PyPNS: Multiscale Simulation of a Peripheral Nerve in Python

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.

Finite-element modeling of neuromodulation via controlled delivery of potassium ions using conductive polymer-coated microelectrodes

Objective. The controlled delivery of potassium is an interesting neuromodulation modality, being potassium ions involved in shaping neuron excitability, synaptic transmission, network synchronization, and playing a key role in pathological conditions like epilepsy and spreading depression. Despite many successful examples of pre-clinical devices able to influence the extracellular potassium concentration, computational frameworks capturing the corresponding impact on neuronal activity are still missing.Approach. We present a finite-element model describing a PEDOT:PSS-coated microelectrode (herein, simplyionic actuator) able to release potassium and thus modulate the activity of a cortical neuron in anin-vitro-like setting. The dynamics of ions in the ionic actuator, the neural membrane, and the cellular fluids are solved self-consistently.Main results. We showcase the capability of the model to describe on a physical basis the modulation of the intrinsic excitability of the cell and of the synaptic transmission following the electro-ionic stimulation produced by the actuator. We consider three case studies for the ionic actuator with different levels of selectivity to potassium: ideal selectivity, no selectivity, and selectivity achieved by embedding ionophores in the polymer.Significance. This work is the first step toward a comprehensive computational framework aimed to investigate novel neuromodulation devices targeting specific ionic species, as well as to optimize their design and performance, in terms of the induced modulation of neural activity.

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.

A flexible, thin-film microchannel electrode array device for selective subdiaphragmatic vagus nerve recording

The vagus nerve (VN) plays an important role in regulating physiological conditions in the gastrointestinal (GI) tract by communicating via the parasympathetic pathway to the enteric nervous system (ENS). However, the lack of knowledge in the neurophysiology of the VN and GI tract limits the development of advanced treatments for autonomic dysfunctions related to the VN. To better understand the complicated underlying mechanisms of the VN-GI tract neurophysiology, it is necessary to use an advanced device enabled by microfabrication technologies. Among several candidates including intraneural probe array and extraneural cuff electrodes, microchannel electrode array devices can be used to interface with smaller numbers of nerve fibers by securing them in the separate channel structures. Previous microchannel electrode array devices to interface teased nerve structures are relatively bulky with thickness around 200 µm. The thick design can potentially harm the delicate tissue structures, including the nerve itself. In this paper, we present a flexible thin film based microchannel electrode array device (thickness: 11.5 µm) that can interface with one of the subdiaphragmatic nerve branches of the VN in a rat. We demonstrated recording evoked compound action potentials (ECAP) from a transected nerve ending that has multiple nerve fibers. Moreover, our analysis confirmed that the signals are from C-fibers that are critical in regulating autonomic neurophysiology in the GI tract.

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.

Optimal pulse configuration for peripheral inductive nerve stimulation

Peripheral magnetic stimulation is a promising technique for several applications like rehabilitation or diagnose of neuronal pathways. However, most available magnetic stimulation devices are designed for transcranial stimulation and require high-power, expensive hardware. Modern technology such as rectangular pulses allows to adapt parameters like pulse shape and duration in order to reduce the required energy. Nevertheless, the effect of different temporal electromagnetic field shapes on neuronal structures is not yet fully understood. We created a simulation environment to find out how peripheral nerves are affected by induced magnetic fields and what pulse shapes have the lowest energy requirements. Using the electric field distribution of a Figure-of-8 coil together with an axon model in saline solution, we calculated the potential along the axon and determined the required threshold current to elicit an action potential. Further, for the purpose of selective stimulation, we investigated different axon diameters. Our results show that rectangular pulses have the lowest thresholds at a pulse duration of 20 μs. For sinusoidal coil currents, the optimal pulse duration was found to be 40 μs. Most importantly, with an asymmetric rectangular pulse, the coil current could be reduced from 2.3 kA (cosine shaped pulse) to 600 A. In summary, our results indicate that for magnetic nerve stimulation the use of rectangular pulse shapes holds the potential to reduce the required coil current by a factor of 4, which would be a massive improvement.

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.

MorphoSONIC: A morphologically structured intramembrane cavitation model reveals fiber-specific neuromodulation by ultrasound

Low-Intensity Focused Ultrasound Stimulation (LIFUS) holds promise for the remote modulation of neural activity, but an incomplete mechanistic characterization hinders its clinical maturation. Here we developed a computational framework to model intramembrane cavitation (a candidate mechanism) in multi-compartment, morphologically structured neuron models, and used it to investigate ultrasound neuromodulation of peripheral nerves. We predict that by engaging membrane mechanoelectrical coupling, LIFUS exploits fiber-specific differences in membrane conductance and capacitance to selectively recruit myelinated and/or unmyelinated axons in distinct parametric subspaces, allowing to modulate their activity concurrently and independently over physiologically relevant spiking frequency ranges. These theoretical results consistently explain recent empirical findings and suggest that LIFUS can simultaneously, yet selectively, engage different neural pathways, opening up opportunities for peripheral neuromodulation currently not addressable by electrical stimulation. More generally, our framework is readily applicable to other neural targets to establish application-specific LIFUS protocols.

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.

