexcitability in patients with neuropathic pain.

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.

Excitation properties of computational models of unmyelinated peripheral axons

Biophysically based computational models of nerve fibers are important tools for designing electrical stimulation therapies, investigating drugs that affect ion channels, and studying diseases that affect neurons. Although peripheral nerves are primarily composed of unmyelinated axons (i.e., C-fibers), most modeling efforts focused on myelinated axons. We implemented the single-compartment model of vagal afferents from Schild et al. (1994) (Schild JH, Clark JW, Hay M, Mendelowitz D, Andresen MC, Kunze DL. J Neurophysiol 71: 2338-2358, 1994) and extended the model into a multicompartment axon, presenting the first cable model of a C-fiber vagal afferent. We also implemented the updated parameters from the Schild and Kunze (1997) model (Schild JH, Kunze DL. J Neurophysiol 78: 3198-3209, 1997). We compared the responses of these novel models with those of three published models of unmyelinated axons (Rattay F, Aberham M. IEEE Trans Biomed Eng 40: 1201-1209, 1993; Sundt D, Gamper N, Jaffe DB. J Neurophysiol 114: 3140-3153, 2015; Tigerholm J, Petersson ME, Obreja O, Lampert A, Carr R, Schmelz M, Fransén E. J Neurophysiol 111: 1721-1735, 2014) and with experimental data from single-fiber recordings. Comparing the two models by Schild et al. (1994, 1997) revealed that differences in rest potential and action potential shape were driven by changes in maximum conductances rather than changes in sodium channel dynamics. Comparing the five model axons, the conduction speeds and strength-duration responses were largely within expected ranges, but none of the models captured the experimental threshold recovery cycle-including a complete absence of late subnormality in the models-and their action potential shapes varied dramatically. The Tigerholm et al. (2014) model best reproduced the experimental data, but these modeling efforts make clear that additional data are needed to parameterize and validate future models of autonomic C-fibers.NEW & NOTEWORTHY Peripheral nerves are primarily composed of unmyelinated axons, and there is growing interest in electrical stimulation of the autonomic nervous system to treat various diseases. We present the first cable model of an unmyelinated vagal nerve fiber and compare its ion channel isoforms and conduction responses with other published models of unmyelinated axons, establishing important tools for advancing modeling of autonomic nerves.