A Multiscale Approach to Axon and Nerve Stimulation Modeling: A Review

Electrical nerve fiber stimulation is a technique widely used in prosthetics and rehabilitation, and its study from a computational point of view can be a useful instrument to support experimental tests. In the last years, there was an increasing interest in computational modeling of neural cells and numerical simulations on nerve fibers stimulation because of its usefulness in forecasting the effect of electrical current stimuli delivered to tissues through implanted electrodes, in the design of optimal stimulus waveforms based on the specific application (i.e., inducing limb movements, sensory feedback or physiological function restoring), and in the evaluation of the current stimuli properties according to the characteristics of the nerves surrounding tissue. Therefore, a review study on the main modeling and computational frameworks adopted to investigate peripheral nerve stimulation is an important instrument to support and drive future research works. To this aim, this paper deals with mathematical models of neural cells with a detailed description of ion channels and numerical simulations using finite element methods to describe the dynamics of electrical stimulation by implanted electrodes in peripheral nerve fibers. In particular, we evaluate different nerve cell models considering different ion channels present in neurons and provide a guideline on multiscale numerical simulations of electrical nerve fibers stimulation.

Modelling the effects of ephaptic coupling on selectivity and response patterns during artificial stimulation of peripheral nerves

Artificial electrical stimulation of peripheral nerves for sensory feedback restoration can greatly benefit from computational models for simulation-based neural implant design in order to reduce the trial-and-error approach usually taken, thus potentially significantly reducing research and development costs and time. To this end, we built a computational model of a peripheral nerve trunk in which the interstitial space between the fibers and the tissues was modelled using a resistor network, thus enabling distance-dependent ephaptic coupling between myelinated axons and between fascicles as well. We used the model to simulate a) the stimulation of a nerve trunk model with a cuff electrode, and b) the propagation of action potentials along the axons. Results were used to investigate the effect of ephaptic interactions on recruitment and selectivity stemming from artificial (i.e., neural implant) stimulation and on the relative timing between action potentials during propagation. Ephaptic coupling was found to increase the number of fibers that are activated by artificial stimulation, thus reducing the artificial currents required for axonal recruitment, and it was found to reduce and shift the range of optimal stimulation amplitudes for maximum inter-fascicular selectivity. During propagation, while fibers of similar diameters tended to lock their action potentials and reduce their conduction velocities, as expected from previous knowledge on bundles of identical axons, the presence of many other fibers of different diameters was found to make their interactions weaker and unstable.

How does the presence of neural probes affect extracellular potentials?

OBJECTIVE

Mechanistic modeling of neurons is an essential component of computational neuroscience that enables scientists to simulate, explain, and explore neural activity. The conventional approach to simulation of extracellular neural recordings first computes transmembrane currents using the cable equation and then sums their contribution to model the extracellular potential. This two-step approach relies on the assumption that the extracellular space is an infinite and homogeneous conductive medium, while measurements are performed using neural probes. The main purpose of this paper is to assess to what extent the presence of the neural probes of varying shape and size impacts the extracellular field and how to correct for them.

APPROACH

We apply a detailed modeling framework allowing explicit representation of the neuron and the probe to study the effect of the probes and thereby estimate the effect of ignoring it. We use meshes with simplified neurons and different types of probe and compare the extracellular action potentials with and without the probe in the extracellular space. We then compare various solutions to account for the probes' presence and introduce an efficient probe correction method to include the probe effect in modeling of extracellular potentials.

MAIN RESULTS

Our computations show that microwires hardly influence the extracellular electric field and their effect can therefore be ignored. In contrast, multi-electrode arrays (MEAs) significantly affect the extracellular field by magnifying the recorded potential. While MEAs behave similarly to infinite insulated planes, we find that their effect strongly depends on the neuron-probe alignment and probe orientation.

SIGNIFICANCE

Ignoring the probe effect might be deleterious in some applications, such as neural localization and parameterization of neural models from extracellular recordings. Moreover, the presence of the probe can improve the interpretation of extracellular recordings, by providing a more accurate estimation of the extracellular potential generated by neuronal models.

Remote Stimulation of Sciatic Nerve Using Cuff Electrodes and Implanted Diodes

We demonstrate a method of neurostimulation using implanted, free-floating, inter-neural diodes. They are activated by volume-conducted, high frequency, alternating current (AC) fields and address the issue of instability caused by interconnect wires in chronic nerve stimulation. The aim of this study is to optimize the set of AC electrical parameters and the diode features to achieve wireless neurostimulation. Three different packaged Schottky diodes (1.5 mm, 500 µm and 220 µm feature sizes) were tested in vivo (n = 17 rats). A careful assessment of sciatic nerve activation as a function of diode–dipole lengths and relative position of the diode was conducted. Subsequently, free-floating Schottky microdiodes were implanted in the nerve (n = 3 rats) and stimulated wirelessly. Thresholds for muscle twitch responses increased non-linearly with frequency. Currents through implanted diodes within the nerve suffer large attenuations (~100 fold) requiring 1–2 mA drive currents for thresholds at 17 µA. The muscle recruitment response using electromyograms (EMGs) is intrinsically steep for subepineurial implants and becomes steeper as diode is implanted at increasing depths away from external AC stimulating electrodes. The study demonstrates the feasibility of activating remote, untethered, implanted microscale diodes using external AC fields and achieving neurostimulation.